Tribological design of machine elements

TRIBOLOGICAL DESIGN OF MACHINE ELEMENTS TRIBOLOGY SERIES 14 TRIBOLOGICAL DESIGN OF MACHINE ELEMENTS edited by D. DO...

Author: D. Berthe | D. Dowson | M. Godet | C.M. Taylor

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TRIBOLOGICAL DESIGN OF MACHINE ELEMENTS

TRIBOLOGY SERIES 14

TRIBOLOGICAL DESIGN OF MACHINE ELEMENTS edited by

D. DOWSON, C.M.TAYLOR, M. GODET AND D. BERTHE

Proceedings of the 15th Leeds-Lyon Symposium on Tribology held at Bodington Hall, The University of Leeds, U K 6th -9th September 1988

-

ELSEVIER Amsterdam - Oxford - New York Tokyo 1989 For the Institute of Tribology, Leeds University and lnstitut National des Sciences Appliqudes de Lyon

ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 P.O. Box 211,1000 AE Amsterdam, The Netherlands Distributors for the United States and Canada:

ELSEVIER SCIENCE PUBLISHING COMPANY INC. 655 Avenue of the Americas New York. NY 10010

ISBN 0-444-87435-6 (Vol. 14) ISBN 0-444-41 677-3 (Series) Elsevier Science Publishers B.V., 1989 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./Physical Sciences & Engineering Division, PO. Box 1991,1000 BZ Amsterdam, The Netherlands. Special regulations for readers in the USA -This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred to the copyright owner, Elsevier Science Publishers B.V., unless otherwise specified. For pages 3 -21,133-142,211-218,229-252,389-396 copyright was not transferred to Elsevier. No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the materials herein. Printed in the Netherlands.

V

CONTENTS Introduction Session I Session I1

Session I11

.............................................................. Keynote Address The tribological design of machine elements H.S. CHENG Review Papers Tribological design - The aerospace industry J.A.DOMINY Tribological design - The railways C. PRITCHARD and T.G. PEARCE Tribological design - The automotive industry P.A. WILLERMET Tribological design - The process industries J.D. SUMMERS-SMITH Seals Design of Controllable Mechanical Seals R.F. SALANT, 0. GILES and W.E. KEY Micro-elastohydrodynamic lubricant film formation in rotary lip seal contacts A. GABELL1 Lubrication of reciprocating seals: Experiments on the influence of surface roughness on friction and leakage A.F.C. KANTERS and M. VISSCHER Radial lip seals, thermal aspects M.J.L. STAKENBORG and R.A.J. van OSTAYEN Cams Lubrication and fatigue analysis of a cam and roller follower B.A. GECIM Predictions of cam wear profiles R.H. FRIES and C.A. ROGERS Cam and follower design A.D. BALL, D. DOWSON and C.M. TAYLOR Belts Power transmission by flat, V and timing belts T.H.C. CHILDS AND I.K. PARKER Power rating of flat belt drives - A wear approach B.G. GERBERT Gears The relationship between uneven tooth contact loading and surface durability in flexible gear designs J.F. HARROPand A. TAM Temperature and pressure measurements in gear contacts with thin-film-transducers H.PEEKEN and p. AYAN(X3J-J. A static and dynamic analysis of misaligned gears with partial contact areas Ph. SAINSOT, Ph. VELEX and D. BERTHE Rolling Element Bearings [11 The Palmgren-Miner rule derived J.J. KAUZLARICH Prediction of rolling bearing life under practical operating conditions E. IOANNIDES, B. JACOBSON and J.H. TRIPP Surface damage on rolling elements and its subsequent effects on performance and life J.C. HAMER, A.A. LUBRECHT, E. IOANNIDES and R.S. SAYLES Debris denting - the associated residual stresses and their effect on the fatigue life of rolling bearing: An FEM analysis C.N. KO and E. IOANNIDES

................................................ ............................................... ............................... ........................................... ....................................... ...........................

...............................................

Session IV

Session V

............................. - - - - - . - - - - .- - - -

............................................... .................................. ......................

.............................. .............................................

Session VI

.....................................

.................................

Session VII

.........................

........................................... ......................

ix

3 15 23 33 41 47 57 69 79 91 101 111 133 143

151 161 167 175 181

....... 189

...................................

199

vi

Session VIII

Plain Bearings [I] Axially profiled circular bearings and their potential application in high speed lubrication S . BASM and D.T. GETHIN Analysis of partial arc journal bearings E.W. COWKING Elapsed time for the decay of thermal transients in fluid film bearing assemblies C.M.M. ETTLES, H. HESHMAT and K.R. BROCKWELL . Design procedures based on numerical methods for hydrodynamic lubrication J.O.MEDWELL

.................................... ............................................

- - - - - - - .- -

229

.............................................

237

Wear The effect of residual stress and temperature on the fretting of bearing steel M. KUNO and R.B. WATERHOUSE The wear of hot working tools. Application to forging and rolling of steel E.FELDER The influence of debris inclusion on the performance of polymeric seals in ball valves B.J. BRISCOE and P.J. TWEEDALE

Session X

..............................

245

.................................................

253

..............................

259

Rolling Element Bearings [2] Tribological characteristics of needle bearings S. BLAIR and W.O. WINER Power loss prediction in ball bearings R.J. CHITTENDEN, D. DOWSON and C.M. TAYLOR The effect of roller end-flange contact shape upon frictional losses and ax91 load of the radial cylindrical roller bearing H. KRZEMINSKI-FREDA and B. WARDA The study of roller end and guiding shoulder construction of roller bearings M. LI and S . WEN

.................................... ................

Session XI

269 277

.........................

287

...........................................

297

Plain Bearings [2] Dynamically loaded journal bearings: a modal approach to EHL design analysis A. KUMAR, J.F. BOOKER and P.K. GOENKA Shape defects and misalignment effects in connecting-rod bearings P. MASPEYROT and J. FRENE Transient dynamics of engine bearing systems S . BOEDO and J.F. BOOKER Thermal considerations in engine bearings G.A. CLAYTON and C.M. TAYLOR

Session XI1

219

a

-

Session IX

21 1

Ceramics

...................... .................................. ................................... ..............................

Design requirements of ceramic sliding contacts R.J. GOZDAWA and T.A. STOLARSKI Unlubricated wear and triction behaviour of alumina and silicon carbide ceramics G. KAPELSKI, F. PLATON and P. BOCH The effects of surrounding atmosphere on the friction and wear of ceramics S. SASAK1 Wear performance of materials for ball screw and spline applications in Candu reactor fuelling machines P.E. DALE and R. TRISTANI

305 317 323 333

............................

345

..........................

349

.................................................

355

...................................

365

vi i

Session XI11

Review Papers Tribological design - The power generation industry P.G.MORTON Tribological design and assessment - The nuclear industry T.C. CHIVERS Tribological design - The spacecraft industry R.A. ROWNTREE, E.W. ROBERTS and M.J. TODD Tribological design - The electronics industry E.A. MUIJDERMAN, A.G. TANGENA, F. BREMER. P.L. HOLSTER and A. v MONTFOORTAND Session XIV Hyrostatic Bearings Optimum-design and automatic drawing of recessed hydrostatic bearings S. XU and B. CHEN Computer aided design of externally pressurized bearings G.J.J. van HEIJNINGEN and C.M. KALKER-KALKMAN A theoretical investigation of hybrid journal bearings applied to high speed heavily loaded conditions requiring jacking capabilities * D. IVES, W. WESTON, P.G. MORTON, W.B. ROWE. * * * * Behaviour of a high-speed hydrostatic thrust bearing with recess inserts and grooved lands. D. ASHMAN, E.W. PARKER and A. COWLEY An experimental comparison between the performance of a ‘total cross flow’ and an equivalent conventional design hydrostatic journal bearing M. ABDOLMALEKI, A. SKORIN, F.P. WARDLE and R.A.E. WOOD Session XV Information storage and retrievallmagnetic bearings Review Paper: Tribological design - information storage and retrieval B. BHUSHAN Active magnetic bearing design methodology - a conventional rotordynamics approach H.M.CHEN Session XVI Knowledge Based Systems The incorporation of artificial intelligence in the design of herringbone journal bearings K. ISHII, B.J. HAMROCK and J. KLINGER Bearing selection using a knowledge based system R.T. GRIFFIN, M.J. WINFIELD and S.S. DOUGLAS Tribology aids for designers C.J. THIJSSE Written Discussions .Contributions LjtofAuthors LktofDelegates

............................................. ............................................. .................. ......................................

373

383 389

397

41 1 .......................................... .............. 419

----

------

......................

.....

..............................................

...............................................

425

435

445

457

47 1

........................ 48 I ................. 489 .............................................. ............................................ 495 501 ........................................................... 513 .......................................................... 517

This Page Intentionally Left Blank

ix

Introduction The fifteenth Leeds-Lyon Symposium on Tribology was held from 6th-9th September 1988 at Bodington Hall, The University of Leeds. On previous occasions each Symposium has focused attention on a current and significant research topic, usually reflecting the interests of the Leeds or Lyon research groups, but this time the vitally important subject of technology transfer was recognized. Delegates appeared to appreciate this rare opportunity to discuss the impact of their studies upon machine design, since some 154 of them from 21 countries attended the Symposium on the "Tribological Design of Machine Elements". We were particularly pleased to welcome a strong group of friends from INSA, Lyon, led by Professor Maurice Godet. The Symposium was dedicated to the late Professor F T Barwell, who died on 15th January 1988 after a long illness. Freddie Barwell was a gentleman. He did much to promote a sound engineering approach to tribology and his book on "Bearing Systems - Principles and Practice" reflected his interest in applying tribological knowledge to bearing design. We know that he would have approved the topic chosen for the 15th Leeds-Lyon Symposium. He regularly attended and contributed to the Symposia and will be sorely missed. The Symposium opened in customary style with the Keynote Address on the Tuesday evening. On this occcasion we were pleased to welcome Professor Herb Cheng of Northwestern University, Evanson, USA, to set the scene, with a wide ranging and personal account of his view of "The Tribological Design of Machine Elements". Delegates then travelled to York to enjoy the Symposium Dinner in the ancient Merchant Adventurers Hall. The Guest of Honour at the dinner was Peter Jost, who took the opportunity to comment on the coming of age of tribology. Peter himself chaired the Working Party which produced the now famous report which introduced the word tribology some twenty one years ago. The somewhat unusual nature of the Symposium provided the organizers with an opportunity to offer a perspective on the current state of tribological design in a number of major industries. This was achieved by inviting selected authors to present Review Papers on Tribological Design in;-

. . .

The Aerospace Industry The Railways The Automobile Industry

.

. . .

The Process Industries The Power Generation Industry The Nuclear Industry The Spacecraft Industry

.

The Electronic Industry

(J A Dominy, Rolls Royce Ltd, Derby U K) (C Pritchard and T G Pearce, British Rail, Derby, U K) (P A Willermet, Ford Motor Company, Dearborn, U S A) (J D Summers-Smith, Guisborough, U K) (P G Morton, GEC Stafford, U K) (T C Chivers, CEGB, Berkeley, UK) (R A Rowntree, E W Roberts and M J Todd, National Centre of Tribology, Risley,

u K) (EA Muijderman, A G Tangena, F Bremer, P L Holster, A V Montfoortand, Philips, Eindhoven, The Netherlands)

X

Information Storage and and Retrieval

We are particularly Papers for preparing these tribological design.

(B Bhushan, IBM, San Jose, USA)

grateful to the commentaries on

authors of these Review contemporary practice in

Some sixteen working sessions were included in the Programme and this necessitated the holding of parallel sessions throughout the morning of Thursday 8th September. The fifty four papers presented nevertheless represented only about fifty percent of those offered, thus facing the organizers with the difficult task of declining many attractive offers. Two sessions were devoted to the Review Papers mentioned earlier, while others dealt with;- Seals; Cams; Belts; Gears; Rolling Element Bearings (2); Plain Bearings (2); Wear; Ceramics; Hydrostatic Bearings; Information Storage and Retrieval/Magnetic Bearings and Knowledge Based Systems. The latter sessions reflect the growing interest in the role of tribology in the computer based information society of the 1980’s. We are particularly grateful to the distinguished Chairmen who presided over the Symposium Sessions and whose names are recorded in this volume. Parallel sessions were also’ introduced into the Social Programme held on the afternoon of Thursday 8th September. The intricacies of the arrangements were described in a specially arranged Wednesday evening session, which is rapidly becoming an established feature of the Symposia in Leeds, by Mr Brian Jobbins. All delegates were taken to Whitby, where the famous explorer Captain Cook learned his seamanship, but this was achieved by following one of three routes. Most of the delegates travelled by coach to Pickering and then crossed the North Yorkshire Moors on the Railway operating on the line originally built by George Stephenson in 1836. Smaller groups visited Kilburn village to see the hand carving of the famous Thompson (Mouseman) oak furniture, or the Fylingdales Early Warning Radar Station. The journey home was broken for dinner at the As far as we know all Crown Hotel, Boroughbridge after a very full day. delegates returned to Bodington Hall! Initial discussion of the arrangements for each Leeds-Lyon Symposium usually commences some eighteen months to two years before the Symposium is held. The Proceedings are then published within the following year. This rolling organizational cycle of some three years duration calls for considerable dedication and support. We are particularly grateful for the financial support for the Symposium generously provided on this occasion by: 111 121 r31 141 r51

British Petroleum Research Centre, Sunbury-on-Thames, UK Fiat Research Centre, Turin, Italy Michell Bearings plc, Newcastle-upon-Tyne, UK SKF Engineering and Research Centre, The Netherlands The US Army Research Development and Standardisation Group, UK

The Symposium literature was once again presented to delegates in handsome wallets provided by Elsevier, Publishers of the Journal WEAR, and we are pleased to acknowledg this most welcome support. The smooth running of the Symposium owes much to the enthusiasm and hard work contributed by colleagues in the Institute of Tribology in

xi

The University of Leeds. We would particularly like to express our appreciation to Mrs Sheila Moore, Mrs Catharine Goulborn, Mr Stephen Burridge, Mr Ron Harding, Mr Brian Jobbins, Mr David Jones, Dr John Fisher, our technicians and our current research students and fellows. We are also most grateful to the staff of Elsevier Science Publishers BV, Amsterdam, for their professional and friendly service in producing the volumes of Proceedings of the Leeds-Lyon Symposia. As we were undertaking the editorial work on the present volume of Proceedings, we heard with great sadness of the death on February 15th 1989 after a long illness of one of our editorial colleagues, Professor Daniel Berthe. Daniel was a great enthusiast for this Anglo-French cooperation and we know that the biennial arrangements in Lyon depended heavily upon him and Professor Godet. His contributions to tribology and his intellect were respected and appreciated by colleagues and friends in Lyon and Leeds. On behalf of all our delegates and his friends in b e d s we would like to send our deepest sympathy to Daniel’s family and his colleagues in Lyon. The beds-Lyon Symposia on Tribology which Daniel Berthe helped to establish have covered a wide range of topics since their inception in 1974, as illustrated by the following list.

[l] [2] [3] 141 [5] [6]

[7l [8] [9] [lo] [ll] [12] [13] [14] [15]

1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988

Cavitation and Related Phenomena in Lubrication Super Laminar Flow in Bearings The Wear of Non-Metallic Materials Surface Roughness Effects in Lubrication Elastohydrodynamics and Related Topics Thermal Effects in Tribology Friction and Traction The Running-In Process in Tribology Tribology of Reciprocating Engines Numerical and Experimental Methods in Tribology Mixed Lubrication and Lubricated Wear Mechanisms and Surface Distress Fluid Film Lubrication Osborne Reynolds Centenary Interface Dynamics The Tribological Design of Machine Elements

-

The 16th Leeds-Lyon Symposium on Tribology will be held in Lyon, France, under the title ”Mechanics of Coatings” from- Tuesday 5th to FAday 8th September 1989. We greatly look forward to meeting our friends in Lyon once again. Duncan Dowson Chris Taylor


SESSION I KEYNOTE ADDRESS Chairman: Paper I(i)

Professor D Dowson The Tri bological Design of Machine Elements


3

Paper I(i)

The tribological design of machine elements H.S. Cheng

History of tribology indicates that many important tribological concepts and theories were stimulated by the needs of new machinery developments, and the new tribological research findings, in turn, have helped to upgrade the design of more efficient and more reliable tribological elements. This mutual dependence is illustrated with some classical examples. Discussions are then given to the tribological design process of generic elements and its application to determine tribological performance of machine elements, and to the needs in improving this design process to meet the requirements of future machineries in aerospace, automotive, and information processing industries.

1. INTRODUCTION Good tribological design has often been recognized as the key to the success in developing new machineries. This was true in the days of Reynolds when railroads relied heavily on good journal bearing design of the axles, true in the days of Model T when automotive engines depended strongly on good design practice of main shaft and connecting rod bearings, and is still true today when computers rely critically on good tribological performance of the head/disc interface. It is now over a century since Reynolds first established the formulation of fluid film lubrication controlling the tribological performance of sliding surfaces. In this past hundred years, a vast amount of design data has been generated in predicting the average lubricant film thickness between the sliding surfaces generated either hydrodynamically or hydrostatically. In some cases, an accurate prediction of the average lubricant film is sufficient to ensure a good tribological design of mechanical components. However, in most other cases, particularly for counterformal contacts, the lubricant film thickness is insufficient to ensure a good design because film thickness alone cannot predict the lubrication breakdown leading to sliding failures by scuffing and wear. It is the lubrication breakdown of the asperity oil film and the surface film which control the failure process. The lack of accurate predictions of the asperity oil film and the surface film breakdown is seen to be the weakest link in the tribological design process. As new technologies emerge in aerospace, energy, manufacturing, and communication industries, machineries are required to operate under much higher temperature with higher efficiency and reliability. These

requirments present new challenges in research and design of tribological elements to discover new lubrication concepts, new materials, new surface modification techniques, and new predictive theories to develop the advanced machineries. In this paper, some significant historical developments in tribology are used to illustrate the mutual dependence of tribological design and machinery development. Weak areas in current methods of tribological design o f machine elements are then indicated and discussed. Some newly emerged tribological concepts for meeting the new challenges in tribological design are also described.

1.1 Historical Developments In tribological design, one is mostly concerned with two basic elements, the conformal sliding bearings and counterformal rolling and sliding contacts. Historically, evidences of conformal slidings can be traced back thousands years ago when iron journal bearings were used in olive crushing machines in Greece and bronze journal bearings were used as the wheel bearings in the Chinese South Point Chariot[l]. Few would disagree that the most significant historical development in design of sliding bearings is the discovery of a continuous oil film in a journal bearing by Tower[2] and the subsequent derivation of the Reynolds equation[3] which established the foundation for prediction of tribological performance for design of sliding bearings. This most important development was motivated by the problems associated with the journal boxes in railcar axles. Thus, it is a classic example in which a critical need in machinery development triggered a major breakthrough in tribological design which in turn benefits the development of many other future machineries.

4

Tribological design of rolling and sliding contacts has been evolved mostly from the needs of better rolling element bearings and gears in machinery development. Unlike the sliding bearings for which rational design was established around the turn of the century, there have been no rational criteria for designing the rolling and sliding contacts until almost half a century later when Blok[4] established the critical temperature concept to predict the scuffing threshold and Lundberg and Palmgren[5] established a method to predict the contact fatigue life. The importance of lubricant film in rolling and sliding contacts was recognized, but satisfactory prediction of lubricant film thickness was not possible until the developments of elastohydrodynamic lubrication[6]. While the detailed influence of lubricant film thickness in contact failures is still being assessed by researchers, its role as an indicater of the severity of asperity contacts is firmly placed in tribological design. Tribological design of very low speed and heavily loaded sliding contacts depends on the protection of boundary films. Historically, the ties between boundary lubrication and machinery development are less evident than hydrodynamic and elastohydrodynamic lubrication from the first publication on boundary film by Hardy[7]. Nevertheless, these films are the last line of defence against severe wear. Unless rational methods are formed in predicting the conditions of breakdown of these boundary films, the process of tribological design will always be incomplete.

5 . Material Properties of Solids, such

as elastic and shear modulus, thermal conductivities, specific heat, yielding stress, fracture toughness, hardness, etc.

COUNTERFORMAL

CONFORMAL

Low Pressure

High Pressure

Thick Film

Thin Film

High Slip

Low Slip

Rigid Surface

Elastic Surface

Fig. 1 Generic Tribo-Elements

2 . TRIBOLOGICAL DESIGN PROCESS

Analvsis

There are two types of elements in tribological design. The first type is simple generic elements involving either conformal sliding surfaces or the counterformal rolling and sliding contacts, as shown in Fig. 1. The second type is tribological machine elements which include all bearings, gears, cams, and other rolling and sliding components. A brief discussion is given to the tribological design process for each of these two types of triboelements.

HPFT

Empirical Data Base

I

I

Satisfactory

2.1 Generic Tribo-Elements The processes for designing a generic triboelement, as illustrated in Fig. 2, begin with the input data, which can be arranged in the following five groups: 1. Geometrical Data, such as the principal radii of the contacts, 2. Roughness Data, such as the average roughness height, average asperity radii, etc. 3 . Operating Conditions, such as range of load, speed, temperature, etc. 4 . Lubricant Properties, such as viscosity, shear modulus, limiting shear stress, thermal conductivity, etc.

Fig. 2

Design Process for a Generic Tribo-Element

One may use a subroutine named "GROLM" to identify the five major groups of input data needed to initiate the tribological design process. At the present time, most of these input data is entered manually in the computer programs for tribological design. This inefficient method of handling the input data can be improved if the lubricant and material database is computerized and interfaced directly with the tribo-design program.

5 The second step in the design process is to determine the tribological performance

described by: 1. The film thickness, H 2 . The contact pressure, P

3 . The friction force, F 4 . The contact temperature, T A subroutine named "HPFT" may be used to

identify the calculation of these tribological performance variables which are used to determine whether the element would fail under the given operating conditions. For contacts operating in thick film lubrication, the distributions of film thickness, pressure, friction, and temperature can be predicted by theories ignoring the surface roughness effects. Indeed, the smoothsurface theories in hydrodynamic, hydrostatic, elastohydrodynamic lubrication have been fully developed in the past century to enable the prediction of these quantities to a high degree of accuracy. Reviews of these developments can be found in the Proceedings of the 1986 Leeds- Lyon Symposium on Tribology[81 . For contacts operating in thin film lubrication, the sliding asperities are no longer separated by a thick oil film. They are protected by a very thin oil film or by a surface film. Tribological performance in the thin film regime, as represented by average quantities of the film thickness, lubricant and asperity pressure, lubricant and asperity sheax stress, and surface temperature, h, p, r , r , Ts, shown in Fig. 3 , may not be :&ficie;t to predict tribological failure. There is a need to extend the tribological

performance to include the characteristics of these quantities at the asperity level considering each asperity as a micro-contact. These micro-quantities are labelled as asperity film thickness, contact pressure, shear stress, and surface temperature, h*, p*, T*, , :T as shown in Fig. 3 . Some analyses of tribological performance in thin-film lubrication in terms of the above described quantities are available[9], but the area has not been fully developed. Moreover, the relation of these performance variables with the major tribological failures such as contact fatigue, scuffing. and wear are not fully understood. They are yet to be identified and quantified. Considerable more efforts are needed in this area. The most important step in tribological design is failure prediction. Ideally, failure predictions should be based on analytical failure models which relate a major failure mode to certain critical tribological variables, such as the relation between contact fatigue life and a critical maximum Hertzian pressure, and the relation between scuffing and a critical total contact temperature. Unfortunately, analytical predictions of sliding failures based on calculated tribological performance variables in the thin-film regime are not always accurate and reliable. One cannot predict analytically the tribological failures as accurately as the structural failures. This most critical block is also the weakest link in the tribological design process. In the case there are no accurate analytical failure models available, alternative methods, based entirely or partially on failure database obtained experimentally, may be used.

A: Design of Machine Elements A+-!-

6

h*

b

?*

r-l

7;

I

Fig. 4 Fig. 3 Average and Micro-Contact Variables in Thin-Film Lubrication

Satisfactory Design -

I

Block Diagram for Design of Tribological Machine Elements

6

2.2 Tribological Machine Elements Fig. 4 shows a block diagram illustrating typical steps for designing a machine element, such as rolling bearings, gears, and cams. AS shown in the top figures, each of the elements may contain many generic tribo-elements like EHL contacts which may interact dynamically and thermally. The design process begins with entering all the geometrical, roughness, operating, lubricant, and material property data, as described earlier for the generic elements. The first step is to determine the cyclic dynamic loads on all the interacting generic elements. In this block, the symbol Wi(99

>99

7.5

97

2.0

77

0.50

36 2.05

0.0047

0.0045

1348 1291

178.0

57

12

>99

83

7.1

1.0

-

L.T.

1661

162.0

94

24

99

98

9.7

1.37

.21

1425

153.0

1.17

.I8

T.T.

1429

188.0

67

17

99

91

7.0

1.0

.15

L.T.

3191

226.0

99

82

>99

>99

8.9

1.25

.20

2517

226.0

30

10

>99

76

7.3

1.03

.16

M.T. -

(in.) (Fig.17)

0.0058

T.T.

M.T. -

OF DEPTH SAFETY

-

2943

L.T.

1

SURFACE SURFACE SURFACE DISTRESS ROUGHNESS O f 5P-ln. MAX. ROUGHNESS OF 32 p-in. PEAK HERTZIAN LOCAL FRICTION LOCAL OIL FILM 5p LOAD CONTACT FRICTION NTENSITY STRESS COEFFICIENT FRICTION COEFFICIENT FRICTION THICKNESS ROUGHNESS R W H N E S S f = .06 COEFFICIENT f .06 COEFFICIENT ( p i n . ) (lblin) (KSI)

I

8

I

3

I

I

66

18

I

I

8.3

.16

T.T.

TABLE 3

- HCR GEAR TOOTH LOADS AT 555 LB.-FT.

"

TORQUE

NO CONTACT AT THE TRAILING PAIR BASED ON O I L VISCOSITY AT 235°F AN0 GEAR BLANK TEMP AT 235'F MARGIN OF SAFETY = (ALLOWABLE STRESSlAPPLIEO STRESS) -1

* **

NOTE:

";r" I

i

MAX. SCORING i !OBABILITY (X)

SURFACE

:ONTACl TOOTH

5p-lnS = .127 pm 32 u-ins = .813 urn

IWIN. FILC THICKNESS CRITERIA

1

SURFACE ROUGHNESS OF 32 p-ln.

lo/j

SURFACE DISTRESS PARAMETER A

SUB-SURFACE SHEAR STRESS RADIAL

; PEAK Tr :O:1ERTZIAN LOAD FRICTION LOCAL FILM INTENSITl STRESS COEFFICIENT FRICTION COEFFICIENT FRICTION THICKNESS (KSI) f .06 COEFFICIENl f .06 COEFFICIENT ( p i n . ) (lb/in)

-

L.T. M.T. -

I

77

18

I

1.69

12

I

.27

1-

0.002

I

T.T. L.T. I

M.T.

-

4147

T.T. ~~

TABLE 4

- LCR GEAR TOOTH LOADS AT 555 LB.-FT.

TORWE

11

CONCLUSION

The tooth load distribution obtained for the HCR gear mesh indicates heavily concentrated loading at the front end of the gear teeth. The results match well with damage patterns found on the test gears. The load distribution can be improved by incorporating a stiff bearing housing support to reduce gear mesh misalignment and by applying appropriate lead modifications to the gear teeth. However, even with these improvements, scoring risk is still high because of excessive flexing and rim coning. The tooth mesh tends to separate tangentially at the rear end and force the contact loading towards the front. The redesigned LCR gear mesh features a thick gear rim, less access holes, a shorter web and consequently a much stiffer gear. The 3D F.E. results indicate a more uniform load distribution in the teeth. The LCR teeth are shorter which reduces tooth sliding velocities and hence improves scoring resistance. Tooth scoring resistance is also significantly improved by better surface finish. Surface distress due to scoring, pitting or spalling is of low probability on the redesigned LCR gear set.

12

REFERENCES

1.

LYNWANDER, P. 'Gear Tooth Scoring Design Considerations', American Gear Manufactures Association (AGMA), P219.10, October, 1981.

2.

KU, P.M. 'Tribology of Gears', Manufacture and Performance, P. 73.

3.

ELKHOLY, A. 'Case Depth Requirements in Carburized Gears', American Gear Manufacturer Association (AGMA), Aerospace Gearing Committee Meeting, San Diego, California, 1982.

4.

SHARMA, V.K., WALTER, G . H . , BREEN, D.H. 'An Analytical Approach for Establishing Case Depth Requirements in Carburized Gears: ASME Publication, 77-DET-152, 1977.

5.

Sundararajan, S. YOUNG, B. 'Finite Element Analysis of Large Spur and Helical Gear Systems', AIAA/SAE/ASME/ ASEE, 23rd Joint Propulsion Conference, 1987, San Diego, California. AIAA-87-2047.

6.

Benedict h Kelley, 'Instantaneous Coefficients of Gear Tooth Friction', ASLE Transaction 4, 59-70, 1961.

Gear

161

PaperVl(ii)

Temperatureand pressure measurements in gear contacts with thin-film-transducers H. Peekenand P.Ayanoglu

The p r o j e c t has t h e aim of i n v e s t i g a t i n g t h e temperature and p r e s s u r e d i s t r i b u t i o n s i n t h e e l a s t o hydrodynamic l u b r i c a t i n g f i l m i n gear c o n t a c t s . A s p e c i a l l y designed gear wheel allows a t h i n f i l m coating of t h e gear tooth. The transducers can t h u s be s p u t t e r e d d i r e c t l y onto t h e t o o t h s u r f a c e . The temperature and pressure c o e f f i c i e n t s of every transducer a r e determined b e f o r e t h e experiments, t o enable an exact evaluation of t h e r e s u l t s . The tests a r e being c a r r i e d o u t on a gear r i g with a continuously v a r i a b l e b e l t d r i v e t o load t h e g e a r s . The experiments with manganin transducers showed t y p i c a l EH pressure d i s t r i b u t i o n s , with much higher peaks than t h e c a l c u l a t e d Hertzian values, a r e s u l t of t h e unequal load d i s t r i b u t i o n over t h e tooth width. Quite high temperature r i s e s were r e g i s t e r e d , t h e temperature increasing with growing load, speed and l u b r i c a n t v i s c o s i t y . 1

INTRODUCTION

P r e c i s e knowledge of t h e l u b r i c a t i n g conditions i s an important design c r i t e r i o n f o r gears. Other than t o o t h breakage, most forms of gear f a i l u r e such a s wear, s c u f f i n g o r p i t t i n g s are c l o s e l y r e l a t e d t o t h e condition of t h e e l a s t o hydrodynamic l u b r i c a t i n g film s e p e r a t i n g t h e t e e t h i n mesh. The experimental i n v e s t i g a t i o n of t h e tooth contact i n r e s p e c t t o t h e elastohydrodynamic l u b r i c a t i o n was previously been confined mainly t o two-disc t e s t r i g s , where it i s simulated. The p r o j e c t intends t o measure temperature and pressure d i s t r i b u t i o n s i n t h e r e a l toothcontact, using s p u t t e r e d t h i n f i l m transducers, which can be applied i n various p o s i t i o n s onto t h e tooth surface. Temperature and pressure d i s t r i b u t i o n s can thus be obtained f o r d i f f e r e n t p o i n t s on t h e l i n e of a c t i o n . This i s necessary because of t h e i n s t a t i o n a r y elastohydrodynamics i n gear c o n t a c t s with changing r a d i i , r o l l i n g and s l i d i n g speeds and s l i p along t h e l i n e of action. 2

TEST STAND AND TEST GEAR

The experiments a r e c a r r i e d o u t on a purposeb u i l t gear-rig (Fig. l ) , driven by a d i r e c t c u r r e n t e l e c t r i c motor. The gears a r e loaded by means of a b e l t - d r i v e with a continuously v a r i a b l e r a t i o . During a c c e l e r a t i o n from stands t i l l , t h e t o o t h flank with t h e transducer i s not under load, a s t h e transducer can otherwise be d e s t r u c t & i n t h e mixed f r i c t i o n zone. The s h o t of the opened t e s t r i g i n Fig. 2 shows a l s o t h e s p e c i a l l y designed t e s t gear wheel with o f f s e t t e e t h . This was necessary t o enable t h e coating of t h e t o o t h s u r f a c e i n the s p u t t e r i n g apparatus..The t e e t h a r e l i m i t e d t o one half of t h e gear width, with four t e e t h o f f s e t t o t h e o t h e r h a l f (Fig. 3 ) . The d r i v i n g gear i s also s p l i t i n t h e middle; when t h e t e s t t o o t h (with the transducer) i s i n mesh, it replaces t h e lacking t o o t h on t h e other s i d e , without influencing t h e r i g i d i t y o r e l a s t i c i t y of t h e mechanism.

3

TRANSDUCER FABRICATION AND CALIBRATION

Thin-film-transducers have been i n use f o r over 2 0 years f o r measurements i n hydrodynamic and elastohydrodynamic c o n t a c t s . They a r e Ohm-resis t a n c e s , which change under pressure- and t e m p e r a t u r e i n f l u e n c e . They a r e applied onto t h e t e s t - o b j e c t s u r f a c e using t h e PVD-coating processes and enable measurements i n t h e t i g h t e s t gaps, without a f f e c t i n g t h e geometry or s t r e n g t h of t h e p a r t s involved. While vapour deposition was t h e most commonly used process previously, s p u t t e r i n g i s g e t t i n g more and more acceptance nowadays. S p u t t e r i n g i s t h e erosion of a s o l i d s u r f a c e under bombardment of highly energized p a r t i c l e s . The energy of t h u s s p u t t e r e d molecules o r e atoms i s many times g r e a t e r than t h a t of thermally evaporated. Consequently, s p u t t e r e d l a y e r s have much b e t t e r wear resistance and adhesion than t h e l a t t e r . The t o o t h f l a n k i s f i r s t covered with an i s o l a t i n g alumina-film. Transducer m a t e r i a l i s manganin f o r pressure- and titanium f o r temperature-transducers. I n o r d e r t o produce t h e defined contours of t h e transducer, e i t h e r a mask is t o be placed on t h e s u b s t r a t e s u r f a c e o r t h e t o o t h s u r f a c e is covered with etchr e s i s t a n t photopaint. The transducer contours a r e t o be coated with t h e transducer m a t e r i a l . The l i t h o g r a p h i c method renders transducers w i t h very f i n e dimensions p o s s i b l e , which can a l s o be positioned anywhere on t h e tooth-flank. F i n a l l y a t h i n , p r o t e c t i n g alumina-layer i s s p u t t e r e d over t h e transducer. Fig. 4 shows a t h i n f i l m transducer on t h e tooth f l a n k . It c o n s i s t s of t h e c o n t a c t a r e a s on both s i d e s and a very f i n e b r i d g e connecting them, which i s t h e a c t i v e p a r t of t h e t r a n s ducer, having a much higher r e s i s t a n c e (lo0 1000 Ohm) than t h e c o n t a c t a r e a s . ( I n t h i s case, a wire s t r a i n gauge is a l s o attached t o t h e r o o t of t h e t o o t h , t o measure dedendum s t r a i n ) . This very f i n e connecting w i r e , t h e a c t i v e p a r t of t h e transducer is about 20 )un wide, 1 mm long and has a height of ca. 0 , l pm (Fig. 5 ) . I t r e a c t s , according t o m a t e r i a l , p r i m a r i l y t o temperature or pressure changes, b u t it has t o be taken i n t o c o n s i d e r a t i o n t h a t a pressure

transducer has a c e r t a i n temperature s e n s i t i v i t y and v i c e versa. Using two transducers with d i f f e r e n t s e n s i t i v i t i e s t h e p r e s s u r e and temperature d i s t r i b u t i o n s i n t h e EH-contact can be determined. To compute t h e temperature and pressure values from t h e recorded r e s i s t a n c e changes, t h e temperature and p r e s s u r e c o e f f i c i e n t s of both transducers must be known. In other words, each transducer must be c a l i b r a t e d f o r temperature and pressure. A s p e c i a l apparatus has been b u i l t f o r t h e pressure c a l i b r a t i o n (Fig. 6) : A defined o i l pressure can be applied t o t h e transducer through a small pressure chamber pressed upon i t s a c t i v e p a r t . The t e s t - p r e s s u r e of t h i s apparatus i s l i m i t e d t o about 1400 bar (0,14 G P A ) , but it enables t h e c a l i b r a t i o n of t h e a c t u a l transducers on t h e t o o t h f l a n k s . A s t h e transducers have t o bear pressures of over 10 OOO bar (1,O GPa) i n t h e EH-contact, p o s s i b l e n o n - l i n e a r i t i e s i n t h e i r behaviour a t t h i s high pressure range should a l s o be determined. The high-pressure c a l i b r a t i o n of t h e t h i n film transducers up t o 1 , 0 GPa has been undertaken i n an autoclave with a chamber diameter of 2 0 mm. For t h i s purpose t h e transducers were sputtered onto gage blocks which f i t t e d i n t o t h e a u t o c k v e chamber. The pressure c a l i b r a t i o n curves f o r titanium and manganin transducers a r e seen on Fig. 7. Manganin has a l i n e a r r e l a t i o n s h i p between i t s e l e c t r i c a l r e s i s t a n c e and pressure. Titanium shows a non-linear behaviour. But by l i n e a r i z i n g i n t h e important zone between 0,15 GPa and 0,65 GPa titanium transducers can a l s o be used i n t h e experiments. The temperature c a l i b r a t i o n i s done i n an oil-bath. 4

RESULTS

One titanium and 3 manganin transducers were used i n experiments so f a r . They were a l l positioned above t h e p i t c h p o i n t , t h e i r p o s i t i o n s being given on t h e diagrammes of t h e recorded r e s u l t s . The pitch-radius i s 80 mm. The measurements proved t o be very good reproducable a s long a s they were c a r r i e d o u t with t h e same tooth of t h e mating gear. Between temperature o r pressure measurements taken with d i f f e r e n t mating t e e t h , q u i t e b i g d i f f e r e n c e s were p o s s i b l e under otherwise s i m i l a r conditions. The reasons f o r t h e s e v a r i a t i o n s a r e t o be found i n t h e various e r r o r s of t h e gears used. The f i r s t measurements of t h e gear geometry showed d i r e c t i o n a l e r r o r s i n t h e p r o f i l e s of t h e mating gear t e e t h (up t o 15 J.UU over a t o o t h width of 2 0 mu) , i n other words t e e t h with a c e r t a i n i n c l i n a t i o n , which r e s u l t s i n unequal load d i s t r i b u t i o n over t h e t o o t h width. This e f f e c t wouldn't be so n o t i c a b l e under higher loads. The tooth with t h e transducer had a crowned p r o f i l e . Another e r r o r i s v a r i a t i o n s i n c i r c u l a r p i t c h , t h i s having a g r e a t influence i f t h e transducer is i n t h e double-mesh-region. Fig. 8 shows pressure d i s t r i b u t i o n s recorded w i t h t h e same mating t o o t h a t a constant speed under t h r e e d i f f e r e n t loads. The curves a r e t y p i c a l of elastohydrodynamical pressure d i s t r i b u t i o n . I n t h e p a r a l l e l gap t h e curve has an e l l i p t i c a l shape s i m i l a r t o t h e Bsrtzian p r e s s u r e d i s t r i b u t i o n , b u t with a slowly growing

g r a d i e n t i n t h e i n l e t zone and an abrupt f a l l i n t h e o u t l e t region. The peak p r e s s u r e i s i n t h i s case 0,4 GPa. Similar pressure d i s t r i b u t i o n s were r o g i s t e r e d f o r another opposing t o o t h under t h e same parameters, b u t t h e peak p r e s s u r e i s i n t h i s case 0,7 GPa (Fig. 9 ) . I n Fig. 8 and 9 , two sets of values a r e given f o r t h e s p e c i f i c normal t o o t h f o r c e : The nominal f o r c e , c a l c u l a t e d from t h e measured torque and t h e f o r c e , which i s c a l c a l a t e d by i n t e g r a t i n g t h e pressure curve. The l a t t e r exceeds i n some cases the nominal force by q u i t e a high margin. Such a high s p e c i f i c f o r c e over t h e whole width is of course n o t p o s s i b l e . The c o n t a c t width i n t h i s c a s e must be much narrower than t h e t o o t h , a s a r e s u l t of t h e geometrical e r r o r s a l r e a d y mentioned. I t can a l s o be seen, t h a t t h e r a t i o of t h e i n t e g r a t e d pressure t o t h e nominal f o r c e decreases with increasing load. The c o n t a c t a r e a becoms l a r g e r with i n c r e a s i n g load. In Fig. 10 t h e same curves a s i n Fig. 9 a r e normed a f t e r t h e corresponding Hertzian pressure and c o n t a c t width. I t i s n o t i c a b l e t h a t they a l l have s i m i l a r shapes, t h e peak pressures being about 1 , 2 times t h e Hertzian peak. Temperature measurements were c a r r i e d o u t with a titanium transducer. The v a r i a t i o n s between values taken with d i f f e r e n t t e e t h were here a l s o n o t i c a b l e . Much higher temperatures were measured i n t h e t o o t h c o n t a c t t h a n , f o r example i n r o l l e r bearings. While i n t h e r o l l e r r i n g c o n t a c t t h e highest measured temperature r i s e was 5 K , up t o 35 K have been r e g i s t e r e d i n t h e gear c o n t a c t (at: a s p e c i f i c f o r c e of 46 N/mm and a curcumferential speed of 8 , 4 m / s ) . The load-influence on t h e c o n t a c t temperature can be seen on Fig. 11. I n Fig. 12 speed i s t h e parameter, while t h e load i s constant i n a l l cases. The curves have d i f f e r e n t widths because they a r e n o t timecorrected. The s l i p i s i n t h i s p o s i t i o n about 40 %. The temperature i n c r e a s e s with t h e s l i d e speed. The experiments with t h e temperaturetransducer were a t f i r s t c a r r i e d o u t an o i l 0 inlet-temperature of 2 0 C . A t t h i s temperature t h e o i l v i s c o s i t y i s 310 mPa s . The l a s t f i g u r e shows tonperature d i s t r i butions a t 3 d i f f e r e n t o i l i n l e t temperatures and v i s c o s i t i e s . The temperature i n c r e a s e i n t h e c o n t a c t becomes less with decreasing l u b r i c a n t v i s c o s i t y (Fig. 1 3 ) . 5

CONCLUSIONS

The experiments have so f a r shown t h e t y p i c a l e l a s tohydr odynamic Sress u r e d i s t r i b u t i o n s i n gear c o n t a c t s , a s w e l l a s t h e r e l a t i v e l y high temperature rises a s a r e s u l t of t h e high s l i d i n g speeds. The sometimes unexpectedly high p r e s s u r e peaks show t h e e f f e c t s t h a t geometrical e r r o r s can have on t h e load d i s t r i b u t i o n over t h e tooth flank. Emphasis i n t h e f u t u r e w i l l . be p u t on t h e i n v e s t i g a t i o n of pressure and temperature d i s t r i b u t i o n s over t h e whole l i n e of a c t i o n and i n l a t e r a l d i r e c t i o n , so a p p r o p r i a t e l y positioned transducers w i l l be b u i l t . It i s planned t o measure dedendum s t r a i n with s t r a i n gages t o g e t a b e t t e r i n d i c a t i o n of t h e

153 a c t u a l f o r c e on t h e t o o t h than t h e p r e v i o u s t o r q u e measurement on t h e s h a f t .

References DOWSON, D . , HIGGINSON, G.R. 'Elasto-hydrodynamic L u b r i c a t i o n ' , S I - E d i t i o n , Pergamon P r e s s L t d . , 1977 RODERMUND, H., ' B e i t r a g z u r elastohydrodynamischen Schmierung von Evolventenzahnradern', D i s s e r t a t i o n TU C l a u s t h a l , 1975 SIMON, M . , 'Messung von elastohydrodynamischen Parametern und i h r e Auswirkungen auf d i e G r i i b c h e n t r a g f a i g k e i t v e r g u t e t e r Scheiben und Zahnrader', D i s s e r t a t i o n TU Munchen, 1984 KANNEL, J . W . , ZUGARO, F.F., DOW, T.A., ' A Method f o r M'lasuring S u r f a c e Temperature Between Rolling/Sliding S t e e l Cylinders', Transaction o f t h e ASME 100 (1978) pp. 110-114 BAUER, P . , ' T h e o r e t i s c h e und e x p e r i m e n t e l l e Untersuchungcn zu t r i b o l o g i s c h r e l e v a n t e n Bet r i e b s g r o R e n an v e r k a n t e t e n Z y l i n d e r r o l l e n l a g e r n ' , D i s s e r t a t i o n RWTH Aachen, 1987

Fig. 3

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Fig. 8

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167

PaperVl(iii)

A static and dynamic analysis of misaligned gears with partialcontact

areas Ph. Sainsot, Ph.Velex and D. Berthe

T h i s paper p r e s e n t s a n e v a l u a t i o n of t h e i n f l u e n c e of misalignments on t o o t h load d i s t r i b u t i o n i n gear systems. S t a t i c and dynamic a n a l y s e s a r e conducted u s i n g a normal c o n t a c t a l g o r i t h m i n c l u d i n g l o c a l and g l o b a l effects. T h i s a l g o r i t h m is s h o r n t o be re11 adapted t o d e t e r m i n e t h e p r e s s u r e f i e l d betneen s u r f a c e s n i t h any manufacturing e r r o r s , i n v e r s e l y , p r o f i l e m o d i f i c a t i o n s can be c a l c u l a t e d t o have a given load distribution. T h e dynamic problem is t r e a t e d on a s i m p l i f i e d r e d u c t i o n u n i t model, some examples of i n s t a n t a n e o u s t o o t h loading, v a r i a t i o n s of c o n t a c t s t i f f n e s s , and c r i t i c a l r o t a t i o n s p e e d s a r e given. R e s u l t s shon t h a t c o n t a c t c o n d i t i o n s may s t r o n g l y depend on t h e o v e r a l l mechanical e n v i ronmen t. 1

INTRODUCTION

l o a d d i s t r i b u t i o n i n g e a r t r a i n s is r a r e l y known. I t depends on t h e manufacturing errore, r o t a t i o n speeds, and on t h e masses, i n e r t i a , and s t i f f n e s s e s of t h e r e d u c t i o n u n i t components. To c a l c u l a t e t h a t load d i s t r i b u t i o n , a normal c o n t a c t a l g o r i t h m is extended and i n s e r t e d i n b o t h s t a t i c and dynamic a n a l y s e s . T h e l o c a l d i s placements n e a r t h e c o n t a c t s a r e found u s i n g Boussinesq r e l a t i o n s and s t r u c t u r a l compliances a r e c a l c u l a t e d by F. B. ti. I n t h e s t a t i c approach, t h e effect of m i s a l i gnment on t h e p r e s s u r e f i e l d betneen c o n t a c t i n g t e e t h . of s p u r i n v o l u t e g e a r is shorn. Inversel y , t h e longitudinal p r o f i l e modifications nhich y i e l d a g i v e n p r e s s u r e d i s t r i b u t i o n a r e compuThe

ted. T h e dynamic problem is t r e a t e d n i t h a s i m p l i f i e d model i n which small misalignments a r e i n t r o d u ced i n t h e c o n s t r a i n t e q u a t i o n t h a t g u a r a n t i e s c o n t a c t d u r i n g motion. T h e corresponding i n s t a n taneous t o o t h l o a d i n g and c r i t i o a l speeds of ro-

t a t i o n are d e r i v e d and compared n i t h t h e response given by a l i g n e d gears. 1.1 c

Notations

longitudinal tooth modification contribution of s m a l l misalignments t o t h e c o n s t r a i n t equation ensuring contact a t t h e i t h p o i n t on t h e p l a n e of a c t i o n k i : meshing s t i f f n e s s a t t h e i t h p o i n t of contact L : tooth face nidth M : module Pi : p r e s s u r e a t t h e i t h p o i n t of c o n t a c t R : t o t a l maximum i n s t a n t a n e o u s load v e r s u s t o t a l s t a t i c l o a d on t h e p l a n e of a c t i o n r(t) : t o t a l i n s t a n t a n e o u s l o a d v e r s u s t o t a l s t a t i c l o a d on t h e p l a n e of a c t i o n Rbl,Rb2 : b a s e o y l i n d e r s r a d i i f o r p i n i o n and nheel vk,uk : s a a l l t r a n s l a t i o n s O f g e a r k X : addendua a o d i f i c a t i o n c o e f f i c i e n t

: Ei :

21,22 : number of t e e t h f o r p i n i o n and nheel F* : a d d i t i o n n a l second member induced by miaalignments a : pressure angle R : h e l i x base angle, h e l i x a n g l e +k q k , 'k : small rotations of g e a r k pV@* small c o n s t a n t a n g u l a r error ( n i s a k k' lignment) &,XI* : r e l a t i v e approach and m o d i f i e d r e l a t i v e approach ( m i s a l i g n e d c a s e s ) a t t h e i t h p o i n t of c o n t a c t E$i : pseudo-modal damping f a c t o r w , : meshing p u l s a t i o n ill : p i n i o n r o t a t i o n speed. 2

GEAR TEETH DBPLECTIONS. MESHING STIFFNESS

I n t h e s t u d y of loaded g e a r t e e t h , one can d e f i ne t n o d i f f e r e n t s c a l e s of a n a l y s i s , namely : h e r t a i a n d e f o r m a t i o n s i n t h e v i c i n i t y of t h e c o n t a c t s and s t r u c t u r a l phenomena involving t e e t h d i s p l a c e m e n t s , hub deformations, bending and t o r s i o n of t h e s h a f t s , ... For f u l l E. 8. D l u b r i c a t i o n , local a n a l y s i s is conducted by assuming t h a t t h e t a n g e n t i a l l o a d i n g on t e e t h may be i g n o r e d nhen coapared t o t h e n o r a a l one. S e m i - i n f i n i t e bodies are consi d e r e d so t h a t Bouseinesq s o l u t i o n s can be used C l l , The p o t e n t i a l a r e a s of c o n t a c t a r e discret i n e d i n t o r e c t a n g u l a r c e l l s on w h i c h normal p r e s s u r e is assuaed c o n s t a n t ( f i g . 1 ) . On t h e o t h e r hand, s t r u c t u r a l d e f l e c t i o n s a r e computed by f i n i t e e l e m e n t s a n a l y s i s ( f i g . 2 ) . T P e i r c o n t r i b u t i o n s are i n t r o d u c e d i n a comp l i a n a e m a t r i x f i l l e d up with t h e normal d i s p l a cements due t o u n i t c o n c e n t r a t e d l o a d which is s u c c e s s i v e l y a p p l i e d on each node of t h e potent i a l contact areas. For d y n a a i c a n a l y s e s , t e e t h s t i f f n e s a e s are used and t h e i r v a l u e s a r e d e f i n e d a t v a r i o u s p o i n t s on t h e a c t i v e f l a n k 8 by t h e l o a d t o t o t a l normal displaceaent r a t i o ( f i g . 3).

168 STATIC AND DYUANIC SOLUTION OF NORNAL CONTACT

3

C o n t a c t problems b e t r e e n g e a r t e e t h are s o l v e d by imposing g e o m e t r i c a l c o m p a t i b i l i t i e s ( n o n i n t e r p e n e t r a t i o n of t h e deformed s u r f a c e s ) , s t a t i c o r dynamic e q u i l i b r i u m of t h e s t r u c t u r e and by imposing p o s i t i v e p r e s s u r e s on t h e c o n t a c t areas. On each e l e m e n t i of t h e c o n t a c t s u r f a c e s , t h e f o l l o w i n g c o n d i t i o n s must be a c h i e v e d : yi = hi

+ ui

-

se

-

(1)

8

Table I i f the areas, yi

>

element

belongs

8

to

the

( 2)

pi = e i f t h e element is o u t s i d e t h e c o n t a c t a r e a s . The s t a t i c o r dynamic e q u i l i b r i u m m u s t be s a t i s f i e d f o r t h e r h o l e mechanism. I n p a r t i c u l a r , re have :

C

P i .ASi = P

(

3)

where :

-

F is t h e s t a t i c o r dynamic l o a d

transmitted by t h e meshing t e e t h , y i is t h e d i s t a n c e b e t r e e n t h e deformed s u r faces, h i is t h e d i s t a n c e b e t r e e n t h e undeformed surfacrs, u i i s t h e r e l a t i v e e l a s t i c d i s p l a c e m e n t of t h e s u r f a c e s , i t i s t h e s u m of t h e l o c a l and s t r u c t u r a l contributions, S8 is t h e r i g i d body d i s p l a c e m e n t r h i c h ensures c o n t a c t b e t r e e n t h e deformed t e e t h , Pi is t h e normal p r e s s u r e f i e l d . ASi is t h e a r e a of t h e i t h cell.

The numerical s o l u t i o n is d e r i v e d by u s i n g a n i t e r a t i v e a l g o r i t h m a s d e c r i b e d by KALKBR I 2 1 . 4

-

Bear c h a r a c t e r i s t i c s

r e a l contact I n t h i s paragraph, t h e c o n t a c t l i n e is a t t h e t o p of a s i n g l e t o o t h c o n t a c t o f p i n i o n , and t h e t o o t h r i d t h is supposed s h o r t enough so t h a t t h e t o r s i o n between t h e t r o hub f a c e s may be ignored. The p o t e n t i a l c o n t a c t a r e a is d i v i d e d i n 28 c e l l s on t h e t o o t h r i d t h and 8 c e l l s on t h e perpendicular direction. I n t h e formulation of t h e contact problem, m i s a l i g n m e n t s a r e i n t r o d u c e d a s a d d i t i o n a l terms modifying t h e h i v e c t o r ( i , e . i n i t i a l undeformed s h a p e s ) . F i g u r e 4 and 5 s h o r t h e p r e s s u r e d i s t r i b u t i o n s b e t r e e n a l i g n e d t e e t h s u b m i t t e d t o a l o a d of 6 8 7 . 5 daN, and results o b t a i n e d r i t h a 1 5 um a l i g n m e n t error. Comparisons r i t h p r e v i o u s res u l t s g i v e n by TOBB and IWOOB f 3 1 , t h e ABMA t 4 1 and IS0 I 5 1 s t r e n g t h r a t i n g f o r m u l a s , and WIBMANN e x p e r i m e n t a l works I 6 1 s h o r q u i t e good agreements. The c o n t a c t a l g o r i t h m a l s o s e r v e s t o c a l c u l a t e t h e longitudinal p r o f i l e modification, modelled by t h e vector h i , needed t o have a d e s i r e d p r e s s u r e d i s t r i b u t i o n along t h e f a c e r i d t h rhen t h e t e e t h a r e pressed together. F i g u r e 6 s h o r s t h e p r e s s u r e f i e l d on t h e c o n t a c t area, and t h e c o r r e s p o n d i n g l o n g i t u d i n a l t o o t h geometry f o r a t r a n s m i t t e d l o a d o f 1868 daW.Aith t h e h y p o t h e s i s used, corrections a r e symmetric r i t h r e s p e c t t o t h e t o o t h center, r h i l e wider f l a n k s r i l l i n d u c e l a r g e r corrections a t t h e s i d e of t h e power e n t r a n c e due t o t o r s i o n a l e f f ects.

STATIC ANALYSIS 5

The r e l i a b i l i t y of g e a r t r a i n s is h i g h l y depend e n t on t h e s t a t e of stresses : c o n t a c t and t o o t h f i l l e t stresses. The l o a d d i s t r i b u t i o n b e t r e e n mating t e e t h and a l o n g t e e t h width is solved f i r s t . Then, t h e main p u r p o s e s of t h e s t a t i c a n a l y s i s developed i n t h i s p a p e r a r e : f o r g i v e n g e o m e t r i e s of t h e c o n t a c t i n g bod i e s , t h e r e s o l u t i o n of t h e l o a d d i s t r i b u t i o n . c o n v e r s e l y , t h e c a l c u l a t i o n of p r o f i l e mod i f i c a t i o n s f o r a desired pressure field. Some examples of l o n g i t u d i n a l l o a d d i s t r i b u t i o n s f o r m i s a l i g n e d i n v o l u t e s p u r gears, and l o n g i t u d i n a l p r o f i l e corrections a r e given. Q e a r ahar a c t e r i s t i c s are l i s t e d i n t a b l e I.

-

DYNANIC BEEAVIOUR OF NISALXQNED QEARS

5.1 Constraint

eauation

A meshing g e a r r i t h r i g i d , u n i f o r m l y s p a c e d i n v o l u t e t e e t h , mounted on r i g i d s u p p o r t s t r a n s m i t s uniform a n g u l a r motions, however, real t o o t h prof i l e s d e v i a t e from i n v o l u t e s u r f a c e s , r o t a t i n g b o d i e s may be m i s a l i g n e d and e v e r y p a r t of t h e r e d u c t i o n u n i t deforms r h e n p o r e r is t r a n s m i t ted. A l l t h e s e phenomena produce e x c i t a t i o n s and uns t e a d y motions. Assuming s m a l l d i s p l a c e m e n t s and r o t a t i o n s near s t a t i o n a r y motions, t h e c o n d i t i o n f o r m a i n t a i n i n g contact a t t h e i t h p o i n t on t h e p l a n e of a a t i o n may be e x p r e s s e d i n terms of t h e g e n e r a l i z e d displacements of t h e t r o r o t a t i n g r h e e l s by [91, t 1 8 1 , [ l l l :

[v1-v2-Rb 1 8 1

- Rb2

e 2 ] c 0 ~ Bb

+ [u2-u1

- Rb141

169 E l r e p r e s e n t s t h e value of t h e r e l a t i v e approach of meshing g e a r t e e t h , e q u a t i o n ( 4 ) shows t h a t ( esli, o n02) al f l e x u r a l ( ~~,v~,$~,,+,~,$~,$~),tor and a x i a l ( u 1, u2) v i b r a t i o n s a r e coupled. 5.2

Lagrange's e q u a t i o n s g i v e t h e a d d i t i o n a l e x c i t a -

t i o n vector

F*.

k= 1,12

Mechanical model

nith

A 12 d e g r e e of freedom s i m p l i f i e d dynamic model (S.D. M I is used ( f i g . 7 ) . E l a s t i c p r o p e r t i e s o f Met h e s h a f t s are approached u s i n g R a y l e i g h ' s thod 1121. Contacts a r e assumed t o o c c u r o n l y on t h e a c t i o n plane nhere c o n t a c t l i n e s a r e d i s c r e t i z e d by e l e m e n t s of c o n s t a n t s t i f f n e s s k i . T h e i r numerical v a l u e s a r e found by t h e s u p e r p o s i t i o n of c o n t a c t and s t r u c t u r a l s t i f f n e s s e s of t h e mat i n g t e e t h a s d e f i n e d i n 6 2. Hhen a g e a r r o t a t e s , t h e number of t e e t h i n cont a c t d o e s not remain c o n s t a n t n h i l e t h e s t i f f n e s s of a n i n d i v i d u a l t o o t h p a i r v a r i e s a s t h e l o c a t i o n o f t h e i r mutual l i n e of contact c h a n g e s d u r i n g t h e motion, T h e r e f o r e , t h e g l o b a l meshing s t i f f n e s s k =Cki is time dependent and p e r i o d i c (fig. 8). Neglecting t a n g e n t i a l l o a d s , t h e p o t e n t i a l energy of e l a s t i c d e f o r m a t i o n of t h e mating t e e t h is : U = 1/2

X

ki(t)

i C i > = B

.

Ci2

and t h e normal t o o t h l o a d d i s t r i b u t i o n is :

The e q u a t i o n s of motion a r e : [MI

xoO

+IC1 xo +C IC( t ) l I

= F( t)

(

q =

R e s o l u t i o n and numerical results

S t a t i c l o a d d i s t r i b u t i o n s o l u t i o n s shon t h a t depending on misalignment a m p l i t u d e t h e e n t i r e t o o t h n i d t h may n o t a l n a y s be i n c o n t a c t ( f i g . 9). F o r r o t a t i n g g e a r s , t h i s nay change t h e mesh i n g s t i f f n e s s i n s t a n t a n e o u s l y , t h e n modify b o t h t h e l o c a t i o n s of c r i t i c a l s p e e d s and e x c i t a t i o n spectra. T h i s n o n - l i n e a r problem is s o l v e d by c o u p l i n g a time s t e p by s t e p i n t e g r a t i o n (Nanmark's t r a p e z o i d a l r u l e ) n i t h t h e c o n t a c t a l g o r i t h m p r e s e n t e d i n 5 3. Although t h a t t h e dynamic model u s e s s i m p l i f i e d d e s c r i p t i o n s of g e a r e d systems, t h e s t a t i c load i n g d i s t r i b u t i o n s found r i t h t h e S. D. M a r e gen e r a l l y close t o t h o s e o b t a i n e d by o t h e r a u t h o r s (fig. 5). Meshing s t i f f n e s s e v o l u t i o n s o b t a i n e d f o r var i o u s v a l u e s of alignment e r r o r s a r e p l o t t e d i n f i g u r e s 18 and I 1 , one n o t e s t h a t t h e c o r r e s ponding i n t e r n a l e x c i t a t i o n form and a m p l i t u d e vary n i t h r o t a t i o n s p e e d s and misalignment amplitude. The r e s u l t i n g dynamic t o o t h l o a d d i a grams, f i g . 12 and 13, e x h i b i t a t h r e s h o l d n h i c h s e p a r a t e s t h e b e h a v i o u r s of g e a r t r a i n s n i t h p a r t i a l c o n t a c t a r e a s and t h o s e n i t h f u l l cont a c t s e s p e c i a l l y i n t h e h i g h f r e q u e n c y domain. The c o r r e s p o n d i n g r e s p o n s e c u r v e s shon t h a t a s t a t i c f u l l c o n t a c t may become p a r t i a l a t c r i t i c a l s p e e d s ( f i g . 141, t h e s e i n s t a n t a n e o u s e v o l u t i o n s a r e t h e n dependent on t h e meshing h i s t o r y .

7)

6

CORCLOSIOHS

nith

-

-

: vector of t h e g e n e r a l i z e d d i s p l a c e m e n t s [ M I : mass m a t r i x CC1 : damping m a t r i x i n t r o d u c e d from pseudo-

x

modal p r o p e r t i e s [ 91 [ K ( t ) l : p e r i o d i c s t i f f n e s s m a t r i x which is t h e mathematical consequence of t h e i n t e r n a l e x c i t a t i o n induced by t e e t h meshing. F( t) : second member v e c t o r made by a p p l i e d t o r q u e s and e x t e r n a l e x c i t a t i o n s .

5.3

I n t r o d u c t i o n of m i s a l i s n m e n t s

By assuming s m a l l a n g u l a r e r r o r s so t h a t t h e rig i d body k i n e m a t i c s remain unchanged, misalignments c a n be i n t r o d u c e d i n t h e e x p r e s s i o n of t h e r e l a t i v e approach b e t n e e n two p o i n t s i n contact as :

A normal contact a l g o r i t h m i n c l u d i n g h e r t z i a n and s t r u c t u r a l compliances o f g e a r t r a i n s , is used t o s o l v e s t a t i c and dynamic problems of l o a d d i s t r i b u t i o n s assuming n e g l i g i b l e tangent i a l effects. For t h e v i b r a t i o n a l a n a l y s i s of m i s a l i g n e d s p u r and h e l i c a l g e a r s , a simplified model of a o n e - s t a g e r e d u c t i o n u n i t is proposed.The s o l u t i o n is conducted s t e p by s t e p i n

time. R e s u l t s may be summarized a s f o l l o n s : t h e i n f l u e n c e of a l i g n m e n t error on t h e s t a t i c p r e s s u r e d i s t r i b u t i o n is shonn,numerical r e s u l t s

-

compare f a v o u r a b l y n i t h p r e v i o u s t h e o r e t i c a l and e x p e r i m e n t a l works. t h e p r o c e d u r e developed c a n c a l c u l a t e t h e l o n g i t u d i n a l p r o f i l e c o r r e c t i o n s needed t o produae a g i v e n p r e s s u r e f i e l d on t h e a c t i v e f l a n k s . t h e v a r i a t i o n s i n dynamic l o a d s on t h e a c t i o n p l a n e f o r d i f f e r e n t misalignment a m p l i t u d e s c a n be computed. t h e c r i t i c a l r o t a t i o n speeds are derived n i t h p a r t i c u l a r a t t e n t i o n t o t h e i n f l u e n c e of p a r t i a l contact a r e a s f o r h i g h meshing f r e q u e n c i e s .

-

-

-

riih : - C i , C i = r e l a t i v e approach a t t h e i t h p o i n t of c o n t a c t d t h and n i t h o u t a l i g n m e n t er-

-

7

ACKIOALBWBNBRT

ror. Ei =

forcing ments.

terms

due t o

small m i s a l i g n -

E i = (Rbl $*+Rb2 $ > s i n b b + ( l l i s i n g b + q i ) $ p ( 1 2 i singb-qi)

I&

The a u t h o r s n i s h t o t h a n k t h e D. R. E. 1. rouchoux) r h o f i n a n c e d t h i s r e s e a r c h .

(Mr. Du-

170 References

r 11

CARNEIRO-ESTEVES (A.1. R e s o l u t i o n du cont a c t e l a s t i q u e e n t r e deux c o r p s rugueux , These de D o c t o r a t , 1.N.S.A Lyon , Nov. 1987, 157 p. r 21 KALKER (J. J ) . -TWO a l g o r i t h m s f o r t h e cont a c t problem i n e l a s t o s t a t i c s . R e p o r t s of t h e Department of Mathematics and Informat i c s , 1982 D e l f t , no 82-26. TOBE ( T . 1 , INOUE (K.1. - L o n g i t u d i n a l l o a d I 31 d i s t r i b u t i o n f a c t o r s of s p u r g e a r t e e t h , Congrbs Mondial d e s Engrenages , P a r i s , J u n e 1977 Pol. 1, p 211-225. ADMA 295-81 , 1966 C 41 IS0 / TC 68 / lid 6 / No 169 E , 1974 . [ 51 NIEMANN (0.1 , REISTER ( D. Konstruktion , I61 18 (19661, 95. QREQORY ( R . 1 . ) , U A R R I S ( S . L . ) MUNRO I71 ( R . Q. 1. - Dynamic b e h a v i o r of s p u r g e a r s Proc. I n s t . Hech. Engrs. , 1963-64 , Vol. 178 , no 8 pp 261-266. WOOD (B. 1 , BUNT ( T . M. 1. E x c i t a t i o n of C 81 r e s o n a n t v i b r a t i o n s i n s p u r and h e l i c a l g e a r . Vol.178 , P a r t 35 , pp 189-281. VELEX (P. 1. Contribution l ' a n a l y s e du [ 91 conportement dynamique d e r h d u c t e u r s ?I eng r e n a g e s & a x e s p a r a l l & l e s , These d e Doct o r a t , I. H. 9. A Lyon, J u i l l e t 1988, 185 p. I 101 LUND ( J . 1 . ) .- C r i t i c a l speeds, s t a b i l i t y and r e s p o n s e of a g e a r e d t r a i n of r o t o r s . A. 3. M. E, J. Mech. Design, Vol. 188, J u l y 1978, pp 535,539 FUJI1 ( Y . ) I 1 1 1 KIYONO (3.) , A I D A (T.) V i b r a t i o n of h e l i c a l g e a r s P a r t 1 :Theor i t i c a l a n a l y s i s and P a r t 2 : E r p e r i r e n t a l J. 3. M. E , 1978 , i n v e s t i g a t i o n s , Bull. Vol. 21 , no 155 pp 915-938 . r 121 LALANNE ( M. , BERTBIER ( P. 1, DER UAGOPIAN (J. 1 . Mechanical v i b r a t i o n s for e n g i neers, New-York , John A i l e y , 1983 , 266 P.

.

-

-

.

.

Fig. 2 : Finite element model of an helicoidal gear in 20 nodes bricks (2= 25, 0(=20°, 0 = 1 5 O )

.-

-

0

0.01

0.02

0.03

(m)

Fig. 3 : Bending stiffnessof an helicoidal war versus the radius of curvature aml the position along the face width of the considerated point (2 = 25, r r ( = 20 ', I3 = 15 ")

a : aligned surface

Fig. 1 : Discretization of the contact area in rectangular cells of constant pressure

b) : misaligned error of 15 pm Fig. 4 : Examples of pressure field between meshing teeth (F/L = 13.75 daN/mm)

171

a) : desired pressure field

b) : Longitudinal modification of the meshing teeth Fig. 6 : Tooth modificationsfor a given pressure field

Fig. 5 : Load distribution between the meshing teeth (F/L = 13.75 daN/mm). Comparison with TOBE, NIEMANN, ISO, AGMA and Simplified Dynamic Model (SDM)

"L 1.2 1

0.8

0.6 I

0

1

1,

= Zff l d m

Fig. 8 : Meshing stiffness evolution for various helix angle

Fig. 7 : Simplified dynamic model of single stage gearing train

172

Fig. 10 : Global meshing stiffness (2 = 25, 2 = 150, rotating speeds and misalignments __

=

20")for various

. .

aligned gears

_ _- 100 rad/s _ _ _ _ BOO rad/s _ _ 1200 radk

0 1 - ~ 2 - 5 1 0 rad _ _ - (q1 --i25 10 fad

dl --o

1500 rad/s

y'l

-

2- 5 10

-42-510

rad rad

aligned gears

8 -

4

Fig. 11 : Global stiffness (Z = 25, 2 = 150,

o(= 20

R 2.5

t

0,

Fig. 12 : Dynamic response for misaligned helicoidal gears (2, = 25, Q = 150d = a ')

0 = 15")

_--

spur gears

-

-

-

$f,--$z

-510

u'l--u;

-210

-4

-4

Fig. 13 : Dynamic response for misrrhPd Spurn gears (2,= 25, 15opl= 20")

5

-

Fig. 14 : Instantaneous load distributions for misaliigned helicoidal gears (Z 1 25,

3 -150,d -203'

SESSION VII ROLLING ELEMENT BEARINGS (1) Chairman: Dr J D Summers-Smith PAPER Vll(i)

The Palmgren-Miner Rule Derived

PAPER Vll(ii)

Prediction of Rolling Bearing Life Under Practical Operating Conditions

PAPER Vll(iii)

Surface Damage on Rolling Elements and its Subsequent Effects on Performance and Life

PAPER Vll(iv)

Debris Denting - The Associated Residual Stresses and Their Effect on the Fatigue Life of Rolling Bearings: An FEM Analysis


175

PaperVll(i)

The Palmgren-Miner rule derived J. J. Kauzlarich

The Pblmgren-Miner linear d a m p rule predicts fatifailure of the caaponent when the slprmation of the cycles of reversed stress amplitude, N I ~ , to the cycles of stress causing failure a t each stress anplitUae, N i , equals unity, i.e., CiN@i/Ni=l. It is shown that t h e failure strength curve for a rolling element bearing represents an llenergy of failure." AS such it is possible to sun the total %ne.rqy of failure1 for a variable loading duty cycle and the rated fatigue l i f e CUrvB errpOnent derive the P M Rule. It is shown that the Rule

incorrectly, mt that it is possible to revise the Rule to take into account the correct rated life exponent. The revised PM Rule predicts a sanewhat longer fatigue l i f e under varying loaaing oonditions than the standard Rule. The method of derivation of the revised PM Rule allows one to f i t agmhental dab. 1 lNmmmTaN

hypothesizing the Rule.

concept of crnmilative fatigue BamcuJe was proposed by palmgren i n 1924 (1, p.89) for ball bearings, and by Miner i n 1945 (2) for beams. The hypothesis is called the PalmgrerrMiner cycle ratio mimation theory, or more popularly, the Papgry-biiner linear damage rule, and it is still n d e l y used. The Pabgren-Miner Rule ( P M Rule) predicts failure of the cunponent when

A

c11

2

IIDLLTNo-L;LFE

The rolling contact fatigue strength of 7205B inner rings taken fran data by mmsch (3) is shuwn in Figure 1. ~n these tests o i l filters

with a naninal mesh of 25 microns ware used. This figure corresponds to the typical stress/cycle curve for fatigue w i t h the cubic power l a w line for the Anti-Friction Bearing Manufacturers Association (AFBMA) rated l i f e as shuwn. lsbave a maximum Hertz contact stress of 3.0 GPa, plastic deformation of the racerway was r e p e d .

for a given cyclic stress or load amplitude, N I i is the lnrmber of cycles applied The AFH~A standard load r a w for bearings and ~iis the nuanber of cycles causing failure a t is a probability equation in which the rated load this stress or load amplitude. at which 90% of a group of apparently identical The PM Rule does not take into account beariqs w i l l give a life of at least 106 prior stress history or sequmce of loadings so revolutions before the f i r s t evidence of failure that when applyinsr the rule to gross cycles w i t h by fatigue is detected, and is few load changes it can be highly inaccurate, with the mimation varying a l l the way fran 0.18 t o 23. w e r , i f the various load amplitude cycles are mixed i n a quasi-andam manner the sunnnation tenas to approach unity a t the time of failure; falling in the range of 0.6 to 1.6 (3, where C is the rated dynamic load listed in p.242). In ball and roller bearing appliCatiOns, tables of standards and P is the actual load. In there are many situations where the bearing will Figure 1 the espdmenm data exceeds the rated be subjected to a duty cycle that repeats every life, but not greatly. It was reportea that for few minutes, and the P M Rule would be enpcted this series of tests inspection of the rings to give reasonable results. showed that fatigue failure was initiated by The P M Rule assumas that the bearing is indentation due to rolling over a particle of properly lubricated, aligned, and loaded as w e l l solid contaminant. For failure initiated by as kept free of abrasives, nroisture, and any indentation of the race by contaminant, the corrosive agents. It then reduces the problem of charadaristic crack initiation time associated the life of the bearing to fatigue damage due to with fatigue failure is essentially eliminated. cyclio loading of the balls and raceways during when contaninant particles larger than 5 microns rotatiOn. Although mrllIy O f the a S V t i o n ~~ v 8 were filt8red out of the o i l cllu5ng the testing often violated i n a typical bearing application, the fatigue damage was found to originate below it is also convenient to assurme these conditions the surfof the raceway, and , L ~ Olife so as to concentrate oarly on fatigw failure of increased up to 4 times the rated life. The the bearing. In the next sections, a semi- raw l i f e equation shclwn in Eq. 2 is remarkably qualitative dewelopmnt of the nature of the simple, and the adequacy of the exponent of 3 has stresses and loads applied to a rolling element been ShCRm to apply to ball bearhqs as well as bearing is raaertaken in order to shcrw that the roller bearings (4, p.452). P M Rule has a basic foundation i n fatigue theory In order to gain a better understanding of which allows a derivation as opposed to simply Eq. 2 let us next Swmcine the Hertz stress field whe.re,

176

1" - %Deformation Shear S t r e s s

-m

3

5

2

m I

L 10 Load CyClOl

Fig. 1 Rolling contact fatigue of 7205B inner rings, after Iarosch ( 3 ) . belaw the ball or roller and raceway oontact.

For a r i g i d cylinder loaded against an elastic solid the stresses a t the surface of contact, which were f i r s t derived by H. Hertz, and the resulting subsurface stress f i e l d have been calculated, e.g., see Johnson ( 5 ) . There is a

significant shear stress rewrsal of the Orthogonal shear Stress below the surface, T y z r and this is shown in Figure 2. The maximum amplitude of the orthogondl shear stress is found to be 0 . 2 5 6 ~at ~ yro.8at a depth 2=0.5b (11, p.379). The tenn po is the maximu stress at the surface of contact. The principal in plane shear stress, rP, is shown for canparison w i t h T ~ . Ixlring mnnal aperation of a rolling element

bearing the rolling elements plllst pass i n and out of the line of applied load and tractive forces are also developed. Including tractive forces has a significant effect on the subsurface stress field. For example, Castleberry (6) finds that the auith-Liu equations which calculate contact stresses due to load and friction shcrw that with a cwfficient of friction of 0.08 the amplitude of the orthogonal shearing stress increases by a factor of 1.67 for a particular example. It w i l l be of interest later to consider the amplitude of the distortion energy density, wS, associated w i t h the orthogonal shear stress, where

Fig.

Hertz orthogonal shear stress due to a loaded rigid cylinder. amplitude due to the orthogonal shear stress given by Equation 3 w i l l suffice. For static Hertz stresses due to a roller on a raceway the mMdrmrm surface stress at the -tact, Por is 2

= ummr = 0.564 [Q' r E*] v2

Po

where 1 -

-us

= Q/L, the lnaxhm roller load par unit of the roller, and E* is the reduced of elasticity given by

Ql

where 1 and 2 xefer to praperties of the roller and raceway respectively. misson's ratio is p. The getmetry factor r defined by the radius R for the roller and inner raceway configuration is

A relation beradial bearing load and maxinun ball or roller load is given by Harris

(4, p.165 & 169)

Ws

Tw2

20

[31

is the shear modulus of elasticity. Since the stress field for a Hertz contact is tridimensional, a calculation of the maximum strain eneqy density auplitude associated w i t h the odahedrdl sheariag stress gives amther approach to fatigua failure, where 0

w, = 3 7, 2 4G

[41

[GI

Q

=5

(19

P/Z

191

z is the nulber of rollers. using the fact that the maxinann orthogonal shear stress amplitude is ~ya=O.256p~,then using E q 3 . 6 and 9, and letting P */I, results , in where

hrm 4. 3,

the lMximun orthogonal shearing stress strain emargy density amplitu!!e is given

and

by

W , for o m purposes the less ccaplicated equation of the maximnu strain e~lsrgy density

where Q applies to the race or roller aepenaing

upon the fatigw site.

177 The most important aspect of the Wysis to this point is that the extarnal load on the bearing, P (P' = P/L), is directly proportional t o the subsurface s t r a i n magym density amplitude, wS (Eq. 11),which is ocmrnng inthe raceway or rollers, so that

Thus, the product of N times P on the fatigue stmngth plot of Figure 1 is proportional to energy, and has a l l of the charactan 'stics of a scdlar fbction. A relation between strain magy density and fatigue failure w i l l be investigated next. 4

~

~

C

F

R

A

c

Z

p

[

I

R

E

~

~

fatigue crack that has h e n initiated by contaminant indentation of the raceway or other ~OUICBSw i l l gmw under sustained cyclic loading until it reaches catastrophic size. Collins ( 7 , p.290) finas that the rate of crack growth can be A

-by

substituting for Ws from ~ q . 11, and absorbing dl1 constants i n N =

c is the crack length, N is Ilunnber of load

q) and p ' a r e empirical constants that depend upon material properties and secondazy variables, and K is the stress intensity factor WlitUaS. For the mll- bearing problem K CM be related to bearing load as follows. The stress intensity factor amplitulae ifue to the orthogonal shearing stress ( 7 , p.62) is cycles,

I'

[PI r%*,ap

1181

Cp-f

oanparins Eq. 18 with the empirical rated l i f e i n %=2, W8 See that the v F Should be pE3. The results of this sectxon give an insight 'sm applicable to into the fatigus crack mecharu roller bearings and ball hiwings with highly confonlling IcLcBwBys. The analysis shrrws that crack growth is an imrerse function of both load and crack length. Refarning to ~ q .16, each load cycle w i l l produce

-

a-oc

crackextensl-on which will affect the subsequent crack extension. If the laad duty cycle is very short the seqwye of loading has a small effect. ~n this paper it w i l l be a s h that the laad duty cycle is short so that the crack length effect can be neglected. Turning back to the results given by Eq. 11, we can lxw investigate a derivation for the PdlmJren-Miner m e . 5

where

get

%@I,

PAuGREWmNERIIuLE

Consider a simple duty cycle applied to a roller bearing where the load continually varies between Pl for NI1 revs and P2 for N g 2 revs, where the mmrbar of revs to failure at the respective loads is N 1 and N2, and after some rmla#rwn number of revs, N, a detectable fatigue failure occurs. Frau the previous analysis the procluct of represents an amormt of energy associated mth progressive crack propagation, so that

1141 where C,

is a function of g-try

and crack aisplacem8nt mode. Bubstituting from Eq. 3, the stress intensity factor may be rewritten i n tenns

Equation 19 is shcRm schmatically on Fig. 3. Defining

ofstrainenergyas

I n w i n g Eq. 15 into 4. w, and collecting the amstants in %' the integrated fonnof the gmwth rate quation ha ran^ (let (P'/~)=P) l O L \

This aplproach is similar to one taken by Kauzlarich and Thacker (8) and Freakley and P a p (9, p.106) for the dynamic crack growth i n rubbers. The i n i t i a l crack length c1 is very much smaller than the final crack length a t failure so that the fatigue life in tenas of cycles to

2

failure N is 101

t171

2

5

101

L t 0 Rated Life

Fig. 3 E f f e c t of duty cycle on fatigue life.

178

n1

+ n2 = 1

1221 29 is plotted for a two load chrty cycle revised P M

-tion

h Fig.

or, ingeneral cini

=1

[231

Equation 23 is the same result as expressed by the Pdlmgrea-MinSr Rule in EQ. 1, and it is seen that the Rule makes a drastic otlon about the slope of the rated life equation, as

well as neglecting the effect of crack Qrerwth

length during progressive fatigue crack extension. In order to use the P M Rule for rollhq elemnt bearing selection, we d e f h 1241 Then, fran Eqs. 2, 20, 23, and 24, get

1251 ZQplicatiom of Eq. 25 are shown i n nrodarn machine design texts (10). Since it is not mcessuq to neglect the slope of the rated life curve u1 the derivation we w i l l consider the possibility of revising the P M Rule to take this into aeunmt i n the next

4. The result sbrrws that the

Rule w i l l predict a higher value for fatigue life aepenaiag upon the loads and cycle ratio enoamtered; for the exanple, 1.39 times larger. A sear~hof the literature did not result in any test data for variable loaded bearings, krt all of the bearing lnanufacturem recarmend that the PM me be used when designiq for variable load. Tests of materials i n robting beam fatigue machines in which the duty cycle is short in aanparison to the cycle life tend to give results i n fair agmement w i t h the P M me (7, p.242) Md (11, p.221). The plot of the rated life curve on Fig. 1, makes the typical assrrmption that rollhq element bearings do not exhibit an eniRrrance l i m i t . In fatigue tests of corrosion cunbined w i t h stress concentrations, C o l l h ( 7 , p.206) shrrws that steel specimens exhibit no endurance l i m i t even unconditions where the corrosive agent was s-ly tap water. ~n the authorls experience, a new ball bearirq suhmrged i n o i l developed p i t s in a few days after water was inadvertently allowed to d ~ 5 pinto the o i l fmm an overhead cold water pipe. Since there is dlwap saae water in bearing oil, and an initial crack represents a severe stress concantration, it aplpears t h a t a bearhq life curve witbut an endmuwe limit is not an unreasanable assrrmption. 8ee Beercheck (12) for a discussion of the effect of dirt and water on bearing life.

Section.

Now reccinsider EQ. 21, w i t h the possibility that pE3, where the generalized form of the equation is 1 .o

1261

0

1.o

0.5

Cycle Ratio,

Q1

=N,'IN

The lmlavrwn average load is

Fig.

1271 27 into 26 with m, and and 24, results i n a n w equation for rolling elment bearing selection w i t h a k x m d u t y c y c l e , as

Q.

Subti-

usby Eqs.

2,

20,

The effect of the revised PM Rule on bearing selection 8s caapared to the usual fom of the P-M Rule is discussed belcrw.

4

cycle failure aanparison predicted by

revised and StandamI PbLmgren-Miner RuJB=

The revised P M Rule, Eq. 29, C E L ~be applied t o empirical curves w i t h other than an exponent of p=3. A t high loads, aa e ~ i r i c a lfatigue &rength a w e for rolling ehnent barings w i t h an eqonent of p=4 or higher w i l l f i t the data better (3), and the revised P M Rule can handle this case. The approach used i n this paper can also be applied to rotating beam fatigue analysis, by SUbstiMing the square of the alternating stress auplitude for the bearing load. The revised P-M Rule gives a m e t w for predicting crack etxtension under variable cyclic loads, but does not predict crack initiation. ~n the case where crack initiation occulg early due

179

to o i l born contadnanb caushq indentation of the bearing raceway, or due to other causes, the revised PMRule is expecbd to give WasoMble results. If early crack initiation does not OCCUI: the revised P-M Rule is expechl to be erramus lut give amsarvative results. References

(1) PdLmgren, A., B a l l and R o l l e r Bearing Eagineeriag, 3rd Ed., SKF Inbustries, Inc.,

Philadelphia, PA, 1959. (2)

Miner,

M.

A.,

Fatiguep J. of -lied

wmmlative Damage in Mecham' m L AGME, V 67,

1945, Pp. Al59-Al.64. (3) mrosch, H. K., lcphe Life of the Rolling Bearing \mder varying UaaS and Emrirornnental c!Ondition!3," Ball and R o l l e r Bearirra Ensineerins, V20, # 1, 1981, pp. 17-23. (4) Harris, T. A., R a l l h q Bearing Analysis, 2nd Ed., Wiley, NY, 1984. (5) Johnson, K. L., 9Hundred Years of Hertz contact," Inst. of Mech. Em., h-oceedinss, V 196, # 39, 1982, pp. 363-378. (6) Castlebarry, 0. A., llAnalyzing Contact stresses More z4cCuratelyfl' Machlne ' Desian,V56, 2, 1984, pp. 92-97. # 7, (7) C o l l h , J. A., FailO f Materials in Mechanical Design, Wiley, NY, 1981. (8) K a u z l d c h f J. J. and J. 0. Thacker, wheelchair Tire ~ a l l i n g Resistance and Fatigue,mm J. O f Rehabilitation R h DL V 221 # 3, July, 1985, Pp. 25-41. (9) Freakley, P. K. and A. R e Paynet Theom and practice of Eh-Jinsering with Rubbar, Applied &-, T6nrbnf 1978. (10) 8pottsf M. F., Design O f Mnehine 6th Ed., mtiCS-ml, NY, 1967. (11) JwindL1, R. C., 8tressf S t r a i n , and 8trengthf M C G r a w m l , NY, 1967. (12) R. C., -1 Dirt Md Water 81-h Beaning Life," mchme Desian, v 49, 13, July 6, 1978, Pp 2-7.

-,

a

x


181

PaperVI I(ii)

Prediction of rolling bearing life under practicaloperating conditions E. loannides, B. Jacobson and J. H.Tripp

The rolling contact fatigue life model of Ioannides and Harris [ l ] evaluates the expected life of any stressed volume from the survival probability of individual independent volume elements determined by the local stress level and fatigue limit. Since the model is not restricted to Hertzian stress fields arising from contact between dry, smooth, semi-infinite elastic half-spaces, i t has been extended in the present work to studying effects of lubricant films, roughness, contaminants and internal Dlastic stresses on life, using various fatigue stress criteria. Predictions of bearing life are discussed in relation-to those obtained using current IS0 bearing life methods, as well a s in comparison to available experimental results.

1

INTRODUCTION

The Lundberg-Palmgren (L-P) method [ 2 , 3 ] for assessment of the expected life of rolling element bearings grew out of the need for life estimates, taking into account the then prevailing influences of materials, manufacturing processes and operating conditions. In the intervening 40 years, the L-P approach has been successful in making relative life predictions for bearings with different sizes and loads, the variables appearing in the original life formulation. Current I S 0 life rating standards are indeed based on this method. Improvements in material properties, in particular, cleaner steels, have resulted in a higher proportion of bearings suffering surface-initiated fatigue compared with the sub-surface-initiated damage in earlier materials. Other influences, such as bearing surface finish, lubricant distribution and bearing kinematics, as well as improvements in the operating environment of the rolling elements themselves through better filtration and sealing, have as a result acquired a greater importance. Their effects combine to extend bearing life very considerably; in some cases, practically and functionally infinite life is observed. To describe such improved life performance and to compare life under, for example, different raceway finishing operations, i t has become necessary to go beyond the so-called ‘life adjustment factors’, which were introduced in an empirical way to describe the observed longer life. An understanding of the physical influence itself, in this example surface finish, on bearing performance is required. A s far as possible, the effects compressed into the life adjustment factors should be extracted in a quantitative way - the number of unknowns remaining hidden should be reduced to a minimum.

The present work links several effects to life through the stress fields they produce in the bearing material. Thus, in one case, the surface stress distribution from the dry contact o f two rough surfaces is calculated from the measured profiles. In another, rheological models going beyond the ideal Newtonian viscous fluid are introduced into the calculation of EHL films, from which surface stress distributions may be extracted. Such surface stresses are then used to generate the volume stresses determining the expected life of the bearing material. When contaminant particles are present in the film, plastic deformation of both the particle and the raceway will generally occur. The residual stresses arising from the residual strains (deformed particle and dent shapes) again are used to find the volume stress distributions in subsequent over-rolling. From these stress fields comes a clearer understanding of the various influences on life.

1.1 Notation a

Hydrostatic stress criterion factor

a,b

Semi-axes of Hertz contact ellipse, [m]

ai

Life adjustment factors, i

A

Probability normalization factor

=

1-3

c,e,h Lundberg-Palmgren exponents C

Basic dynamic load rating, [N]

G(N)

Elementary survival probability

H(x)

Heaviside step function

Ln

Life (nX Failure),

[Mrev]

182

N

Number of cycles

P

Load-life exponent

pli

Hydrostatic stress, [Pa]

PO

Maximum Hertz pressure, [Pa]

P

Bearing equivalent load, [N]

r

Position vector, [m]

RQ

Root-mean-square roughness height, [ml

Rn

normalized n th moment of height distribution

S(N)

Survival probabl Volume [ m 3 1 Transverse coord nate, [m] Depth coordinate

[ml

Depth of maximum Hertz shear stress, [in] Stress weighted average depth, [m] Viscpsity pressure coefficient, [Pa- I Shear strength pressure (traction) coefficient

putting an elementary volume at risk (the stress criterion) and z is a measure of the depth below tRe raceway to which this stress extends. V is the effective volume within which T differs sensibly from zero. The exponents c , e and h (assumed to be history-independent) were determined to give a best fit to the then available test data. From the form of Eqn.(2) i t is clear that T can only represent an average stress throughout the volume s o that the life N at any given survival level S cannot reflect sensitivity to localized domains of high stress. Moreover, since T and z o were calculated from Hertz theory, no account could be given of surface shear stresses arising from frictional sliding or lubricant viscosity. Finally, according to Eqn.(2), no bearing life can be infinite. The new life theory extends the L-P model in two essential respects. First, Eqn.(2) is interpreted local1 s o that T becomes a local v a r i a b l d h e right side of Eqn.(2) becomes a 'risk function'. Second, a fatigue limit T is introduced, patterned on structural fatigue initiation, such that any volume element for which T < T makes no contribution to the risk function. With these new features, the survival probability becomes:

1

In

-= AS

Root-mean-square roughness slope Film parameter von Mises stress, [Pa]

( T- T..)

A

h

N' H(T-T~)AV

(3)

20

where H(x) is the Heaviside step function. As a first approximation, this may be written in integral form as follows :

Maximum surface traction, [Pa] Shear stress (orthogonal, fatigue limit, elastic limit, etc.), [Pa] where

FORMULATION The L-P theory of bearing life begins with the assumption that the probability for a given volume element AV to survive N stress cycles and to fail in the next dN is proportional t o its size, and is a function not only o f its location r but also of N itself. The probability actually increases slowly with N, this memory effect being an essential part of fatigue behaviour. Integrating over all volume elements to obtain the survival probability of the volume V thus yields: 1

In

S(N)

=

J

G(N,r)

dv

1

region where the stress criterion exceeds threshold. The fatigue limit itself may also assume local values. The factor z o , originally introduced to include the propagation interval between internal damage initiation and its appearance in the surface, is retained but should now be regarded a s a stressweighted average depth, z'. The L-P exponents remain the same. The L-P formulation leads to a relation between N and S depending on bearing design and load, which is readily reduced to the simple form,

(1)

V

where G(N,r)AV is the accumulated survival probability over N cycles for element AV. I n the absence of knowledge of actual subsurface stresses, L-P chose simply to give a functional form to the right side of Eqn.(l) as follows: ln-aS(N)

is the volume-averaged value of

A and the integration runs only over the

TCN' h

V

zo

where T is some characteristic stress

Here, L is the expected life (N in MRev) under load P , while C , the basic dynamic load rating is the load for which (100 S)% of a population of bearings will survive for at least 1 MRev. The I S 0 standard is based on this expression with S = 0.9 (10% failure rate defines the L life) and, using Hertz analysis, T is tRe maximum orthogonal shear stress and p, the load-life exponent, is 3 or

1013 respectively for ball or roller bearings. I n full, the I S 0 definition is written, Lna

= ‘1‘2’3

]:[

P

which includes the familiar three life adjustment factors, a,, i = 1,2,3. On a logarithmic plot, the basic (nonadjusted) life rating thus decreases linearly with load. The a, factors serve to shift this line to longer life, but with no change in slope. 2.1 Fatigue criteria In order to carry out actual life calculations, i t is necessary to determine the proper fatigue criterion to use in Eqn.(4). The choice becomes even more critical when the model is applied to the localized type of stress fields encountered in roughness and contaminant studies. Examples of criteria proposed in the literature are:- p,, maximum Hertzian pressure; , orthogonal shear stress (ISO); T. x,Tiaximum shear stress; u t , maxfmum surface traction; u, von Miges stress; T , maximum shear amplitude regardless o t plane and direction. I n the general multiaxial stress case there have been many other suggestions for criteria, involving both instantaneous and cycle-average values of the stress components [4]. Most direct material tests, however, have been performed under conditions where the deviatoric stress components are proportional to, and thus in phase with, each other. Such conditions do not pertain t o rolling contact fatigue, s o that the influence of the principal stresses on endurance strength must be explicitly included. An illustration of the differences between the old and new life models is given in Figure 1 , which shows both the basic and adjusted life ratings of a 6309 DGBB as a function of contact pressure according to the standard catalogue procedures, Eqn.(6), together with the new model load-life behaviour. For the model calculations, T~ was selected as the fatigue criterion, while local modifications of the fatigue limit were made according to the absolute maximum value, T a x , of this shear stress in the cycle. Tfius, T” = 0.35 GPa for -crpax below the elastic limit T., decreasing linearly to zero at the fracture strength T ~ . (This form for ‘cU was based on independent data fitting 111). The curve predicted by the new model is normalized to a single experimental point obtained at 2.9 GPa (2900 N/mm ) . Also displayed are some experimental data of Zwirlein and Schlicht [5] taken from a 7205 B ACBB, with a basic life rating virtually indistinguishable from the DGBB. This shows good agreement with the predicted behaviour in the region of overlap, particularly with respect to slope. A t the lower stress levels, where test results become progressively more difficult to obtain, the predicted curve asymptotically approaches the fatigue limit, corresponding to normal pressure

4 x T,, =1.4 GPa. The effect of the life adjustment factors in this case is clearly inadequate, both quantitatively and qualitatively. Calculations based on the von Mises stress criterion for this example led to rather similar conclusions. (Test 7205 B

m

pooo

.

/Calculated 6309

0

S

O

5 0 2000

6309

0

1500 1 o5

1 07

I

\\

\Theoretical endurance strength

108

L1o

10” Life rev.

Figure 1 Variation with normal contact pressure of rating and theoretical lives of a 6309 DGBB. The rating and experimental values for a 7205 B ACBB are shown for comparison. I n the following example, a simple multiaxial criterion is introduced which modifies the damaging effect of the shear stress with a term linear in the local hydrostatic pressure: T; = T~

+ ap,

(7)

The value a = 0 . 3 is chosen to agree with many experiments carried out with shear stress in combination with compressive or tensile stress [6,7]. The effect of the ‘ a r term in Eqn.(7) is illustrated in Figure 2. showing the L life v. Load relation for a 6309 DGhi, computed from Eqn.(4) using Eqn.(7) with a = either 0 or 0.3. Values have been normalized to the Catalogue value for C/P = 2.8. The first case (upper curve) is thus essentially the same as given in Figure 1. The second case shows life reduction factors of no more than about 4 at low loads, while at higher loads the differences become negligible. This is in general agreement with the lack of sensitivity to criterion noted in the previous example. Both are based on the nominal ideal raceway geometry. 2.2 Internal and residual Stresses The criterion of Eqn.(7) has been used, also with a = 0.3, to simulate experimental results obtained from modified NU 209 rolling bearing inner races, subjected to different hoop stresses and run in a five roller fatigue test (at 5000 rpm, Hertz pressure = 0.7 GPa, A = 3 ) as described in [El. Table I compares relative fatigue life measured in these experiments with predictions using either no fatigue limit or the rather low value T’ = 70 MPa. This value was determinej a s giving the best overall agreement between experiment and theory. The important conclusion is

184

CIP

(6309) Shear stress fatique criterbn

Shear stress and hydrostatic pressure

faliaue criterion

1 01 lo2

10

1'03

i04

10

Llo(Mrevs)

Figure 2 The effect on 6309 L,, fatigue life of modifying the criterion by including a hydrostatic pressure term. thus that the hoop stress alone cannot account for the observed life reduction. Only the combination of internal stress with the fatigue limit shows the correct stress-life behaviour at the three measured levels. TABLE 1: Experimental and predicted relative L life of an NU 209 inner ring under different &ile stresses. CLANPING KOOP EXPERINENTAL PREDICTED PREDICTED PRESSURE STRESS RELATIVE L,, RELATIVE L R E Y T I V E L (T; 0 MPi? (T" 70 Nbi) ( M P a ) (MPa)

-

-

is a particularly damaging combination. The solidification pressure of the lubricant can also be important. As long a s the oil in the contact remains liquid, rather high slip velocities can be accommodated without causing excessive shear stresses. Taking again as example a 6309 DGBB, some of the effects of EHL films with different rheology may be demonstrated. First, for a given bearing load, the pressure distribution in the most heavily loaded ball contact is computed. The fatigue life, relative to the measurement at C/P = 2 . 8 , is then calculated from the subsurface stresses based on this distribution, using the criterion of Eqn.(6), with a = 0.3. Next, the surface stresses are modified by adding a shear stress proportional in magnitude to the normal stress and in the direction opposite to the local microslip velocity. This is a good approximation at high pressure and high slip, when the lubricant operates at its shear strength limit. A typical value of traction coefficient for poly-alpha olefinic oils is y = 0.05, while for oils with stiffer molecules, such as a naphthenic raffinate, values a s high as 0 . 2 0 are possible. Stress fields for these two values of traction are then used to obtain relative load-life curves. Results are plotted in Figure 3 , normalized to the experimental point for which y = 0.05 is assumed. The Catalogue Rating Life is also included. High Oxygen Content Steel

5 40 80

21.4 163.0 325.0

1.0 0.07 0.0125

1.0 0.329 0.102

1.0 0.084 0.0096

CIP (6309)

3-

3

EHD LUBRICANT FILMS 5-

Modification of the stress fields in bearing elements by an EHL film can be considerable. Parameters of lubricants most influential on the stresses at the film boundaries include:- viscosity (and its coefficients of pressure, u , and temperature variation), elasticity, shear strength (and its coefficient of pressure increase, y ) and solidification pressure. The original L-P calculations assumed that the film pressure distribution was the same as the dry, frictionless Hertz contact solution. However, the dynamics of a viscous fluid film imposes a relationship between the pressure and the shape of its boundaries which is different from that of dry elastic contact. Lubricant films in fact require a local film thickness decrease near the outlet, resulting in very steep pressure gradients and often a local "spikett [9]. Such rapid pressure variations produce high shear as well as normal stress fields in the bearing material close to the surface. Lubricants with high U-values building up large pressure spikes also tend to show large y-values, which permits high shear stresses in the oil and correspondingly on the boundaries. The result

10-

151 10

10

lo3

lo4

10'

L1o (Mrevs)

Figure 3 The effect of surface traction on 6309 L,, life. Comparison with Figure 2 shows that, at low loads, the effects of increasing friction from 0 . 0 5 to 0.20 are comparable to the effects of modifying the fatigue criterion according to Eqn.(7). Life reduction by a factor of about 4 is predicted. The effect does not, however, disappear entirely at higher loads, where a reduction of about 30% is still seen.

185

4

SURFACE ROUGHNESS

As for EHL films, surface roughness also has a large influence on the local stresses close to the bearing surfaces, producing significant deviations from the Hertzian stress distribution of smooth body contact. The actual topography imposed by the manufacturing finishing processes - grinding, honing, polishing, etc. - as obtained directly from surface profilometry provides a sampling of heights representing the true surface within the usual limitations of random signal analysis. Such a height sample is regarded as containing all the geometrical information obtainable on the surface, s o that interpolation between sampled points, such as that implied by introducing an asperity model, is at best uninformative and at worst dangerous. The gap between two unloaded rough surfaces is known from their step height representations, s o that specification of a nominal geometry and load suffices to determine the normal contact stress, computed also as a step distribution [9]. From such stresses, accurate subsurface stress fields may be calculated in the raceway. Discretization effects are confined to depths less than the sampling interval. An example of these calculations is given in Figure 4 , showing the surface height and contact pressure profiles along a transverse section of a 6309 DGBB inner raceway (sampling interval 20 pm). The honing process which follows grinding was in this case stopped before some deep marks left by grinding had been completely removed. Three such circumferential grooves, each about 1 pm deep, may be seen in the loaded zone. Corresponding to the steep local slopes associated with these features, large local pressure deviations, of the order 2 GPa relative to the smooth Hertzian distribution, are produced. The smooth Hertz maximum pressure here has the realistic value of 2.7 GPa, s o that contact at the bottom of the groove towards the outside of the track is almost lost. The effect of these strong local features on the subsurface shear stress field is still evident at a depth of order b, here about 200 urn. Table 2 shows the effect on the fatigue life of such topographygenerated stresses. The L,, life given is relative to the ideal smooth contact geometry, a reduction in life by a factor of nearly 4. The rms height, R q , and slope, A , values also appear. For comparison, jhe same calculation was performed for an unhoned ring with no deep marks. Corresponding to rms slope some 2% times that of the first surface, the pressure profile across the track of this ring fluctuates with an amplitude exceeding 1 GPa relative to the Hertz distribution, some 2% times the amplitude seen in Figure 4. Despite these large stress variations, the calculated life of this raceway is only slightly reduced.

Height (pd

Pressure (GPa)

41

t4

3

3

2

2

1

1

0

0

0

I

vO.2

0.6 3 8

0.:

1.0 X/A

0.5 1 1.5

2

2.5

ZIB

Figure 4 Dry contact pressure distribution across the raceway of a honed 6309 ring, showing a profile with residual grinding marks. The subsurface shear stress field, normalized to p o l is also given. TABLE 2:

-

Effect of surface topography on bearing life, relative to smooth surface ( R q 0).

L,,(T;),

1 1

I I

I I I

I

I

1

I

6309 DGBB INNER RING Rq (#m) Ap (deg) R,,

c

I

I

I

Boning, with residual 0 . 2 7 1 1 0 . 3 9 1 grinding grooves Normal grinding

0.523

0.913

I

Ll0(~;)

(133010.aaa

I1

360 0 . 7 3 4

Contrary to expectations, the reduction of life in these two cases is smaller for the surface with larger R and A , roughness parameters containiig both vertical and horizontal surface information. Because of the large value, 3113, of exponent ‘ c f in Eqn.(4), volume elements where the fatigue criterion is large receive very large weighting in the risk integral. A few vulnerable points in the risk volume, corresponding to a few extreme surface events, may thus completely dominate the

186

life behaviour, reflecting the physical nature of the fatigue process itself. In support of this, some high order moments R,, of the raceway height distributions were obtained. Normalized values of the 10th moment have been included in Table 2 as an example, showing the expected inverse relationship with L, [The normalized 2n th moment of a haussian height distribution has the value (2n-l)!!] This indicates that damage due to surface finish may result more from isolated defects than from average surface properties, an indication borne out in actual experience. The statistical description of such events is clearly a task much harder even than conventional surface characterization.

.

5

CONTAMINANTS

Lubricant film thicknesses lie typically in the range 0.1-3.0 p m , while contaminant particles carried through the contact may well be an order of magnitude larger, in the range 1-30 urn. Studies, both experimental and theoretical, of raceway deformations caused by entrained particles have shown the occurrence of quite severe denting, even when the raceway has greater hardness than the squashed particle 111,121. Indeed, particles as soft even as common plastics can permanently deform the bearing surfaces if their size lies toward the top of this range. For hard particles, such as steel debris or ceramic fragments from a grinding wheel, i t is necessary that their size be only slightly larger than the oil film thickness before plastic deformation occurs. Such damage features are always surrounded by a local residual stress distribution which does not disappear within the life of the bearing. Calculation of the residual stress distribution around such dents has in fact revealed the existence of regions of tensile stress at the surface near the dent edge [13]. As already mentioned, reduction of compressive principal stresses by superposition of tensile components decreases the endurance strength of bearing steels. Thus, a tensile residual stress not only raises the local stress but also decreases the local fatigue limit of the material. Such dents thus have a particularly deleterious effect, as may be demonstrated by including the residual stress in the fatigue criterion of Eqn.(3). This has been used to evaluate the risk function at each point beneath a roller as a function of time, i.e., as a function of the distance of the contact patch from the dent as the roller overolls i t [14]. For certain positions of the roller, the risk of damage near the edges of the dent is dramatically enhanced. 6

CONCLUSIONS

With the computation facilities currently available, i t is possible to obtain very detailed stress fields associated with surface features as well as to combine them with internal

stresses or residual stresses arising from plastic deformations. Moreover, these stresses can be combined with surface stresses coming from the pressure and shear stress in the lubricant. The present fatigue life model can also handle a detailed description of the local material properties. However, at present such exact knowledge of material behaviour is not available but must be deduced, chiefly from bearing tests. The individual effects of surface topography and lubricant parameters on the estimated life of a bearing actually amount to less than one order of magnitude each. These effects may, however, combine with those of residual or other internal stresses to produce more drastic reductions on the endurance life of rolling bearings. Thus, considerable progress has been made towards the goal o f extracting the hidden physical content of the life adjustment factors, which hitherto have been the empirical means of making quantitative estimates of a number of unknown factors. I n addition, this approach is applicable to life prediction for lubricated machine elements in general. 7

ACKNOWLEDGEMENTS

The authors would like to thank Dr. I.K. Leadbetter, Managing Director of the SKF Engineering and Research Centre, for permission to publish these results. Thanks are also due to Mr. E. van Amerongen for valuable discussions on experimental aspects of this work. REFERENCES IOANNIDES, E. and HARRIS, T.A., ‘ A new fatigue life model for rolling bearings’, J. Tribology 1985, 107, 367-378. LUNDBERG, G. and PALMGREN, A., ‘Dynamic capacity of rolling bearings‘, Acta Poly. (Mech. Eng. Ser. l), Roy. Swedish Acad. Eng. Sci. 1947, 7, 5-32. LUNDBERG, G. and PALMGREN, A., ‘Dynamic capacity of rolling bearings‘, Acta Poly. (Mech. Eng. Ser. 2), Roy. Swedish Acad. Eng. Sci. 1952, 96, 5-32. KAKUNO, H. and KAWADA, Y., ‘ A new criterion of fatigue strength of a round bar subjected to combined static and repeated bending and torsion‘, Fatigue of Engng. Mat. and Structures 1979, 2 , 229. ZWIRLEIN, 0. and SCHLTCHT, H., ‘Material stressing during rolling loading - influences of friction and residual stresses’, Z. Werkstofftech. 1980, II, 1-14. BURNS, D.J. and PARRY, J.S.C., J. Mech. Engng. Sci. 1964, 6 , 293. DANG VAN, K., GRIVEAU, B. and MESSAGE, O . , ‘Bi-axial and multiaxial fatigue‘, Proc. 2nd Intl. Conf. on Multiaxial Fatigue (Dec. 1985, Sheffield), Mech. Eng. Publ. 1988.

187

[8]

[9]

[lo]

[ll]

[12]

[13]

(141

CZYZEWSKI, T., 'Influence of a tension stress field introduced in the elastohydrodynamic contact zone on rolling contact fatigue', Wear 1975, 34, 201-214. HOUPERT. L., IOANNIDES, E., KUYPERS, J.C. and TRIPP, J.H., 'The effect of the EHD pressure spike on rolling bearing fatigue', J. Tribology 1987, 109, 444-451. TRIPP. J.H., H O U P E R C L . G . , IOANNIDES, E. and LUBRECHT, A.A., 'Dry and lubricated contact of rough surfaces', Proc. Inst. Mech. Engrs. Intl. Conf. 1987-5, 'Tribology - 50 years on', 1987, 171-79. KAMER, J.C., SAYLES, R.S. and IOANNIDES, E. 'Deformation mechanism and stresses created by 3rd body debris contact and their effect on rolling bearing fatigue', Proc. 14th Leeds-Lyon Symp. on Trib. (Lyon 1987, to appear). HAMER, J.C., SAYLES, R.S. and IOANNIDES, E. 'Particle deformation and counterface damage when relatively soft particles are squashed between hard anvils', J. Tribology 1988, 110, (to appear). HAMER, J.C., L U B E H T , A.A., IOANNIDES, E. and SAYLES, R.S. 'Surface damage on rolling elements and its subsequent effects on performance and life', Proc. 15th Leeds-Lyon Symp. on Trib. (Leeds 1988, this conference). KO, C.N. and IOANNIDES, E., 'Debris denting - the associated residual stresses and their effect on the fatigue life of rolling bearings: an FEM analysis', Proc. 15th Leeds-Lyon Symp. on Trib. (Leeds 1988, this conference).


189

PaperVI I(iii)

Surface damage on rolling elements and its subsequent effects on performanceand life J. C. Hamer,A. A. Lubrecht, E. loannides and R. S. Sayles

The i n f l u e n c e o f l u b r i c a n t c o n t a m i n a t i o n a n d s u b s e q u e n t s u r f a c e damage on r o l l i n g b e a r i n g f a t i g u e h a s formed t h e b a s i s of s e v e r a l s t u d i e s o v e r r e c e n t y e a r s . Webster e t a 1 (1) c a l c u l a t e d t h e e l a s t i c s u b s u r f a c e stress f i e l d s from r e a l d e n t p r o f i l e s and used t h e s e a s i n p u t t o a f a t i g u e l i f e model t o d e t e r m i n e t h e r e d u c t i o n i n l i v e s . I n t h i s p a p e r a s l i p l i n e f i e l d a n a l y s i s h a s been u s e d t o c a l c u l a t e t h e s u b s u r f a c e r e s i d u a l stresses f o r d i f f e r e n t i d e a l i s e d d e n t / r o l l e r c o m b i n a t i o n s . These stress f i e l d s were superimposed upon t h o s e c a l c u l a t e d from a d r y c o n t a c t a n a l y s i s o f t h e o v e r r o l l i n g of t h e d e n t which u s e d n o v e l m u l t i - l e v e l t e c h n i q u e s t o a c c e l e r a t e c o n v e r g e n c e , and t h e r e s u l t a n t stress f i e l d s p r o v i d e d i n p u t t o t h e f a t i g u e l i f e model. The i n f l u e n c e o f t h e d e n t i t s e l f on l i f e a p p e a r s t o b e s m a l l a n d o n l y becomes s i g n i f i c a n t on i n c l u s i o n o f t h e r e s i d u a l stresses. These have a p a r t i c u l a r l y marked e f f e c t a s t h e r o l l e r r a d i u s a n d l o a d a r e r e d u c e d , s u g g e s t i n g e x p e c t e d l i v e s may n o t i n c r e a s e a s r a p i d l y w i t h d e c r e a s i n g l o a d a s would b e e x p e c t e d from c o n v e n t i o n a l models.

1 INTRODUCTION

L u b r i c a n t c o n t a m i n a t i o n and s u b s e q u e n t s u r f a c e damage i s i n c r e a s i n g l y r e c o g n i s e d a s h a v i n g a s i g n i f i c a n t e f f e c t on b e a r i n g f a t i g u e l i v e s which would n o t n o r m a l l y b e p r e d i c t e d b y t h e t r a d i t i o n a l Lundberg and Palmgren model (2). I n ( 3 ) Ioannides and H a r r i s p r e s e n t e d an important g e n e r a l i s a t i o n of t h e c l a s s i c a l m o d e l i n which t h e s t r e s s p e r t u r b a t i o n s r e s u l t i n g from n o n - p e r f e c t l y smooth c o n t a c t i n g s u r f a c e s c a n be i n c l u d e d . E s s e n t i a l l y t h e new model is a n e l e m e n t a l form o f t h e e a r l i e r a n a l y s i s where t h e p r o b a b i l i t y o f f a i l u r e i s c a l c u l a t e d from t h e c u m u l a t i v e c o n t r i b u t i o n o f stresses above a t h r e s h o l d v a l u e i n s m a l l volume e l e m e n t s o f t h e m a t e r i a l . T h e r e f o r e t o a p p l y t h e model a c o m p l e t e h i s t o r y o f t h e stress f i e l d u n d e r n e a t h t h e d e n t a s it p a s s e s through t h e c o n t a c t i s required. This f i e l d w i l l be e f f e c t i v e l y made up o f two components t h e r e s i d u a l stress f i e l d from t h e i n d e n t a t i o n and t h e EHD stress f i e l d from t h e s u b s e q u e n t o v e r r o l l i n g of t h e d e n t . Un f o r t u n at el y t h e s e a r e not n e c e s s a r i l y independent as f u r t h e r p l a s t i c d e f o r m a t i o n o f t h e d e n t e d g e s and some shakedown w i l l p r o b a b l y o c c u r , b u t a u s e f u l f i r s t a p p r o x i m a t i o n c a n b e made by t r e a t i n g them a s s u c h . T h i s problem was f i r s t t a c k l e d by Webster, I o a n n i d e s a n d S a y l e s (l), where t h e y measured t h e p r o f i l e s o f d e n t s from a r e a l b e a r i n g s u r f a c e . T h i s i n f o r m a t i o n was t h e i n p u t t o a n u m e r i c a l c o n t a c t model c o u p l e d t o a f i n i t e element a n a l y s i s t o determine t h e s t a t e o f stress i n a n i n d e n t e d b e a r i n g raceway. The stress i n f o r m a t i o n was u s e d i n c o n j u n c t i o n w i t h t h e m o d i f i e d f a t i g u e model t o determine t h e r e d u ct i o n i n f a t i g u e l i f e . (4) approximate solutions were In p r e s e n t e d f o r t h e i n t e r f a c i a l p r e s s u r e s and d e f l e c t i o n s r e s u l t i n g f r o m debris p a r t i c l e s b e i n g squashed i n t h e i n l e t t o a n EHD c o n t a c t .

t o allow t h e a p p l i c a t i o n of 2 dimensional e x t r u s i o n t h e o r y . The p r o b l e m i s s i m i l a r t o s t r i p r o l l i n g , b u t i n t h i s c a s e t h e r o l l e r s cannot be expressed a s circular arcs as the e l a s t i c deflections d u e t o t h e EHD a n d e x t r u s i o n p r e s s u r e s a r e s i g n i f i c a n t . The s o l u t i o n was f o u n d b y n u m e r i c a l l y i t e r a t i n g between t h e p r e s s u r e and d e f l e c t i o n e q u a t i o n s u n t i l convergence. As t h e r o l l i n g s u r f a c e s c o n t i n u e t o approach one a n o t h e r i n t h e i n l e t , the interfacial pressures may increase s u f f i c i e n t l y such t h a t p l a s t i c deformation of t h e raceways c a n o c c u r . The c r i t i c a l v a l u e o f p r e s s u r e may b e e s t i m a t e d f r o m i n d e n t a t i o n e x p e r i m e n t s or t h e o r e t i c a l c o n s i d e r a t i o n s s u c h a s ( 4 ) . By a p p l y i n g t h e s e c r i t e r i a t o t h e model, t h e approximate dent shapes and p r e s s u r e d i s t r i b u t i o n s may b e f o u n d a n d compared w i t h t h o s e m e a s u r e d e x p e r i m e n t a l l y ( 5 ) . The m e a s u r e d p r o f i l e s o f t h e s e d e n t s c l o s e l y approximate a c i r c u l a r a r c s i m i l a r t o t h e impression l e f t by a rigid c y l i n d r i c a l i n d e n t e r . Dumas a n d B a r o n e t ( 6 ) p r o d u c e d a f i n i t e element s o l u t i o n t o t h e c i r c u l a r i n d e n t e r problem and f o u n d t h a t a t s i g n i f i c a n t d e p t h s o f d e p r e s s i o n , where t h e s u b s u r f a c e zone w a s e n t i r e l y p l a s t i c t h e c a l c u l a t e d p r e s s u r e p r o f i l e w a s f a i r l y c o n s t a n t o v e r most of t h e i n t e r f a c e . A t s m a l l e r d e p t h s of depression t h e pressure p r o f i l e is not f l a t , b u t r e a c h e s a maximum a t t h e c e n t r e where t h e pressure i s approximately 50% g r e a t e r than it i s n e a r t h e p e r i p h e r y of t h e d e n t . This suggests that for relatively small indentations the interfacial pressure is still i n c r e a s i n g t o w a r d s t h e c e n t r e of t h e d e n t , t h u s g e n e r a t i n g a r a d i a l e x t r u s i o n f o r c e on the debris particle resulting i n a surface t r a c t i v e f o r c e on t h e b e a r i n g raceway. A t g r e a t e r depths of i n d e n t a t i o n t h e p r e s s u r e p r o f i l e f l a t t e n s and t h e r e s u l t a n t s u r f a c e traction force diminishes. Outside t h e A p l a n e s t r a i n a p p r o a c h was u s e d

i n d e n t e d zone where t h e d e f l e c t i o n s a r e e n t i r e l y e l a s t i c , debris deformation w i l l c o n t i n u e t o o c c u r and t h e p r e s s u r e p r o f i l e w i l l b e d e f i n e d by t h e e x t r u s i o n and e l a s t i c i t y equations a s discussed i n ( 4 ) . The r e s i d u a l stresses r e s u l t i n g from t h e i n d e n t a t i o n e s p e c i a l l y i n t h e p r e s e n c e of a s u r f a c e t r a c t i o n f o r c e may e n c o u r a g e f a t i g u e c r a c k i n i t i a t i o n a s p o s t u l a t e d by O l v e r ( 7 ) . I n t h i s p a p e r a s l i p l i n e f i e l d model b a s e d on t h a t d e v e l o p e d by O l v e r was u s e d t o e s t i m a t e t h e p l a s t i c stresses i n t h e s u b s u r f a c e and t h e r e s u l t a n t r e s i d u a l stresses on u n l o a d i n g . A f t e r i n d e n t a t i o n t h e squashed d e b r i s p a r t i c l e i s l o s t a n d t h e damaged s u r f a c e r e p e a t e d l y p a s s e s t h r o u g h t h e EHD c o n t a c t . Modelling t h i s p r o c e s s i s n o t p r a c t i c a b l e a t p r e s e n t , however a s t h e f i l m t h i c k n e s s i s s m a l l compared t o t h e e l a s t i c d e f o r m a t i o n o f t h e s u r f a c e and w i l l probably be f u r t h e r r e d u c e d a r o u n d t h e e d g e s of t h e d e n t , a d r y contact approximation may not be too u n r e a l i s t i c . Clearly, although t h e r e s i d u a l stress d i s t r i b u t i o n i s f i x e d r e l a t i v e t o t h e d e n t t h e superimposed c o n t a c t stress f i e l d w i l l be changing during o v e r r o l l i n g and t h e f u l l h i s t o r y w i l l be r e q u i r e d f o r t h e l i f e calculations. 1.1

Notation

constant half-width of Hertzian co n t act , m i n c r e m e n t a l a r e a of t h e c r o s s s e c t i o n o f t h e r i n g , mm2 e l i f e exponent H dimensionless f i l m thickness HOO constant i n dimensionless f i l m thickness equation k y i e l d s h e a r stress, N/m2 N fatigue l i f e P dimensionless pressure R r e d u c e d r a d i u s of c u r v a t u r e , m S p r o b a b i l i t y of s u r v i v a l x,x'coordinates i n rolling direction, m X,X' dimensionless coordinates y coordinate i n a x i a l direction, m z c o o r d i n a t e normal t o t h e s u r f a c e , m z' stress w e i g h t e d a v e r a g e d e p t h , mm R domain a' e x t e n d e d domain A

b dB

If t h e t r a c t i o n f o r c e extends r a d i a l l y from t h e c e n t r e t h e n t h e zone below t h e c e n t r e l i n e w i l l be p l a s t i c and t h e s l i p l i n e s m u s t m e e t a t 90°, f i g u r e 2 . From symmetry a s q u a r e s e c t i o n BEFG c a n be drawn and a s b e f o r e a f a n i s c o n s t r u c t e d b e t w e e n BC a n d BE. The s l i p l i n e s i n r e g i o n s CDHE a n d EHIF c a n b e c a l c u l a t e d numerically by f i n i t e d i f f e r e n c e s . Although t h e s l i p l i n e f i e l d c o u l d b e e x t e n d e d i n d e f i n i t e l y t h e a c t u a l zone o f p l a s t i c i t y w i l l o n l y e x i s t d i r e c t l y below t h e i n d e n t e r . D e f i n i n g t h e e l a s t i c / p l a s t i c boundary e x a c t l y i s n o t p o s s i b l e , b u t an approximation can b e made by a p p l y i n g t h e i n t e r f a c e p r e s s u r e s t o a n e l a s t i c h a l f s p a c e a n d c a l c u l a t i n g where t h e y i e l d s h e a r stress i s exceeded, a s s u g g e s t e d by O l v e r ( 7 ) S i g n i f i c a n t p l a s t i c d e f o r m a t i o n w i l l p r o b a b l y o n l y o c c u r i n t h e r e g i o n OADCB, whereas i n t h e remainder of t h e f i e l d t h e m a t e r i a l may b e p l a s t i c b u t w i l l n o t deform. Having c o n s t r u c t e d t h e f i e l d t h e stresses may b e c a l c u l a t e d i n t h e n o r m a l manner see ( 7 ) . D u r i n g u n l o a d i n g , a t e n s i l e normal f o r c e e q u a l i n magnitude t o t h e p l a s t i c p r e s s u r e s i s effectively applied t o the interface. C o n s e q u e n t l y t h e r e s i d u a l stresses c a n b e f o u n d b y summing t h e stress d i s t r i b u t i o n r e s u l t i n g from t h i s e l a s t i c t e n s i l e f o r c e t o t h e p l a s t i c stress d i s t r i b u t i o n . The e l a s t i c stresses w e r e c a l c u l a t e d a n a l y t i c a l l y a s d e s c r i b e d by F o r d ( 1 0 ) . A map o f t h e p r i n c i p a l r e s i d u a l stress d i s t r i b u t i o n s f o r t r a c t i o n c o e f f i c i e n t s o f 0 and 0 . 2 are shown i n f i g u r e s 3 ( a ) a n d ( b ) a n d a c o n t o u r map o f t h e o r t h o g o n a l r e s i d u a l s h e a r stresses i n f i g u r e ( 4 ) . The e f f e c t of t h e s u r f a c e s h e a r stress i s t o reduce t h e t e n s i l e r e s i d u a l stresses i m m e d i a t e l y below t h e s u r f a c e b u t t o i n c r e a s e t h o s e below t h e d e n t s h o u l d e r .

.

3 DRY CONTACT EQUATIONS

To s o l v e t h e d r y c o n t a c t p r o b l e m i t i s necessary t o f i n d a pressure d i s t r i b u t i o n P(X), t h a t s a t i s f i e s the film thickness equation ( l ) , ie solve t h e integral equation (2) f o r t h e pressure P.

H(X) = 0

a

(1)

i n t h e one d i m e n s i o n a l c a s e , reads :

2 SLIPLINE FIELD

In the s l i p l i n e f i e l d analysis the debris i n d e n t a t i o n of t h e b e a r i n g s u r f a c e i s modelled by a r i g i d die impressing a r i g i d - p l a s t i c halfspace coupled with a t r a c t i o n f o r c e e x t e n d i n g from t h e c e n t r e l i n e . I f t h e t r a c t i o n force is zero t h i s reduces t o t h e c l a s s i c a l f i e l d f o r a r i g i d i n d e n t e r a s p r e s e n t e d by H i l l ( 9 ) i n t h e d e f o r m i n g zone. I n ( 7 ) O l v e r presented a solution f o r a single unidirectional traction force applied t o the i n t e r f a c e , f i g u r e 1. A s t h e s l i p l i n e s w i l l n o t m e e t t h e i n t e r f a c e a t 45' a n e x t r a f a n must b e drawn i n ( r e g i o n BCF). I n t h e r e g i o n DCFE t h e l i n e s w e r e c a l c u l a t e d n u m e r i c a l l y by a f i n i t e d i f f e r e n c e t e c h n i q u e p r o p o s e d by H i l l ( 9 ) a n d t h e e l a s t i c boundary (BE) was d e r i v e d a n a l y t i c a l l y b y Johnson ( 8 ) . I f t h e t r a c t i o n f o r c e i s made e q u a l t o z e r o t h e s l i p l i n e s m e e t t h e s u r f a c e a t 45O a n d t h e f i e l d r e d u c e s t o t h a t p r o p o s e d f o r a p u r e l y normal i n d e n t a t i o n .

XE

H,

+ --

-

'I

t h i s equation

P(X') K(X , X') dX' = 0

X2L I t n

where K ( X , X '

XE a

(2)

)=In 1 X-X' I

U n f o r t u n a t e l y t h e domain on which e q u a t i o n (1) h o l d s i s g e n e r a l l y n o t known i n a d v a n c e . T h e r e f o r e (1) i s e x t e n d e d t o ( 3 ) s u c h t h a t (1) h o l d s i n t h e o r i g i n a l domain a n d P ( X ) = O X E ~ '

a

P(X) > 0

H(X) = 0

XE

P(X) = 0

H(X) > 0

XER'

(3)

191

A second condi t i o n t h a t has t o be s a t i s f i e d i s t h e force balance equation :

c a l c u l a t e d d u r i n g t h e o v e r r o l l i n g of t h e d e n t . I n common w i t h s t r u c t u r a l f a t i g u e , t h e f a t i g u e s t r e s s t h r e s h o l d z, i s m o d i f i e d a c c o r d i n g t o t h e a b s o l u t e v a l u e o f t h e s h e a r stress. z,

b(X) dx =f

n

is

assumed t o r e m a i n unchanged i f ,,,T does not exceed t h e y i e l d stress and t o diminish l i n e a r l y t o z e r o f o r Tmax v a r y i n g between r e a n d

(4)

The i n t e r a c t i o n o f these equations is i d e n t i c a l t o t h e l u b r i c a t e d c o n t a c t c a s e , see f o r i n s t a n c e (11). In t h i s dry contact analysis t h e f i l m t h i c k n e s s i s set t o z e r o o v e r t h e domain ( a ) and t h e n o n l y t h e p r e s s u r e d i s t r i b u t i o n h a s t o b e c a l c u l a t e d . The problem h a s t r a d i t i o n a l l y been s o l v e d b y direct methods (Newton R a p h s o n ) , r e s u l t i n g i n l o n g computing t i m e s f o r l a r g e p r o b l e m s . AS a l a r g e number o f solutions is required i n applying the l i f e model the computing time can become e x c e s s i v e l y l o n g . To a l l e v i a t e t h i s problem a n a l t e r n a t i v e i t e r a t i v e t y p e s o l u t i o n was u s e d which h a s been d e s c r i b e d i n (12). Convergence w a s f u r t h e r a c c e l e r a t e d by t h e a p p l i c a t i o n o f n o v e l m u l t i - l e v e l t e c h n i q u e s which h a v e b e e n a p p l i e d previously t o t h e s o l u t i o n of d i f f e r e n t i a l equations. The computing t i m e f o r t h e u s u a l i t e r a t i v e s o l u t i o n t e n d s t o b e dominated by t h e i n t e g r a l computation, so t h e s o l u t i o n t i m e i s p r o p o r t i o n a l t o o r d e r n2 where n i s t h e number of p o i n t s , a s c a n b e s e e n i n T a b l e 1. However it i s p o s s i b l e t o r e d u c e t h e c o m p u t i n g , t i m e t o o r d e r n l o g n by t h e a p p l i c a t i o n o f m u l t i l e v e l techniques, s p e c i f i c a l l y Multilevel MultiI n t e g r a t i o n ( M L M I ) . The b a s i c i d e a was g i v e n i n ( 1 3 ) and worked o u t i n d e t a i l i n ( 1 2 ) . A s c a n b e s e e n from T a b l e 1, column 3 s i g n i f i c a n t t i m e s a v i n g s can be o b t a i n e d from l e v e l 6 onwards, s o t h e a p p r o a c h i s most u s e f u l f o r problems with many grid points. The c a l c u l a t i o n o f t h e s u b s u r f a c e stresses i s a task similar t o t h e film thickness solution, when one c o n s i d e r s o n l y one p a r t i c u l a r v a l u e o f t h e d e p t h z, a t a t i m e . P l o t s o f t h e d r y contact s u r f a c e pressure and a s s o c i a t e d subsurface orthogonal shear stress d i s t r i b u t i o n are shown i n f i g u r e 5 .

t h e f r a c t u r e s t r e n g t h zf. A s t h e c r a c k might b e e x p e c t e d t o b e c r e a t e d more e a s i l y i n t h e p r e s e n c e of a t e n s i l e r a t h e r t h a n compressive stress f i e l d , an a d d i t i o n a l h y d r o s t a t i c w e i g h t i n g was i n c l u d e d i n t h e model. I n t h i s t h e c r i t i c a l stress Ta was m o d i f i e d t o fa+ a.Hp, where Hp i s e q u a l t o t h e h y d r o s t a t i c p r e s s u r e and a i s t a k e n a s a = 0 . 3 . U s i n g t h e s e v a l u e s , t h e p r o b a b i l i t y of s u r v i v a l of t h e i n n e r r i n g can be expressed a s :

The e f f e c t i v e p e r t u r b a t i o n on t h e g l o b a l p r e s s u r e d i s t r i b u t i o n b y t h e d e n t w i l l depend v e r y much o n t h e r a t i o of t h e d e n t w i d t h t o t h e H e r t z c o n t a c t s i z e . To a s s e s s t h i s e f f e c t f o u r d e n t / r o l l e r c o m b i n a t i o n s w e r e c h o s e n . An a r t i f i c i a l c i r c u l a r d e n t o f 2 0 0 micron w i d t h and 3 m i c r o n d e p t h was o v e r r o l l e d by r o l l e r s of 2 , 4 , 8 and 16mm r a d i u s . The o v e r r o l l i n g o f t h e d e n t is s i m u l a t e d u s i n g 9 d i f f e r e n t p o s i t i o n s o f t h e r o l l i n g element with r e s p e c t t o t h e d e f e c t , i n o r d e r t o p i c k up t h e maximum stresses. The p o s i t i o n o f t h e c e n t r e x c o f t h e r o l l i n g e l e m e n t i s g i v e n by: xc

=

b (n-5)/2

for

n=1,2

,..., 9 .

The stress h i s t o r y i n e a c h p o i n t i s a n a l y s e d with r e s p e c t t o t h e s e n i n e p o s i t i o n s and t h e n t h e l i f e i n t e g r a l i s c a l c u l a t e d . A s t h e number of p o s i t i o n s i n t i m e and space a r e r e l a t i v e l y s m a l l , 9 a n d 49x17 r e s p e c t i v e l y , t h e v a l u e s o f t h e l i f e i n t e g r a l s a r e r a t h e r jumpy a n d consequently t h e numerical r e s u l t s should be interpreted with care.

4 L I F E PREDICTIONS

5 RESULTS I n t h e t r a d i t i o n a l Lundberg a n d Palmgren b e a r i n g f a t i g u e l i f e model, t h e p r o b a b i l i t y o f f a i l u r e can be expressed i n t e r m s of t h e stressed volume a n d t h e m a g n i t u d e a n d d e p t h below t h e s u r f a c e o f t h e maximum o r t h o g o n a l s h e a r stress. I n ( 2 ) I o a n n i d e s and H a r r i s p r o p o s e d a g e n e r a l i s e d model i n which t h e s t r e s s e d volume i s d i v i d e d i n t o d i s c r e t e volume e l e m e n t s i n which t h e maximum stress i s c a l c u l a t e d a c c o r d i n g t o some stress r e l a t e d f a t i g u e c r i t e r i o n . I n common w i t h s t r u c t u r a l f a t i g u e l i f e p r e d i c t i o n s f o r steels i n r e v e r s e d b e n d i n g or t o r s i o n , a t h r e s h o l d stress v a l u e i s d e f i n e d below which f a i l u r e w i l l n o t o c c u r . Each e l e m e n t i s w e i g h t e d a c c o r d i n g t o i t s d e p t h below t h e s u r f a c e a n d t h e p r o b a b i l i t y of f a i l u r e i s expressed i n terms o f t h e i n t e g r a l o f t h e e l e m e n t a l stresses o v e r t h e e n t i r e volume. A m o d i f i e d l i f e c r i t e r i o n h a s been u s e d t o compute t h e Ll0 b e a r i n g l i v e s i n t h e p r e s e n t c a s e . The maximum s h e a r stress a m p l i t u d e z,

is

The l i f e i n t e g r a l s were c a l c u l a t e d f o r f o u r d i f f e r e n t values of t h e reduced r a d i u s of curvature and f o r s i x d i f f e r e n t loads (corresponding t o Hertzian pressures ranging f r o m 2 . 0 t o 3 . 3 GPa) T h r e e cases were examined, a smooth raceway, a raceway w i t h one d e n t and a raceway w i t h one d e n t and a s s o c i a t e d r e s i d u a l stress f i e l d . The e f f e c t of t h e s e stress f i e l d s on p r e d i c t e d l i v e s c a n b e g r a p h i c a l l y e x p r e s s e d i n t e r m s of r i s k maps. I n t h e s e a s e c t i o n o f t h e x, z p l a n e i s drawn on a g r i d w i t h t h e ' f a t i g u e c r i t e r i o n ' stress e x p r e s s e d a s t h e y c o - o r d i n a t e . Each map i s n o r m a l i s e d t o t h e smooth c a s e b y a s c a l i n g f a c t o r . The smooth c a s e r i s k map i s shown i n f i g u r e 6 ( a ) where a s e x p e c t e d t h e h i g h e s t r i s k o c c u r s a t t h e p o s i t i o n of t h e maximum o r t h o g o n a l s h e a r stress, 0 . 8 b below t h e b e a r i n g s u r f a c e . AS t h e d e n t ( f i g u r e 6 ( b ) ) a n d t h e d e n t p l u s r e s i d u a l stresses ( f i g u r e 6 ( c ) ) a r e i n c l u d e d t h e map i s m o d i f i e d ,

.

192 p a r t i c u l a r l y around t h e dent shoulders. A s a r e s u l t t h e s c a l e f a c t o r , e f f e c t i v e l y a measure of t h e i n c r e a s e d r i s k , i n c r e a s e s d r a m a t i c a l l y , by a f a c t o r o f a l m o s t 50 on t h e i n c l u s i o n o f t h e r e s i d u a l stresses. The p r e d i c t e d l i v e s f o r e a c h d e n t / r o l l e r combination a r e p l o t t e d i n f i g u r e 7 . From t h i s d a t a a n a p p r o x i m a t e map of r e l a t i v e l i v e s c a n b e c o n s t r u c t e d i n t e r m s of t h e d e n t s i z e , c o n t a c t s i z e and r o l l e r r a d i u s of c u r v a t u r e ( f i g u r e 8). A s c a n b e s e e n t h e l i f e o f t h e smooth raceway increases rapidly with d e c r e a s i n g l o a d and t h e l i f e g e n e r a l l y increases with increasing radius. The i n f l u e n c e of t h e d e n t w i t h o u t t h e a s s o c i a t e d r e s i d u a l stresses on l i f e i s minimal. A s i g n i f i c a n t l i f e reduction only occurs f o r t h e s m a l l e s t r a d i u s under t h e t h r e e l i g h t e s t loads. T h i s c h a n g e s d r a m a t i c a l l y when t h e ( t e n s i l e ) r e s i d u a l stress f i e l d below t h e d e n t i s t a k e n i n t o a c c o u n t . The r e s i d u a l stresses were o b t a i n e d a s s u m i n g n o r a d i a l t r a c t i o n force a t t h e interface, ie a f l a t pressure d i s t r i b u t i o n . Under h i g h l o a d s t h e i n f l u e n c e o f t h e r e s i d u a l stress f i e l d s a r e r e l a t i v e l y s m a l l , b u t a s t h e load i s reduced t h e l i v e s d e c r e a s e m a r k e d l y r e l a t i v e t o t h e smooth c a s e s . A s t h e r a d i u s of t h e c o n t a c t i s i n c r e a s e d t h e i n f l u e n c e of t h e r e s i d u a l stresses and of t h e d e n t geometry i s diminished. I n s p e c t i o n o f t h e o r t h o g o n a l s h e a r stress c o n t o u r s ( f i g u r e 9) h e l p s e x p l a i n why t h i s might b e so. A t h i g h e r l o a d s a l t h o u g h t h e o r t h o g o n a l s h e a r stresses o f t h e m o d i f i e d H e r t z i a n f i e l d a r e of a h i g h e r magnitude, t h e maxima a r e s i t u a t e d w e l l below t h e s u r f a c e . The stress c o n c e n t r a t i o n s from t h e s h o u l d e r of t h e d e n t and p a r t i c u l a r l y t h e t e n s i l e stresses o f t h e r e s i d u a l s t r e s s f i e l d l i e much more c l o s e l y t o t h e s u r f a c e and cannot t h e r e f o r e combine w i t h them t o g e n e r a t e h i g h v a l u e s o f t h e f a t i g u e c r i t e r i o n . A s t h e l o a d i s reduced t h e s t r e s s c o n t o u r s l i e more c l o s e l y t o t h e s u r f a c e a n d c a n combine w i t h t h e t e n s i l e r e s i d u a l stresses t o c a u s e more damage. The r e s u l t s s h o u l d b e i n t e r p r e t e d w i t h some c a u t i o n b e c a u s e o f t h e s i m p l i f i c a t i o n s made a n d t h e c o a r s e g r i d n u m e r i c s and s t r i c t q u a n t i t a t i v e c o n c l u s i o n s s h o u l d n o t b e made. However, the qualitative results are i n t e r e s t i n g enough t o c o n t i n u e t h e r e s e a r c h i n t h i s d i r e c t i o n , i n c o r p o r a t i n g more r e a l i s t i c d e n t s h a p e s , r e s i d u a l s t r e s s f i e l d s a n d more a c c u r a t e c a l c u l a t i o n s on f i n e r g r i d s . 6 CONCLUSIONS

The e f f e c t o f b o t h d e n t s i z e and s u b s u r f a c e r e s i d u a l stresses have been added t o t h e o r i g i n a l l i f e r e d u c t i o n work. The s l i p l i n e f i e l d a n a l y s i s can o n l y b e r e a l i s t i c a l l y a p p l i e d t o d e e p t r a n s v e r s e i n d e n t a t i o n s where t h e a s s u m p t i o n s of p l a n e p l a s t i c s t r a i n c a n b e j u s t i f i e d and t h e d r y c o n t a c t a n a l y s i s i s probably only reasonable f o r r e l a t i v e l y t h i n f i l m c o n d i t i o n s . However t h e t r e n d s i n t h e l i f e r e d u c t i o n f a c t o r s a r e d i s t i n c t i v e and t h e e x p l a n a t i o n f o r them would s e e m r e a s o n a b l e and applicable to any d e n t profile/roller c o m b i n a t i o n . The most s t r i k i n g outcome i s t h a t where f a i l u r e i s i n i t i a t e d t h r o u g h s u r f a c e i n d e n t a t i o n a n d a s s o c i a t e d r e s i d u a l stresses (and c o n s i d e r a b l e ev i d en ce e x i s t s t o s u g g e s t

t h i s i s s o ) t h e e x p e c t e d l i v e s may n o t increase with decreasing load a s rapidly a s would b e p r e d i c t e d by c o n v e n t i o n a l models. The reduction i n expected l i v e s i s very s e n s i t i v e t o t h e s i z e of d e n t i n r e l a t i o n t o t h e r o l l e r r a d i u s a n d t h i s may w e l l h a v e i m p o r t a n t consequences i n t e r m s of c r i t i c a l p a r t i c l e s i z e and s a f e and u n s a f e l e v e l s o f f i l t r a t i o n . To be able to draw quantitative c o n c l u s i o n s f u r t h e r r e s e a r c h i s needed t h a t uses more r e a l i s t i c r e s i d u a l stress f i e l d s and f i n e r grids i n t h e l i f e c a l c u l a t i o n s . 7 ACKNOWLEDGEMENTS W e would l i k e t o t h a n k D r Andrew O l v e r f o r h i s

h e l p f u l a d v i c e i n t h i s work a n d t o r e g i s t e r o u r g r a t i t u d e t o SKF-ERC, The N e t h e r l a n d s , who h a v e s p o n s o r e d t h i s work, a n d t o D r I a n Leadbetter, Managing D i r e c t o r o f SKF-ERC f o r permission t o publish. APPENDIX

References Webster, M . N . , I o a n n i d e s , E . and S a y l e s , R. S., (19851, "The Effect of T o p o g r a p h i c a l D e f e c t s on t h e C o n t a c t S t r e s s and F a t i g u e L i f e i n R o l l i n g Element B e a r i n g s " , P r o c e e d i n g s o f t h e 1 2 t h LeedsLyon Symposium o n T r i b o l o g y , Lyon, B u t t e r w o r t h s , Vo1. 12, p p . 121-131. Lundberg, G . a n d P a l m g r e n , A . , (1947), "Dynamic C a p a c i t y o f R o l l i n g B e a r i n g s ", A c t a P o l y t e c h n i c a , Mechanical E n g i n e e r i n g s e r i e s , R o y a l Academy o f E n g i n e e r i n g S c i e n c e s , Vol. 1, No 3, 7 . (1985), 31 I o a n n i d e s , E . a n d H a r r i s , T . A . , "A N e w F a t i g u e L i f e Model f o r R o l l i n g B e a r i n g s ", ASME J o u r n a l o f L u b r i c a t i o n , Vol. 107, pp. 367-378. Technology, 4 1 Hamer, J . C . , S a y l e s , R . S . and I o a n n i d e s , E., ( 1 9 8 5 ) , " D e f o r m a t i o n Mechanisms a n d S t r e s s e s C r e a t e d b y 3 r d Body D e b r i s C o n t a c t s and T h e i r E f f e c t s on R o l l i n g B e a r i n g F a t i g u e ", P r o c e e d i n g s of t h e 1 4 t h Leeds-Lyon Symposium on T r i b o l o g y , Lyon, B u t t e r w o r t h s , Vol. 1 4 . Hamer, J . C . , S a y l e s , R. S . and I o a n n i d e s , E., " P a r t i c l e Deformation and C o u n t e r f a c e Damage When R e l a t i v e l y S o f t P a r t i c l e s a r e S q u a s h e d Between H a r d A n v i l s " , Trans ASME/STLE t o b e p u b l i s h e d Dumas, G . a n d B a r o n e t , C . N . , (1971), " E l a s t o - p l a s t i c i n d e n t a t i o n of a h a l f rigid cylinder", space by a long International J o u r n a l of Mechanical S c i e n c e s , Vol. 13, 519. O l v e r , A . V . , (19861, "Wear o f Hard S t e e l i n Lubricated, Rolling Contact", Phd Thesis, Imperial College. O l v e r , A . V . , S p i k e s , H . A . , Bower, A . and Johnson, K . L., ( 1 9 8 6 ) , "The R e s i d u a l Stress Distribution i n a Plastically Deformed Model A s p e r i t y " , Wear, Vo1. 107, pp. 151-174. 91 H i l l , R . , ( 1 9 5 0 ) , "The Mathematical Theory o f P l a s t i c i t y ", Oxford U n i v e r s i t y Press. 101 Ford, H., ( 1 9 6 3 ) , "Advance Mechanics o f M a t e r i a l s " , Longmans 113 L u b r e c h t , A . A . , "The Numerical S o l u t i o n of t h e Elastohydrodynamically L u b r i c a t e d L i n e a n d P o i n t C o n t a c t Problem, U s i n g M u l t i g r i d Techniques", Phd T h e s i s , Twente U n i v e r s i t y , l 9 8 7 , The N e t h e r l a n d s .

.

.

193 [121 Brandt, A. and Lubrecht, A. A., 'Multilevel Multi-Integration and Fast Solution of Integral Equations", to be published in the Journal of Computational Physics. [131 Brandt, A. , "Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics", monograph available as GMD studien 85 from GMD postfach 1240 , Schloss Birlinghofen D5205 St. Augustin 1 BRD.

Half-width of dent

(a)

-- x

+c--.(L

IN %\-*

++-IHalf-width

Figure 1

Olver slipline field for sliding asperity.

Figure 3 Dent Width A

i y

i

I z

%/A

-I

D

Residual stress distribution for radial traction coefficient (p) of: (a) p = 0 and (b) p = 0.2.

1

000

?

Figure 4 Figure 2

Slipline field for normal indenter plus radial traction force.

Residual orthogonal shear stress (Q contour map.

194

0

c ?o w a

A presswe

h f LCm-Ch.

0

-,

a3 .O

-1.5

0.0

4.5

3 .O

r-

Figure 5

Plots of the dry contact surface pressure and associated subsurface orthogonal shear stress (2,) distribution during the overrolling of the dent.

195

Figure 6(b) Risk map of indented surface. Scale facto-5.7

Figure 6(c) Risk map of indented surface plus residual stresses. Scale factor49.7

196

Figure 7

Nonnalised lives &)versus load at differing radii of curvature (R) for; a smooth surface,*indented surface,^ indented surface plus residual stresses.

0.06

0.05

s 0.04

0.03 .1

.3

1

3

d/b

Figure 8

Map of relative lives (4) of indented surfaces to smooth surfaces as a function of b (Hertz contact), R (reduced radius) and d (dent size).

197

No residual stresses

Figure 9

Table 1:

Plus residual stresses

Plots of maximum orthogonal shear stress (T,).

n

time

time *

9 17 33 65 129 257 513 1025

0.8 1.5 2.4 3.9 8.4 23.0 79.0 306.0

6.2 12.3 24.3 48.4

Computing time as a function of the level (L), the number of points n, in seconds on a VAX 785, for the smooth dry line contact problem, with (*) and without MLMI.


199

PaperVI I(iv)

Debris denting -The associated residual stresses and their effect on the fatigue life of rolling bearing: An FEM analysis C. N. KOand E. loannides

The squashing of contaminant ductile particles in rolling bearings was simulated using FEM (Finite Element Methods). Calculated dent shapes from this elastic-plastic analysis are in good agreement with experimentally measured dent shapes. The calculated residual stress fields associated with the dents are discussed and used to estimate rolling bearing life reduction. 1

INTRODUCTION

Evaluation of rolling contact fatigue life has historically been based on elastic stress analysis. The elastic assumption is no longer valid when the stress level exceeds the yield limit. High stresses can be caused by high contact loads or by contacting local geometrical features such as dents, scratches or other defects which may be present in the rolling contacts. When the stresses become high enough, plastic flow will occur and cause subsequent permanent deformations. This in turn will change the contact conformity, produce residual stress fields, alter the material properties by strain hardening. All these effects will naturally contribute to the endurance ability of the machine element and should be considered in the rolling contact fatigue analysis. The present investigation is focused on denting caused by debris and thus associated with contamination in rolling bearings. Contamination is highly detrimental to bearing operations and i t is strongly connected to local plastic deformation. Overrolled contaminant particles form dents on the raceways which cause surface-initiated spalling and thus shorten bearing lives. It has been demonstrated by Hamer et a1 111 that even soft particles can cause dents if they are large enough. A zone of plastically deformed material is generated under the dent and the localized plastic strains in the raceway will subsequently produce residual stresses. Two major effects on fatigue initiation caused by the denting process can be identified: (i) the dents generated will become local stress raisers during overrolling, and (ii) local selfequilibrating residual stress fields will develop in the material. There has been a suggestion that the existence of tensile residual stresses thus generated will have a significant influence on crack initiation [Z], and ultimately on fatigue life. The primary objective of this investigation is to model with the use of FEM the deformation process leading to the formation o f a dent.

This allows the calculation of residual stresses which can be subsequently used in the estimates of the fatigue lives of raceways with dents. I n previous work, researchers have also calculated the distribution of residual stress fields resulting from rigid indentors pressed onto a finite or infinite half space. However, the indentor solution due to Hill [3] and also Johnson's cavity solution [4] are quite limited as they only apply to 2 dimensional problems. Moreover, such solutions depend crucially on the positioning of the elastic/plastic boundary. Such limitations are not necessary in FEM analyses. The present analysis was carried out using the multi-purpose computer program ABAQUS [5-71. In this respect the present work resembles other FEM analyses of contact problems [8,9], but i t differs from them in that the contact pressure profiles used in the generation of the dents have been extracted from the work of Hamer et a1 [ l ] and are applicable to particles undergoing heavy plastic deformation. 1.1 Notation

a

Contact width of the axisymmetric soft indentor [mm]

a'

Contact width of the axisymmetric rigid indentor [mm]

b

Contact width for ideal line contact [mm]

E

Young's Modulus [N/mm2 ]

P"

Maximum Hertzian pressure [N/mm2]

pY

Load to initiate yield [N]

r,z,6 Cylindrical coordinate system for the axisymmetric models R

Rig d indentor radius [mm]

x,y,z

Rec angular coordinate system for the plane strain model

Y

Yield stress (Plastic limit) [ N/mmz J

urr

Radial stress [ N / m m 2 ]

uzz

Axial stress [N/mm*]

'e e

Circumferential stress [N/mm2J

=r

Shear stress in the rz plane [ N/mm2 ]

2

V

Poisson's Ratio

2

METHOD OF ANALYSIS

Most of the debris deformation takes place in the inlet of an EHD contact where both the convergence angle and the surface separation between the rolling element and the raceway of a bearing are very small. The simplification of treating the two surfaces as parallel can therefore be made. Under these conditions a simple extrusion solution to the problem of a small sphere denting two flat platens has been obtained in Dent shapes calculated the past [l]. from this extrusion method agree favourably with dent shapes observed in experiments conducted by the same authors [lo]. Similar simplifications were exploited in the present work where FEM were used in axisymmetric and plane strain cases, as shown schematically in Figures 1 and 2 respectively.

Figure 2

bodies with E = 207000 MPa, Y = 1000 MPa, and v = 0.3, whilst the material of the particle is assumed to be perfectly plastic. As indicated earlier o n , only the interfacial pressure between the particle and the platen was used to simulate the denting, which was obtained from the work of Hamer et a1 [lo]. An incremental loading procedure was followed during which this pressure was increased in steps until its full magnitude was reached. No attempt was made to follow the real loading history experienced in the actual squashing process, and the frictional stresses were ignored. Finally, in the fatigue life calculation the combined stress fields of the roller-induced stresses and the residual stresses were used. It should be noted that in this work no secondary yielding is allowed for as this will involve additional time-consuming elasticplastic calculations. Therefore, when the combined stresses exceed the plastic limit the life estimates should be interpreted with caution and used only as guidelines. 3

Figure 1 Axisymmetric model. In the present work, however, instead of solving the complete extrusion problem of three bodies, the contact pressure as derived in [l] was applied directly to one of the platens (both in the plane strain and the axisymmetric cases). Furthermore, symmetries were exploited as indicated in Figures 1 and 2 s o that the computational effort was kept to a minimum The low carbon steel platens of hardness 3 4 0 Vickers are modelled as isotropic, elastic-perfectly plastic

Plane strain model.

FINITE ELEMENT ANALYSIS

As indiciated previously the computational effort can be substantially reduced by appropriate use of symmetry. In the case of spherical particles, axisymmetric models are used, Figure l , whilst in the case of cylindrical particles plane strain models are used instead, involving only half o f one of the platens, Figure 2 . Three different FEM models were used in the present analysis. Two of them are axisymmetric with different mesh densities, AXFINE (fine) and AXCOARSE (coarse), and a plane strain model DENT for life calculations. The axisymmetric models were intended for comparison with the measurements obtained in [lo], while the plane strain models were used in fatigue life predictions. The details of these models are given in Table 1.

20 1

MODEL

DIMENSIONS ELEMENT T Y P E (vidthxheight)

ELEMENTS

N O , OF NODES

NO.

OF

DOF*

AXFINE Fig. ( 3 . )

1 0 m m x 10m

8 noded parabolic axirvmmetric vith-reduced integration

2240

7021

14042

AXCOARSE

loam x l O m m

4 noded billnear axisymmetric vith f u l l integration

1521

1600

3200

100ma x 230mn

4 noded billnear plane strain vith f u l l intrgration

1645

1728

3456

Fig.(3b)

L Fig.(Jc)

DOF

-

T o t a l n u m b e r o f d e a r e e a o f freedom

For the elastic-plastic calculations the von Mises yield criterion was used, together with the Prandtl-Reuss flow rule [5]. The boundaries of the platens were set sufficiently far away to prevent spurious stresses from developing at the boundaries which will influence the distribution of the residual stress fields. The dimensions of the models have therefore been carefully chosen, as shown in Table 1 above. Axis or planes o f symmetry, as well as supporting boundaries, were restricted only in the perpendicular directions, Figure 3 .

RADIUS ( m m l CONTACT PRESSURE LOADING

nN

THE C Y L I N O R I C A L

i*gencl :

A

DENTI

DENT2

..........................

V

4a

PLATEN

--.GENT3

V

Figure 3

D , DENT?

PEII mesh f o r t h e three models:

(a) A X F I N E ,

F

(b) AXCOARSE, DENT.

(c) a

4

110

Y

x 10

U)

WIDTH l m r n l

4b

Figure 4 Contact pressure distribution for the: (a) Axisymmetric models; (b) Plane strain dent life models.

4

(10

" x 10

UJ

3b

X 2 -

I

3c

RESULTS AND COMPARISONS

Prior to the elastic-perfectly plastic calculations, the suitability of the FEM mesh was checked by reproducing the Hertzian solutions for both the axisymmetric and plane strain models. I n both cases a particle of 2 m m in diameter was used to simulate the contact. The maximum contact pressure difference between the FEM and the Hertzian solutions was 7% After these preliminary numerical tests the axisymmetric models were used to simulate the experiments of Hamer et a 1 [ l o ] where actual dents were produced and measured by squashing particles. Before comparing with the experimental results, the two axisymmetric models (AXFINE and AXCOARSE) were first compared and checked against each other. The stresses and the deformations predicted by AXFINE and AXCOARSE are almost identical, except from differences I

The platen was first loaded by progressive increase of pressure until its full value and then unloaded by complete removal of the pressure. The pressure loading for the axisymmetric models has a peak pressure of 2790 MPa and its distribution is shown in Figure 4a. For the plane strain model, where life evaluations were to be carried out, there are 4 different pressure loadings (see Figure 4b) t o simulate 4 different denting processes.

202 (approximately 13%) in high stress gradient regions where AXFINE seems to be more capable of picking up the peak stresses. This is expected because AXFINE has a finer mesh as well as higher order elements. In addition, the elastic deformations obtained by AXFINE and AXCOARSE are practically the same, being 47.2 pm and 47.1 pm respectively. The dent depth predicted by AXFINE is slightly higher than that of AXCOARSE; the difference is about 3.4%. This is because AXFINE repesents a more flexible structure than AXCOARSE as i t has more degrees of freedom. On the whole, i t can be concluded that these 2 axisymmetric models are converging towards the same results and are thus reliable. L”

solutions [ 4 , 8 , 9 ] , the indentor radius must be known. The shape of the dent obtained by FEM analysis appears substantially spherical, and consequently the dent can be compared to one caused by a rigid sphere with a certain radius. From the deformed shape of the platen under full load, Figure 6 , the radius of

Legend:

AH e

8

W EXPT (la1

. *... AXCOARSE

t‘ RADIAL DISTANCE I m m I

Figure 6

DENT SHAPE IVERTICAL Y A L E 35 X HORIZONTAL SCALE1

Figure 5

Comparisons of dent depths: experimental [lo], AXFINE, AXCOARSE.

From Figure 5 it can be seen that the calculated dent depths are very close to the value measured experimentally. The depths calculated using AXFINE and AXCOARSE were 63.5 pm and 61.4 pm respectively. The measured value was estimated from Figure 8(c) in [ l o ] to be 50 pm. Moreover, from the same figure i t can be seen that the measured diameter of the dent is approximately 2.3 mm, which agrees well with the calculated values of 2.49 mm. The difference of 20% in dent depth between the calculation and the measurements can be attributed mainly to the lack of strain hardening in the model (elastic-perfectly plastic). In reality, strain hardening will take place, inhibiting the plastic flow and thus reducing the dent depth. Next, the predictions from the FEM models were compared with the analytical indentor solution [ 3 ] , cavity solutions [ 4 ] and other FEM indentor solutions [ 8 , 9 ] . The main difference between the present work and the indentor solutions is that the shape of the pressure distribution caused by the plastically deforming particle, Figure 4 , is different from the one caused by the rigid indentor. I n order to compare the subsurface stress and strain fields with other

Deformed and undeformed shapes of AXFINE under full load (magnification factor = 20).

a rigid indentor can be estimated by curve fitting of the dent shape with a sphere. The radius of this sphere was approximately 3 3 mm (with a correlation coefficient of 0.98). For axisymmetric contact of solids of revolution, the load to initiate yield (P,) according to the von Mises criterion is: K3 R 2 (1.6Y)3

Py

=

6 E*’

where R

=

Y

=

E*

=

indentor radius yield limit of the contacting bodies E/(Z(l-v2)) where E = Young‘s Modulus of the contacting bodies; v = Poissonfs ratio of the contacting bodies

I n our axisymmetric analyses, P is 1782 N. The applied load is 44000 Nr which corresponds to a modest 24.7 P y . According to Figure 6.17 in [ 1 6 ] , we fall well within the early part of the elastic-plastic regime, which implies that the effects of elastic strain-s cannot be ignored. This is because the elastic strains are felt over a much bigger domain than the plastic ones. Moreover, the ratio between the elastic and the plastic strains is between 10 to 30%, suggesting that the rigid1 perfectly plastic material moder-may not

203 be appropriate for the current load level. This further confirms the limitations of the rigid-plastic assumption of the indentor solution of Hill [3] and the cavity solution of Johnson [4].

indentor is much more uniform and looks rather like a rectangular distribution. Thus, in order to keep the same contact load o f 44000 N , the contact width (ar)

Figure 7 Total displacement (mm) distribution of AXFINE under full load (magnification factor = 1).

Figure 8 Plastic octahedral shear strain of AXFINE under full load (magnification factor = 20).

From Figure 7 i t can be seen that the displacements produced under load are approximately radial from the bottom of the dent, with roughly hemi-spherical contours of equal strain. The results match the observations of Samuels and Mulhearn [ll]. These observations were the basis of the cavity solution which was later developed by Marsh [12] and Johnson [4]. One of the major difficulties in the cavity problem, as mentioned before, is to find the elastic-plastic boundary in the body. In contrast, this boundary is obtained as part of the FEM solution, as can be seen in Figure 8. Also, from Figure 9 it can be seen that there is a spherical layer of elastic material with rather high elastic hoop strains surrounding the plastic core (region A in Figure 9). The magnitude of such circumferential elastic strain is found to be between 0.00156 and 0.00257 and the corresponding stress is between 122 and 303 MPa. The elastic deformation obtained by the current FEM models is 47 pm. The total deformation due to a rigid indentor with a radius of 33 mm on an elastic half space under the same load (44000 N) is found to be 86 pm, and the corresponding maximum contact pressure 4600 MPa. I n reality, the maximum contact pressure should be less since the platen is elastic-plastic. According to Hardy et a 1 [8], the maximum pressure corresponding to a load of 24.7 Py should amount to 2310 MPa which is 20% less than our maximum contact pressure (2790 MPa). However, the contact pressure distribution of a rigid

.for the rigid indentor h a i t o be smaller and should be equivalent to 0.77a, where 'a is the contact width of our soft indentor. Again according to Hardy et a 1 [8], the depth of the plastic core is estimated to be 6a' or 4.7a, whereas the present model's prediction is 1.3a. The

t'

A

Figure 9 Elastic circumferential strain of AXFINE under full load (magnification factor = 20).

204

difference is attributed to the rectangular shape of the pressure distribution imposed by the rigid indentor. Consequently, the amount of plastic flow developed in the core under the rigid indentor will be larger and hence the plastic core itself will be larger. Additional supporting evidence has been obtained from the denting processes simulated in the fatigue life calculations, the detailed results of which will be discussed in the next section. It was there observed that the dent depth as an indicator of the size of the plastic core depends mainly on the shape of the pressure distribution and not directly on the total contact load. When the plastic limit is first exceeded, the plastic zone is small and fully contained by the elastic material surrounding i t . The elastic strains and the plastic strains are therefore expected to be of the same order of magnitude. When the load is further increased, the pressure beneath the indentor will increase to accommodate the necessary expansion. Eventually the pressure inside the plastic zone will become s o intense that plastically flowing material will break through the free surfaces near the edge of the

t'

10a

t'

R--I

1oc

Figure 10 Plastic strains of AXFINE under full load: (a) radial, (b) axial, (c) circumferential (magnification factor = 20). indentor. From Figure 10 i t can be seen dent in the unloaded state. This is that a substantial amount of plastic expected a s equilibrium has to be strain is accumulated at the edge of the maintained at the centre of the dent. contact, even for the present moderate The distributions of u r r and uz load. along the axis are shown in Figure 1 1 . Along the axis of symmetry, is Within a thin layer of 0.05a below the found to be equal to see, and ~ ~ : ~ l s surface, the radial stress is found to found to be zero. These results are not change sharply from -2500 MPa to surprising because o f symmetry. Similar -1800 MPa when the platen is under full results have been obtained by Hardy [ 8 ] load. This stress gradient is only and Sinclair 191 in their FEM analyses, slightly reduced when the platen becomes a s well as by Johnson in his cavity unloaded and the residual radial stress solutions ( 4 1 . I n addition, u z 8 is varies from - 4 4 6 MPa to 4 0 MPa. This found to be zero at the bottom of the suggests that the indentation creates

205 Legend:

A

SlGRR I L I

.-% SlGRR I U I

,*. SIGZZ I L I .p,

SlGZZ I U I

,' ,'

i/ -I

M

0 SlRESS IMPoI

Figure 11 Distribution of az and u r r against the axis of symmetry of AXFINE for both loaded (L) and unloaded (U) states. rather high compressive residual radial stresses near the dent bottom, in a layer very close to the surface. Moreover, in the residual state, small but tensile radial residual stresses are found at two locations along the axis of symmetry. In these locations, sharp stress gradients are present which are similar to the ones obtained in Hardy [S] but not in Sinclair 1 9 1 . Such residual stress patterns closely resemble the axial stress distribution of an elastic-plastic beam after severe bending. 5

EFFECTS OF RESIDUAL STRESSES ON ROLLING CONTACT FATIGUE

RADI AL 0 ISTANCE Imm 1

DENT WAPE (VERTICAL SCALE 35 X HORIZONTAL SCALE1

Figure 12 Dent shapes for fatigue life predictions. Only a plane strain model with 4 noded elements is used in the investigation o f the effects of residual stresses on rolling contact fatigue because of CPU

time constraints. Thus various denting pressure distributions (see Figure 4b) have been used to simulate the formation of different dents and their effects on fatigue life. The corresponding dents are shown in Figure 12. A previously published fatigue life model [ 1 3 ] which was recently extended 1141 was used to evaluate bearing lives. For this evaluation the residual stress field was added to the stress field induced by the load a s a roller passes over the dent. This is the same procedure as that used in [15] but now the residual stresses are calculated from the FEM analysis rather than from the simpler slipline method of [15]. As in [15], no secondary yielding is :allowed and therefore the life calculations are only indicative and should be treated with care when large combined stresses are encountered. For the fatigue evaluation, a roller with a reduced radius of 8.0 m m (p, = 3000 MPa, b = 0.425 mm) was selected. The results of the present fatigue life calculations are summarized in Table 2. TABLE 2: Fatigue life ratios of raceway with dents to raceway without dents.

r DENTl DENT2 DENT3 DENT4

NO RESIDUAL WITH RESIDUAL STRESS STRESS 1.0 0.0013 0.0044 0.024

1.0 0.0013 0.0052 0.12

In this table the fatigue lives of the four dents are shown under two conditions: (i) when only the geometry of the dent is taken into account (no residual stresses), and (ii) when the residual stresses are considered together with the geometry of the dent. It can be seen in this table that DENTl with its very smooth transitional curvature at the edges does not affect the life predictions as compared to the smooth case. In contrast, DENT2 with very pronounced bulging at the edges reduces life by three orders of magnitude and this reduction remains unaffected by the introduction of the residual stresses. The geometry of the dent is therefore the cause of the life reduction in this calculation. (The very high stress which develops during overrolling will produce secondary yielding and therefore the present life estimates should be treated with care.) From the same table it can also be seen that for DENT3 the residual stresses improve the life slightly whilst for DENT4 this improvement is substantial. This result contrasts with the findings of [15] where the reduction in life was attributed to the residual stresses rather than to the roller stresses. It can be generally stated that the life reduction of dented raceways can be attributed to two effects: the residual stresses generated during the denting process and the higher stresses generated when a roller passes

206 over the dent. The contribution of each of these two effects depends on the particular case and cannot be generalised. I n [15] the tensile residual stresses calculated near the surface are higher than the ones calculated here, and furthermore the shallowness of the assumed dent shape (a circular arc) makes the residual stresses the dominant feature in the life calculations. I n contrast, here we have calculated smaller tensile residual stresses and more realistic dent shapes with bulging edges, which may account for the differences in life reduction. Finally, as the roller-induced stresses (which depend on the size and the load of the bearing) are superposed on the residual stresses, i t is clear that the importance for the life predictions shifts from these individual stress fields to their combination. For example, hard particles (which may more closely resemble rigid indentors) may produce dents and residual stress distributions which are different from the ones produced by softer particles, and consequently can be more detrimental to life. The present solution methods can provide answers to these important questions relating to bearing performance in practical operating conditions. 6

REFERENCES [ l ] HAMER, J.C., SAYLES, R.S. and

IOANNIDES, E., IIDeformation mechanisms and stresses created by 3rd body debris contacts and their effects on rolling bearing fatigue", Proc. of the 14th Leeds-Lyon Symposium on Tribology, Lyon, 1987. Butterworths, Vo1.14.

[Z] OLVER, A.V., SPIKES, H.A., BOWER, A. and JOHNSON, K.L., "The residual stress distribution in a plastically deformed model asperity", Wear, Vol. 107, pp.151-174 (1986). [3]

HILL, R., "The mathematical theory of plasticityll, Oxford University Press.

[4] JOHNSON, K.L., "The correlation of indentation experiments", J. of Mechanics and Physics of Solids.

CONCLUSIONS

The current elastic-perfectly plastic FEM model has been found to agree well with experiments in terms of both dent depths and diameter. The small differences between calculations and measurements could be improved if strain hardening were introduced into the calculations. The calculated residual stresses are in broad agreement with previous solutions which indicated the presence of tensile residual stresses surrounding the plastic core, in a central region underneath the dent, as well as in small regions of high intensity under the edges of the dents. A dependence of fatigue life reduction on both the geometry of the dent and the residual stress is indicated by the fatigue life calculations of the dents studied. The relative importance of these two causes appears to vary from case to case. It is therefore of interest to establish in general terms the effect of the hardness of the debris particle, its size, and o f the applied load and the size of the rolling elements. This can point the way to the filtration requirements of particular applications and to the bearing material requirements when contamination cannot be prevented. These aspects of debris denting, the modification of dent geometry and the associated residual stresses during overrolling, as well as the extension of life calculations to 3-dimensional dents are subjects of continuing research into the effects of contamination. 7

results. The authors are also grateful to Hibbit, Karlsson & Sorensen, Inc. for making available the newest version of their multi-purpose finite element program ABAQUS. Thanks are also due to Dr. A. Lubrecht for his help in performing the life calculations.

ACKNOWLEDGEMENTS

The authors would like to thank Dr. I.K. Leadbetter, Managing Director o f the SKF Engineering and Research Centre, for permission to publish these

"51

HIBBIT, H.D., KARLSSON, B. and SORENSEN, P., tlABAQUSTheory Manual", Version 4.6, Providence, Rhode Island, USA (1987).

[6]

HIBBIT, H.D., KARLSSON, B. and SORENSEN, P., "'ABAQUS User's Manual", Version 4.6, Providence, Rhode Island, USA (1987).

[7]

HIBBIT, H.D., KARLSSON, B. and SORENSEN, P. , ' "ABAQUS Example Manual", Version 4.6, Providence, Rhode Island, U S A (1987).

[8] HARDY, C., BARONET, C.N. and TORDION, G.V., "Elastoplastic indentation of a half-space by a rigid sphere", J. of Numerical Methods in Engineering, 3,451 (1971). [9] SINCLAIR, G.B., FOLLANSBEE, P.S.

and JOHNSON, K.L., "Quasi-static normal indentation of an elastoplastic half space by a rigid sphere - 11. Resultstt,Int. J. of Solids and Structure, Vo1.21, No.8, (1985).

[lo] HAMER, J.C., SAYLES, R.SI and IOANNIDES, E., "Particle deformation and counterface damage when relatively soft particles are squashed between hard anvils", J. of Tribology, 110, 1988 (to appear). [ll] SAMUELS, L.E. and MULHEARN, T.O., "The deformed zone associated with indentation hardness impressions", J. of Mechanics and Physics o f Solids, 5,125 (1956).

207 1 2 1 M A R S H , D.M., " P l a s t i c f l o w in glass", Proc. of Royal Society, A 2 7 9 , 4 2 0 (1964). [ 1 3 ] I O A N N I D E S , E. a n d H A R R I S , T., "A new fatigue life model for rolling b e a r i n g s " , A S M E J. of L u b r i c a t i o n T e c h n o l o g y , Val. 1 0 7 , pp.367-378 (1985). ( 1 4 1 I O A N N I D E S , E., J A C O B S O N , B. and T R I P P , J.H., " P r e d i c t i o n o f r o l l i n g bearing life under practical operating conditions", Proc. 15th Leeds-Lyon Symposium o n Tribology, ( L e e d s 1 9 8 8 , this conference).

'I151 HAHER, J.C., LUBRECHT, A.A., IOANNIDES E. and SAYLES, R.S., "Surface damage on rolling elements and i t subsequent effects on performance and life", Proc. 15th Leeds-Lyon Symposium on Tribology, (Leeds 1988, this conference). [16] JOHNSON, K.L., CUP (1985).

"Contact Hechanics",


SESSION Vlll PLAIN BEARINGS (1) Chairman: Mr F A Martin PAPER Vlll(i)

Axially Profiled Circular Bearings and Their Potential Application in High Speed Lubrication

PAPER Vlll(ii)

Analysis of Partial Arc Journal Bearings

PAPER Vlll(iii)

Elapsed Time for the Decay of Thermal Transients in Fluid Film Bearing Assemblies

PAPER Vlll(iv)

Design Procedures Based on Numerical Methods for Hydrodynamic Lubrication


21 1

PaperVlll(i)

Axially profiledcircular bearingsand their potentialapplication in high speed lubrication S. Basriand D. T. Gethin

The isothermal and thermal characteristics of an axially profiled circular bore bearing are determined using the finite element technique. These are compared with the predicted performance characteristic of a cylindrical bearing operating over the same range of conditions. The results obtained lead to the conclusion that the present analysis may be used to obtain general design data for an axially profiled bore bearing operating at high sliding speed. Axial profiling reduces the bulk operating film temperature by a small amount and it decreases the load carrying ability of the film and frictional losses also.

PrinciDal Notation

Introduction

C cf

The application of numerical methods to synthesise journal bearing behaviour has been established for a number of years. The early models were usually isothermal in nature and were directed mainly towards cyllndr ical bore bearings operating at slow or moderate sliding speeds. More recently models have been developed to analyse bearing stability and thermal effects. Thermal effects become important when the shear stresses in the film are large which usually occurs w h e n the sliding speed is high, for example, in turbo alternators, gearboxes and pumps. Under this circumstance, oil film stability can be a problem, unstable behaviour resulting in the journal precessing around the clearance space in the bush causing machinery vibration which c a n lead to premature bearing failure. Prediction of this along with methods of establishing film stiffness and damping characteristics has also been described in the literature. The latter are important when the design of rotodynamic systems is addressed.

D H, fi

N p, Qs

Q

Qco :in Tco Tf U a,b 1

P c P

u 4b Y

radial clearance lubricant specif c heat capacity journal diameter Power loss, non dimensional power loss Lubricant therma conductivity bearing length Journal rotational speed Load, non-dimensional load side flow, non-dimensional side flow lubricant carried through the cavitating film lubricant inflow radius of journal oil temperature upstream of the groove Lubrlcant feed temperature, ' C Journal sliding speed m/s constant (Walther equation) cylindrical land width film pressure eccentricity ratio lubricant density lubricant dynamic viscosity attitude angle lubricant kinematic viscosity

Under conditions of high shear stress ( o r sliding speed) i t is important to be able to e s t i m a t e t h e m a x i m u m film temperature accurately since this can establish the o p e r a t i n g limit f o r t h e b e a r i n g [ l ] . Additionally, the power loss associated with s h e a r i n g of the lubricant film will be reflected in the size of the cooling system for the bearing. The parameter which may be readily controlled in the design and which can be chosen to limit temperature rise is the film clearance ratio; a large value gives a reduced temperature rise since it permits a larger o i l through flow. However, this is also reflected in a reduction of load carrying ability and, as mentioned above, the need for an oil supply of large capacity.

212 With the development of modern m a n u f a c t u r i n g t e c h n o l o g i e s , i t is n o w practical to produce circumferentially profiled bore bearings accurately [2]. The same technology m a y be used to p r o d u c e bearings which are profiled over their axial length a l s o , i n d e e d t h i s is a m u c h l e s s d e m a n d i n g m a n u f a c t u r i n g process. The advantage of these bearing types i s that they m a y be designed to have a thick film centre section to maintain c o o l o p e r a t i o n a n d a thinner film close to the edge to retain load carrying ability and t o r e d u c e l u b r i c a n t s i d e f l o w . T h e t h r u s t o f t h e present investigation is to determine theoretically t h e e f f e c t o f a x i a l p r o f i l i n g on the performance o f a c i r c u l a r b o r e b e a r i n g . B e f o r e t h i s is described, a review of numerical models for synthesising profiled bore bearing behaviour will be considered. Over the last 30 y e a r s , a s e r i e s o f investigations have been directed to predict the characteristics of profile bore bearings. In 1956 Pinkus [3] reported an analysis of elliptic bearings and later in 1959 [4] he r e p o r t e d a n investigation of a three lobe bearing. In his papers i t was demonstrated as a method of solving Reynolds' equation using a numerical technique for a fluid film of finite length. Since then, a number of investigations have used isothermal models to analyse various profile bore configuration. A f e w (for example r e f e r e n c e s [ 5 - 8 ] ) , h a v e studied selected cases of profile bores for dynamic performance and associated stability. The latter i s summarised by Garner et a1 [9] for a variety of bore profiles and loading c o n d i t i o n s . Apart from some very limited experimental studies and a f e w theoretical i n v e s t i g a t i o n s o f t h e types described in references [3-91, so f a r , l i t t l e t h e r m a l m o d e l l i n g h a s b e e n carried out for hydrodynamic journal bearings having c i r c u m f e r e n t i a l profile geometries. Even fewer have considered the effect of a x i a l profiling.

For thermal analysis, M c Callion et a1 [lo] have presented a solution method with uncoupling of the energy equations f r o m the R e y n o l d s e q u a t i o n . T h i s a p p r o a c h is applicable for bearings of modest aspect (L/R) ratios operating at moderate eccentricity. Conversely, Medwell a n d G e t h i n [ l l ] h a v e p r e s e n t e d a m o r e c o m p r e h e n s i v e thermal solution for a cylindrical bore bearing by using the finite element method featuring the rigorous solution of both the equations of fluid mechanics and heat transfer. These studies utilise the fact that in practice, the viscosity at any point depends on local film temperature w h i c h i s coupled hydrodynamically to the film pressure and in some cases shear rate [12].. The temperature in film lubricated bearings increases rapidly with s p e e d d u e t o t h e i n c r e a s e d r a t e o f frictional heat production, which on constant viscosity theory i s proportional t o s p e e d squared. At higher speeds, severe temperature gradients are set up, both across the film because of heat removal by conduction and In

the p l a n e o f r e l a t i v e m o t i o n b e c a u s e o f increased shear stress and reduced convective heat transfer.This arises from the reduced oil flow associated with the thin lubricant film. The finite element method has been used in a w i d e range of scientific and engineering problems. The technique i s suited to solve complex coupled engineering problems [13]. I t h a s s i m p l i c i t y in c o n c e p t , e l e g a n c e i n development and potency in application. A number of investigators over the years have reported the results of their studies on the application of F a in fluid film lubrication a s a p p l i e d t o N e w t o n i a n or Non-Newtonian lubricants [see references 14-17]. In this paper, the isothermal and thermal analysis of axially profiled hydrodynamic journal bearing u s i n g t h e f i n i t e element technique i s presented This h a s received little attention previously and which has motivated the present study.

.

2.

Analysis

The Navier Stokes e q u a t i o n s [ 1 8 ] a r e fundamental to the analysis of problems in fluid m e c h a n i c s . For hydrodynamic l u b r i c a t i o n , t h e s e m a y b e s i m p l i f i e d as explained in [ 1 9 ] t o g i v e t h e c l a s s i c a l Reynold equation w h i c h m a y be written with respect to a Cartesian coordinate system (see Figure 1) for laminar flow as dh

2.1

As explained in [lo], w h e n the thermal effects are included a number of models have been proposed to synthesise i t . W h e r e the film thickness i s comparatively large (C/R = 0.004) an equation w h i c h equates convective heat transfer to viscous generation is usually a d e q u a t e s i n c e h e a t removal is mainly by convection. As d e r i v e d in [ZO], t h i s is expressed by the equation

In equation 2.2, the volumetric flowrates are given by: Uh

h' ap

Q X = T - E Z E

2.3 2.4

E q u a t i o n s 2.1 a n d 2 . 2 a r e c o u p l e d h y d r o d y n a m i c a l l y b y t h e p r e s s u r e terms. Additionally, they are linked by the lubricant viscosity and its dependence on temperature can be derived from the Walther equation which relates kinematic viscosity with temperature i.e. log 1 0 [loglo(v + 0.6)] = a log 1 0 T + b

2.5

The constants a and b c a n be determined from the measured lubricant viscosity. W h e n equations 2.1 and 2.2 are s o l v e d u s i n g t h e finite element method, they are

213

usually discretised using the G a l e r k i n w e i g h t e d residual method which i s well documented in the literature [21]. For each equation this yields a set of matrix equations which may be solved to yield either pressures or temperatures appropriately. Closure of the equation set i s completed by a r e l a t i o n s h i p which expresses the variation of film thickness. At some position relative to the maximum film thickness this is given by an equation of the form h

=

C(l + c COS 0) + f(z)

2.6

The latter term (f(z)) i s included to incorporate the axial variation of film thickness due to profiling in this direction. Admissible profiles will be discussed later in section 3 .

3.

update the temperature boundary conditions (2.8b)

4.

solve the energy equation

5.

update the viscosity field and film thickness profile

T h i s p r o c e d u r e w a s repeated until solution convergence which was assumed when the changes in the pressure field between successive iterations was less than 5%.

On completion of the solution, the usual bearing design parameters of load capacity, power l o s s , and flowrate were det rmined. For the case of isothermal opera ion, these parameters were cast in dimens onless form according to 2.10a

Before the equations can be solved it is necessary to prescribe boundary conditions. For a journal running aligned with the bush, advantage can be taken of centreline symmetry and consequently the boundary prescription can be written with reference to Figure 1 as

For equation 2.1 2.7a 2.7b

= o

-

a) (x,Z)= 0 ax

-

2.7c 2.7d

Similar y for equation 2 . 2 , they may be

writ ten

= o =

Tin

2.8a 2.8b

E q u a t i o n s 2 . 7 a and 2 . 8 a r e f l e c t centreline symmetry while 2.7b expresses the ambient pressure condition. At the downstream end of the film, equation 2.7d expresses the Reynold boundary condition while at the film inlet, equation 2.712 embodies the assumption that the feed pressure i s small in comparison with expected excursions in the film under realistic loading conditions. Also at the f i l m inlet, equation 2.8b embodies the assumption that there are no signlficant axial temperature excursions. The method of calculating T i n i s based on an enthalpy balance at the feed groove which may be expressed mathematically for a constant lubricant density as [Qco Tco + Qf Tf] 2.9 Qin The solution of the equation set was encoded into a Fortran program and t h e strategic steps in the solution procedure are: Tin -

1.

assume an initial viscosity field

2.

solve Reynolds equation (2.1)

2.10b

-Q = - Q

2.10c

2CLDN

These equations require the specification o f a r a d i a l c l e a r a n c e C w h i c h is not straightforward to define for an axially profiled bore. This will be considered further in section 3 . 3.

Results and Discussion

The performance of three types of axially profiled circular bore bearings was considered and the shapes and associated nomenclature used are illustrated in Figure 1. Profile 1 incorporates axial film thickness variation over the full bearing width while profiles 2 and 3 are shaped over a central band only. The reason for this is that under stationary o r start up conditions, f o r profile 1 , the load will be supported on a very small part of the bearing edge which may result in local damage and consequently less effective bearing o p e r a t i o n . F o r p r o f i l e s 2 and 3 the cylindrical lands at either side of the bearing are intended to be used for supporting the s t a t i o n a r y s h a f t o r f o r start-up conditions. These can be of different width and in the present study two were considered l/L = 0.25 and l/L = 0 . 5 (i.e. profile 2 and 3 respectively) The axial profile was assumed to be made up of a circular arc since this i s convenient to manufacture. The radius of the arc was derived by specifying a deviation a (see Figure 1). In both cases lubricant supply was assumed to be by a twin axial groove arrangement as shown.

.

In the following sections both isothermal and thermal studies are addressed and these will be considered separately. 3.1

Isothermal Studies

A serles of calculations were carried out for the condition of an isotheral film and an a s p e c t r a t i o (L/R) of 1.0 was assumed throughout. The load-carrying part of the f i l m w a s m a p p e d b y 100 e i g h t n o d e

214 isoparametric elements ( 5 axially b y 2 0 circumferentially). Figure 2 illustrates the pressure contours for the full width bearing in the load carrying part of the film for a cylindrical bore, and the 3 axial profiles. Detailed operating conditions are tabulated on the figure where the clearance, C , is f o r convenience that at the edge of the bearing and the profiling extent is the same for each i.e. a/R = 0.002. From this it can be seen that the contours are quite different for the various film shapes. The cylindrical bore shows the most gentle fall-off at the bearing edge whereas the introduction of profiling results in a more uniform distribution over the load carrying area of the bearing but with steep gradients at t h e s i d e o f t h e film. These results are similar to those presented for a bearing having a deformable shell [ 2 2 ] w h e r e t h e p r e s s u r e field gives a film thickness profile which shows similar axial variation. Also, the axial pressure profiles under the load line are shown in Figure 3. These are presented for a nominal dimensionless load (P) of 5.07 and these s h o w clearly the axial form of the pressure profile for the different bearing geometries. Clearly to support an equivalent load, the different bearing t y p e s will o p e r a t e at d i f f e r e n t eccentricity ratios and these are listed in Figure 3 also. For the nominal load c a s e p r e s e n t e d (P = 5 . 0 7 ) the choice of axial profile 1 results in the need for the most eccentric operation and therefore the thinnest film occurs under this circumstance. However, f o r p r o f i l e 1 , t h e s m a l l i n c r e a s e in eccentricity over that for the other profiles gives a very significant reduction in peak pressure in the f i l m w h i l e the load carrying ability is not changed so dramatically. This accrues since for profile 1 , there is little a x i a l v a r i a t i o n in pressure over the film width. This has clear advantage where there is a need to minimise bearing bush deflection due to hydrodynamic action. This may occur in polymeric bearing liners, for example, or it may happen naturally during operation [22]. Additionally, the highest pressure under the load line is a s s o c i a t e d w i t h p r o f i l e 3 , however, from the form of the contours (Figure 2) this higher pressure does not extend into the region close to the minimum film thickness and t h e r e f o r e t h e c e n t r e l i n e p r e s s u r e s associated w i t h this profile are lower than those for a cylindrical bore.

section. Also, it is evident that w i t h axial profiling, hydrodynamic leakage from the film exceeds that for a cylindrical geometry. This a c c r u e s s i n c e a l a r g e r g a p s e c t i o n is presented at the upstream edge and the steeper pressure gradients at the bearing edge result in increased sideflow from the film. This can be considered to be a disadvantage for the design schemes f e a t u r i n g a x i a l p r o f i l e s , fortuitously it is not too significant.

F i g u r e 4 illustrates the variation in bearing parameters f o r the various profiles w h e n o p e r a t i n g at different eccentricity ratios. For load carrying ability, the most n o t i c e a b l e changes occur at e x t r e m e eccentricity ratios ( e > 0.85) where the effect of profiling is to reduce load carrying ability at these extreme conditions. T h e parameter which i s affected most significantly is the power loss associated with the bearing. The profiled bores give reduced power loss and this occurs since the shear stresses on the b e a r i n g c e n t r e p l a n e are reduced w i t h the thicker film. This is a significant factor since i t m a y be reflected in lower operating temperatures in t h e film. T h i s will b e considered in further detail in the following

F o r t h e c a s e s s h o w n , t h e associated performance parameters are listed b e l o w in Table 1.These show similar trends t o those predicted from isothermal analysis.

Additionally, Figure 5 illustrates the effect of using different profiling parameters ( W R ) for axial profiles 1 and 3. Clearly, its i n f l u e n c e is n o t too significant for either geometry. 3.2

Thermal Considerations

Calculation w a s carried out using t h e t h e r m a l m o d e l d e s c r i b e d in section 2. A supply temperature of 30°C was assumed for the c o m p l e t e s e t of c a l c u l a t i o n s . Also, the coefficients in the Walther E q u a t i o n w e r e assigned values of a = -3.79 and b = 9.64 which are pertinent for an oil of IS0 viscosity grade 32. In the series of calculations, speed, eccentricity ratio and aspect ratio were considered to be design variables. Figure 6 illustrates isotherm contours for t h e f o u r p r o f i l e s c o n s i d e r e d . As expected, the contours for the cylindrical bearing show no axial variation whereas those f o r all the profiles considered do. Additionally, the effect of profiling is to r e d u c e centreline temperature w i t h the greatest effect being obtained by profile 1. The reason for this has been suggested in 3.1 and accrues from the reduced shear stress on the bearing centreline. When the temperature excursions on the bearing edge are considered, examination of the contours suggests that the maximum excursion takes place o n the bearing e d g e f o r p r o f i l e s 1 t o 3 and it becomes similar to that for a cylindrical geometry. However, i t is clear f r o m this calculation that due to the axial temperature excursions the usual assumption of zero axial temperature gradient is not applicable to simplify the more rigorous analyses which will be reflected in the need to develop m o r e s o p h i s t i c a t e d thermo-hydrodynamic models when thinner film bearings are considered.

Load (kN)

Shaft Torque (N.m)

5.27 4'. 33 4.83 5.21

1.15 0.98 1.02 1.13

Table 1

Sideflow Attitude Ang 1 e (' 1 (l/min) 2.02 2.13 2.09 2.04

Comnent

40.80 Cylindrical 40.65 Profile 1 40.70 Profile 2 40.80 Profile 3

Bearing Performance Parameters

215

p

12.5 10.0

;,

75

6

.E 5.0

2.5 0.1

0.5

0.8

p= ap = ax

Unwrapped Film

T:Tin

0.7

L 0.3 b.5 0.7 0.9

0.1

0.9

Eccentricity' Ratio

(a1 Bearing Nomenclature

"lfl

Ibl

03

o

,

65

0.7

-

0.6

%

0.5

::

0.4

6

60 55

LL

i

Cylindrical

! 1"* I-

!

RP\

1 I

Profile 1 (c)

Profile 2

Profile 3

2

-

45

=

2 0.3

m

0.2

4

0.1

2

35

-Cylindrical FIGURE 1.

BEARING NOMENCLATURE AND AXIAL PROFILES CONSIDERED

Cylindrical

Profile 1

Profile 2

P=54

P = 5.25

P =524

FIGURE 2.

FILM PRESSURE CONTOURS FOR THE AXIAL PROFILES CONSIDERED ; L/R = 1.0 ; 8 = 0.7 ; C/R = 0.004 ; A/R=0.002

1000

"E

800 600

\

I

L

400 200

0.0

-

18.75

37.5

Axial Position

----_ ___ FIGURE 3.

P =52

Cylindrical Profile 1 Profile 2 Profile 3

E

= 0.647

E=

0.703

E

= 0.67

E

i

0.65

AXIAL PRESSURE PROFILES UNDER THE LOAD LINE FOR NORMALLY EQUIVALENT LOAD L / R = 1.0 ; P = 5.07., A/R = 0 002

40

I

0.1

Admissable P r o f i l e s

50

m

FIGURE 4.

03

05

07

-----Profile

09 1 ----Profile

L--+--d 03

0.1

2 ----Profile

07

0.5 3

BEARING PERFORMANCE FOR DIFFERENT PROFILE SHAPES L/R = 1.0 A /R = 0,002.

0.9

216

I

1

20.0

20 0 I

17.5 15.0 12.5 ,a100

7.5 50 2.5 0.1

9.0-0

0.3

0.5

0.7

1

t 0.1

0.3

0.5

0.7

0.9

- - - - - - 0 0 0F 1-

FIGURE Sa.

0.1

0.3

0.5

0.7

0.9

9

-

0

- - ---#=0.004

)=O.OOZ

i L

:

,

:

0.1

0.3

0.5

0.7

0.9

01

03

05

07

09

:

Eccentricity Ratio

Eccentricity Ratio

O'l

0.9

-.-a-

-0001

BEARING PERFORMANCE FOR VARIOUS PROFILE PARAMETERS L/R= 1.0 : PROFILE 1.

FIGURE 5b

------=O 004

-0 002

BEARING PERFORMANCE FOR VARIOUS PROFILE PARAMETERS L/R= 1 0 , PROFILE 3

Cylindrical

------

-----_

_--__ 30C

FIGURE 6

ISOTHERM MAP FOR THE AXIAL PROFILES CONSIDERED IL/R=1.0 , E =0.71

20.0 A

17 5

''

150

'

40

1.5 I

12.5

; 100 '.

2.0

.z

-

-1

7.5

'

5.0

.

15

I

3

a

2.5

0.7 01

0.3

0.7

05

1.0

1

,

0.1

0.9

0.3

05

0.7

0.9

;

O

0.5

rpm IL Y 1000 1 o

5

Eccentricity r a t i o

25t

I

120 T

4.5

110

10 rprn

I

Y

15 1000 1

20

I

100

I

-m 90

Y

:

80

E

E

70

E

,I60 9

50

40 O

m

----Profile

FIGURE 7

. 1

-----Profile

r 0.1

9 2

0.3

---Profile

0.5

0.7

0.9

3

BEARING PERFORMANCE AT DIFFERENT ECCENTRICITY RATIO N = lOOOOrpm , L/R:lO , C/R=O 002 , A/R=O 001

5

I 10

----Profile L/R=1.0 ,

FIGURE 8 .

is

rpm I x I000 I 1

27,

5

10

---__ Profile 2 ---profile C/R 0.002 , A/R=0.001

15

= 0.7 , i COMPARISON OF BEARING PERFORMANCE TRENDS FOR DIFFERENT ROTATIONAL SPEEDS.

20 3

21 7

Figure 7 illustrates performance trends with eccentricity ratio changes for profiles 1, 2 and 3. In comparing the load carrying ability, it can be seen clearly that profile 3 h a s the best load c a r r y i n g a b i l i t y w i t h profile 1 having the lowest. T h i s o c c u r s since profile 3 is closest to a cylindrical form. The difference in load carrying ability is most noticeable at the extreme eccentricity ratio where for an eccentricity ratio of 0 . 8 , for the case considered, the load carrying capacity for profile 1 i s about 80% that for profile 3.

Conclusions

Similar results are presented for power loss in that profile 3 has the highest loss associated w i t h i t while profile 1 has the l o w e s t . D e s p i t e t h e i n t r o d u c t i o n of cylindrical lands, the reduction in sideflow Is only marginal, however, the trends shown exclude any pressure induced components.

The main conclusions of the study are as f01 lows :

A d d i t i o n a l l y , F i g u r e 7 s h o w s the variation in maximum film temperatures on the bearing centreline for the three profiles and again t h e r e a r e o n l y s m a l l d i f f e r e n c e s . Profile 3 gives the highest temperatures while the lowest is associated with profile 1. For the axial profiling shown, the difference in thermal behaviour i s t o o s m a l l t o a f f e c t bearing performance trends significantly and therefore, the reduction in load c a p a c i t y arises mainly from the profiling effect.

Axial profiling gives lower bearing cent re 1 i ne temperatures particular 1 y where the deviation from a cylindrical geometry is significant.

Figure 8 illustrates the performance of the bearing types over a range of rotational speeds and a g a i n p e r f o r m a n c e t r e n d s a r e bounded by profiles 1 and 3. However, at the more extreme operating conditions m o r e s i g n i f i c a n t differences between models is evident particularly w i t h r e g a r d t o l o a d c a r r y i n g a b i l i t y and m a x i m u m centreline temperature. The highest f i l m temperatures and load carrying ability are associated with profile 3. The trends in Figures 7 and 8 have been comphted for a film having only a small amount o f a x i a l p r o f i l i n g (O/R = 0,001) and a comparatively thin film (C/R = 0.002) and therefore the bearing performance trends have shown little difference being close to that f o r a c y l i n d r i c a l geometry. Figure 9 Illustrates bearing performance trends for two clearance ratios (C/R = 0.002 and C/R = 0.004) and for different axial profiles (O/R = 0.001 to O/R = 0.004). Clearly the effect of using a b e a r i n g having a large clearance ratio is to reduce both the maximum centre1 ine temperature and t h e load c a r r y i n g ability. This is most noticeable f o r p r o f i l e 1. A s e x p e c t e d , maximum centreline temperature falls off with an increase in axial profiling since under this circumstance the shear stress is reduced and a larger volume of oil is available to remove the heat from this part of the film.

In this paper, a study of the performance characteristic of an axially profiled circular bore b e a r i n g h a s b e e n presented. Where appropriate the result8 in this p a p e r a r e p r e s e n t e d a s a c o m p a r i s o n between the cylindrical b o r e b e a r i n g a n d an a x i a l l y profiled counterpart. Since information on cylindrical bearing performance is readily available [l], this comparison shows a direct indication o f t h e b e h a v i o u r o f a n a x i a l profile bore bearing.

Axial profiling affects b e a r i n g p e r f o r m a n c e m o s t n o t i c e a b l y by reducing load carrying capacity and power loss.

Axial profiling may be introduced with benefit to reduce bearing temperatures where extreme operating conditions are encountered.

I

1.20 1.15 1.10 0.001 0.002 0.003

0.004

0.001

R [a)

0.002 0.003 0.004

A R

d = 0.004 R

I

0.001

0.002 0.003

--_Profile 1 FIGURE 9.

Q

0.004

(bl

0.001

c = 0.002

R ------Profile

2

0.002 0.003 0.004

---Profile 3

COMPARISON OF BEARING PERFORMANCE WITH DIFFERENT CLEARANCE AN0 AXIAL PROFILES. N = 10000rpm. E 0.7

218 References 1.

2.

Martin, F A and Garner, D R . Plain Journal Bearings Under S t e a d y Loads: Design Guidance f o r Safe Operation, 1st European Tribology Congress. I Mech E paper C 313/73, 1973. Albin, F T, Champbell, J and Garner, D R. The Technical Development and M a r k e t E x p l o i t a t i o n of Novel Manufacturing Techniques for High Speed Plain Bearings; Proc.I.Mech E. 200, 1986, p77-78.

14. Allan, T. The Application o f Finite Element Analysis to Hydrodynamic and Externally Pressurized Pocket Bearing. Wear, $ 3 1972, p.169 15. Tayal, S P; Sinhasan, R and Singh, D V. Analysis of Hydrodynamic Journal Bearing h a v i n g N o n - N e w t o n i a n Lubricant (Prandt Model) by a Finite Element Method, Journal Mech. Engineering Science, 1981 p63-68, 16. Booker, J F and Huebner, K H. Application of Finite E l e m e n t M e t h o d s to Lubrication: an Engineering Approach. Trans. ASME (JOLT) 94, 1972, p.313.

3.

Pinkus, 0. A n a l y s i s of Elliptical Bearings; Trans. ASME, B, 1956, p965-973.

4.

Pinkus, 0. Analysis and Characterist'ic of the Three Lobe Bearing; Trans A M , Journal of Basic Engineering, 81, 1959, p49-55.

17. Gethin, D T. An Application of Finite E l e m e n t Method to the Thermohydrodynamic Analysis o f a Thin Fi Im Cylindrical Bore Bearing running at High S1 iding Speed. Trans. ASME (JOT), 1987 p 283-289.

5.

Malik, M: Sinhasan, R and Chandra, M. Design Data for Three Lobe Bearing. Trans. ASLE, 24, 1981 p.345-353.

18. Schilichting, H. Boundary Layer Theory, published by Pergamon Press, 1955.

6.

Malik, M ; Chandra, N and Sinhasan R. Performance Characteristics of Tilted Three Lobe Journal Bearings. Tribology International, 14,1981, p.345-349.

19. D m s o n , D. A G e n e r a l i s e d R e y n o l d s Equation for Fluid Film Lubrication. Int. J Mech. Eng. Sci., 4, 1962, p.159-170.

7.

Malik, M. The Analysis of Symmetric and Tilted Four-Lobed Journal Bearing Configurations ASLE Transaction, 26, 1983, p.264-269.

20. Constaninescu, V N. Basic Relationship in Turbulent Lubrication and Their Extension to i n c l u d e T h e r m a l Effects. Trans. ASME (JOLT), 95, 1973, p147-154.

8.

9.

Mehta, N P and S i n g h , A. S t a b i l i t y Analysis of Finite Offset Halves Pressure D a m Bearing. T r a n s . A S M E , (JOLT), 108,April 1986, p.270-274. Garner, D R ; Lee, C S and Martin, F A. Stability of Profile Bore Bearings. Influence o f Bearing Type. Selection: Tribology International 13, 1980, p 204-210.

10. McCallion, H ; Yousif, E and Lloyd, T. The Analysis of Thermal Effects in A Full Journal Bearing Trans. ASME (JOLT), 1970, p578.

a,

11. Medwell, J 0 and Gethin D T. A Finite Element Analysis of Journal Bearing Lubrication Proceeding of t h e Leeds-Lyon Symposium Fluid Film Lubrication 1983, (Eds. Dawson et all. 12. Ng, C W and Pan, C H T. A Linearised Turbulent Lubrication Theory. Trans ASME Journal of Basic Engineering, 87, 1965, p.675-688.

-

13. Huebner, K H. Finite Element Analysis Fluid Film Lubrication - A Survey, Finite Element in Fluids-Volume 2 p.225-254 (Ed. R H Gallagher, J T Oden, C Taylor and 0 C Zienkiewicz).

21. Zienkiewic, 0 C . The Finite Element Method, 3rd Edition, 1977 (McGraw

Hill). 22. Jain; S C , Sinhasan, R and Singh, D V. A S t u d y of EHD Lubrication in a Journal Bearing with Piezovisions Lubricants; Trans ASLE, 27, 1984 p.168.

219

PaperVI II(ii)

Analysis of partial arc journal bearings E.W. Cowking

Two computer programs a r e d e s c r i b e d which c a r r y o u t thermohydrodynamic analyses o f m u l t i - a r c j o u r n a l bearings. A v a l i d a t i o n procedure f o r t h e programs i s a l s o described. Some thermohydrodynamic r e s u l t s a r e presented as p o s s i b l e benchmarks. 1 INTRODUCTION

Before s o f t w a r e can be used i n an e n g i n e e r i n g o r g a n i s a t i o n i t i s u s u a l l y necessary t h a t qua1 it y assurance requirements be met which i n c l u d e a f u l l v a l i d a t i o n o f t h e r e s u l t s . The purpose o f t h i s paper i s t o d e s c r i b e a p o s s i b l e approach t o t h e v a l i d a t i o n o f b e a r i n g a n a l y s i s software, as a p p l i e d t o two p a r t i a l a r c j o u r n a l b e a r i n g programs. The two computer programs were developed t o analyse s t e a d i l y - 1 oaded j o u r n a l b e a r i n g s w i t h f i x e d p a r t i a l arcs. They b o t h p r o v i d e f o u r thermal o p t i o n s r a n g i n g from i s o t h e r m a l up t o f u l l y thermohydrodynamic. They a1 so produce l i n e a r dynamic c o e f f i c i e n t s f o r use i n rotordynamic c a l c u l a t i o n s . The f i r s t program c a r r i e s o u t a two-dimensional s o l u t i o n and has been d e s c r i b e d p r e v i o u s l y i n (1). The second program, which has been completed more recently, c a r r i e s out a s i m i l a r s o l u t i o n i n t h r e e dimensions. The methods o f a n a l y s i s a r e d e s c r i b e d more f u l l y i n s e c t i o n 2, b u t t h e main emphasis o f t h i s paper i s on t h e v a l i d a t i o n process d e s c r i b e d i n s e c t i o n 3. I n v a l i d a t i n g t h e programs, t h e aim has been t o r e l y on p u b l i s h e d r e s u l t s and on checks which can be c a r r i e d o u t by hand. Comparisons a r e made w i t h t h e i s o t h e r m a l r e s u l t s o f Lund and Thomsen ( 2 ) and t h e simple a d i a b a t i c s o l u t i o n s o f Hakansson ( 3 ) which p r e d i c t e d t h e average temperature across t h e f i l m . Each program uses t h e same s u b r o u t i n e s f o r c a l c u l a t i n g t h e pressure, o i l forces, power l o s s and o i l f l o w f o r a l l temperature o p t i o n s . Thus t h e checks on s i m p l e r e s u l t s a r e g e n e r a l l y useful i n v a l i d a t i n g t h e program. F u r t h e r work which has been done t o v a l i d a t e t h e f u l l thermohydrodynamic o p t i o n s i s a1 so described. I d e a l l y , i t should be p o s s i b l e t o benchmark thermohydrodynamic s o l u t i o n s u s i n g p u b l i s h e d r e s u l t s . However, analyses o f p a r t i a l arc bearings i n v o l v e empirical data f o r t h e i n l e t r e g i o n which w i l l vary between d i f f e r e n t implementations. Some sample r e s u l t s a r e p r o v i d e d f o r a s i n g l e p a r t i a l a r c under a d i a b a t i c c o n d i t i o n s . These a r e intended t o p r o v i d e some checks on t h e thermohydrodynamic a n a l y s i s o f t h e o i l f i l m alone.

1.1

Notation S p e c i f i c heat o f l u b r i c a n t Radial c l e a r a n c e o f b e a r i n g Journal diameter Shear f l o w f a c t o r i n g e n e r a l i s e d Reynolds e q u a t i o n Film thickness Thermal c o n d u c t i v i t y o f l u b r i c a n t Axial length o f bearing Pressure i n f l u i d f i l m Flows p e r u n i t l e n g t h i n f l u i d f i l m Journal radius Temperature i n f l u i d f i l m V e l o c i t y component r e l a t i v e t o (X9YYZ) Transformed v e l o c i t y Local c a r t e s an c o - o r d i nates F i x e d co-ord nates w i t h Y v e r t c a l l y upwards Pressure and temperature c o e f f c i e n t s of viscosity Pad r a d i u s d i f f e r e n c e Transformed y- c o - o r d i n a t e Fluid viscosity F1u i d

density

Non-dimensi onal v i s c o s i t y - t e m p e r a t u r e parameter Angular v e l o c i t y o f j o u r n a l

220

2

A f t e r t h e s t e a d y - s t a t e s o l u t i o n has been obtained t h e programs can c a l c u l a t e l i n e a r i s e d dynamic c o e f f i c i e n t s by n u m e r i c a l l y d i f f e r e n t i a t i n g t h e f o r c e components. A b l o c k f l o w diagram which shows t h e v a r i o u s i t e r a t i o n s i n v o l v e d i s g i v e n i n F i g . 2. A l l t h e i t e r a t i o n s a r e o p t i o n a l , dependent on t h e d a t a so t h a t t h e programs can be used f o r a wide v a r i e t y o f j o u r n a l b e a r i n g problems.

DESCRIPTION OF PROGRAMS

Both programs analyse a j o u r n a l b e a r i n g w i t h up t o f i v e f i x e d p a r t i a l arcs. These a r c s a r e u s u a l l y separated by i n l e t gutterways which a r e produced by t a k i n g a c y l i n d r i c a l c u t o u t o f t h e b e a r i n g s u r f a c e as shown i n Fig. 1. The end-lands which seal t h e i n l e t gutterways can generate small hydrodynamic f o r c e s b u t i n t h e p r e s e n t analyses t h i s i s n e g l e c t e d and t h e a r c s a r e t r e a t e d as separate r e c t a n g u l a r r e g i o n s o f fluid film.

itemtion contml

-

L

I -u-f

x

G

IPressure

solution

I

-u-

.-

2

I Moss ord heat flows wt of nrc

Ned inlet

11

Inlet geometry

CJ Complete relnxotion

Output results

Chamfered split

Fig. 2

Block Flow Diagram

F i g . 1 Example o f B e a r i n g Geometry

2.1

A separate pressure-temperature i t e r a t i o n i s c a r r i e d o u t f o r each o f t h e s e r e c t a n g u l a r r e g i o n s o f f i l m . The programs support t h r e e a l t e r n a t i v e t y p e s o f thermal a n a l y s i s depending on t h e i n p u t parameter ITEMP:

The equations a r e f o r m u l a t e d r e l a t i v e t o a l o c a l l y r e c t a n g u l a r c o - o r d i n a t e system and t h e e f f e c t o f f i l m c u r v a t u r e a r e neglected. The f l u i d f i l m i s transformed i n t o a rectangular r e g i o n u s i n g t h e change o f v a r i a b l e :

F l u i d F i l m Equations

ITEMP =

0

Isothermal s o l u t i o n

1

Temperature averaged across t h e f i l m thickness

2

THD a n a l y s i s o f f i l m

3

THD a n a l y s i s o f f i l m w i t h heat conduction i n a c y l i n d r i c a l bearing housing

The programs t r e a t each i n l e t gutterway as a lumped system a t a s i n g l e temperature which i s determined f r o m a heat balance. The programs a l s o c a r r y o u t an o v e r a l l h e a t balance i t e r a t i o n t o ensure t h a t t h e temperatures i n t h e i n l e t s are c y c l i c a l l y consistent. The outermost i t e r a t i o n i n t h e programs determines t h e j o u r n a l p o s i t i o n f o r a g i v e n l o a d u s i n g a r o o t - f i n d i n g a l g o r i t h m i n two dimensions. A l t e r n a t i v e l y , i f t h i s i t e r a t i o n i s n o t requested, t h e programs produce t h e f l u i d f i l m forces f o r a given journal position.

Yo . . . . . . . . . . .( 1)

where y i s r a d i a l l y inwards, yo i s t h e p o s i t i o n o f t h e b e a r i n g surface and h i s t h e f i l m t h i c k n e s s . It i s shown i n (1) t h a t t h i s l e a d s t o a transformed c o n t i n u i t y equation:

where t h e transformed t r a n s v e r s e v e l o c i t y v* is:

T h i s t r a n s f o r m e d v e l o c i t y component has t h e u s e f u l p r o p e r t y o f b e i n g z e r o a t t h e two s u r f a c e s 3 = 0 and S = 1. The thermohydrodynamic a n a l y s i s i s c a r r i e d o u t u s i n g values f o r t h e d e n s i t y , s p e c i f i c h e a t and thermal c o n d u c t i v i t y which a r e averages across t h e f i l m t h i c k n e s s . T h i s s i m p l i f i e s t h e formulae, w i t h o n l y a m i n o r e f f e c t on accuracy.

22 1 For l a m i n a r f l o w , t h e v e l o c i t y components i n t h e f l u i d f i l m are:

S o l u t i o n Methods f o r F l u i d F i l m Equations

2.2

The two dimensional program implements a v a r i a t i o n a l s o l u t i o n o f Reynolds e q u a t i o n which i s d e s c r i b e d i n ( 1 ) . T h i s l e a d s t o a second o r d e r o r d i n a r y d i f f e r e n t i a l e q u a t i o n which i s s o l v e d by standards numerical methods. The t h r e e dimensional program s o l v e s Reynolds e q u a t i o n by r e l a x a t i o n methods. C a v i t a t i o n i s s i m u l a t e d by s e t t i n g p r e s s u r e s equal t o pcav when t h e y drop below t h a t v a l u e d u r i n g t h e r e 1 axat ion process The THD energy e q u a t i o n ( 7 ) i s s o l v e d by a simple i m p l i c i t method. Backflow regions a r e handled by s e t t i n g n e g a t i v e values o f t h e t a n g e n t i a l v e l o c i t y t o z e r o whenever t h e y occur. T h i s i s found t o be reasonably a c c u r a t e since backflow regions a r e not usually very s i g n i f i c a n t i n t h e i r e f f e c t i n p a r t i a l arcs o f r e l a t i v e l y small l e n g t h / d i a m e t e r radius. I n t h e THD a n a l y s i s t h e j o u r n a l s u r f a c e temperature i s assumed n o t t o vary c i r c u m f e r e n t i a l l y . I t s v a l u e can o p t i o n a l l y be determined from a s i m p l i f i e d analysis o f heat conduction i n t h e j o u r n a l . The boundary c o n d i t i o n a t t h e b e a r i n g s u r f a c e i s based on a s p e c i f i e d h e a t t r a n s f e r c o e f f i c i e n t when ITEMP = 2. When h e a t c o n d u c t i o n i n t h e housing i s i n c l u d e d (ITEMP = 3) a standard heat c o n d u c t i o n boundary c o n d i t i o n i s used. The s i m p l e energy e q u a t i o n ( 9 ) i s s o l v e d by marching i n t h e d i r e c t i o n o f r o t a t i o n .

.

The g e n e r a l i s e d Reynolds e q u a t i o n f o r l a m i n a r f l o w can be w r i t t e n i n t h e f o r m

where

qe =

i s an e f f , ective . L

J2CJ23,- J,')

F = ?

- J, z

v i s c o s i t y and

i s a flow factor.

The program can a l s o handle t u r b u l e n t f l o w u s i n g t h e 1i n e a r i sed t u r b u l e n t 1u b r i c a t i o n t h e o r y o f Ng and Pan (4). I n t h i s case e f f e c t i v e v i s c o s i t i e s 3x and 9, a r e used instead o f q e The energy e q u a t i o n f o r l a m i n a r f l o w i n t h e f i l m i s used i n t h e form:

I n l e t Heat Balance

2.3

Each i n l e t r e g i o n i s t r e a t e d as a lumped thermal system a t a mean temperature T The mass f l o w and i n l e t f l o w balances a r e is f o l 1 ows:

.

-f , Fp and k a r e average values across t h e f i l m . d

The c o n v e c t i o n t e r m r e t a i n s i t s o r i g i n a l form a f t e r t h e change o f v a r i a b l e (1):

M2 t M,

= Mp t M i

C ( M +M ) ( T -T ) = H2 P

2

S

where M2,H2

However, t h e p a r t i a l d e r i v a t i v e s w i t h r e s p e c t t o x and z have d i f f e r e n t values when t h e y a r e evaluated w i t h 3 fixed. I n t h e case o f t u r b u l e n t f l o w t h e programs c a l c u l a t e t h e average temperature across t h e f i l m from t h e e q u a t i o n :

.

t

Hp

-

HJ

-

HB

3

..(lo)

Mass and h e a t f l o w a t t r a i l i n g edge o f p r e v i o u s a r c

MI

=

Mass f l o w a t l e a d i n g edge o f next arc

MS

=

Mass f l o w o f f r e s h f l u i d

Mp

=

Side-leakage from i n l e t

=

Power l o s s due t o shear f l o w

=

Heat conducted t o j o u r n a l and bearing

HJ,HB

H i s t h e heat f l u x t o t h e metal s u r f a c e s wh ch i s c a l c u l a t e d from e m p i r i c a l heat t r a n s f e r c o e f f i c i e n t s The simple temperature c a l c u l a t i o n uses t h i s formula w i t h ? = 9, = 7? = 7 . The v a l i d a t i o n process w7v1 c o n c e n t r a t e on l a m i n a r f l o w and d e t a i l s o f t h e t u r b u l e n t f l o w o p t i o n have been k e p t correspondingly b r i e f .

S

=

HP

(9)

P

The i n l e t i s assumed t o t h o r o u g h l y mix t h e f l u i d so t h a t t h e l e a d i n g edge temperature o f t h e n e x t a r c i s uniform. T h i s l e a d s t o s t e p d i s c o n t i n u i t i e s i n temperature a t t h e j o u r n a l and b e a r i n g surfaces. T h i s i d e a l i z a t i o n m a i n l y a f f e c t s t h e heat f l u x t o t h e j o u r n a l which i s p r e d i c t e d t o peak s h a r p l y a t t h e l e a d i n g edge o f t h e arc. The f l o w i n t h e i n l e t pocket i s assumed t o n o r m a l l y be t u r b u l e n t and t h e power l o s s and heat t r a n s f e r c o e f f i c i e n t s a r e c a l c u l a t e d f r o m e m p i r i c a l d a t a f o r t u r b u l e n t shear f l o w s . The power l o s s and f l o w o v e r t h e end l a n d s a r e calculated from l u b r i c a t i o n theory.

222

2.4

Film Shape

The two dimensional program analyses a well-aligned bearing w i t h c i r c u l a r arcs. The film shape f o r t h e n t h arc i s calculated from t h e standard formula:

h = AR,

- en c ~ 'sp- 9%)

..(11)

where R n i s t h e radius d i f f e r e n c e of t h e a r c and ( ) i s t h e position of t h e journal centre r e l a t i v e t o t h e c e n t r e of t h e a r c . The t h r e e dimensional program analyses an a r c of a general film shape. The f i l m thicknesses i s calculated from t h e formula: h = h,- (-e.,+ $z)-sp

- kx++yz)anp

..(15) The present programs require data in SI u n i t s and use a d i f f e r e n t formula (13) f o r the viscosity. The f o l l owing t e s t case was t h e ref o r e cons i de red : Diameter, D = 200 mm Length, L = 100 mm Radius d i f f e r e n c e , A R = 0.2 mm Arrangement: c e n t r a l l y loaded 120" a r c Leading edge temperature, T i = 60°C

..(iz)

where h i s a basic film shape which can be calculaked from a formula o r read a s data. 4 and 4 a r e t h e angles of t i l t of t h e journaf about tXe X and Y axes. ex and e a r e the rectanaular co-ordinates of t h e yournal c e n t r e r e l a t i i e t o t h e bearing centre. 2.5

where T i i s the temperature a t t h e leading edge of t h e arc. He t a b u l a t e s r e s u l t s a s functions o f t h e non-dimensional vi scosi ty-temperature parameters :

Lubricant d a t a : T( " C ) 9 ( c P ) f ( k g / l i t r e )

40

27.4 4.37

100

Cp(kJ/kg"C) k(W/m'C)

0.83 0.83

0.13 0.13

2.1 2.1

A value of

Lubricant Properties

The viscosity of t h e f l u i d i s calculated by t h e programs from Roelands' formula ( 5 ) , w i t h a 1 inearised pressure term:

= 0.030"C'1 was chosen t o f i t the Roelands curve c l o s e l y over the range 60-90°C a s shown i n Fig. 3.

w h e r e 7 i s t h e v i s c o s i t y i n c e n t i p o i s e , T i n "C and p i n bar. Go, So and Z a r e constant parameters The density and s p e c i f i c heat a r e assumed t o vary l i n e a r l y w i t h temperature. These 1 ubricant p r o p e r t i e s can a1 1 be determi ned from two i n i t i a l l y specified values a t two d i f f e r e n t temperatures, except f o r Z which i s specified separately.

.

3 VALIDATION The programs contain a wide range of options so i t i s necessary t o adopt a step-by-step approach t o validation. Comparisons were f i r s t made w i t h t h e r e s u l t s f o r a s i n g l e c i r c u l a r a r c published by Hakansson ( 3 ) . Then i t was shown t h a t t h e programs build u p s o l u t i o n s c o r r e c t l y f o r multi-arc bearings. The heat balances f o r t h e i n l e t regions were checked manually. Dynamic c o e f f i c i e n t s f o r an isothermal s o l u t i o n were compared with Lund and Thomsen ( 2 ) . F i n a l l y , the thermohydrodynamic a n a l y s i s was checked as f a r as possible by comparison with t h e simple temperature c a l c u l a t i o n and by checking mass flow and heat balances. 3.1

Single P a r t i a l Arc Results

Hakansson ( 3 ) provides t a b l e s of non-dimensional r e s u l t s f o r a s i n g l e c i r c u l a r a r c with laminar flow and v a r i a b l e viscosity. A c a v i t a t i o n condition i s applied and t h e average temperature across t h e film was evaluated assuming no heat loss by conduction. He uses the exponential formula f o r v i s c o s i t y :

7

= 3; exp[.cp - ~ [ T - T ) ]

..(14)

1

so

40

60

70

eo

90

loo

110

120

Temperature, T ("0

Fig. 3

Lubricant Viscosity

Hakansson's r e s u l t s a r e such t h a t 1 4 C p 4 p = 1.2. T h i s corresponds t o a value of Z = 0.80 i n the present case. Results were produced f o r X = D (isoviscous s o l u t i o n s ) and X = 0.05 ( a t 8558.5 rpm w i t h ITEMP = 1).

The isothermal s o l u t i o n s were a l s o obtained a t 8558.5 rpm. Hakansson quotes r e s u l t s a t a s e r i e s of e c c e n t r i c i t y r a t i o s whereas the present program c a l c u l a t e s the journal position f o r a given load vector. The programs were run a t a s e r i e s of loads: W = 2,5,10,20,50,100,200

kN

Hakansson's r e s u l t s a r e on page 160 of ( 3 ) .

223 They a r e non-dimensional, a t s p e c i f i e d e c c e n t i c i t y r a t i o s , and a r e b e s t compared g r a p h i c a l l y w i t h t h e present r e s u l t s . T h i s i s done i n Figs. 5-10 i n terms o f Hakansson's non-dimensional parameters. The r e s u l t s from t h e t h r e e dimensional THD program a l o n e a r e p l o t t e d s i n c e d i f f e r e n c e s between t h e two programs would n o t show up on graphs. The values o f t h e r e l e v a n t parameters a r e as f o l 1 ows: Quantity

\

D iv i sor

-1

= 29050 N

Load F1ow

CARRLAR

Power l o s s and Heat f 1ow

7;

Temperature (The v a l u e o f

(t.dRP L R

= 107.9 l i t r e s / m i n

a ) Example of two-arc bearing

= 5.226 kW

be

&Y

= 1.667'C

a t 60°C i s 12.920cT )

The agreement i n Figs. 5-10 i s c l e a r l y good. S l i g h t d i f f e r e n c e s can be d i s c e r n e d a t h i g h loads, probably due t o t h e d i f f e r e n t v i s c o s i t y f o rmu 1ae

.

3.2

Two Arc B e a r i n g Example

I

Pre-load A b e a r i n g w i t h two 120" c i r c u l a r a r c s was used as an example f o r t h e checking o f t h e i n l e t a n a l y s i s and t h e combined r e s u l t s . T h i s was chosen w i t h b o t h h o r i z o n t a l and v e r t i c a l a r c displacements i n o r d e r t o p r o v i d e a more general check on t h e programs. A s k e t c h o f t h e b e a r i n g i s shown i n F i g . 4a. The d a t a were as f o l 1 ows: Diameter, D = 200 mm Length, L = 100 mm Arc r a d i u s d i f f e r e n c e , OR = 0.2 mm C o n f i g u r a t i o n : two 120" a r c s d i s p l a c e d by 0.2 mn h o r i z o n t a l l y and by 0.1 mm v e r t i c a l l y . I n l e t geometry: G 50 mm H = 3mm (Fig 1) U 12.5 mm L u b r i c a n t p r o p e r t i e s as i n 3.1 above Supply temperature, Ts = 50°C Supply pressure, ps = 1 b a r S h a f t speed, N = 3000 rpm Load, W = 10 kN A d i a b a t i c c o n d i t i o n s were assumed. The r e s u l t s from t h e two programs, r e f e r r e d t o as 2Dthd and SDthd, a r e shown i n Table 1. It i s p o s s i b l e t o check f l o w and h e a t balances d i r e c t l y from t h i s t a b l e . Spot checks were a l s o c a r r i e d o u t on t h e r e s u l t s f o r t h e i n l e t s by hand. There a r e some d i f f e r e n c e s between t h e two programs which were found t o be m a i n l y due t o d e t a i l e d d i f f e r e n c e s i n t h e w a y t h e i n l e t geometry i s s p e c i f i e d t o t h e two programs.

Cver tlcol

1- AR

b) Lemon- bore bearing with preload of 0.5 Fig. 4 3.3

Arc Geometries

Dynamic C o e f f i c i e n t s

The most a c c u r a t e pub1 ished c o e f f i c i e n t s appear t o be t h o s e produced by Lund and Thomsen ( 2 ) . These were o b t a i n e d by d i r e c t d i f f e r e n t i a t i o n o f Reynolds e q u a t i o n w i t h respect t o displacement and v e l o c i t y components. T h i s a v o i d s e r r o r s due t o d i f f e r e n t i a t i o n o f t h e f o r c e components. A comparison was made f o r a lemon b o r e b e a r i n g w i t h L/D = 0.5, 160D a r c s and a p r e l o a d f a c t o r The r e s u l t s a r e o f 0.5, as shown i n F i g . 4b p l o t t e d non-dimensionally i n F i g s 13 and 14. Note t h a t Lund and Thomsen's r e s u l t s a r e non-dimensional w i t h r e s p e c t t o t h e a r c r a d i u s d i f f e r e n c e . The good agreement c o n f i r m s t h a t t h e f o r c e d e r i v a t i v e s are evaluated c o r r e c t l y and a c c u r a t e l y by t h e program. I n thermohydrodynamic analyses some assumption has t o be made concerning temperature v a r i a t i o n s i n t h e o i l f i l m under dynamic c o n d i t i o n s . The r e s u l t i n g c o e f f i c i e n t s cannot be checked e x t e r n a l l y .

.

3.4

Thermohydrodynamic A n a l y s i s o f t h e O i l

Film . . ....

The two a r c example d i s c u s s e d i n 3.2 above was a l s o used t o check t h e t h d a n a l y s i s o f t h e o i l f i l m (ITEMP = 2). The j o u r n a l was k e p t f i x e d a t t h e same p o s i t i o n so t h a t t h e r e s u l t s c o u l d be compared more d i r e c t l y w i t h t h o s e o f 3.2. The j o u r n a l s u r f a c e was assumed t o be a t a s i n g l e , f i x e d temperature which was determined so t h a t t h e r e i s no n e t heat f l o w t o t h e j o u r n a l . The r e s u l t s a r e g i v e n i n Table 2.

224 The c a l c u l a t e d f o r c e s a r e reduced by thermohydrodynami c e f f e c t s and t h e maximum pressure, power l o s s and o i l f l o w s a r e a l s o lower. The mean temperatures across t h e f i l m c a l c u l a t e d i n t h e t h d cases agree c l o s e l y w i t h those determined d i r e c t l y by t h e s i m p l e r a n a l y s i s o f 3.2. The t h d a n a l y s i s determines t h e heat conducted t o t h e j o u r n a l from each a r c (HCFJ) and from each i n l e t (HCIJ). The heat f l o w s can be seen t o balance when t h e s e a r e included. These t y p e s o f checks enhance c o n f i d e n c e i n the v a l i d i t y o f the results, but ideally a f u l l e x t e r n a l comparison would be p r e f e r a b l e . A p o s s i b l e approach t o such e x t e r n a l benchmarking i s suggested i n t h e n e x t sub-section. 4

THERMOHYDRODYNAMIC BENCHMARKS

S i n g l e a r c r e s u l t s a r e most s u i t a b l e as benchmarks s i n c e t h e y do n o t i n v o l v e e m p i r i c a l assumptions. Because o f t h e l a r g e number o f parameters i n v o l v e d , o n l y dimensional r e s u l t s w i l l be presented. These a r e f o r t h e same a r c geometry and l u b r i c a n t as i n 3.1 above. A d i a b a t i c c o n d i t i o n s were assumed w i t h no n e t heat conducted t o t h e j o u r n a l . The o p e r a t i n g c o n d i t i o n s were t a k e n as f o l l o w s : Speed, Load, Inlet Inlet

N = 3000 rpm W = 1, 2, 5, 10, 20 kN temperature, Ti 60°C pressure, pi = 0

The f i n i t e d i f f e r e n c e mesh had 30 c i r c u m f e r e n t i a l i n t e r v a l s , 10 i n t e r v a l s over h a l f t h e b e a r i n g l e n g t h and 16 i n t e r v a l s across t h e f i l m . The r e s u l t s f r o m t h e two programs a r e shown i n Tables 3 and 4. The r e s u l t s do not cover t h e a n a l y s i s o f i n l e t s o r o f heat conduction i n t h e b e a r i n g housing o r j o u r n a l . However, t h e s e can be checked s e p a r a t e l y w i t h r e l a t i v e ease. 5

CONCLUSIONS

Two computer programs a r e d e s c r i b e d which c a r r y o u t thermohydrodynamic analyses o f p a r t i a l a r c j o u r n a l bearings. A v a l i d a t i o n procedure f o r t h e programs i s discussed which r e l i e s m a i n l y on comparisons w i t h p u b l i s h e d r e s u l t s and on checks which can be c a r r i e d o u t by hand. A d i a b a t i c s o l u t i o n s f o r a s i n g l e p a r t i a l a r c have been found t o p r o v i d e u s e f u l checks on t h e s o l u t i o n methods. Some examples a r e p r o v i d e d o f thermohydrodynamic r e s u l t s o f t h i s type.

REFERENCES

COWKING, E.W. 'Thermohydrodynamic analysis o f multi-arc journal bearings' T r i b o l ogy i n t e r n a t i o n a l , August 1981.

,

LUND, J.W. and THOMSEN, K.K. ' A c a l c u l a t i o n method f o r t h e dynamic coefficients of o i l lubricated journal b e a r i n g s ' , Topics i n F l u i d F i l m B e a r i n g and R o t o r B e a r i n g System Design and Optimus a c t i o n , ASME, 1978, pp 1-28. HAKANSSON, B. 'The Journal B e a r i n g c o n s i d e r i n g V a r i a b l e V i s c o s i t y ' , Trans. o f Chalmers U n i v e r s i t y o f Technology, Nr 298, 1965. NG, C.W. and PAN, C.H.T. 'A linearized T u r b u l e n t L u b r i c a t i o n Theory', ASME J. o f Basic Engineering, September 1965, p 48.

ROELANDS , C .J .A. ' C o r r e l a t i o n a l aspects of t h e v i s c o s i t y temperature pressure r e l a t i o n o'f l u b r i c a t i n g o i l s ' , PhD Thesis, Technische Hogeschool t e D e l f t , A p r i l 1965.

-

-

225

Table 1.

2Dthd Program I Bearing Arc 2

I

Arc 1 Eccenti c i t y , e ( m ) A t t i t u d e angle, (deg O i1 FX(N) Force FY(N Power Loss, E (kW) Inlet , E (kW) Oi1 Q1 Flows 42 ( l / m i n ) Qs Qs ( i n l e t ) Heat H1 Flows H2 kW Hs Hs ( i n l e t ) Pmax ( b a r ) I n l e t Temp T ("C) Mean F i l m Tmax ("C)

Two Arc Bearing.

0.1339 43.84 1467 -15244 2.91 0.54 18.31 6.62 11.69 5.02 2.45 3.12 2.24 0.67 23.04 54.61 66.26

ITEMP = 1

I

I

l t h d Prograi

' 0.0471 -8.88 -1.4 -9997 5.86

0.1073 -91.84 -1469 5247 1.83 0.57 26.57 11.15 15.42 6.96 2.92 2.58 2.18 0.77 7.92 53.79 57.88

39.10

5.87 23.04 66.26

Arc 2

-

-

1452 -15273 2.90 0.47 18.68 6.59 12.06 3.84 2.51 3.11 2.32 0.52 23.03 54.63 66.58

1454 5274 1.81 0.47 27.33 11.13 16.27 4.57 3.07 2.55 2.34 0.51 7.82 53.86 58.06

66.58

Arc 2

Bearing

Bearing 0.0472 -8.68 -1.5 -9999 5.65

36.73

5.69 23.03

I

I

Table 2.

Arc 1

Two Arc Bearing.

ITEMP = 2

Ykd I I Progr?

Arc 1

Arc 2

Bearing

Arc 1

I E c c e n t i c it y , e(mn) A t t i t u d e angle, (deg O i1 FX(N) Force FY(N) Power Loss, E (kW) Inlet , E (kW) Oi 1 Q1 Flows 02 ( l / m i n ) Qs Q s (i n 1 e t ) H1 Heat H2 Flows Hs (kW) HCFJ Hs ( i n l e t ) HCIJ Pmax(bar) Inlet T ('C) Mean F i l m Tmax ("C) White metal Tmax ("C)

0.1339 43.84 963 -13743 2.84 0.54 18.42 7.19 11.23 5.02 2.48 2.77 2.20 0.33 0.68 -0.05 20.89 54.64 66.41 74.75

0.1073 -91 -84 -1345 4942 1.80 0.57 26.65 11.53 15.11 6.90 2.72 2.57 2.14 -0.19 0.71 -0.09 7.37 53.52 58.74 64.05

0.0471 -8.88 -8801 5.75

38.28

5.73 20.89 74.75

-

-

88 1 -13687 2.83 0.47 18.80 7.12 11.63 3.84 2.52 2.74 2.25 0.31 0.51 -0.05 20.66 54.61 67.12 75.89

-1329 4990 1.78 0.47 27.45 11.51 16.01 4.52 2.83 2.51 2.27 -0.19 0.47 -0.08 7.29 53.54 59.12 65.31

0.0472 -8.68 -448 -8698 5.56

35.99

5.50 20.66 75.89

226

Table 3.

1

Case Number Load, W (kN) E c c e n t i c i t y , e(mm) A t t i t u d e angle, (deg) Power Loss, E (kW)

Flows Oil (l/min)

I"' 92 Qs

-Pmax(bar) Tmax ('C) Tmax ('C) TJ ('c)

1 0.0370 67.97 1.350 20.22 16.28 3.94 0 1.188 0.156 1.18 63.63 67.74 60.92

THD Benchmarks.

2 2 0.0614 57.36 1.496 19.98 13.89 6.09 0 1.244 0.244 2.44 64.35 68.85 61.16

Table 4. THD Benchmarks.

2Dthd Program

3 5 0.1012 45.70 1.891 18.54 10.12 8.42 0 1.487 0.391 6.81 66.82 72.26 62.02

Flows O( li/lm i n )

I"' 42

Qs

-Tmax Pmax( b a r ) ("C) Bearing, Journal,

Tmax ('C) TJ ("C)

1 0.0370 68.29 1.350 20.24 16.28 3.92 0 1.189 0.162 1.18 63.83 68.12 60.98

2 0.0615 57.47 1.496 20.00 13.88 6.05 0 1.241 0.249 2.45 64.65 69.44 61.20

5

10 0.1301 38.91 2.373 16.76 7.36 9.39 0 1.838 0.546 15.36 70.88 77.24 63.64

20 0.1543 32.82 2.976 14.54 4.97 9.56 0 2.219 0.804 35.34 78 30 85.65 67.46

4

5

3Dthd Program

Case Number Load, W (kN) Eccenticity, e ( m ) A t t i t u d e angle, (deg) Power Loss, E (kW)

4

5 0.1014 45.92 1.893 18.59 10.09 8.40 0 1.473 0.391 6.81 67.19 73.07 61.94

10 0.1302 39.17 2.382 16.85 7.33 9.37 0 1.786 0.538 15.36 71.09 77.90 63.33

20 0.1542 33.15 3.008 14.72 4.94 9.56 0 2.113 0.761 35.34 77.93 85.64 66.58

227

o Hdkansson

0

3Othd program

I

Fig. 5

I

I

I

I

It 0

I

1

1

Fig. 6

Load Capacity

,

Hhkansson 30 thd program

I

I

,

I

I

I

I

A t t i t u d e Angle

0

0

Hdkansson 3Othd program

i

i

03

A

CL

a CL 3 02

a

d 0

r

3

9 r

2

0 01

0

0

I

I

03

05

03

09

07

Fig. 8

Power Loss

Figs. 5

-

8

05

Eccentricity ratio. c = e / c

Eccentricity ratio. c = e l c

Fig. 7

Hdkansson 3Dthd program

Oil Flow

Comparison w i t h Hakansson

07

09

228

I

0

Hbkansson 3Dthd program

0 0

0

01

01

03

Eccentricity ratio,

Figs. 9 and 10

01

07

05 E

=e/c

I

I

03

Hdkansson 3Dthd program

I

I

05 Eccentricity ratio.

I

1

07 E

= elc

Comparison w i t h Hakansson

a 0

0

2Dthd program Lund & Thomsen. Ref

2

0

LID = 0 5 , 160° arcs Pre-load factor = 0 5

oc

'\

~\o~o-o-o-o-o

LID = 0 5. 160° arcs PR-load factor = 0 5

K xx

'*a \om

05

Figs. 11 and 12

, 10

K,, ,

.O-a-o

Load factor. A -

& (F)'

2D thd program Lund 8 Thomsen, Ref 2

1S

A

C

Comparison w i t h Lund and Thomsen

I

I

09

229

PaperVlll(iii)

Elapsedtime for the decay of thermal transients influid film bearing assemblies C. M. M. Ettles, H. Heshmat and K. R. Brockwell

The decay time o f thermal t r a n s i e n t s i n a b e a r i n g assembly i s o f p r a c t i c a l i n t e r e s t , s i n c e premature measurements c o u l d be m i s l e a d i n g . In a d d i t i o n , t h e thermal d e f o r m a t i o n t h a t o c c u r s d u r i n g a t r a n s i e n t does n o t v a r y smoothly o r m o n o t o n i c a l l y . I n s e v e r e c a s e s t h i s c a n l e a d t o a n i n s t a b i l i t y and f a i l u r e of t h e b e a r i n g , The p r i n c i p a l f a c t o r s governing thermal t r a n s i e n t s a r e i n f e r r e d from c l a s s i c a l s o l u t i o n s . More a c c u r a t e p r e d i c t i o n s may b e made from a coupled s o l u t i o n o f t h e f i l m and bounding components. Experimental d a t a from s i x t h r u s t b e a r i n g s and two j o u r n a l b e a r i n g s a r e examined. I t i s found t h a t , f o l l o w i n g a s t e p change o f o p e r a t i n g c o n d i t i o n , t h e h e a t i n g o r c o o l i n g r a t e v a r i e s a p p r o x i m a t e l y exponentially.

1. INTRODUCTION When t h e o p e r a t i n g c o n d i t i o n s o f a b e a r i n g a r e changed, a f i n i t e t i m e must e l a p s e b e f o r e thermal e q u i l i b r i u m i s r e e s t a b l i s h e d . I n t h e t r a n s i e n t period t h a t follows, say, a s t e p change o f l o a d o r speed, t h e b e a r i n g f i l m t h i c k n e s s i s a f f e c t e d by v a r y i n g v i s c o s i t y and v a r y i n g thermal deformation. Thermoelastic e f f e c t s w i l l always l a g on observed changes o f s u r f a c e t e m p e r a t u r e , and may n o t b l e n d smoothly from one c o n d i t i o n t o t h e n e x t . Temporary r e d u c t i o n s i n c l e a r a n c e c a n o c c u r , which i n extreme c a s e s l e a d t o s e i z u r e o f t h e b o r e from a thermal r a t c h e t t i n g p r o c e s s . Two a s p e c t s o f t r a n s i e n t t h e r m a l b e h a v i o r a r e s t u d i e d i n t h i s paper: The t i m e d e l a y f o r some p r o p o r t i o n (50%, 70%) of t h e f i l m t e m p e r a t u r e change t o occur, f o l l o w i n g a s t e p change i n c o n d i t i o n s . T r a n s i e n t thermoelastic deformations and t h e i r e f f e c t on t h e t i m e d e l a y . I n t h e f i r s t s e c t i o n some s i m p l e , c l a s s i c a l s o l u t i o n s o f t h e r m a l t r a n s i e n t s i n s o l i d s are c o n s i d e r e d . These g i v e g u i d e l i n e s c o n c e r n i n g t h e i m p o r t a n t p a r a m e t e r s and boundary c o n d i t i o n s . The r e s u l t s a r e used i n s e t t i n g up t h e second s e c t i o n of t h e paper, which i s a more d e t a i l e d , n u m e r i c a l a n a l y s i s that c o u p l e s t h e s e p a r a t e components o f pads, f i l m and r o t o r o f a t h r u s t b e a r i n g i n t h e t i m e domain. The n u m e r i c a l s o l u t i o n i s c o n s i d e r e d t o b e more a c c u r a t e t h a n t h e c l a s s i c a l s o l u t i o n s , b u t it is, of course, a p p l i c a b l e o n l y t o p a r t i c u l a r cases and genera l i t y is lost. In t h e f i n a l s e c t i o n of t h e p a p e r a c o l l e c t i o n of e x p e r i m e n t a l r e s u l t s f o r t h r u s t and j o u r n a l b e a r i n g s i s c o n s i d e r e d . An a t t e m p t i s made t o c o r r e l a t e a l l t h e r e s u l t s w i t h Newton's l a w of h e a t i n g ( o r c o o l i n g ) . This l a w s t a t e s t h a t t h e c u r r e n t rate of t e m p e r a t u r e change o f a body i s p r o p o r t i o n a l t o t h e c u r r e n t temperat u r e d i f f e r e n c e between t h e body and ambient. This r e s u l t s i n an e x p o n e n t i a l change of tempera t u r e w i t h t i m e which, t o a n approximation, w a s t h e observed b e h a v i o r of most o f t h e e x p e r i m e n t a l results.

1.1 N o t a t i o n A c

C k

kf F G

H Nu

r R t T U

cy

ATF

Bush o u t e r r a d i u s l b o r e S p e c i f i c heat o f s h a f t , pad o r bush m a t e ri a 1 Journal bearing r a d i a l clearance Thermal c o n d u c t i v i t y o f s h a f t , pad o r bush m a t e r i a l Thermal c o n d u c t i v i t y o f l u b r i c a n t F o u r i e r number, Eq. (3) Surface h e a t t r a n s f e r c o e f f i c i e n t Pad t h i c k n e s s N u s s e l t number, GR/k o r GH/k Radial coordinate Radius o f s h a f t Time Temperature Radial displacement C o e f f i c i e n t o f expansion O v e r a l l t e m p e r a t u r e change

(6)

G*

Thermal s t r a i n , E q s . ( 5 ) ,

p

D e n s i t y o f s h a f t , pad o r bush material.

T

2. CLASSICAL SOLUTIONS FOR THERMAL TRANSIENTS The e q u a t i o n o f t r a n s i e n t h e a t c o n d u c t i o n w i t h axisymmetry i s "

When t h i s i s s e t i n nondimensional form, t h e result is

where nondimensional t i m e t* i s d e f i n e d as

(3)

230 where t is time and R is a r e f e r e n c e radius. This parameter is a l s o known a s t h e Fourier number F, and f o r given boundary conditions i s t h e most important parameter in any t r a n s i e n t heat solution. 2.1

developed laminar flow of f l u i d between p a r a l l e l walls a distance h apart. For uniform w a l l temperature:

Boundary Conditions

To simulate a s t e p change i n a j o u r n a l bearing t h e most a p p r o p r i a t e boundary condition i s (apparently) t o allow t h e s u r f a c e of t h e s h a f t o r bush t o be s e t in c o n t a c t with f l u i d a t a temperature 4T with a convection c o e f f i F' c i e n t G e f f e c t i v e a t the surface. I f G i s i n f i n i t e t h e s u r f a c e temperature r i s e s t o AT F instantaneously. When s e t i n nondimensional form, t h e convection c o e f f i c i e n t G appears a s GR/k = Nu, the Nusselt number. 2.2

r e s u l t s t o be meaningful. Some c l a s s i c a l s o l u t i o n s e x i s t f o r Nusselt number Nuf i n t h e f u l l y

Results

Figures l a , 2a show t h e s u r f a c e temperature change of a j o u r n a l and bush r e s p e c t i v e l y f o r various Nu. The r a d i u s of t h e j o u r n a l i s taken a s R and t h e i n n e r and o u t e r r a d i i of t h e bush a r e taken a s R and 2R, with t h e boundary condit i o n aT/ar = 0 a t t h e o u t e r r a d i u s . The r a t e of s u r f a c e temperature r i s e i s dominated by t h e value of Nu, so the c o r r e c t choice of value f o r Nu is important f o r t h e s e

I 1 ' ! Shaft surtace temperature rise

For uniform h e a t f l u x : Nuf =

f Here, k

f t h e f l u i d , 2h i s t h e h y d r a u l i c depth and h e a t t r a n s f e r takes place t o o r from t h e f l u i d . TO s e t Nu in terms of Nu, t h e s e s i m p l i f i c a t i o n s f could be made: Clearance r a t i o , 2h/R= 2C/R = 26

I

Fig.la

(4c)

I

1

+ 8.24)

Nuf = 0.5 (7.54

'

~

'

(4d)

= 7.89

~

'

'

1

'

1

Bush surface temperature rise

01

Fourier N u m b e r

R2

Fig. 2a

b.

a.

10

PC

R

The Inner Surface Temperature of a Bush Following Exposure of t h e Bore t o an Ambient Temperature AT (Outer r a d i u s / F' i n n e r r a d i u s = A = 2.) The numerical values are Nusselt number e f f e c t i v e a t t h e bore, GR/k. I

I

' ' ' ~ ' 1 1 1

Shaft thermal strain

(4a)

Journal & bush conductivity, k = 50 W/m°C

a.

The Surface Temperature of a Shaft Following Exposure t o a n Ambient Temp e r a t u r e AT F' The numerical values a r e Nusselt number e f f e c t i v e a t the s u r f a c e , GR/k.

-3

10

(4b)

L.L PC

X

Lubricant c o n d u c t i v i t y , kf = 0 . 1 5 W / m a C

0 01

Fourier N u m b e r

i s t h e thermal c o n d u c t i v i t y of

I

" ' l l l

7 * 2 h = 8.24

b.

Bush. thermal strain of bore 10

10cWt

08

2

5 -

06

m

E

&

04

.c I02

0 01

1

01

10

0 0 01

t F o u r i e r Number - -T PC R

Fig. l b

The Proportional Thermal S t r a i n

01

k t F o u r i e r N u m b e r -*-F

k

PC

Fig.2b

R

The Proportional Thermal S t r a i n of t h e Bore

23 1 This g i v e s t h e v a l u e of Nu t o b e used i n F i g s . 1 and 2 as Nu = GR/k = 11.8516, where 6 c l e a r a n c e r a t i o d e f i n e d by ( 4 a ) . U n f o r t u n a t e l y t h i s can g i v e o n l y bound of Nu, s i n c e t h e f l u i d i n which j o u r n a l o r bush is suddenly "immersed" t o be a t t h e f i n a l temperature, AT,.

is t h e a n upper the i s taken In

p r a c t i c e , t h e t e m p e r a t u r e d i f f e r e n c e between t h e midpoint ( s a y ) o f t h e f i l m and t h e s u r f a c e s i s much l e s s t h a n t h i s ( a s w i l l emerge from t h e numerical s o l u t i o n ) . I n summary, t h e v a l u e o f Nu = GR/k L 11.8516 is p r o b a b l y r e a s o n a b l e , b u t t h e temperature d i f f e r e n c e l'across'' G i s always less t h a n t h e assumed v a l u e . The e x p e r i m e n t a l d a t a t o b e p r e s e n t e d sugg e s t an e f f e c t i v e v a l u e of Nu i n t h e r a n g e 1 5 . For Nu = 1, t h e 50% response t i m e f o r t h e s u r f a c e of t h e s h a f t is F = 0.29 and f o r t h e s u r f a c e of t h e bush i s F = 0.79. S i n c e t h e p a r t i c u l a r bush c o n s i d e r e d h e r e h a s a g r e a t e r thermal c a p a c i t y t h a n t h e s h a f t , t h e 50% response t i m e f o r t h i s assembly w i l l b e c l o s e r t o 0.79 t h a n 0.29.

F i g u r e s l b and 2b show a n upper bound t o t h e rate a t which a s h a f t o r bush w i l l expand. This c o r r e s p o n d s t o Nu = m, o r a stepwise i n c r e a s e of t h e s u r f a c e t e m p e r a t u r e t o t h e f i n a l value

.

2.4

T r a n s i e n t Thermal Deformatj.on o f a Beam

To e x p l o r e t h e t r a n s i e n t d e f o r m a t i o n of t h r u s t pads i t is c o n v e n i e n t t o t r e a t them as beams. F i g u r e 3 shows t h e t h e r m a l d e f l e c t i o n of a beam s u b j e c t e d t o a s t e p i n c r e a s e i n temperat u r e on one f a c e . The d e f o r m a t i o n r e a c h e s a

-

04

2.3

Thermal S t r a i n

02

The thermal s t r a i n o f t h e s h a f t is g i v e n b y 1 e* = aATF

e T = urSR/R = aATF

T

2

J Txr*

dr*

(5)

0

Fig.3

The t h e r m a l s t r a i n of t h e bush is ( f o r z e r o r a d i a l stress a t t h e i n n e r and o u t e r boundaries): 2 e T = ubore/R = aAT e* = aATF ( 2 1 (A 1))

-

T A

'I?r*

0

dr*

i where A = Router/R

= 2 i n F i g u r e 2.

10-

10-1

When t h e

deformation is complete, t h e thermal s t r a i n i s @ATF and e; = 1. For t h e p a r t i c u l a r c o n d i t i o n s a n a l y s e d (no r e s t r a i n t of t h e bush a t t h e o u t e r r a d i u s ) , when t h e t r a n s i e n t p r o c e s s i s complete t h e r a d i a l c l e a r a n c e o f a j o u r n a l b e a r i n g w i l l b e unchanged, s i n c e both components deform by t h e same amount, aRATF. However t h e c l e a r a n c e w i l l t e m p o r a r i l y expand f o l l o w i n g ( s a y ) a d e c r e a s e o f speed o r w i l l temporarily c o n t r a c t following a n i n c r e a s e of speed. The timewise b e h a v i o r o f a n expansion o r c o n t r a c t i o n may b e found from F i g u r e s 1 and 2 b y s u b t r a c t i n g ;E f o r t h e two components. Under s e v e r e c o n d i t i o n s a c o n t r a c t i o n may b e u n s t a b l e and l e a d t o s e i z u r e . The c l o s u r e o f t h e cleara n c e from a thermal r a t c h e t t i n g p r o c e s s is a p o t e n t i a l danger w i t h t i l t i n g pad j o u r n a l b e a r i n g s [l]. With t h i s t y p e of b e a r i n g , t h e o n l y conduction p a t h from t h e f i l m t o t h e h o u s i n g i s through t h e p i v o t s , c o n s e q u e n t l y t h e h o u s i n g t e m p e r a t u r e and b o r e s i z e i s o n l y s l i g h t l y i n c r e a s e d f o l l o w i n g a r i s e i n speed. However t h e s h a f t w i l l expand outwards, w h i l e t h e pads w i l l expand "inwards," which under normal c i r cumstances w i l l i n c r e a s e t h e b e a r i n g p r e l o a d . Examples o f u n s t a b l e increase are g i v e n by Conway- Jones and Leopard [11.

I

10-3

Fouriw Number($) 9

When t h e expansion o r c o n t r a c t i o n is complete, t h e thermal s t r a i n i s CY ATF and e; = 1.

F

I 10-

10

&

The T r a n s i e n t Thermal D e f l e c t i o n o f a S t e e l Beam S u b j e c t t o a Sudden Temperat u r e I n c r e a s e on one Face

peak q u i t e e a r l y i n t h e p r o c e s s a t F = 0.086 and s u b s e q u e n t l y d e c r e a s e s as e q u i l i b r i u m i s established This perhaps unexpected b e h a v i o r h a s been v e r i f i e d e x p e r i m e n t a l l y by Zerbe [21, u s i n g beams o f v a r i o u s materials, h e a t e d suddenly on one f a c e by a stream o f h o t water under l a m i n a r flow c o n d i t i o n s . The c o n v e c t i o n c o e f f i c i e n t G f o r flow o v e r a p l a t e h a s been w i d e l y r e s e a r c h e d . The c l o s e d form r e s u l t f o r G was used i n s u b s e quent c a l c u l a t i o n of t h e N u s s e l t number, GH/k where H is t h e t h i c k n e s s of t h e beam. F i g u r e 4 shows Z e r b e ' s e x p e r i m e n t a l r e s u l t s o f peak d e f l e c t i o n and t i m e t o peak d e f l e c t i o n a g a i n s t t h e t h e o r e t i c a l c u r v e s . The agreement is q u i t e good, a l t h o u g h n o t many d a t a p o i n t s a r e shown. The r e s u l t s of F i g u r e s 3 and 4 i n d i c a t e t h a t t r a n s i e n t thermal d e f l e c t i o n i n a t h r u s t b e a r i n g might p r e c i p i t a t e f a i l u r e i f t h e pads a r e a l r e a d y h i g h l y deformed from t h e r m a l c a u s e s b e f o r e some change i n t h e o p e r a t i n g c o n d i t i o n s i s made.

.

3. NUMERICAL MODEL OF TRANSIENT CONDITIONS The s i m p l e s o l u t i o n s i n t h e p r e v i o u s sect i o n a r e u s e f u l f o r g i v i n g guidance as t o t h e i m p o r t a n t p a r a m e t e r s and boundary c o n d i t i o n s , b u t i n p r a c t i c e t h e f i l m and t h e two components a r e coupled, which is b e s t t r e a t e d n u m e r i c a l l y . A n u m e r i c a l s o l u t i o n c a n g i v e more r e a l i s t i c p r e d i c t i o n s a l t h o u g h , a s i s usual i n any thermohydrodynamic a n a l y s i s , g e n e r a l i t y is l o s t . Previous n u m e r i c a l models o f t r a n s i e n t e f f e c t s have been d e s c r i b e d by Ezzat and Rhode [SI f o r t h r u s t b e a r i n g s and by Czeguhn [41 f o r j:ournal bearings.

232

-

Beam response 0.4 -

-

Deflection 04

I

1

90 0.3 -

- 03

0.2 -

- 02

I

..^

L

a

70 V

-65

01

a

01

- 60 v) b c 1

10

100

701 0.001

1000

HG/k

Fig.4

2

u-

0.1 -

I

I

I

I

0.a

0.I

I

10

(a)

a ) The thermal i n e r t i a o f t h e film i s neglected. A t the completion of a time s t e p , a new film shape and film temperature d i s t r i b u t i o n a r e found t o s a t i s f y t h e c u r r e n t load r e q u i r e ment. During t h i s i t e r a t i o n the s u r f a c e tempera t u r e of t h e pad and r o t o r a r e rpaintained cons t a n t and t h e temperature w i t h i n t h e film i s allowed t o vary. A t t h e completion of t h i s i t e r a t i o n t h e l o c a l h e a t f l u x a t t h e boundaries of t h e s o l i d components i s known, which allows t h e next t i m e s t e p t o be made. b ) The t i m e s t e p i s made by c a l c u l a t i n g the new temperature d i s t r i b u t i o n s i n t h e shoe and r o t o r , using the updated f l u x values a t t h e boundaries. c ) The temperature i n t h e f i l m i s then reevaluated as i n a ) , using the updated s u r f a c e The operations i n a ) , b ) form temperatures, those f o r a time s t e p . d ) Thennoelastic d e f l e c t i o n of the shoe i s considered, t o g e t h e r w i t h h o t o i l carryover. Reverse flow i s allowable and i s accommodated by up-winding. More complete d e t a i l s a r e given i n [51. Figures 5a,b show t h e change i n bearing temperature, d e f l e c t i o n and minimum film t h i c k ness consequent t o a sudden doubling of t h e load a t constant speed. The r e s u l t s a r e p l o t t e d t o a base of Fourier number, where t h e charact e r i s t i c dimension i s H = 30 mm and i s t h e shoe o r r o t o r thickness ( s e t equal f o r a l l cases t o be shown). A time s c a l e i n seconds i s a l s o given, and t h e expected equilibrium temperatures a t t h e end of the t r a n s i e n t period a r e i n d i c a t e d . The d e f l e c t i o n reaches a s l i g h t peak a t F w 0.2, which corresponds approximately t o t h e behavior of a beam, as discussed i n t h e previous s e c t i o n . Figure 5c shows a c o r r e sponding c a s e where t h e load i s suddenly halved.

__ K

Sec

The Peak Thermal Deflection of a Beam and t h e T i m e Required f o r Peak Deflection t o Occur. The p o i n t s a r e experimental d a t a and t h e curves are r e s u l t s of a numerical model.

m e r e s u l t s shown i n t h i s p r e s e n t paper a r e taken from E t t l e s [51, and concern a t h r u s t beari n g viewed i n elevation. This allows t h e approp r i a t e f l u x c o n t i n u i t y conditions t o be applied a t the f l u i d - s o l i d i n t e r f a c e s and a t the e x t e r i o r surfaces. The a n a l y s i s i s two-dimensional, with coordinates normal t o the f i l m (and through the pad and r o t o r ) and i n the d i r e c t i o n of s l i d i n g . The equation of t r a n s i e n t h e a t conduction i s solved i n t h e pad and r o t o r a t each t i m e s t e p . The a n a l y s i s has t h e s e f e a t u r e s :

(%&

Fourier Number

L

0.01

30.001

10

0.I

Fourlar Number

(b)

Sec I

75.0;

15

PC

10

100

200

Y

Y

e

Rota 7

0

L

-

u

-

~

-56; -55 5 _.__ 54 v, - 53 - 52

5

B

e Max in film

-

6010 001 (c)

Fig.5

I 0.01

I 0.I Fourier Number

I

I

I

10

$1

Model Result Showing Changes i n (a) Temp e r a t u r e and (b) Deflection and Minimum Film Thickness i n a Thrust Bearing, Following a Step I n c r e a s e i n Load from 2.8 t o 5.6 MPa. The pad i s 120 mm long and 30 mm thick, speed i s 30 m/s. ( c ) (c) Changes i n temperature of same beari n g when load i s halved from 1.4 MPa.

Figure 6 shows a s i m i l a r r e s u l t f o r a much l a r g e r pad of 250 mm thickness. The s i m i l a r i t y w i t h Figure 5 i s q u i t e s t r i k i n g . I n both cases the p r o p o r t i o n a l changes of temperature AT/ATF appear t o be c o r r e l a t e d a g a i n s t the Fourier number. ?%is suggested a p o s s i b l e treatment o f experimental r e s u l t s , i n which t h e p r o p o r t i o n a l temperature r i s e i s p l o t t e d a g a i n s t Fourier

233 number, u s i n g t h e t h i c k n e s s o f t h e pads o r r o t o r (whichever b e i n g t h e g r e a t e r ) as t h e c h a r a c t e r i s t i c dimension.

4.

This g i v e s t h e f o l l o w i n g nondimensional times F f o r 50%, 70% and 90% r e s p o n s e :

EXPERIMENTAL RESULTS

4.1

Thrust Bearings

The a u t h o r s were a b l e t o c o l l e c t t r a n s i e n t r e s u l t s for s i x bearing assemblies t h a t varied i n s i z e by a b o u t a n o r d e r o f magnitude. Two s e t s o f r e s u l t s a p p e a r i n t h e open l i t e r a t u r e [6,71. The remainder a r e p r o p r i e t a r y . Figure 7 s h o w s - t e m p e r a t u r e d a t a from Chambers and Mikula [6], t a k e n d u r i n g t h e s t a r t up of a h y d r o e l e c t r i c t u r b i n e . The t h i c k n e s s o f t h e pad H is a p p r o x i m a t e l y 80 mm. The r e s u l t s shown a r e f o r a thermocouple on t h e mid r a d i u s w i t h i n 9 . 7 nun o f t h e f a c e . The measurement p o i n t i s s u f f i c i e n t l y f a r from t h e f i l m t o "damp" t h e s h a r p i n i t i a l r i s e shown i n t h e model s o l u t i o n s . The r e s p o n s e , i n t h e form AT/ATF, resembles t h e model s o l u t i o n s . The

% Response

F

50 70 90

0.433 0.752 1.44

dashed l i n e i s t h e c h a r a c t e r i s t i c : -1.89 F 1-e

(7)

which i s s e t t o p a s s through t h e 60% r e s p o n s e p o i n t . The matching of t h i s c u r v e w i t h t h e e x p e r i m e n t a l d a t a i s q u i t e good.

Fig.6

Fig.7

The I n c r e s e of T h r u s t B e a r i n g Temperature Following t h e S t a r t - u p o f a Hydrogenera t o r . The t e m p e r a t u r e i s measured on t h e mid r a d i u s a t a p p r o x i m a t e l y t h e 70% p o s i t i o n . The dashed l i n e i s t h e e x p o n e n t i a l From Chambers and Mikula law, E q . ( 7 ) . [61.

Model R e s u l t Showing Changes i n Temperat u r e f o r a Large Shoe (Length 1 m, Thickness 250 mm) Subsequent t o a Sudden I n c r e a s e i n Load from 1.8 MPa t o 3.6MPa. (The arrows show known a s y m p t o t i c values. )

To f u r t h e r check t h e u s e of t h e F o u r i e r number a s a common time scale, t h e 50% r e s p o n s e t i m e of a l l s i x b e a r i n g s was p l o t t e d a g a i n s t t h e pad t h i c k n e s s H, as shown i n F i g u r e 8 . The l i n e drawn through t h e p o i n t s h a s t h e c h a r a c t e r i s t i c t a H2, and f o r t h e d a t a shown:

Ax=1 ATF

-1.6 - e

F

Fig.8

The 50% Response Time o f S i x T h r u s t B e a r i n g Assemblies P l o t t e d A g a i n s t t h e Pad Thickness H. The open t r i a n g l e s a r e f o r h y d r o g e n e r a t o r u n i t s . The numbers 6, 7 a r e r e f e r e n c e s .

234

The r e a s o n a b l e c o n c u r r e n c e o f t h e d a t a p o i n t s i n F i g u r e 8 w i t h H2 must, t o some e x t e n t , be f o r t i t o u s . For t h e h y d r o g e n e r a t o r b e a r i n g s (shown as open t r i a n g l e s ) t h e r o t o r t h i c k n e s s is d i f f i c u l t t o estimate since the t h r u s t runner r i n g i s l o c a t e d a g a i n s t a massive s h o u l d e r on t h e s h a f t . In g e n e r a l , t h e r o t o r t h i c k n e s s c a n b e t a k e n a s a b o u t t w i c e t h a t of t h e pads. 4.2

The same t y p e o f b e h a v i o u r i s shown f o r t h i s b e a r i n g on rundown, F i g u r e 10a, where a = 4.58. Agreement w i t h t h e e x p o n e n t i a l l a w i s l e s s good f o r F i g u r e l o b , t h a t shows t h e rundown o f a 305 mm j o u r n a l b e a r i n g . The a v e r a g e t e m p e r a t u r e from s e v e r a l thermocouples c l o s e t o t h e f i l m i s p l o t t e d a g a i n s t t i m e and a g a i n s t F o u r i e r number. For t h e dashed l i n e shown, a = 9.21.

Journal Bearings

F i g u r e s 9a,b show t h e t e m p e r a t u r e i n c r e a s e a t a p o i n t c l o s e t o t h e f i l m o f a t i l t i n g pad j o u r n a l b e a r i n g , These d a t a a r e f o r a 76 mm b e a r i n g w i t h f i v e c e n t r a l l y p i v o t e d pads, no p r e l o a d and a c l e a r a n c e r a t i o o f 0.00157 ( 6 = 1 . 5 7 ) . The thermocouple was l o c a t e d a t t h e 65% p o s i t i o n i n t h e h o t t e s t pad. The c e n t r e o f t h e thermocouple j u n c t i o n was a b o u t 1.5 mm from t h e f i l m . The b e a r i n g and t e s t r i g a r e d e s c r i b e d i n [81. The two r e s u l t s shown a r e f o r sudden speed i n c r e a s e s from d i f f e r e n t i n i t i a l conditions. In t h e e x p o n e n t i a l e x p r e s s i o n

-AT= l - e ATF

2

1

1

t h e exponent a i s 4.58 f o r F i g u r e 9a and 5.73 f o r Figure 9.b. The r a d i u s o f t h e s h a f t i s used as t h e dimension i n F. The c o n c u r r e n c e o f t h e e x p e r i m e n t a l r e s u l t s w i t h t h e e x p o n e n t i a l law i s quite close.

20 3040 '

1

'

100 I

1

200

'

Tilting Pad Jrnl Erg 2 05 MPa : 90 9000 RPM 1800 RPM

-

685

y

: z2 -80

04-

1

2

1 7 5

:

06-

-70

E EF

08-

: 85

ioI

.

,

I I I I I I I

I

,,"In

1

The Local Temperature i n a 76 mn T i l t i n g Pad J o u r n a l B e a r i n g Following a Sudden Decrease of Speed a t C o n s t a n t Load

Fig.lOa

-aF

3 4 5 6 810

Seconds f r o m Start of Record I

120

100

10

1

- b

start of event

'

1000 '

' " , ' . ' I

1

'

"

'

Pedestal Type Jrnl Brg , 2 05 MPa 2650 RPM 200 RPM

-

3000

Seconds 2

1

3 4 5 6 810 I

20 3040 60 80100 ~

~

Tilting Pad Jrnl E r g , 2 05 MPa

'

l

200 1'

t

-!L

/'

,,,I 62

,

Ol;

, , ,

,,,,I

,

,

, ,

10

Seconds 1

2

3 4 5 6 810 I

10

20 3040 6080100 ' " " I

Fig.LUb

.L R2

(where t is f r o m start of event)

The Average Temperature i n a 305 mm J o u r n a l B e a r i n g Following a Sudden Decrease i n Speed a t C o n s t a n t Load

5 . DISCUSSION AND CONCLUSIONS

200 '

- Tilting Pad Jrnl E r g , 2 05 MPa - 5000 RPM - 9000 RPM

PC

I

b

-92

- 88

The d e c a y t i m e of t h e r m a l t r a n s i e n t s i n a b e a r i n g assembly i s o f p r a c t i c a l i n t e r e s t s i n c e a ) Errors can arise i n laboratory o r f i e l d tests i f p r e m a t u r e r e a d i n g s a r e made. b ) Temporary r e d u c t i o n s i n c l e a r a n c e (below t h e e q u i l i b r i u m v a l u e ) c a n occur i n j o u r n a l b e a r i n g s following a change t o more severe c o n d i t i o n s . c ) Thermal d e f l e c t i o n o f t h r u s t s h o e s c a n o c c u r t h a t exceed t h e e q u i l i brium v a l u e .

Fig.9

The L o c a l Temperature i n a 76 Pad J o u r n a l B e a r i n g Following I n c r e a s e of Speed a t C o n s t a n t ( a ) 1 8 0 0 - 5000 rpm, ( b ) 5000-

nun T i l t i n g a Sudden Load. 9000 rpm.

Some guidance as t o e l a p s e d t i m e and t r a n s i e n t t h e r m a l d e f o r m a t i o n may b e found i n t h e c l a s s i c a l s o l u t i o n s o f s i m p l e s h a p e s . It i s d i f f i c u l t t o o b t a i n q u a n t i t a t i v e d a t a from t h e s e s o l u t i o n s , due t o u n c e r t a i n t i e s i n t h e e f f e c t i v e N u s s e l t number. The N u s s e l t number d i r e c t l y a f f e c t s the f l u x at the surfaces. U n f o r t u n a t e l y t h e c l o s e d form s o l u t i o n s f o r Nuf

235 f o r flow between p l a t e s c a n o n l y g i v e a n upper bound v a l u e . I n F i g u r e s 1 and 2 t h e upper bound o f Nu i s a b o u t 10 f o r a j o u r n a l b e a r i n g . P r a c t i c a l values f o r journal bearing assemblies a p p e a r t o b e i n t h e r a n g e 1 5. These u n c e r t a i n t i e s d o n o t a r i s e i n a numerical s o l u t i o n t h a t c o u p l e s t h e film, j o u r n a l and b e a r i n g , a l t h o u g h t h e complexity i s i n c r e a s e d . I n p a r t i c u l a r cases, i n v o l v i n g thermal r a t c h e t t i n g o r u n f a v o u r a b l e pad deformation, i t may be w o r t h w h i l e t o d e v e l o p a n u m e r i c a l model s o t h a t v a r i o u s o p t i o n s may b e explored. The n u m e r i c a l models developed h e r e c o n s i d e r o n l y t h e f i l m and t h e two components bounding t h e f i l m . I t i s assumed t h a t t h e l u b r i c a n t s u p p l y t e m p e r a t u r e ( o r chamber temp e r a t u r e ) i s u n a f f e c t e d by t h e change i n o p e r a t i n g c o n d i t i o n s , This w i l l n o t b e t h e case i n some s e l f - c o n t a i n e d b e a r i n g a s s e m b l i e s t h a t i n c l u d e a sump w i t h p a r t i a l c o o l i n g o r c o o l i n g by c o n v e c t i o n t o ambient. I n t h e s e c a s e s a t h i r d t h e r m a l mass should b e i n c l u d e d ( i n a d d i t i o n t o t h e two bounding components). I n most cases i t w i l l be d i f f i c u l t t o quantify the " t h i r d mass'' e f f e c t , e x c e p t by experiment. I n some o f t h e d a t a g a t h e r e d f o r t h i s paper, t h e c o o l i n g t i m e f o r a n assembly was ( f o r some a s s e m b l i e s o n l y ) a b o u t t w i c e a s l o n g a s t h e h e a t i n g t i m e . This d i f f e r e n c e i n h e a t i n g and c o o l i n g rates was less f o r smaller s t e p changes i n c o n d i t i o n s . The m a j o r i t y o f t h e e x p e r i m e n t a l d a t a c o u l d be matched f a i r l y w e l l w i t h a n e x p o n e n t i a l l a w of t h e form o f Eq.(9). This i m p l i e s t h a t each f l u i d f i l m b e a r i n g h a s a " t i m e c o n s t a n t , " and t h a t t h e decay time f o r , s a y , a 90% change i s u n a f f e o t e d by t h e magnitude o f t h e change. change.

-

REFERENCES

1.

2.

3.

4.

5. 6.

7.

8.

,

Conway-Jones J . M . and Leopard, A. J . , " P l a i n Bearing Damage," Proc. Fourth Turbomachinery Symposium, Gas Turbine L a b o r a t o r i e s , Texas A & M U n i v e r s i t y , C o l l e g e S t a t i o n , Texas, October 1976, 59-63. Zerbe, Glenn H., " T r a n s i e n t Thermal R e f l e c t i o n s o f a C a n t i l e v e r Beam," S e n i o r P r o j e c t , Dept. o f Mech. Engr., R e n s s e l a e r P o l y t e c h n i c I n s t . , Troy, NY, 1987. Ezzat, H.A. and Rohde, S.M., "Thermal T r a n s i e n t s i n F i n i t e S l i d e r Bearing," ASME J r n l . o f Lubn. Tech., 96, J u l y 1 9 7 4 , 315-321. Czeguhn, K., " V a r i a b i l i t y w i t h Time o f B e a r i n g C l e a r a n c e Due t o Temperature and P r e s s u r e , " Proc. I n s t . o f Mech. Engrs., 1966-67, 187, P a r t 30, pp.216-223. E t t l e s , C.M.M., "Transient Thennoelastic E f f e c t s i n F l u i d Film B e a r i n g s , " Wear, 79, 1982, 53-71. Chambers, W.S. and Mikula, A.M., "Operat i o n a l Data f o r a Large V e r t i c a l T h r u s t B e a r i n g i n a Pumped S t o r a g e A p p l i c a t i o n , " Trans. STLE, 3, 1988, 61-65. Nelson, D.V., P l m e r , M.C. and McCulloch, R.C., "Overload Performance T e s t i n g and E v a l u a t i o n o f a Hydrogenerator T i l t i n g Pad T h r u s t Bearing," Proc. American Power Conference, 46, 1984, 1057-1062. Brockwell, K.R. and h o c h o w s k i , V., "Calcul a t i o n and Measurement of t h e S t e a d y S t a t e O p e r a t i n g C h a r a c t e r i s t i c s o f t h e Five Shoe T i l t i n g Pad J o u r n a l B e a r i n g , " Proceedings of t h i s Conference.


237

PaperVI II(iv)

Design procedures basedon numerical methodsfor hydrodynamic lubrication J. 0. Medwell

T h i s p a p e r p r e s e n t s a r e v i e w of numerical schemes for predicting the performance of cylindrical bore journal bearings which have been developed under the initial guidance of F. T. Barwell at Swansea. The schemes are based on the finite element and finite difference methods which are used t o solve the lubricant momentum and energy equations. T h e effects of recirculatory flow, bush conduction and deformation, shaft expansion and misalignment have been considered.

INTRODUCTION B C

P

=

-

C

DP

P r R Re T U

U V W X,Y,Z

8

V' al

B e fl Y Y

X

Y Y

z

8 l . U P Q,

@ 0

si

bush thickness radical clearance specific heat journal diameter Young's Modulus local film thickness thermal conductivity bearing length mesh coordinate point local pressure radial coordinate journal radius WRC film Reynolds number [= 7 1 temper at u r e v e l o c i t y c o m p o n e n t in x direct ion velocity vector ui + U] + wk v e l o c i t y c o m p o n e n t in y d i rec t i on v e l o c i t y c o m p o n e n t in z direct ion Cartesian coordinates see Figure l(a) or circumferential coordinate the Laplacian operator see Figure l(a) see Figure l(a) eccentricity ratio molecular viscosity kinematic viscosity turbulent viscosity turbulent viscosity Poisson's ratio parametric coordinate directions lubricant density see Figure l(a) disslpatlon function rotational speed

The theory of operation of hydrodynamic j o u r n a l b e a r i n g s w a s we1 1 established by Reynolds over a century ago. H o w e v e r , a s p o i n t e d o u t b y B a r w e l l et a 1 [ I ] the application of this theory to design w a s not simple because I t is not possible to o b t a i n a general analytical solution to the Reynolds equation i t i s d i f f i c u l t to provide the correct value of viscosity for use in the e q u a t i o n because of its temperature dependence. Strictly, s i n c e large differences in temperature can arise the consequent variation of viscosity can only be determined by i n c l u d i n g the energy equation, c o n t a i n i n g t h e a s s o c i at ed dissipative terms, in the design procedure. This usually involves u s i n g i t e r a t i v e t e c h n i q u e s in order that the Reynolds and the e n e r g y e q u a t i o n s can be solved simultaneously.

t h e a v a i l a b i l i t y of modern day numerical and computational methods, this does not p o s e a n y particular problem. The numerical techniques which have been used most o f t e n a r e f i n i t e d i f f e r e n c e methods a n d , latterly, in the last decade or so, finite element methods. The former has been used in the generation of design charts and also forms t h e b a s i s of s o f t w a r e s e r v i c e s such as provided by ESDU. However, although these may be u s e d w i t h confidence in normal journal bearing d e s i g n c a l c u l a t i o n s t h e y c a n b e suspect w h e n o f f design conditions are met. Typical of these are: recirculatory flows that can occur in the highly eccentric lobes

of profile bore bearings, shaft misalignment and t h e r m o - e l a s t i c distortion in bearing bushes and shafts. T h i s p a p e r will d'iscuss h o w t h e s e conditions may be incorporated into standard numerical design procedures that have been developed, initiated by the late Professor F T Barwell. at Swansea. In this respect most of the b o u n d a r y conditions imposed in the solution procedures relate t o t h e e x t e n s i v e e x p e r i m e n t a l p r o g r a m m e s that h a v e been carried out in Swansea. These have b e e n c o n c e r n e d w i t h a s s e s s i n g t h e p e r f o r m a n c e of s t a n d a r d cylindrical bearings which w e r e fed by two diametrically opposed axial grooves at 90' to the load line as shown in Figures ](a) and I(b). Wide ranges of speeds (both laminar and turbulent lubricant films) clearance ratios and load capacities were investigated (see Ref [2]). However, in the interests of brevity, detailed boundary conditions have been omitted and attention focused on the governing equations and solution strategies. Design Procedures The equations of motion and energy of an incompressible lubricant flow are based on the conservation l a w s of m a s s , m o m e n t u m and e n e r g y . Generally, the three dimensional momentum equations may be written as

[31 and continuity 0.u

= 0

[41

Similarly, the energy equation may be written as pCp W.T

=

kV2T +

U@

In t h e above equations the lubricant film has been assumed to be laminar in motion and therefore the transport quantities (u and k) and the viscous dissipation term @ reflect t h e s t r e a m l i n e nature of the flow. I t is possible with extensive modification to cast the equations in a form suitable for turbulent motion. This can be accomplished by replacing the molecular properties w i t h corresponding t u r b u l e n t v a l u e s , and t h e n i n t r o d u c i n g a p p r o p r i a t e models to describe them. The additional e q u a t i o n s r e q u i r e d g e n e r a l l y i n c r e a s e s the difficulties in obtaining a solution to such problems. However, as mentioned earlier, in many practical applications the above equations can be s i m p l i f i e d c o n s i d e r a b l y by making appropriate assumptions. Typical of these are the neglect of cross stream velocities, all

fluid advection terms, all conduction effects in the lubricant film. Thus the problem is reduced to solving the Reynolds equation and an energy equation which simply balances the generated heat with that convected through the f i l m . A d d i t i o n a l l y , t u r b u l e n c e c a n be accounted for by r e p l a c i n g t h e m o l e c u l a r v i s c o s i t y by e x p r e s s i o n s that m o d i f y i t depending on the position considered in the film [3]. The above e q u a t i o n s m u s t be solved s u b j e c t t o t h e v a r i o u s i m p o s e d boundary conditions which will depend on the type of equations to be solved. For example, in their i n v e s t i g a t i o n of t h e r o l e o f i n e r t i a in lubricant films, Medwell et a1 [4] used the finite element method w h i c h , because of the elliptic nature of the equations of motion, required t h e s p e c i f i c a t i o n s i x b o u n d a r y values. These were either prescribed or cast in the form of gradients a n d , in some cases, updated during the solution procedure since t h e y c o u l d not b e s t a t e d a p r i o r i . A s mentioned earlier, the solution procedure is necessarily iterative in form because of the dependence of the lubricant film profile on the bearing attitude a n g l e and t h e r e f o r e r e q u i r e s c o n t i n u o u s u p d a t i n g . In t h e s e investigations the three dimensional films profile w a s generated conveniently by scaling a unit cube (suitably discretized) to produce the a p p r o p r i a t e film geometry through the relationships

w h e r e the overbar denotes a fixed coordinate. T h i s technique w a s first proposed by Gethin [ 2 ] and has been s u b s e q u e n t l y u s e d successfully in analysing other performance aspects of journal bearing operation [5], [6] and [7]. In all analyses i t is c o n v e n i e n t t o unwind the loaded part of the lubricant film because the radius of curvature of the film is v e r y l a r g e in c o m p a r i s o n w i t h t h e f i l m thickness Figures l(a) and l(b) s h o w s t h e journal bearing geometry and the unwrapped film discretized in a form suitable for the f i n i t e e l e m e n t m e t h o d of solution, using eight-node isoparametric elements. If heat conduction in the journal bush is important it is necessary t o include the appropriate f o r m of the energy equation and boundary conditions into the solution viz.

V'T

=

0

[81

wlth the inclusion of conduction terms in the fluid film also. A suitable discretization of the bush is also depicted on Figure l(c).

239 So far, the equations that have b e e n d i s c u s s e d a r e f u l l y three dimensional in nature and reference has only been made to the finite element method of solution. This i s because finite difference methods [ 8 ] and [ 9 ] solve parabolized form of the equations of motion w i t h solution stability being maintained using upwind techniques. Where recirculatory flows occur the v a l i d i t y o f these procedures becomes questionable. The importance of recirculatory flows has been demonstrated for isothermal lubricant films [ 4 ] by solving the equations of motion in which only fluid advertion across the film w a s ne.glected. A l t h o u g h t h e a n a l y s i s c o n f i r m e d that lubricant inertia does not affect bearing performance significantly i t does indicate that large areas of recirculation occur at h i g h e c c e n t r i c i t y ratios as shown on Figure 2. As pointed out earlier, this phenomena can be expected to appear in the lobes of profile bore bearings which can be operating in a highly eccentric c o n d i t i o n even though the overall bearing eccentricity is modest. T h e p r o b l e m in the type of rigorous analysis mentioned above is that i t can be e x p e n s i v e to compute and which can become prohibitive if thermal and elastic behaviour are included. Obviously, it i s important to the designer to use methods which will compare favourably with both the rigorous analyses and experimentally determined performances and be e c o n o m i c c o m p u t a t i o n a l l y . A n excellent exposition of this has been given by Gethin [5] w h o presented two models. One was based o n the s o l u t i o n of t h e f u l l e q u a t i o n s including bush conduction (i.e. equations 1 4 and 8) and in the other the equations of motion w e r e reduced to a generalized Reynolds equation, viz.

a

[Gg] +a z[ G g ]

= O R zdh iji-

dF dx

r91

where G

=

1:

(y-F)dy; F

=

FI FO

where

A consequence of embodying the laws of c o n s e r v a t i o n of m a s s and momentum into a Reynolds equation is the simplification of the boundary conditions which were now in the form of specified pressrues or gradients o f pressure. The imposition of several different thermal boundary conditions w a s assessed and discussed fully while the viscosity dependence on temperature was 'inbuilt' into the solution procedure in the form of the Walther equation. The strategy for the solution of both s e t s o f e q u a t i o n s w a s b r o a d l y the s a m e consisting of the follawing basic steps: (i)

the bearing geometry and boundary conditions for the hydrodynamic e q u a t i o n s w e r e s e t up for a n assumed value of attitude angle

which w a s used to generate a film thickness profile for a specified eccentricity ratio. The film thickness equation used was

h = C (1 +

E COS

(0 +

01

- fb)}

1101

(11) the load w a s calculated and the n e w attitude angle w a s evaluated which was then used to update the film geometry. This procedure was repeated unt i 1 convergence w a s achieved and any parameters such as velocity g r a d i e n t s and/or pressure gradients that may be required for s u b s i t u t i o n into the energy equation were calculated. (iii) the boundary conditions for the energy equation w e r e set u p and this w a s solved to give temperature distributions. (iv) the nodal values of viscosity were updated throughout the film and t h e s t e p s ( i ) , (ii), ( i i i ) and ( i v ) repeated until e i t h e r t h e velocity o r pressure fields converge to a p r e s c r i b e d tolerance. Some of the results from the two models are displayed on Figures 3 and 4 together with some experimental results. I t can be seen that generally the more sophisticated model does not p r e d i c t r e s u l t s w h i c h a r e s i g n i f i c a n t l y more accurate than those predicted by the method based o n R e y n o l d s e q u a t i o n . However, in terms of computing requirements the latter model used just 10% of the CPU time of the more rigorous analysis - a very significant saving. T h e s i m u l t a n e o u s solution of the Reynolds and energy equations using the above s t r a t e g y f o r m s t h e b a s i s f o r m a n y other journal bearing performance predictions using b o t h f i n i t e element and finite difference techniques. It w a s first used [ l o ] to assess the influence of heat dissipation in high speed b e a r i n g s w h e r e t h e lubricant f i l m w a s in turbulent motion. Thus was done by using very crude turbulence models [ 3 ] , viz. uX = and

Y

(1 +

0.000175 Re

1.06

uZ = u ( 1 + 0.000375 Re

)

1.08

)

to replace molecular viscosity terms in the R e y n o l d s e q u a t i o n s . T h e energy equation employed neglected crossfilm and streamwise cnduction effects (the adiabatic condition) which r e s u l t s in t h e t e m p e r a t u r e o f t h e lubricant film at any point being represented by a mean value. Both equations were cast in conventional finite d i f f e r e n c e f o r m b a s e d o n c e n t r a l differences. The Reynolds equation was solved

240

90

L

E l

\A

la)

Solution of full equation Solution based on Reynolds equation Experiment

(b)

--0

Journal bearing geometry Shaft surface

Unwrapped lubricant film and finite element mesh f o r fluid and solid FIGURE 1 12 l6

1I 0

/

Isothermal

02

01

04

03

05

07

06

08

E FIGURE 2

RECIRCULATING FLOW AT BEARING INLET

Solution of f u l l equation Solution based on Reynolds equation

FIGURE 5

THEORETICAL VARIATION OF LOAD WITH ECCENTRICITY RATIO FOR ISOTHERMAL AND ADIABATIC FLOW SPEED = 30,000 rev/min

--_

10

-

5

Isothermal

-

0

03

05

07

09

Eccentricity r a t i o FIGURE 3

VARIATION OF LOAD WITH ECCENTRICITY RATIO Bearing speed = 10,000 rev/min.

$

0.002 ,

‘/R = 1.0

0 1 0

I

I

I

I

I

I

10

20

30

40

50

60

Speed FIGURE 6

(x

lo3 rev/min.)

THEORETICAL VARIATION OF LOAD WITH SPEED FOR ISOTHERMAL AND ADIABATIC FLOW. E = 0.7

24 1

using a Gauss Seidel iterative technique while the simpler form of the energy equation allowed a straight through march to be used in obtaining a solution.

In polar coordinates the radical and circumferential components of strain w e r e written in terms of a displacement matrix as

Some of the findings of the investigation are displayed on Figures 5 and 6 .

1

The above method was extended by Medwell and Gethin [ll] to account for off-design bearing operation such as misalignment. Identical Reynolds and energy equations were solved using the same models of turbulent viscosity and employing a modified film thickness equation which included an extra term to account for the misalignment. This i s measured as the inclination of the shaft axis to that of the bush and is measured in the plane in which the shaft i s loaded. The main consequence of misalignment i s shown in Figure 7 where maximum and bulk temperatures of the lubricant film are plotted as a function speed for an eccentricity of 0 . 6 5 and a misalignment angle of only 0.12'. I t can be seen that although the bulk temperatures exhibit modest rises over the inlet lubricant temperature the maximum temperatures generated are dangerously high and would certaily be a limiting parameter in such a bearing operation and which confirms the importance of misalignment effects in journal bearing applications.

Generally, when both finite element and finite difference methods are applied to similar problems as above, it is found that the difference methods are less demanding on computational requirements. However, as pointed out earlier, when recirculatory flow occur,s the governing equations lose their parabolic form and the vality of upwind techniques introduced to achieve solution stability in the difference methods becomes questionable. A further disadvantage of the finite difference method is its inability to cope efficiently with coupled problems such as those where bush conduction and thermo-elastic deformations are important. I t is in these types of situations that the finite element method is particularly effective. This derives from the capacity of the method to cope which property changes in adjacent elements either side of the fluidsolid interface that makes i t extremely attractive to designers. An excellent example of this has been given by Gethin [12] in his theoretical investigation into the effect of thermoplastic bush deformation and shaft thermal e x p a n s i o n o n j o u r n a l bearing performance. He accounted for the distortion of the bush due to the temperature and pressure fields by introducing the relevant equations of solid mechanics. However, based on experimental evidence, computational economy w a s achieved by assuming that the distortion occurring on the bearing centre line only could be applied over the entire width of the bearing.

I

I

1

II

l a

The stresses were related to strain by the constitutive equations

or {o} = [D] {el}

[I21

where e l ,as and 7 arise from the applied r6 pressure and thermal loading. Applying an energy minimization principle and equations ( 1 1 ) and (12) an expression of the following form was obtained In[BIT[D]

[B] (6)dQ

=

I I

pdQ - qdr

[I31

or [Kl (6)= {F} which can be solved for {a}, the displacement of the domain. In equation ( 1 3 ) the integral over the solid domain includes the thermal loading while the surface integral over r contains contributions arising from the imposed pressure that is at an elemental level.

where f(T) i s the temperature field over the element edge. Similarly

where f(p) is the pressure field over the element edge. The applied pressure obtained from solution of the equations while the thermal determined from solution of equation in the bush.

loading w a s hydrodynamic loading was the e n e r g y

A further a s s u m p t i o n m a d e in the analysis was that the bush was constrained in a rigid housing s o that the computational domain was confined to the load carrying zone of the bearing. The solution procedure follows that outlined earlier with the additional steps requried to calculate the distortion of the bush and shaft expansion which were then included in the calculation of the new film thickness. Gethin presented a large amount of data to illustrate the e f f e c t o f i n c l u d i n g distortion for a wide range of speeds (he assumed that the film w a s turbulent) and

242

which highlight the success of his method is the maximum film temperature variation with shaft speed as shown on Figure 8.

10. Bowen, E.R. a n d M e d w e l l J . O . ; "A therrnohydrodynamic analysis of journal bearings operating under turbulent conditions." Wear, Vo1.51, 345, 1977.

CONCLUSIQNS This paper has been concerned with the u s e of finite element and finite difference methods in the prediction of journal bearing performances. Several aspects of journal bearing operation have been considered and i t is concluded that the finite element method is a very powerful design tool which can cope w i t h many a.spects of bearing behaviour hitherto neglected.

11. Medwell, J . O . a n d G e t h i n , D . T . ; "Synthesis of thermal effects in misaligned hydrodynamic j o u r n a l bearings". Int. J. Num. Methods in Fluids, Vo1.6, 445, 1986. 12. Gethin, D.T.; "An investigation into plain journal bearing b e h a v i o u r inlcuding thermo-elastic deformation of the bush." Proc. Instrn. Mech. Engrs. Vo1.199, 215, 1985.

REFERENCES 1. Barwell, F.T. and Medwell, J.O.; "Journal B e a r i n g C a 1 cul a t ions" , Euromech

Maximum temperature

Colloquium No. 1 2 4 , T u r i n , Italy, 1979. 2.

Gethin, D.T.; "Superlaminar f l o w i n j o u r n a l bearings" PhD Thesis, University of Wales, 1983.

150

U

e E! +

2

3. Ng, C.N. and Pan, C.H.T.; "A linearised turbulent lubrication theory." Trans. A S M E , J . Basic Engineering. Vol. 87.675.1965. 4. Medwell, J.O., Gethin D.T. and Taylor, C.; "A finite element analysis of the Navier-Stokes equations applied to high speed thin film lubrication." Trans. ASME J. Tribology Vol.109, 71, 1987.

100

n

Q

30

20

40

Shaft speed rev/min. FIGURE 7

50 x

lom4

VARIATION OF MAXIMUM AND BULK TEMPERATURES WITH BEARING SPEED Inlet temperature = 40'C Shaft misalignment = 0.12" Eccentricity ratio = 0.65

5. Gethin, D.T.; "A finite element approach to ana 1 ys i ng thermohyd r o d y h a m i c lubrication in journal bearings. Tribology International, Vo1.21, 67, 1988 6. . Gethin, D.T. and Medwell, J.O.; "Analysis of high speed bearings operating with incomplete films." T r i b o l o g y International Vo1.18, 340, 1985. 90

7. Medwell, J.O. and Gethin D.T.; "A finite element analysis of journal bearing lubrication." Proc.lOth Leeds-Lyon Symposium on Tribology (Eds. D Dowson et al), Butterworth Scientific, UK, 1983.

-e

-

80 -

U

$

70

No deformation 0 Bush deformation 0 Shaft bush A

4-

m

8. Launder, B.E. and Leschziner, M.A.; "An efficient numerical scheme for the prediction of turbulent flow in thrust b e a r i n g s " Proc. 2nd Leeds-Lyon Symposium on Tribology (Eds. D Dowson et al) Mech Eng Publications, UK, 1975.

aI L

E60

-

e

50

-

0

9. King, K . F . a n d T a y l o r , C . M . : " A n estimation of the effect of f l u i d inertia on the performance of the plane inclined slider thrust bearing with particular regard to turbulent lubrication" Trans. ASME, J . Lub. Technology, Vol.99, 129, 1979.

10

I

I

20

30

Shaft speed rev/min x103 FIGURE 8

VARIATION OF MAXIMUM FILM TEMPERATURE WITH ROTATIONAL SPEED .

'/o

'/o

0.002, = 0.5, B = lOmm Eccentricity ratio = 0.5

SESSION IX WEAR Chairman: Professor T.H.C. Childs PAPER IX (i)

The Effect of Residual Stress and Temperature on the Fretting of Bearing Steel

PAPER IX (ii)

The Wear of Hot Working Tools. Application to Forging and Rolling of Steel

PAPER IX (iii) The Influence of Debris Inclusion on the Performance of Polymeric Seals in Ball Valves


245

Paper IX(i)

The effect of residualstress and temperatureon the fretting of bearingsteel M. Kunoand R. B.Waterhouse

An apparatus was designed to study the fretting wear of contact between a ball bearing and bearing steel flat (hardness 715VHN) over a range of slip amplitudes from 5Lbo to 50/dn. The normal load was

varied between 135 and 437N and the frequency was 50Hz. It was possible to subject the flat to a static tensile stress, and this was raised in steps up to 6OOMF'a. The steel flat itself had a surface residual compressive stress of EOOMPa, so the applied stress caused a reduction in magnitude and depth of influence of the residual stress. Two types of wear scar were produced in the test. Where there was partial slip (T/.tm). The scar in this case was a full circle and its diameter increased with number of fretting cycles. When a tensile stress was applied cracks were generated in both types of fretting area. In the full slip regime these propagated to failure. The shortest time to failure was associated with a critical amplitude of 35m which corresponded to a peak in the coefficient of friction of 0.72. Raising the temperature to 200% led to the development of a "glaze oxide" on the surfaces with a much reduced coefficient of friction. No cracks were generated in this case. The presence of a residual compressive stress in the surface appears to have very little influence on the initiation of cracks by fretting. The development of fretting wear damage is discussed in relation to the mechanisms of fretting wear both when TW. 1 INTRODUCTION

High carbon chromium bearing steel quenched and then tempered at low temperature is used as a material for rolling bearings. The microstructure is tempered martensite, and the hardness is approximately 720 VHN. The hardness is carefully controlled as there is a close correlation between the hardness and the rolling contact fatigue life. Hardness of the material is the most effective mechanical factor to prevent the raceways from surface damage. On the other hand, it is well known that there is a proportional relationship between brittleness and hardness. Hence, toughness of the material is decreased if hardness is increased. In fact, fracture of the rings arising from surface damage can often be seen in practice. Fracture of the rings of rolling bearings is predominantly the result of heavy radial and axial loads and occurs even under lubricated conditions on the raceways. Surface damage should not arise as long as the rolling bearings are sufficiently well lubricated and the operating conditions are controlled. It has been observed that surface damage primarily occurs on the raceway, from which fracture is initiated. Therefore, in order to obviate fracture, the most effective countermeasure is to prevent the raceways suffering the initial surface damage. Hawever, the cirm+stances where rolling bearings are used are extremely varied and becoming increasingly severe. In particular,

miniature rolling bearings and solid lubricant rolling bearings are likely to be surface-damaged, because these bearings are not continuously operated for long periods. Hence, these bearings are often subject to fretting wear arising from vibration when they are nominally at rest. Rolling bearings are usually subjected to a hoop stress as they are placed between shafts and housings. The hoop stress is large when the rolling bearings are used in machinery where accuracy is particularly required. The hoop stress of the outer ring is usually compressive, while that of the inner ring is usually tensile when the rolling bearing is installed as a machine component. For example, when the machine containing the rolling bearings is transported, vibration is likely to cause fretting damage on them. Fracture resulting from fretting damage tends to occur when the inner ring of the rolling bearing is subjected to a tensile hoop stress.

A new fretting wear test apparatus used in this study can apply tensile loads to the lower stationary specimens. The applied tensile load to the lower stationary specimens can be adjusted to equal the tensile hoop stress which is experienced by rolling bearing rings. Therefore, the fracture mechanism induced by fretting wear on the high carbon chromium bearing steel can be investigated with this test apparatus. The relationship between the factors which can be considered as affecting the fracture, i.e. applied tensile

246

load, normal load (maximum Hertzian contact stress), slip amplitude and temperature, have been studied. In this study, the fretting wear tests have been carried out under unlubricated conditions. The specimen temperatures used were room temperature and 200°C, because 200OC is considered to be approximately the maximum temperature to which ordinary rolling bearings are subjected.

2 EXPERIMENTAL PROCEDTJRE Fig. 1 shows a schematic diagram of the fretting wear test apparatus. The fretting contact consists of a sphere-on-plate arrangement. The plate is stationary and the upper spherical rider oscillates. As shown in Fig 2, a tensile stress can be applied to the lower stationary specimen. Fig. 3 shows the geometry of the specimen used in this study. The upper spherical specimen is positioned at the centre of the lower guage length in the stationary specimen. A tensile stress is applied via a screw. One of the ends of the grips is linked with a load cell. The magnitude of the applied tensile stress The can be adjusted by turning the nuts. apparatus is described in detail in a previous paper. (1)

The upper moving specimen is a commercial 25.4mm diameter high carbon chromium bearing steel ball. The lower stationary specimen is also made of the high carbon chromium bearing steel. The lower stationary specimen was quenched (83OOC + 60%) and tempered (170OC for 1 hour) after machining, and was subsequently ground and polished with l/& diamond polishing medium. The microstructure of the specimen is a typical tempered martensite, and the hardness is 715 VHN. The chemical composition is shown in Table 1. The stress distribution below the surface of the lower stationary flat specimen has been measured by X-ray residual stress measurement, and is shown in Fig. 4. The experimental conditions used in this study were as follows: : 135-437N normal loads maximum Hertzian contact stresses : 812-1200MF'a radius of static contact area : 28-42Lbn slip amplitudes : 5-50/& applied tensile stresses to the lower stationary specimens : 0-6OOMPa specimen temperatures : in laboratory (17-22'C) 200'C

Fig 1 A schematic diagram of the fretting wear apparatus used.

UDDW

sDecimen

17.L

50 ,.

I i

)lower specimen

Fig 2

Fretting wear test arrangement.

Fig 3 Geometry of the lower stationary Specimen.

247 Chemical composition of tha material used

Table 1

c

si

nu

P

S

Cr

No

Ui

A1

Cu

V

1.12

0.23

0.38

0.006

0.013

1.26

3, cf. figure 1). For this stationary process, the rolls undergo uniform wear and integration of eq.(3) along the arc of contact provides the radial loss (4):

to

I

0t I

tom

0.2 bh

Fig. 4 : results of thermomechanical analysis of the upsetting of cylinders under dissymemcal conditions, and wear depth profile (7) steel cylinder 2% = 30 mm ;ho = 40 mm ;height reduction 75%; N=1000 forgings; Flat dies Z38CDV5 ;HV=4GPa upper die (lubricated) lower die (dry) 4.2 The wear rate coefficient k

In order to describe the results obtained in forging (7), we assume that the wear rate coefficient k has the form: k = KF K w HV -2.1 (5) First k decreases very markedly (exponent -2.1) as the Vickers hardness HV of the tool material increases, this is probably in close relation to the relatively small difference in hardness between the tool and the workpiece scale under the contact conditions (cf paragraph 3). Moreover, k

256 depends on the microstructural features of the tool material (amount of carbides for instance); this effect is described by the factor KW which can be written:

I

I

~~

workpiece radius of the

I

ICw = 1 + 5.1 exp(-O.O85W) W = (%W) + 2(%Mo) + 4(%V)+ 0.5(%Cr)

final

_ _ - I-

I_

TOP DIE

initi,al

I

I (lubricate

1000 f.

(6)

4

-W is called the tungsten equivalent. BOTTOM DIE

Finally, the wear rate depends on the superficial films (lubricant film, transfer film formed by scale). The experimental values of the corresponding factor K are given in table 5.

s=0.015 to 0.05

I

0.85

(MPa1.1) m

0.4

I

0.15

I

0.95

10 ~m

s0.2

11

i I

\'th.

-1

IZGZXZJ

KF

dry 1

lower die: dry;workpiece

upper die

(forgings

(

22.5

Fig. 6 : theoretical and experimental wear depth profiles in upsetting (conditions: same as figure 4). Z38CDV5 flat dies ( H V 4 GPa) (7) a: mechanical press N = 1 0 forgings b: drop hammer; bottom die

2.25

I

I

0.8

Table 5 : influence of contact time on KF and friction

4.3 Exuerimental test of the model In figure 6 we compare the theoretical and experimental wear depths profiles under various forging conditions. Under drop hammer forging conditions, we assume that the workpieces are randomly shifted horizontally by +3mm

(the positioning system is not perfect).We can note some interestingfeatures from table 5 and figure 6: - the lubricant diminishes drastically the wear rate at all contact times. Therefore, although lubrication increases the sliding distance (cf figure 4), lubricated wear is very low under our experimental conditions (figure 6); in industrial workshops where contact conditions are more severe, lubrication most of the time increases wear. - for very small contact times such as with drop hammer (S=0.2), the scale of the lateral surface of the workpiece, which comes progressively in contact with the dies at the periphery, is not very abrasive (it remains hot). So at the periphery, under dry conditions, the wear depth is smaller on drop hammer than on press. - on the contrary, in the central part of the dry lower die, the scale of the plane surface of the workpiece is cooled during the time lag before forging, and the wear rate is very high.

b) Hamm o r

The values of the wear rate coefficient deduced from a few measurements performed in hot rolling with formula (4) are in good agreement with the values observed in hot forging.

5 EFFECTIVE HARDNESS OF FORGING DIES The thermal solicitations of the forging dies are much more severe than those of the rolls of rolling mills, and can produce marked metallurgical, hence hardness changes in the superficial layers.Hence, the damage rate may greatly vary with the number of forgings performed. Depending on the maximal values of die surface temperature OM (Fig. 7), superficial softening or hardening may occur.

OM

em t I

Fig. 7 : thermal cycle of the die surface

257

5.1 Surface softening

5.2 Surface hardening

Let us fiist assume that the maximal surface temperature exceeds the tempering temperature of die material, but remains smaller than the temperature for start of austenitization AC 1 . The additional tempering can be calculated from the master tempering curve of the tool material (10,ll). As the hardness decreases, wear rate can increase drastically according to formula (5). moreover, in the central part of the dies, where the sliding distance and wear remain small, thermal fatigue can increase drastically as demonstrated in figure 8. Due to the progressive reduction of the die flow stress, the plastic extension occuring after each forging increases steadily.

At the periphery of the drop hammer die, the sliding velocity can reach very high values (a few m/s), and induce very high die surface heating. If the maximal surface temperature OM exceeds AC1, the hardening occurs by redissolution of the carbides in the matrix (all the more complete as OM is higher) during heating followed by martensitic transformation (all the more complete as the bulk temperature Om is lower) during cooling. We have built a model of this metallurgical change; the hardening occurs after a few forgings, increases with an increase in @Mand a decrease in Om (figure 9).

Fig. 8 : evolution of the superficial thermal and stress cycles with the number of forgings performed on Z38CDV5 dies (9)

Fig. 10 : influence of nitriding treatment in hot forging with a mechanical press (conditions: same as fig. 6 ) a: transfer film on dry die N=1000 forgings b: maximal depth of cracks vs distance from centre

258

The high hardness of the "white layers" (6,ll) so produced avoids abrasion, but they are brittle and most of the time appear cracked. It is interesting to notice that hardening of die surface by nimding treatment has similar effects (figure 10): in press forging, the surface hardness of nimded dies remain high enough (HV>8GPa) to prevent any wear, but promotes thermal fatigue (figure lob). Under dry conditions, nitriding promotes formation of highly adherent transfer films which reduce the cracking rate in comparison with the lubricated die: lubricant hinders the adhesion of the scale and the thermal cycles are more severe.

6 CONCLUSION The prediction of tool life in industrial practice clearly reveals that hot working is not easy: changes of some process parameters usually can modify the tool damage pattern. We have seen for instance that high tool surface hardness induced by thermal cycles or surface treatment hinders absasive wear but promotes transfer films under dry conditions and thermal fatigue. Despite their simplicity, the models presented in this paper have been successfully applied to simple geometries. Work is presently in progress to introduce these models into Finite Element models of metalworking processes (12) to account for wear in the design of more complex operations. REEERENCES ( 1 ) THOMAS, A. : "wear of drop forging dies" in TRIBOLOGY IN IRON AND STEEL WORKS. Publ. by THE IRON AND STEEL INST. (LONDON) (1970), 135141

(2) STEVENS,P.G., IVENS,K.P. and HARPER,P. : 'Increasing work roll life by improved roll cooling practice. J. Iron Steel Inst. (Jan. 1971) 1-11 (3) BAQUE, P., FELDER, E., HYAFIL, J. and D'ESCATHA, Y.: MISE EN FORME DES METAUX. CALCULS EN PLASTICITE. Publ. DUNOD (PARIS) (1974) (4) FELDER, E. : "Interactions mCtal-cylindre en laminage" CESSID-IRSID lectures (MAIZIERES-LESMETZ) (1985), 85-171 (5) THORE,Y. and FELDER, E. :'htheoretical and experimental study of the interface conditions during the hot forging of steel using a dissymetrical flow model."J. Mech. Working Tech. 13 (1986) 51-64 ,I

(6) FXLDER, E. and BAUDUIN, P. :"usure et frottement ,I en forgeage B chaud. Mtcanique, Matkriaux, Electricitt (Jan. 1981) 4-15 (7) THORE,Y. ?Etude thtorique et exPCrimentale du frottement et de l'usure par abrasion des rnatric.7; de forge B chaud des aciers. Influence d'une nitruration. Thbse Dr Ing. (Ecole des Mines de Paris, CEMEF, 1984) (8) FELDER, E., RENAUDIN, J.F. and THORE,Y. : "The tribology of a simple hot forging process: influence of lubrication and nimding treatment.'boc. Conf. Advanced Techn. Plasticity (1984) Vol 1,231-234 (9) BAUDUIN, P. , FELDER, E. , BATIT, G. and MONTAGUT, J.L. :"Study of the thermomechanical It conditions and the wear of hot forging dies. Proc. 10th Int. Conf. Stamping (LONDON, JUNE 1980) (10) PAYSON, P. : THE METALLURGY OF TOOL STEELS. Publ. J. WILEY and Sons (LONDON) (1962) (11) FELDER, E. and COUTU, L. : "Aspects thermodynamiques de l'usure des mamces & forge B chaud de l'acier.'Bull. Cercle Etude des MCtaux 4, 14 (Dec. 1978) 153-176 (12) CHENOT, J.L. and ONATE, E. : MODELLING OF METAL FORMING PROCESSES. Publ. KLUWER (DORDRECHT) 1988

259

Paper IX(iii)

The influenceof debris inclusion on the performance of polymeric seals in ball valves B. J. Briscoeand P. J.Tweedale

This paper describes a simulation procedure which seeks to evaluate certain facets of the performance of polymeric valve seat in particle contaminated environments. The important feature of the simulation is the control of the rate of hard particle debris entrapment into a model contact and the subsequent effect on the magnitude of the friction. Two engineering polymers in common seal use (PTFE and GFPTFE) as well as several unproven materials (PEEK, a fluororelastomer modified PEEK and an aromatic polyester) are evaluated. The experimental results and their analysis indicate that by using the current simulation polymers may be effectively ranked in terms of their propensity to accumulate debris in particle contaminated environments. PTFE is shown to accumulate debris almost three times as rapidly as PEEK for example. The results of supplementary experiments correlate well with the ranking parameters provided by the simulation.

1.

INTRODUCTION.

Many of the problems encountered with pipeline valves, and in particular ball valves, can be traced to the unsatisfactory performance of the valve seat materials. This subject has been researched and the type of service valve failure have been identified for the common valve types (1,2,3). A previous study of the catastrophic failure of ball valves by debris inclusion has been reported in the literature ( 4 ) . Ball valves seats are generally fabricated from polymeric materials. The requirements of these seats are wide ranging. Ideally the valves should possess zero leakage rates at low and high differential pressures across the valve. They should have low operating torques to open and close, as well as providing good wear resistance. The engineering specification and design of effective seals invariably gives rise to a compromise in the main operating variables, such as operating torque and leakage, to yeild a practicable working design. Materials which are generally 'hard' have low creep compliance which allows for the onset of leakage to occur quickly due to poor sealing. A 'softer' material has better a creep compliance but tends to generate a higher operating torque particularly when the inclusion of debris from the fluid stream occurs. The service requirements of all valves are that they should maintain their design characteristics over the prescribed lifetime. There are many field uses where such valves can be utilised. These include the relatively mild conditions in plant onshore, where short maintenance intervals may not be as important. At the other extreme, there are the hostile environments and the reliability demanded in offshore applications. This latter environment can be particularly demanding in that the fluid flow is invariably contaminated. This is the case on North Sea oil rigs where the operational temperature is ca. 80C and the fluid stream contains significant amounts of contaminants in the form of hard particles. This is a particularly frequent problem for ball valves as

they are often chosen for this latter application due to their relative simplicity and light weight. 1.1

Valve Seat Materials.

It is useful to briefly review, in general terms, some the important features of the different types of valve seat materials. The ball is invariably constructed from a steel which has a hard steel coating. Metallic seats have major advantages centred on their reliability. They have long service lifetimes and tolerance to wide ranging operating conditions. Their disadvantages are the difficulty in obtaining a satisfactory seal at low differential pressures and also the operating torques are often high. This later characteristic necessitates the use of larger actuators than are required for other types of seat. Elastomeric seating materials possess very good sealing characteristics at low differential pressures with low operating torques. Such sealing materials are unfortunately susceptable to material production variability and also the deterioration in material properties in conditions of high dissolved gas content. The latter encompasses the so-called 'explosive decompression' phenomena where pressure cycling of gas into the seal can give rise to material failure. In addition, interaction with the gas (particularly hydrogen sulphide) can cause material modification. The combination of these factors has discouraged the use of these materials in certain applications especially offshore. Polymeric materials as seats offer both good sealing and low operating torques, as well as being chemically inert to many of the fluids of comnon interest. Polymeric components are comnonly included as one of the primary sealing members in ball valves. Usually the polymer elements are in the form of rings which are loaded against a metal ball which rotates about an axis which is parallel to the plane of the

260 r i n g s ( s e e F i g u r e 1). Normally two polymeric r i n g s a r e used and t h e b a l l i s f a s h i o n e d w i t h a d i a m e t r a l h o l e whose a x i s i s o r t h o g o n a l t o t h e r o t a t i o n a x i s . Flow c o n t r o l i s e f f e c t e d by r o t a t i n g t h i s h o l e . T h i s o p e r a t i o n exposes t h e s e a l i n g element t o t h e suspended p a r t i c u l a t e material i n v a r i a b l y p r e s e n t i n t h e f l u i d s . These p a r t i c l e s become embedded i n t h e polymeric s u r f a c e . The consequent d e t e r i o r a t i o n i n t h e v a l v e seat c h a r a c t e r i s t i c s can l e a d t o f a i l u r e due to the operating torque increasing s i g n i f i c a n t l y and e v e n t u a l l y c a u s i n g f a i l u r e by s e i z e . A l t e r n a t i v e l y , f a i l u r e c a n o c c u r by t h e s e a l i n g e f f i c i e n c y b e i n g compromised i n a major way and c a t a s t r o p h i c l e a k a g e o c c u r r i n g .

f r i c t i o n and r a t h e r h i g h c r e e p under normal l o a d produces a m a t e r i a l w i t h a n u n u s u a l l y e f f e c t i v e i n t r i n s i c s e a l i n g c a p a b i l i t y . These materials however have r a t h e r poor w e a r r e s i s t a n c e and debris accumulation characteristics. Also e x t r u s i o n may o c c u r a t h i g h o p e r a t i n g p r e s s u r e s and t e m p e r a t u r e s . Another i m p o r t a n t class of polymers are t h e polyamides o r n y l o n s which are apparantly preferred for high pressure applications. The t e s t i n g of f u l l scale v a l v e s i n a r e l i a b l e and s y s t e m a t i c manner i s a n e x p e n s i v e and t i m e consuming t a s k , a l t h o u g h t h i s t y p e of t e s t i n g i s c a r r i e d o u t (1,3). The aim of t h e work d e s c r i b e d h e r e w a s t o u n d e r s t a n d a t a fundamental l e v e l some of t h e material c h a r a c t e r i s t i c s i m p o r t a n t i n the i n c l u s i o n of h a r d p a r t i c u l a t e d e b r i s i n t o b a l l v a l v e seats. T h i s h a s i n v o l v e d t h e d e s i g n and c o n s t r u c t i o n of a l a b o r a t o r y a p p a r a t u s t o s i m u l a t e t h e p r o c e s s of p a r t i c l e i n c l u s i o n and t h e measurement of t h e e f f e c t on t h e f r i c t i o n i n metal/polymer c o u p l e s .

2.

F i g u r e 1. Diagram of a t y p i c a l polymer b a l l valve.

1.2

seated

Mechanism of Entrapment.

The mechanism of entrapment o c c u r s by t h e d e b r i s being drawn i n t o t h e s e a l i n g zone w h i l s t t h e s e a l i s i n c o n t a c t w i t h t h e f l u i d flow and t h e b a l l i s i n motion. The p a r t i c l e s a r e t h e n s l o w l y f o r c e d i n t o t h e s e a l s u r f a c e . The d e b r i s may t h u s p r o g r e s s i v e l y accumulate i n t h e s u r f a c e of t h e seal i f i t i s n o t e x p e l l e d when t h e c o n t a c t i s unloaded. C l e a r l y t h e f i n e s t p a r t i c l e s w i l l tend t o i n g r e s s most r a p i d l y , although an a n a l y s i s of f a i l e d seal components shows v e r y substantial particles (some of t h e o r d e r of millimetres i n d i a m e t e r ) c a n become t r a p p e d i n t h e s e a l i n g zone d u r i n g t h e l i f e t i m e of t h e p a r t . The i n i t i a l p o l y m e r / s e a l c o n t a c t which i s an e f f e c t i v e s e a l and low f r i c t i o n c o n t a c t is g r a d u a l l y transformed i n t o , f o r example, a s i l i c a / s t e e l c o n t a c t which i s n o t a n e f f e c t i v e seal and which h a s a much h i g h e r s l i d i n g a n d / o r static friction. 1.3

Commercial P r a c t i c e , .

A wide r a n g e of o r g a n i c polymers have been c o n s i d e r e d f o r u s e a s v a l v e s e a t materials. Amongst the most p o p u l a r have been the f l u o r o c a r b o n s , i n p a r t i c u l a r t h e PTFE's. These are a t t r a c t i v e materials due t o t h e i r chemical i n e r t n e s s , low f r i c t i o n and r e l a t i v e l y low c r e e p compliance. The combination of low s l i d i n g

EXPERIMENTAL PROCEDURE.

The c o n t a c t c o n f i g u r a t i o n a d o p t e d f o r t h e simul a t i o n of d e b r i s a c c u m u l a t i o n i n t o polymeric s u b s t r a t e s w a s t h a t of a metal r o l l e r loaded a g a i n s t a polymeric p l a t e . The r o l l i n g a c t i o n of t h e former t r a p p e d d e b r i s i n t h e l a t t e r . The r o l l i n g speed d e f i n e d t h e c o n t a c t t i m e of t h e d e b r i s i n t h e c o n t a c t zone. The d e b r i s r e t e n t i o n and i t ' s e f f e c t on t h e s l i d i n g f r i c t i o n was t h e n measured by p e r i o d i c a l l y clamping t h e r o l l e r and s l i d i n g it r e l a t i v e t o t h e p l a t e . T h i s c o n t a c t configuration was designed t o s i m u l a t e t h e t y p i c a l o p e r a t i n g c o n d i t i o n s which o c c u r s i n b a l l v a l v e s seats; 3.5-14 MPa c o n t a c t p r e s s u r e . Selected sand p a r t i c l e s were used as a c o n t a m i n a n t s a t approx. 500ppm c o n c e n t r a t i o n i n aqueous s u s p e n s i o n s . A series of model e x p e r i m e n t s were a l s o u n d e r t a k e n t o i d e n t i f y t h e c r i t i c a l material parameters a f f e c t i n g d e b r i s i n c l u s i o n s . The e x p e r i m e n t a l c o n f i g u r a t i o n chosen h e r e c o n s i s t e d of sliding rigid conical indentors over polymeric f l a t s and measuring t h e f r i c t i o n and r e s u l t i n g scar w i d t h s ( 5 ) . These s t u d i e s sought t o s i m u l a t e t h e c o n t a c t stresses g e n e r a t e d a t p a r t i c l e -polymer c o n t a c t s . An a p p a r a t u s was c o n s t r u c t e d t o perform t h e s i m u l a t i o n d e s c r i b e d above. T h i s i s shown i n F i g u r e 2 and c o n s i s t e d of b a s e p l a t e upon which was mounted a l o a d i n g arm and t h e e x p e r i m e n t a l p l a t f o r m . The former c o n s i s t e d of compound arms t o a l l o w t h e a p p l i c a t i o n of t h e r e q u i r e d f o r c e s t o t h e r o l l e r from managable l o a d i n g w e i g h t s . The l a t t e r u n i t comprised of a n immersion b a t h , connected t o a r e s e r v o i r equipped w i t h a s t i r r e r and circulator, mounted on two machine s l i d e w a y s . A motor d r i v e a t t a c h e d t o t h e lower s l i d e w a y p r o v i d e d t h e motion i n t h e c o n t a c t , whilst the f r i c t i o n was monitored by a displacement transducer constructed from f l e x i b l e beams c o n n e c t i n g t h e r o l l e r h o l d e r t o t h e l o a d i n g arm. A n a l o g / d i g i t a l i n t e r f a c i n g of the displacement t r a n s u c e r a d j a c e n t t o t h e f l e x i b l e beams allowed t h e e x p e r i m e n t a l r e s u l t s t o be logged i n r e a l t i m e t o a microcomputer. The o p e r a t i o n of t h e s i m u l a t i o n experiment c o n t a i n e d t h e f o l l o w i n g major e l e m e n t s : (1) The r o l l e r was r o l l e d backwards, f o r w a r d s and backwards a g a i n over t h e sample b e f o r e b e i n g l o c k e d i n t o p o s i t i o n . The l o c k e d r o l l e r was t h e n s l i d a c r o s s t h e s u r f a c e and t h e f r i c t i o n a l f o r c e developed w a s measured.

26 1

KEY A LOADING ARM B COUNTERBALANCING WEIGHT C FRICTION HEAD D LOADING PLATFORM E ELEClWC MOTOR F FLEXIBLE BEAMS

\ Loading Arm (1:s Lever ratio) Flexible Beams

i

Cast Iron Roller

‘ i S u p p o n Tower

I ~

f

I

D

I ~

Loading Beam‘ ( 1 2 loading ratio) Spacing Pillar

I

I

L

Levelling Screw

Baseplate

U

I

Motor Drive for Slideway

F i g u r e 2. S i d e view of s i m u l a t i o n a p p a r a t u s . ( 2 ) Three c y c l e s of t h e o p e r a t i o n d e s c r i b e d i n (1) were undertaken i n c l e a n water i n o r d e r t o c r e a t e a conforming c o n t a c t and assess t h e f r i c t i o n i n nominally c l e a n c o n d i t i o n s b e f o r e i n t r o d u c i n g t h e contaminants. ( 3 ) D e b r i s accumulation c y c l e s were then performed on a c o n t i n u o u s b a s i s w i t h t h e d e b r i s contaminanted water b e i n g pumped i n t o t h e accumulation b a t h . The f r i c t i o n f o r c e development w i t h t i m e was monitored i n t h e manner o u t l i n e d above u n t i l i t p l a t e a u e d o r reached a v a l u e t o o h i g h f o r t h e s a f e c o n t i n u a t i o n of t h e experiment. The l o a d s imposed on t h e specimens were s c a l e d by t h e r a t i o of t h e i r h a r d n e s s e s i n o r d e r t o produce comparable c o n t a c t p r e s s u r e s of ca. 14MPa. The speed of movement over t h e sample was 2.4 x 10-5 m / s . The s c r a t c h hardness e x p e r i m e n t s were performed u s i n g a f r i c t i o n machine h a s been described i n d e t a i l elsewhere ( 6 ) . A g e n e r a l view i s shown i n F i g u r e 3 . The main f u n c t i o n a l p a r t was a l o a d i n g arm which i s p i v o t e d a b o u t t h e p o i n t ( A ) , t o t h e r e a r of t h i s i s a c o u n t e r balancing weight ( B ) . Loads were applied d i r e c t l y t o t h e f r i c t i o n head (C) by means of a dead w e i g h t s once t h e arm h a s been balanced. The f r i c t i o n head w a s i n t e r c h a n g e a b l e and h e r e i s used t o s u p p o r t a c o n i c a l i n d e n t o r . Beneath t h e f r i c t i o n head a l o a d i n g p l a t f o r m (D) s u p p o r t e d t h e polymer specimin. The l o a d i n g arm was mounted on a p a i r of machine s l i d e w a y s a t r i g h t a n g l e s t o one a n o t h e r . The r e l a t i v e motion of t h e cone and specimen was a c h i e v e d by a small e l e c t r i c motor ( E ) , d r i v i n g one of t h e s l i d e ways. The f r i c t i o n i n t h e c o n t a c t was monitored by s t r a i n gauge mounted on f l e x i b l e beams c o n n e c t i n g t h e f r i c t i o n head t o t h e l o a d i n g arm. The o u t p u t was recorded on a c h a r t r e c o r d e r . The s l i d i n g v e l o c i t y used w a s 4.2 x 10-5 m / s . The e x p e r i m e n t a l work w a s performed u s i n g v a r i o u s l o a d s w i t h one cone a n g l e 60 d e g r e e s ( r e l a t i v e l y sharp) i n order t o simulate t h e c o n t a c t c h a r a c t e r i s t i c s g e n e r a t e d by rough sand p a r t i c l e s . The polymers s t u d i e d were PTFE, GFPTFE, a f l u o r o e l a s t o m e r modified PEEK (Raychem V200) and an a r o m a t i c p o l y e s t e r (Celanese V e c t r a ) . Where s u s c e p t a b i l i t y t o a n aqueous environment was suspected the scratching experiments were c a r r i e d o u t w i t h a short c o n t a c t time w i t h w a t e r ( o f t h e o r d e r of t h e experiment d u r a t i o n ) , and a l s o a l o n g e r c o n t a c t t i m e ( w i t h t h e samples immersed i n water f o r approx. 72 h r s . ) . Experiments w i t h complete saturation of t h e polymer m a t r i x were n o t

F i g u r e 3 . S i d e view o f E l d r e d g e a p p a r a t u s .

c a r r i e d o u t due t o t h e p r o t r a c t e d times r e q u i r e d f o r t h e f l u i d m i g r a t i o n i n t o t h e m a t r i x . The f r i c t i o n a l work was monitored. The t r a c k w i d t h s were measured immediately a f t e r s c r a t c h i n g u s i n g a t r a v e l l i n g microscope.

3.

SIMULATION RESULTS.

The e x p e r i m e n t a l r e s u l t s are g i v e n i n F i g u r e s 48. The i m p o r t a n t f e a t u r e s are: (1) PTFE and GFPTFE r e s u l t s have a s h a p e t h a t reveals a significant increase i n the f r i c t i o n i n i t i a l l y . This then decreases t o a lower v a l u e i n t h e l a t t e r p a r t of t h e e x p e r i m e n t . The l e v e l of b o t h of t h e s e f e a t u r e s i n c r e a s e s d u r i n g t h e c o u r s e of t h e simulation. ( 2 ) The remaining polymers produce experiment a l r e s u l t s which are c h a r a c t e r i s t i c a l l y d i f f e r e n t from t h o s e of t h e PTFE s y s t e m s . The i n i t i a l large increase is absent with the f r i c t i o n a l work b e i n g more s t a b l e a t a n o v e r a l l l e v e l d u r i n g t h e c o u r s e of each c y c l e . The o v e r a l l f r i c t i o n a l l e v e l is higher i n i t i a l l y but tends t o i n c r e a s e more s l o w l y t h a n t h e PTFEs. T h i s i n d i c a t e s t h e d e b r i s accumulation f o r t h e s e materials is s i g n i f i c a n t l y less t h a n f o r t h e PTFE based systems. There i s a l s o some e v i d e n c e of s t i c k / s l i p b e h a v i o u r . The q u a l i t a t i v e f e a t u r e s of t h e s e r e s u l t s a r e p r e s e n t e d s c h e m a t i c a l l y as i n F i g u r e 9. These r e s u l t s r e f l e c t t h o s e s e e n d u r i n g t h e t e s t i n g of f u l l scale v a l v e s . A r e p r e s e n t a t i v e set of such d a t a , f o r a PTFE based s e a l system which shows a d r a m a t i c rise i n f r i c t i o n which i s not t y p i c a l , i s shown i n F i g u r e 10. These d i f f e r from t h e r e s u l t s of t h e c u r r e n t s i m u l a t i o n due t o t h e g e o m e t r i c a l changes i n t h e b a l l v a l v e c o n t a c t i n o p e r a t i o n . However, t h e e s s e n t i a l f e a t u r e s of t h e rise i n t h e f r i c t i o n a l work of t h e c o n t a c t w i t h d e b r i s i n c l u s i o n can be s e e n . The s i m u l a t i o n t h e r e f o r e shows t h e e s s e n t i a l f e a t u r e s of b a l l v a l v e o p e r a t i o n i n contaminated conditions. 4.

ANALYSIS OF SIMULATION DATA.

A s e m i q u a n t i t a t i v e r a t i o n a l i s a t i o n of t h e experi m e n t a l d a t a c a n be made on t h e b a s i s of a model o r i g i n a l l y used by Bowden and Tabor t o p r e d i c t t h e e f f e c t of t h e a d s o r p t i o n of boundary l u b r i c a n t s on t h e f r i c t i o n of metal s u f a c e s ( 7 ) . T h i s approach h a s r e c e n t l y been a d o p t e d t o i n t e r p r e t f r i c t i o n a l phenomena i n polymer boundary l u b r i c ytion (8). Many o t h e r a u t h o r s have u n d e r t a k e n

262

F i g u r e 7. S i m u a l t i o n r e s u l t s f o r V e c t r a . F i g u r e 4 . S i m u l a t i o n r e s u l t s f o r PTFE.

.$

F i g u r e 8. S i m u l a t i o n r e s u l t s f o r f l u o r o e l a s t o m e r modified PEEK. F i g u r e 5. S i m u a l t i o n r e s u l t s f o r GFPTFE. PTFE's: PTFE, GFPTFE

Sliding Distance.

Engineering Polymers: Vectra, PEEK, V200

F i g u r e 6 . S i m u l a t i o n r e s u l t s f o r PEEK. s i m i l a r s t u d i e s , and c u r r e n t l y t h e i d e a is b e i n g a p p l i e d t o p r e d i c t f r i c t i o n v a l u e s in composite t r i b o l o g y ( 9 ) . The o r i g i n a l models c o n s i d e r t h e f r a c t i o n a l coverage of a s u r f a c e by s u r f a c e a c t i v e s p e c i e s and t h e i r e f f e c t on t h e measured f r i c t i o n a l response. The e f f e c t of debris p a r t i c l e s b e i n g i n c l u d e d i n t o a polymer s u r f a c e c a n , as we s h a l l see, be modelled in a similar manner. F i r s t w e adopt t h e a d h e s i o n model of f r i c t i o n where F , t h e magnitude of t h e f r i c t i o n , is g i v e n by :F = A T

S

.

T

Then we d i s t i n g u i s h two s i t e s on t h e s u r f a c e ;

F i g u r e 9. Characteristic observed in s i m u l a t i o n .

behaviour

patterns

F = A s + A s , P P s s one is t h e polymer and t h e o t h e r i s t h e d e b r i s . A c t u a l l y t h e problem i s a more s u b t l e one t h a n j u s t t h e coverage of t h e s u r f a c e . The a d h e s i o n model of f r i c t i o n a d d r e s s e s areas of c o n t a c t , and hence t h e s p e c i f i e d s i t e s are t h e c o n t a c t sites. Then w e have a t o t a l c o n t a c t area AT, made up of Ap o r A s , t h e c o n t a c t areas of p o l y m e r / s t e e l and s a n d l s t e e l r e s p e c t i v e l y d u r i n g sliding. Each t y p e of c o n t a c t zone h a s a d i f f e r e n t i n t e r f a c e shear stress, s p and s s , f o r polymer / s t e e l and sand/s t e e l contacts r e s p e c t i v e l y . The i m p o r t a n t p o i n t h e r e is t h a t

263

300 BREAKTORQUES AT 14 barA P

200 z E

y

100

B

P

F i g u r e 10. T y p i c a l t o r q u e t r a c e / d i s p l a c e m e n t c u r v e s from f u l l scale t e s t i n g of P"TFE seat supported ball valves.

ApIAT = @ may n o t be e q u a l t o f r a c t i o n a l s u r f a c e coverage deduced by o p t i c a l examination of t h e s u r f a c e of t h e d e b r i s e n c r u s t e d polymer s u r f a c e a f t e r unloading. Then

+ A therefore A = A - A P S S T P then, F = s A + ( A - A ) s P P T P S and F = A ( s + ( s - s ) @ ) T s P S F = A s ( l + @ a ) (1) T s where a c o r r e s p o n d s t o ( s s ) / s P S S I n order t o render t h i s equation useful f o r t h e a n a l y s i s of t h e e x p e r i m e n t a l r e s u l t s , t h i s e x p r e s s i o n f o r t h e f r i c t i o n a l work d u r i n g t h e s i m u l a t i o n i s s u b t r a c t e d from a n estimate of t h e f i n a l f r i c t i o n a l work. The l a t t e r was o b t a i n e d from t h e a s s y m p t o t i c v a l u e t h a t a l l s u r f a c e s approached when f u l l y e n c r u s t e d w i t h sand. Equation (1) i s a c o r r e c t d e s c r i p t i o n of t h e problem but t h e a p p l i c a t i o n t o t h e d a t a p r e s e n t s s e v e r a l i n t r a c t a b l e problems. We assume t h a t d u r i n g e a c h c y c l e of t h e s i m u l a t i o n (N) a f r a c t i o n ( x ) o f t h e c o n t a c t a r e a , o r i g i n a l l y AT, is covered by p a r t i c l e s . Then by enumerating a series of terms t h a t may be w r i t t e n f o r t h e d e c r e a s e i n t h e c o n t a c t area of polymer and t h e r e s u l t i n g accumulation of sand, 0 c a n be shown t o be of t h e form ( 1 x ) N (see Apppendix 1). The e x p r e s s i o n f o r t h e sand a c c u m u l a t i o n , t h a t i s t h e i n c r e a s e in A s , i s a more complex summa t i o n of terms. A

=

A

T

Figure 11. polymers from no.).

r e s u l t i n g p l o t s f i t t e d using l i n e a r a n a l y s i s , are g i v e n i n T a b l e I.

F = A s then F T s F - F = A s - A s ( 1 + 0 a ) F T s T s F = - A s ( @ a ) N T s (2) F = - A s ( 1 - x ) a T s

Since

and

-

l o g (- A s a ) + N l o g (1 x ) T s The i n t e r c e p t of t h e r e s u l t i n g l i n e w i l l c o n t a i n a n estimate of t h e i n t e r f a c i a l s h e a r stress of t h e s a n d , w h i l s t t h e s l o p e w i l l c o n t a i n a parameter which d e s c r i b e s t h e e f f i c i e n c y of i n c l u s i o n of d e b r i s i n t o t h e polymer c o n t a c t as t h e term l o g ( 1 x). The a n a l y s i s of t h e e x p e r i m e n t a l d a t a a c c o r d i n g t o t h i s scheme are shown in F i g u r e 11 for- t h e polymers conside r e d h e r e . The s l o p e s and i n t e r c e p t s of t h e

or

log

F =

-

regression

Table I . T a b u l a t i o n o f material r e s u l t s from t h e s i m u l a t i o n experiment a n a l y s i s , and t h e consequ e n t material p a r a m e t e r s d e r i v e d and t h e i n c l u sion e f f i c i e n c y of d e b r i s i n t o t h e polymer. Material

-

-

Graphical a n a l y s i s r e s u l t s f o r simulation r e s u l t s (log F/cycle

Intercept

Slope

x

PTFE

1.851

-0.165

0.316

GFPTFE

1.72

-0.134

0.265

Vectra

1.62

-0.081

0.17

PEEK

1.74

-0.055

0.119

v2 00

1.66

-0.074

0.156

The estimate made of t h e f r i c t i o n a l v a l u e f o r t h e f u l l y sand e n c r u s t e d s u r f a c e , FF, e f f e c t s t h e i n t e r c e p t values given, but t h i s is common t o a l l . The i n c l u s i o n p a r a m e t e r , x , i s however of c o n s i d e r a b l e v a l u e as t h i s i s independent of t h e assumptions made w i t h r e g a r d t o t h e i n t e r p r e t a t i o n of t h e s e r e s u l t s . I t may t h u s be regarded a s a s e n s i t i v e i n d i c a t o r f o r t h e prope n s i t y of t h e m a t e r i a l i n q u e s t i o n t o i n c l u d e d e b r i s i n t o i t ' s s u r f a c e . The v a l u e s of x a r e s e n s i b l e and of t h e o r d e r e x p e c t e d . Thus f o r example, PTFE a c c u m u l a t e s d e b r i s a t a r a t e which is a b o u t t h r e e times f a s t e r t h a n t h a t of PEEK. 5.

SCRATCH HARDNESS RESULTS.

The d a t a are n o t p r e s e n t e d i n d e t a i l as a seperate e n t i t y b u t combined w i t h d a t a o b t a i n e d from t h e s i m u l a t i o n t o test t h e v a l u e of two c o r r e l a t i o n s . The s c r a t c h w i d t h d a t a i s r e g a r d e d a s a measure of t h e p l a s t i c s t a i n c a p a c i t y of t h e polymer s u r f a c e and hence should c o r r e l a t e w i t h t h e i n c l u s i o n parameter, x. The f r i c t i o n c o e f f i c i e n t , t h e work done i n t h e experiment may o r may not c o r r e l a t e w i t h i n t e r c e p t p a r a m e t e r of t h e s i m u l a t i o n depending upon t h e n a t u r e of t h e f r i c t i o n p r o c e s s e s i n t h e s i m u l a t i o n . These c o r r e l a t i o n s are p r e s e n t e d in F i g u r e s 12 and 13 r e s p e c t i v e l y . The former shows e x c e l l e n t c o r r e l a t i o n f o r PTFE, GFPTFE, PEEK and t h e a r o m a t i c p o l y e s t e r . The f r i c t i o n and i n t e r c e p t c o r r e l a t i o n is i n d i f f e r e n t but follows t h e c o r r e c t trend.

6.

CONCLUSIONS.

We have demonstrated t h a t it i s p o s s i b l e u s i n g a

264

O2

'is

1

/

1.2

0. l i

0.0

I

0.0

I

I

0.1

0.2

0.3

simple and r e l a t i v e l y i n e x p e n s i v e e x p e r i m e n t a l s i m u l a t i o n t o s e n s i b l y r a n k , i n terms of t h e i r relative performance, the time dependent f r i c t i o n a l behaviour of polymeric v a l v e seat materials o p e r a t i n g i n p a r t i c l e contaminated aqueous media. Systems based on PTFE show low i n i t i a l s l i d i n g f r i c t i o n which i n c r e a s e s r a p i d l y as d e b r i s accumulates i n t h e c o n t a c t . They a l s o show s t a t i c f r i c t i o n v a l u e s t h a t a r e much h i g h e r than t h e k i n e t i c values, even when d e b r i s accumulates i n t h e c o n t a c t . T h i s i s a common f e a t u r e of c e r t a i n t y p e s of PTFE c o n t a c t (10, 11, 12), where s i g n i f i c a n t r e o r i e n t a t i o n o c c u r s i n t h e polymer s u r f a c e . The non PTFE based materials show a less interesting type of behaviour. They are c h a r a c t e r i s e d by h i g h e r i n i t i a l f r i c t i o n which a l s o i n c r e a s e s w i t h d e b r i s accumulation b u t less r a p i d l y t h a n f o r t h e PTFE systems. The s t a t i c and dynamic c o e f f i c i e n t s of f r i c t i o n a p p e a r t o be very similar. The s i m p l e s c r a t c h h a r d n e s s experiments provides two e x p e r i m e n t a l q u a n t i t i e s t h a t c a n be measured e a s i l y , one of which shows a s t r o n g c o r r e l a t i o n w i t h t h e i n c l u s i o n parameter of t h e s imula t ion. Only t h e f r i c t i o n a l c h a r a c t e r i s t i c s of t h e v a l v e seats w i t h d e b r i s accumulation are a d d r e s sed by t h i s s i m u l a t i o n . In t h e o v e r a l l d e s i g n o t h e r f a c t o r s such as environmental s t a b i l i t y , w e a r rates, s e a l i n g a b i l i t y and t o a lesser extent c o s t are a d d i t i o n a l considerations. However t h e s i m u l a t i o n procedure d e s c r i b e d above does p r o v i d e a means of q u a n t i f y i n g one a s p e c t of v a l v e seat performance. ACKNOWLEDGEMENT,

The a u t h o r s would l i k e t o thank BP Research, Sunbury on Thames f o r t h e f i n a n c i a l s u p p o r t f o r t h i s work, and i n p a r t i c u l a r D r . D. H a r r i s o n f o r support and encouragement, and a l s o p r o v i d i n g Figure 10. References. 1.

2.

3.

1 .o

1.2

1.4

1.6

1.8

Intercept 2.0

0.4

Figure 12. C o r r e l a t i o n of t r a c k width in s c r a t c h i n g and i n c l u s i o n parameter ( x ) from simulation.

7

0.0

x, Inclusion Parameter I I

BILLINGTON M J , HARRISON D, and V I V I A N B E. Paper J1 g i v e n a t I n t l . Conf. Developments i n Valves and A c t u a t o r s f o r F l u i d C o n t r o l , Oxford, (10-12 September 1985). 'The identification and e v a l u a t i o n of v a l v e problems.' V I V I A N B E. Process E n g i n e e r i n g , 33, October 1985. ' I d e n t i f y i n g and e v a l u a t i n g v a l v e problems.' BILLINGTON M J , HARRISON D, and V I V I A N B E.

F i g u r e 13. C o r r e l a t i o n of f r i c t i o n c o e f f i c i e n t i n s c r a t c h i n g and i n t e r c e p t parameter from simulation.

4.

Paper g i v e n a t 2nd. I n t l . Conf. Developments i n Valves and A c t u a t o r s f o r F l u i d C o n t r o l , Manchester, (28-30 March 1988). 'Performance t e s t i n g t o i d e n t i f y r e l i a b l e valves. ' CONNELL R A, SUMMERS G G, SHEPHERD J P, and SHONE E B. Proc. 3 r d . Leeds-Lyon Symposium on T r i b o l o g y , (1976), P a p e r I X ( i v ) . 'The u s e of a f i l l e d PTFE as a b a l l v a l v e seat

material. 5.

6. 7. 8.

9.

10.

11.

12.

'

BRISCOE B J , EVANS P D, and LANCASTER J K. J. Phys. D: Appl. Phys., 20, 346-353, (1987). ' S i n g l e p o i n t d e f o r m a t i o n and abrasion of gamma i r r a d i a t e d PTFE. ' BOWDEN F P, and TABOR D. ' F r i c t i o n and L u b r i c a t i o n of S o l i d s . ' P a r t 2 . Clarendon P r e s s , Oxford, 1964. BOWDEN F P, GREGORY J N , and TABOR D . N a t u r e , 156, ( 1 9 4 5 ) , 97-101. 'Lubrica t i o n of metal s u r f a c e s by f a t t y a c i d s . ' SKELCHER W L. i n Microscopic Aspects of Adhesion and L u b r i c a t i o n , pp. 719-728, Ed. J..M-Georges. 'A proposed a d h e s i v e mechanism of boundary l u b r i c a t i o n f o r polyphenylene o x i d e and s i l i c o n e f l u i d . ' BRISCOE B J , and TWEEDALE P J. P r o c . I n t l . Conf. ICCM V, h e l d a t I m p e r i a l C o l l e g e , London, J u l y 1987. 'A c r i t i c a l reveiw of t h e t r i b o l o g y of polymer composites.' POOLEY C M, and TABOR D. P r o c . Roy. SOC., A329, 251, (1972). ' F r i c t i o n and m o l e c u l a r s t r u c t u r e : The b e h a v i o u r of some thermoplastics.' BRISCOE B J , and STOLARSKI T A. Wear, 104, ' T r a n s f e r w e a r of polymers 121, (1985). d u r i n g combined l i n e a r motion and l o a d a x i s spin.' BRISCOE B J . P h i l . Mag. A43, 511-527, (1981). ' F r i c t i o n and wear of o r g a n i c s o l i d s and t h e a d h e s i o n model of f r i c t i o n . '

APPENDIX 1. DERIVATION OF DECREASE I N POLYMER SURFACE AREA W I T H SAND INCLUSION.

For a c o n t a c t o r i g i n a l l y composed of polymer of s u r f a c e area, Ap, a t t h e s t a r t of t h e experiment t h i s w i l l be t h e t o t a l s u r f a c e area, AT; i f t h e c o n t a c t i s t h e n covered by sand p a r t i c l e s a f r a c t i o n , x, o,f t h e a v a i l a b l e area d u r i n g each c y c l e of t h e s i m u l a t i o n , N. Then t h e f o l l o w i n g e x p r e s s i o n s f o r t h e amount of f r e e polymer s u r f a c e may be w r i t t e n down

265 Cycle Number

Term f o r Polymer Area.

Start

1

1

1 - x

2

1

3

Equivalent Expression.

-

x

(1

-

x(1

-

(1

- x) -

x(1

(1

-

-

x)(l

- x)

x)

-

x)

2

x)

(1

-

x)

(1

-

x) N

(1

-

x)

1-x-x(l-x)-x(l-x-x(l-x)) (1-x)-x( 1-x)-x( ( 1-x)-x( 1-x)) (1-x)( (1-x)-x( 1-x))

(1

N

- x)(l -

x)(l

-

x)

3


SESSION X ROLLING ELEMENT BEARINGS (2) Chairman: Dr E loannides PAPER X(i)

Tribological Characteristics of Needle Bearings

PAPER X(ii)

Power Loss Prediction in Ball Bearings

PAPER X(iii)

The Effect of Roller End-Flange Contact Shape Upon Frictional Losses and Axial Load of the Radial Cylindrical Roller Bearing

PAPER X(iv)

The Study of Roller End and Guiding Shoulder Construction of Roller bearings


269

Paper X(i)

Tribological characteristics of needle bearings S. Blair and W. 0.Winer

A Needle Bearing Test Rig has been constructed which allows the measurement of frictional torque, axial thrust, needle axial skew angle, and needle complement velocity for an applied radial load of up to 3500 N and a speed of up to 7000 rpm. Either shaft rotation or cup rotation can be accommodated, Preliminary data indicate that frictional torque is greater for full-complement bearings than caged bearings, that torque is higher for cup rotation than shaft rotation, and that torque is minimized when the needles (full-complement) are axially aligned with the shaft in the load zone. A correlation was found between needle skew angle and axial thrust. Less than one degree change of needle skew is required to go from no thrust to the maximum thrust developed (about 5% of the radial load). Full complement bearings tend to operate with a preferred needle skew direction and attending thrust direction with occasional spontaneous reversals. Operation without thrust and needle skew is not stable. identical openings so the drive module and the torque module may be interchanged among them. The center block contains a load diaphragm and 1 INTRODUCTION load cell for radially loading the test bearing which is always contained in the Needle roller bearings are a special case of center block. Regulated gas pressure is cylindrical roller bearing in which the roller supplied to the diaphragm at the top fitting. has a high length to diameter ratio for When the drive module containing the test reduced radial space requirements. They are bearing is in the center block, the cup used in both the caged and full-complement rotation mode is available. In Figure 2 the variations. Empirical estimates of roller bearing shaft is supported in the right block by a frictional torque have been made (Ref [ 1 , 2 ] ) journal bearing. For cup rotation, the journal bearing sleeve is replaced by a and are frequently used for design purposes. special ball bearing which allows both Roller skew is known (Ref [ 2 ] ) to occur in rotation and translation of this right shaft roller bearings and was measured for a single journal. Also at the right block is a ball roller through one revolution of a roller thrust bearing, thrust cell and micrometer for bearing by Nypan (Ref [ 3 ] ) . Axial forces were measurement of the axial force (thrust) measured for imposed needle skew angles by applied to the shaft by the needles. The Ulezelski et al. (Ref [ 4 ] ) . Needle skew is micrometer, pushing through the thrust cell believed to produce axial force (Ref [ 4 ] ) . A and thrust bearing, preloads the shaft against force transducer on the needle bearing shaft the drive module (or alternatively, the torque of an automotive roller tappet produced the module) at the left block. A flexure on the axial force data in Figure 1 using a simulator left end of the shaft increases the axial described in Ref [ S ] . The axial force is seen compliance of the shaft at the left support to occur at the frequency of needle passage relative to the axial compliance at the thrust and can be positive or negative with magnitude cell end. of as much as 140 N. A preload at the micrometer of A Needle Bearing Test Rig was designed and 0.076 mm is used for axial force measurements, assembled in the Georgia Tech Tribology and resulting in 92 N preload on the thrust cell. Rheology Laboratory to provide measurements of The drive module spool is rotated by a 3 frictional torque, axial thrust, needle skew mm V-belt, the pulley for which serves as an angle, and needle complement velocity. encoder for a rotational velocity pick-up. Details of the machine design and some Optical probes (Figure 2 ) of 0.49 mm diameter preliminary data are reported here. active element are positioned at the left and right top (load zone) ends of the test bearing by a pair of 3-axis micropositioners (not 2 NgEDLBBEARINGRIG shown in Figure 2 ) . 2.1 Construction 2 . 2 Torque Transducer The Needle Bearing Simulator is shown in Figure 2 in the shaft rotation mode. The cup The torque module (Figure 2 ) provides a housing for the specimen bearing for shaft may also be rotated with the shaft fixed in another mode. The shaft spans three support rotation mode and support for the shaft in cup blocks. The left and center block have rotation mode while allowing low friction

270 freedom of rotation of the inner spool. Friction torque may be measured by determining the magnitude of the force required to resist rotation of the inner spool at the force cell link in Figure 2. However, it is necessary to correct for the frictional torque of the bearings which support the inner spool. The inner spool is supported by two ball bearings which are housed inside an intermediate spool which, in turn is supported by two ball bearings. Jogging of the intermediate spool or the inner spool causes jogging (oscillating rotation) of the support bearings while the specimen (or the shaft in cup rotation mode) is stationary. If support bearing friction is symmetric with respect to rotation direction, jogging causes a noise on the torque signal which if averaged gives the true test bearing torque. 2.3

Needle Optical Probes

Two fiber optic probes

(MTI Fotonic Sensors) transmit light to and receive reflected light from the trunnions (Figure 3 ) at both ends of the needles. The 0 . 9 nun diameter trunnion ends are lapped (600 grit paper) for this purpose. The test bearing cup flanges are machined such that the flange inside diameter is at the needle center line. This way, the flange still axially locates the needles but exposes enough of the trunnions to be optically detected. The needle skew angle changes the phase relationship of the optical probe signals as shown in Figure 3 . 2.4

Data Acquisition System

Six channels of data were sampled concurrently. They included signals from the thrust, load, and torque charge amplifiers, the drive module speed pickup and the two needle optical probes. Sampling rate was 2 to 10 kH, for 8192 points per channel. Raw data was stored on disc as ASCII files for later reduction. 3

2)

3) 4)

5)

The thrust signal level was found to be sensitive to normal load, possibly due to deflection of the shaft which would shorten its effective length. For this reason, the thrust signals that were recorded during these tests are not reported as the zero thrust signal level is not known. However, any transients in thrust which occurred are stored on disc. If the inner spool support bearing friction is symmetric, averaging data while jogging these bearings removes this source of error. 3.2 Needle Angle/Thrust Measurements

Needle anglejthrust tests were performed in the shaft rotation mode without jogging of the inner spool. A grease (NU1 reference system "A") was chosen for the lubricant for these tests to reduce the possibility of oil drops interfering with the optical path between the probes and the needle ends. A Gould Waveform Recorder was used to sample data with the trigger set for a f 20% window on the thrust range. Pretrigger is set at 50% so that the trigger event occurs in the center of the data file. Sample rate should provide at least 10 points per needle passage. The test procedure follows: Bring the shaft to speed then apply the load. Adjust the position of the two optical probes to maximize their signals as viewed on an analog scope. Zero the load, thrust, and torque charge amplifiers. Arm the recorder. The recorder triggers when the thrust level rises or falls by 20% of the recorder range. When the record is complete, brake the motor. Jog the drive by hand with normal load still applied and the thrust signal level being sampled by the Nicolet scope. Graphically average the thrust signal level during ( 6 ) to be supplied as the zero thrust signal level to software later. Transfer the 4 8 k bytes of data to the computer and store on disc.

~ A L P R O C K D U R E

In this work, the measurement of absolute frictional torque was a result of averaging several revolutions and the thrust and needle angle measurements were transient measurements with no averaging. For this reason, two test procedures were used. Test bearings were cleaned in acetone in a "sonic" cleaner before being pressed into the torque or drive module. 3.1

The load was applied for about five (unless noted) seconds. Averaged data of this period of time yielded the torque level. The load was removed and the drive motor braked. The drive module was jogged by hand several times. Data of this period of time were averaged to give the zero friction level. Voltage levels from data averaged during ( 4 ) were subtracted from those averaged during ( 2 ) to give absolute frictional torque.

Absolute Friction Measurements

For all absolute friction tests, the inner spool support bearings in the torque module were jogged at a frequency of 1 H, and an amplitude of 1l0 for a maximum velocity of 13 rpm. Each test bearing was lubricated once with a 1OW-40 commercial engine oil. Oil was added by syringe until it overflowed from the horizontal bearing. The test procedure follows:

4 TESTRESULTS 1)

Without load, the bearing was brought to speed and jogging of the torque module begun.

4.1

Friction Torque Tests

The friction coefficient, p, can be defined as

27 1

v=-

T

rSW

where T is frictional torque, rs is the radius of the shaft and W is the radial load on the bearing. Friction coefficients for shaft rotation and 5 seconds of operation with 1OW-40 motor oil are plotted vs. shaft speed for four loads in Figure 4. The test bearing is B1212, an unmodified full-complement 19.05 nun bore drawn cup needle bearing with 27 needle rollers. Similar data for the same bearing and cup rotation is plotted in Figure 5, along with results for a caged bearing. The caged bearing was 51212, a 19.05 mm bore drawn cup bearing with 17 retained needles. In all cases at lower loads the friction coefficient is sensitive to speed with values that increase with speed. At high load, the friction coefficient is reduced from that at low load and is relatively insensitive to speed. These effects can be attributed to the predominance of viscous losses at light load (speed sensitive) and Coulomb type friction at high load (speed insensitive). To check, these tests might be repeated for a low viscosity oil or a grease. The frictional torque of the caged bearing was less than half that of the full-complement version for the same load. This can be attributed to the replacement of a roller/roller contact of infinite slide to roll ratio (for which hydrodynamic lubrication is difficult to achieve) with a cage/roller contact with slide to roll ratio of 2. The cage also guides the needles to reduce axial skew and attending friction (see later section). The rotating cup consistently showed higher friction than the rotating shaft mode for the full-complement bearing (the caged bearing was only used in the cup rotation mode). At low load the ratio was about 2 to 1 and for high load about 1.5 to 1. Since the affect of rotation mode is greatest at light load, viscous drag may be the cause of the difference. The rotating cup would tend to retain oil in the cup while the rotating shaft would not. 4.2 Needle AnRle/Thrust Tests All results in this section are for shaft rotation in a full-complement bearing lubricated with grease. Figure 6 illustrates typical behavior when a reversal (sign change) in thrust occurs. The needle bearing appears to operate somewhat stably with a non-zero preferred thrust which will occasionally and unpredictably reverse. In fact, most attempts to record a spontaneous thrust change on this rig were unsuccessful. Often, acceleration of the drive brought on a thrust change. This observation is in agreement with Ref 141 where it was concluded that the needles in a loaded full-complement bearing operate skewed. Note the similarity between Figures 1 and 6. Figures 7-8 present relative needle angle, absolute thrust, relative frictional torque, and needle complement to shaft speed ratio as functions of time. Needle angle is calculated from the phase difference between the signals from the two optical probes at needle ends (in

the bearing load zone) and the average complement velocity for the entire record and the length of a needle. Needle angle is defined in Figure 3 . The frictional torque which is plotted is relative since the zero torque signal level is undetermined for these tests. Also the support bearings are not jogged so that the attenuation of the signal due to support bearing friction is not known. The torque data is presented here, however, since the transients that are plotted not only show the trend of the torque response but also represent the lower limit of torque variations during a record. The needle complement speed to average shaft speed ratios plotted are for both the measured complement speed (calculated from the time required for 27 needles to pass the optical probes) and the complement speed calculated for the no slip condition from the measured shaft speed using Ncompl I

-

I

Nshaft no slip

-

r

Nshaft -

2(rstrn)

Nshaft

where the over-bar indicates an average over the data record and rs and rn are shaft and needle radii respectively. This presentation was selected because it shows the acceleration of the shaft during a record. Measured complement speed was consistently about 1.5% below the no slip speed. It should be noted that data was only collected when a significant change in axial thrust was encountered. In Figures 7-8 there is apparently a correlation between needle angle and thrust and torque. For the data of Figure 8 frictional torque and thrust were plotted as functions of needle angle in Figure 9. The record was divided into one hundred equal time intervals. Angles, torques, and thrusts were averaged over each period before being plotted. Therefore, in Figure 9 each point represents about six needle passages. The thrust vs. needle angle curve clearly shows the characteristic "S" shape of traction vs. side slip angle (Ref [61). The traction coefficient saturates at about 0.05. Of interest also is the minimization of frictional torque at the relative needle angle for zero thrust. It can be argued that the relative angle at which thrust is zero and torque is minimized should correspond to a needle angle of zero, i.e., the needles are axially aligned. Then, for the data of Figure 9, the needle angle is equal to the relative angles less 0.8'. The reduction in frictional torque when the needles are axially aligned is 0.014 N-m which for the load of 860 N gives a change of friction coefficient of Ap = 1.7 x or about 25% of the friction coefficient shown in Figure 5 . As this Ap value has likely been attenuated by support bearing friction, the actual torque reduction may have been much greater. In Figure 10, the angle data of Figure 7 are plotted as individual needle angles for one-fourth of the data record, centered about the middle of the record.

272 5

6

CONCLUSION

ACKNWLKLIGWE"

The authors gratefully acknowledge the support of The Torrington Company and the assistance of Michael Brauer, Dr. Y. P. Chiu and Robert Lugosi in the conduct of this research.

Frictional torque is greater for fullcomplement bearings than caged bearings, torque is higher for cup rotation than shaft rotation, and torque is minimized when the needles (full-complement) are axially aligned with the shaft in the load zone. A correlation was found between needle skew angle and axial thrust. Less than one degree change of needle skew is required to go from no thrust to the maximum thrust developed (about 5% of the radial load). Full complement bearings tend to operate with a preferred needle skew direction and attending thrust direction with occasional spontaneous reversals. Operation without thrust and needle skew is not stable. In many full-complement needle bearing applications a means of reacting the thrust generated by the needle bearing must be provided , e.g., thrust bearing surfaces on the faces of transmission planet gears. If a geometry (needle aspect ratio, clearance, etc.) can be found which minimizes needle skew and thereby thrust, this requirement may be relaxed and limiting speed would probably be higher. Frictional torque would be reduced. All of which would increase the applications for these full-complement bearings.

References

Tedric A. Harris, Rolling Bearing Analysis, John Wiley and Sons, 1984, p. 425-427. Eschmann, Hasbargen, Weigand, Ball and Roller Bearings, John Wiley and Sons, 1985.

L. J. Nypan, "Roller Skewing Behavior in Roller Bearings," ASME, JOLT, Vol. 104, July 1982. Ulezelski, Evans, Haka, Malloy, "Needle Bearing Axial Thrust Study," Society of Automotive Engineers, 830568, 1983. Bair, Winer and Griffioen, "The Tribological Behavior of an Automotive Cam and Lifter System," Trans. ASME, JOT, 108, 1986. Johnson, K. L., and Tevaarwerk, J. L., "Shear Behavior of Elastohydrodynamic Oil Films," Proc. Roy SOC. of London, 365A, 1977.

11

\I Y

-

NEEDLE COMPLEMENT PASSAGE TIMING

NEEDLE PASSAGE TIMING

I 0

v

-

Ill1 I

I' I

I I

0.05. Figure 1. S h a f t A x i a l Force f o r a Needle Roller Tappet a t 2 7 0 0 rpm of cam

O-'*

t TIME

273

Figure 2. Needle Bearing Simulator

LOAD I APROBE 2

,x/NEEDLE

ANGLE

THRUST FIBER OPTIC

t

I

SHAFT

Figure 3. Definitions of Rotation Directions, Load, Thrust and Needle Angle and Optical Probe Detail

274

-8 1 2 1 2 FULL COMPLEMENT - - 5 1 2 1 2 CAGED *OI

30

"i

X a 20

lo/ 5

0

0 r

X a 0

2

4

6

SHAFT RPM 1 1000

.'

8 10

1815N v

3341 Figure 4 . F r i c t i o n C o e f f i c i e n t , p , for s h a f t r o t a t i o n , 5 s e c runnlng, 1OW-40 ? l o t o r O i l . R a d i a l l o a d on

1

n

shaft as noted.

0

2

4

6

-I 8

CUPRPM / 1000 F i g u r e 5. F r i c t i o n C o e f f i c i e n t , & , f o r c u p r o t a t i o n , 5 sec r u n n i n g , IOW-40 M o t o r O i l

Figure 6. Axial Thrust for B1212 at 3000 rpm of S h a f t and 1815 N Load, Oil Lubricated.

275

Figure 7 .

Figure 8.

Run D,

Sshaft =

-

Run E, Nshaft

841 rpm, 860 N load, grease

= 850 rpm, 860 N load, grease

276

100

0.1

x THRUST

0

r l

RELATIVE TOROUE

N

O

-100

-2

0

-

N-m

-0.1

1 1.5 Figure

-

D, Nshaft = 841 r p m , 860 N and Corresponding Thrust

10. Run

2.5

-

Indjvidual Needle Angles

IOC

277

Paper X(ii)

Power loss prediction in ball bearings R. J. Chittenden, D. Dowson and C. M.Taylor

SYNOPSIS The determination of power losses and traction forces in modern ball bearings typical of aerospace applications is a complex task. The high rotational speeds commonly experienced by such bearings cause inertia effects to be important, and this inturn loads the balls heavily against the outer raceway of the bearing. The resulting disparity in contact angle tends to introduce a spin component to the motion of the inner raceway/ball contacts on top of the usual sliding and rolling motion. A complete analysis of the contacts would have to include the elastohydrodynamic analysis of heavily loaded contacts, and conjunctions with continuously variable surface velocities. The iterative solution required for such conditions, despite the use of powerful, modern numerical methods, still requires many tens of minutes processing on a large mainframe computer. The computations required for a bearing having 20-30 rolling elements (40-60 contacts) is therefore unreasonable, and even if this were possible its incorporation into the overall dynamic analysis of the bearing would again introduce many more levels of difficulty. For many years the design of bearings for aerospace applications has been based on knowledge gained experimentally, but with the slow introduction of various theoretical work to aid the designer in such calculations as minimum lubricant film thickness. The ever increasing cost of experimental work and the need to make the initial design the best possible, however, provide a requirement for much improved theoretical methods, and hence the need for developments of the type described in this paper. The purpose of the work has been to unite an analysis of bearing dynamics with realistic elastohydrodynamic pressure and film thickness profiles, and then to calculate realistic values for power loss and parer transfer within the bearing together with the provision of information on the contact traction forces. A well tried analysis was adopted for calculation of the bearing dynamics, and the use of a simple extrapolation allowed existing solutions to the elastohydrodynamic lubrication problem to be introduced. Calculations of power loss and traction force were then undertaken with the fluid assumed to be either Newtonian or Non-Newtonian, firstly for a single contact and secondly for the whole of an example bearing. The results obtained were then compared with other computations for the same bearing which were known to agree well with the available experimental evidence, and finaly the sensitivity of the analysis to various lubricant parameters was examined. The conclusions drawn from the work were that realistic power loss calculations could be made with a Non-Newtonian fluid model,,Fd that the most important lubricant parameters were the pressure-viscosity coefficient and the limting-shear-stress-pressure coefficient.

1 INTRODUCTION

It has been known for many years that bearing systems may generate considerable amounts of heat which must be removed to ensure the correct operation of the associated mechanical system. The requirement is particularly demanding in aerospace applications where the trend has been to seek bearings which are able to operate in ever more arduous conditions. The design process is far from simple since the amount of additional weight that can be introduced must be minimised, as must the size of the installation, and hence the bearing is often closely incorporated within the surrounding engine components. In oFder to satisfy all of these restrictions successfully at the design stage, therefore, reliable knowledge of the heat generation and heat transfer between components is essential. In the past this information has often been gained by incorporating an experimental test programme into the design effort and arriving at a satisfactory result by a trial and error method. Owing to the complexity of a modern gas

turbine and the cost of running an associated experimental programme the initial design is critical to the success of an engine. It is important, therefore, that designers must have access to improved methods of calculating parameters such as the power loss associated with viscous effects in the bearing chamber. The starting point for analytical methods developed to predict the power loss within the bearing chamber must be a dynamic analysis of the whole bearing, or a representative ball where conditions are such as to result in a purely axial load. Compared to many areas of tribology, however, the amount of attention paid to this type of analysis of high speed bearings has been small. This is partly explained by the complexity of the analysis required to determine the load, surface velocities, and geometry associated with each conjunction within the bearing, a task most readily undertaken by an iterative procedure on a modern high speed digital computer. In reality there must be an interaction between the traction forces acting upon the

278

conjunctions and the dynamic modelling of the bearing, but by neglecting the lubricant and assuming a coefficient of friction over the contact area Jones(1,Z) managed to simplify the analysis and the resulting procedure has been used as a standard by engineers for many years. More recent studies were able to include some of the influences of a lubricant into the calculations by employing experimentally derived expressions for such features as traction forces and viscous drag. (For example the work of Gentle and Boness ( 3 ) and Pasdari and Gentle (4)).

(b) Estimate the elastohydrodynamic lubrication features of each contact within in the bearing by extrapolating from existing solutions obtained for similar geometrical configurations. (c) Compute traction force and paver loss for each contact based upon the extrapolated elastohydrodynamic pressure and film thickness profiles, and hence the total power loss and power transfer for the whole bearing by summation. [A Non-Newtonian lubricant could also be used at this stage.]

A more complete analysis, in which the traction forces and power losses are determined from the shear forces acting on the surfaces of the contacting solids poses many problems. The high loads, particularly at the outer raceway/ball contacts, where inertia forces are significant, mean that the local elastic deformation of the solids can be large when compared with the resulting lubricant film thickness, and hence the appropriate type of analysis for these contacts, as well as those between inner raceway and ball, is that of elastohydrodynamic (E.H.D.) lubrication. The solution procedure for these contacts requires the simultaneous solution of the expressions governing the local elastic deformation and the associated Reynolds' equation for fluid film lubrication, which must include the effects of pressure (and perhaps temperature) upon the lubricant density and dynamic viscosity. The typical contact between a ball and a raceway may be represented by a "line contact" (Dowson and Higginson (5)) for the calculation of minimum film thickness, but the evaluation of power loss requires the possibility of spin to be included into the analysis. This can only be accomplished by the use of the more complex elastohydrodynamic "point contact" analysis of the type presented by Dowson and Hamrock (6,7,8,9) and further developed to allow the influence of typical conjunction loads to be examined (Evans and Snidle (lo)), and by Chittenden et a1 (11). Recent developments in numerical techniques (Lubrect et a1 (12,131) can also be introduced with advantage. The modifications required to allow for spin were made hy Xu (14), whose work also indicated the need to consider the lubricant to be Non-Newtonian as shear rates could reach levels where a Newtonian analysis would be unrealistic. This feature had been indicated in earlier rheological studies, Sandborn and Winer (15) and Adams and Hirst (16). The effort to merge all these effects into a single analysis would clearly be immense, especially when it is remembered that a single E.H.D. solution can still consume many tens of minutes of computer time on a large, high-speed, mainframe computer. At the outset it was recognised that by making several simplifying assumptions it would be possible to evaluate power loss and traction force with a fair degree of accuracy, and it is this work that is described in this paper. The major steps in the analysis are indicated below and, with the exception of the dynamic analysis of the bearing, are detailed in subsequent sections:-

Having set out the assumptions embodied in the analysis and dealt with the operation of its components, for which a flow diagram is provided as an overview, the procedures are applied to a representative bearing. Single contacts are first considered to show the effects of considering a Non-Newtonian fluid, and then by expanding to include the whole bearing the influences of several lubricant parameters are examined.

(a) Determine the conjunction loads and surface velocities by the use of a standard dynamic analysis of the unlubricated bearing.

1.1 Notation constants used for film thickness and pressure extrapolations ball diameter (m) distance between raceway curvature centres (m) reduced elastic modulus (Pa) applied axial load (N) load applied to a particular conjunction (N) load obtained from a numerical solution (N) applied radial load (N) pressure-represeptative shear stress coefficient (Pa- ) elastic shear modulus of the lubricant (Pa) fluid shear modulus (Pa) dimensionless central film thickness dimensionless film thickness at node "j" in the computational zone dimensionless minimum film thickness dimensionless film thickness constant used for definition of elastohydrodynamic film thickness dimensionless central deformation due to Hertz pressure distribution largest dimensionless film thickness within the computational zone axial distance between ball centre and outer raceway curvature centre (m) radial distance between ball centre and outer raceway curvature center (m) fluid pressure (Pa) dimensionless pressure at node I'j", p = P/E' S(x,y) geometrical separation of the contacting bodies W(x,y) elastic deformation coordinate directions (see text) xar y pressure-viscosity coefficient (Pa-1) 6, free contact angle (degrees) inner race contact angle (degrees) 6, outer race contact angle (degrees) axial displacement of inner raceway (m) radial displacement of inner raceway (m) 8: Sx ,Sy elemental dimensions of the computational area associated with each node -0 lubricant dynamic viscosity (Pas) h dimensionless lubricant viscosity n, lubricant dynamic viscosity at conjunction inlet (Pas)

279

contact strain rate ( s - l ) shear stress (Pa) representative shear stress, indication the point at which the fluid becomes appreciably non linear (Pa)

X T TO

2

DESCRIPTION OF THE PROBLEM

(a)Assumptions In order to undertake the computations presented in this paper it was necessary to make use of a few additional assumptions. These significant additional assumptions are listed below:That an existing solution of the elastohydrodynamic lubrication problem could be used as the basis of an extrapolation to yield pressure and film thickness profiles for similar contact geometries within the bearing. (ii) That the extrapolated profiles may be used as an approximation to a contact which is spinning and/or sliding in addition to rolling, the only surface motion of the original solution, and that a non-Newtonian lubricant model could be imposed on these conjunction features. (iii) That the extrapolated isothermal conjunction characteristics would not be significantly changed by the heat generation within the contact associated with its spinning, sliding or rolling motions.

regular grid structure specified with respect to the centre of contact. In order to extrapolate the pressure profile it was necessary to determine the values of conjunction load and geometry from the bearing dynamics analysis. These parameters then allowed the semi-major and semi-minor axes of the Hertzian contact ellipse to be evaluated by the one point iteration technique of Hamrock and Anderson (18). With these parameters and the reduced elastic modulus if the contact known it was then possible to redefine the existing, normalised, elastohydrodynamic solution and to evaluate a real conjunction load as:-

(i)

The details of the extrapolation process are given in a later section, however, use of these procedures was found to result in good agreement between the small number of solutions available for testing. (A good extrapolation being deemed to be one where there were no observable differences between the isometric projections of the extrapolated film thickness or pressure profiles and those of an existing solution with the extrapolated characteristics.). At the outset of the project knowledge of the likely effects of spin and non-Newtonian lubricant characteristics was limited, but recent work at Leeds has allowed a clearer picture to be obtained. Xu (14) investigated the elastohydrodynamic lubrication of contacts with spin and found that with spin speeds typical of those in rolling element bearings the film thickness and pressure profiles were changed only slightly. A similar situation has been found by Esfahani (17) concerning the influence of a non-Newtonian lubricant model. This work found that with a slide-roll ratio twice that typically found in ball bearings the computed elastohydrodynamic solution differed from the Newtonian situation by approximately 10%. The third assumption is based upon the knowledge that conditions within the contact are largely determined by situation at the conjunction inlet and provided that these are specified correctly the effect of a rise in fluid temperature within the conjunction should not be significant. (b) Pressure Profile Extrapolation The extrapolation of pressure, and of film thickness, is based on existing elastohydrodynamic results which define a solution in a normalised form with respect to a

A pressure multiplier was then computed from the ratio of applied load to integrated load, and the specified load obtained by multiplying all the pressures forming the integrated load by this constant. P.

=

3118,

F.PP -

P.

(2)

Fint

]old

It should be noted that this simple form of extrapolation takes no account of the changes in pressure profile likely to result from the differences in operating conditions between the inner and outer raceway/ball contacts. This would be particularly noticeable for some of the relatively high speed, low load conditions on the inner raceway where the extrapolated profile might be a poor approximation to a specific E.H.D. calculation. (c) Film Thickness Extrapolation The development of a procedure for the extrapolation of the film thickness profile proved to be somewhat more difficult than that for pressure. Minimum and central film thickness were calculated for the conjunction operating conditions by means of the formulae presented by Chittenden et al. (1985). Initial attempts to extrapolate the film thickness were based on the linear relationship:H. JIl8l.4

=

C, H.

+ C,

(3)

]old

C, and C, being determined such that the extrapolated profile had the predicted values of minimum and central film thickness set into it. Observation of the resulting film profile, however, indicated that as H. increased above the predicted central film thickness value the extrapolation became more and more unrealistic. This problem was particularly severe around the first point on the solution grid (H , the greatest distance from the centre ok contact.), and hence this node was chosen as the third film thickness value that should be specified in the extrapolation procedure, along with Hmin and Hcen. The standard approximation for the film thickness at node "j" in the elastohydrodynamic solution process is:Hj

Ho + S(X,Ylj + W(X,y)j

(41

In order to allow H, to be determined it was assumed that the elastic deformation (W(x,y) was negligible at the first grid node, and that the film thickness constant (Ho) could be

280 approximated by the predicted central film thickness minus the deformation at the centre of contact. Hence the film thickness at (HI) may be written as:-

Stress-Strain relationship from Johnson and Tevaarwerk (19).

0

1 dr G* dt

= -

(5) The film profile was then extrapolated by the use of the following expression:H.

=

C

3naw

d. + C, ]old

H. ]old

+ C,

(6)

H -H - minnew Cennew H -H mino,,

- H . H1old

H. =

H minold

1

mnold

-H cenn

minn e w

c,

‘enold

ew

-H

- ‘1

CHmin0 - Hceno 1

‘enold

(d) Shear Stress Calculations The shear stresses associated with each node in the solution grid were determined for the driving surface (z=O) and the driven surface (z=h) by means of the following expressions:-

are the surface where ulowerand uu velocities at z=O ahr i=h respectively, and ax , 6 define the area of each grid element. The p%essure gradients were specified by a finite difference approximation, and the viscosity was evaluated using the Barus pressure-viscosity expression - (oj = %e*j 1. It may be seen from these two expressions that for an increasing load (increasing viscosity, pressure gradiants and reduced central film thickness) and/or increasing sliding speed the Newtonian lubricant has no limit to the possible values of local shear force. The prediction of unrealistic values is therefore possible and in order to keep them within reasonable bounds a non-Newtonian model must be introduced. (el The non-Newtonian Mdels It may be seen from equations (7) and (8) that the local shear forces have been represented by a term involving pressure gradient, and another involving velocity gradient. The influence of these terms is a function of position since the pressure gradients are greatest around the edge of the Hertzian region whilst the velocity gradient term would tend to be more significant within the Hertzian region where the film thickness was smallest, and the viscosity highest. In order to facilitate the inclusion of Non-Newtonian effects it was assumed that the two components could be evaluated separately, and that the sliding component of shear force could be replaced by a term developed from either of the following Non-Newtonian expressions:-

ran

e ‘

]

Stress-Strain relationship from Gecim and Winer (20). 1 dr

where -H

no +si*[

t

=

q

rL

+n tanh-l

(10)

In cases where spinning caused the local slip direction to be displaced from the rolling direction the appropriate resolved component was used, and for production of the results shown in this paper the only stress-strain relationship used was that according to Johnson and Tevaarwerk. 3 COMPUTATIOE~PROCEDURE The computational scheme is illustrated by means of a flow chart, Figure 1. If a new bearing was to be analysed then the first stage was to run the bearing dynamics analysis. This followed the analysis of a high speed bearing presented by Jones (1,2) as set out by Harris (21). The analysis assumed values of the axial and radial displacement of the inner raceway (6 , S r ) together with bearing misalignment (el, which was taken to be fixed at zero degrees for the computations presented in this paper. Expressions governing the bearing geometry and equilibrium of forces were then solved for the secondary unknowns of axial and radial ball centre/outer raceway curvature centre distance ( L a , L r ) together with the deflections at the inner and outer ball/raceway contacts. The primary unknowns could then be altered by checking for axial and radial equilibrium and the iteration was continued until the change in the primary unknowns was less than a pre-defined limit. ( A full analysis of the bearing should also consider equilibrium of moments, but because of the difficulty of specifying the resistance to misalignment of the bearing on its own this feature was not included. During the initial testing of the analysis misalignment was permitted to such an extent that the residual moment from the fully aligned case was reduced by 50% and for this situation very little change was observed in the computed power losses.) The power loss/traction force analysis involved calculations for each contact in the bearing starting with the inner raceway and then dealing with the outer raceway. The operating conditions for each contact were used to extrapolate an existing elastohydrodynamic solution to represent the specified conditions (Section 2(b)-(c)). The local shear stresses and associated shear forces were then evaluated with non-Newtonian effects incorporated if required. (The term 1 dr being approximated by 1 Us dr 1. The calculation of local shear stress could also be repeated for a Hertzian pressure profile, in which case the Hertzian flat was separated by the predicted central film thickness.

a

The summation of the local shear forces carried out to give the total shear force and moment acting on the two surfaces, and the spin power loss was then easily determined:-

was

28 1

-

____-_-------

r----

4

+

m

Output Results

Slip Speed

Start

I Input Existing

I I I I

END

Result

Extrapolate pressure and fi

I

Sum shear stresses to obtain traction force and contact torque

Evaluate power losses

No c

Calculate bearing power losses and output results

I No

Figure 1

Flow diagram f o r c a l c u l a t i o n procedure

TO illustrate the use of the above analysis a

( Q denoting spin speed).

Separation of the rolling and sliding power losses was undertaken by specifying the rolling power loss to be that expected for a contact without spin or sliding, hj aPj

Y o l l E

L e e r

1 [ T ax

1

(12)

The sliding power loss was the rolling/sliding power loss less the rolling power loss.

typical aerospace bearing of 250mm diameter running at 10,000rpm was taken as an example. The basic operating conditions of the bearing are set out in Table 1, whilst typical conjunction parameters are provided in Table 2 together with the changes in these values around the bearing. The bearing dynamics were then determined for these conditions, and although not specified to the analysis the raceway control was that of the outer raceway. To allow the power loss/traction force analysis to be undertaken it was necessary to specify a number of lubricant constants, see Table 3, taken from manufacturers data or estimated from the work of Johnson and Tevaarwerk (19) or Evans and Johnson ( 2 2 ) . The bearing and its operating conditions were chosen so that they

282 could be compared with others analysed by Rolls-Royce using a heat transfer analysis, (Nicholson (2311, which were also known to have good agreement with experimental measurements. The bearing dynamics were first evaluated, assuming 3% inner raceway slip and before computations commenced on the whole bearing, changes in sliding speed were examined for a conjunction on the inner raceway. The results show the difference in power loss predictions between the Newtonian and non-Newtonian fluid models, Figure 2. Results for the whole bearing are shown in Table 4. This contains values for inner raceway rolling, spinning and sliding power loss together with power transfer across to the outer raceway contacts, together with the predicted outer raceway power loss for four different analysis techniques:-

The contribution to the overall power loss by each contact is illustrated in Figure 3 for both inner and outer ball/raceway contact with the elastohydrodynamic analysis (non-Newtonian lubricant 1. As may be seen from this table there is a noticeable difference between the Rolls-Royce results and those obtained by the analytical techniques presented in this paper. To investigate the sensitivity of the analysis to changes in the lubricant characteristics, computations were carried out with the elastohydrodynamic film and pressure profiles and a Non-Newtonian fluid model for five-fold changes in the following parameters compared with those given in Table 3:-

conjunction viscosity at inlet ( ) lubricant pressure/viscosity coef icient

P

( a)

Rolls-Royce calculation procedure. This analysis is based upon the calculation of heat balance for the bearing and, as noted above, is detailed in Nicholson (1986). (ii) Elastohydrodynamic analysis, (Newtonian lubricant). Here, the film thickness and pressure profiles obtained according to the extrapolations described in Sections 2(a) and 2(b) are used in conjunction with the local shear stress expressions given as equations (7) and (8). (iii) Elastohydrodynamic analysis, (non-Newtonian lubricant). In this situation the same film thickness and pressure profiles are used as in case (ii). The Newtonian sliding shear stress (denoted by the right hand term within the brackets of equations (7) and (8)) is replaced by a non-Newtonian expression derived from equation (9). (iv) Hertz approximation. This analysis employs the well known Hertz pressure profile and dry contact surface shape. The latter, however, is separated by the predicted elastohydrodynamic central film thickness to represent the typical lubricant film over the majority of the contact area.

(i)

critical shear stress ( T ~ ) critical shear stress/pressure coefficient

(9, Axial load

4500 N

Radial load

1000 N

Rotational speed

10,000 rpn

Slip speed

Number of Balls -

Ball Diameter

Reduced Elastic Modulus for Ball Raceway Contacts (E') ~~

0.022m

217 x lo9 Pa

~

Side leakage radius of curvature ( R E )

3.9 x 10-lm

Entraining radius of curvature

(Re)

9.8 x

Inner Raceway

Rolling velocity

(Vri

46 m/s

Ball Contacts

Sliding velocity

(VSi1

3.6 m/s

Spin speed

(OEi )

6000 rad/sec

Ball load

(FBi 1

210 N

Side leakage radius of curvature (Rs)

8.5 x 10-1

Outer Raceway

Entraining radius of curvature

(Re)

1.3 x lo-'

Ball Contacts

Rolling velocity

(Vro

82.5 m/s

Ball load

(FBo

2920 N

Table 2

Conjunction Parameters for a Typical Ball

m

283

(n)

Inlet dynamic viscosity

1.65x1Q5 Pas

1 4- Power Loss llnner Race) 2 0 Power t o s s IOutsr Race1

Viscosity-pressure coefficient Representative shear stress

3.0~10~Pa

Shear-stress-pressure coefficient

( s)

6 .Oxlo-' 1OQ

1-

0

30

Lubricant shear modulus (G*) 2.5~10' Pa

60 90 120 150 180 210 2L0 210 300 330 Angle from Direction of the Radial Load Idegreesl

Figure 3

(m)

Shear-modulus-pressure coefficient

360

P r e d i c t e d Power Loss from t h e Bearing. Non-Newtonian, Barus P r e s s u r e V i s c o s i t y Expression

4.0

-~

Table 3

1

2

Lubricant Parameters

4 N e w t o n i a n Model non-Nwtonian Mod81

+

lo'

/ /

-2 -

m

7 . .

1

2 3

4

*

iklet viscosity -cL pressure-viscosity coelficient -+critical shear stress -*- strmss-pressure coefficient

e

Y

2

d

..-

500

-

2

2 3

_ _ o- - ' --- -

-m-. k

0

I

'

12

'

16

0

-.

*

1

'

'

24

20

28

1

.

32

1

36

'

b

B

I

I

I

40

Fractional Slip W1 .

Figure 2

T o t a l Power Loss f o r a S i n g l e Conjunction

Rolls-Royce

Rolling Spinning Inner Race Sliding

'

I

lpmr Race Outer

Transmitted

I

Total Power Loss

qF

I I I I I 1200

Newtonian

220

I

II

non-Newtonian

100

63

14 88

1300

160

5200

2100

~

3100

5200 7290

~

3710

I

3100

I

110

3593 ~~

Table 4

Hertz

Power Losses for the Di lferent Models (All results

372 L

1

Watts)

284

The results of these sensitivity tests are displayed in Figures 4 to 8, which illustrate inner raceway rolling power loss, inner raceway sliding power loss, inner raceway spinning power loss, power transfer and outer raceway power loss respectively. 5 DISCUSSION

The results shown in Figures 2 clearly show the need to introduce the non-Newtonian fluid model, since as the fractional slip increases the shear stresses generated within the contact reach the stage where the p e r loss predicted by a Newtonian analysis is totally unreasonable. Indeed if the bearing operating characteristics were such that it was operating towards its design limit of perhaps 10,000 N axial load, then the power losses given by the Newtonian analysis would be many orders of magnitude greater than the corresponding Non-Newtonian analysis, and therefore beyond the level which would be considered realistic for these situations. The influence of radial load on the power loss at each conjunction, shown in Figure 3, also shows the large difference between inner and outer raceway power loses caused by the effects of inertia acting on the rotating elements. The slight increase in the outer raceway power loss, from a minimum at 0 degrees to the radial load to a maximum at 180 degrees, may be attributed to the change in contact surface velocity rather than to any change in the loading conditions.

1 2 3 I

i

* -p- *-I-

i i c t viscosity pressure-viscosity cocfticient critical shcar'strcss stress-pr~ssurc coefficient

/

The results presented in Table 4 show that for the particular conditions considered there is only a small difference between the Newtonian and non-Newtonian results for full elastohydrodynamic profiles. The overall level of agreement is not good, with the Hertz approximation yielding very unsatisfactory results for the rolling power losses. It is a little surprising that the Newtonian results fall short of those obtained by Rolls-Royce, but although the model was simple, neglecting asperity interaction and thermal effects, it is likely that these differences can be explained by modest changes in the parameters defining the lubricant characteristics. The powerful effect of these values is examined shortly. The way in which power loss is ascribed to the various components should not be used to choose the best method for calculation, however, since correlation with experimental work can be made only in terms of the total power loss. Two further points must be noted regarding this table, the first being that the rolling power loss for a Hertzian situation employing both positive and negative pressure gradients should be zero. The non-zero value in the table was attributed to numerical errors associated with the finite difference approximation of pressure gradients which were induced by the slight displacement of the solution grid in the entraining direction coupled with the application. Secondly, during early testing of the computer codes the local shear stresses were checked and it was found that large pressure gradients around the edge of the conjunction could produce local traction 1 2 3

P

4

-A-inlet viscosity -+pressure-viscosity cocfticicnt -+-critical shear stress --str~sr-presswe cosllirient

/ 0

/

A

/ 100

:'

/

:

I! I !

/

;

/ 4 ,

10 0.1

,

/

/

. . . . .I

I 10.0

1.0

Figure 6

1 2 3 4

0.1

Figure I

-

-+ prcssurc-vircority

cocfficient critical shear r l r e s r stress-prassure coefficienl

. . . ,1.0,

I

iao

/

The E f f e c t of Changes i n t h e L u b r i c a n t P a r a m e t e r s upon the

2

-P- pry ruri-viscosity cocllicieni

L

-*-

3

/

, ,

Power T r a n s m i t t e d from the I n n e r Race

--b inlet viscosity -*-

,

Ratio of paranctcr to bare value

The E f f e c t of Changes i n t h e L u b r i c a n t p a r a m e t e r s upon t h e I n n e r Race S p i n Power Loss

-+-

d

10'

Ratio of parameter to base value

5000

P

-+-

cr&l shear r l r c r s strcss-pressure cocfficicnt

P

-

/

/ /

1

10' 0.1

{

kl

.

,

. , ,,,

I

1.0

I

100

Ratio ot parmeler to base value

Figure 5

The E f f e c t of Changes i n t h e Lubricant: Parameters upon t h e I n n e r Race S l i d i n g Power Loss

1oM) 0.1

Figure 8

Ratio of paranctcr 1.0 to base valuc

The E f f e c t of Changes i n the L u b r i c a n t - P a r a m e t e r s upon t h e O u t e r Race R o l l i n g Power Loss

10.0

285

coefficients well in excess of unity. To restrict the local traction forces at these points to within reasonable limits a limiting local traction coefficient of 0.7 was imposed. (This procedure was applied to all computations and was influential in the calculation of the non-zero Hertzian rolling power loss when coupled with point one, above). An interesting feature observed from the calculations with the full elastohydrodynamic film profiles was the production of a side force acting on the contact, shown in Figure 9. This feature resulted from the shape of the elastohydrodynamic conjunction in which the side force at a point some distance from the transverse centre line is not balanced by that of a point at an equal distance on the other side of the centre line. The size of this force, however, is some two orders of magnitude less than the corresponding traction force.

The influence of the lubricant characteristics on inner race rolling power loss, shown in Figure 4, may be seen to be most significant for the inlet viscosity value, which acts through the film thickness formulae to affect the local shear stresses by being raised to a greater power than the pressure-viscosity coefficient. As neither the critical shear stress nor critical shear stress-pressure coefficient appear in these formulae or are included in the pressure extrapolation, these value have no effect on the rolling power loss. The inner race spin power loss, Figure 5, is most dependent upon the pressure viscosity coefficient, and comparison of the y-axis scale of this figure with that of Figure 4 shows that the changes produced are much more marked. An increase in this parameter also increases the predicted film thickness and hence decreases the local sliding shear stresses. The associated increase in viscosity due to the Barus expression, however, more than makes up for this deficiency. The comments made for Figure 5 also apply to the transmitted power shown in Figure 6. The effect of changes in the critical shear stress is also noticeable in this figure. Its influence is by setting the level at which Non-Newtonian effects are important and hence is a measure of the extent to which Newtonian effects still hold. The final illustration in this set, Figure 8, exhibits the same effects as Figure 4 although the magnitudes are slightly different.

O'lOh

The last item of Table 4 that has not yet been conunented upon is the balance between the power transfer and the paver lost at the outer racewaymll contacts. Since the outer race was taken to be stationary, the power transferred should match the power lost by these contacts. To ensure this balance the missing link, shown as the dashed line in Figure 1, would be required. An estimate of the necessary inner race slip ratio, however, was obtained by additional computations for slip values of 0.6% and 15% (a value rather higher than typical in aerospace bearings). These results are recorded on Figure 10, and from this it may be seen that the required balance point is at approximately 7% slip. 6

CONCLUSIONS

The results of this study can be summarised as follows:-

. A method has been developed for the calculation of power loss in deep groove ball bearings based purely upon theoretical considerations. Simple extrapolations have allowed realistic elastohydrodynamic film thickness and pressure profiles to be included and a non-Newtonian lubricant model has been incorporated into the computations. Predictions of power loss in a representative aero-engine bearing have been made and, with the exception of sliding power loss, found to be of similar magnitude to those predicted by Rolls-Royce using a different approach. The latter was found to agree well with experimental measurements. (The total power loss being in agreement to almost a factor of 2 although the constituent parts do not show the same correlation).

. The influence of the lubricant characteristics upon the predicted components of power loss has been examined. This indicated that lack of precise knowledge of these values, particularly the pressure-viscosity coefficient, could account for much of the difference between the power loss predicted by the computations detailed in this paper and those obtained by Rolls-Royce. Finally, the missing link in the interaction between the bearing dynamics analysis and the parer loss calculations was approximated by undertaking calculations for

I I

+outer race rolling power loss -p. power transmitted from inner race

/

/

4

0.02

0.00

/

1 0

d/

d M

Figure 9

60 90 120 IS0 180 210 240 210 Anqle from the Direction of the Radial Load

300

330 3bO

The S i d e Force on t h e Contact due t o Spinning a t t h e Ball/ I n n e r Raceway Contact

w)'

10'

10'

Inner Race Slip Ratio 1%1

Figure 10

The E f f e c t o f Changes i n t h e Inner Race S l i p R a t i o upon Power T r a n s f e r and Outer Race R o l l i n g Power

different assumed slip ratios. This then allowed the slip ratio required to balance the power transfer and outer race power loss to be estimated. 7 ACRNOWLEDGEMENTS The authors would like to thank Rolls-Royce plc. and the S.E.R.C. for the funding of this project as part of the Roll-Royce/S.E.R.C. co-funded scheme, and in particular Dr J. Dominy and Mr R. Nicholson of Rolls-Royce for their invaluable help and comments. References JONES A.B. (1959) 'Ball Motion and Sliding Friction in Ball Bearings', Trans. A.S.M.E., J. Basic Eng., 1-12. JONES A.B. (1960) 'A General Theory for Elastically Constrained Ball and Roller Bearings under Arbitrary Load and Speed Conditions', Trans. A.S.M.E., J. Basic En9 , 309-320. GENTLE C.R. and BONESS R.J. (19761, 'Prediction of Ball Motion in High-speed Thrust Loaded Ball Bearings', J. Lubr. Technol., 98(3), 463-471. PASDARI M. and GENTLE C.R. (1986), 'Computer Modelling of a Deep Groove Ball Bearing With Hollow Balls', Wear, 111, 101-114. DOWSON D. and HIGGINSON G.R. (19651, 'Elastohydrodynamic Lubrication, The Fundamentals of Roller and Gear Lubrication', Pergamon, Oxford. HAMROCK B.J. and DOWSON D. (1976a1, 'Isothermal Lubrication of Point Contacts, Part I, Theoretical Formulationr,J. Lubr. Technol., 98(2), 223-229. M X K B.J. and DOWSON D. (1976131, 'Isothermal Lubrication of Point Contacts, Part 11, Ellipticity Parameter Results', J. Lubr. Technol., 98(3), 365-378. HAMROCK B.J. and DOWSON D. (1977a), 'Isothermal Lubrication of Point Contacts, Part 111, Fully Flooded Results', J. Lubr. Technol., 99(2), 264-276. M O C K B.J. and DOWSON D. (1977b), 'Isothermal Lubrication of Point Contacts, Part IV, Starvation Results', J. Lubr. Technol. , 99( 1), 15-23. (10) EVANS H.P. and SNIDLE R.W. (19811, 'Inverse Solution of Reynolds' Equation Of Lubrication Under Point Contact Elastohydrodynamic Conditions', J. Lubr. Technol. 103(4), 538-546.

.

(11) CHITTENDEN R.J., DOWSON D., DU" J.F. and TAYLOR C.M. (1985), 'A Theoretical Analysis of the Isothermal Lubrication of Concentrated Contacts, Part 11, General Case, with Lubricant Entrainment along either Principal Axis of the Hertzian Contact Ellipse or at Some Intermediate Angle', PKOC. R. SOC. Land., A397, 271-294. (12) LUBRECr. A.A., TEN NAPEL W.E. and BOSMA R. (1987), 'Multigrid, and Alternative Method of Solution for Two-Dimensional Elastohydrodynamically Lubricated Point Contact Conditions', J. of Tribology, 109(2), 437-443. (13) LUBFWT A.A., VENNER C.H., TEN NAPEL W.E. and BOSMA R. (1987), 'Film Thickness Calculations in Elastohydrodynamically Lubricated Circular Contacts, Using A Multigrid Method' , J. of Tribohgy, 110(3), 503-507. (14) xu H. (19881, P~D.Thesis, Department of Mechanical Engineering, Leeds University. (15) SANDBORN D.M. and WINER W.0. (1971!r 'Fluid Rheological Effects in Sliding Elastohydrodynamic Point Contacts with Transient Loading: 1- Film Thickness,, J. Lubr Technol. 93( 2) 262-271. (16) AaAMs D.R. and Hirst W. (19731, 'Frictional Traction in Elastohydrodynamic Lubrication,, Proc. R. SOC. Lond., A332, 505-525. (17) ESFAHANI M.Z. (1988) Private Communication. (18)HAMROCK B.J. and ANDEFGON W-J. (1973)r 'Analysis of Arched Outer-Race Ball Bearing Considering Centrifugal Forcesr, J. Lubr. Technol., 95(3), 265-276. (19) JOHNSON K.L. and J.L. 'Shear Behaviour of Elastohydrodynamic Oil Films', PKOC. R. SOC. Lond., A356, 215-236. (20) GECIM B. and WINERW.0. (1980) 'Lubricant Limiting Shear Stress Effect on EHD Film Thickness', J. Lubr. Technol., 102(2), 213-221. (21) HARRIS T.A. (1984) 'Rolling Bearing Analysis', John Wiley and Sons, New York. (22) EVANS C.R. and JOHNSON K.L. 'The Rheological Properties of Elastohydrodynamic Lubricants' , Proc. Inst. Mech. Engrs., 200(C5), 303-312. (23) NICHOLSON R. (1986), 'The prediction of Operating Temperatures in High Speed Angular Contact Bearings', Paper XXI(ii), Fluid Film Lubrication- Osbourne Reynolds Centenary, Proceedings of the 13th Leeds-Lyon Symposium on Tribology. Editors D. DOWSon, C.M. Taylor, M. W e t and D. Berthe, Elsevier.

.

287

Paper X(iii)

The effect of roller end-flange contact shape upon frictional losses and axial load of the radial cylindrical roller bearing H. Krzeminski-Fredaand B.Warda

The subject o f the consideration i s the r a d i a l c y l i n d r i c a l r o l l e r b e a r i n g o f the NJ type w i t h c o n i c a l flanges and spherical ends r o l l e r s . In the paper, t h e o r e t i c a l bases have been presented f o r s e l e c t i o n o f the r o l l e r end radius and the flange i n c l i n a t i o n angle r e s u l t i n g f r a n the c m p r a n i s e between an a t t e npt t o minimizing f r i c t i o n a l losses i n the b e a r i n g and the n e c e s s i t y t o guarantee an a p p r o p r i a te shape o f the o i l gap conducive t o f o m t i o n o f an o i l f i l m a t the r o l l e r end - f l a n g e c o n t a c t .

1 I NTRODUCT I ON The r a d i a l c y l i n d r i c a l r o l l e r bearing o f the NJ type can a l s o carry, apart f r a n r a d i a l l o a d , s m a x i a l load. This load i s c a r r i e d by the bearin g r o l l e r end - flange contacts. NorrmI forces occurring a t the contacts and f r i c t i o n forces accmpanying them d u r i n g the bearing operation, cause the r o l l e r t i l t i n two r e c i p r o c a l l y perpendicular planes i n t e r s e c t i n g i t s a x i s ( F i g . 1). The t i l t i n the plane p a r a l l e l t o the bearing a x i s , r e f e r r e d t o as the skew (angle ~1 1, causes a S I ide a t the r o l l e r - main race contacts and, as a r e s u l t , an increase i n the f r i c t i o n a l losses i n the bearing. The t i l t i n the plane i n t e r s e c t i n g the bearing a x i s (angle q t ) leads t o an occurrence o f unfavourab l e d i s t r i b u t i o n s o f pressure a t the r o l l e r m i n race contacts, r m n i f e s t i n g themselves as a pressure increase i n one o f the ends o f the cont a c t area. I t i s one o f the f a c t o r s reducing bearing d u r a b i l i t y .

1 I

Fr

HOwever, the r o l l e r end - f l a n g e r m t i n g c o n d i t i o n s have a d e c i s i v e e f f e c t on the d u r ab i l i t y of a r a d i a l c y l i n d r i c a l r o l l e r bearing loaded w i t h an a x i a l and a r a d i a l f o r c e . Cue t o s l i d e s and accmpanying f r i c t i o n , a t the r o l l e r end - flange contacts a l a r g e m u n t o f heat i s generated, which causes f a s t wear o f the r m t i n g surfaces. The m u n t o f heat generated i n the b e a r i ng can e f f e c t i v e l y be reduced by such m d i f i c a t i o n o f the shape o f the c o n t a c t surfaces, which w i l l guarantee a decrease i n t h e f r i c t i o n a l losses. One should a i m a t the f o l l o w i n g : - ensuring such a shape o f t h e o i l gap a t the r o l l e r end - flange contact t h a t would be conducive t o f o r m t i o n o f an o i l f i l m , - m i n i m i z i n g pressures a t the contacts, - m i n i m i z i n g the skew angle o f the r o l l e r . N m r o u s e x p e r i m m t a l and t h e o r e t i c a l inves t i g a t i o n s ( 1 , 2 , 3 , 4 , 5 , 6 ) have shown t h a t the m s t favourable m t i n g c o n d i t i o n s o f the r o l l e r end and the f l a n g e a r e c r e a t e d by c o n i c a l f l a n ges and s p h e r i c a l r o l l e r ends. However, d e s p i te m n y a c h i e v m n t s i n t h i s f i e l d , the o p e r a t i n g c o n d i t i o n s o f the r a d i a l c y l i n d r i c a l r o l l e r b e a r i n g subjected t o ccnbined load have n o t been investigated s u f f i c i e n t l y . I n the paper, an atterrpt was m d e t o c a r r y out a c a r p l e x a n a l y s i s o f the r o l l e r balance conditions, considering a l l the m s t inportant f a c t o r s a f f e c t i n g t h i s balance. The subject o f the a n a l y s i s i s the b e a r i n g w i t h c o n i c a l flanges and s p h e r i c a l ends r o l l e r s ( F i g . 2 ) . I t s a i m i s t o c r e a t e t h e o r e t i c a l bases f o r s e l e c t i o n o f the m s t advantageous - f r a n the viewpoint o f f r i c t i o n a l losses i n the b e a r i n g values o f the angle o f i n c l i n a t i o n of flanges (J3) and t h e r o l l e r end r a d i u s (R ) . A m r e d e t a i l e d d i s c u s s i o n o f the probl&s d e a l t w i t h the paper can be found i n the work ( 7 ) .

1.1 N o t a t i o n

F i g . 1. Skew and t i l t o f the r o l l e r i n the r a d i a l c y l i n d r i c a l r o l l e r bearing subjected t o ccnbined load.

a b b ,b ,b C

- m j o r semiaxis o f the contact e l l i p s e - minor semiaxis o f t h e contact e l l i p s e - p a r m e t e r s d e t e r m i n i n g the p o s i t i o n o f the r o l l e r end-flange contact area c e n t r e - dynamic b a s i c load r a t i n g

288 - o u t s i d e d i m t e r o f the bearing

D Di( 0 )

- d i a m t e r of the m i n race - roller diamter

DW

d

- bore diarreter

e

- distance of the r o l l e r end - flan g e contact area centre fran the m i n race

H

-

co nvexity o f the g e n e r a t r i x o f the r o l l e r or r a i n race

k

-

nurber o f the contact l i n e d i v i s i o n elmnts

la

- length o f the g e n e r a t r i x of the roller

U

- slide velocity

V

- linear velocity

oc

- angle determining the p o s i t i o n o f the contact area c e n t r e on the f l a n g e

6"

- d i m n s i o n l e s s contact d e f o r m t i o n

P

- coefficient of f r i c t i o n

7-

- f r i c t i o n force per the unit o f the contact l i n e length

w

- angle determining the r o l l e r p o s i t i o n i n the bearing

0

- angular v e l o c i t y

$ ,

- angledetermining the d i r e c t i o n o f a c t i o n o f the f o r c e Qr.

Subscripts i - inner ' ring o - outer r i n g f - f lange w - roller

3. The pressure d i s t r i b u t i o n s a t the contacts have been assured according t o h e r t z i a n theory. 4 . The r o l l e r - b e a r i n g race m t i n g takes p l a c e i n the c o n d i t i o n s o f f l u i d f r i c t i o n . 5. The mass forces, t h e e f f e c t o f the cage on t h e r o l l e r s and the losses o f the r o l l i n g f r i c t i o n i n the b e a r i n g have been neglected. 6. The b e a r i n g r i n g s can d i s p l a c e r e l a t i v e t o one another o n l y i n r a d i a l and a x i a l d i r e c t i o n s , but they cannot t i l t . Lhder t h e a c t i o n o f the r a d i a l load (FT) and a x i a l load (Fa) a t the r o l l e r - b e a r i n g race contacts pressures appear, accarpanied by s u r fa ce d e f o r m t i o n s ( F i g s . 3a, c ) . The pressures and deformations a t the r o l l e r end - f l a n g e c o n t a c t s were determined acc. t o hertzian forrmlae for the p o i n t contact:

-1

.

i n N, xqfl(o) i n rrm The l a t t e r f o r n u l a i s r i g h t f o r the m t e r i a l s o f modulus,of e l a s t i c i t y E = 2.08 lo5 W a and of Poisson s r a t i o J = 0 . 3 . 1 f f i i O ) i s t h e s u n o f curvatures a t th e p o i n t b e i n g the c e n t r e o f the contact area o f th e r o l l e r end and t h e f l a n g e o f the inner o r t h e outer r i n g . Pressure d i s t r i b u t i o n s a t t h e r o l l e r - F i n r a c e c o n t a c t s w e r e determined u s i n g Lundberg s f o r r m l a ( 8 ) , i n which t h e value o f f o r c e per contact l i n e l e n g t h u n i t i s dependent on the d e f o r m t i o n s r e s u l t i n g fran i n t e r p e n e t r a t i o n o f the surfacesof the r o l l e r and the races. The d e f o r m t i o n w i t h i n t h e range j + 1 o f t h e c o n t a c t l i n e ( Fi g . 3c) can be expressed by the f o r n u l a : Qf,[O)

-

(3)

2

A,(o)(,+l) =

2

( - 4 (Hw+Hl(o))/LI*rj+(4(Hw+ Hi(o))/la-tan q2)*rj +Ai(o)l

(4)

II r-y

r, =I;j/k

j = O J,....k.

The d e f o r m t i o n A i ( o ) ( j + l ) depends on t h e r e c i p r o c a l approach o f t h e b e a r i n g rings i n the radial direction:

LW

F i g . 2.

Inner g e m t r y o f the m o d i f i e d r a d i a l c y l i n d r i c a l r o l l e r bearing.

2 THE ANALYSIS OF THE ROLLER BALANCE CONDITIONS The a n a l y s i s o f the r o l l e r balance condit i o n s i n the r a d i a l c y l i n d r i c a l r o l l e r bearin g subjected t o c m b i n e d load was c a r r i e d out w i t h the following asswptions: 1. The bearing r m t e r i a l i s i d e a l l y e l a s t i c and isotropic. 2. The surfaces i n contact have ideal shapes.

The d i s t r i b u t i o n o f f o r c e s per the c o n t a c t I ine length unit ( F i g . 3b) i s d e f i n e d by t h e f orrm I a:

w h i l e t h e d i s t r i b u t i o n o f the r m x i m m pressure ( F i g . 3a) by t h e dependence:

Ai[O1(J+l)

roller

-

and l a i n r r m , ~ Q i ~ o ) i n K 1 . I Q i ( o ] i s the s u n o f the curvatures a t the m i n race c o n t a c t s .

289

fy

a.

C.

b.

F i g . 3. a - P r e s s u r e d i s t r i b u t i o n s a t the r o l l e r - flange c o n t a c t s . b - Resultant n o r m 1 forces a t the r o l l e r - race c o n t a c t s ; d i s t r i b u t i o n s o f forces per the contact l i n e length u n i t . c - D e f o r m t i o n s a t the r o l l e r - race c o n t a c t s .

In the a nalysis o f the balance conditions, continuous pressure d i s t r i b u t i o n s were raplaced by concentrated forces: - Q f i and Q f o - a t the r o l l e r end - flange contacts, - Qi and Qo - a t the r o l l e r - m i n race contact s Norm1 forces Q j and Q o a n d the p o i n t s o f t h e i r a p p l i c a t i o n ( F i g . 3b) were determined by i n t e g r a t i n g the d i s t r i b u t i o n s o f forces per the contact l i n e length u n i t :

1V'

.

An analysis o f the inner g e m t r y o f the bearing, t a k i n g the skew (q,) and the t i l t (Vz) angles i n t o consideration, provided i n f o r m t i o n about the p o s i t i o n o f the centres o f the r o l l e r end - flange contact areas, w h i l e an analysis o f the b earing k i n m t i c s m d e i t p o s s i b l e t o deter mine the d i r e c t i o n s o f s l i d e v e l o c i t i e s and the values o f r e l a t i v e s l i d e s a t the contacts ( F i g. 4 ) . The r e l a t i v e s l i d e s a t the r o l l e r - m i n race contacts are defined by the forrmla:

F i g . 4 . K i n m a t i c s of the r o l l e r and b e a r i n g r i n g fragnsnts.

290 The f r i c t i o n f o r c e d i r e c t i o n s a r e i n accordance w i t h the s l i d e v e l o c i t y d i r e c t i o n s a t the p o i n t s which a r e t h e centres o f t h e r o l l e r end - f l a n g e contacts areas ( F i g s . 4 and 6 ) . The r e s u l t a n t m n t s o f f r i c t i o n a t t h e c o n t a c t s w i t h the flanges were determined accord i n g t o the f o r m l a :

The r e s u l t a n t f r i c t i o n forces a t the r o l l e r main race c o n t a c t s a r e determined by the f o r m l a :

and the p o s i t i o n o f p o i n t s o f a p p l i c a t i o n o f these forces by the dependence:

The s l i d e v e l o c i t y d i r e c t i o n s a r e determined by the angles 8, and Qo which are the functions o f the r o l l e r skew and t i l t angles and the inner bearing g e m t r y . The c o e f f i c i e n t o f f r i c t i o n was presented i n the f u n c t i o n o f the r e l a t i v e s l i d e ( s in%) and the m a x i m pressure a t the contact (p, , F i g . 5 ) . The r e s u l t s o f the e x p e r i m n t s described i n the papers ( 9,10,11) and the dependence given i n 'the paper (12) were used.

The e q u i l i b r i m s t a t e o f the r o l l e r and the b e a r i n g o u t e r r i n g f r a g m n t i s presented i n F i g . 6.

r 0.1

aog

008 0.07 0.06 0.05 0.04 0.03 0.02 0.01

, I

1

2 3

4

5 6 7 8 9 10 s%

F i g . 5. The c h a r a c t e r i s t i c s o f the c o e f f i c i e n t of f r i c t i o n . The r e s u l t a n t f r i c t i o n forces a t the r o l l e r end - flange contacts are described by the dependence: F i g . 6. I l u s t r a t i o n o f t h e e q u i l i b r i u n s t a t e o f t h e r o l l e r and the b e a r i n g o u t e r r i n g f ragnent

.

29 1 The adequate balance equations have the f o l l o w i n g form:

(211 EQx=Qfo~Tfox-Qfix -Tfix + S o - S i - O ,

(22\EQy=Qfiy+T,iy-Qfoy - Tfoy

+

Qi

- Qo=O,

(231~Qz=Qfiz-Tfiz-Qfoz+Tfoz-Ti +To - O J

(die). F i g . 7 presents the curves o f dependence o f the forces Qa and Qr on t h e p a r m t e r s Iio anddio f o r the NJo2316 E b e a r i n g and the angle /3= 0.9550 These diagrams m k e i t p o s s i b l e t o determine d i s t r i b u t i o n s o f load on p a r t i c u l a r r o l l e r s f o r any r a d i a l and a x i a l load (Fr , Fa) and any r a d i a l clearance o f t h e b e a r i n g ( 9 ) . F i g . 8 presents d i s t r i b u t i o n s o f r a d i a l and a x i a l load on t h e r o l l e r s f o r thg NJ 2316 E b e a r i n g and the angle p= 0.9550 , the r a d i a l clearance g = 0.025 mn, the r a d i a l load Fr*O.ll.C and two cases o f the a x i a l load Fa/Fr = 0.15 and Fa/Fr = 0.6. I t can be seen t h a t t h e r a d i a l load d i s t r i b u t i o n i s similar t o the d i s t r i b u t i o n corresponding t o the a c t i o n o f t h e p u r e r a d i a l load (F,), denoted by broken I ine i n F i g . 8. The area o f the loaded r o l l e r s i s then d e f i n e d by the angle l+fE HOwever, due t o t h e t i l t of the r o l l e r s caused by the a x i a l f o r c e a c t i o n , a greater nurber o f r o l l e r s a r e loaded r a d i a l l y . The angle d e f i n i n g the area of the loaded r o l l e r s i s the g r e a t e r the b i g g e r the Fa/Fr r a t i o . A c h a r a c t e r i s t i c f e a t u r e o f the a x i a l load d i s t r i b u t i o n i s alrmst i d e n t i c a l load o f the r o l l e r s i n the wide range o f the angles virI t causes the r a t i o t u a l l y up t o the angle I&. Qa/Qr f o r the m s t loaded r o l l e r t o be about twice as s m l I as the r a t i o Fa/Fr. The p o s i t i o n and d i m n s i o n s o f the r o l l e r end - flange c o n t a c t area a r e d e c i s i v e o f the shape o f the o i l gap. The p o s i t i o n o f t h e contact area depends on t h e skew and t i l t angles o f the r o l l e r . Fi g u r e s 9 and 10 present c h a r a c t e r i s t i c s o f the f o r the m s t loaded r o l l e r angles v a n d (I# = Oo)’in the f u n c t i o n o f the r a t i o Fa/Fr and t h e angle /3 , f o r the bearings under i n v e s t i g a t i o n . They were m d e , as the c h a r a c t e r i s t i c s o f t h e o t h e r p a r n t e r s , f o r the constant v a l u e o f t h e r a t i o Fr / C % O . l l . Such r a d i a l load corresponds t o t h e average, m s t o f t e n found o p e r a t i n g c o n d i t i o n s o f r a d i a l c y l i n d r i c a l r o l l e r bearings. I t r e s u l t s form these diagrans t h a t the angle o f i n c l i n a t i o n o f t h e flanges i n i t s p r a c t i c a l selec t i o n range has a n e g l i g i b l e e f f e c t on the r o l l e r t i l t ( y2), thereby on the pressure d i s t r i b u t i o n s a t the r o l l e r - m i n race c o n t a c t s , w h i l e i t has a s u b s t a n t i a l e f f e c t on the v a l u e o f thg skew angle ( IJ 1. Yet, f o r the angles J?J< 1 the value o f [he angle does n o t exceed 2, and the phencrrena r e l a t e d w i t h t h e skew have a n e g l i g i b l e e f f e c t on the b e a r i n g o p e r a t i o n , e s p e c i a l l y upon t h e f r i c t i o n a l losses. F i g . 11 presents changes o f p o s i t i o n and d i m n sions o f the t h e o r e t i c a l r o l l e r end - inner r i n g f l a n g e contact area and the o i l gap shapes c o r responding t o them in the f u n c t i o n o f t h e angle /?I As the angle decreases, the t h e o r e t i c a l contact e l l i p s e encarpasses a g r e a t e r and g r e a t e r f r a g r e n t o f t h e r o l l e r end - f l a n g e m t i n g area. The a c t u a l c o n t a c t area occupies s t i l l g r e a t e r p a r t o f t h i s area. In F i g . 11, the boundaries o f the a c t u a l contact area and the shape o f the o i l gap corresponding t o i t f o r th e have been marked w i t h broken = 0.2386 angle l i n e . Small angles o f i n c l i n a t i o n o f the flanges ( ~ c3 0.25’) m y lead t o a considerable r e d u c t i o n o f t h e i n l e t zone, and i n t h e e x t r a m case, a t great a x i a l f o r c e s , even t o i t s disappearance, which w i l l m k e f o r m t i o n o f t h e o i l f i l m a t the r o l l e r end - f l a n g e contact irrpossible.

.

.

(W,)

W,

(271I Q x g = Q rsin . x -Qfo~-~ox,-Tox,+So~~ox,-O,

vpc

- Qox3.Do/2 -ToY;t;siny +Qoy’.f;sin y, - Mfozl-Mz = 0. The balance equations were solved n m r i c a l l y , usin g Hook-Jeeves m t h o d .

3 THE ANALYSIS OF THE ROLLER MATING CONDITIONS I N THE BEARING SUBJECTED TO COMBINED LOAD The analysis c a r p r i s e d a nurber o f bearings o f d i f f e r e n t sizes and d i f f e r e n t d i m n s i o n s e r ie s. Ca lculations were m d e f o r a few values o f angles o f i n c l i n a t i o n o f the flanges, fi2O.25O * 4’. The s o l u t i o n o f the balance equations m d e i t p ossible t o determine a nurber o f p a r n t e r s d e scrib ing the r o l l e r balance s t a t e f o r d e f i n i t e inner g e m t r y o f the bearing and set values o f the forces Qr and Qa f a l l i n g t o one r o l l e r . The rrost irrportant o f t h m are the f o l l o w i n g : - angles o f skew and t i l t o f the r o l l e r , - p o s i t i o n and d i m n s i o n s o f the r o l l e r end flange contact area, - pressure d i s t r i b u t i o n s a t the contacts, - m g n i t u d e o f f r i c t i o n a l losses r e s u l t i n g f r c m the a x i a l load, - r e c i p r o c a l p o s i t i o n o f the bearing r i n g s i n the a x i a l ( I io, F i g . 3c) and r a d i a l d i r e c t i o n

v,

.

fi

292

33890 900

.9lO

920

.930

940

950

1-

960 llolmm]

F i g . 7. The c h a r a c t e r i s t i c s o f the forces Qa and Q i n the function of the p a r m t e r s I . a6d 6 io. 10

4'

3' Qr

Qa

"1

2' 1' 0

'p2 5' 4'

"

3' '.

FaIF, -0.15 Nl2316E F, 0.L1500 N , p 90.9550'

Fa IFr -0.60

, 9-0.025

rnm

F i g . 8. D i s t r i b u t i o n s of r a d i a l and a x i a l load on the r o l l e r s .

1-NJ2308E 2-NJ 2316E 3- NJ 2324 E 4-NJ 316E 5-NJ2216 E 6-NI 216E

0-agsp --- B-047 5 v-0' Fr/C-O.ll

Fig. 9. E f f e c t o f the a n g l e p on the angle o f

t i l t o f the m s t loaded r o l l e r .

293

'41 2'

h I l e r angles b a r e accci-rpanied by s m l l e r pressures a t the roller end - flange contacts ( F i g . 121, and as a r e s u l t s , by s r m l l e r f r i c t i o nal losses i n the bearing. For the angle /3= 0.5", the c o e f f i c i e n t o f m n t o f f r i c t i o n r e s u l t i n g f r c m the a x i a l load ( f 2 , F i g . 1 3 ) f o r a wide range o f a x i a l loads i s 0.001 t 0.0015. I t i s about s i x t i m s m l l e r than the c o e f f i c i e n t f 2 f o r the b e a r i n g w i t h f l a t r o l l e r ends and w i t h f l a t flanges. The m n t o f f r i c t i o n can be determined frcm the f o r m l a :

t -

'6

2

where ,d = (D diameter.

+

d ) / 2 i s the m a n b e a r i n g

400

O

a5

0;1

-

1.0

-

Fa/Fr

b 49550' --- B-0.4775'

1 NJ 2308E 2- N.j 2316 E 3-NJ 2324E 4-NJ 316E 5-NJ 2216 E 6-KI 216E

300 200 100

v -0' Fr/C* 0.11

F i g . 10. E f f e c t o f the angle p on the angle o f skew o f the m s t loaded r o l l e r .

I

O+ 01 05 1 - NJ 2308E 2- NJ2316 E 3- NJ 2324 E 4-NJ 316E 5- NJ 2216 E 6-NJ 216E 1 2 3

I

10

Fa/Fr

---0p -- 09550: 1.9103 ' --- 8-0.4775 y - 0' Frl C-0.11

4 5

F i g . 12. E f f e c t o f the a n g l e f i on the value o f t h e m x i m m pressure a t the r o l l e r end - inner r i n g f l a n g e c o n t a c t .

-

1 fi -0.2386' 2-/3-0.4775' 3 -/3-O.955Oo 4 b 1,9103' 5 j3 3.0225O

-

-

--

a,

-0.25.a, - 3 8 2 5 ~

N J 2316 E

F i g . 11. E f f e c t o f the anglefi on the o i l gap shape and on the p o s i t i o n and dimensions o f the t h e o r e t i c a l r o l l e r end inner r i n g flange contact area.

294 o f the b e a r i n g . The value o f the r o l l e r end r a d i u s i s r e l a t e d w i t h the value o f the angle o f i n c l i n a t i o n o f the flanges by t h e dependence:

(321

R, 4 D W / 2-einl/sinp.

The r o l l e r end r a d i u s should be so s e l e c t e d as t o m k e t h e d i s t a n c e o f the r o l l e r end - inner r i n g f l a n g e c o n t a c t p o i n t f r c m the rrain race f u l f i l the e q u a l i t y :

(33)

e i n = ( l / +1/2).hie+hi 3 -hie,

h i e i s the e f f e c t i v e h e i g h t o f the inner r i n g flange ( F i g . 1 4 ) .

F i g . 13. E f f e c t o f the angle p on the value o f c o e f f i c i e n t o f m n t o f f r i c t i o n f2. 4 SELECTION OF THE INCLINATION ANGLE FLANGES AND THE ROLLER END RADIUS

OF

angles Of i n c l i n a t i o n o f the flanges ensure the rrost advantageous operating c o n d i t i o n s o f the bearing. Small pressures a t the r o l l e r end - fla nge contacts, s m l l angles o f skew o f the r o l l e r s and consequently m a l l f r i c t i o n a l losses i n the b earing correspond t o them. The angle o f i n c l i n a t i o n of the flanges, however, r m s t be b i g enough t o guarantee an appropriate shape o f the o i l gap a t the r o l l e r end - flang e contact. The f a c t o r s that l i m i t the s m l l e s t p e r m issible value o f the angle fi , apart fran the dimensions o f the contact area, are a l s o the tolerances o f the a n g l e p and the r o l l e r end radius. In the case o f very s m I I angles ( P ( O . 2 5 " ) and, i n t h i s connexion, o f b i g r a d i i o f t h e r o l l e r end, even s l i g h t deviations o f b o t h these q u a n t i t i e s from the n m i n a l values m y cause unfavourable changes i n the o i l gap shape. In p a r t i c u l a r , i t m y lead t o the r o l l e r end - flange edge contact, which w i l l render f o r m t i o n o f the o i l f i l m d i f f i c u l t o r inpos s i ble. Basing on the above observations, the range o f i n c l i n a t i o n angles have been established, which rrake i t p ossible t o achieve a caTpranise between an atterrpt t o m i n i m i z i n g f r i c t i o n a l losses in the bearing and the necessity t o guarantee a favourable shape o f the o i l gap conducive t o f o r m t i o n o f an o i l f i l m a t the r o l l e r end - flange contact. The values o f angles proposed range within 0.4" + 0.6", depending on the s i z e and the dimension s e r i e s

p=

F i g . 14. S e l e c t i o n o f the r o l e r end r a d i u s Rw.

5. CONCLUS I ONS 1 . The a n a l y s i s m d e a l l o w s ne t o e s t a b l i s h the range o f the angles o f i n c l i n a t i o n o f t h e flanges e n s u r i n g a favourable shape o f t h e o i l gap conducive, w i t h a p p r o p r i a t e s e l e c t i o n o f l u b r i c a n t , t o f o r r r a t i o n o f an o i l f i l m a t th e r o l l e r end - f l a n g e c o n t a c t s . The values o f these angles range within = 0.4" + 0 . 6 " . 2. %all f r i c t i o n a l losses i n the b e a r i n g correspond t o the values o f the angles J3 proposed. 3. In view o f v e r y s m l l values o f the skew angles o f the r o l l e r s ( f o r the g i v e n range o f , Yl H l-

0

W

LL

b

INLET OIL TEMPERATURE (C) ,

FIGURE 7. EFFECTIVE OIL TEMPERATURE VARIATION WITH INLET OIL TEMPERATURE-FILM HISTORY SOLUTION (Note f a l s e o r i g i n ) ,

SESSION XI1 CERAMICS Chairman: Dr J C Bell PAPER Xll(i)

Design Requirements of Ceramic Sliding Contacts

PAPER XlI(ii)

Unlubricated Wear and Friction Behaviour of Alumina and Silicon Carbide Ceramics

PAPER Xll(iii)

The Effects of Surrounding Atmosphere on the Friction and Wear of Ceramics

PAPER Xll(iv)

Wear Performance of Materials for Ball Screw and Spline Applications in Candu Reactor Fuelling Machines


345

Paper Xll(i)

Design requirements of ceramicsliding contacts R.J. Gozdawa andT. A. Stolarski

The main aim of this paper is to discuss, using design case study, factors controlling the performance and affecting the utilization of engineering ceramics, particularly the silicon carbide, as a material for the components of a sliding bearing. The bearing system, comprising combined radial and thrust tilting pad bearings and designed for Framo Engineering, was destined for a special pump used in North Sea oil exploration.

1 INTRODUCTION The science of interacting surfaces in relative motion has arisen, principally, from experience with metallic and organic materials, but advances in the technology of non-metallic inorganic materials now open the way to use them as the bearing materials as well. The advantages seem to be quite significant promising lower friction, longer lives, high temperature capability and relaxation of the lubricant specification (1). However, it is recognized that the use of refractory, inorganic non-metallic compounds and the advantages their unique combination of such properties as high hardness and chemical inertness bring to bearing surfaces should be considered in the light of strict precautions which must be observed in their application ( 2 ) . It is especially true when the ceramics are used as inserts and liners or structural and load bearing components in their own right. Although ceramics offer a significant potential advantages for sliding contact applications there is insufficient amount of information regarding their behaviour, performance and requirements related to the design of sliding contact components. The majority of research on friction, wear and load carrying capacity has been restricted to specimen testing (3,4,5) and there is very little information about real systems behaviour or design recommendations in the form of suitable design rules exploiting the obvious advantages at acceptable level of risk. 2 DESIGN CONSIDERATIONS

The bearing system designed for Framo Engineering, Norway, consisted of radial and thrust tilting pad bearings combined together in one unit. The system is shown,sehematically, in Fig.1. The design brief required that the system, supporting vertically positioned shaft of the pump, should be lubricated with the working fluid which was a mixture of a cooling oil and hard, abrasive particles. This requirement excluded a number of traditional bearing materials and put ceramics at the top of the list. Additional requirements of specific loads up to 13 MPa, rotational speed of

r-T

T

Fig.1 Bearing system: radial/thrust tilting pad 1 - journal sleeve assembly, 2 - journal pads, 3 - journal housing, 4 - inactive thrust pads, 5 - thrust collar assembly, 6 - active thrust pads, 7 - shaft. 6000 rpm and the toemperature of the working

fluid of up to 130 C provided further support for ceramics as the only suitable type of material for this particular application. Silicon carbide (reaction sintered) was finally chosen for bearing elements. Having decided on ceramic-to-ceramic contact, a number of essential factors have to be considered in the final design of the ceramic component and its associated metal counterpart. For example, the attachement or anchoring of ceramic components

346 to the metal structure must be carefully considered and the possible differences in coefficients of thermal expansion between two materials ought to be taken into account. Moreover, high tensile stress concentrations must be rigorously avoided. During the design stage of the bearing system in question and subsequent testing of a prototype the following problems were addressed and carefully considered: (i) load capacity of actual ceramic bearing components to the point of failure in order to establish the prevailing mode of failure and to derive satisfactory safety factors, (ii) ways to minimize and diffuse tension forces and any stress concentration, (ii ) means to attach brittle materials to themselves, and to ductile materials with the possible utilization of compressive loads acting away from edges, ( iv design and fit of mating surfaces since it is not possible to use force in the assembly of components, (V) the importance of close tolerances and high quality surface finish in contact stress reduction, (vi design ways to accomodate differential thermal expansion, (vii) the significance of creep and relaxation over extended periods of time as press fits were used. Some of the above problems could only be properly investigated on experimental way. Therefore, it was decided that extensive testing of a prototype system should precede the final implementation of it. 3 TESTING OF PROTOTYPE

3.1 Test prbcedure and conditions A full scale prototype of the bearing syscem was tested in a specially constructed test rig in order to establish the limits of operating conditions safe for a long service life. A schematic lay-out of the rig is shown in Fig.2. The axial load on thrust bearing was generated by a hydraulic ram and was at two levels that is 25 and 40 kN. Radial load on the journal bearing was applied by means of a load screw turned manually and was kept constant at 2000 N. A load cell was used to measure the radial load while the axial load was assessed by measuring the pressure of oil in the hydraulic ram. The position of the radial bearing was such that the load was acting between two adjacent pads and was equally shared by them. Thermocouples, located near the contact zone between a shaft and the pads, were used to monitor the temperature in the bearing. Temperature of the lubricant at the inlet to the bearing was the main variable used to assess the performance of the bearing system. By changing the inlet temperature of the lubricant it was possible, through the change in its viscosity, to affect the lubrication conditions to a considerable extent. A diesel oil and Tellus T-37 were used as lubricants. Five different oil inlet temperatures were used, namely: 80, 90, 100, 110 and 12OoC. Inlet temperature was thermostatically controlled but, nevertheless, there were some difficulties in keeping it constant throughout a given test. Lubricant flow rate for all tests was constant at 38 l/min. All tests were carried out at the speed of 6000 rpm.

Fig.2 Lay-out of the test rig 3.2.

Discussion of results

The results can best be expressed in terms of bearing temperature rise over the oil inlet temperature. The results of prototype testing are shown in Fig.3-6. During the course of testing, two failures occurred. First failure of the thrust bearing pad took place under specific load of 12.75 MPa and speed of 6000 rpm. The lubricant was a diesel oil. Figure 7 shows the scanning electron micrograph of the failure surface. The silicon carbide face of the rotating thrust collar was also slightly damaged, mainly in the form of deep scratches, by loose particles generated by fracture of the silicon carbide pad at the pivot point. This failure was apparently caused by excessive loading which was approximately three times greater than the design load. The second failure of the thrust bearing pad

347 occurred at much less specific load of 8 MPa and after a relatively short period of time of 4.5 hours. A hydraulic oil, Tellus T-37 was used as a lubricant. The test programme leading to the failure consisted in the progressive oil inlet temperature increase of 0 10°C every 60 minutes starting from 80 C. At 12OoC oil inlet temperature, the bearing was run for only 30 minutes when the failure occurred. After failure, an inspection of the pads showed that carbide-to-carbide contact had occurred on some pads presumably due to the loss of the oil film. Unfortunately, there was no way of measuring the film thickness during running. However, taking into account high specific loads and low lubricant viscosity caused by elevated temperature, it is reasonable to say that boundary lubrication was a prevailing mode of lubrication prior to failure. Inspection of the failed pad also suggested brittle fracture. This is clearly seen in Fig.8 in the form of scanning electron micrograph. As in the previous case, loose particles produced by fracture process scratched the surface of the rotating thrust collar.

deg

160

140

80

60 40

20 0

I

I

I

1

5

10

15

20

I

I

I

25 30 35 time [minl

I

I

*

40 45

t

1140 I

160

Fig.4 Results of prototype testing. Test conditions: oil inlet temperature - 90°C, speed - 6000 rpm, thrust load - 25 kN, radial load - 1 kN.

A

1'""

1130 deg C

1180 deg C

120

1

1

1 1

0

6o

- 80

40

-60

2o I

I

I

I

5

10

15

20

I

I

1

25 30 35 time [minl

I

I

*

40 45

Fig.3 Results of prototype testing. 0 Test conditions: oil inlet temperature - 80 C, speed - 6000 rpm, thrust load - 25 kN, radial load - 1 kN. Further visual inspection of the bearing after the second failure suggested that the load was not equally shared by all the pads and was probably caused by the variations in pad thickness. This point to the importance of precision during the manufacture of ceramic elements as they do not deform sufficiently to absorb any eventual inaccuracies. As it can be seen in Fig.3-6, temperature rise in the bearing was consistent with oil inlet temperature. For the oil inlet temperature from 80 to 120°C, corresponding temperature

- 40

Fig.5 Results of prototype testing. Test conditions: oil inlet temperature - 100°C, speed - 6000 rpm, thrust load - 25 kN, radial load - 1 kN.

rise in the radial bearing was in the range of 0 20 to 30 C respectively. Temperature rise in the thrust bearing, however, was roughly constant 0 and equal to, approximately, 34 C regardless oil inlet temperature.

348

t

180 deg C

I

1

I

0

5

10

I

I

15 20

1

1

I

I

Fig.8 Micrograph of the failure surface of a thrust pad. Failure occurred at specific load of 8 MPa and inlet oil temperature of 120° C. The lubricant was Tellus T-37 and speed was 6000 rpm.

1 -

25 30 35 40 45 time [minl

Fig.6 Results of prototype testing. Test conditions: oil inlet temperature - n o o speed - 6000 rpm, thrust load - 25 kN, radial load - 1 kN.

c,

for traditional bearing materials. A dimensional check of an assembled bearing revealed only a small variations. The maximum variation in inner and outer diameter was 0.022 mm and the maximum circumferential variation in thickness was 0.025 mm. Individual components showed even smaller variations. Pad thickness varied in the range of 0.006 mm while the backing plate thickness variation at the pad pivot point was only 0.018 mm. The second pad failure emphasizes the importance of proper lubrication of ceramic sliding bearing as it is quite sensitive to any disruption in lubrication. Ceramic sliding bearing failure is usually sudden and occurs without any clear prior warning. It is now quite clear that sliding bearings with ceramic components can be operated at significant and considerably higher unit loads than that used for conventional materials. However, to ensure long service life a proper and effective lubrication must be secured. 5 ACKNOWLEDGEMENT

Fig.7 Micrograph of the failure surface of a thrust pad. Failure occurred under specific load of 12.75 MPa and speed of 6000 rpm. The lubricant was a diesel oil.

4 CONCLUSIONS The main conclusion to be drawn from data accqmulated during prototype testing is that the silicon carbide tilting pad readial/thrust bearing system seems to offer a good solution for the conditions specified in the design brief. The first pad failure was presumably due to high loading and excessive bending stress resulting from it. The pad fracture originated at the pivot point. Specific loads applied were very much higher than that normally used

The authors would like to thank Mr V.A.Lumpkin Chief Engineer, Framo Engineering for making prototype test data available. References

(1) CRANMER, D.C. 'Ceramic tribology - Needs and opportunities', Tribology Trans, 1900, ~01.31, 164-173 (2) GARDOS, M.N. 'On ceramic tribology' , Lubrication Engineering, 1988, May, 400-407 ( 3 ) SCOTT, D.and BLACKWELL, J. 'Hot-pressed silicon nitride as a bearing material, Wear, 1973, ~01.24, 25-30 ( 4 ) FISHER, T.F.and TOMIZAWA, H. 'Interaction of tribochemistry and microfracture in the friction and wear of silicon nitride', Wear, 1985, ~01.105, 124-131. ( 5 ) MOROLIKE, B.L. 'The frictional properties of carbides and borides at high temperatures Wear, 1960, vo1.3, 234-241.

349

Paper Xll(ii)

Unlubricatedwear and friction behaviour of alumina and silicon carbide ceramics G. Kapelski, F. Platon and P. Boch

Ceramics are brittle materials in which fracture develops when the stress field reaches a critical state. In the case of wear and friction tests with high contact pressures, cracking of the friction track can develop during the very beginning of the test. The extent of damage and the production of wear debris are sensitive to such cracking. This means that the entire life of a tribological couple can be affected by its initial instants. This work was thus focused on the study of the damage which can occur during the first instants of the life of a ceramic-toceramic couple, tested using a ball-on-disc configuration. Several ceramics were studied and in particular silicon carbide and alumina. Friction tests were compared to indentation tests, in order to determine the correlation between the different fracture strengths which can be defined. 1 INTRODUCTION Ceramics behave as brittle materials at low and medium temperatures. Fracture suddenly develops when the stress field reaches a critical state. In the case of wear and friction tests with high contact pressures, cracking of the friction track can develop during the very beginning of the test. The extent of damage of the contact surfaces as well as the production of wear debris are very sensitive to the presence of cracks. This means that the entire life of a tribological couple can be affected by its initial instants, and that the wear and friction behaviour of a ceramic-to-ceramic couple is very dependent on an accidental overload. The critical state for the stress field above which fracture develops depends on many parameters. The critical values of the three principal stresses depend on whether the stress field is uniaxial or multiaxial. Therefore, it is sometimes difficult to correlate the damages which are observed in tribological studies of ceramics - which correspond to multiaxial stress states - with the damages which are observed during fracture tests. In particular, the "tribological strength", understood as the yield value above which cracking develops, is generally higher than the macroscopic strength (as can be determined using, for instance, a uniaxial bending test). This work has been focused on the study of the damage which occurs during the first instants of the life of a ceramicto-ceramic couple, for a ball-on-disc configuration. Different ceramic materials were studied and in particular silicon carbide and alumina. The friction tests, called "dynamic" because they involve the displacement of the ball on the disc, were completed by indentation tests, called

"static" because they simply correspond to loading a disc by a ball. 2 INDENTATION TEST AND DYNAMIC TEST

For the static test of a ball (radius R) loaded on a slab by a normal load (F), and assuming that materials behave in a perfectly elastic manner, the value of the radius of the contact area is (1) : a = (0.75 k R F/E)'l3 with :

(1)

k = (1-32) + (l-+'z)E/E'

where E, E', ?, and 4 ' are Young's modulus and Poisson's ratio of the materials of the slab and ball, respectively. The principal tensile stress within the slab ( 0 1 s ) reaches its maximum at the surface, on the circle of radius "a" : uiS = (1-23)(0.75 k R/E)-2/3 F1I3/(2 n) (2)

Cracks develop along a circular cone when 01s exceeds the static fracture strength ( u l s f ) . For the dynamic tribological tests, Hamilton & Goodman ( 2 ) and Lawn ( 3 ) have taken into account the tangential force at the surface. The maximum of the principal tensile stress ( O l d ) is now located at the rear of the friction contact, and its value depends on the friction coefficient : Old

=

( 0 1 s )(l+kv

f)

(3)

with kv = 3x1 (4+1)/(8(1-23)) Correspondingly, cracks now initiate at the rear of the friction contact, and they develop along a cone section.

3 EXPERIMENTAL

3.1 Static indentation tests Indentation tests were carried out using a laboratory-made device, loaded by a tensile machine working in its compression mode. Either a JJ-M30K model or an Instron-1121 model was used. 3.2 Dynamic tests : tribometer The tribometer was a laboratory-made model (4). It allows the use of two tribological configurations, namely i) ball-on-disc or ii) disc-on-disc. Trapping of debris is minimized in the former case, whereas it is maximized in the latter case. The experimental device is located inside a chamber with a controlled atmosphere (e.g. dry air, or air with a fixed humidity). The chamber is surrounded by an electric furnace, which allows the tests to be performed from room temperature to approximately 1000°C. Most of the experiments were carried out using the ball-on-disc configuration, with loads varying from 5 to 50 N, at room temperature, and with humidity ranging from 45 to 55%. Sliding velocities were 0.01 or 0.1 m/s.

tests were performed to determine the range of loads leading to cracking, then subsequent tests were performed to determine the mean critical load ( F s . ~ vwhich ) is required to crack 50% of the disc batch. For Sic, cracks can be easily imaged by optical microscopy. However, a chemical etching improves the optical contrast (Figure 1). The cracks exhibit a regular, nearly perfectly circular shape. For Alz03, the cracks do not exhibit such a regular shape. They form a diffuse circular array, composed of connected microcracks. A dye penetrant liquid helped us to visualize the extent of cracking.

4 MATERIALS

The discs were made of silicon carbide (Sic) or alumina (Alz03). Balls were generally made of alumina. However, ball-bearing steel, silicon nitride (Si3N41 , and "SiAlON" ceramics were used in some instances. Table 1 gives the main characteristics of the various materials (with E Young's modulus, 9 Poisson's ratio, e and e ' the density and the apparent density, respectively, and usp the 3-point flexural strength). Mat.

Figure 1 Crack array in a silicon carbide disc loaded by an alumina ball (F = 500 N). Relations (1) and (2) are used to evaluate the Hertz radius (a) and the indentation strength ( u l s r ) , in function of the load (F) :

Sic A1203 SiAlON Si3N4 Steel a = A F1I3 and

E GPa 420

313

310

310

210

l3 1~ glcm3 3.15

.22

.31

.28

.30

3.71

3.20

3.20

7.88

Imp MPa 450

285

-

-

.14

I I

- I

UIS

=

B F113

Table 2 gives A and B, and the corresponding values of the radius of the contact area (a), of the mean critical load (Fs.av), and of the strength ( u l s r ) . Materials A B pm/N1/3 N213 mz

N

pm

MPa

A1203 on Table 1 Main characteristics of the materials used in this study (Sic from CBramiques et Composites, Tarbes, France, A 1 ~ 0 3from C.I.C.E., Montreuil, France).

A1203 on 1 ~03 1 ~

21

154

434 206 1164 f 9

28

108

1250 305 1160 f 5

5 RESULTS AND DISCUSSION 5.1 Static indentation tests Indentation tests were carried out using alumina balls on Sic and A1203 discs. Initial

Table 2 A, B, a, F s . n v , and u i s f values for static indentation tests.

I

35 1

The values of Fs.av are different for A1203 (1250 N) and Sic (434 N). However, strength values appear to be nearly the same (approximately 1160 MPa) for both materials. This "indentation strength" values are high in comparison with bending strength values. In the case of Sic, for instance, u i s f is 1160 MPa whereas m P is only 450 MPa. Three complementary reasons can explain this discrepancy :

curvature is more pronounced, and they are more closely packed. At the end, the cracks are longer, their curvature is less pronounced, and the mean distance between them is larger.

(1) Indentation tests yield a biaxial stress state, with a compressive component (02) superimposed on the tensile component (a1 = - UZ). The presence of a compressive component could increase the fracture strength (5).

(2) The stress value is overevaluated, because the real diameter of the crack zone is not "a" but af, with af > a. The corrected stress value (Slsf) is : Sls

f

= (l-P$)F(a/af l 2 /2naz

For Sic, it was found ar = 235 k 5 pm, which yields Slsf = 895 f 50 MPa. For alumina, a similar derivation gives Slsf = 1050 f65 MPa. (3) The stressed volume is approximately 6000 times larger for the flexural test than for the indentation test (in the case of silicon carbide) and approximately 80000 (for the case of alumina). Therefore, the Weibull probability of finding a critical flaw of a given severity is much lower in the former case than in the latter. It can be shown (6) that : (V3P/V)"m

= S*lSf/asp

where m is Weibull's modulus, and V3p, V, u s p , and S*isf are the volumes and strengths corresponding to the flexural and the indentation tests, respectively. For Sic, "m" is about 12, which yields a corrected value of usp, S*lsf, of 945 MPa. This corrected value is in a good agreement with the experimental result which is Slsf = 895 f 50 MPa. For A 1 ~ 0 3 ,"m" is about 9, which yields a corrected value of 0 3 ~ of 1000 MPa, in very good agreement with the value of Slsf (1050 f 60 MPa). 5.2 Dynamic tribological tests 5.2.1

A1203 ball on Sic disc

For the first tests, the ball was loaded on the disc for only one revolution. The sliding velocity was low. Actually, the results were independent on the sliding velocity, at least for the range of velocities (0.01 to 0.1 m/s) which was studied here. The crack array on the wear track was observed after chemical etching (Fig.2). Most of the cracks are 100 to 250 pm long. However, the crack array is not exactly the same at the beginning of the track compared t o its end. At the beginning, the cracks are smaller, their

Figure 2 Crack array for a alumina ball-onSic disc test (F = 10 N). The extension of cracking below the surface was determined on specimens cut along a plane tangential to the wear track (Fig.3). For a load of 10 N, the mean extension is 30 to 35 pm, with some cracks extending to 45 pm. Cracks are nearly perpendicular to the surface, with a slight inclination towards the f r o n t of the contact. This result disagrees with some literature data (3) where cracks are said t o be initiated perpendicularly to the surface with a subsequent inclination towards tbe rear of the contact. Cracking is very sensitive to the value of the coefficient of friction. In some cases, a load of 10 N is not enough to allow cracking to develop on the entire wear track. The zones where the coefficient of friction is higher are cracked, whereas the zones where it is lower are uncracked. Fig.4 shows a typical chart of the coefficient of friction (f) vs. the distance of friction (1). The cracked zones correspond to places where "f" exceeds a critical value, fc. It was found that 0.36 < fc < 0.43. Such a value i s in good agreement with the theoretical value which can be derived from the relation : Fd.av = Fs.av/(l+kv

fcl3

where fc = 0.37. The "tribological dynamic strength" (Uldf) which can be derived from the given values of parameters (1.e. Fd.av = 10 N and fc = 0.4) is 1230 f 72 MPa. It is in a good agreement with the "tribological static strength" (ulsf = 1164 MPa) It must be pointed out that, in the tribological test, it is not possible to determine the difference between Hertz's radius (a) and the radius of

.

the cracked zone (af). Therefore, it was not possible to calculate a corrected value (say : Sldf) which would have been the counterpart of Slsf. This means that the comparison was carried out between the Uldf and ulsf values.

760 MPa, and no cracking is observed. It is necessary to increase the load up to 40 N (where f = 0.22) to observe cracking. The critical value of the coefficient of friction is 0.2, which corresponds to O l d f = 1240 f 94 MPa. Complementary tests were carried out to study the evolution of the crack array when the number of revolutions (n) increases. Observations were made for n = 2 , 10, 100, and 1000. The results are as indicated below :

(1) n = 2. New cracks develop. They do not constitute a new array but they connect with the initial array (Fig.5). (2) n = 10. New cracks of small size develop between the former cracks (Fig.6). ( 3 ) n = 100. Several new crack arrays develop and superimpose on the initial array. The mean length of cracks is smaller than that of the initial cracks. (Fig.7). ( 4 ) n = 1000. The wear track is densely cracked, with numerous, connected cracks of small length (10 pm). This microcracking favours the formation of wear debris (Fig.8).

Figure 3 View of a section of a Sic disc (cut perpendicularly to the surface and tangentially to the wear track).

0.80 r f

0.60

IA

1 (mm) Zones of cracks

on

the wear track

Figure 4 Coefficient of friction vs. distance of friction (alumina ball on silicon carbide disc). The coefficient of friction (f) is approximately 0.4 in the case of dry friction, with no lubrication. It can be decreased below 0.2 by lubricating the disc with distilled water. For f = 0.15 and F = 10 N, O l d is only

Figure 5 Crack array after 2 revolutions ( A 1 2 0 3 ball on Sic disc). The evolution of cracking is associated to the evolution of the tribological configuration. The diameter of the worn area on the ball increases as the number of revolutions increases. Therefore, debris are trapped in a more efficient manner, which leads t o a "third body" effect and modifies the stress field.

353 balls of other materials (silicon nitride, SiAlON, and ball-bearing steel), in the hope of increasing the coefficient of friction up to values sufficient to yield cracking. Table 3 gives the mean value and the maximum values of the coefficient of friction, for one revolution under a load of 10 N, and the corresponding stress values. It can be seen that they continue to be low, which explains why no cracking was observed.

Figure 6 Crack array after 10 revolutions (A1203 ball on Sic disc).

Figure 8 Crack array after 1000 revolutions (A1203 ball on Sic disc). Ball

fav

A1203

0.22

MPa

fmax

Uldmax

708

0.25

770

Si3N4 0.36

1015

0.42

1115

SiAlON 0.32

1090

0.36

1190

Steel 0.41

980

0.48

1113

Uldav

MPa

Table 3 Mean and maximum coefficient of friction, and stress values, for tests of one revolution under a load of 10 N. Figure 7 Crack array after 100 revolutions ( A 1 2 0 3 ball on Sic disc). 5.2.2

Alumina disc

The alumina ball-on-alumina disc configuration was studied first. Under a load of 10 N, the coefficient of friction is only 0.22-0.25. This yields a maximum stress within the disc of 770 f 60 MPa, which is well below the tribological strength, and no cracking was observed. Since the stress intensity increases as the cubic root of the load, cracks were not expected to develop unless very high loads were used. However, such high loads were forbidden by the design of the tribometer. Therefore, the alumina ball was replaced by

Figure 9 shows the diagram of (Jld vs. f , for different ball materials. It must be pointed out that the diameter of the SiAlON ball was 7.9 mm, instead of 10 mm for the other balls. Therefore, SiAlON balls yield to the highest stress, although they do not yield the highest coefficient of friction. Tests were carried out with loads of 30 N, which gives f = 0.42. In this case, some cracking was observed. However, cracks were very difficult to observe, and it was not possible to determine the critical value of the coefficient of friction. Only the maximum stress was evaluated, from data on the maximum of the coefficient of friction. It was found that U l d f = 1920 MPa.

354

Q l d (MPal

. = L/D >=0.5 (b). 0.5 > = La/L > = 0.1 (c). Tt/(2.No) > = Lr/D (d). 0.9

>=! > = 0.

(el. 12.

> = K > = 0.

>=

0.

(f). WNO > = Wo (8). P,max (h). rmax

> = Ps > = >=

P,min

>=f'min

3 . THE ANALYSIS OF THE BEARING

AND ITS PROGRAMMING In the hydrostatic and hybrid bearings , a dimensionless form of the Reynolds' equation can be stated as follows :

a($-) aP' + (D/L) -(H-) 3 ax ax az az 2

where,

3ap

X = x/D,

241rS~-aH

ax ( 2 )

Z = z/L, H=h/h,

.

.

.

D, N, W,

Wo

8

W, , No, EP, EPA, Ho

is Now , the speed variable S introduced , which is a synthetic parameter of the bearing performance Then , it is so convenient for the computer programming that the supply are pressure Ps and dynamic viscosity not needed to know first.Al1 we have to do is to select the suitable values and according to the solved factor at last. It is easy to obtain the following expressions:

.

The flow factor of the bearing concentric condition is B= 12 .P.B

The following independent dimensionless parameters which mainly affect the bearing performance are considered as the design variables in optimization. X=IL/D,La/L,Lr/D,

0 ,K

1

It is essential that some bearing performances.(e.g. load capacity) can be regarded as an objective function at In general, with the user's desire speed and power increasing in machine, the engry comsumption and the temperature rise become a critical problem, so

.

at

(3)

- nD where B=-

(4)

6 LA

The optimal hybrid bearing is

speed

variable

........................................

*

the

in

Also, the other objective functions , such as minimization of flow rate of bearing , minimization of temperature rise , can be used here , only the subprogram of the objective function should be changed.

41 3

Where

b=

-

Af - DfL

SK d,O 32 4: , l c

less design restrictor. (7)

is the area of a recess, and A L is the area of the land around a recess The speed variable in hybrid bearing is

the

parameter of

a

dimensioncapillary

3i.odoL

I=

is the dimensionless m design parameter of an orifice restricand

where, A R

is

42 - .. .

tor. Now, according to its expression at concentric condition, we can obtain

0r -

I= Aftef the dimensionless load capacity W is known, variables PA and will be determined as follows :

W (9)

J1.The finite difference method The solution domain of the bearing is divided into the differential mesh lines with inequal steps and the general five-point difference formula is used.(see Fig.2)

(13)

1-B

a=* The flow rate out of a recess consists of two components, i.e. axial flow rate and circumferential flow rate. Using the differential quotient ,their formula can be obtained easily. The flow rate feeding a recess is equal to the flow rate through a restrictor, so that the flow continuity equation can be written simply as

- -

(14)

Bin= Q e d

Because the design parameter of each restrictor which can be calculated first is used to express the flow rate through a restrictor, the dimensionless pressure of the recess P p can be solved out by the flow continuity equation (14) directly without iteration, so that much computer time may be saved. Using the super relaxation iteration technique, the pressures at all nodal points of the bearing mesh can be obtained by solving both the Reynolds' equation (2) and the flow continuity equation (14) simultaneously. Therefore, the bearing load capacity and the attitude angle can be calculated easily as follows: (see Fig.3)

where,

-=

DLOAD F;j = Aij tB;j tC;j tDij The pressure distribution of the bearing can be obtained by solving both the Reynolds' equation and the flow continuity equation. the traditional solution is that suppose the variables Ps and f are known, the flow through the bearing and the restrictor can be calculated respectively and got equilibrium by iteration. In this paper, a more effective solution is taken successfully. The dimensionless design parameters of the restrictors are used and according to the corresponding formulas given by the fluid mechanics,the flow continuity equation can be carried out as follows. The dimensionless flow rate through the restrictor is

VLOAD

=

ULOAD =

MUJ-

Pij

jrI

afi4h

A*+&

(7) (7 ) (15)

mz-

-DLOAD

.COS&

(16)

-2 DLOAD .sin&

(17)

j-

The dimensionless load in X direction is d

Wx

=

V m - s i n gt m D . c o s 9

and the total load capacity is

dimensionless

(18) bearing

The attitude angle is

9

= arctg

(-

u r n

)

vmi5

where, m D and V m D are the dimensionless bearing load in U and V direction respeotively, The computer algorithm of finite difference method for analysis and optimum design of hydrostatic and hybrid bearinpa is given in Fig.4

414

Fig. 2

6 data input I

to calculate I size of mesh

I

Fig. 3

t q=(901 1

to solve P accordingI to the flow continuity1

t

x,

1

I

on the lands to solve pressures I

-

I

‘4

r’

Ti-‘ land

recess

Fig. 5

I

t

I 1

k o calculate the attitude angle1 -

-

1

Z

Fig.4 The Flow Chart For Finite Difference Solution

41 5

3.2

The finite element method

The finite difference method is easy and quite efficient, but it is difficult to coincide with the curve boundary of the solution domain. However, the got a finite element method has widespread application in lubrication field since the equivalent functional of Reynolds' equation was found out in the middle of 60's. Because the configuration of bearing are various and the relationship between the pressure and the flow rate through the restrictor may be nonliear,the following functional of dimensionless Reynolds' equation is employed.

its boundary conditions are:(see Fig.15)

(1).

(2

-PIr

=O ,it means the pressure

at the edge of circumferential lands is zero.

- ,it means the pressure at . -P Ir,=pP the edge of a recess is equal to the recess pressuze . Where, the Pp can be made out by

the equilibrium of flow rate out from a recess. (3

into

and

2 1 =o

-

22 I T;.

,it means the domain of bearing is symmetrical at the centre of bearing in axial direction. According to the kind of element ,such as a triangular, quadratic or isoparametric element,we can define the suitable interpolation function and got the representative pattern of functional for each element. Then,minimizing the functional and assembling the element stiffness matrix and viscosity-flow rate matrix to the overall stiffness matrix and viscosity-flow rate matrix respectivelly, we have generated a linear equation group as follows:

Where, [K] is the overall stiffness or fluidity matrix, {P] is a column matrix of nodal pressure and IF) is the velosity-flow rate metrix. It is practicable to solve this linear equation group when all the boundary conditions are taken into account. The whole precedure to analyse and calculate the bearings by finite element method is shown in Fig.6. It is well known that a large amount of work in finite element analysis is the preparation of all the input data. This job is tedious,time-consuming and easy to make mistakes, espacially for the mesh containing hundreds or even thousands of nodes. To reduce the preparation time and improve the quality of input data, a versatile two-dimensional mesh gene-

rat ion with automatic bandwidth reduction is employed in the finite element analysis. It is only necessary to put in a little information which describes the geometric characteristics of domain , the kind of element and the density. The nodal numbering, nodal coordinates and some other information of element can be given out automatically by computer.

4. THE OPTIMIZATION METHOD For a bearing design , there are a number of design parameters and Besides , bearing performance performances ( such as load capacity and power losses ) is difficult to describe with a functional expression and more difficult to provide analytical function for its derivatives, therefore, the direct optimization method seems to be more suitable for this kind of problem. Some of them are employed , such as Flexible Polyhedron Method and Complex Method and the SUMT which transforms a constrained optimization into a sequential unconstrained minimization. After some caculation and test, it is found that the Complex Method is the most efficient of these three methods owing to the characteristics of the mathematiIts computer cal model of the bearing algorithm can be found easily in the most of books on optimization. Users can also connect this program with the library of optimization methods to select a much more effective algorithm. The objective function and constraints have to be found by solving Reynolds' equation and it is well known that the analysis of the bearing must proceed with two iterations : one is for the attitude angle and the other is for the pressure P, which usually costs long time. Obviously, it takes much more computer time for optimization of a bearing. In order to make the optimum design a series of available for use , technical approaches are applied to save computer time, such as the selection of the initial values and the modification of the superThe relaxation factors automatically most effective one is the higher and/or lower accuracy iteration technique , that is, at the beginning of the optimization, the design variables are far from the optimum values ,so that the lower accuracy could be used in the analysis program to save computer time. Then, after certain iterations , they might be around the optimum values, the higher accuracy should be immediately used. In fact, more than 50% computer time is saved by this approach.

.

.

.

5.

THE

AUTOMATIC DRAWING

The standard graphic software package Auto-CAD is employed in this program. However, it is an effective To apply program to edit a drawing

.

41 6

t

identification of boundary elements and nodal points

I

calculation of element geometry and some variables

I

[initial estimation of the attitude angle1

I calculation of

I

element matrix [ K ] e ,[Flel

I I initial estimation of the recess presure lassembling [ K l e ,[Fie to [kl IF] 1 ~

~~~

to modify the overall equation in consideration of the boundary condition

t

Ito solve the overall equation1

I

to calculate the bearing performance

!to solve the F&b! equilibrium of flow rate] to calculate the

Fig.6 The flow chart for finite element solution

41 7

Table 1. A Comparision of The Parameters Unit Supply pressure

pS

Flow rate

Q

Total power

Ht

Bearing diameter Bearing length

Original Design Parameters

0.20 x lo7

pa

0.676

Kw

O* 056

0.04 I

D

mm

so.00

Bo.00

L

mm

&Loo

95. s4

2 0.00 LA

Attitude angle ~

Pressure ratio Power ratio

6

0.167A lo7

0.55 2

l/min

Axial flow land width Circumferential flow land width

Optimal Result

I

I

K

Fig. 7

22./6* ~

~~~

30-26 11.68

8.00

mm

-

I I

23.17"

0.546

4.503

2.364

1.154

418 to the computer-aided design ,it is very important t o endow it with the capacity of "parametric drawing". That means what the user want to do is giving out the parameters, not the commands , "text", etc. such as "line" Therefore, the interface between the graphic software and the programming language should be carried out. In another situation, we can use this interface to develop and improve the drawing drafted by Auto-CAD using the programming languages. Because the graphic data base of Auto-CAD is stored in a compressed pattern, the user can not get information directly by the program written in programming language. Therefore, to realize the exchange of Auto-CAD and drawing generated by programming language, it is necessary to use a concise and precise ASCII text to describe the drawing in Auto-CAD, that is "draft exchange file" (DXF) When we connect the Auto-CAD with programming languages, the internal data base of drawing should be changed into text in DXF first, then it is read out and developed by programming languages. After that, the DXF is sent back to Auto-CAD to generate the desired drawing. According to the above principle, the interface between Auto-CAD and programming languages has been carried out. Now, we can generate the drawing of bearings by the software written in FORTRAN and modify the parameters of drawing freely according to the design parameters. Finally, all the files are transmitted to Auto-CAD to draft the desired drawing.

.

6. DISCUSSION AND CONCLUSIONS Using the optimum design program developed by the authors, the analysis and the optimum design of a concrete bearing which is used in a high precision lathe have been carried out. The specifications of the bearing are as follows: Bearing type: Recessed bearing without axial grooves Type of restrictor: Orifice restrictor Number of recesses: No = 4 Bearing Diameter: D = 50.0 mm Bearing Length : L = 50.0 mm Eccentricity: Ep = 0.30 All the data above are stored in a data file, then to run the program, some results are given in Tab.1. It has been shown that the total power loss has been decreased by 27% from 0.056 kW to 0.041 kW. It is very convenient to design a hybrid bearing by using the dimensionless speed variable S H The iteration procedure of the flow rate can be omitted by means of the dimensionless design parameters of the restrictors. Because a series of technical approaches are employed , much more

.

computer time is saved. Therefore, it has become practical and available to do the optimum design of a bearing by solving the basic equation of the lubricated system -- Reynolds' equation directly. The drawing of the bearing has been generated simultanuously.(see Fi8.7') The program has been tested by many concrete examples and it has been found that this program is correct , reliable and efficient This program package can be applied to the calculation , analysis , optimum design and automatic drawing of a hydrostatic and hybrid bearing easily on a microcomputer. The program is versatile and can be provided for the designer directly.

.

REFERENCES (1) W.B.Rowe, D.Koshal,'A New Basis for The Optimization of Hybrid Bearings' Wear 1980,vo1.64 (2) M.K.Ghosh, B.C.Majumdar,'Design of Multirecess Hydrostatic oil Journal Bearings' Tribology Int. April, 1980 (3) M.El-Sherbiny, et al, ' Optimum Design of Hydrostatic Journal Bearings ' Tribology Int. June 1984, Vol. 17 (4) Xu Shangxian, 'Analysis and Optimum Design of Hydrostatic Bearings' (in Chinese) Journal of Nanjing Institute of Technology,No.l 1980 ( 5 ) Xu Shangxian, 'Hole-entry Hybrid Bearing and Its Optimum Design' Journal of Nanjing Institute of Technology, No.4 1983 (6) Xu Shangxian, ' Optimum Design of The Slot-entry Hybrid Bearing' Lubrication Engineering No.4 1984 (in Chinese) (7) Xu Shangxian, Chen Baosheng, ' optimum design of hydrostatic and hybrid bearings' (in Chinese) Machine Tool ti Hydraulics, No.5 1986 (8) Xu Shangxian, Chen Baosheng,' Finite Element Analysis of hydrostatic and hybrid bearings' (in Chinese) Machine Design, No.4 1986 9 ) W.B.Rowe ,Xu Shangxian,F.S.Chong and W.Weston , 'Hybrid Bearings ---- with particular reference to hole-entry configuration' Tribology Int. Dec. 1982 10) W.M.Newman, et a1,'The principles of interactive computer graphics' McGraw-Hill , 1981

41 9

Paper XIV(ii)

Computer aided designof externally pressurizedbearings G. J. J. van Heijningenand C. M. Kalker-Kalkman

A method is presented for the selection and specifation of externally pressurized bearings, and calculation of the design-variables involved. An expert system is proposed to process the information about the bearings and to handle the different kinds of design problems. Two ways of implementing such a system are discussed, one for a personal computer and one for a CAD-system.

1 INTRODUCTION The selection and calculation of suitable bearings for a given mechanical application is a significant problem for a mechanical engineer. He meets the difficulty of comparing different types of bearings and making the best choice from the most promising types. The designer should be an expert on all competing types to make a meaningful comparison. There is,however,scopefor making the necessary information available through a computer, which in effect acts as the expert and operates in an interactive consultation mode. A research program has been set up at the Delft University of Technology which aims at introducing such a computer-aided technique into the bearing selection process. As a first example the bearing type: "externally pressurized bearing" has been selected. Two programs have been developed to implement the system. In section 2 information is given about those implementations. The selection criteria can be reduced to a small number of basic items, in our case 8 . An account is being kept of existing bearings on the base of all those factors ,including the selection criteria and the names or the numbers of the drawings and necessary shapeparameters. This is presented in section 3.1. When a bearing type has been chosen, it is presented on the screen by a simple drawing. If the designer wants to go on with the selected bearing,he has to specify certain shapeparameters. This is treated in section 3.2. Several variables have to be calculated in order to get an impression of the properties of the chosen bearing. The designer has a certain freedom in choosing the variables he wants to specify, and the variables to be calculated and plotted by the computer. This gives rise to a number of design problems, which have to be solved for all possible bearings. A method to do this as generally as possible i s treated in section 3.3. In section 3.4. a method is presented to select the problem. In section 4 a conclusion apd recommendation for further research is presented.

1.1 Notation Symbol

Name

W

Load Maximum outer dimension(radius) Stiffness Supply pressure film-thickness flow rate power maximum temperature rise Reynolds number Re 1(h/l ) film-length pressure ratio,Precess/Psupply density lubricant dynamic viscosity lubricant specific heat lubricant maximum number of cholces for selection criteria number of selection criteria for application number of selection criteria for physical principle line number selected from block i of application line number selected from block i of physical principle shape-parameters outer diameter inner diameter

R S Ps

h

Q N AT Re1 Re2

1

B P

rl C

n

N aPP1 N PhYS ai i

f

A 1 to A5 D1 D2

2 IMPLEMENTATION Two programs have been written :

a. A program LAGERKEUZE written for a personal computer in Data Manipulation Language using the database system DBase 111 and using the spreadsheet-program SuperCalq for the calculations. A number of graphic functions has been used with the aid of a colorgraphics card. Drawings and listings of results are produced by a plotter and printer. b. A program BEARINGCHOICE in FORTRAN has been written and implemented on a TECHNOVISION CAD-system. With this system it is possible to file prepared drawings and call them by a Fortran program.

420

It is possible to set up a database (SIBAScodasyl-database) with this system and to approach this database either interactively or with a Fortran-program. The drawings and plots produced by the program can be filed and sent to a plotter for making a hard-copy. The drawings prepared for this program can be written into IGES(Initia1 Graphics Exchange Specification) files. This feature makes it possible to implement the program in another system. It is not possible to implement the database calls. The program would have to be adapted to another database- system. However, it is a relatively simple matter to construct a file or data structure which can handle the same task. 3 GENERAL THEORY In this section we present the methods employed in as general as possible a way and illustrate those methods with examples used in both programs. 3.1 Selecting Drocedure We have to structure the expertise on bearings and put this into a Knowledge Base. In this Knowledge Base all factors and parameters by which a bearing is specified will have to be grouped in a convenient manner. The selection criteria for choosing a bearing can be divided into two categories: a. Selection with respect to the application of the bearing. b. Selection with respect to the physical principle of its operation. For the application a) we distinguish the following factors: al) the kind of load to be supported, a2) the bearing geometry and the configuration of the machine in which the bearing is projected. As to al), it is important to know the direction of the load, which can be axial or radial or both. Moreover, the load can be constant or variable, so that opposed pads may be necessary. As to a2), the shape of the bearing and the presence of slots have to be considered. The physical principle b) has to do with the way a

load is supported and the type of pressurecontrol system to be used. We confine ourselves to externally pressurized bearings, having one o f three different types of flow control devices, viz. constant flow, orifice or capillary restrict0rs.A~ to the shape of the film, we consider bearings with stepped, tapered and slotted films. The stiffness is an important factor, especially when tilting stiffness is required. The presence of recesses is also a factor of consideration. Summarizing all those factors we arrive at the selecting criteria given in fig.1, giving rise to 4 series of choices for both application and physical principle. We note that this number of selection criteria and the number of choices for each criterion are not relevant to the method presented here, and that it can be applied to any way of grouping bearing-properties.Looking at fig.1, we see that the designer can specify his wishes by making a choice from a menu in each block, a choice is given by a number in the block. Let us denote the maximum number of choices in all blocks by n. In figure 1 we have 11-16, being the number of possible choices in the menu of the block bearing film stiffness. The total number of blocks belonging to and the number of Application we call N appl' blocks belonging to Physical Principle is called In the example of figure 1 both have the N PhYs * value 4. We now create two numbers in the number-system with base n: N i-1 aPP1 K -z (a -1) n 3.1.(1) appl i-1 i N PhYS

i-1 K -I: ( f -1) n 3.1. (2) phys i-1 i where ai and fi denote the integers chosen from block number in the blocks for "Applications" and "Physical Principle" respectively. depend on the choices K and K PhYS aPP1 made. For instance, if n-10 we have to do with the decimal system and if the choices 1,2,3,4,5,6,7,8from the menus from left to right were made, then the decimal number

I

I

PARALLEL STIFFNESS 1 Par.fl1.w. constant flov

7 J Par.flln.var.flovrrpillary restr.f

4 Prestressed ax. b r.1 5 Cyllndrlcal. full 6 Spherlcal ? Spher. vlth shaft L 0 Conclcal 9 Con vlth shaft L 10 Yates 11 Cirde + partlcal cyL 12 flrcle + full c y l 13 Part. cyL annular 14 full cyi. annular

Ag.1 Selection criteria for externally pressutimd bearings

3 Pu.f~n.var.flov.clplllary r 4 r . h b Par.flln,var.flovra~lla~restrg 5 Par.flln,var.flovnrlflce rash., f 6 Par.fllm,iar.flornrlflce restr..h 'I Par.flln.var.flovar1flce restr., p 8 Variable fllm. rdge. f 9 Variable flln. vedqe. h 10 Varlable mn. vedge p 11 Varlable flln, step, f 12 Varlable film. step. h 13 VarlaMe fllm. step. p 14 Variable flh dot, f 6 Varlable fllm. slot. h 16 Varlable fNm. slot. p

h fixed valve h: regulated by film-thickness h p: pressure-regulated restriction

42 1 01234567 would be constructed, which represents the selected bearing uniquely. When we number the blocks i in such a way that the number of choices in a block is highest for smallest i, the values for K and K are kept as aPP1 PhYS small as possible.This is important for representing the numbers in the computer by single-length integers. In figure 1 we have n-16 and the maximum values for K appl and PhYS resulting from the highest values of the chosen numbers are: K -13 + 3.16+2.162+ 163 aPP1 2 3 K -15 + 4.16 + 2.16 + 16 PhYS

3.1.(3) 3.1.(4)

Both numbers are sufficiently small to be represented by an integer. We note that the numbers K and K are unique numbers for aPP1 PhYS every n and represent a certain combination of choices. The combination of K and K can aPP1 PhYS be used as a search-key for finding the corresponding bearing and the drawing of that bearing. This means that actually only one table is needed for finding a specific bearing and its drawing, that is the table containing all possible values and combinations of K K appl’ phys’ and drawing number or name. Conversely,the kind of bearing represented by the number in the table can be found by decomposing the numbers K and K in the sums 3.1.(1) and 3.1.(2). aPP1 PhYS In the Fortran-program figure 1 was prepared as a drawing and called by the program. The designer is prompted to select a bearing by pointing to the numbers with a stylus on a tablet. From the selected numbers K and aPP1 K were calculated and the corresponding PhYS bearing was found with this ‘compound key’. When a combination of choices is made which has no physical meaning or that has not been implemented, it is simply not found in the database and the search-call results in an indicator being set. This indicator is detected by the program-and the designer is prompted to modify his choice.

3.2 Drawinvs and shaDe-parameters Once a bearing has been chosen with the aid of the selection procedure described in the previous section, a drawing is presented. In this drawing with text the choice of the designer is evident. With both implemented systems, these drawings have been prepared for all possible bearings and filed. For the Technovision system of Norsk Data, they can be stored in the archive of the system under an unique name, referred to as Drawing Name. The Fortran-interface of the ND-system makes it possible to call the drawing by name and present it on the screen. Hence, only one table is needed, containing Nappl,Nphysand the name of the drawing. In this table the combination of is the search-key. For an and N N aPP1 PhYS example of a drawing, see fig.2. As many drawings are similar, one can utilize the possibility of copying frequently occurring parts into a drawing when preparing them. The drawings are qualitative, that is the shape and size of the bearing is not set yet. To specify these, we define so-called dimensionless shapeparameters. As an example,we see from figure 2 that in this case we have one shape-parameter, X1- D2/D1 (ratio of diameters) This parameter can be chosen by the user. By preparing the drawing in a ‘parametric way‘ one can redraw the bearing after X has been chosen, see fig.3. As 1 we have more shape-parameters for other bearings, one feels the need to store information about those parameters for all the bearings in the same table as K appl ’ Kphys and Drawing Name. In the evolved programs a maximum of 5 different shape-parameters X1 to X can be 5 specified, their number and lower- and upperboundaries were stored in the table for each tuple representing a bearing. The designer is prompted to specify the values of the shapeparameters which are relevant for the selected bearing. The bearing is then redrawn accordingly.

L OAD A ND POSl TIONING POSSIBIL I TIES

-

axial circle single pad

P D1 D2

c

OPERA TlNG PRINCIPLE externally pressurized fixed capillary restrictor recess

I

SHAPE-PARAMETERS lambda 1 = DZ/Dl I Fg.2 Example of a selected bearing (qualitative drawing)

422

Data machine derlgn and operatlng condltlons: Fig.3 Selected bearing , drawn with hl-0.75

t Load W Istationaryl In N 2. Maximum outer dimension R In m Wanted stiffness S in N/m Pressure Ps in N/n2

6

Data Manufacturing:

[9Allowed film thickness In n Optional:

6. Number of revolutions In rev./min. Varlabler are calculrted according to: 3wIl-nl=hs Wsons t.Ps.R2 const depends on bearing kpressure ratio * Plrecessl/Plsourcel

L OA0 A NO POSITIONING POSSlBlL I TIES

-WJ01 02

externally pressurized fixed capillary restrkhr recess

SHAPE-PA RAM€ TERS lambda I = DZml

Lubricant:

-hSW

When the type of bearing has been selected and the shape has been specified with the aid of the shape-parameters,a number of variables has to be calculated in order to find out the properties of the bearing. In designing externally pressurized bearings, the following variables play a role:

W R S

Ps h

Q

N AT Re1 Re2

B P r)

C

3(1

-

/3)

- const B

W

Q hSPs

- const

Name Load (carrying capacity) Maximum outer dimension (radius) Stiffness supply pressure film-thickness flow rate pumping power maximum temperature rise Reynoldsnumber Re Re (h/l) pressure ratio,O

3000

k

= 6.8

(6)

5 BASIS FOR COMPARISON OF RESULTS

The results for the conventional generator bearings and the slot entry bearings were based

428 on different dimensionless groups. Thus it was necessary to formulate a basis on which to compare the performances of the bearings. As the efficiency of the bearings was an important aspect of the study, the ratio of loadltotal power was identified as the basis for comparing the performances of the different bearings. The usefulness of a loadftotal power ratio and a coefficient of merit was illustrated by Rowe and Koshal [15]. In the work presented here a similar load/total power ratio and coefficient of merit were used. For the conventional generator bearings, the expression for the load is given in equations (l), and the total power is given by equation (10)

.

These expressions for load and power can be combined to give the expression for load/power ratio, in equation (11).

Similarly using the load equation given in equations (2) and the total power given by equation (12), an expression for load/total power ratio can be found for the hybrid slot entry bearings, equation (13).

The coefficient of merit (Mt) is a comparison of the loadftotal power ratio for any bearing with the load/total power ratio for a reference bearing or reference condition, equation (14).

where * refers to the reference bearing. For the purpose of this work, the reference bearing was defined as a conventional generator bearing, of length-diameter ratio LID = 0.805, and landwidth ratio a/L = 0.25. 6 OPTIMISATION OF THE CONVENTIONAL GENERATOR BEARING The effect of the axial position of the jacking pockets on the load capacity of a conventional generator bearing using laminar and superlaminar analysis methods is shown in fig.3. A s can be seen, the load capacities predicted by the two analysis methods are similar and substantial increases in the load capacity can be achieved by moving the pockets out to the edge of the bearing, especially at high eccentricity ratio. In order to assess whether this increase in load capacity is accompanied by an increase or decrease in efficiency, the variation of load/ total power with land width ratio is presented

in fig.4. This figure confirms that moving the jacking pockets out to the bearing edge increases the efficiency of the bearing on a loadftotal power basis for both laminar and superlaminar predictions. However the superlaminar predictions show a lower value of load/ total power than the laminar predictions. This is due entirely to the increase in predicted friction torque when superlaminar flow is considered. Further optimisation of the conventional generator bearing on a laminar basis is somewhat limited. Equation (ll), for load/total power is independent of viscosity, indicating that variations in viscosity will not directly affect the efficiency on a loadftotal power basis. As shown in equation (ll), varying the clearance directly affects the value of load/ total power. Decreasing the clearance will increase the loadftotal power, however any decreases in clearance have to take into account minimum film thickness requirements. When superlaminar effects are considered, it is possible to consider variations in Reynolds number, which can arise from either variations in viscosity or variations in clearance. As with the purely laminar case, variations in clearance have to take account of minimum film thickness requirements. From equation (ll), it is clear that reducing the clearance will increase the value of loadftotal power. Reductions in clearance will also reduce the Reynolds number at which the bearing operates. Thus there is a reduction in friction power, and a further increase in the value of loadftotal power. The datum bearing for all the optimisation studies was the conventional generator bearing with jacking pockets positioned at a land width ratio of afLz0.25. When superlaminar effects were considered, the datum bearing was assumed to operate at a Reynolds number of Re=2000. Any value of coefficient of merit greater than Mt=l.O indicates that the bearing under consideration is more efficient than the datum bearing on a loadftotal power basis. Fig.5 shows the variation of coefficient of merit based on varying viscosity, for a conventional generator bearing land width ratio a/L=O.l at an eccentricity ratio of ~=0.8. If the Reynolds number of the bearing is reduced, by increasing the viscosity, then there is an increase in the coefficient of merit, indicating that the bearing is more efficient on a load/ total power basis.

7 OPTIMISATION OF THE SLOT ENTRY GENERATOR BEARING Optimisation of the slot entry generator bearing is a complex process due to the number of inter-related parameters which can be varied. Fig.6 shows the variation of coefficient of merit against land width ratio for various pressure ratios, for laminar and superlaminar analysis methods. For both analysis methods the slot entry generator bearing is more efficient if the land width ratio is a/L=O.l. It may be possible to further increase the efficiency of the bearing by further reductions in land width ratio, however, there is a limit to this imposed by machining requirements. The effect of pressure ratio f3 on the efficiency of the bearing is dependent on the eccentricity ratio. At low eccentricity ratio,

429

(b)

(a 1

Fig.1

Bearing geometries: (a) Conventional generator bearing. (b) Slot entry generator bearing.

-

6.0

-Laminar -

5.0

___-

Superlaminar

4 .O

3.0 3

-

c?

m

2.0 .-.. U 0 _J

Land Width Ratio

Fig.2

I2O

alL

1.0

0 I

Bearing nomenclature.

r

I

I

I

I

I

0.2 0.3 0.4 Land Width Ratio a l l

01

0

05

Fig.4 Load/total power against land width ratio for conventional generator bearing.

Laminar

eccentricity ratio E = 0.8

f 3.0

'

U 1 0

0' 0

I

0.1

0.2

0.3

0.4

0.5

Land Width Ratio a l L

Fig.3

Load against land width ratio for conventional generator bearing.

0' lo2

I

I

1

1

1

1

1

1

1

I

lo3 Reynolds Number Re

I

I

I

I I I I I

lo4

Fig. 5 Coefficient of merit against Reynolds number for variations in viscosity, conventional generator bearing, superlaminar.

430 6.0 -

5.0

-

0.0.8

4.0

-

0.0.5

c W x

3.0

-

eccentricity ratio € = 0.4

\

c

x

r

eccentricity ratio E = 0 . 2

L

Y-

%

2.0

I-

\

---

0

c c

.-W

.-U

2.0 .

5 u-

Y-

0 W U

0 W U

t

t

- Laminar - - - Superlaminar "O

L

0

I

I

I

I

0.1

0.2

0.3

0.4

I

I

0.5

0

1

0.1

Land Width Ratio a l L

I

2-

1I

I

eccentricity ratio E=0.6

3'0

\

I

I

0.1

I

I


Fig.6

I

I

0.5

(bl

1

eccentricity ratio E.O.8

--0' 0

Laminar Superlaminar

0.2 0.3 0.4 Land Width Ratio alL

(a)

3.0

--

I

0.S

0' 0

I

0.1

I

Laminar Super Laminar I


Coefficient of merit against land width ratio for slot entry generator bearing.

I

0.5

43 1 hydrostatic effects are apparent and it is advantageous to use a high pressure ratio. At high eccentricity ratio the effect of pressure ratio is greatly reduced, especially at a/L=O.l, due to the dominance of hydrodynamic effects. Fig.6 indicates that the slot entry generator bearing is more efficient than the conventional generator bearing, and fig.7 shows that the slot entry generator bearing is capable of supporting the required load. As previously stated, the geometries of the bearings are identical, apart from the jacking sources. This results in negligible differences in friction power when operating under the same conditions. This, together with the fact that the total power for the slot entry generator bearing includes a term for the pumping power, indicates that the increase in loadltotal power for the slot entry generator bearing is due entirely to an increased load support compared to that of the conventional generator bearing. The variation of coefficient of merit against speed parameter sh for variations in clearance and variations in viscosity is shown in fig.8, for laminar theory. For variations in clearance, reducing the clearance increases the coefficient of merit. The clearance selected should be the minimum compatible with minimum film thickness requirements. Variations in viscosity indicate that significant increases in coefficient of merit can be achieved at the power ratios less than K=12, and that efficiency is increased by reductions in viscosity. When superlaminar effects are considered, optimisation based on varying clearance, fig.9, shows the advantage of operating at a low Reynolds number. The Reynolds number is reduced by reducing the value of clearance, however, minimum film thickness requirements will still have to be taken into account. Variations in viscosity, fig.10, again show the need to operate at low Reynolds number. Reducing the Reynolds number by varying the viscosity means increasing the viscosity, and this is contrary to the findings of the optimisation carried out using laminar flow theory.

8 DISCUSSION Optimisation studies for the conventional generator bearing and the slot entry generator bearing have shown that the optimim geometry derived from laminar theory is identical to that derived from superlaminar theory. This is significant in that a bearing geometry can be optimised using simple laminar techniques. The results of that optimisation can then be applied to the superlaminar regime. It must be understood that this does not mean that the actual values of loadltotal power are identical for the two analysis methods. Indeed due to the increases in friction torque predicted by superlaminar theory the values of loadltotal power are significantly different, as illustrated in fig.4. The optimisation studies for the conventional generator bearing showed that improvements could be made to the performance of the bearing by moving the jacking pockets away from the centre to a position of land width ratio a/L=O.l. This was in fact adopted and generator bearings with an improved performance have been manufactured.

The slot entry generator bearing was shown to be capable of supporting the required load and to be more efficient than the conventional generator bearing, for a wide range of operating parameters. The optimisation studies showed that reducing the clearance increases the efficiency of the bearing on a loadltotal power basis. The same conclusion was drawn by Rowe and Koshal [15] for the plain hybrid slot entry bearing, There was however, a discrepancy between laminar and superlaminar results when variations in viscosity were considered. From equation 12, it is seen that a major effect of reducing viscosity is to reduce the friction power. Thus for the laminar case, increases in efficiency are predicted. With superlaminar theory, turbulent shear stresses become a dominant feature and large increases in friction torque are predicted with increasing Reynolds number. For bearings operating in or near the transition and turbulent regimes, reductions in the magnitude of Reynolds number are of prime importance. It must be remembered that variations in clearance and viscosity may adversely affect the temperature rise through the bearing. In order to indicate the level of power saving available by optimising the conventional generator bearing or using the slot entry generator bearing, a comparison was conducted for a specific case, and the results are presented in table 1. The bearings considered approximate to generator bearings of 457nm (18 inch) diameter, operating at a speed of 3000 rpm. For all cases the viscosity and clearance were kept identical in order to minimise any differences in temperature effects between the bearings. The table indicates that the slot entry generator is capable of meeting the general requirements whilst operating with a lower power loss. The actual values presented are different for laminar and superlaminar theories indicating the need to use superlaminar theory to obtain performance predictions. Further improvements in the conventional generator bearing performance may be possible, by correct desggn of the jacking pocket restrictors and constant application of external pressurisation. It is considered that an optimised slot entry configuration will always have some level of superiority over conventional configurations, due to the maximisation of bearing area for hydrodynamic load support. The slot entry bearing has the further advantage of the ability to tailor the static and dynamic performance to suit the operating conditions. This is achieved by adjusting parameters such as supply pressure and pressure ratio. However, there are other commercial considerations which may offset these advantages. These include the need to provide an additional constant supply of pressurised oil and possible increases in complexity of manufacture.

9 CONCLUSIONS The optimisation studies conducted on the conventional and slot entry generator bearings have indicated that the following conclusions may be drawn:

(1) The optimum geometry is consistent for both the laminar and superlaminar analysis methods, allowing bearing geometry to be optimised using simple

432

300

r

200

-

-z -

required load

Y

U

m

0 1

TABLE

1

I

0.2 0.4 Eccentricity

Fig.7

7.0

r

6.0

~ I1

X

5.0

r

n

I1

Y

-2

0.6

1.0

E

Load against eccentricity ratio for slot entry and conventional generator bearings.

decreasing clearance

N

06 Ratio

7.0

-

6.0

-

z I1

increasing viscosity

Y

P

-

5.0

-

___)

+

E

c 4.0 u-

0

3'02.0

1.0

--

-2

p . - m

u0

I1

I1

Y

Y

Y

W

u .u-

% I

2.0

-

U

1.01 Y

I

1

0 Speed Parameter (a)

Fig.8

3.0 -

+ c

N

II

-

sh

I

0

0

7/

,

,

,

Y

0.1

0.2 0.3 0.4 Speed Parameter Sh (bl

Coefficient of merit against speed parameter for (a) variations in clearance and (b) variations in viscosity. Slot entry generator bearing, laminar.

0.5

433

(2)

(3)

(4)

(5)

TAYLOR, C.M. 'Turbulent lubrication theory applied to fluid film bearing design', Tribology Convention, Brighton, Proc. Instn. Mech. Engrs., 1970, 18 (A), 3L. CONSTANTINESCU, V.N. 'On the influences of inertia forces in hydrostatic turbulent lubrication', Rev. Roum. Sci. Tech-Mec. Appl., 1973, 18 (2), 282-310. CONSTANTINESCU, V.N., PAN, C.H.T. and HSING, F.C. 'A procedure for the analysis of bearings operating in the transition range between laminar and fully developed turbulent flow', Rev. Roum. Sci. Tech-Mec. Appl., 1971, 16 (5), 945-982. ROWE, W.B. and KOSHAL, D. 'A new basis for the optimisation of hybrid journal bearings', Wear, 1980, 64, 115-131.

laminar theory. However superlaminar theory is required for actual performance predictions. The performance of the conventional generator bearing can be improved by placing the jacking pockets at a land width ratio of a/L=O.l. Further savings in power consumption are possible by adopting an optimised slot entry configuration. The slot entry bearing also has the benefit of being able to tailor performance. The bearing should be designed with the minimum clearance, with due consideration for minimum film requirements. For bearings operating in or near the transition or turbulent regimes, reducing the magnitude of the Reynolds number is of prime importance for efficiency on a load/total power basis.

REFERENCES SHIRES, G.L. and DEE, C.W. 'Pressurised fluid bearings with inlet slots', Gas Bearing Symposium, 1967, Paper No.7, University of Southampton. ROWE, W.B., KOSHAL, D. and STOUT, K.J. 'Slot entry bearings for hybrid hydrodynamic and hydrostatic operation', J. Mech. Eng. Sci., 1976, 18, 73-78. ROWE,W.B. and KOSHAL, D. 'Fluid film bearings operating in a hybrid mode: Part 1 - Theoretical analysis and design', Trans. ASME, 1981, 103 (4), 558-565. ROWE, W.B., XU, S.X., CHONG, F.S. and WESTON, W. 'Hybrid journal bearings with particular reference to hole entry configurations'. Tribology International, 1982, 339-348. IVES, D. and ROWE, W.B. 'The effect of multiple supply sources on the performance of heavily loaded pressurised high speed journal bearings'. Int. Conf. on Tribology, Inst. Mech. Engrs., 1987, Paper No. C199/87. ROWE, W.B. and CHONG, F.S. 'Computation of the dynamic force coefficients for hybrid (hydrostatic/hydrodynamic) journal bearings by the finite disturbance technique and the perturbation technique', Tribology International, 1986, 19 (5), 260-271. ROWE, W.B., CHONG, F.S. and WESTON, W. 'A linearised stability analysis of rigid and flexible rotors in plain hybrid (hydrostatic/hydrodynamic) journal bearings', Proc. Conf. Vibrations in Rotating Machinery, York, Instn. Mech. Engrs., 1984, Paper C262/84. NG, C.W. and PAN, C.H.T. 'A linearised turbulent lubrication theory', Trans. ASME, J. Bas. Eng., 1965, 87 (31, 675-688. ELROD, H.G. and NG, C.W. 'A theory for turbulent films and its application to bearings', Trans. ASME, J . Lub. Tech., 1967, 346-362. CONSTANTINESCU, V.N. 'On turbulent lubrication', Proc. Instn. Mech. Engrs., 1959, 173 (38), 881-896. HIRS, G.G. 'A bulk flow theory for turbulence in fluid films', Trans. ASME, J. Lub. Tech., 1973, 95 (2), 137-146.

+

E

.-L

,,,i- \

increasing clearance

8.0

P

6.0

.I-

2

4.0

-

2.0

-

1.0

-

0

.I-

.-El "

.-

v-

uW

0.8 06 0.4

-

1

I

I

I

I

Fi9.9

I

I I I

I

I

I

1000 2000 4000 Renolds Number Re

500

,

, , , I

104

Coefficient o f merit against Reynolds number for variations in clearance, slot entry generator bearing, superlaminar.

-

decreasing viscosity

01 102

I

I

I

I

I

,

,

,

I

Reynolds Number Fig.10

I , , , , , , ,

I

lo3

lo4

Re

Coefficient of merit against Reynolds number for variations in viscosity, slot entry generator bearing, superlaminar.


435

Paper XIV(iv)

Behaviour of a high-speed hydrostaticthrust bearing with recess insertsand grooved lands D. Ashman, E. W. Parker and A. Cowley

The programme o f r e s e a r c h r e p o r t e d i n t h i s p p e r was u n d e r t a k e n w i t h t h e aim o f i m p r o v i n t h e h i g h - s p e e d p e r f o r m a n c e of a m u l t i - r e c e s s e d d r o s t a t i c t h r u s t bearin The e f f e c t s of g h i g h p e r i p h e r a l speeds a r e d i s c u s s e d and how r e c e n t l y proposed b e a r i n g modiff:ations, i n t h e form of r o o i e d l a n d s and changes i n r e c e s s geometr are- used- t o reduce t h e f r i c t i o n a l power consumption, qower t h e o p e r a t i n g t e m p e r a t u r e s , and reiAce unwanted h y d r o d y n a m i c p r e s s u r e v a r i a t i o n s . The r e s u l t s confirmed t h e merits of t h e new b e a r i n g d e s i g n under high-speed c o n d i t i o n s . 1.

INTRODUCTION

In m a n u f a c t u r i n g i n d u s t r i e s

t h e s p e e d s of many m a c h i n i n g o e r a t i o n s h a v e i n c r e a s e d s t e a d i l y due t o t i e i n t r o d u c t i o n of c u t t i n g t o o l s made f r o m c o a t e d c a r b i d e s , c e r a m i c s , p o l y c r y s t a l l i n e diamonds and boron n i t r i d e s . In r e c e n t y e a r s , such new m a t e r i a l s have made p o s s i b l e c u t t i n g speeds up t o 20 m / s f o r s t e e l and 60 m / s f o r aluminium (1). During t h i s period complementary developments i n Com u t e r Numerical C o n t r o l l e d ( r e f e r r e d t o a s CN )! machining c e n t r e s have demanded e v e r i n c r e a s i n g s p e e d and power requirements. Normally such machines h a v e l a r g e diameter s p i n d l e s t h a t o e r a t e a t r o t a t i o n a l s p e e d s i n e x c e s s of 5,800 r m f o r l i h t m a c h i n i n g o f c o m p o n e n t s an{, in high l o a d s during heavy adfition, carr a t low s eeds. These roughing o e r a t i o n s re u i r e bearinf s p f n d l e systems amping c a p a c i t w f t h h i h s t i l f n e s s and r e l i a b i f i t y and h i g h l i f e e x e c t a n c TKi s t a g e h a s b e e n r e a c h e d i n N!C( maccining o p e r a t i o n s where t h e machine t o o l and not t h e cutting ti i s t h e l i m i t i n g !actor. The load-carryThg bearing elements i n p a r t i c u l a r have become t h e f o c u s of a t t e n t i o n .

operations

A t y p i c a l h y d r o s t a t i c b e a r i n g used i n machine t o o l a p l i c a t i o n s c o n s i s t s of d e e p p o c k e t s and t h f n l a n d s . L u b r i c a t i n g o i l i s s u p l i e d t o t h e b e a r i n g r e c e s s e s by a h l r a u l i c pump, v i a compensating elements, and t i e n c e o v e r t h e l a n d s . A ma o r c o n t r i b u t i o n t o t h e s u b j e c t was made by Odonoghue and Rowe ( 2 ) who l a i d down d e s i g n p r o c e d u r e s a n d described the quasi-static o erating c h a r a c t e r i s t i c s f o r a v a r i e t y of h y l r o s t a t i c bearings

.

The h y d r o s t a t i c b e a r i n g has been e x p l o i t e d by t h e machine t o o l i n d u s t r y b e c a u s e of c e r t a i n d e s i g n c h a r a c t e r i s t i c s , namely, high load-carrying c a f a c i t p v i r t u a l l y i n d e p e n d e n t o f s p e e d , no s t ck-s i p c h a r a c t e r i s t i c s and v e r low f r i c t i o n a t low o r z e r o speed, h i g h s t i f f n e s s and damping g i v i n h i g h m a c h i n i n g accuracy and e l i m i n a t i n g machfning v i b r a t i o n s , and z e r o wear of b e a r i n g s u r f a c e s . However, under high-speed c o n d i t i o n s , u n d e s i r a b l e h y d r o d y n a m i c , f l u i d i n e r t i a and tem e r a t u r e e f f e c t s impair s e r i o u s l y the quasf-static d e s i g n c h a r a c t e r i s t i c s . C o n s e q u e n t l y , much r e s e a r c h has c o n c e n t r a t e d on t h e t h e r m a l and i n e r t i a l a s p e c t s of h d r o s t a t i c b e a r i n g s . Such work t a k e s t h e Form o f t h e o r e t i c a l a n a l y s e s of t h e e f f e c t o f t e m p e r a t u r e and inertia (3 4 ) , together with several e x p e r i m e n t a l i n v e s t i g a t i o n s ( 5 , 6 ) . It w a s found t h a t a t h i h speed t h e e l e v a t e d working t e m p e r a t u r e s re%uce t h e a b s o l u t e v i s c o s i t y and, a s a conse uence, reduce t o r q u e a t t h e e x e n s e of a n I n c r e a s e i n f l o w r a t e o r a r e l u c t i o n of f i l m t h i c k n e s s which c o u l d l e a d t o f a i l u r e . Also, f l u i d i n e r t i a e f f e c t s i n an

annular recess a l t e r the pressure d i s t r i b u t i o n i n t h e deep pockets and under t h e l a n d s which c o u l d produce p r e s s u r e s below ambient c a u s i n g a e r a t i o n and a g a i n p o s s i b l e b e a r i n g f a i l u r e . S h i n k l e and Hornun (7) p u b l i s h e d a a p e r which d e s c r i b e d a s i m p f e t h e o r e t i c a l a n a 5 y s i s of t h e f r i c t i o n a l t o r q u e r e s i s t i n t h e motion of a c o n v e n t i o n a l m u l t i - r e c e s s e d a y d r o s t a t i c j o u r n a l b e a r i n g , and backed t h i s up w i t h some experimental r e s u l t s . The e f f e c t of r o t a t i o n on t h e b e a r i n g i s shown i n F i g . l a . Their main c o n c l u s i o n s were t h a t : ( 1 ) The l i n e a r v e l o c i t d i s t r i b u t i o n i n t h e p o c k e t s was m o d d i e d by a p r e s s u r e g r a d i e n t a l o n g t h e l e n g t h of t h e r e c e s s e s producing a c o r r e s p o n d i n g i n c r e a s e i n drag.

( 2 ) The r e s s u r e g r a d i e n t under high-speed c o n d f t i o n s may b e l a r g e e n o u g h t o produce p r e s s u r e s below ambient c a u s i n g a e r a t i o n of t h e f l u i d i n t h e pockets.

(3) The

ocket drag which c a n be s i g n i A c a n t when f l u i d f l o w i n t h e deep recesses i s l a m i n a r becomes d o m i n a n t a t h i g h Reynolds numbers.

O t h e r w o r k , u n d e r t a k e n by M o h s i n a n d S h a r r a t t (1, 8, 9 ) , i n v o l v e d t h e re-desi n of t h e l a n d and pocket geometry of c o n v e n t f o n a l hydrostatic bearin s i n order t o correct the u n d e s i r a b l e t h e r m a q , h y d r o d y n a m i c and f l u i d i n e r t i a e f f e c t s b o t h u n d e r t h e l a n d s and i n t h e d e e p recesses. In t h e d e s i g n shown i n F i g . l c t h e l e a d i n g and t r a i l i n g e d g e s were connected b e x t e r n a l c o n d u i t s ( r e f e r r e d t o a s a n e x t e r n a l r e c e s s f l o w s y s t e m o r ERFS) i n o r d e r t o reduce t h e p r e s s u r e d i f f e r e n c e f o r a g i v e n speed, by a l l o w i n t h e f l o w t o c i r c u l a t e a r o u n d t h e system. M o f s i n and S h a r r a t t a l s o roduced f l o w and f r i c t i o n a l d r a g c o e f f i c i e n t s f o r v a r i o u s o r t h o g o n a l g r o o v e d l a n d s (8). They concluded t h a t : ( 1 ) The h a r m f u l h y d r o d y n a m i c e f f e c t s in t h e recesses were reduced c o n s i d e r a b l y by an ERFS u s i n g e x t e r n a l c o n d u i t s ,

( 2 ) A b e a r i n w i t h r o o v e d l a n d s and a n ERFS r e d i u c e d t%e f r i c t i o n a l power consumption, ( 3 ) The grooved l a n d s a r o d u c e d a n e g l i g i b l e l e v e l of h y d r o y a m i c a c t i o n t h u s e l i m i n a t i n g c a v i t a t i o n , a e r a t i o n and whirl.

(4) The dynamic s t i f f n e s s was s l i g h t l y reduced due t o t h e volume.

l a r g e r pocket

436

+ve

I

I

ERFS 1

,/ Z

Return channel Inlet Slot Width

Recess

Inlet Pressure

-

Aeration a t Leading Edge a ) Pressure d i s t r i b u t i o n s

1 1

Return Channel Outlet Slot Width

s\ P l a i n

Return

Ambient Pressure

Distribution

-Thickness

Fig.2

Geometry of an ERFS using r e c e s s i n s e r t .

b) Geometry of a p l a i n r e c e s s C i r c u l a t i n g Flow

velocity

Profile

/

II-'f

- - - - - - -+ -, 7-External Conduits

-

\ . \ \ , \ , .

Moving Member

c) Geometry of an ERFS using e x t e r n a l conduits Fig.1 Operation of a p l a i n r e c e s s and an ERFS with e x t e r n a l conduits under speed c o n d i t i o n s . An improved d e s i n was p u t f o r w a r d t a c h i e v e a n ERFS whi& i n v o l v e d t h e u s e of pocket i n s e r t s t o o b t a i n t h e same e f f e c t s (1). Fig. 2 shows a n ERFS c o n t a i n i n a r e c e s s i n s e r t , which a g a i n was d e s i g n e s t o a l l o w f l u i d t o c i r c u l a t e around t h e system. Preliminary a n a l y t i c a l work was undertaken by I t was shown t h a t Mohsin and S h a r r a t t (1). t h e pocket e x h i b i t e d s i m i l a r characteristics t o the system using e x t e r n a l conduits. The work presented i n t h i s pa er d e s c r i b e s an ex erimental i n v e s t i a t i o n o? t h e l o a d i n and !low c h a r a c t e r i s t q c s , and h i g h - s p e e i e r f o r m a n c e of a n a n n u l a r m u l t i - r e c e s s e d R y d r o s t a t i c t h r u s t b e a r i n g w i t h v a r i o u s land and p o c k e t g e o m e t r i e s i n which t h e f o r m e r c h a r a c t e r i s t i c s a r e compared w i t h d a t a from e x i s t i n g t h e o r e t i c a l a n a l y s e s . The p r o j e c t was c a r r i e d o u t i n o r d e r t o a s s e s s t h e a d v a n t a es of a b e a r i n g w i t h a n e x t e r n a l r e t u r n f l o w s y s t e m u s i n g r e c e s s i n s e r t s and grooved l a n d s o v e r a h d r o s t a t i c bearing with p l a i n r e c e s s e s and f K a t l a n d s , around t h e c r i t e r i a of f r i c t i o n a l power consum t i o n minimum tem e r a t u r e r i s e and r e d u c t f o n oP u n d e s i r a b l e iydrodynamic and i n e r t i a e f f e c t s . 2

6

sEcrioN-'1*'

\o

b) Axial cross-section

THE TEST R I G

A d e t a i l e d d e s c r i p t i o n of t h e b e a r i n g r i g i s i v e n i n r e f e r e n c e (10). Figs. 3 - 5 f;ll u s t r a t e t h e components of t h e test bearing. The bearing b l o c k s [items I0 and 151, each had t h r e e r e c e s s e s . S p a c e r [ i t e m 261 and r e t u r n f l o w i n s e r t s [ i t e m 2 7 1 , which were p l a c e d i n e a c h o c k e t t o change t h e r e c e s s e o m e t r were i e l d i n p o s i t i o n by s c r e w s [[item 257: The pocket depth could be v a r i e d between 1.5 4.0 mm i n s t e s o f 1.25 mm. The r e t u r n f l o w i n l e t and o u t f e t s l o t s could be v a r i e d between 1.5 4.0 mm i n s t e p s o f 1.25 mm. However f o r a g i v e n i n s e r t t h e r e t u r n f l o w i n l e t and o u t l e t s l o t s were e q u a l t o t h e d e p t h of t h e return flow channel. For a bearing c o n f i g u r a t i o n which c o n t a i n s a n ERFS t h e i n s e r t t h i c k n e s s , and l e a d i n g and t r a i l i n g edge r a d i i , were 3.0 mm, 1.5 mm and 1.5 mm respectively. The o i l i n l e t p o s i t i o n t o t h e b e a r i n r e c e s s c o u l d a l s o be v a r i e d i.e. i n t h e po&et o r r e t u r n f l o w sections.

-

0

100

I

200

I

MILLIMETRES

a ) P l a n view Fig.3

Test Bearing Assembly

390

437 F r onvenience t h numerous b e a r i n ocket and f a n s geometry c o n f i g u r a t i o n s were l i t e n an i d e n t i f i c a t i o n format as f o l l o w s : where s = depth of r e c e s s (mm) v = d e p t h of r e t u r n c h a n n e l , and w i d t h of t h e r e t u r n f l o w i n l e t and o u t l e t s l o t s (mm), w = land eometry. (F f o r f l a t l a n d s o r G f o r grooved lands), z o i l i n l e t o s i t i o n . (C f o r i n t h e r e t u r n f l o w channel or R f o r i n t h e pocket).

-

The top bearin block was fixed t o the top r e t a i n i n g p l a t e [?ten 11 * t h e bottom bearing block was constrained a g a i n s t r o t a t i o n o n l y b r o d s [ i t e m 221. The moving member i t e m 28 was keyed on the t e s t bearin s h a f t \item 20 which was supported by two se!lf-aligning b a l b e a r i n s [ i t e m s 8 and 211. A d i a g r a m of t h e roove% l a n d geometry i n c o r p o r a t e d i n t h e % e s i g n i s g i v e n i n Fig. 4 .

I

!

Y

-

"

m " Fig.4

TEST PROGRAMME AND RESULTS

The t e s t made up

s/v/w/z

I

3

D e f i n i t i o n of grooved-land geometry

The test bearings and l o a d i n i s t o n s [item 161 w e r e s u p p l i e d by v a r i a % f e p r e s s u r e supplies, the t e s t bearing v i a s i x v a r i a b l e r e s t r i c t o r s . The l u b r i c a n t used t h r o u g h o u t t h e e x p e r i m e n t a l q u a s i - s t a t i c l o a d i n g and speed t e s t s was S h e l l T e l l u s O i l 27.

reported i n t h i s paper i s OK rogramme f o u r s e c t i o n s , i.e. t h e s t u d y o f :

(1) Q u a s i - s t a t i c l o a d i n g characteristics,

and

flow

( 2 ) F r i c t i o n a l power consumption,

( 3 ) St e a d y - s t a t e t e m p e r a t u r e d i s t r i b u t i o n under speed c o n d i t i o n s , ( 4 ) V a r i a t i o n of ressure distribution under speed c o n i i t i o n s .

B e f o r e e a c h t e s t , i t was n e c e s s a r y t o balance the r e s t r i c t o r s t o o b t a i n t h e required pocket/sup l y pressure r a t i o f o r a desi n This was achieved f y operating c!earance, a p p l i n g a l o a d of e v e r a l tonnes t o t h e b e a r J n g v i a t h e s t a t i c l o a d i n g c i r c u i t and l o a d rams, b r i n g i n g t h e b e a r i n faces an% ocket t o g e t h e r ; t h e supp 1y p r e s s u r e , Pr , were t R z z t ' t o P s ) h e i r a e s i g n v a l u e s , and t h e v a r i a b l e r e s t r i c t o r s a d j u s t e d t o o b t a i n t h e required working c l e a r a n c e , h on b o t h b e a r i n g s . F i n a l l y , t h e o i l c o o l & w a t e r f l o w r a t e was r e u l a t e d t o m a i n t a i n a constant bearing o i l i n f e t temperature.

3.

D u r i n g t h e t e s t s t h e c o r r e c t v a l u e s of pocket r e s s u r e and f i l m t h i c k n e s s were obtaine! w i t h b o t h f l a t and g r o o v e d l a n d s . The q u a s i - s t a t i c c h a r a c t e r i s t i c q u a n t i t i e s such a s f l o w r a t e s u p p l y and p o c k e t p r e s s u r e s , d o u b l e f i l m c l e a r a n c e and o i l temperatures were recorded. These c h a r a c t e r i s t i c s were t h e n compared w i t h t h e o r e t i c a l p r e d i c t i o n s , a s calculated using the governin e q u a t i o n s d e v e l o p e d by O'Donoghue an% Rowe ( 2 ) a n d M o h s i n a n d S h a r r a t t (8). T y p i c a l r e s u l t s a r e shown i n F i g s . 6 and 7.

Provision was made f o r t h e measurement o f : (1)

The f i l m thickness.

(2)

The r e s s u r e and temperature d i s t r i t u t i o n i n t h e bearing r e c e s s and l a n d s ( s e e Fig. 5 ) and a t t h e i n l e t and o u t l e t of t h e c o m p e n s a t i n g restrictors.

(3)

KEY

f

Theoretical Prediction

8.0

1.5/O/G/R 40OC

.

The o i l f l o w r a t e t h r o u g h t h e t e s t be a r i ng

(4) The r o t a t i o n a l speed. (5)

The power input t o t h e e l e c t r i c motor.

1

/+

/

1 .5/OiG/R

3OoC 4.0

Direction of Rotation of the noving nernber

T

-

1.5/O/F/R 4OoC

3.0 Trailin9

1.5/O/F/R 3OoC

2 .o

1 .o

0 0

Fig.5

P o s i t i o n of instrumentation p o i n t s

Fig.6

1.0

2.0

3.0

4.0 5.0 P o c k e t P r e s s u r e (bar)

O i l flow r a t e c h a r a c t e r i s t i c s

438

-

Ps = 5.0 bar

H I.5lOI~lR

Pr = 2.5 bar at rd

= 0.05

'"&hd

.Q

mm

1.5/0/G/R

W

1.5/1.5/CIC

ce

t.l/4/0/C

-Theoretical Experimental A 4/4/G/C 0 1.5/O/F/R

O

i

i

'

I

I

I

,

olos

,

0.1

Speed lrpml

Single

F i l m Thickness (mm)

Fig.7

Fig.8

F r i c t i o n a l power consumption v e r s u s s p e d p o c k e t d e p t h = 1.5 mm.

-

V a r i a t i o n of pocket p r e s s u r e w i t h f i l m thickness.

The f r i c t i o n a l p o w e r c o n s u m p t i o n w a s o b t a i n e d under i s o t h e r m a l conditions. This was a c h i e v e d by s e t t i n g t h e r o t a t i o n a l speed of t h e b e a r i n g p r i o r t o t e s t i n and measuring the ower c o n s u m p t i o n the bearing immedyately a f t e r s t a r t i n t o eliminate t e m p e r a t u r e v a r i a t i o n s i n t%e d e e p r e c e s s e s and under t h e lands. Throughout t h e programme a n o p e r a t i n s i n g l e f i l m c l e a r a n c e 06 hd = 0.05 mm and g e a r i n g t e m p e r a t u r e o f 50 C were maintained. The f r i c t i o n a l ower consumption of t h e b e a r i n g was o b t a i n e d !or a speed range of 0 3000 rpm. T h i s s p e e d r a n g e was c h o s e n because a t higher speeds, v i s c o u s and t u r b u l e n t d r a g t o r ue produced l a r g e b e a r i n g t e m p e r a t u r e rises, A i c h reduced c o n s i d e r a b l y t h e accuracy of t h e e x p e r i m e n t a l r e s u l t s .

OF'

-

The f i n a l o p e r a t i n g c o n d i t i o n w a s o b t a i n e d b r o t a t i n g t h e b e a r i n g a t a g i v e n speed u n t i l t z e b e a r i n g t e m p e r a t u r e d i s t r i b u t i o n remained c o n s t a n t f o r 3 minutes. During t h i s time t h e b e a r i a g was sup l i e d w i t h o i l a t a t e m p e r a t u r e of 4 0 c. The r n i t i a l s i n l e f i l m t h i c k n e s s f o r a l l t h e t e s t s w a s %.05 m m , a n d t h e e x p e r i m e n t a l p r o ramme was based on a range of s eeds between 4 0 0 0 rpm. Tables 1 t o 6 temperature d i s t r i b u t i o n s f o r various bearing confi gur at i o n s .

8-

SROW

Speed Irpmn)

Fig.9

F r i c t i o n a l power consumption v e r s u s speed p o c k e t d e p t h = 4.0 mm.

-

The p r e s s u r e d i s t r i b u t i o n was a l s o recorded when t h e a v e r a g e t e m p e r a t u r e i n t h e o c k e t ( a s measured by t h e thermocouples embedled i n t h e r e c e s s i n s e g t ) had r e a c h e d t h e r e q u i r e d t e s t v a l u e of 50 C f o r s e e d s w i t h i n t h e range 0 The i n i t f a l s i n g l e f i l m c l e a r a n c e 5000 r m. was a l j u s t e d t o 0.065 mm a s a s a f e g u a r d a g a i n s t p o s s i b l e c o n t a c t d u r i n g o p e r a t i o n , and t o reduce t h e o p e r a t i n g t e m p e r a t u r e s .

-

The t e s t c o n d i t i o n s a n d k e y t o t h e s p e e d test r e s u l t s a r e a s f o l l o w s : (1)

Test c o n d i t i o n s :

Ps = 10 b a r

Pr =

5 bar

*----* (2)

Load = 12.8 kN

Key f o r P r e s s u r e P r o f i l e R e s u l t s Stationary

-@-@

3000 rpm

1000 rpm

4000 rpm

2000 rpm

5000 rpm

Fig.10 F r i c t i o n a l power consumption of an ERFS with o i l feed i n t o pocket s e c t i o n .

439

ROTATIONAL SPEED (rpm)

TEMPERATURE ALONG THE TRAILING EDGE AND AT THE ADJACENT POSITIONS I N THE INNER ANTI OUTER LANDS (OC) T2

T3

T4

TI

TO

38 38 40.5 41 47 47.5 53.5 53.5 69.5 '70

38 42 48 53

38 38.5 45 51

40 43.5 50 63

70

65

40 42 48 56 72

T1 0 1000 2000 3000 4000

TEMPERATURE ALONG THE LEADING EDGE AND AT THE ADJACENT POSITIONS I N THE INNER AND OUTER LANDS ('(3) L2

L3

L4

LI

LO

38 38 38.5 38.5 43 44 51 49 67 61

38 38 42 49 62

38 38 42 49

40 41 46.5 57 73

40

L1

80

63

43 52 66 81

AVERAGE DOUBLE FILM THICKNESS (mm)

0.1 0.098 0.091 0.085 0.0787

TABLE 1

Temperature d i s t r i b u t i o n s

-

b e a r i n g c o n f i g u r a t i o n 1.5/O/F/R

TABLE 2


-

b e a r i n g c o n f i g u r a t i o n 1.5/O/G/R

TABLE 3


- bearing

0 280 1790 4860 6400

c o n f i g u r a t i o n 1.5/4/G/C

TABLE 4


-

b e a r i n g c o n f i g u r a t i o n 4/O/G/R

TABLE 5


-

b e a r i n g c o n f i g u r a t i o n 4/4/G/C

FRICTIONAL POWER

LEADING EDGE AND AT THE

TRAILING EDGE AND AT THE ONS I N THE

FRICTIONAL POWER CONSUMPTION (Watts)

THICKNESS

CONSUMPTION (Watts)

3300 3100 3000 Speed TABLE 6

-

=

3000 rpm

Temperature d i s t r i b u t i o n s ERFS b e a r i n g c o n f i g u r a t i o n s which had t h e o i l i n l e t p o r t i n t h e recess s e c t i o n of t h e pocket

440

PRESSURE

PRESSURE bar

" TRAILING EDGE

TI

a)

T1

T2

T3

TI

Trailing edge

a)

T1

b)

'

Trailing edge

LEADING EDGE

LEADING EDGE

LI

f

12

PRESSURE bar

PRESSURE

I

'

I'

TO

' f

L1

'

' I '

L2

'

>3'

c;

L1

'

Leading edge PRESSURE bar

PRESSURE bar

6.5

6.51

+

"

5.5

5.5

5

5

4.5

4.5

4

4

CIRCUMFERENTIAL SECTION

12

c)

Circumferential section

Fig.11

/

I ' L2

Experimental pressure distributionsobearing configuration 1.5/O/F/R (50 C)

c)

( 12

/

/

CIRCUMFERENTIAL SECTION

I " ' / /

T4

24'

.,L2I /


Fig.12

Experimental pressure distributions bearing configuration 1.5/O/G/R (5OoC)

44 1

a)

Trailing edge

b)

Leading edge

b)

Leading edge

bar


Fig.13

Trailing edge

PRESSURE

PRESSURE bar

c)

a)

Experimental pressure distributionsobearing configuration I .5/4/G/C (50 C)

c)


Fig.14

Experimental pressure distributionsobearing configuration 1.5/4/G/R (50 C)

442

I

PRESSURE

PRESSURE DISTRIBUTIONS I N LANOS HAVE BEEN DRAW1 EUT IHDlVlDUAL POINTS NOT PLOTTED.

bar

71

bar

71

1

I

TRAILING EDGE

a)

TRAILING EDGE

.I/

/ I " T1

TI

/

T2

a)

/

I

11

TI

Trailing edge

,

f

T2

,

(

/

T3

TO

Trailing edge

PRESSURE bar

71

1

I

L1

b)

LI

Leading edge

b)

PRESSURE

L1

L2

L3

LO

Leading edge

PRESSURE bar

bar

I 5 4.5

-

CIRCUMFERENTIAL SECTION /

f

T2

c)

/

/

I / T4

'

/

/

/

L2


Fig.15

Comparison of pressure distributions for bearin configurations 2.151 O f GfR and 2.75/4$GfR (5OOC).

T2

c)

T4

L4

L2


Fig.16

Experimental pressure distributiogs bearing configuration 4fOfGfR (50 C)

443 4

DISCUSSION OF RESULTS

The q u a s i - s t a t i c r e s u l t s show c l o s e agreement with t h e t h e o r e t i c a l p r e d i c t i o n s using t h e g o v e r n i n e q u a t i o n s d e v e l o ed by O'Donoghue and Rowe $2) and Mohsin and i h a r r a t t (8). The r e s u l t s i n c l u d e s t u d i e s of t h e pocket pressure a a i n s t o e r a t i n g c l e a r a n c e and f l o w r a t e c g a r a c t e r f s t i c s . The experimental f l o w r a t e was s e n s i t i v e t o s m a l l v a r i a t i o n s of t h e o p e r a t i n g c l e a r a n c e and o i l i n l e t temperature. I n t h e c a s e of g r o o v e d l a n d s , c a r e f u l machining of t h e land y o f i l e was required i n order t o o b t a i n reasona l e agreement between t h e t h e o r e t i c a l and e x p e r i m e n t a l f l o w r a t e results. R e s u l t s i n Fig. 7 show no v a r i a t i o n in static stiffness a s i n d i c a t e d by s l o p e s of t h e graphs.

-

a)

It can be seen from Fig. 8 t h a t a reduction of t h e f r i c t i o n a l power consum t i o n was a c h i e v e d , a t a p o c k e t d e p t h of 1.5 mm, when t h e r e t u r n f l o w d e p t h was used. The r e t u r n f l o w channel had t h e e f f e c t of decreasing t h e v e l o c i t y g r a d i e n t of t h e f l u i d a t t h e moving s u r f a c e , and t h e r e f o r e r e d u c i n g t h e d r a g t o r q u e on t h e moving member a s a r e s u l t of a c o r r e s p o n d i n g r e d u c t i o n of t h e i n d u c e d p r e s s u r e d i f f e r e n c e between t h e l e a d i n g and t r a i l i n g edges. The e x e r i m e n t a l r e s u l t s shown i n F i g s . 1 2 a n d P 3 c o n f i r m e d t h i s hypothesis.

T r a i l i n g edge

From e x a m i n a t i o n o f t h e e x e r i m e n t a l r e s u l t s i n F i s. 1 6 a n d 1 7 , t i e maximum p r e s s u r e dif%erences f o r the bearing c o n f i g u r a t i o n s 4/O/G/R and 4/4/G/C a t a n o p e r a t i n g t e m p e r a t u r e of 5OoC and s p e e d of 3 0 0 0 r m w e r e 0 . 3 5 b a r a n d 0.1 b a r r e s e c t f v e l y . Consequently, t h e two bearing c o n f i g u r a t i o n s had s i m i l a r f r i c t i o n a l power con sumpt i on c h a r a c t e r i s t i c s .

b)

During t h e experimental i n v e s t i a t i o n i t was observed t h a t t h e o i l i n l e t p o s l t i o n had l i t t l e e f f e c t u on t h e f r i c t i o n a l ower consumed by an ERPS. With p l a i n pocket Xepths of 1.5 mm and 4 mm a r e d u c t i o n of t h e power consumption, observed i n t h e case of grooved l a n d s , s u b s t a n t i a t e d t h e r e s u l t s of Mohsin and S h a r r a t t (8, 9 ) . When g r o o v e d l a n d s were t e s t e d an i n c r e a s e of t h e o i l f l o w r a t e was a l s o recorded. T h i s i n c r e a s e d t h e pumping ower r e u i r e d t o o p e r a t e t h e system. Rowever, t i e f r i c t i o n a l power consumption was predominant under high-speed conditions. For e x a m p l e , when t h e b e a r i n g c o n f i g u r a t i o n 1.5/O/G/R was t e s t e d w i t h P = 10 b a r , Pr = 5 bar,. ly = 0.05 mm and an o i l s i n l e t temperature o f 50 C t h e e x e r i m e n t a l pum i n g power consumed by t h e g e a r i n g s y s t e m (f.e. pum i n g power consumed = t o t a l f l o w x p r e s s u r e s r o 208 a c r o s s t h e s y s t e m ) was a p p r o x i m a t e 1 watts. Experimental d a t a presented i n Jig. 8 shows t h a t u n d e r i d e n t i c a l o p e r a t i n g c o n d i t i o n s t h e f r i c t i o n a l power consumed by t h e b e a r i n g a r r a n g e m e n t , when t h e moving member was r o t a t e d a t a speed of 3000 rpm, was 2700 w a t t s i.e. i n e x c e s s of 1 3 t i m e s g r e a t e r than t h e pumping power.

Leading edge

PRESSURE bar

The o p e r a t i n g t e m p e r a t u r e i n c r e a s e d o v e r the e n t i r e bearing s u r f a c e when the r o t a t i o n a l s p e e d was i n c r e a s e d . When f l a t l a n d s were t e s t e d t h e tem e r a t u r e s i n t h e inner and outer c i r c u m f e r e n t i a f l a n d s were c o n s i d e r a b l y higher t h a n t h a t i n t h e r e c e s s . When r o o v e d l a n d s were u s e d , t h e tem e r a t u r e i n &e o c k e t and l a n d s showed a marfed r e d u c t i o n . $ h i s c o u l d be a t t r i b u t e d t o a decrease of t h e f r i c t i o n a l ower consumption, t o g e t h e r w i t h a n i n c r e a s e n flow rate.

P

c)

Circumferential s e c t i o n

Fig.17

Experimental pressure d i s t r i b u t i o g s bearing c o n f i g u r a t i o n 4/4/G/C (50 C)

-

When p l a i n r e c e s s e s were t e s t e d , t h e f i n a l o p e r a t i n g t e m e r a t u r e s a l o n g t h e l e a d i n g ed e were l o w e r t\an t h e t e m p e r a t u r e s a l o n t E e t r a i l i n g edge. T h i s would s u g g e s t t h a f t h e v e l o c i t y d i s t r i b u t i o n of t h e f l u i d i n t h e r e c e s s was s i m i l a r t o t h e v e l o c i t y d i s t r i b u t i o n p r e d i c t e d by S h i n k l e and Hornung The c o l d e r s u p p l y f l u i d f l o w e d t o t h e \:din edge f i r s t , t h e lowest temperature i n t h e mafn b e i n g a t p o s t i o n L4, and t h e n t o t h e t r a i l i n edge a f t e r v i s c o u s s h e a r i n g of t h e f l u i d ha% caused an i n c r e a s e i n temperature. From examination of t h e r e s u l t s i n Tables 2 and 3 f o r t h e bearing c o n f i g u r a t i o n s 1.5/O/G/R and 1.5/4/G/C i t can be observed t h a t t h e use of a n ERFS had l i t t l e e f f e c t on t h e p o c k e t temperature under low speed conditions.

444

c o u l d be f u r t h e r i n f l u e n c e d b h y d r o d y n a m i c effects. The e f f e c t of h y d r o i y n a m i c a c t i o n was u n c e r t a i n as i t was d e p e n d e n t on l a n d geometry, f i l m t h i c k n e s s and o p e r a t i n g temperature. produced t h o r o u h mixing of t h e o i l a s i t c i r c u l a t e d a r o u n d t h e system. Com a r i s o n of t h e r e s u l t s i n T a b l e s 4 and 5 w i t h t i e b e a r i n g c o n f i g u r a t i o n s 4/O/G/R and 4/4/G/C i n d i c a t e s t h a t s i m i l a r e f f e c t s t o t h e a b o v e were r e c o r d e d i.e. t h e temperature d i f f e r e n c e b e t w e e n the l e a d i n and t r a i l i n g e d g e s w a s r e d u c e d w h e n t % e ERFS w a s incorporated i n t o t h e design. A n a l y s i s of d a t a u s i n t he above b e a r i n c o n f i g u r a t i o n s , produce% i d e n t i c a l power c o n s u m p t i o n c h a r a c t e r i s t i c s , and t h e r e f o r e t h e c o n f i g u r a t i o n s had s i m i l a r e x p e r i m e n t a l f i n a l o p e r a t i n g a v e r a g e recess t e m p e r a t u r e s . Com a r i s o n of t h e e x p e r i m e n t a l d a t a p r e s e n t e d in g a b l e 6 w i t h t h a t i v e n i n T a b l e s 3 and 5 suggests that the o i f i n l e t position i n the c a s e of a n ERFS h a s l i t t l e e f f e c t on t h e f i n a l ope r a t i n g c o n d i t i o n s .

frictional

The r e s s u r e d i f f e r e n c e between t h e l e a d i n and t r a f l i n e d g e s i n c r e a s e d r a d i a l l y outwar% and a t h i g i e r r o t a t i o n a l s p e e d s u n d e r a l l o erating conditions. However, t h e p r e s s u r e d T f f e r e n c e d e c r e a s e d when a n ERFS was u s e d . F o r exam l e , w i t h t h e b e a r i n c o n f i g u r a t i o n 1.5 / 0 / G ?R, t h e m a x i mum i n f u c e d p r e s s u r e d i f f e r p c e f o r a n o p e r a t i n pocket t e m e r a t u r e o f 5 0 C and s p e e d o f 5 0 8 0 rpm was 5.9 b a r . However, when t h e 4.0 mm r e t u r n f l o w c h a n n e l was used, t h e maximum r e s s u r e d i f f e r e n c e was r e d u c e d t o 0.7 b a r u n z e r t h e same o p e r a t i n g c o n d i t i o n s , as shown i n Fig. 14. A r e d u c t i o n of t h e p r e s s u r e d i f f e r e n c e was

a l s o o b t a i n e d when d e e p e r p l a i n p o c k e t s were used. When t h e b e a r i n g c o n f i g u r a t i o n s 1.5/O/G/R, and 4/O/G/R were t e s t e d , o p e r a t i n w i t h a pocket t e m p e r a t u r e of 50 C and speed o f 5000 r g m , t h e maximum p r e s s u r e d i f f e r e n c e s were 2. b a r and 0.9 bar r e s p e c t i v e l y . I n t h e c a s e of a p o c k e t d e p t h o f 1.5 mm t h e p r e s s u r e a l o n g t h e t r a i l i n g edge i n c r e a s e d r a d i a l l y outward a s a r e s u l t of t h e i n c r e a s e d v e l o c i t y and pocket l e n t h , w h i l s t t h e p r e s s u r e a l o n t h e l e a d i n e i g e remained c o n s t a n t . Fluis i n e r t i a e f g e c t s , p r e d i c t e d by Coombs a n d Dowson ( 5 ) c o u l d b e r e s p o n s i b l e f o r s t a b i l i s i n g the pressure along the leading edge. The t e s t s s u g e s t t h a t t h e e f f e c t s of t u r b u l e n c e and f l u f d i n e r t i a were b o t h p r e s e n t For t h e b e a r i n g c o n f i g u r a t i o n 1.5/O/G/R t h e r e was n o s u b s t a n t i a l i n c r e a s e i n t h e pocket p r e s s u r e a t o s i t i o n T4, o v e r t h e range of s p e e d s between - 50.00 r p m . In t h e c a s e of t h e c o n f i g u r a t i o n 4/O/G/R, u n d e r t h e same o p e r a t i n g c o n d i t i o n s , a decrease i n ressure was r e c o r d e d . M o r e o v e r , u s i n g t h e g e a r i n g c o n f i g u r a t i o n 1.5/4/G/C, which i n c o r p o r a t e d in t h e d e s i n a n ERFS s u p l i e d w i t h o i l i n t h e r e t u r n f Bow c h a n n e l , t$e p r e s s u r e was reduced a t p o s i t i o n s T1 T4 a s shown i n Fig. 13. The d e c r e a s e of p r e s s u r e a t t h e t r a i l i n edge and i n t h e mid-pocket r e g i o n was r e d u c e 3 t h e b e a r i n g c o n f i u r a t i o n s which had b?he%?f i n l e t p o r t i n t%e r e c e s s s e c t i o n o f t h e pocket.

in t h e b e a r i n g p o c k e t s .

8

-

The p r e s s u r e i n t h e l a n d s was a l s o i n f l u e n c e d by h i g h - s p e e d e f f e c t s . With bearin c o n f i u r a t i o n s which i n c o r p o r a t e d g r o o v e % l a n d s 3 n t h e i r d e s i g n , t h e c h a n g e of pressure i n t h e i n n e r and o u t e r c i r c u m f e r e n t i a l l a n d s c o u l d be a t t r i b u t e d t o t h e p r e s s u r e v a r i a t i o n s in the adjacent recess. A s a n e x a m p l e i n t h e c a s e of t h e b e a r i n g c o n f i g u r a t i o n i.5/0/G/R, t h e i n c r e a s e of p r e s s u r e a t t h e t r a i l i n g ed e i n c r e a s e d t h e p r e s s u r e a t p o s i t i o n s T I and T8. S i m i l a r l y a r e d u c t i o n i n p r e s s u r e a t t h e l e a d i n g edge produced a c o r r e s p o n d i n r e d u c t i o n of p r e s s u r e a t p o s i t i o n s L I a n d LO. The p r e s s u r e d i s t r i b u t i o n when f l a t l a n d s were t e s t e d shows similar characteristics t o those observed i n t h e c a s e of g r o o v e d l a n d s . H o w e v e r , i n t h e c a s e of f l a t l a n d s , t h e p r e s s u r e d i s t r i b u t i o n

5

CONCLUSIONS

The q u a s i - s t a t i c o p e r a t i n g c h a r a c t e r i s t i c s of a multi-recessed hydrostatic thrust bearing w i t h b o t h f l a t and g r o o v e d l a n d s , c a n be g F e d i c t e d by t h e a v a i l a b l e t h e o r y o f D o n o g h u e a n d Rowe ( 2 ) a n d M o h s i n a n d S h a r r a t t (8). The s t a t i c s t i f f n e s s o f t h e test b e a r i n g i s not a f f e c t e d by u s i n g grooved l a n d s and a n ERFS c o n t a i n i n g c h a n n e l l e d inserts. The h i g h - s p e e d p e r f o r m a n c e o f a m u l t i r e c e s s e d h y d r o s t a t i c t h r u s t b e a r i n g was found t o b e i m p r o v e d c o n s i d e r a b l y by t h e i n t r o d u c t i o n of a n ERFS and g r o o v e d l a n d s . The m o d i f i e d b e a r i n g g e o m e t r y l o w e r e d t h e f r i c t i o n a l power c o n s u m p t i o n a n d o p e r a t i n g t e m p e r a t u r e s and, i n a d d i t i o n , reduced t h e hydrodynamic p r e s s u r e v a r i a t i o n s i n t h e d e e p o c k e t s and under t h e l a n d s . The e x p e r i m e n t a f r e s u l t s i n d i c a t e d t h a t t u r b u l e n c e and f l u i d i n e r t i a e f f e c t s were p r e s e n t i n t h e d e e p recesses. 6 ACKNOWLEDGEMENT The a u t h o r s r a t e f u l l y a c k n o w l e d e The P o l y t e c h n i c , t o l v e r h a m p t o n f o r t h e ?unding w h i c h made t h e i n v e s t i g a t i o n i n t h i s p a p e r possible. References MOHSIN M.E. a n d SHARRATT A.H. 'The Behaviour of a T o t a l Er,oss Flow H y d r o s t a t i c J o u r n a l B e a r i n g , Proc. 23rd I n t . M.T.D.R. Conf., M a n c h e s t e r , 14-15 September, Pages 13-24 (1982). O'DONOGHUE, J.P. a n d ROWE Y.B. 'H d r o s t a t i c B e a r i n Desi n Tribology, V l , N1, February, %;ages 35-71 (1969). T I N G L.L. and MAYER, J.E., (Jr.) 'The k f f e c t s of Temperature and I n e r t i a on H d r o s t a t f c T h r u s t B e a r i n g Perzormance J. Lubr. Tech. ASME Trans., V93, A p r i l , Pages 303-312 (1971).

,

DOWSON, D. ' I n e r t i a , E f f e c t s i n Hydrostatic Thrust Bearings ASME Trans., J. Basic En S e r i e s D,' V 8 3 , N2, J u n e , Pages 227-2% (1961). COOMBS, J.A. a n d DOWSON, D. 'An E x p e r i m e n t a l I n v e s t i g a t i o n of t h e E f f e c t s of L u b r i c a n t I n e r t i l a i n a H y d r o s t a t i c T h r u s t B e a r i n g , I n s t . Mech. E h g r s . London, P r o c . LubF.-and Wear-Third Convention Pa er 1 2 , V179, P t . 3 J , P a g e s 96-108 (19645. ?HER, A.K. and COWLEY, A. An E x p e r i m e n t a l I n v e s t i g a t i o n i n t o t h e TemDerature Effects i n Hvdrostatic r - - - - - - J o u r n a l Bearin s ' T r i b o l o V3, N 1 , August, Pages ?65)167 ( 1 9 7 8 : ~

SHINKLE, J.N. a n d HORNUNG, K.G. ' F r i c t i o n a l C h a r a c t e r i s t i c s yf L i u i d H y d r o s t a t i c J o u r n a l B e a r i n s , ASJE Trans., J. B a s i c En S e r f e s D, V87, N 1 , March, Pages 1&3'i169 (1965). MOHSIN M.E. a n d SHARRATT, A.H. 'The Behaviou: of H d r o s t a t i c Pads w i t h Grooved Lands T r i i o l o V14, N1, February, Page)s 33-45 f?d81). MOHSIN M.E. a n d SHARRATT, A.H. 'The B e h a v i o u r of a T o t a l C r o s s Flow H y d r o s t a t i c T h r u s t Bearing', Proc. 2 1 s t I n t . M.T.D.R. Conf., S w a n s e a , P a g e s 449-459 (1980). ASHMAN, D. 'Hi h-speed Performance of ,a H f r o s t a t i c Thrust B e a r i n g Ph.D. d e s i s , Wolverhampton Poly. (1987).

,

445

Paper XIV(v)

An experimental comparison between the performanceof a 'total crossflow' and an equivalent conventional design hydrostatic journal bearing M. Abdolmaleki, A. Skorin, F. P. Wardle and R. A. E. Wood

This paper presents the results of an experimental investigation into the advantages of a "Total Cross Flow" bearing design over an equivalent conventional hydrostatic bearing. Practical designs of journal and thrust hydrostatic bearings embodying the features of "Total cross (TCF), "External Return Flow System" (ERFS) and "Grooved Lands" are described. The bearings set-up in a journal and journal plus double thrust arrangement are evaluated. For a 75 mm diameter With journal hydrostatic TCF bearing steady speeds up to 1 million DN have been reached so far. the properties of good damping, stiffness and low temperature rise the TCF hydrostatic bearings are considered suitable for wide speed range machine tool spindle applications.

-Flow"

Experimental comparisons between the performance of TCF design and equivalent conventional pocket and flat land hydrostatic journal bearings clearly demonstrate the advantage of the former particularly in terms of much higher running speed capability with no penalty in temperature rise and shear power losses. Furthermore pocket pressure stability with respect to increased shaft speed for TCF journal bearings tested up to 1 million DN is over 4 times better than that for the equivalent conventional design tested up to 0.6 million DN with a similar temperature rise.

1

INTRODUCTION

With advances in cutting tool technology, high speed machining to increase productivity has received a great deal of attention particularly for applications where the machine tool and not the cutting tip is the limiting factor. In manufacturing industries, the speeds of many machining operations have increased steadily due to new cutting tool materials such as coated carbides, ceramics, polycrystalline diamonds and boron nitrides. For steel and aluphqium, have been cutting speeds up to 20 and 60 m/s reached in recent years. The ever increasing demands for heavy cuts at low speed and light cuts at high speed operations have led relevant industries to consider alternative spindle supports to conventional rolling element bearing systems. This is due to the fact that at such critical operations, complicated additional provisions are needed for rolling element bearing spindles and even then the bearing life is inevitably limited. Furthermore continuous developments in computer numerical controlled (CNC) machining also dictate the need for higher speed operations with good overall performance in terms of optimum power, stiffness and damping characteristics together with longer life requirements. One of the most important components in a machine are the load carrying members, i.e. the bearings. Primarily due to their long life and good stiffness characteristics, hydrostatic bearings are used in machine tool applications. A typical conventional hydrostatic bearing (Figure 1) consists of a number of

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F I G S - DIAGRAM OF A TYPICAL I CIRCUIFFREWTIAL POCKET C W C N l l f f l A L IllfflOSlAllC

BEARING

circumferentially recessed plain pockets and narrow lands. A hydraulic pump is required to supply pressurised lubricating oil into the bearing pockets and over the lands via compensating devices (usually termed as restrictors). The hydrostatic bearing has certain meritorious designed characteristics, namely high load-carrying capacity virtually regardless of speed, no stick-slip and very low friction at low or zero speed, high stiffness and damping giving high machining accuracy and eliminating machining vibrations, and zero wear of bearing surfaces hence virtually unlimited life. At high-speed conditions, however, due to turbulence and cavitation in the pockets and hydrodynamic effects, the oil temperature rises critically which could lead to bearing surface touchdown. The critical rise in oil

446 temperature reduces oil viscosity, consequently followed by a reduction in torque at the expense of an increase in flow rate or a reduction of oil film thickness which eventually leads to failure. Also, fluid inertia effects in an annular recess alter the pressure distribution in the pockets and under the narrow lands which could produce pressures below ambient causing aeration and again possible metal to metal contact failure. The design of hydrostatically supported spindle systems for machine tools has received more attention in recent years and various optimisation procedures have been presented to generally improve the static stiffness and total power requirements as the mzin parameters of interest.

The main object of this paper is to report the results of an independent practical investigation to confirm the advantages of a "Total Cross Flow" (TCF) hydrostatic bearing concept (Figure 2) with additional design features of pocket inserts and grooved lands (invented by Dr M E Mohsin, British patent number 2021705A, filed in May 1979). Two hydrostatic journal bearing spindle arrangements, one with TCF journal bearings and the other with conventional hydrostatic journal bearings having an equivalent flat land and plain pockets were designed, made and tested. The TCF bearing set-up comprising a journal and journal plus double thrust arrangement incorporated in a test rig was also evaluated experimentally. 1.1

Considerable research and development work has been done at the Machine Tool Industry Research Association (MTIRA) presently known as the Advanced Manufacturing Technology Research Institute (AMTRI). Notes for designers and computer programs have been published to enable the design of hydrostatic bearings for specific applications. cedures describe and Stansfield O'Donoghue and RZ;: aimed to optimise the hydrostatic bearing design with static stiffness and total power of interest. consumption as the main paramet and Two books w@e written by Rowe Stansfield to formulate and simplify design rules for hydrostatic bearings as a result of ir invaluable experience, Cowley and Kher ""investigated the dynamic performance of a hydrostatic journal bearing system. They also presented a computer-aided design procedure which takes into consideration both the static and dynamic aspects of ormance. The work involved the by Mohsin and Sharrat ("' re-design of the pocket and land geometry of conventional hydrostatic bearings to improve the undesirable hydrodynamic effects at high speeds.

"'

eq

T AXIAL W D

I FIG.2-PRD.ICIPLE OF A TGTAL CROSS FLOW H Y ~ ~ R O S T A ~BEARING ~C WiiY FEATURES O F N S AND O ~ T H O T R O P I C L4NDS.l A TYPICAL GROOVED LAND GEDYIETRICAL PROFILE IS SHOWN ABOVE I

-

The Hydrostatic Bearing

A conventional hydrostatic bearing unlike a hydrodynamic bearing has its sliding surfaces continuously and completely separated by a pressurised oil film under static and dynamic conditions within the design range. This type of bearing usually comprises a number of circumferential pockets and flat lands (Figure 1) and has the advantage of complete freedom from wear, hence making for reliability and durability. Apart from the inertia of the spindle the only resistance to sliding motion, even when starting from rest, is that due to the viscosity of the fluid. However, such an arrangement requires pumps and a cooler (an ancillary hydraulic system) to pump pressurised oil into the bearing pockets and adequate discharge and cooling facilities to return the oil back into a supply reservoir. The main problem with conventional designs of hydrostatic bearings has been the undersirable hydrodynamic effects associated with the oil turbulence in the pockets under critical dynamic conditions. This is because friction losses due to the shearing of oil both in the pressurised pocket and under the lands can become excessive. At high speeds, oil temperature rises within the bearing can eventually result in deterioration of the oil film between the sliding surfaces and failure due to metal to metal contact. Research and design engineers have optimised and developed different designs and the most effective solution to enhance the performance of hydrostatic bearings so far is the total Cross Flow concept. 1.2

The Total Cross Flow Hydrostatic Bearing

Figure 2 illustrates the principle of operation for a TCF design bearing, the subject of European patent number 0,00500,624B1. Figure 3 (a & b) shows the photographs of a journal bearing and a combined journal plus thrust bearing. The additional design features of pocket inserts and grooved lands are clearly visible on the journal and thrust members of the combined bearing. Figure 4(a) shows the end cover thrust bearing and these three bearing components together with the spindle form the horizontal head for the experimental rig. In addition to pocket inserts, each of the two bearings shown in figure 3 consists of three main parts. The centre parts are identical and

447

Fig.3(a) - Drive End TCF Journal Bearing Fig.4(a)

Fig.3(b)

-

-

End Cover Thrust Bearing

Non-Drive-End Journal & Thrust Flange Fig. 4(b) - Another TCF Journal Bearing Design for A Vertical Milling Machine

include the 4 journal pockets and inserts. The other two members embody the oil feed ports into the pockets, the circumferential grooved lands and the oil scavenge holes. The thrust flange member also comprises the axial pockets and inserts together with grooved axial lands. Figure 4(b) shows another TCF bearing design developed for a vertical milling machine at UMIST. The novel features of external return flow system and grooved lands were added to the conventional hydrostatic bearing design to reduce the adverse effects of turbulence and cavitation in the bearing pockets and undesirable hydrodynamic action beneath the lands. The external return flow system makes it possible for the oil to circulate around the pocket insert from its trailing edge to the leading edge to reduce the pressure gradient of the couette type flow which would otherwise dominate inside a conventional type hydrostatic bearing pocket. The other TCF bearing feature of grooved land reduces hydrodynamic effects on the shearing oil film beneath the lands. It is proved that a grooved wide land gives much less drag resistance than the equivalent narrow flat land and behaves almost entirely hydrostatic. Therefore employing the pocket inserts and grooved lands in the design of TCF hydrostatic

bearings enhances the properties in terms of reduced temperature rise and lower shear power loss which are essential for high and ultra-high speed application. 2

THE 75MM DIAMETER SPINDLE TEST RIG

The general set-up of the rig is shown in figure 5(a). It comprises the main elements :(a) (b) (c) (d)

(el

Test head, including hydrostatic bearings. Bank of external restrictors. Auxiliary equipment including high pressure oil supply, cooler and scavenge Pump * Drive motor with inline pulley drive mechanism. Torque transducer and instrumentation.

The rig was designed to run at speeds up to 16,200 rpm, test bearings permitting, and provide continuous measurements of test head drive torque; bearing, oil in and oil out temperatures; oil flow rate; oil supply and bearing pad pressures. The test head (Figure 5(b) and Figure 6) contains a journal and journal plus opposed thrust bearing arrangement representative of a practical machine tool spindle bearing arrangement. Spacing of the journal bearings was optimised to give maximum

448

Fig.S(a) - General Set-up of the Hydrostatic Rig.

IIGl-SCHCHATIC OlAfiR+ HIURUlLlC CIRCUII

Fig.5(b)

-

Hydrostatic Test Head.

W I N O W E CLOSED LOOP BEMINOS HEAD L DRIVE

After a pressure relief valve the supply oil passes through a 25 micrometer absolute filter and E. manually adjustable pressure reducing valve (pressure achieved is around 70 bar). The oil then flows to the external fixed annular gap restrictors which in turn deliver oil into the bearings. There are 10 feed lines to the bearings from the 5 back-back restrictor arrangements, eight of the feed lines supply the journal bearings; each line feeding one journal pocket. The other two feed lines deliver oil to the thrust bearings; each line feeding the 4 pockets of one thrust bearing. The oil pressure in each bearing pocket is measured downstream of the restrictors with the flow being measured prior to the oil entering the restrictors. Figure 8 shows two fixed annular gap restrictors arranged back-back. They are used external to the bearings. The restriction is provided by a circular land and a designed gap set by a shim thickness. The parameters, gap size, inner and outer land radii are shown which were designed to give laminar oil flow and reduce oil supply pressure by about 50% for feeding to the This design of bearings (Appendix B). restrictor exhibits an oil flow - pressure relationship clo7S)to that expected from a simple analysis over a wide temperature range of 0 to 7 O O C . The restrictors are also mechanically reliable.

spindle rigidity at an overhang of 138 mm. Diametral internal clearance of the journal bearings was set at 100 pm whilst the thrust bearings were set to have 100 tim total axial clearance. Static stiffn ss of each journal 8 bearing was around 4 x 10 N/m at an oil supply Although the pressure of 70 bar (Appendix A). bearing arrangement was optimised from a rigidity standpoint it was the lubrication and thermal aspects of performance at speed which were of primary interest. Figure 7 shows a simple block diagram of the components for the closed loop hydraulic circuit. Shell Tellus oil R22 is pumped through a swash plate pump from a reservoir The maximum oil (capacity around 200 litres). delivery rate of this pump is 45 litres/minute at a maximum supply pressure of 70 bar.

From the bearing pockets the pressurised oil film between the surfaces of the spindle and the bearing lands is maintained and the oil is then discharged over the grooved lands into the bearing scavenge annulus at atmospheric pressure. The galleries in the housing block direct the discharge volume to the scavenge lines.

i -\

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OURET PO71

FIO.8- MAORAU OF T W O i I l l R U A L F I X E D LAMIIIAR FLW RCllRICIORS

IOACK-BACK A S f t MOLY ARIAWGCMLWI I

449 The h e l i c a l r o t o r s c a v e n g e pump, d r i v e n by a 0.55 kW motor a t 9 2 0 rpm w i t h a d e q u a t e d e l i v e r y removal r a t e , p r o v i d e s t h e b a c k p r e s s u r e n e c e s s a r y t o d i s c h a r g e t h e o i l o u t of t h e bearings through t h e galleries i n t h e housing block t o t h e o i l c o o l e r . The c o o l e d o i l i s the n discharged back i n t o t h e t a n k ; t h e o i l s t a r t and t e r m i n a t i o n p o i n t f o r t h e c l o s e d l o o p hydraulic c i r c u i t . The s p i n d l e d r i v e u n i t c o n s i s t s o f a 37 kW c ontinuously v a r i a b l e speed motor, b e l t d r i v e n p u l l e y s and a f l e x i b l e t o r q u e t r a n s m i t t e d pin-drive coupling. The d i a m e t e r r a t i o s of t h e p u l l e y s f o r t h e p r i m a r y and s e c o n d a r y d r i v e s are 1 5 : 7 and 7 : 2 . 5 r e s p e c t i v e l y . Therefore with t h e d r i v e motor r u n n i n g a t 2700 rpm, a 6 times s p e e d o f 16200 rpm c a n b e a c h i e v e d f o r t h e s p i n d l e . The t o r q u e t r a n s d u c e r is mounted a x i a l l y i n l i n e with the spindle. I t is a V i b r o m e t e r TG2 i n d u c t i v e t r a n s d u c e r capable o f t r a n s m i t t i n g 40 Nm a t s p e e d up t o a maximum o f 20,000 rpm. B e a r i n g and o i l t e m p e r a t u r e s a r e measured u s i n g J t y p e t h e r m o c o u p l e s c o n n e c t e d t o a micron O i l s u p p l y and b e a r i n g pad d i g i t a l meter. p r e s s u r e s a r e measured u s i n g a n a l o g u e s t a t i c s r e s s u r e gauges w h i l s t o i l flow rate t o t h e j o u r n a l b e a r i n g s is determined w i t h a v a r i a b l e area f l o w meter. 3

TEST PROCEDURE AND MEXSUREMENT

J o u r n a l and t h r u s t b e a r i n g s p e e d - t o r q u e measurements c o u l d b e s e p a r a t e d by f i r s t t a k i n g measurements f o r t h e c o m p l e t e b e a r i n g a r r a n g e m e n t and t h e n removing t h e t h r u s t b e a r i n g housing t o enable j o u r n a l bearing speed - torque measurements t o b e o b t a i n e d . Subtracting the l a t t e r from t h e former g i v e s t h e t h r u s t b e a r i n g speed - torque r e l a t i o n s h i p . The c o m p a r i s o n b e t w e e n c o n v e n t i o n a l and TCF b e a r i n g s was made f o r j o u r n a l b e a r i n g s o n l y . The e q u i v a l e n c e between t h e TCF and c o n v e n t i o n a l d e s i g n s i s b a s e d upon t h e same :hydrodynamic impedance a c r o s s t h e c i r c u m f e r e n t i a l l a n d s , i . e . 5.5 mm wide g r o o v e d l a n d e q u i v a l e n t t o 3 . 4 mm f l a t land ; ( i i ) w i d t h f o r a x i a l l a n d s o f 3 mm between t h e journal pockets; ( i i i ) p o c k e t d e p t h of 1 mm ( b e t w e e n s h a f t and p a d i n s e r t for TCF); ( i v ) diametral internal clearance, but i n p r a c t i c e t h a t o f TCF j o u r n a l s was 100 pm and t h a t f o r e q u i v a l e n t c o n v e n t i o n a l j o u r n a l s was 78 pm due t o p r o d u c t i o n t o l e r a n c e errors. (i)

Experimental procedure c o n s i s t e d of s e t t i n g s p i n d l e speed, allowing a t least one hour f o r s t e a d y s t a t e c o n d i t i o n s and t h e n n o t i n g measurements. S p e e d was i n c r e m e n t e d t o a maximum d e t e r m i n e d by f a i l u r e of t h e o i l temperature t o s t a b i l i s e . A maximum s t a b l e o i l t e m p e r a t u r e o f a b o u t 70aC c o u l d b e a c h i e v e d . 4

RESULT AND DISCUSSION

Comparison o f s c a v e n g e o i l t e m p e r a t u r e r i s e p l o t t e d a g a i n s t o p e r a t i n g s p e e d b e t w e e n TCF and conventional design journal bearings c l e a r l y

fIG.9-SCAVENGE OIL TENPEAATWLE $5 SPEED UIIPNUSON BETWEEN TCF L QWMlllfflAL BEARIHOS

I

I

I

a,

om

I! SPEED IRPUl

I

r e v e a l e d t h e much h i g h e r s p e e d c a p a b i l i t y o f t h e TCF b e a r i n g s ( F i g u r e 9 ) . For c o n v e n t i o n a l j o u r n a l s , t e m p e r a t u r e r o s e s t e a d i l y up t o a s p e e d of 6000 rpm f o l l o w e d by a 4 . 3 times s h a r p e r r a t e o f i n c r e a s e up t o a s a f e l i m i t i n g s p e e d of a r o u n d 8000 rpm w h e r e a s f o r h i g h s p e e d TCF t e s t s i t r o s e a t a r e l a t i v e l y l o w e r r a t e up t o 8000 rpm f o l l o w e d by o n l y 2 . 7 times s h a r p e r r a t e o f i n c r e a s e t o a n optimum s p e e d of 13,300 r p n . The s i g n i f i c a n c e of t h e c h a n g e i n g r a d i e n t s i n b o t h cases i n d i c a t e d o n s e t o f turbulence. The t r e n d a l s o r e v e a l e d a much g r e a t e r d e g r e e of t u r b u l e n c e f o r t h e f l o w i n t h e c o n v e n t i o n a l t h a n t h e TCF d e s i g n b e a r i n g pockets. The c a l c u l a t e d R e y n o l d s Numbers o f t h e f l o w a t t h e c o r r e s p o n d i n g t e m p e r a t u r e and s p e e d (Appendix C ) , shown i n t h e b r a c k e t s o n F i g u r e 9 , c o n f i r m e d similar t r e n d s . The c r i t i c a l v a l u e s were 1071 and 1 3 9 6 f o r It c o n v e n t i o n a l and TCF d e s i g n s r e s p e c t i v e l y . t h e r e f o r e f o l l o w s t h a t t h e TCF added d e s i g n f e a t u r e s e f f e c t i v e l y delayed t h e onset of t u r b u l e n c e , moreover, usage o f p o c k e t i n s e r t s and g r o o v e d l a n d s a l l o w e d a much h i g h e r o p e r a t i n g speed due t o m a i n t a i n i n g l o w o i l temperatures. However, i t s h o u l d b e e m p h a s i s e d t h a t t h e TCF a d d i t i o n a l f e a t u r e s r e d u c e b u t d o not e n t i r e l y eliminate the undesirable hydrodynamic e f f e c t s u n d e r t h e b e a r i n g l a n d s and t u r b u l e n t f l o w a n d i t s a s s o c i a t e d w h i r l and c a v i t a t i o n a l e f f e c t s i n t h e b e a r i n g p o c k e t s and lands.

fIGPPA0 PRESSWE VARIATION WITII SPEED FOR C W E N r l O N M J W ( I A L BEARIN0 IEST!

450

t

With the reduction in viscosity at high operating speeds for conventional bearings the pocket pressure is reduced which results in an increased flow rate and reduction of film thickness which could ultimately lead to failure. This is most likely for conventional design hydrostatic bearings with lower speed capability and worse pocket pressure stability. The test head torque variation with speed is plotted against measuring time (Figure 13) for similar TCF and conventional bearing pocket pressures. The trend is more or less identical and no claim is made for better TCF torque characteristics. IrnI

~lOll4OFW~llME FOR. TCF AND GDNVENllONAL JOURNAL BEARINOS A1 4 OIFFERENI SPEEDS FORWHHON PAD P R S M E S

,--,tfE

, Perhaps the key difference between the performance of the two different journal bearing a-rangements is the pocket pressure stability The results with respect to increasing speed. of the pocket (pad) measurements for cmventional and TCF design journal bearings for tests up to 0000 rpm at speed intervals of 2000 rpm are summarised in Figures 10 and 11 where pad pressure variation with speed is plotted for the pockets of the drive and non-drive end journal bearings. The conventional bearing tests show significant drop in pocket pressures with increase in speed. The maximum drop was over 200 psi (1.38 Mpa) whereas that for the TCF design was only about 50 psi (0.34 Mpa). Therefore the pad pressure stability is far better for the TCF design. A much higher supply pressure at high speeds was also found to be required to maintain the conventional pocket pressures. This is better demonstrated in Figure 12 where pocket pressure variation with increasing speed (up to 13,300 rpm) is plotted.

llG.CHlGHSPEED RANOE P M PRESSVAE

-

P E JOUMU

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30

10

Ib

50

5

CONCLUSION

i.

Temperature rise variation with speed is considerably lower for TCF design than equivalent conventional journal bearings. Moreover the onset of turbulence occurs at a relatively higher operating speed with a much reduced degree of turbulence compared The approximate to conventional bearings. critical Reynolds Numbers for transition from laminar to turbulent flow in the pockets of conventional and TCF bearing designs are 1071 and 1396 respectively.

ii.

Pocket pressure stability with increasing speed is significantly better f o r TCF than equivalent conventional journal bearing tests.

iii. The much improved performance characteristics of TCF bearings are due to the pocket inserts and grooved lands which effectively reduce the undesirable hydrodynamic effects.

iv. The significant delay in turbulence and much better bearing pocket pressure stability for the TCP design can be explained as follows : it is found that under high speed conditions, the oil temperature rose due to greater degree of viscous shearing which effectively reduced the oil viscosity. This caused the drop in the pocket pressure which was far worse for the plain pockets of the equivalent conventional bearings than TCF design with additional features.

10

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1

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VIRlAIlON FOR 1s X M I N U BEARINO TESIS N.0E m

,CON

With the superior performance of TCF bearings in terms of running at higher speed with acceptable temperature rise and stable pocket pressures under reduced power supply - there could be many industrial applications particularly in the machine tool industry where good spindle-bearing characteristics over a wide operating speed range are required.

45 1 6

ACKNOWLEDGMENT

Thanks are due to Dr C M Taylor for his expert advice and guidance. REFERENCES Ashman, D. High-speed Performance of a Hydrostatic Thrust Bearing, Ph.D. Thesis, Wolverhampton Polytechnic, (1987)

.

(13) Tsanis, K. and Leutheusser, J . The Structure of Turbulent Shear-Induced Countercurrent Flow, J Fluid Mech. V189 (1988). (14) Taylor, C. M. and Dowson, D. Turbulent Lubrication Theory Application to Design, ASME. Paper No. 73-Lub 5-10 (1973) (15) Wilcock, D. F. Turbulence in High Speed Journal Bearings, ASME Trans., V72 (1950).

Mohsin, M. E. and Sharratt, A. The behaviour of a Total Cross Flow Hydrostatic Journal Bearing, Proc. 23rd Int. M.T.D.R. Conf., Manchester, (1982). O'Donoghue, J . P. and Rowe, W. B. Hydrostatic Bearing Design, Tribology, V2, N1, (1961). Stansfield, F. M. The Design of Hydrostatic Bearings for Machine Tools and Similar Applications, Machine Publ. Co. (1970). Rowe, W. B. Hydrostatic and Hybrid Bearing Design, Butterworth (1983). Cowley, A. and Kher, A. K. The Dynamic Characteristics of a Hydrostatic Supported Spindle Bearing System, Proc. 10th Int. MTDR Conf., UMIST Manchester (1969). Mohsin, M. E. A Hydrostatic Bearing for High Speed Applications (The Total Cross Flow Hydrostatic Bearing), Tribology, V14, N1, (1981). Mohsin, M. E. and Sharratt, A. The Behaviour of Hydrostatic Pads with Grooved Lands. Tribology, V14, N1, (1981). Mohsin, M. E. and Sharratt, A. The Behaviour of a Total Cross Flow Hydrostatic Thrust Bearing Proc. 21st Int. M.T.D.R. Conf. (1980). Kher, A. K. and Cowley, A. An Experimental Investigation into the Temperature Effects in Hydrostatic Journal Bearings, Tribology, V3, N1, (1970). Baloglu, B.

A Theoretical Investigation of a High Speed Hydrostatic Spindle-Bearing System for a Milling Machine, Ph.D. Thesis, UMIST (1984). Hall, G. S. Investigation of RHP's Laminar Radial Flow Restrictors, Project Report, Department of Mechanical Engineering, The University of Leeds (1988)

APPENDIX A TCF BEARING PERFORMANCE CALCULATIONS The most important parameters in the study of a hydrostatic bearing are :(a) (b) (c) (d) (e) (f)

Load carrying capacity Stiffness Friction characteristics and power losses Flow rate Temperature rise Dynamic behaviour

Over the years, many studies have been presented by various authors d' cussing one or several of However, all such the above aspects ' 3 - B s . work has been pursued without taking the special feature of TCF bearings into account. ( mainly on the work by Kher and Cowley on conventional hydrostatic bearings and taking into consideration the two major design changes for TCF in conventional bearing geometry bearings, a theoretical analysis was established to determine the TCF important design parameters in view of ERFS and grooved lands. This analysis includes the derivation of expressions to evaluate the above parameters for both TCF design journal and thrust bearings. Also, using these expressions, two coryYfe;o programs were developed by B Baloglu evaluate the performance of each bearing for given dimensions.

6Bhsf6)

ra@

It should be noted that the use of grooved lands would alter the damping capacity of a hydrostatic bearing. Therefore two shear and flow factors determined empirically were used for the analysis of a particular grooved land profile. Furthermore, due to the external return flow system provided by using inserts in the pockets of TCF bearings, provision for different shearing characteristics were made to that of a conventional hydrostatic bearing pocket. Moreover, using the finite-element packages available at UMIST, the dynamic and static performance of the TCF bearing spindle system was examined under expected practical cutting conditions.

452 The computer program f o r a TCF j o u r n a l o r t h r u s t b e a r i n g r e c e i v e s i n p u t v a l u e s s u c h as b e a r i n g dimensions, s u p p l y p r e s s u r e and v i s c o s i t y . For e c c e n t r i c i t y ( d e f l e c t i o n ) r a t i o s from 0 t o 1 w i t h i n c r e m e n t s o f 0.1 and 0.05, i t d e t e r m i n e s t h e l o a d c a r r y i n g c a p a c i t y and s t i f f n e s s f o r a It also calculates the given loading case. v i s c o s i t y f o r t h e s p i n d l e speed 0 t o 4500 rpm (low speed r a n g e ) a t i n c r e m e n t s o f 500 and f o r 5000 t o 15000 rpm w i t h i n c r e m e n t s o f 1000 rpm Hence f o r a computed ( i . e . h i g h speed r a n g e ) . v i s c o s i t y , t h e following parameters a r e calculated f o r t h e zero-eccentricity case:T o t a l pumping power Total shear l o s s e s Temperature r i s e Damping c o n s t a n t and t h e r e s u l t s l i s t e d f o r each s p i n d l e speed i n a t a b u l a r form. A t y p i c a l computer p r i n t f o r t h e 75 mm d i a m e t e r TCF j o u r n a l b e a r i n g is shown in Figure 14. Many i m p o r t a n t d e s i g n p a r a m e t e r s o f TCF h y d r o s t a t i c b e a r i n g s a r e i n t e r r e l a t e d , making an e x a c t c h o i c e a l m o s t impossible. T h e r e f o r e , i t is n e c e s s a r y t o compromise between a l l d e s i g n p a r a m e t e r s concerned s u c h a s : supply p r e s s u r e , b e a r i n g dimensions and t h e g r a d e cf o i l used ( v i s c o s i t y ) .

I

---

APPENDIX B DESIGN PROCEDURE FOR THE LAMINAR RADIAL FLOW RESTRICMR The t h r e e v a r i a b l e s r e q u i r e d t o d e f i n e t h e e s s e n t i a l geometrical parameters of a fixed r e s t r i c t o r as shown i n F i g u r e 8 are gap ( h ) , l a n d r a d i i (R ) ( R 2 ) , a n d l a n d w i d t h (1) e q u a l t o Together with t h e v i s c o s i t y o f t h e o i l R -R 1' f l o w i n g t h r o u g h t h e r e s t r i c t o r , t h e impedance ( r e s i s t a n c e t o f l o w ) i s g i v e n by:-

where : Ir

=

p

=

Pr

=

qr

=

sf

h y d r a u l i c impedance the r e s t r i c t o r i n N.S.mdynamic v i s c o s i t y o f t h e o i l i n N.S.m7 supply i n l e t o i l pressure i n N.m' flow t h r u h t h e r e s t r i c t o r -P i n m3 .S

The gap h is always a f r a c t i o n o f a millimetre and i s e x p r e s s e d i n metres. Consequently h3 is an e x t r e m e l y small v a l u e and i t i s more c o n v e n i e n t t o e x p r e s s t h e d i s t a n c e t r a v e l l e d by t h e o i l a c r o s s t h e land as a r a t i o ( h of land width t o gap i . e . = 1 h T h i s is similar t o t h e r a t i o used f o r o i l f l o w i n p i p e s ; p i p e l e n g t h t o p i p e diameter d Experimental work on a d j u s t a b l e and f i x e d r e s t r i c t o r s showed t h a t f o r l a m i n a r f l o w t o predominate ), s h o u l d be between 100 and 200.

.

3.1

u.w46a 3.0a 71.724

1.

Experimental r e s u l t s showed t h a t t h e r e l a t i o n s h i p between p r e s s u r e , f l o w and c a n t l y from temperature d e v i a t e d s i g theoretical predictions based on t h e formula (1) f o r s i m p l e l u b r i c a t i o n t h e o r y as a p p l i e d t o an a n n u l a r r e s t r i c t o r . The c u r r e n t theory does n o t adequately d e s c r i b e t h e practical physical s i t u a t i o n i n t h a t it ignores, f o r example, t h e i n e r t i a l p r e s s u r e changes and elastic deformation.

?fhi

F I G W - A TYPICAL COMPUTER PRINT FORTHE 7Sma DIAHLTCR T.C.F. HYDROSTATIC JOURNAL BEARING AT o RPn.

To p r o c e e d w i t h t h e d e s i g n of a s u i t a b l e r e s t r i c t o r i t w a s n e c e s s a r y t o make f a c t o r i s e d a d j u s t m e n t s , based on e x p e r i m e n t a l work, t o compensate f o r t h e d e v i a t i o n s between t h e o r y and practice. The d e s i g n p r o c e d u r e a d o p t e d t o d e t e r m i n e t h e v a l u e s o f h , R and R t o g i v e a p r a c t i c a l s i z e 2 f o l l o w s :t o t h e r e s t r i c k o r is as

1.

Determine t h e impedance of t h e b e a r i n g by d i v i d i n g t h e r e q u i r e d average pocket p r e s s u r e by t h e o i l f l o w rate t h r o u g h t h e b e a r i n g as :Ib

=

2

................. . ( 2 )

453

2.

3.

Decide on the pressure ratio to be used, i.e. the ratio of the average bearing pocket pressures to the inlet oil supply pressure to the restrictor. For the case described a ratio of 0.5 was aimed at. However, experimental results showed that due to increasing temperature the pressure ratio was reduced. To compensate for an unexpected loss of pressure on the outlet side of a fixed restrictor of the type used, the presure ratio in the calculations was increased to 0.6. Since there is one restrictor per bearing pad the required impedence of each restrictor was set at a % of the bearing impedance :

Ir

=

0.25 Ib,

...................(3)

However, experimental results showed that oil flow rate, almost regardless of temperature, was approximately 75% of that calculated from theory. This was compensated for the practical model by reducing the impedance by a factor of 0.75. 4.

Use a trial and error method for different values of h, R and R in equation (1) to I 2 give a practical size to the unit.

where V is the velocity of the shearing surface,sh is the depth of the shearing thin layer of oil beneath the bearing pocket insert and 3 is the kinematic viscosity of the oil determined graphically from the typical viscosity-temperature characteristics of Shell Tellus oils R chart. Furthermore the corresponding temperature values for different operating speeds are given in figure 9 where the experimental scavenge oil temperature is plotted against the rotational The interesting phenomenon speed of the shaft. of increTf@g gradient was first reported by Wilcock in 1950. His finding was reported similarly in terms of power loss plotted against rotational speed. As a typical example, the critical Reynolds numbers for the conventional design and TCF pockets of two hydrostatic journal bearings were determined as follows:Case 1 - A conventional design pocket

Nominal pocket depth = 1 x m Critical shaft speed = 6000 rpm3 Shaft nominal diameter = 75 x 10- m The critical shaft speed is the speed at which laminar to turbulent transition occurs, therefore :Vs

V D N

=

60

where D is the nominal diameter of the shaft, N is $he rotational shaft speed.

vs

so

APPENDIX C

=

fl x (75 x

THEORY (COUNTERCURRENT OIL FLOW IN THE HYDROSTATIC BEARING WCKETS) The oil flow beneath the pocket inserts of the TCF or under the pocket of the conventional design hydrostatic bearing consists of pressure and shearing shaft surface velocity induced components. This type of flow is termed as "countercurrent flow" which is a generalised plane couette flow. Under these circumstances a shear-induced drift current is opposed by a pressure- driven return flow, as illustrated in figure 2, such that the resulting mass flux is zero. This type of flow is encountered in both environmental fluid mechanics and tribology (elastohydrodymamic lubrication ) such as the case discussed here. The Reynolds number, expressed in terms of surface velocity3yd depth of flow, varies from 200 to 20 000 ; the critical Reynolds number of laminar to turbulent transition as determined herein are approximately 1071 and 1396 for the oil flow in a conventional and the TCF design pockets respectively. The area of transition from laminar to turbulent flow expressed in Reyn Number (Re) values is 1000 < Re < 2000 For the countercurrent oil flow at hand the appropriate Reynolds number is defined as:

?I@ .

V

=

23.562 m/s

The measured scavenge oil temperature at 6000 rpm is 41.5OC from figure 9. The kinematic viscosity of Tellus 22 oil from- he Shell chart at this temperature is 22 x 10 m'/s.

E

thus :

ReCrit, 6000 Re

Case 2

-A

V .h

s V

Crit ,6000

=

23.562 X 1 & 22 x 10 "

=

1071

TCF design pocket

Nominal pocket depth = (under the insert) = Critical shaft speed Shaft nominal diameter = Then :

V

=

1 x

m

8000 rpm3 75 x 10- m

x 8000

W x (75 x 60

V

=

31.416 m/s

The measured scavenge oil temperature at 8000 rpm for the TCF bearing test is 40.5OC and the corresponding kinematic viscosity at this ternperaturg for the Tellus 22 oil is 22.5 x 10- m'/s, thus :-

Re Crit ,8000 Re =

x 6000 60

=

31.416 x 1 x LO-3 22.5 x 10 "

454 The other Reynolds numbers indicated on the temperature/speed graph (figure 9 ) were also similarly calculated. The following considerations should be noted:1.

Scavenge oil temperatures were measured in the scavenge pipe line about one metre away from the bearing pockets.

2.

Transition from laminar to turbulent countercurrent flow of Tellus 22 oil was approximately determined from the experimental temperature-speed graph for conventional and TCF design bearing tests.

3.

The nominal values for the pocket depth and shaft diameter were taken rather than the exact values.

4.

The kinematic viscosity values were extracted from the Shell Tellus oils R chart.

SESSION XV INFORMATION STORAGE AND RETRIEVAL/MAGNETIC BEARINGS Chairman: Dr C M Taylor

-

Information Storage

PAPER XV(i)

Review Paper. Tribological Design and Retrieval

PAPER XV(ii)

Active Magnetic Bearing Design Methodology Conventional Rotordynamics Approach

-

A


457

Paper XV( i)

-

Review Paper:Tribologicaldesign Information storage and retrieval B. Bhushan

This paper presents the status of our current understanding of the tribology of head-medium interfaces in magnetic storage devices. To start out, designs and materials used in the construction of heads and media for tape, floppy, and rigid disk drives are presented. Theories of conventional friction, stiction, interface temperatures, wear, liquid/solid lubrication, and compressible hydrodynamic lubrication relevant to magnetic media are presented. Whenever necessary, experimental data are presented. 1.0 INTRODUCTION Magnetic recording process is accomplished by relative motion between magnetic media against a stationary (audio and data processing) or rotating (video) read/write magnetic head. Under steady operating conditions, a load carrying air film is formed. There is a physical contact between the media and the head during starting and stopping. In modem high-end computer tape and rigid disk drives, the head-to-media separation ranges from about 0.1 to 0.4 pm. In floppy disk drives, head-to-media separation is even less ( 1, plastic contact

(2b)

+ p = ( E J Y X U ~ ~ R ~for ) ”polymers ~,

(2c)

$ = (EJHXI,~~R,)”~, for metals/ceramics

(2d)

and

where A, is the apparent area of contact; pa is the apparent pressure; E, is the composite modulus of elasticity, H and Y are the hardness and yield strength of the softer material, and up and & are the composite standard deviation and radius of curvature of the surface roughness. Bhushan (1984) and Bhushan and Doerner (1988) have measured the mechanical properties and surface roughnesses of various particulate tapes and particulate and thin-film (metal and oxide) disks. Mechanical properties of magnetic coatings of tapes were measured by

dynamic mechanical analysis (DMA) system and of rigid disks were measured by a nanoindentation apparatus. Surface roughness parameters of tapes and disks were measured by a noncontact optical profder (Bhushan et al., 1988). Measured values were used in the contact model and they found that most contacts in typical head-medium interfaces are elastic. Experimental measurements of the real area of contact of magnetic tapes by optical-interference technique verified that most contacts are elastic (Fig. 2). Therefore, the real area of contact and friction is governed by the E, and uJ& of the magnetic media surface. Figure 3(a) shows an example that the friction of various magnetic tapes depend significantly upon the complex modulus. Stable frictional behavior was exhibited only by those tapes which displayed a complex modulus of greater than 1.2 to 1.5 GPa. Figures 3b and 4 show the examples that the friction also strongly depends on the surface roughness. Typical contact diameters for tapes and rigid disks were found to be about 6 pm and 2 pm,respectively. In the case of magnetic tapes, creep compliance and hydrolytic degradation characteristics of the binder also need to be optimized for sustained low friction after storage at high pressure (e.g., near end-of-tape on a reel) and high temperature/humidity (Bhushan, 1989). 3.2 Stiction Stiction can arise from meniscus/viscous effects, microcapillary evacuation, or changes in surface chemistry (Bhushan et al., 1984a). In this section, we will only concentrate on the meniscus/viscous effects. Generally, any liquid that wets or has a small contact angle on surfaces will condense from vapor in the form of

459

an annular-shaped capillary condensate in the contact zone. The pressure of the liquid films of the capillary condensates or preexisting film of lubricant can sigmiicantly increase the adhesion between solid bodies. Liquid-mediated adhesive forces can be divided into two components: meniscus force (FM) due to surface tension and a rate-dependent viscous force (Fv). The total tangential force F required to separate the surfaces by sliding is equal to an intrinsic force (FA)and stiction force F, (combination of friction force due to meniscus effect and the peak viscous force) (3) where f, is true static coefficient of friction. Figure 5 shows a model of contact region between smooth surfaces with different level of “fius” of the interface and it depends on the mean interplanar separation and the liquid levels (Matthewson and Mamin, 1988). Two are the extreme regimes in which either a small quantity of liquid bridges the surfaces around the tip of a contacting asperity (the “toe-dipping” regime) or the liquid bridges the entire surface (the “flooded” regime); and in the third regime, the liquid bridges around from few asperities to large fraction of the apparent area. The different regimes can be modelled and the expressions for F M and Fv can be obtained. We note that in the toe-dipping regime, the adhesion force is independent of the apparent area and proportional to the normal load. However, the flooded regime shows the opposite tendencies. The pill box regime is intermediate and can exhibit either behavior at the extremes. An increase in the lubricant thickness and its viscosity, relative humidity of the environment, rest period, and head-slider area generally increases the stiction of a head-medium interface (Bradshaw and Bhushan, 1984; Liu and Mee, 1983; Yanagisawa, 1985a). Figure 6 shows lubricant thickness dependence on a thin-film (metal) disk surface for two surface roughnesses. The coefficient of static friction increased significantly above critical thickness of liquid lubricants. The critical thickness depends on the surface roughness, namely, critical thickness values is about half of the r m s roughness. Yanagisawa (1985a) has also shown that ifthe interface was in flooded regime, the static coefficient of friction increased linearly with slider area. Miyoshi et al. (1988) have measured the effect of water vapor on adhesion of a Ni-Zn ferrite pin in contact with a flat of Ni-Zn ferrite or of magnetic tape A, Fig. 7. They found that the adhesive force (normal pull-off force) of ferrite-ferrite or ferrite-tape A contact remained low below 40%, the adhesion increased greatly with increasing relative humidity above 40%. Changes in the adhesion of contacts were reversible on humidifying and dehumidifying. They concluded that ferrites adhere to femtes or tapes in a saturated atmosphere primarily from the surface tension (or meniscus effects of a t h i n - f h of water adsorbed on the interface). Matthewson and Mamin (1988) measured the static friction force as a function of start-up rate (proportional to sliding velocity) between smooth and lubricated surfaces, Fig. 8. They found that the static friction force increases linearly with an increase of the square root of the loading rate. This is attributed to viscous effects. 4.0 INTERFACE TEMPERATURES

In a sliding operation, almost all of the frictional energy input is directly converted to heat in the material close to

the interface. During a sliding situation, asperity interactions results into numerous high temperature flashes. Bhushan (1987a) recently presented a detailed thermal analysis to predict the interface temperatures and applied it to predict temperatures in a head-medium interface (Bhushan, 1987b). He showed that the total flash temperature consists of temperature of an individual asperity contact and effect of other asperity contacts on an individual asperity temperature (interaction). The head-medium interface can be modelled as the case of sliding two equally rough surfaces and the relevant equations for the average and maximum asperity temperature rise of the interface are given as (Bhushan, 1987a):

-

8 = r,[0.65 fp,(AdA,xu&a/Kly’2/

plcpi

+~P~(uG/K~I”~/P~cP~]

emax = r1[0*95fPa(AJA,XU&ax/Klf’2/

P~C+ P ~1.5 ~ P ~ ( u G / K ~ Y ’ ~ / P ~ c P ~ ] and (4) where, pCp is the volumetric heat capacity, K is the ,is the thermal diffusivity, k is the thermal conductivity, 4 maximum contact diameter, and G is the half length of the slider. Average and maximum interface temperatures predicted for the assumed particulate media were 7” and l O T , respectively (Bhushan, 1987b). These predictions compared fairly with the infrared measurements conducted at head-tape interface (Gulino et al., 1986). The asperity-contact temperatures at head-tape interface are relatively low because of its high real area of contact, as compared to that of metal-metal or ceramic-ceramic contacts. The interface temperature of 7-10°C rise can lead to high friction in some tapes because the transition temperature of some tapes’ mechanical properties is within 5°C above the ambient temperature. In isolated cases, if the magnetic particles are exposed (or get exposed in a high-speed rub) and contact the head surface, the average and maximum instantaneous temperature rise could be about 600°C and 900”C, respectively. These temperatures potentially will cause a breakdown of the medium lubricant and a degradation of the medium binder leading to excessive friction and seizure of medium motion. 5.0 WEAR AND LUBRICATION

5.1

Heads

The wear of oxide magnetic particles and ceramic head body materials is different from metallic wear because of the inherent brittleness and the relatively low surface energy of ceramics. The first sign of ferrite head wear with a magnetic tape is the appearance of very small scratches on the head surface (Fig. 9a). The physical scale of scratches is usually very fine and scratches as small as 25 nm have been reported (Bhushan, 1985). Ferrite surface is microscopically removed in a brittle manner as stripes or islands, depending on the smoothness of the tape surface. Wear generally occurs by microfragmentation of the oxide crystals in the ceramic surface. Fragmentation is the result of cleavage and transgranular fractures, one dominated by intergranular fracture. We note that worn head surface is work hardened which reflects a shifl from

460

a mechanism dominated by transgranular fracture to one dominated by intergranular fracture. Figure 9b shows a region where fracture and rupture have occurred. Such regions are commonly called “pullouts.” Debris originating from these regions causes additional small scale plastic deformation and grooves (three-body abrasion) as shown in Fig. 9c. At the recording gap, chipping of ferrite may occur which depends on the width of the gap and type of epoxy used in the gap. An example of ferrite chipping adjacent to the recording gap is shown in Fig. 9d. We also note that ferrite head surface is work hardened with a large compressive stress field after wear which is detrimental to magnetic signal amplitude (Chandrasekar et al., 1987a. 1987b). Wear mechanisms of floppy and rigid disk head sliders against particulate disks are similar to those just discussed for tape heads. Head slider wear occurs by abrasive and fracture mechanisms. Head sliders after usage are sometimes become coated with thin layers of a new organic material of high molecular weight called “tribopolymers.” Friction is essential for the formation of these materials. Another requirement for the formation of friction polymers in a rubbing contact is that one of the surfaces, lubricant, or even a material nearby should be organic (Lauer and Jones, 1986). It seems clear that all friction polymers are products of chemical reaction, whether they derive initially from solid polymers or from organic liquids or vapors. Friction polymers are found on head surfaces. These result in discoloration of the head surface and give an appearance of brown or blue color, and, therefore are sometimes called brown or blue stains, respectively. Head wear depends on the physical properties of head and medium materials, drive operating parameters, and environmental conditions. Wear data of common head materials against a y-FezO3 tape is shown in Fig. 10. We observe a linear relationship between wear rate and material hardness for abrasive wear mode. Head wear as a function of surface roughness of tapes and isolated asperities on the tape surface are shown in Figs. 11 and 12. We note that head wear increases with an increase in the surface roughness or number of isolated asperities of the tape surface. Wear rate also increases humidity above about 40-60% relative humidity, Fig. 13. An increase in abrasive wear at high humidities is believed to be due to moisture:assisted fracture of the grains to yield finer particles (Bhushan, 1985; Bhushan, 1989). 5.2

During contact of particulate tape with the head in contact start/stops or during partial contact in streaming, binder and magnetic particle debris is generated primarily by adhesive wear mode. Tape debris, loose magnetic particles, worn head material or foreign contaminants are introduced between the sliding surfaces and abrade, material off each. The debris that adheres to drive components lead to polymer-polymer contact, whose friction is higher than that of rigid material polymer contact and can lead to magnetic errors and sometimes to catastrophic failures. Microscopic examinations of worn particulate disk show circumferentialwear grooves and support either of the two-body or three-body abrasive wear (Fig. 14). In the case of thin-film disk, Gatzen et al. (1987) have shown that wear of the overcoat is primarily adhesive in nature. Once the overcoat is depleted, the wear of metallic film is adhesive in nature and is generally catastrophic. An example of wear track on dc sputtered amorphous carbon

on plated Co-Ni-P magnetic film aRer head crash in contact start/stop (CSS) test is shown in Fig. 15. An increase in overcoat hardness improves the wear resistance of the thin-film disks (Yanagisawa, 1985b). Figure 16a shows Vickers hardness dependence on baking temperature for Si02 films. Increase in hardness results in improvement in wear resistance as shown in Fig. 16b, where the normal load is 185 mN and the sliding velocity was 1.12 m/s. Ohta et al. (1987) studied the wear rate and effective hardness of the sputtered y-Fe20pdisks as a function of alumite underlayer thickness, Fig. 17. They found that microhardness increases and wear rate decreases, significantly if the alumite thickness is increased up to about 5pm. Figure 18 shows the coeficient of static friction as a function of number of contact start-stops (CSS) passes for a carbon overcoated thin-film (metal) disk against Mn-Zn femte, CaTiO,, and AlZ0,-TiC sliders (Ishikawa et al., 1986; Doan and Mackintosh, 1988). We note that static friction increases with CSS and the rate of increase is highest in the case of A1203-Tic,next higher in case of CaTiO, and the least in case of Mn-Zn femte slider. Since A1203-TiC,is hardest (2300 kg/mm2),it burnishes the disk surface more than CaTiO, (950 kg/mm2),or Mn-Zn ferrite (600 kg/mmz)and CaTiO, burnishes more than Mn-Zn femte. Examination of Mn-Zn ferrite shows that the scratches along the air-bearing surface suggesting that the Mn-Zn ferrite is slightly soRer than the disk structure, therefore, ferrite is gentle to the disk surface. We believe that matching of slider and disk hardnesses is essential for low wear. Liquid lubricants are used to reduce the wear rate of disks. Figure 19 shows the wear life of a particulate disk lubricated with two grades of perfluoropolyether-Fomblin 2-25 (nonpolar) and Fomblin AM2001 (polar with reactive end groups) as a function of lubricant thickness. We note that relative wear life increases with an increase in the lubricant thickness and polar lubricants have longer wear life than nonpolar lubricants. We have seen earlier that an increase in lubricant thickness increases the static friction, therefore, a compromise in lubricant thickness is necessary for optimum friction and wear performance. Figure 20 shows the static friction as a function of storage time for disks with a nonpolar lubricant (perfluoropolyetheror PFPE) and disks with dual lubricant consisting of polar (aminosilane) and nonpolar (PFPE) fraction. Increase in friction from aging the disks with dual lubricant film was found to be less than that for a disk with only nonpolar lubricant (Hoshino et al., 1988). Lubricant is also spun off with a disk rotation during use. Yanagisawa (1985a) and others have shown that polar lubricants spin off less than nonpolar lubricants. Mechanism of interface failure was studied by Kawakubo et al. (1984) for particulate disks in CSS test. Friction force, acoustic emission (AE) signal (to monitor head-disk contact) and read back signal were measured during the test. The changes in read back signal, friction force, and AE signal are shown in Fig. 21. At the point of interface failure, the read back signal decreased to almost zero and friction force and AE signal rose significantly. This implies that head was virtually in contact even at full speed. Kawakubo et al. (1984) also videotaped the wear process through a transparent sapphire slider. 6.0 HYDRODYNAMIC AIR FILMS

Head-medium interface is designed so that the magnetic head is separated form the media by a thin air film during

46 1

calculate the air film thickness. The Reynolds equation is based on the continuum theory of fluid mechanics. In today’s magnetic storage devices the mean free path of the molecules is comparable to the film thickness, therefore, the gas does not behave entirely as a continuum fluid but exhibits rarefaction effects. In order to account for the rarefaction effects, Reynolds equation is modified by a Knudsen number (= local mean free path/film thickness). In some magnetic storage devices, film thickness is very small and is only 3 to 6 times the surface roughness. In that case, roughness effects must be included. These effects are accounted for by using the pressure flow factor approach (Bhushan and TBnder, 1989a, 1989b). Figure 22 shows the results of head-tape spacing and pressure profiles over a cylindrical head. It takes about 8 ms for the film thickness profile to reach steady state. The film thickness reaches a minimum value near the trailing edge. Figure 23 shows the three-dimensional pressure contours of the air bearing in a typical 3370-type head-rigid disk interface. In the longitudinal direction, we note the two peaks, one at the end of the taper and another near the trailing edge. From leading edge towards the trailing edge, the pressure continues to drop because of side leakage. However, near the trailing edge, because of the pitching of the slider, the gap decreases resulting in smaller side leakage and recompression of the gas, consequently leading to an increase in the air pressure. In the transverse direction, the pressure profile is symmetric about the center line and is parabolic in shape. Mitsuya (1986) has shown that the load capacity of a head-disk interface is reduced, roughly by a factor of 2 if Knudsen number (M) is 1 for a smooth or rough surface (Fig. 24). Thus, rarefaction effects can be significant. In some head-tape interfaces, the head-to-tape spacing (h) is signifkantly correlated with nns tape roughness, u (Fig. 25). As h/u becomes smaller (c6) for future high-density disk drives, the effect of roughness on h would become significant. Bhushan and Tfinder (1989b) have calculated roughness-induced effect in shear- and squeeze-flow for magnetic storage devices. They found that roughness-induced changes in the shear flow cannot account for the measured changes in h. However, roughness-induced changes in the squeeze flow can account for the measured changes in h. Vertical motion of one of the surface necessary for squeeze effects to become dominant can be generated by the isolated asperities present of heights larger than the minimum film thickness, bearing load variations, and/or modulations of the interface from other instabilities. Submicron film thicknesses in the steady and dynamic conditions have been measured by using capacitance and optical interference techniques (Mizoshita et al., 1985; Millman et al., 1986). Dynamic vibrations of less than 1 nm peak-to-peak have been measured from 0 to 100 kHz. Millman et al. (1986) measured slider dynamics during an actuator stroke from a 3380 head-disk assembly. They used a four-comer capacitance probe on a particulate disk, Fig. 26. They found that actuating has very little effect (< 10% of the mean value) on the slider attitude (trailing-edge film thickness, pitch, and roll). The change in film thickness was about 40 nm p-p primarily at a frequency of 2.2 kHz. 7.0 SUMMARY Analytical models and the experimental data available for the tribology of magnetic media are signifcant. A majority of the publications have appeared since 1984 after the author initiated the symposium on “Tribology and

Mechanics of Magnetic Storage Systems” now held annually. As the film thicknesses and surface roughnesses of the head-medium interface reduce in the future, our understanding will have to be fine tuned to design a reliable product. We will require measurement techniques with better resolutions to characterize the interface. New materials and processes will be required to meet the new challenges. References Bhushan, B., 1984, “Analysis of the Real Area of Contact Between a Polvmeric Maenetic Medium and a Rigid Surface,” J. Lib. Tech., T;ans. ASME, Vol. 106. DD. 26-34. Bhushan, &B.,1985, “Assessment of Accelerated Head-Wear Test Methods and Wear Mechanisms,” Tribology and Mechanics of Magnetic Storage Systems, Vol. 2, Ed. by B. Bhushan and N. S. Eiss, SP-19, ASLE, Park Ridge, pp. 101-111. Bhushan, B., 1987a, “Magnetic Head-Media Interface Temperatures Part I - Analysis,” J. Trib., Trans. ASME. Vol. 109. DD. 243-251. Bhushan, B., 1987b, “M‘a’g;etic Head-Media Interface Temperatures, Part 11 - ADplication to Magnetic Tap&,” J. Tnb., Trans. ASME, Vol. 109, pp. 252-256. Bhushan, B., 1989, Tribology and Mechanics of Magnetic Storage Devices, Springer Verlag (in Dress). r Bhushan, B., Shanna, B. S . , and Bradshaw, R. L., 1984a, “Friction in Magnetic Tapes I: Assessment of Relevant Theory,” ASLE Trans., Vol. 27, pp. 33-44. Bhushan, B., Bradshaw, R. L., and Sharma, B. S., 1984b, “Friction in Magnetic Tapes 11: Role of Physical Properties,” ASLE Trans., Vol. 27, pp. 89-100. Bhushan, B., Wyant, J. C., and Meiling, J., 1988, “A New Three-Dimensional Digital Optical Profiler,” Wear, Vol. 122, pp. 301-312. Bhushan, B. and Doemer, M. F., 1988, “Role of Mechanical Properties and Surface Texture in the Real Area of Contact of Magnetic Rigid Disks,” J. Trib., Trans-ASME (in press). Bhushan, B. and T$nder, K., 1989a, “ Roughness-Induced Shear and Squeeze-Film Effects in Magnetic Recording Part I: Analysis,” J. Trib., Trans.-ASME (in press). Bhushan, B. and TBnder, K., 1989b, “Roughness-Induced Shear and Squeeze-Film Effects in Magnetic Recording Part 11: Applications,” J. Trib., Trans. ASME (in press). Bowden, F. P. and Tabor, D., 1950, Friction and Lubrication of Solids, Claraden Press, Oxford. Bradshaw, R. L. and Bhushan, B., 1984, “Friction in Magnetic Tapes Part 111: Role of Chemical Properties,” ASLE Trans., Vol. 27, pp. 207-219. Bradshaw, R. L., Bhushan, B., Kalthoff, C., and Wame, M., 1986, “Chemical and Mechanical Performance of Flexible Magnetic Media Containing Chromium Dioxide,” IBM JT Res. Develop., Vol. 3 6 pp. - - 203-216. Calabrese. S. J., 1986, Rensselaer Polytechnic Institute, Troy. Chandrasekar, S., Shaw, M. C., and Bhushan, B., 1987a, “Comparison of Grinding and Lapping of Femtes and Metals,” J. Eng. for Indus., Trans. ASME. VOl. 109. DD. 76-82. Chandasekar, S:,’ihaw, M. C., and Bhushan, B., 1987b. “Morphology of Ground and Lapped Surfaces of Ferriteand Metal” J. Eng. f& Indus., Trans. ASME, Vol. 109, pp. 83-86. Doan. T. 0. and Mackintosh. N. D.. 1988. ‘The Frictional Eehavior of Rigid-Disk Carbon ‘ ---I

Overcoats,” Tribology and Mechanics of Magnetic Storage Systems, Vol. 5, Ed. by B. Bhushan and N. S. Eiss, SP-25, STLE, Park Ridge (in press). Gatzen, H. H., Smallen, M. J., and Tedrow, P. T., 1987, “Head-Media Wear in 5 1/4 in. Rigid Disk Drives,” Tribology and Mechanics of Magnetic Storage Systems, Vol. 4, Ed. by B. Bhushan and N. S. Eiss, SP-22, STLE, Park Ridge, pp. 116-122. Greenwood, J. A. and Williamson, J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proc. Roy. SOC.(Lond.), Vol. A295, pp. 300-319; Gulino, R., Bair, S., Wmer, W. O., and Bhushan, B., 1986, “Temperature Measurement of Microscopic Areas Within a Simulated Head/Tape Interface Using Infrared Radiometric Technique,” J. Trib., Trans. ASME, Vol. 108, pp. 29-34. Hahn, F. W., 1984, “Head Wear As a Function of Isolated Asperities on the Surface of Magnetic Tape,” IEEE Trans. on Magn., Vol. Mag-20, pp. 918-920. Hendriks, F.. 1988. “A Design Tool for Steady Gas Bearings Using Finite Elem&ts,” Tribology and Mechanics of Magnetic Storage Systems, Vol. 5., Ed. by B. Bhushan and N. S . Eiss, SP-25, STLE, Park Ridge (in press). Hoshino, M., Kimachi, Y., Yoshimura, F., and Terada, A., 1988, “Lubrication Layer Using Perfluoropolyether and Aminosilane for Magnetic Recording Media,” Tribology and Mechanics of Magnetic Storage Systems, Vol. 5 , Ed. by B. Bhushan and N. S. Eiss, SP-25, STLE, Park Ridge (in press). Ishikawa, M., Tani, N., Yamada, T., Ota, Y., Nakamiura, K., and Itoh, A., 1986, “Dual Carbon, A New Surface Protective Film for Thin-Film Hard Disks,” IEEE Trans. Magn., Vol. Mag-22, pp. 999-1001. Kawakubo, Y., Ishihara, K., Seo, H., and Hirano, Y., 1984, “Head Crash Process of Magnetic Coated Disk During Contact Start/Stop Operations,” IEEE Trans. on Magn., Vol. Mag-20, pp. 933-935. Kelly, J., 1982, “Tape and Head Wear,” MaEnetic Tape Recording for the Eighties, NASA Ref. Publ., 1075, pp. 7-22. Klaus, E. E. and Bhushan, B., 1985, “Lubricants in Magnetic Media - A Review,” Tribology and Mechanics of Magnetic Storage Systems, Vol. 2, Ed. by B. Bhushan and N. S. Eiss, SP-19, ASLE, Park Ridge, pp. 7-15. Lauer, J. L. and Jones, W. R., 1986, “Friction Polymers,” Tribologv and Mechanics of Magnetic

Storage Systems, Vol. 3, Ed. by B. Bhushan and N. S. Eiss, SP-21, ASLE, Park Ridge, pp. 14-23. Liu, C. C. and Mee, P. B., 1983, “Stiction at the Winchester Head-Disk Interface,” IEEE Trans. Magn., Vol. Mag-19, pp. 1659-1661. Matthewson, M. J. and Mamin, H. J., 1988, “Liquid-Mediated Adhesion of Ultra-Flat Solid Surfaces,” MRS Society (in press). Mizoshita, Y., Aruga, K., and Yamada, T., 1985, “Dynamic Characteristics of a Magnetic Head Slider,” IEEE Trans. Magn., Vol. Mag-21, pp. 1509-1511. Millman, S. E., Hoyt, R. F., Home, D. E., and Beye, B., 1986, “Motion Pictures of In-Situ Air Bearing Dynamics,” IEEE Trans. Magn., Vol. Mag-22, 1031-1033. .DD. * Mitsuya, Y., 1986, “Stokes Roughness Effects on Hydrodynamic Lubrication, Part I1 - Effects Under Slip Flow Boundary Conditions,” J. Trib., Trans. ASME, Vol. 108, pp. 159-166. Miyoshi, K.. Buckley, D. H., Kusaka, T., Maeda, C., and Bhushan, B., 1988, “Effect of Water Vapor on Adhesion of Ceramic Oxide in Contact With Polymeric Magnetic Medium and Itself,” Tribology and Mechanics of Magnetic Storage Systems, Vol. 5, Ed. by B. Bhushan and N. S. Eiss, SP-25, STLE, Park Ridge (in press). Ohta. S., Yoshimura, F., Kimachi, Y.and Terada. A., 1987, “Wear Properties of Sputtered y - Fe20i Thin Film Disks,” Tribology and Mechanics of Magnetic Storage Systems, Vol. 4, Ed. by B. Bhushan and N. S. Eiss, SP-22, STLE, Park Ridge, pp. 110-115. Stahl., K. J., White, J. W., and Deckert, K. L., 1974, ‘‘Dynamic Response of Self-Acting Foil Bearines.” IBM J. Res. Dkvelop., Vol. 18, pp’: 513-520. Tanaka, K. and Miyazaki. O., 1982. “Wear of Magnetic Materialsand Audio Heads Sliding Against Magnetic Tapes,” Wear, Vol. 66, pp. 289-306. Yanagisawa, M., 1985a, “Lubricants on Plated Magnetic Recording Disks,” Tribolonv and Mechanics of Magnetic Storage Systems, Vol. 2, Ed. by B. Bhushan and N. S. Eiss, SP-19, ASLE, Park Ridge. - . up. _ . 16-20. (40) Yanagisawa, M., 1985b, “Tribological Properties of Spin-Coated Si02 Protective Film on Plated Magnetic Recording Disks,” Tribology and Mechanics of Magnetic Storage Systems, Vol. 2, Ed. by B. Bhushan and N. S. Eiss, SP-19, ASLE, Park Ridge, pp. 21-26. I .

463

Head-Tape Interface

Head-Floppy Disk Interface Temperature

Temperature

0.1-0.3 gm

Substrate Roller coating Spring-

Disturbance

Time Humidity

Head-Rigld Disk Interlace Temperature

Protective coating Substrate

’

Head-Slider flvina state

Rest state Humidity

Time

Figure 2. Optical interference photographs of tapes taken at 28 kPa; then subjected to higher pressures for short duration and brought back to 28 kPa and rephotographed. We see no change in the real area of contact implying an elastic contact (Bhushan, 1984).

464

Tapes stored at 50°C/600/~RH

I

I

I

J

1

2

3,

"Toe Dipping"

Complex Modulus at 5OoC, GPa

Figure 3a. Coefficient of friction during start at 30°C/85% RH measured on a commercial tape drive versus complex modulus at 50°C. The CrO, tapes were stored at 50°c/60% RH for 14 days before the tests (Bhushan et al., 1984b).

x

"Dry" Figure 5. Regimes of different liquid levels in the intcrface between smooth surfaces (Matthewson and Ma&, 1988).

Tape A

:i E 0 E

A

2.0 0.6

0

m

tj

0.4

0

4-

50 100 Surface RMS, nm

0

C

150

.-a, 0

6+ Q, 0

Figure 3b. Effect of surface roughness on coefficient of friction for CrO, particulate tapes (Bhushan et al., 1984b).

0.2

" t 01

A

I

100 I

I

1 10 Lubricant Film Thickness, nm

Figure 6. Lubricant thickness dependence on coefficient of static friction for liquid perfluoropolyether on a thin-film rigid disk at 2 and 20 nm rms surface roughness (Yanagisawa, 1985a).

C

0 .40 .-

t .c

0 -0-

z3.

0.14 1 0.5

I

I

I

I

I

I

1.5 2.5 3.5 RMS roughness, nm

Figure 4. Coefficient of friction as a function of degree of disk texturing for a thin-film (metal) rigid disk with sputtered carbon overcoat against femte slider (Doan and Mackintosh, 1988).

+e--

Particulate Tape A Add water vapor (humidifying) Reduce water vapor (dehumidifying)

I

0

20 40 60 80 Relative Humidity, Percent

100

Figure 7. Effect of humidity on adhesion of CrO, tape A in contact with a Ni-Zn femte pin (Miyoshi et al., 1988).

465

2.0 1.5

z

Oa5 0.0

t*

0

10

20

30

Loading Rate’l2, ( N / s ) ’ / ~ Figure 8. Static friction force as a function of loading rate (or velocity) during start up between smooth and lubricated surfaces (Matthewson and Mamin, 1988).

Figure 9. SEM micrograph of worn Ni-Zn ferrite head with a CrO, tape A (a) abrasion

marks (direction of tape motion-left to right), (b) surface pull out, (c) extensive surface pull out and associated plastic deformation (direction of tape motion-top to bottom), (d) ferrite chipping adjacent to the recording gap (Bhushan, 1985).

466

Ferrite

100 w c ._

v) + .c 8

K

x

tPermaI Ioy

m

Brass

= I

L

L c .-

2

3

L. a

.2 6

lo

EPOXY

+?a

L

m

;

5

a

4

U

L

$ 2 0.1

10

1

Vickers Hardness, GPa

0

Figure 10. Wear rate of magnetic materials slid against a diamond cone as a function of Vickers hardness (Tanaka and Miyazaki, 1981).

-

120

-

20

40 60 RH, percent

80

Figure 13. Head wear rate as a function of relative humidity (Kelly, 1982).

- Streaming g

0

Mode Tape changed each 400 passes

ru

E o 80 E ai ru LI: 40 m r"

.c

0

CD

r

\

t

+ L

I

0

I

I

I

1

1

I

1

Figure 14. SEM micrograph of a worn particulate disk surface against Alz03- Tic slider aRer a head crash in

RMS Surface Roughness, nm Figure 11. Ni-Zn femte as a function of rms surface roughness of a CrO, tape A (Bhushan, 1985).

25 r

""""10 0

400 600 Asperity Counts, 500 m

200

800

Figure 12. Ni-Zn femte head wear rate as a function of asperity counts on Cr02 tape A (Hahn, 1984).

Figure 15. SEM micrograph of wear track on sputtered carbon film against Mn-Zn femte slider after 61000 CSS (Gatzen et al., 1987).

467

AI,OQ-TiC c c l

1.o C

.o c

0.8

.-0 L LL

.c

0.6

0 e

5

.-

0.4

.-0

. YI -

8

0.2

0 0

100

200

300

400

500

600

0

Baking Temperature, " C

4000

2000

6000

No. of CSS Passes "C

Baking Temperature, 0

25

A 200 X 0

-

300

/"

E E

Figure 18. Change of the coefficient of static friction as a function of number of passes of Mn-Zn femte, CaTiO,, A120,-TiC head sliders on a t h i n - f b disk with carbon overcoat (Ishikawa et al., 1986; Doan and Mackintosh, 1988).

0 A

600

Fomblin AM2001 2-25

A

L

a

P */*-

Ilk

~Lj-*':~, 0

dm 10 20 30 Sliding Distance, m

40

Figure 16. (a) Dependence of Vickers hardness on baking temperature for SiO, films (b) Relation between sliding distance and wear volume for SiO, films exposed to air, baked at various temperatures, slid against A1203-TiC slider (Yanagisawa, 1985b).

Po--

0.4

4

m

3 % ui

0.2

LL

m

2 2m

c

m

n

-

0

.i 0 .c

I 0

l: Y

10 15 Alumite Thickness, prn

20

Figure 17. Wear depth and Knoop hardness of sputtered y-Fe203as a function of alumite (underlayer) thickness at two loads in a pin-on-disk wear experiments (Ohta et al., 1987).

0.3

0.2

0 e

C

.-a, 0

E a, 0

5

r

0 .c

C

L

0

I 20

Figure 19, Wear life as a function of lubricant film thickness on a particulate disk slid against Mn-Zn femte slider (Scarati and Caporiccio, 1987).

a,

u)

0.1

I 15

Lubricant Film Thickness, nm

C

a 5

5

I 10

0.4

= 0.2 N = 0.6 N

E 0.3

% n

I 5

0

O

0.1

c

I + PFPE

Arninosilane

I

I 0

1

I

I

I

I

I

10 20 30 Storage Time, days

I

I

40

Figure 20. Coefficient of static friction as a function of exposure at 50°C and lo-, torr for spin coated SiO, film on a sputtered oxide magnetic film (Hoshino et al., 1988).

468

1 CSIS Cycle I 1 min

#

siart

6

2

time

at the Start of CSIS

o

LL

1 min

c

.o c

5 4

.-0

4 ; Figure 23. Three-dimensional pressure profiles for a 3370-type slider with zero skew (Hendriks, 1988).

1 0

Head Crash at the Moment of Head Crash

r

Head Crash

cum a-

Head Crash

Figure 21. Friction force, AE signal and read back signal near the head crash in CSS test of a particulate disk (Kawakubo et al., 1984).

Figure 24. Effect of rarefaction on load capacity (W) for a head-disk interface (Mitsuya, 1986).

2

0.5 5 1

i

0

I

I

I

5

10

15

x, rnm

20

10 Y

'm

t o

V

-1 0 -~~

0

10

5

0.1 15

-

0

10

*tape'

20

30

nm

x, rnrn

(W

Figure 22. Film thickness and air-bearing pressure rise profdes of a tape over cylindrical head (Stahl et al., 1974).

Figure 25. Effective head-to-(particulate)-tape spacing as a function of nns surface roughness of a tape for a data processing application (Bhushan and Tgnder , 1989a).

469

0.5 0.4

0.3 140

L

4

100 60 40 20 0 -20 -40

0

2

6

4

8

Time, ms

Figure 26. Film thickness, pitch angle and roll angle of a slider during the first quarter of an actuator stroke in a 3380 HDA (Millman et al., 1986).

10


47 1

Paper XV(ii)

-

Active magnetic bearing design methodology A conventional rotordynamics approach H. M. Chen

The essential components of an active magnetic bearing (AMB) i.e., the electromagnets, amplifier, controller, sensor, and their associated parameters are discussed and quantified using a technical language that is more acceptable to mechanical engineers. AMB dynamics are represented by a set of first-order differential equations in formulating a rotor-AMB system model. The system dynamics design guidelines are presented through use of a flexible rotor example and are consistent with conventional rotor-bearing design methodology.

1 INTRODUCTION

1.1 Notation active magnetic bearings surface area per pole AP phase-lead parameter B AMB damping coefficient saturation flux density BS phase-lead parameter b radial air gap C proportional feedback gain cd derivative feedback gain CV integral feedback gain Ce AMB controller output E magnetic pole constant for a given number f of windings AMB perturbed magnetic force F Fmax maximum load amplifier gain Ga displacement probe sensitivity GP inductance of electromagnets L AMB axial length LP bias current I control current i c i j AMB stiffness coefficient K current stiffness Ki magnetic (negative) stiffness Km mass supported by AMB M number of winding turns per pole Nt integrator output 9 Laplace variable S Time t a DC source VS VP static load W AMB journal displacement in Y-direction Y displacement sensor output in Y-direction yP phase-lead circuit output z excitation frequency w displacement probe cut-off frequency w amplifier cut-off frequency w: integrator cut-off frequency wO differentiator cut-off frequency d/dt AMB

The recent advances of active magnetic bearing (AMB) technology [1,2] are best studied in the context of the well-developed rotordynamic experience base. A long-standing and currently routine analytical procedure used in the early design stage of a rotor-bearing system involves [31. reviewing an undamped critical speed map and modeshapes for potential unbalance and instability problems. performing stability and unbalance response analyses. The AMB presents a new challenge to the rotor dynamists. This new type of bearing has many advantages over the conventional type, such as, no contact, low power loss, and most important, the feature of adjustable stiffness and damping. However, many rotor dynamists lack a thorough understanding of these new bearings because mathematical modeling of AMBs is traditionally performed in electrical engineering and control languages to which the mechanical engineer is not accustomed. To fill the communication gap, the author promotes the features of the AMB from a rotor dynamist's viewpoint [ 4 1 : AMBs should be treated as locally controlled devices similar to other types of bearings, not actuators. ' Like other bearings, the main functions of AMBs are to provide load capacity, stiffness and damping for rotor support. A similar approach was adopted by Hustak, et a1.[5]; however, a different emphasis is presented herein. First, the essential AMB components and parameters will be discussed using terminology more familiar to the mechanical engineer. Second, a rotor-AMB system modeling technique will be formulated for rigorous dynamics analysis.

%

5

472 2 AMB PRINCIPLE The practical AMBs are mostly the attractive-force type, the principle of which was well explained by Habermann and Liard [l]. This presentation concentrates on radial AMBs. The radial AMBs generally adopt an &pole stator configuration as shown in Figure 1. Both the stator and journal are stacks of laminations of ferromagnetic material. The journal is shrunk on a shaft without windings. The use of laminations reduces eddy current, which not only causes a power loss, but degrades the dynamic performance of the bearing. The stator poles are separated into four quadrants 121. In each quadrant, the electromagnetic windings are wound in such a way that the magnetic flux will mainly circulate inside the quadrants [61. Therefore, each quadrant of poles can be controlled independently. It is well known that the magnetic force is proportional to the current to air-gap ratio squared (Figure 2 ) . To support a static load, W, in a controlled axis (Figure 3), unequal steady state or bias currents are induced in opposite pairs of poles, such that (1) where I1 > I3 C = radial air gap f = a magnetic pole constant for a given number of windings. The bias current produces an I2R loss, which is a major power l o s s in an AMB. However, the total resistance including the windings and other parts in the current path is not large; the AMB power loss is in general insignificant compared to conventional oil-film bearings. The journal floating in the magnetic field due to the bias currents alone is not stable. This is analogous to supporting a vertical rod at its base using an uncontrolled hinge. Linearized feedback control of the AMB is achievable by making the air gap large, relative to the journal normal vibration amplitude. To create stability at the AMB center, the journal motion must be sensed and corrected instantaneously and continuously by superimposing a small control current to each bias current. For example, as shown in Figure 3, when the journal moves upward off the center by a small displacement Y, the current in the top quadrant will be reduced by a small amount, i, and the bottom quadrant increased by i. The control currents produce a net downward force, F, which pulls the journal back to the center. From sensing Y to producing F, a series of AM6 components are involved, namely, the sensor, controller, power amplifier and electromagnets

.

3 AMB COMPONENTS

3.1 Electromagnets For a given maximum load including static and dynamic loads, the AMB physical size is determined by the saturation flux density of the lamination material. F o r the 8-pole configuration, it is easily shown that

,,F

= 5 . 7 5 x 105

B,~

where, Fmax = maximum load, N A~ = surface area per pole, m2 Bs = saturation flux density, Weber/m2 The maximum value of the flux density in linear range which is about 90% of the actual Es value should be used in applying Equation 2. Choosing the axial length, Lp, the circumferential pole width is Ap/Lp. The radial dimensions can be determined outward from a given shaft diameter at the AMB. The sizing guidelines are: The cross-sectional area at any point of the flux path is not less than Ap. Adequate wiring space is provided. The axial length is no greater than the journal

OD. As a rule, the air gap should be ten times the expected journal vibration. Note that the pole surfaces are the most effective areas for heat dissipation by convection. The ampere-turns per pole is fixed for a given ferromagnetic material; the optimal choice of winding turns, Nt is a trade-off of total current and inductance load, L, to the power amplifiers. The latter is proportional to Nt2ApC which is a crucial parameter causing control delay and bearing instability. More than 8 poles can be designed for the stator, such as, 16 o r 24 poles evenly spaced. A large number of poles saves radial space because it better localizes flux circulation. The coil pairs can be in series o r parallel to a power amplifier with the same trade-off. 3.2 Power Amplifiers Converting a low power control voltage signal to a high power control current and actuating the electromagnets requires power amplifiers. Two types of power amplifiers are commercially available, the linear type and the pulse-width-modulation (PWM) type. The linear amplifier applies the control signal to a power transistor in an "active mode". The transistor continuously regulates the current through the windings from a DC source, V,, with the current directly proportional to the control signal. The PWM type applies the control signal to generate high voltage pulses at a fixed frequency above audible range. The on-time period of each pulse is proportional to the input signal. The voltage pulse train produces current to the windings. The PWM type is electrically noisy and needs its own filters. The power transistors operate in a "saturation mode" with much less power loss. Schweitzer and Traxler [ 7 1 had indicated that the borderline in favoring one type over the other is about 0.5 kVA. There are three limiting parameters in the power amplifiers. First, the control current, i, can not be larger than the bias current. Second, the inductance of the electromagnets causes the control current to diminish and delay above a certain frequency (cut-off frequency). The PWM amplifiers usually apply their own current feedback to increase this frequency. Third, the value of Vs/L, called the current slew rate limit, is the maximum amperes per second that the amplifier can provide. The amplifier frequency

473

response as constrained by these interrelated parameters was well explained by Bradfield, et a1 [el. To account for this in AMB dynamics, an approximate transfer function is shown in Equation 3 . i/E = GaWn/(S + Wn) where

wn

(3)

= amplifier cut-off frequency, rad/sec

S =

Laplace variable E = controller output Ga = amplifier gain, A/V 3.3

Controller The function of the controller is to generate a low power voltage signal, E, to drive the power amplifier and achieve the control current, i, in the windings. If i t is assumed that no delay occurs in the other components (Wn = and Ga = l ) , the requirement of the controller can be described as follows: At any rotor vibration mode, the AMB will see a dynamic mass, M. The AMB equation of motion is (41

N Yr' = Ki i + K, Y

and disadvantages, but all relate the small distance between the stationary sensor and the rotating shaft to an output electrical signal in volts. A low-pass filter is usually included in the sensor conditioning device to eliminate high frequency noise, including its own FM carrier. This filter, similar to the power amplifier cutoff charateristics, may cause a significant time delay in the frequency range of interest. A phase-lead circuit implanted in series in the feedback loop can reduce the delay. An inexpensive and reliable sensor is not yet available for measuring the journal velocity, Y'. Different analog circuits, such as a differentiator with a low-pass filter, and phase-lead circuits have been used to produce a psuedo velocity from the displacement measurement. An analog surrogate called a Velocity Observer is an alternative recently reported by Chen and Darlow [6]. Instead of differentiating displacement, it integrates journal force, (equivalent to acceleration) to obtain velocity. The output of any pseudo velocity circuit is a combination of displacement and velocity signals. Thus, its feedback not only produces damping, but also contributes to the stiffness.

where Y is the displacement of the mass. 4 AMB STIFFNESS AND DAMPING

Ki and -Km are, respectively called the current stiffness and the negative spring of the magnetic field due to the bias current [61. Without the small control current i, Equation 4 represents an unstable dynamic system. To make it stable, it is simple and sufficient to have

i

= E = -cdY

-

CvY'

(5)

The small control current should be made proportional to the journal displacement and velocity. The minus sign is indicative of "negative feedback" - a common regulating mechanism. Cd and Cv are constants, called proportional and derivative control gains. Substituting Equation 5 into Equation 4 , we have M Y" + KiCv Y' + (KiCd

-

Km) Y = 0

(6)

If Cd is large enough such that KiCd > K, we achieve a stable, one degree of freedom system in Y-axis, which has a damping coefficient KiCv and a stiffness coefficient (KiCd - Km). If the static load W, is miscalculated, or there is an occasional slow varying load, as may occur from the gyroscopic effect in spacecraft manuvering, the journal will sag or drift off the bearing center. To avoid this potential problem, a third corrective mechanism called the integral control can be added to Equation 5 : E = -CdY

-

CvY'

-

From the previous discussion, a practical single axis control [9,101 can be represented by the block diagram of Figure 5 . A radial AMB needs two independently controlled axes like this, while a thrust AMB needs only one. A second-order (Butterworth) low-pass filter was assumed to be part of the sensor. It as easily could have been a fourth-order or other type of filter. Gp is the sensor sensitivity, 1000 V/in. ( 4 0 V/mm). Note that a e.g., phase-lead circuit is applied in series here for compensating the time delay mainly caused by the inductance loads to the power amplifiers. One may set the phase-lead parameter "a" to be equal to the amplifier cut-off frequency, W Thus a system "zero1' cancels a system ''pol:'' in the S-plane. This does not improve the current slew-rate of the amplifier, but does increase the The other damping-to-stiffness ratio around W phase-lead parameter "b" is set in t%e range 5a 5 b 5 10a.

.

The AMB stiffness, K, and damping, B, of this controlled axis can be calculated by using Equations 8 and 9 with S equal to j w . -F/Y = K + jWB = -Ki(i/Y)

-

K,

i/Y = (Ts )(Tc )(Tp) (Ta) where

Ce $Ydt

(7) W

shown in Figure 4 , the accumulated journal position error over a period of time will produce a part of the control voltage. The integral control does not respond to high frequency vibrations. Equation 7 represents a proportional integral derivative (PID) controller.

= excitation frequency, rad/sec

As

3 . 4 Sensors Three displacement sensors prove to be practical, the capacitance probe, inductance probe, and eddy current probe. Each differs with its advantages

Ts = GaWn2/(S2+ ~~W,S+W,~)

Ta = Gawn/(S + un) Equations 8 and 9 indicate that both K and B are functions of excitation frequency W , not rota-

474

tional speed. Numerical example results are plotted in Figure 6 using the AMB data in Table 1. The frequency axis in this plot is normalized with respect to 50 Hz which is the average of two rigid-body critical speeds of a rotor. The amplitude is normalized with respect to At the low frequency range where the integral control dominates, the plot shows negative damping value. This should not cause alarm, however, since mechanical system resonances seldom exist in that low range. Yet, at the high frequency range, especially where the first two bending criticals exist, the negative damping can cause resonances. This will be discussed in an example later. 5 ROTOR-AMB SYSTEM DYNAMICS 5.1 System Design Guidelines AMBs are generally less stiff than rolling element, o r hydrodynamic oil-f ilm bearings: Therefore, the first two system criticals have relatively rigid mode shapes, and their vibrations are easily controlled. The third and the fourth criticals with bending mode shapes must be given careful design considerations for high speed turbomachines. Taking the rotor model in Figure 7 as an example, its critical speed map (Figure 8 ) shows that the rotor operates between the third and the fourth criticals. Two identical &pole AMBs are chosen to support the rotor with dimensions in Table 1. The first design issue is finding the best method for determining the stiffnesses. In this case, the stiffness per bearing ca be made 1000 lb/in. or 10,000 lb/in. (1.75~13 N/m or 1 . 7 5 ~ 1 0 N/m). ~ The answer depends on rotor shock load. To take 1 g shock, this rotor of approximate 100 lb (45 kg) moves radially 50 mil and 5 mil (1.25 mm and .125 mm) respectively, for the lower and higher stiffnesses. The catcher bearing is set at 10 mil (.25 mm) away fromthe rotor To for a designed air gap of 20 mil ( . 5 mm). avoid pounding the catcher bearing when shocked, the higher stiffness is chosen. Reviewing the mode shapes at the chosen stiffness (Figure 9) reveals that there are sufficient relative displacements at the bearings for control of the first and second modes. The third and the fourth modes are lacking the displacement at one bearing. To help control the third mode, the displacements sensor is mounted at the outboard side of each AMB where the sensor sees more than only the AMB center motion. The second design issue is to determine how many bending modes should be controlled. To keep the control electronics relatively simple, the frequency range with acceptable control response is limited by two factors, namely, the inductance load and the filtering delay. It is imperative to have an adequately damped bending mode below the operating speed (the third mode in this case), because of the unbalance excitation during traversing the critical. The bending mode immediately above the operating speed (the fourth mode in this case) should be 15 to 20% away in frequency. However, it still can be excited by harmonics as the rotor is going up in speed, or by a shock load. But, less damping is required for controlling this mode.

The higher bending modes normally are less likely to be excited. The rotor material damping is a source to resist the minor, or occasional excitation. Note that oil-film bearings always provide positive damping but there is no guarantee of this for AMBs. The control current at the high critical frequency may lag behind the displacement measurement, or the probe may be at the wrong side of the AMB. The AMB may become a small exciter for that mode. When it happens, a band-reject filter for the excitable mode can be implemented in series in the feedback loop to block the control at that modal frequency. For the example herein, the power amplifier and the sensor low-pass filter are assumed to have the cut-off frequencies at 500 and 5000 Hz, respectively. Applying the normalized stiffness and damping of Figure 6, the normalized frequency of 1.0 is 50 Hz, which is between the first and the second criticals as read from the map. The values of UB/K for the lower four modes range from 0.2 to 0.6, which is adequate for properly designed vibration modes. More damping can be achieved by increasing the value of Cv. 5.2 Rigorous Dynamic Analysis After component sizing and cursory analysis, rigorous system analysis is needed to prove the expected rotor vibration behavior. Considering the fact that the AMB stiffness and damping are functions of excitation frequency, the state vector of the conventional rotor model is extended to include the state variables of the AMBs 1113. The control dynamics of each AMB axis are represented by a set of first-order linear differential equations as shown in Figure 5, in terms of the extended states (i, E, Q, Z, Y , V,). The coupling terms between the rotor moBel and the AMB model exist in the AMB force equation, which is also shown in Figure 5 . The mathematical rotor model is the same as the conventional model including sections of shaft with specified ID, OD, length, and concentrated masses and inertias. The model for each bearing would be the bearing station number, the measurement station number, and the key parameters of Table 1 (presented earlier). Using this electromechanical model, the lower four damped frequencies of the example rotor running at 15,000 rpm were computed and presented in Table 2. The first three modes are adequately damped because the associated log decrement values are all significantly above 0.4. The latter is a damping value generally accepted for a rotor system supported in oil-film bearings. The fourth mode has a log decrement value of 0.06 without considering the rotor material damping. It should be acceptable since it is much higher in frequency than the third mode and the operating speed. Note that in Table 2, the cross-coupling stiffness produces a destablizing seal effect at the wheel, but only affects the first mode damping. The reason for this is that only the first mode shape has significant lateral displacment at the wheel. The rotor/AMB system can sustain a value of 4000 lb/in. (7x10’ N/m) before becoming unstable. Figure 10 presents an unbalance response at the third critical speed using the same electromechanical model. It indicates that the response

475

peak is well damped and far away from the operating speed of 15,000 rpm. The peak dynamic current of AMB 1 2 was calculated to be 0.45 A (0-peak) at 11,500 rpm. It specifies that a current slew rate no less than 550 A/sec must be provided by the power amplifier design.

3.

Malanoski, S. M., "Rotor-Bearing System Design Audit", Proc. 4th Turbomachinery Symposium, Texas AhM Univ., Oct. 1975, 65-70.

4.

Chen, H. M. h Dill, J., "A Conventional Point of View on Active Magnetic Bearings", NASA Langley Workshop on Magnetic Suspension Technology, Feb. 2-4, 1988.

5.

Hustak, J. F., Kirk R. G., h Schoeneck, K. A., "Analysis and Test Results of Turbocompressors Using Active Magnetic Bearings", Journal of ASLE, Lubrication Engineering, May 1987, 43, 356-362.

6.

Chen, H. M. h Darlow, M. S., "Design of Active Magnetic Bearings with Velocity Observer", ASME 11th Biennial Conference on Mechanical Vibrations and Noise, Boston, September 1987.

7.

Schweitzer, G. h Traxler, A., "Design of Magnetic Bearings", Proc. of Intl. Symp. on Design and Synthesis, Tokyo, Japan, July 1984, 423-428.

8.

Bradfield, C. D., Roberts, J. B., h Karunendirkan, R., "Performance of an Electromagnetic Bearing for the Vibration Control of a Supercritical Shaft", Proc. Instn. Mech. Engrs., 1987, 201, No. C3, 201-211.

9.

Fukata, S., et al., "Dynamics of Active Magnetic Bearings Composed of Solid Cores and Rotor" Memoirs of the Faculty of Engineering, Kyushu University, 1986, 46, No.3, 279-295.

6 CONCLUSIONS The properties of active magnetic bearings and the essence of rotor-AMB system control have been described and quantified in a language that is more familiar to mechanical engineers. In doing so, the following viewpoints on AMB development have been emphasized: 1.

The AMB should be treated as a locally controlled device similar to other types of bearings. The two axes of a radial AMB should be controlled independently.

2.

Pitfalls exist in controlling the rotor bending critical modes; the reasons and design guidelines are explained by conventional rotordynamics terminology.

3.

A modified rotordynamics analysis method with an extended state vector including the AMB state variables is needed for rigorous system performance prediction.

In presentation of this paper, the author aims to broaden the understanding of AMBs and thus, accelerate the development of AMB technology. References

1.

Habermann, H. h Liard, G., "An Active Magnetic Bearing System", Tribology International, April 1980, 85-89.

2.

Weise, D. A,, "Active Magnetic Bearings and Their Industrial Applications", 5th Annual Rotating Machinery and Controls Industrial Research Conference, San Antonio, Texas, 1985.

10. Hurnphris R. R., et al., "Effect of Control Algorithms on Magnetic Journal Bearing Properties", 1986, ASME 86-GT-54. 11. Chen, H. M., 1988, "Magnetic Bearings and Flexible Rotor Dynamics", ASLE Annual Meeting at Cleveland, Ohio, May 1988.

/1' .

Air Gap Decreased

Designed Air Gap

\

f!

51

Air Gap Increased

/'

i

Journal Laminated Stator

Bias Current

881078

882681

Fig. 1 An 8-pole magnetic bearing

configuration of an active

Fig. 2 Nonlinearity of magnetic force

476

Measured Journal Displacement Bias 1, Adiustment

Low-Frequency Drift -i

i Controller

e

Ydl =

.Sensor

Algebraic Sum of Shaded Area

Without Integral Control c

C

El' Y + I

Power

Adjustment 881061 - 2

Fig. 3

881079

Fig. 4 Elimination o f through i n t e g r a l c o n t r o l

An i n d e p e n d e n t l y c o n t r o l l e d a x i s

-

Journal Motion at AM0 Q

Adjustable PID Gains

Gpf sz+J2ur,S+wf I y . - Journal

Sensor

Displacement

Low-Pass Filter

luo

s+..]

Phase-Lead Circuit

S

Amplifier

stlu,I

Controller

Rotor/AMB Force Coupling Equation F = Ki i + K, Y

AMB State Equations i' + o, i = GawaE

E' + b E = -b/a [C, Y i + C, Q'+ C, 2'

Q'

+ a (C, Y, + C, Q + C, Z)]

+ 0, Q = oOYp

Z'+

0,z

low-frequency

= vp

v; = v, V i +Goc V, +a:

Y, =G,w:

Y 882086

Fig. 5

A single-axis c o n t r o l diagram

Electromagnets

drift

477

(i/

Thrust

8 Y Disk

200 r

E

100

Sensor

-100 -200

I

I

I

l

0.08

0.02

0.002

l

I

0.2

l

I

l

0.4

I

1.0

I

I I I I

4

20

8

Normalized Frequency 882071

Fig. 6 AMB stiffness and damping example

-

-

Fig. 7 A rotor model

a numerical

AMB,No 1

15,000rpm

AMEN0 2

+l 0

-1 0

!,, 3

1

1.75X 10' Nlm

5

,

I , , i ,,,I

,

30 50 100 StiHness/Bearing llO00 Iblin.)

300 500

10

1.75X

lo" Nim

, , I , , ,J

5

0

10

15

20

25

30

Rotor Length (in )

1000 I

250

0

I

I

500

750

1.75X 10' Nlm 882072

Fig. 9 Rotor critical mode shapes

Fig. 8 Rotor critical speed map

0.3 - = 1.2 -

1 .8 gm-cm a1 Thrust Disk

1.4

1 6 gm-cm a1 Coupling -3.6 gm-cm a1 Wheel

/ 6

7

8

AM0 NO. 1

9

10

11

12

13

14

15

Speed (10W rpm) 882069

Fig. 10 Unbalance response at 3rd critical speed

35

478

Table 1 Lp

D C Ap Nt Fmax I1 I3 Ki Km cd C,

ce Cp

Ga W

C

Wn

z:

Table 2

-

AMB Dimensions and Parameters

= 2.0 in. (50.8 mm) = 2.5 in. (63.5 mm) = 0.020 in (0.5 mm) = 1.25 in.' (8.06 x m2) = 100 turns = 200 l b (890 N) = 3.5 A = 2.0 A = 80 lb/A (356 N/A) = 12,500 lb/in. (2.19 x lo6 N/m) = 0.26 = 0.60 = 1.00 = 1000 V/in. (40 V/mm) = 1 V/A = 5000 Hz = 500 Hz 1 Hz 500 Hz

1

- Damped Natural Frequencies of Forward Modes

rotor speed =15,000 rpm cross-coupling stiffness (Kxy) at Wheel Kxy = -4000 lb/in. (-7

Kxy = 0 Frequency (cpm)

Log Decrement

Frequency (cpm)

x

lo5 N/m) Log

Decrement

2318

1.05

23 74

-0.00

5263

2.20

5623

2.19

11,154

0.89

11,144

0.88

34,156

0.06

34,156

0.06

SESSION XVI KNOWLEDGE BASED SYSTEMS Chairman: Dr C M Taylor PAPER XVl(i)

The Incorporation of Artificial Intelligence in the Design of Herringbone Journal Bearings

PAPER XVl(ii)

Bearing Selection Using a Knowedge Based System

PAPER XVl(iii)

Tribology Aids for Designers


48 1

Paper XVI(i)

The incorporationof artificial intelligence in the design of herringbone journal bearings K. Ishii, B. J. Hamrock and J. Klinger

Research was conducted to develop an intelligent computer program to aid in tribological design. Our focus is to integrate artificial intelligence (AI) and conventional numerical design techniques. As a vehicle for our effort, we focus on an example problem: the optimal design of hemngbonejournal bearings. We utilize an established numerical optimization method which, given the bearing parameters (requirements),finds the groove parameters (design variables) such that the radial load capacity of the bearing is maximized. A1 techniques add another level of computer aid that incorporates qualitative issues as well as numerical. We use the method of design compatibility analysis (DCA) to form an outer, intelligent design loop that applies to the numerical optimization. DCA identifies any incompatibility between the design requirements and the design solution, explains the flaw, and suggests modifications to improve the design. Design issues considered include. (1) suitability of a hydrodynamic bearing, (2) safe minimum film thickness, (3) adequacy of load capacity and stiffness, (4) self-excited whirl instabilityratio, and (5) flow rate, power loss, and attitude angle. We implemented both the numerical and A1 programs on an IBM PC. The program uses Turbo-Prologfor DCA and Fortran for numerical optimization.

1. INTRODUCTION Design is a creative process arrived at finding a solution to a particular problem. In all forms of design a problem may have many different solutions mainly because design requirements can be interpreted in many ways. For example, it may be desirable to produce (1) The cheapest design (2) Or the easiest to build with available materials (3) Or the most reliable (4) Or the one that is lightest in weight (5) Or the one that takes the smallest space (6) Or the best from any of a whole variety of possible standpoints The task of the designer is therefore not clear cut, because he or she has to choose a reasonable compromise between these various requirements and then has to decide to adopt one of the possible designs that could meet this compromise. The design of bearings is one of the critical ingredients of machine design. Designers need to understand the problem specification, to select the appropriate type of bearing, and then to assign values to the design variables such that all the functional requirements are satisfied. The difficulty arises from the varying nature of the specification. The problem specification involves not only functional requirements such as load capacity but also maximum bearing envelope, operational speed, bearing life, type of lubricant, etc. Note that some of these items could be considered as design variables over which designers have control (e.g., bearing envelope, speed, and lubricant type). In addition, the designer should pay attention to the manufacturing method. For example, the machining method dictates the surface finish of a bearing and a journal, which in turn, influences the allowable minimum film thickness. The process of bearing design usually involves the following steps: (1) Selecting a suitable type of bearing (2) Estimating a bearing size that is likely to be

satisfactory

(3) Analyzing the performance of the bearing to see whether it does in fact meet the requirements (4) Modifring the design and operatingparameters until the performanceis near to whichever optimum is considered most important The last two steps in the process can be handled fairly easily by someone who is trained in analytical methods and understands the fundamental principles of the subject. The fist two steps, however, require some creative decisions to be made and for many people represents the most difficult part of the design process. Hence one can easily see that the design process is complex, requiring a thorough understanding of the field. It takes years of training to acquire the experience and intuition needed to be a good bearing designer. Computers are a powerful tool for bearing designers. The recent development of personal computers has accelerated the trend of using computer programs to aid aibological designs. Most of the programs developed and used to date have focused on numerical requirements,either for analyzing or simulating the performance of a proposed design, or for optimizing the design parameters given an objective function and design constraints. These programs typically use procedural languages such as Fortran and Pascal and do not consider qualitative issues. The emerging field of AI offers techniques that add another level of computer aid to the already established numerical design programs. The symbolic computation ability allows A1 programs to accommodate qualitative design issues as well as numerical issues. Among the many possibilities are: (1) Help designers understand and organize problem specifications. (2) Determine the most suitable type of bearing. (3) Help designers identify limiting factors of design and use numerical tools. (4) Evaluate the compatibility of a proposed solution at various stages of design. (5) Identify incompatibilitiesin the proposed solution and provide suggestions.

482

Many researchers have applied A1 to the design of machine elements. Dixon (1983, 1985) uses A1 to guide designers of mechanical devices through relatively simple but iterative design problems such as the design of V-belts and heat fins. Ishii and Barkan (1987a) take an example of a hydraulic cylinder and developed the concept of Rule-based Sensitivity Analysis (RSA) that aids in optimization. Knowledge based approaches to bearing selection have been reported by Lin (1988), and Waldron (1987). These studies fall under step (2) above. Little work has been reported on the applicationof A1 to the more detailed stages of bearing design that involve numerical programs. (steps 3,4, and 5). This research was conducted to develop an intelligent computerprogram for use in tribological design. Our focus was to integrate A1 and conventional numerical design techniques. As a vehicle for our effort we selected an example problem: the optimal design of herringbone grooved journal bearings. This paper describes our development effort for this particular example. Specifically,we focus on the already established numerical optimization program, and the evaluate-suggestcapability of AI techniques (steps 4 and 5 above).

self-pressurizationcan increase the load capacity over that of a smooth bearing; it is also responsible for the herringbone bearing's good stability. The bearing shown in figure 1 is unidirectional; that is, it pumps inwardly for one direction of rotation. Bearing parameters 1. A*!=

2

2KB CKB(s) ckbdata Ho hl0 h2o L L1

M O MI MR M(s) N Pa

R U W Wr

a

P

Y

A

width of groove, m width of ridge, m compatibility knowledge base the compatibility knowledge base concerningthe element s a data in ClKB film thickness ratio, h1&20 film thickness in groove region when journal is concentric,m film thickness in ridge region when journal is concentric,m length of journal, m total axial length of groove, m a set of matching compatibility data match index match range match coefficient number of grooves ambient pressure, N/m2 bearing radius, m bearing speed, ds bearing load, N radial load capacity of herringbone journal bearing, N groove width ratio, bl/(bl+b2) groove angle, degrees groove length ration, Ll/L dimensionless bearing number, 6 p U R / ~ ~ h ~ ~ 2 absolut viscosit N s/ g r o o v or ~ smoori mem%r rotating

2 . HERRINGBONE JOURNAL BEARING DESCRIPTION

A herringbone journal bearing is a fixed geometry journal bearing that has demonstrated good load capacity and stability characteristics for both incompressible and compressiblelubrication. The bearing consists of a circular journal and bearing sleeve with shallow, herringbone-shaped grooves cut into either member. Figure 1 illustrates a partially grooved herringbone concentric journal bearing. Note the angled, shallow grooves in the journal surface. The grooves can be partial, as shown, or extend the complete length of the bearing. Also, the grooves can be placed in either the rotating or nonrotating surface. The purpose of these grooves is to pump the lubricant toward the center of the bearing, thereby raising the lubricant pressure in the bearing. This

A.6IIUR Pa&

v

Groove parameters

1.1 Notation bl

2R

Fig. 1Bearing and Groove Parameters In figure 1 the number of grooves is six. However, the Vohr and Chow (1965) analysis used in this paper assumes essentially an infinite number of grooves. Reiger (1966) develops a criterion for the minimum number of grooves such that the infinite groove analysis yields valid results. This criterion indicates that the minimum number of grooves placed around the journal can be represented conservativelyby

N T -A 5

(11

where N = number of grooves A=--

6pUR

- bearing compressibilitity number

Plh, In this paper we will adhere to the inequality given in (1). Figure 2 indicates the groove and bearing parameters. Hamrock and Fleming (1971) report a study on the optimization of self-acting herringbone journal bearings. Hamrock and Fleming developed a program that, given the bearing parameters h. and A (design requirements), finds the groove parameters (design variables) such that the radial load capacity of the bearing is maximized.

Input Specifications W bearingload

u

Bearing Parameters

bearingspeed

Groove Parameters

h10

Ho= Go

pa: am. pressure p: lub. viscocity

a=- bl

Parameters L bearing length R bearingradius

P

b*+b2

y=L,/L

h&adial clearance I

Fig. 2 Optimizationof groove parameters

483

3 , THE ROLE OF A1 IN THE DESIGN PROCESS

the method used is a Newton-Raphson method of solving simultaneousequations.

As indicated previously, knowledge based techniques add another level of computer aid to a design synthesis program. Such techniquescould identify incompatibilities between the design solution and factors not considered in the optimization program: bearing load requirement, method of surface finish, constraints on speed, etc. A knowledge based program also catches obvious overdesign, such as an unnecessarily large bearing envelope. Another important task for our program is to make intelligent suggestions to remedy the incompatibilities: use of a different lubricant or modify speed, radial clearance, or bearing envelope. The suggestions should also take into account the effectiveness (sensitivity) of each remedy and its implicationsfor other design constraints. Ishii and Barkan (1987b, 19888) develops a framework for knowledge based design called design compatibility analysis (DCA) that accommodates the features described above. DCA focuses on the compatibility, both qualitative and quantitative, between design requirements and design solutions. DCA matches a given requirement and its solution with compatibility knowledge: good and bad templates of design. DCA combines the matching compatibility knowledge and gives a total evaluation. In addition, DCA provides justifications for the evaluation and suggestions for improvement that apply not only to the design solution, but also to the design Specification. This paper reports the use of DCA as a knowledge based design loop that applies to the optimization program developed by Hamrock and Fleming. The typical flow of a design session is as follows. The user of the program first enters the design requirements: bearing envelope (L and R), lubricant viscosity p, bearing speed U, radial clearance hZ0, and the bearing load W. DCA will perform a preliminary evaluation of the consistency of the input. Then the optimization program calculates the value of the groove parameters &, a,p, y (i.e., the design solution). Then DCA asks additional questions (e.g., surface finish) and evaluates the compatibility of the design solution. If the design solution is unacceptable or is obviously an overdesign, the user can seek suggestions from DCA. DCA will suggest changes in bearing envelope, lubricant, bearing speed, or radial clearance. The overall program helps the designers to consider manufacturing concerns in their design and thus helps them make tradeoffs between performance and cost. (Section 4 gives a more detailed discussion and a flowchart.) We implemented both the numerical and A1 programs on an IBM PC. The program uses Turbo-Prolog for DCA and Fortran for numerical optimization. The overall program generates an executable file that the user can run without compilers or loaders. 4 . OPTIMIZATION PROCEDURE FOR

BEARINGS The task completed by Hamrock and Fleming (1971) was to find the optimal herringbone journal bearing for maximum radial load capacity for various bearing parameters [A, h, and whether the grooved or smooth member is rotating (a)]. The radial load component is the component of the total load capacity in the direction of journal displacement. Therefore the problem reduces to Given: A, h and a Find H,,,a,p, and 'y, which statisfy aw,

aw,

aw, aw,

~ H , = E - ap

- 7 = O

(2 1

. ..

5. DESIGN COMPATIBILITY ANALYSIS 5.1 ConceDt of D& Co-ilitv Analvsis One of the important tasks in engineering design is to ensure the compatibility of the elements of the proposed design with each other and with the design specifications (requirements, constraints, and production method). Major design decisions such as selection of components, determination of system type, and sizing of components must be made with the compatibility issue in mind. Some design features make a good match, but others may be totally incompatible for the required design specifications. Experienced designers usually know of a good combination of design choices for a particular situation. This knowledge can be viewed as good or bad templates of design. The knowledge can also be interpreted as an understanding of compatibility. For example, a rolling-elementbearing is not suitable for an automobile connecting rod bearing. A1 techniques provide us with a framework for storing this compatibility information in a knowledge base and for evaluating the overall degree of compatibility of a given design. Examples of such compatibility knowledge are expressed below in a rule format.

ExamQu (Machining of bearing is to be done by grind, lap, and superfinish) (Minimum allowablefilm thickness for this machining process is between 0.0001 and 0.00025 in.) (Design film thickness is 0.0002 in.) => (Design of bearing using grind, lap, and superfinish is EXCELLENT) Reason: (Grind, lap, and superfinish will meet the required surfacefinish.) Suggestion: (none) (3)

ExamQu (The load specification for the bearing is 1 Ib.) (The maximum load from optimization is 10 lb.) => (Design for load requirement is POOR) Reason: (You have overdesigned your bearing for the required load) Suggestions: (Reduce the bearing envelope (1engWdiameter)) or (Increase the radial clearance) or (Use a higher viscosity lubricant) (4)

(The Reynolds number for this design is greater than 2000) => (You are operating with Taylor vortex flow. Your design is VERY BAD) Reason: (The optimizationprogram is valid only for laminar flow) Suggestions: (Decrease the radial clearance) or @ecrease the required speed) (5)

In addition to the task of expressing the compatibility itself, we must deal with the degree of confidence of such compatibility data. Some data may indicate total incompatibility; others may only suggest avoiding a certain type of design. We cannot altogether rule out undesirable

484

choices or costly designs, since they may, in some cases, provide the only alternative given all the other constraints. Also, we need to weight the evaluation depending on the importance of each individual element. An undesirable combination of major components should be weighted higher in the evaluation than an undesirable combination of minor parts. The theory of fuzzy measure (Ishii and Sugeno, 1985) provides a sowid mathematical basis for the treahent of the degree of confidence. We can consider the evaluation of compatibility, or the match index (MI), as the utility of design. The utility of individualcomponentscan be defined as the normalized weight of importance. The match index essentiallydepends on the compatibility templates that apply to a given situation. Design compatibility analysis (DCA) utilizes the compatibility knowledge in helping designers generate a good design. The fundamental strategy of DCA is as follows (figure 3). The user first defines the specifications and describes the proposed design The proposed design may be a partial design of the entire system with some parts of the design left undecided. The expert system then infers some physical characteristics of the proposed design and some physical requirements from the user-provided data. Once all these data are complete, the expert system evaluates the compatibility of the proposed design and indicates it in terms of the utility of the entire design and the match index, and also provides a justification for the evaluation and suggestions for improvement.

.

designer to make flexible decisions that will remedy the incompatibilities, thereby making the decision process rapidly converge to a sound solution. The theory of fuzzy measure provides DCA with the match index as an indicator for the soundness of design. The computation of the MI is based on the utility of the design. The designer can control the weight of each element in DCA evaluationsof the MI by assigning an appropriate utility value for each design element. 5.2

Measure

of C

. ..

w

By focusing on the theory of fuzzy measure (Ishii and Sugeno, 1985), we define a quantitative measure for the compatibility of design, which we call the match index (Ishii and Barkan, 1987b). Figure 4 illustrates how DCA computes the match index and compiles justifications and suggestions.

I Attribute Compatibility Inference

Specification! Requirement

Mapping MC Justification

Suggestions

c,,nnsrtinn

Weighted Average & Range

Fig. 4 The deduction process in DCA. Fig. 3 Concept of DCA The match index is a normalized scale between 0 and 1: An MI of 0 indicates an absolutely incompatibledesign, an MI of 1 is a perfectly balanced design, and an MI of 0.5 indicates that no compatibility information is available. Ideally, if compatibility KB is reasonably rich, the user would rarely obtain an MI of 0.5. The MI is a normalized compatibility evaluation of the proposed design; the match index depends on physical interpretation of the the user's interpretationof compatibility. If the knowledge base represents qualitative compatibility information between components and their specifications,then the MI is best interpreted as thefractionalpart of the entire design that is compatible and well matched. If the knowledge base represents the cost of the design elements, the MI is interpreted as the normalized cost index with respect to a certain standard cost. Overall, the designer can then utilize this information to update and improve the proposed design, or alternatively, to compromise on the specifications. (Note that DCA flags not only bad designs, but also inappropriate specifications.) The designer can start by eliminating obvious incompatibilities and then further seeking an improved design. The advantages of taking this approach in DCA over the conventional decision-making methods, where each decision is made in a sequential fashion, are as follows: (1) By evaluating the entire design, and detecting every incompatible aspect of design, DCA allows the

Given a description of the proposed design and the design specification, DCA uses the attribute knowledge base (KB) to establish more detailed requirements and physical characteristics of the proposed design. DCA next matches the situation with the compatibilityKB and infers a set of matching compatibility data (MCD) for each design element. DCA then maps MCD into [0,1] to obtain a match coefficient(M(s)) compatibilityevaluationfor each element, according to a function MC. Finally, the weighted sum of the match coefficientsyields the match index (MI). The range of match coefficients represents the match range

(MR).

The following sections give a mathematical description of the deduction process of the match index and the associated justifications and suggestions. 5.2.1

Def. 5.1: The match index (MI). Consider a design comprising a set of elements K. MI = & utility@) * M(s), SEK (6) where: utility (s) is the weight of the evaluationof a components. (&tility(s) = 1.0) M(s) is the compatibilityof an elements with the rest of the elements and the design specification. Hence, the match index is essentially the weighted sum of the match coefficient (M(s)). The match coefficient (M(s)) is the compatibility evaluation of a design element with the rest of the design and with the specification (c.f.

485

section 5.2.2). Def. 5.1 gives the MI a meaning of overall utility. If all the elements are deduced to be totally compatible (i.e., M(s) = 1.0 for all s), then our MI is 1.0, indicating an excellent design. If there are incompatibilities or inadequacies associated with a certain element, the design loses some of its utility.

Def. 5.2: The Match Range (MR). Consider a design comprising a set of elements K. MR = [ min(M(s)l s e K ) , max(M(s)l SEK) 3

Next, we further map the set of matching compatibility data to a [0,1] assessment according to an application-specific mapping MC. (7)

The match index is only an averaged measure of compatibility and does not reflect situations where most design elements are compatible but some minor elements are not (low M(s)). This element may seriouslyjeopardize the entire design. The match range will indicate such unbalance in the design. Hence a good design gives a high MI and a nmow MR. Note that the designer should use these measures in conjunction with the deduced information: justifications for the evaluation and suggestions for improvement. 5.2.2

In order to compute the match index, equation (6) requires the match coefficients (M(s)) of design elements s. The match coefficient is a [0,1] evaluation of the compatibility of the design element with respect to the rest of the design and the design specifications. For a given proposed design under a certain design specification, the match coefficients are derived from the compatibility knowledge base. The derivation comprises the following steps: (1) Deducing the set of compatibility data that matches the situation. (2) Mapping the deduced set of compatibility data into the range [0,1]. The nature of mapping depends on the field of application. The compatibility knowledge base C KB contains the compatibility data in the following form:

ckb-data (, <Elements>, < Descriptor>, < Reason>, )

MC: MCD + [0,11.

(8)

is the identification number of this compatibility

data. <Elements> is the set of design elements concerned. d)escriptor> indicates the evaluation of compatibility. Descriptor could be an adjective describing the match (e.g., poor, good) or numerical values indicating relative cost, etc. dieason>is the justification for the match. is a list of preconditions for this clause. First, for any given proposed design under certain design specifications and constraints, we can derive a set of matching compatibilitydata from the compatibility knowledge base. We label this deduction CD. For a given design element s, (9)

where C is a conjunction of predicates describing the specifications. D is a conjunction of predicates describing the design elements.

(10)

Def. 5.3: Match coefficient (M(s)) is a [0,1] scale derived by equations (9) and (10). M(s) = CD MC ( C u D uCKB(S) ) (11) As mentioned before, the mapping MC depends on the application. Specifically, users should define M C according to how they describe compatibility in the compatibility data. The main reason behind applying MC is to normalize the evaluation of each design element and thus allow us to compare uniformly the compatibility of each element. In this paper, we use compatibility data with qualitative descriptors. Here, an adjective w describes the level of compatibility. For example, w E W=(excellent, very good, good, poor, bad, very bad). Hence, the set of matching compatibility data (MCD) contains n numbers of adjective descriptors (i.e., MCD = W n). In order to map Wn to [0,1], we use a function Translate: W+ [0,1] to each descriptor. For example, (excellent, very good, good, poor, bad, very bad) + (1.0, 0.8, 0.6, 0.4, 0.2, 0.0) Hence, we obtain n numbers (i.e., [O,lIn). We further introduce a mapping Bestinfo: [O,l]n + [0,1] to derive the match coefficient.

Def. 5.4: Bestinfo(V) is defined as follows: (1) The maximum in the set V , if the set consists only of numbers greater than or equal to 0.5 (i.e., there is no "negative" comment about the design). (2) The minimum in the set V, if the set contains at least one number less than 0.5 (i.e., if there is at least one "negative"comment about the design). (3) 0.5 if the set V is empty, indicating neutral compatibility. Def. 5.5: MC = bestinfo( translate (MCD) )

where

CD: C u D u CKB(s) => MCD

CKB(s) is the compatibility knowledge base concerning the elements, that is, s E (list of elements in CKB) MCD a set of matching compatibility data. A => B indicates that A implies B.

(12)

Hence, we first take the matching compatibility data ( M C D ) , which contains n numbers of adjective descriptors, map each of them to the range [0,1], and then apply bestinfo to obtain a [0,1] number.

6. INTEGRATED PROGRAM: HERRINGBONE-EXP The integrated program called Hemngbone-exp combines the concepts of DCA and the use of a hemngbone groove journal bearing optimization program. Hemngbone-exp uses the power of Prolog's object-oriented programing and recursion for DCA and the power of Fortran's procedural computation ability for the optimization. This combination provides a strong useful design tool, because in the design of any mechanical system both qualitative and quantitative issues are considered. The DCA portion was implemented by using Turbo-Prolog; and the optimization section, by using standard Fortran 77. The integrated program runs on an IBM PC as an executable file. The user interaction with Hemngbone-exp is shown in figure 5.

486

1

START

the Prolog user interface and DCA module is to run the compatibility analysis. As previously discussed,DCA will evaluate the present design and give suggestions for improvement. After DCA is completed,control will then go to the top executive module and the design parameters will be passed to the Fortran herringboneload optimizationmodule. In the Fortran herringbone load optimization module the design parameters are used to find the groove configuration that will maximize the load capacity. Once the optimum values are obtained, the top executive module will transfer the data to the Prolog user interface and DCA module. This interaction will continue between the three modules until a satisfactory design is achieved.

Completed Design

Fig. 5 Flow of design using Heningbone-exp Users start by entering the design specification for the bearing, the required load, the bearing speed, and the lubrication used. Then the user enters a few design parameters, the bearing length and radius, the radial clearance, the machining process that will be used to manufacture the bearing, and whether the smooth or the grooved member will be rotating. After the initial design specifications and design parameters are entered, the user does an initial DCA. If the evaluation is less than satisfactory, modifications can be made to the design parameters, the specifications, or both. If the initial design is satisfactory,the herringbone groove optimizationis carried out on the initial design. The results of the optimization program are then used to do another DCA on the bearing. Suggestions are made for improvements to the design. Again the user can change the design parameters, the specifications, or both and continue the design cycle. The process is carried out until the user is satisfied with the results. For this example of herringbone-grooved journal bearings, specific design and performance rules are containedin the knowledge base of the program. Examples of some of the compatibility knowledge were given in section 5.1. The information contained in the examples 1 to 3 is very powerful to the user. The knowledge base when used with DCA will evaluate the design as excellent, very good, bad, etc., list the reasons for the evaluation, and list suggestions for improvements. This type of knowledge base will help the designer obtain the best possible solution for the design cycle of the bearing in a short time. 7. IMPLEMENTATION The Herringbone-exp program comprises of three main modules that share a common data base. The top executive module's main purpose is to control the flow of data between the Prolog user interface and DCA module, and the Fortran herringbone Optimization load module. (figure 6) When the program is run, the top executive module is initiated first and proceeds to give control to the Prolog user interface and DCA module. The Prolog user interface and DCA module has two principal functions. The first is the user interface function. The user interface plays an important role in allowing the user to enter the design specifications and design parameters in a user-friendly way. The second function of

OptimizationModule

Fig. 6 Program structure of Herringbone-exp 8. ILLUSTRATIVE EXAMPLE

The power of the Herringbone-exp program is best observed through an example. Suppose we need a herringbone journal bearing with the following specifications: load: 55.0 lb. Speed: 38 000 rpm Viscosity: Air The initial design parameters are taken to be Bearing length: 1.0 in. Bearing radius: 0.5 in. Radial clearance: 0.0007 in. Grooved member rotating Machining process: grind, lap, and superfinish Figures 7 and 8 show the menus that the user will interact with when entering the information. After the first DCA the match index yields 0.4 which is poor. The machining process is over specified for the required minimum film thickness. In order to improve the design, the designer changes the machining process to grind and lap. Again the DCA is done and our design seems satisfactory to this point, without taking into account the groove design from the optimizationroutine. Now the optimization routine is run. After the results from the optimization routine are obtained; the user will check DCA to see if the design is satisfactory, figure 9. The match index now indicates that our design is 0.01, which is very bad, figure 10. We have not met our load requirements. One suggestion is to decrease the radial c l m c e . The user changes the clearance to 0.0006 inches and runs DCA to make sure new incompatibilities do not arise. The optimization routine is then conducted on the new design, figure 11. Finally, the user checks the compatibility. This time The match index is 1.0, which is an excellent design. The user, being satisfied with the design ends the program.

487

The Ohio State Universitv

I

I


I

Required Bearing Load (Ib)........ 55.0 Required Bearing Speed (rpm)... 3800 Viscosity of the Lubricant........ Groove Angle 27.04 degrees Groove Width Ratio 0.47177

Enter Design Specifications

Fig. 11 Final result

Fig. 7 Specification menu screen

I

The Ohio State University

1 9.

Enter Bearing Design Parameters Bearing Length (in)................. 1.0 Bearing Radius (in).................. 0.5 Radial Clearance (in)............... 0.000

II

Grind, File, Lap

I %oothMember

I Enter .Design Parameters

I

I

Fig. 8 Parameter input screen

I


I

Fig. 9 Optimizationoutput screen

I

I

~~

The Ohio State University

Your Design Has A Match Index of 0.01

I

I

o Your bearing design is incompatible. You did not meet your load requirements.

This research is funded partly by the National Science Foundation DMC-8810824, and the Ohio State University seed grant.

SUGGESTDNS:

Fig. 10 DCA output screen

A unique computer aid was developed to assist the engineer in designing a herringbone grooved journal bearing. Generally, software packages deal with only optimization or design rules. However, this program is unique because, it integrates both the numerical optimization methods required for the design of hemngbone journal bearings, and A1 techniques needed for life cycle design. We feel that by incorporating both optimization and A1 that the design for hemngbone journal bearings will be easier and a less expensive bearing will be produced. Conventionally, the design decisions are made sequentially with an iterative process until a satisfactory design has been reached. Combining DCA with the optimization has the advantages of evaluating the overall design at once from various viewpoints. DCA handles not only totally acceptable and unacceptable compatibilities, but assesses the relative desirability of a possible choice. In the future, we plan to expand this program to include additional design rules. (eg. material selection, type of bearing mounting, etc.) Also, we plan on incorporating the numerical optimization analysis for stability of externally pressurized herringbone grooved journal bearings. Finally, we would like to utilize the concept of Rule-based Sensitivity Analysis (RSA). RSA would review the suggested design changes from DCA and evaluate their effectiveness on the entire design. For example, DCA may suggestion changing the radial clearance or the bearing length. RSA would take this information and analyze the effects of the entire design when one of the suggested changes is made. Then, RSA would inform the designer of the best fix solution to the design. We believe that by combining the power of both numerical optimization and DCA, we have created a useful tool for engineers. Our system will prevent subtle incompatibilities that may seriously undermine the design. This feature will help not only novice designers, but also experienced designers.

1 0 . ACKNOWLEDGEMENTS

o Reduce Radial Clearance

Press the Space Bar to Continue

CONCLUSION

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References Dixon, J.R. and Simmons, M.K. (1983) Computers that design: expert systems for mechanical engineers. ASME Computers in Mechanical Engineering, Nov., pp.10-18. Dixon, J.R. and Simmons, M.K. (1985) Expert system for mechanical design: a program of research. ASME paper No. 85-DET-70. Grassam, N. and Powell, J. (1964) Gas Lubricated Bearings. Butterworths, London. pp. 27-84. Hamrock, B.J. and Fleming, D.P. (1971) Optimization of self-actidg Hemngbone journal bearings for maximum radial load capacity. NASA Technical Note, NASA TN D-6351. Ishii, K. and Sugeno, S. (1985) A model of human evaluation process using fuzzy measure. Int. J. of Man-Machine Studies, 22, pp.19-28. Ishii, K. and Barkan, P. (1987a) Rule-based sensitivity analysis--a framework for expert systems in mechanical design, in Gero, J. (ed.), Expert systems in Computer -aided Design, North-Holland, Amsterdam, pp. 1979-198. Ishii, K and Barkan, P. (1987b) Design Compatibility Analysis--a framework for expert systems in mechanical design. ASME Computers in Engineering 1987. Vol. one, pp.95-102. Ishii, K., Adler. R. and Barkan, P. (1988a) Knowledge-basedSimultaneous Engineering using Design CompatibilityAnalysis. Artificial Intelligence in Engineering: Design, Computational Mechanics Publications, Southampton. pp.361-378. Juvinall R. (1983) Fundamentals of Machine Component Design. John Wiley and Sons. pp 387-425. Lin, G. (1988) A Knowledge-based Expert System for the Design of Bearings, MS Thesis, Department of Mechanical Engineering, The Ohio State University. Rieger, N.F. (1966) Design of Gas Bearings. Vol. I Design Notes. Mechanical Technology, Inc., p. 6.1.35. Vohr, J.H. and Chow, C.Y. (1965) Characteristicsof Hemngbone-Grooved,Gass Lubricated Journal Bearings. J. Basic Engineering., vol. 87, no. 3, pp. 568-578. Waldron, K.J. and Waldron, M.B. (1987) An Expert System for Initial Bearing Selection. ASME paper #86-DET-125.

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PaperXVl(ii)

Bearingselection usinga knowledgebasedsystem R.T. Griffin, M. J. Winfield and S. S. Douglas

I n d u s t r y i s b e g i n n i n g t o realize t h e need f o r t h e u t i l i z a t i o n o f e x i s t i n g t r i b o l o g i c a l knowledge v i a e f f i c i e n t , a c c e s s i b l e and i n t e l l i g i b l e t e c h n o l o g y t r a n s f e r t e c h n i q u e s . One a p p r o a c h which may b e s u i t a b l e f o r p r o v i d i n g s u c h a t r a n s f e r p a t h is a r t i f i c i a l i n t e l l i g e n c e ( A I ) . To d e m o n s t r a t e i t s s u i t a b i l i t y , two p r o t o t y p e knowledge based s y s t e m s (KBS) were d e v e l o p e d f o r t h e a p p l i c a t i o n domain o f r o t a r y r o l l i n g - e l e m e n t b e a r i n g s e l e c t i o n , o n e w i t h a n e x p e r t s y s t e m (ES) s h e l l , t h e o t h e r a n a r t i f i c i a l i n t e l l i g e n c e programming l a n g u a g e . The p r a c t i c a l i t i e s of a c q u i r i n g knowledge a b o u t t h e domain from d o c u m e n t a t i o n and r e l e v a n t a u t h o r i t i e s is o u t l i n e d and t h e r e p r e s e n t a t i o n of t h e knowledge is d e s c r i b e d . The s y s t e m d e s i g n , o p e r a t i o n and r e s u l t s are d e s c r i b e d and a comparison of t h e two s y s t e m s d e v e l o p e d is p r o v i d e d . 1

INTRODUCTION

I t is r e c o g n i z e d t h e t r a n s f e r of t r i b o l o g i c a l knowledge from academia t o companies competing i n t h e m a r k e t p l a c e r e q u i r e s improvement ( 1 ) . Recent developments i n t e c h n o l o g y t r a n s f e r u t i l i z e d a t a b a s e t e c h n i q u e s . Another a p p r o a c h which p o t e n t i a l l y e x h i b i t s f a v o u r a b l e characteri s t i c s f o r e f f e c t i n g t e c h n o l o g y t r a n s f e r is knowledge b a s e d s y s t e m s ( 2 ) . Knowledge b a s e d s y s t e m s ( 3 ) have t h e a b i l i t y t o e x p l i c i t l y r e c o r d knowledge i n a form r e a d i l y u s e f u l t o u s e r s t o g e t h e r w i t h a computer program to m a n i p u l a t e and ' r e a s o n ' w i t h t h a t knowledge. The aim o f t h i s p a p e r i s t o i l l u s t r a t e t h e s u i t a b i l i t y of knowledge b a s e d s y s t e m s as a means t o e f f e c t t e c h n o l o g y t r a n s f e r . The a p p l i c a t i o n domain chosen t o e v a l u a t e a knowledge b a s e d a p p r o a c h was t h e s e l e c t i o n of r o t a r y rolling-element bearings. Bearing s e l e c t i o n was chosen f o r i t s i m p o r t a n c e t o m e c h a n i c a l e n g i n e e r i n g , and h a s been l i m i t e d t o two s u p p o r t i n g b e a r i n g l o c a t i o n s which i s t h e most common a p p l i c a t i o n . Knowledge based s y s t e m s are b e i n g used i n many m a n u f a c t u r i n g and e n g i n e e r i n g a p p l i c a t i o n s ( 4 , 5 ) , e s p e c i a l l y i n t h e d e s i g n domain (6,7,8). Bearing s e l e c t i o n is frequently e n c o u n t e r e d w i t h i n t h e d e s i g n a c t i v i t y and t e c h n i q u e s are a v a i l a b l e t o assist i n t h i s p r o c e s s ( 9 , 1 0 ) , g i v i n g f u n c t i o n a l and q u a l i t a t i v e g u i d a n c e . I n order t o f u l l y t r a n s f e r a t e c h n o l o g y i t is o u r recommendation t h a t f u n c t i o n a l , q u a l i t a t i v e and q u a n t i t a t i v e a s p e c t s of t h e s e l e c t i o n p r o c e s s need t o b e c o n s i d e r e d . T h i s p a p e r r e p o r t s t h e development of knowledge b a s e d s y s t e m s d e s i g n e d t o assist t h e s e l e c t i o n of r o t a r y r o l l i n g - e l e m e n t b e a r i n g s .

2.1 Knowledge a c q u i s i t i o n T h i s is a demanding t a s k and t h e f o l l o w i n g g e n e r a l d i f f i c u l t i e s were e n c o u n t e r e d : ( 1 ) A s a p r o c e s s i t is time consuming. ( 2 ) Access t o r e l e v a n t e x p e r t ( s 1 was usually limited. ( 3 ) E x p e r t ( s ) t e n d t o meander from s p e c i f i c p o i n t s under discussion. ( 4 ) The knowledge o b t a i n e d from a n e x p e r t is n o t u s u a l l y i n a form e a s i l y encoded w i t h i n a knowledge b a s e d system. Many knowledge a c q u i s i t i o n t e c h n i q u e s are c u r r e n t l y e s t a b l i s h e d , t h e most commonly used b e i n g d e s c r i b e d by Hart ( 1 1 ) . T h r e e knowledge a c q u i s i t i o n t e c h n i q u e s were used Por t h e b e a r i n g s e l e c t i o n p r o j e c t . F i r s t l y , documentat i o n a s s o c i a t e d w i t h b e a r i n g s and b e a r i n g select i o n were s t u d i e d ( 1 2 ) . S e c o n d l y , t h e r e p e r t o r y g r i d t e c h n i q u e ( 1 3 ) was u s e d d u r i n g d i s c u s s i o n s and i n t e r v i e w s w i t h a b e a r i n g s e l e c t i o n e x p e r t . I n e s s e n c e , t h e g r i d p r o d u c e s a relief map of t h e i m p o r t a n t c o n s i d e r a t i o n s of t h e e x p e r t during t h e s e l e c t i o n process. Figure 1 i l l u s t r a t e s a g r i d , h e r e a number o f b e a r i n g t y p e s are r a t e d a g a i n s t a number of b e a r i n g a t t r i b u t e s . An a n a l y s i s performed on t h e g r i d is used t o e x t r a c t a h i e r a r c h y of b e a r i n g t y p e s and i n f e r e n c e r u l e s f o r s e l e c t i o n . The i n f o r m a t i o n o b t a i n e d u s i n g t h e r e p e r t o r y g r i d c a n b e viewed a s a set of examples of s e l e c t i o n strategies. T h i s enabled a t h i r d t e c h n i q u e called rule i n d u c t i o n ( 1 4 ) t o b e u s e d which a u t o m a t i c a l l y g e n e r a t e s i n f e r e n c e r u l e s from examples. 2.2 Knowledge r e p r e s e n t a t i o n

2

KNOWLEDGE ENGINEERING

T h e r e are two p h a s e s a s s o c i a t e d w i t h knowledge e n g i n e e r i n g ; t h e f i r s t p h a s e is t h e a c q u i s i t i o n of knowledge and t h e second is t h e r e p r e s e n t a t i o n of knowledge w i t h i n a formalism:

Many r e p r e s e n t a t i o n f o r m a l i s m s are a v a i l a b l e , t h e most common and p o p u l a r b e i n g p r o d u c t i o n r u l e s (151, frames ( 1 6 ) , s e m a n t i c n e t s ( 1 7 1 , and l o g i c ( 1 8 ) . A r i s i n g from t h e knowledge a c q u i s i t i o n a h i e r a r c h y of c o n s i d e r a t i o n s were

490 i d e n t i f i e d which p r o v i d e d a p r o c e d u r a l view of how t h e e x p e r t u t i l i z e d h i s knowledge i n t h e form o f a tree s t r u c t u r e similar t o t h a t of f i g u r e 2. T h i s t y p e of knowledge s t r u c t u r e readily lends itself t o translation i n t o r u l e s f o r a r u l e - b a s e d s y s t e m , which u s e s knowledge c o n s t r u c t s of t h e form shown i n f i g u r e 3. If a set of c o n d i t i o n s e x i s t t h e n a c o n c l u s i o n c a n b e d e r i v e d . Using s u c h a r e p r e s e n t a t i o n formalism allows e i t h e r a n e x p e r t s y s t e m s h e l l s u c h as Apes (191, which is a f r o n t - e n d t o Micro-Prolog, o r a n a r t i f i c i a l i n t e l l i g e n c e programming l a n g u a g e s u c h a s , M i c r o - P r o l o g ( 2 0 ) t o b e cons i d e r e d f o r s y s t e m development. A s h e l l is a c o m p l e t e system w i t h o u t a knowledge b a s e . S h e l l s are used f o r r a p i d development o f p r o t o t y p e s by i n s e r t i o n of a knowledge b a s e .

Micro-Prolog is a s o f t w a r e t o o l w i t h which bespoke s y s t e m s c a n b e d e v e l o p e d . It is a l o g i c programming l a n g u a g e and is a v a i l a b l e upon p e r s o n a l c o m p u t e r s . F i g u r e 4 shows examples of Micro-Prolog c o d i f i c a t i o n f o r t h e knowledge i l l u s t r a t e d i n f i g u r e 2. SYSTEM SPECIFICATION

3

F o l l o w i n g t h e knowledge e n g i n e e r i n g a c t i v i t y t h e s y s t e m r e q u i r e m e n t s were i d e n t i f i e d as:

select a previously i d e n t i f i e d b e a r i n g a r r a n g e m e n t from a s e t of s t a n d a r d a r r a n g e m e n t s f o r

( 1 ) Where p o s s i b l e ,

w

I-

z x W w

wo

z

a a a

FIGURE 2-TREE STRUCTURE FOR BEARING SELECT10 N IF < CONDITION-1 > AND < CONDITION-2 >

FIGURE 1 -EXAMPLE REPERTORY GRID FOR BEAR ING SELECT1ON

AND < CONDITION-N > THEN < CONCLUSION >

FIGURE 3-GENERAL FORM OF RULES

49 1 WI

((ARRANGEMENT -COMB) ( COMBl -COMB) ) ((ARRANGEMENT -COMB) (COMB2 -COMB) ((ARRANGEMENT -COMB) (COMB3 -COMB) 1 ((ARRANGEMENT -COMB) (COMB4 -COMB) ((COMB1 -COMB) (FIXED-END-CLASS-A -TYPE11 (FREE-END-CLASS-B -TYPE21 (EQ -COMB (-TYPE1 -TYPE2))

a) Micro-Prolog code for rules if then if then if then if then

the the the the the the the the

COMBl is -COMB ARRANGEMENT is COMB2 is -COMB ARRANGEMENT is COMB3 is -COMB ARRANGEMENT is COMB4 is -COMB ARRANGEMENT is

-COMB -COMB -COMB -COMB

if the FIXED-END-CLASS-A is -TYPE1 and the FREE-END-CLASS-B is -TYPE2 then the COMBl is (-TYPE1 -TYPE21 b) English translation for rules

FIGURE 4-RULES CODED IN MICRO-PROLOG s p e c i f i c a p p l i c a t i o n s and select t h e i n d i v i d u a l b e a r i n g from t h e d a t a b a s e , or ( 2 ) Undertake a fundamental b e a r i n g s e l e c t i o n study. I n e s s e n c e t h e f u n d a m e n t a l s t u d y must be capable o f s e e k i n g the best p o s s i b l e arrangement o f b e a r i n g t y p e s f o r a n a p p l i c a t i o n , and u l t i m a t e l y convert t h e bearing type i n t o a physical component e x t r a c t e d from a d a t a b a s e o f b e a r i n g s . To s a t i s f y t h i s , t h e s y s t e m h a s t h r e e l e v e l s of i n f o r m a t i o n which i t u t i l i z e s t o i n f e r a s o l u t i o n . On t h e f i r s t l e v e l t h e f u n c tional requirements associated w i t h t h e applicat i o n are e s t a b l i s h e d , a n example b e i n g t h e requirement f o r a bearing to take both r a d i a l and a x i a l l o a d s . The s e c o n d l e v e l i d e n t i f i e s t h e q u a l i t a t i v e a s p e c t s of t h e a p p l i c a t i o n . For example a t t h i s l e v e l c o s t and r e l i a b i l i t y c o u l d be c o n s i d e r e d . The t h i r d l e v e l i d e n t i f i e s t h e q u a n t i t a t i v e a s p e c t s f a c i l i t a t i n g t h e datab a s e s e a r c h . For e x a m p l e , b e a r i n g l i f e , b e a r i n g b o r e diameter. The domain h a s i n i t i a l l y b e e n c o n s t r a i n e d to a s i n g l e g e n e r i c arrangement o f bearings, t h a t o f o n e o r more b e a r i n g t y p e s a t two s u p p o r t i n g l o c a t i o n s . The b e a r i n g t y p e s a d d r e s s e d are shown i n f i g u r e 5. 4

SYSTEM DESIGN

The s y s t e m has f o u r major c o m p o n e n t s , t h e i r r e l a t i o n s h i p s are shown i n f i g u r e 6 and d e s c r i b e d as follows:

3 NIN 3 I l V 3 1 3 s

13Vl N03-1 NIOd' dnod 3h00tl9'333 0-Mod-3 19NIS

FIGURES-HIERARCHY OF BEARING TYPES WITHIN BEARING SYSTEM ( 1 1 The KNOWLEDGE BASE i s a s t o r e f o r t h e

domain knowledge. T h i s i n c l u d e s : a d i c t i o n a r y o f knowledge items, menus and forms; a s e t of f a c t s a b o u t t h e domain; a s e t of c o n s t r a i n t s on t h e allowable combinations of user input d a t a ; a s e t o f s e l e c t i o n r u l e s ; and a s e t of p r o c e d u r e s f o r n u m e r i c a l calculations. ( 2 ) The PROBLEM SOLVER c o n t r o l s t h e s e a r c h f o r a s o l u t i o n a n d t h e method by w h i c h i n f e r e n c e s are made. The d e p t h - f i r s t search and backward c h a i n i n g i n f e r e n c e s t r a t e g y o f MicroProlog h a s b e e n selected. I n t h i s

492 s t r a t e g y t h e p r o b l e m s o l v e r is g i v e n an a b s t r a c t g o a l to prove o r otherwise, i n a top-down a p p r o a c h . A goal is a c o n f i g u r a t i o n o f b e a r i n g s . The knowledge base and d a t a b a s e is s e a r c h e d i n a d e p t h - f i r s t manner t o i d e n t i f y and s e l e c t a b e a r i n g t y p e a n d component t o m a t c h t h e r e q u i r e m e n t s of t h e a p p l i c a t i o n . ( 3 ) The INTERFACE p r o v i d e s a f a c i l i t y f o r communication b e t w e e n u s e r and s y s t e m u s i n g forms, windows and menus. ( 4 ) The DATABASE i s a s t o r e f o r c o n s t a n t domain d a t a . T h i s i n c l u d e s a s e t of c o m p o n e n t s from w h i c h a s o l u t i o n c a n be s e l e c t e d , t o g e t h e r w i t h i n t e r p o l a t i o n tables t o s u p p o r t n u m e r i c a l calculations. 5

SYSTEM OPERATION AND RESULTS

The s y s t e m o p e r a t e s a t t h r e e l e v e l s as shown i n f i g u r e 7. On t h e f i r s t l e v e l t h e u s e r i s i n t e r a c t i v e l y r e q u e s t e d v i a a s e t of f o r m s t o e n t e r d a t a concerning t h e a p p l i c a t i o n under i n v e s t i g a t i o n . A t t h e second l e v e l t h e problem s o l v i n g a c t i v i t y which is t h e s e l e c t i o n p r o c e s s i s e n c o u n t e r e d . Here t h e p r o b l e m s o l v e r i n t e r r o g a t e s t h e knowledge b a s e t o i d e n t i f y t h e b e a r i n g a r r a n g e m e n t and b e a r i n g t y p e f o r t h e

a p p l i c a t i o n , and also selects t h e i n d i v i d u a l component from t h e d a t a b a s e . D u r i n g t h i s a c t i v i t y , i n t e r a c t i v e q u e s t i o n s are prompted t o the user to supply additional information i f and when t h e s y s t e m r e q u i r e s i t . The t h i r d level reports the solution t o t h e user. Figure 8 i l l u s t r a t e s a typical set of applicat i o n r e q u i r e m e n t s and a s o l u t i o n d e r i v e d t o s a t i s f y t h e requirements. 6

CONCLUSIONS

Two s y s t e m s h a v e b e e n d e v e l o p e d , i n i t i a l l y a n e x p e r t s y s t e m s h e l l was u s e d t o test a n d v a l i d a t e some o f t h e s i m p l e r knowledge s t r u c t u r e s . U n f o r t u n a t e l y , a s t h e knowledge a s s o c i a t e d w i t h t h e s e l e c t i o n p r o c e s s was b u i l t up t h e s h e l l performance d e t e r i o r a t e d t o an unacceptable l e v e l . The s e c o n d s y s t e m was d e v e l o p e d as a b e s p o k e s y s t e m u s i n g t h e M i c r o - P r o l o g programmi n g language and encouraging r e s u l t s have been o b t a i n e d . A d i s a d v a n t a g e of t h e p r e s e n t s y s t e m is t h e l a c k o f a n e x p l a n a t i o n f a c i l i t y t o support t h e user during interactions with the system. T h i s work d e m o n s t r a t e s t h a t a form of technology t r a n s f e r can be achieved through a knowledge b a s e d s y s t e m s a p p r o a c h . An e x p e r t ' s knowledge is e n c a p s u l a t e d i n t h e form o f r u l e s w i t h i n a c o m p u t e r s y s t e m . The c r u x of s u c h s y s t e m s i s t h e knowledge w h i c h t h e y encompass. T h e r e f o r e t h e q u a l i t y of t h e knowledge base i s a r e f l e c t i o n of t h e knowledge e n g i n e e r i n g a c t i v i t y . A c a v a l i e r a t t i t u d e t o knowledge e n g i n e e r i n g w i l l r e s u l t i n a system i n which t h e u s e r w i l l have dubious confidence. F u t u r e d e v e l o p m e n t s i n c l u d e t h e d e s i g n of a n e x p l a n a t i o n f a c i l i t y a n d t h e i n t e g r a t i o n of g r a p h i c s w i t h i n t h e system. I n a d d i t i o n , t h e

FILLING^

FILLING

USER

I

D ATAl

d

I

REPORT

1

I

NOTHER,

E NO FIGURE 6 -COMPONENTS OF BEARING SYSTEM

FIGURE 7 -OPERATION OF BEARING SYSTEM

Data: application-domain = OTHER env-temp-changes-negligible dist-fixed-free-negligible angular-misalignment = very-small degree-of-rigidity = very-low applied-radial-load-fixed-end = 3 kN applied-radial-load-free-end = 2 kN applied-axial-load = 2 kN shaft-diameter-max = 500 mm shaft-diameter-min = 258 mm housing-bore-diameter-max = 600 nun housing-bore-diameter-min = 510 mm snap-ring-type = without protection = none rotational-speed = 750 rpm environmental-temperature-max = 50 C time-or-revs-life = revs revs-life = 6 million revs

fixed-end = free-end BEARING TYPE: single-row-deep-groove-ball FEASIBLE COMPONENT NUMBERS: 6068, 6072, 6976, 6076, 6980, 6080

FIGUREB-SOLUTION INFERRED USING DATA operation of the system will be enhanced to include the recording and analysis of selection failures (9) given that the user's requirements are too stringent and no solution is found.

7 ACKNOWLEDGEMENT The authors gratefully acknowledge Jack Schofield of Liverpool Polytechnic and Mike Goodwin of North Staffordshire Polytechnic for their participation during knowledge acquisition sessions. We also thank Dr. Conway-Jones of The Glacier Metal Co. Ltd. together with Tony Cuff and Gerry Madden of NSK Bearings Europe Ltd. for their useful comments concerning the system operation.

(8) GRIFFIN, R.T., DOUGLAS, S.S. and WINFIELD, M.J. 'SELECTOR A Knowledge Based System for Mechanical Engineering Design', 1 2 t h International Congress for Statistics, Scientific Computations, Social and Demographic Research, Ain Shams University, Cairo, Egypt, March 28 April 2, 1987. (9) DEWAN, D. and LARSEN, K.A. 'DABKON a knowledge based system for the selecticn of bearings', 6th International Workshop on Expert Systems and their Applications, Avignon, France, 28-30 April, 1986, Volume 2, 1237-1250. ( 1 0 ) FAGAN, M.J. 'Expert systems applied to mechanical engineering design - experience with bearing selection and application program', Computer-Aided Design, Sept. 1987, Volume 19, Number 7, 361-367. ( 1 1 ) HART, A. 'Knowledge Acquisition for Expert Systems', 1986 (Kogan Page). (12) NSK 'NSK Ball and Roller Bearings Catalogue', 1987 (Nippon Seiko K.K.). (13) BEAIL, N. (Ed) 'Repertory Grid Technique and Personal Constructs: Applications in Clinical and Educational Settings', 1985 (Croom Helm Ltd. ) (14) BLOOMFIELD, B.P. 'Capturing expertise by rule induction', The Knowledge Engineering Review', March 1987, Volume 2, Number 1 , 55-63. (15) DAVIS, R. and KING, J. 'An Overview of Production Systems', Machine Intelligence 8, 1977 (Ellis Horwood Elcock and Michie EdS.), 300-332. (16) FIKES, R.E. and HEHLER, T.P. 'The Role of Frame-Based Representation in Reasoning', 1985 (Intellicorp Technical Article). (17) BRACHMAN, R.J. 'What's in a Concept: Structural Foundations for Semantic Networks', International Journal of ManMachine Studies, 1977, Volume 9, 127-152. (18)HAMMOND, P. and SERGOT, M. 'Logic Programming for Expert Systems', 1984 (Chapman and Hall 1 . (191 HAMMOND, P. and SERGOT, M. 'Apes: Augmented Prolog for Expert Systems', 1987 (Logic Based Systems Ltd.). (20)CONLON, T. 'Learning Micro-Prolog: A Problem Solving Approach', 1985 (AddisonWesley)

-

-

.

-

.

References SIBLEY, L.B., PETERSON, M.B. and LEVINSON, T. 'An Assist for Tribological Design', Mechanical Engineering, September 1986, 68-74. TALLIAN, T.E..'Tribological Design Decisions Using Computerized Databases', Journal of Tribology - Transactions of the ASME, July 1987, Volume 109, 381-387. WATERMAN, D.A. 'A Guide to Expert Systems', 1986 (Addison-Wesley). BERNOLD, T. (Ed) 'Artificial Intelligence in Manufacturing', 1987 (North-Holland). SRIRAM, D. and ADEY, R. (Eds) 'Applications of A1 in Engineering Problems', 1986 (Springer-Verlag) GERO, J.S. (Ed) 'Knowledge Engineering in CAD', 1985 (North-Holland). SMITH, A. (Ed) 'Knowledge Engineering and Computer Modelling in CAD', 1986 (Butterworths).

.


495

Paper XVl(iii)

Tribologyaids for designers C. J. Thijsse

This paper deals with a systematic approach of the tribological knowledge with the intention to render it easily accessible for designers. Delimitation of the knowledge that is suited for this purpose is required. Tribological evaluation of a construction takes place via a checklist. It has been indicated where it is necessary to implement the knowledge in readily applicable computer programs. In those w e s where insufficientdata is available or where use has to be made of empirical facts, the tribological knowledge has been implemented in the TRIBEXSY expert system. The set-up of this system is given. 1. INTRODUCTION

Within the Philips Concern, R&D activitiesare carried out at a central level by approximately So00 people. Roughly 4OOO people, distributed between eight laboratories in six countries, are occupied in research. Of these, 2400 work at the Research Laboratories in Eindhoven. Apart from the Research Laboratories, Eindhoven also has the Centre For manufacturing Technology (CFT), which operates as a centre of knowledge within Philips. The CFT has about lo00 employees and provides technical support in the form of turnkey projects, research projects and consultation to the various Product Divisions, where the products are manufactured. Tribological research is carried out at both the Research Labs and the CFT. In view of its set-up, the CFT's research must be aimed at finding solutions for tribological problems. Within the CFT, in the Mechanics and Mechanisms Department, there is a tribology group of eight people. The objective of this group is the reduction of tribological problems in both products and production means. This can only be achieved if the tribological knowledge availableat the CFT and the Research Labs is transferred in a user-friendly form to the countless designers at Philips. A designer designs a mechanical construction from a list of specifications.The designer therefore thinks more in functions than in physical principles. In this train of thought, it is not important to know, for example, whether the construction lifetime is limited by adhesive or abrasive wear. It is more important to determine beforehand whether a certain design will attain the desired Lifetime. This means that clear ways must be indicated for the evaluation of the tribological aspects of a design. Seeing that tribology is merely one aspect of the design, the evaluation may not take up too much time and the knowledge required for the evaluation must be easily accessed. If we look at the above, we see that a subdivision of tribology into full film lubrication, mixed and boundary lubrication and dry running systems,although desirable from a research point of view, is of little use to the designer. The subdivisionis too strongly based on physical principles. A better approach is obtained by subdivision into construction, lubrication, (surface of) material and environment. The most important mechanical specifications for Philips' constructions are static and dynamicbehaviour (in time) and, where cleanrooms are concerned, the dust production (the quantity and type of wear particles). In view of the fact that dustfree construction is a still-developing discipline, we have not yet started developing tribological evaluation aids. The activities are at the moment concentrated in the research phase. We therefore limit ourselvesto the static and dynamic behaviour of the construction during its lifetime. For the parts that move with respect to each other, we translate the design specifications directly into constructive aspects, such as loading, type of movement, shape and permissible wear height. The specifrcationswith respect to static and dynamic behaviour are therefore enclosed in the construction.

For an actual realisation of the design, one requires building blocks which are formed by: a) the lubrication film, whereby the type of pressure build-up and the lubricant are important parameters. b) the (surface of) materials, with elasticity, hardness and roughness as parameters. The environment forms the operating boundary conditions in which the system has to work. This allows us togive the followingproblem definition (which is useful for designers): "Which sort of building blocks has to be selected so that the design specifications can be satisfied under the environmental boundary conditions?" It is necessary to indicate which failure criteria have to be included in the tribological evaluation and which (simple to handle) aids have been developed. This is explained in more detail in the following sections. 2. FAILURE CRITERIA

The tribological failure criteria can be subdividedinto two main groups: wear and friction. 2.1 Failure criteria with resoect to wear

The most frequently occurring wear mechanisms in Philips' constructions are:

- plastic deformation: - adhesive wear; - abrasive 2-body wear; - abrasive 3-body wear; - surface fatigue; - fretting corrosion. The evaluation means available to the designer are now described in succession. 2.1.1 Plastic deformation

Most Philips products are small and therefore have small contact surfaces. This means high contact pressures, with resulting high wear. In production machines with cam to cam-followerroller drives, high contact pressures occur. It maybe assumed that, for reliable operation, the contact materials (seen at macro scale) may not undergo any plastic deformation in most cases. We use the Hertzian contact stress as a measure of the contact pressure and have developed a computer (PC) program for a quick calculation of this contact stress. For doubly curved surfaces that are pressed together with a certain force, this program can calculate the Hertzian contact tension, the size of the contact ellipse and the contact

496 stiffness.Literature information from Horowitz [6] have been included in the program. Should a traction force be present along the surfaces, a proposed estimated correction from Bayer and Ku [l]is added. By correctly comparing the actual contact stress with the permissible stress for various materials, an insight is obtained into the applicability of certain materials for a selected contact geometry. If the correct materials cannot be found, it will be necessary to modify the contact geometry.

correct material choice can be made for the contact, with the aid of a database. This database, which operates on a PC, is filled with the data of roughly 600 test series. The tests (mainly pin-disc and pin-ring) have been carried out in our laboratory under varying conditions for:

- the constructional aspects (load, contact shape, speed); - the lubrication (dryrunning, boundary lubrication, type of lubrication);

- the surfaces (metal, plastic, surface treatment, coating,

2.1.2 Adhesive and abrasive 2- and 3-body wear

roughness) and - the environment (temperature, humidity, type of gas).

As already mentioned, a designer is more interested in the lifetime of

An identical database with literature data is being built.

a construction (i.e. speed of wear) than in the physical background of the wear. For this reason, a construction is evaluated with the aid of the wear factor (k-value) proposed by Archard. If we involve the innuence of the wear on the static and dynamic behaviour, then the only important parameter is the change in shape of the wearing surfaces. This change is closely related to the wear height. For general usability, however, wear values are mostly presented in the form of wear factors. To be able to quickly assess the performance of the construction on the basis of the permissible wear height with the aid of actual wear factors, it is necessary to make a simple translation from wear height to wear factor. For this reason, a computer (PC) program has been written to calculate the maximum permissible wear factor oE

Plastic-metal systems can be tested for the permissible pv- and ptvalue with a computer program based on Erhard's and Strickle's formulae [4].

- the permissible wear height - the desired lifetime - the movement pattern of the surfaces with respect to each other; -the contact point with respect to the surfaces; -the contact force; -the shapes of the contacting parts. This value must be compared with the probable actual wear factor that is found under various tribological circumstances. In this way, we can determine from which materials the wearing surfaces have to be made and what the desired lubrication regime must be. To quickly obtain a first impression of the applicable material lubrications and lubrication regimes, use is made of the graph (see fig. 1) from Verbeek [lo]. This graph is composed from the many experiments carried out in our laboratory and shows the relationship between the probable wear factor and the various tribological systems. If one enters the permissible wear factor (determined by the previously-mentionedcomputer program) for a selected construction on the y-axis, and the selected tribological system on the x-axis, then a quick insight is obtained into the size of the wear problems due to a low permissible wear factor to be expected. In the area above the indicated band, no wear problems are expected; in the area below the band, the chance of wear problems is virtually 100%. In the area inside the band, wear problems can be expected. If one comes out inside or below the band, then the design can be improved either by increasing the permissible wear factor (modifying the construction) and/or by selecting another "more to the left" tribology system (different materials, different lubrication conditions). Should it appear that a certain measure of lubrication is required to fulfil the required lifetime (e.g. full film lubrication), then it must be possible to easily assess whether this can be achieved with the aid of self acting bearing systems. For contra-shaped contacts, we have therefore developed a PC program that calculates the lubrication conditions for various lubricants, on the basis of the work by Hamrock, Dowson and Higginson [2], [5] and by Johnson [7]. For conformal situations, although more than sufficient knowledge is available, we have not yet developed a user-friendly program for the designer. This must be one of our activities for the near future. Should the required lubrication regime not appear feasible, then externally pressurised bearing systems must be considered. If these bearing systems are not used, then the construction will have to be modified in such a way that the maximum permissible wear factor is increased. In most cases, this will mean a reduction of the contact pressure. If the construction has an acceptable maximum wear factor, then a

fig.1

T r i b o s y s t e m s and t h e i r s p e c i f i c wear f a c t o r s

2.1.3 Surface fatigue

If certain parts of a design are subject to a varying contact load, than a check will have to be made to see whether the lifetime of the parts is limited by surface fatigue. Empirical formulae have been compiled for example of data from the Literature [3], [8] and [9]. They express the relationship between the magnitude of the contact stress, the number of changes in loading, lubrication conditions and hardness. These formulae have proved their use in many places, both for our products and for our production means. 2.1.4 Fretting corrosion

Fretting corrosion does not only occur in joints where the components unintentionally vibrate with respect to each other. In precision engineering constructions, we often see a situation where two components have a low amplitude oscillating movement with respect to each other.

497

If the double amplitude is smaller than the length of the contact and if the contacting components are made of metal, this almost always leads to fretting corrosion problems. Take note that the contact area can increase in contra-shaped situations. We maintain, therefore, the simple rule that constructions must be so designed that the contact length is (much) less than the double amplitude of the contacting components. This has the dangers of plastic deformation and of a too small permissible wear factor. After redesign, the contact must therefore always be assessed according to the procedures described in sub-paras. 2.1.2 and 2.1.3. If problems ensure, then the amplitude with respect to the rest of the construction is mostly very small and the solution can be found in the application of elastic elements, such as leaf springs or intermediate layers of plastic. 2.2 Failure criteria with resDect to friction

The problems involved with friction arise because the friction is:

- too high; - too low; - unstable.

To the right of the Stribeck curve we find the desirable situation with positive damping coefficient. This is the reason why the following rule applies: "The lower the relative speed in a guide, the lower the contact pressure and the higher the viscosityof the lubricant to be applied." If these attempts to end up sufficientlyto the right of the Stribeck curve are without success, use will have to be made of externally pressurised bearings because full film lubrication always shows a positive damping behaviour. 3. CHECKLIST

For the designer, the above-mentioned facts have been summarized in a checklist as an aid in the design of guides. 1) Because of all kinds of constructional boundary conditions, among them those from the viewpoint of friction, a first selection of the principle of guidance of force is determined by the wearing surfaces (e.g. solid, liquid, elastical element, magnetic). 2) Next, every mechanical contact has to be post-calculated and possibly adapted so as not to exceed the permissible contact stress (by means of the Hertz PC program).

To obtain an insight into the size of the friction coefficient that occurs under various tribological circumstances, we use the database mentioned in sub-para. 2.1.2. In practice, however, it appears that a deviation of 50% with respect to the values found in the database can be expected under not too unfavourable circumstances. The lowest and highest values of the coeficient of friction can therefore differ by a factor 3. With fluctuating environmental conditions, the value of this value can increase to 6 or more. The only advice we can give our designers is the rule that the friction requirements that is placed on a guide is always such that the coefficient of friction is either higher or lower than a certain value. Material combinations and lubrication conditions can then be selected such that the nominal value of the coefficient of friction is sufficiently far away from the danger zone. The integration of functions in a design which creates the requirement that the magnitude of the friction must be between two values must be avoided because it gives too little room for play. A stable dynamic behaviour is essential, in connection with a high positional accuracy requirement on both our products and production means. This means that stick-slip phenomena may not occur.For this reason, we have included Stribeck curves for many types of bearings. These types of curves can also be included for other guides than radial bearings. If the working area of a guide is too far to the left of the Stribeck curve (see fig. 2), the friction force along the surfaces will decrease as the speed of the surfaces with respect to each other increases. The guide displaysthe behaviour of a damper with a negative damping coefticient. If the rest of the construction contains insufficient damping, unstable behaviour (stick-slip) occurs.

3) In the case of oscillating movements, check whether the risk of fretting corrosion is present. If so, adapt the design according to the rules given in sub-para 2.1.4 and proceed to point 2.

4) Determine (by means of PC program "k-value")the permissible wear factor of the selected construction. By means of the graph in fig. 1and the empirical formulae for surface fatigue, estimations of the lifetime can be made. In case the required lifetime is greater than the estimated lifetime, the selected tribological system (contact material, lubrication) and/or the construction (load, movement, shape) require(s) adaptation. 5 ) If the conclusion from 4) is that lubrication is inevitable, it will be necessary to examine how far it is possible to build a lubrication film (PC program "EHL" and probably also externally pressurised bearings). If it turns out to be impossible to build a satisfactory lubrication film, the design will require renewed study and it will be necessary to return to point 1. 6) Because of points 2,3,4 and 5, the main dimensions of the wearing surfaces and the selection of the tribological system are fuced.

7) Make a choice from the two wearing surface materials (bulk material and possibly surface layer) and the lubricant (by means of the PC databases). 8) If the environment is too much of a limitingfactor in finding the correct solution, the environment must be adapted; if necessary through application of seals each having its own tribological problems. 9) In case full film is applied, optimization calculations can be performed.

We will not deal any further with the optimization calculations mentioned sub 9 since this topic is discussed in a separate contribution to this Leeds-Lyon conference. 84. EXPERT SYSTEM

Although the checklist with the mentioned evaluation aids appears to be very useful in practice, it was felt that a more extensive system was needed for the following reasons. IObNDAAY P-contact pressure I N / ~ I ?=dynamic viscosity I N r e c l d l

I

I I

fig.2

I I

The Stribeck curve

~ = f n c t i o nroefteient

I-]

W=arqular veluily

Illrecl

The way of evaluation mentioned above is rather complex so that automation will increase its user-friendliness. Upon the start of the design process, the desi er does not always have all the requested data at his disposal. TEs asks for a system that can work with these uncertainties; an expert system. The evaluation tools given above are based on knowledge that can be com rised fair1 well in models. However, more tribological knowlejge is availatle. But this knowledge is based more on separate facts known from practice. It is impossible to process all this

498 knowledge by hand during an evaluation cycle. Only the knowledge relevant to a certain design must be included in the evaluation and must thus be so stored that only the relevant data will be presented in a simple way. In those cases in which the knowled e is applied for an existing design that presents tribological probfems in practice, it will usually be more effective both for malung the diagnosis and for finding the correct solutions to discover the physical principles that play a role. Here it is possible to think of a solution model UI which ph sics are learnrepresented but do not at all come to the fore, or inview ing effect, only to a limited extent.

era

4.1 Svstemtwe The reasons cited above have led to the development of a prototype cxpert system. To achieve this we have fdled a commercially available shell (ENVISAGE of System Designers) with tribological knowledge. The first question to be answered is what the set-up of the system should be like; a tool during the design proces or a diagnosidrepair system for problems occurring in practice. One set-up does not automatically exclude the other. General experience with expert systems has taught us that it is many times more difficult to build a design system than to build a diagnosishepair system (fig. 3). Consequently, we started with a diagnosidrepair system in which we have tried to implement the knowledge in such a way that in future it can be used in an expert system for the design stage.

EASY

HARD

itself and, in case of a central lubrication system, in other contacts. It is important that the system knows its limitations. In case it is not possible to make the correct diagnosis, the telephone number of the CFT tribological group appears on the screen. If a diagnosis is made, which may also imply that the problem comprises more than one failure mechanism, a subset relevant to the diagnosis is taken from the total set of remedies present. The total set of remedies consists of approximately 100 constructive, materials and lubrication solutions. Next, this subset is passed through two filters. The first filter consists of process constraints. If a possible solution should consist of the application of a CVD-TiN layer, it will fust of all be necessary to check whether the dimensions of the part correspond with the dimensions of common CVD reactors. Moreover, other parts of the construction element that the wearing surface must be able to withstand the process temperature, whereas it must also be taken into account that the entire part will be provided with aTiN layer. If necessary, the possibility of building the part from smaller subparts will have to be examined. The second filter is formed by user constraints. If, for example, the mechanical point of contact also acts as an electric contact, full film lubrication will not be directly applicable. As previously mentioned, this filter also includes the requirements with respect to friction. The complete system comprises the above-mentioned checklist with evaluation tools, and further, about 200 empirical rules in the form of "IFA AND IF B THEN C . Here C represents an algorithm which performs an operation on the chance that something occurs or that something is possible.

IMPOSSIBLE

INTERPRETATION TRIBOLOGICAL

DIAGNOSIS

PROBLEM(S)

,

REMEDIES

MONITORING PREDICTION PLANNING

FRICTION

WEAR

DESIGN

DIAGNOSIS

I

REPAIR INSTRUCTION PROCESS CONTROL fig.3

4

PROCESS CONSTRAINTS

Feasibility of application classes

4.2 Failure criteria

Expert systems are only useful if the implemented knowledge is considered to be sufficientlyestablished by experts. There must also be sufficient knowledge available on the subject. This is the reason for implementing the wear problems occurring most frequently in our environment, i.e. the failure criteria mentioned subpara 2.1. As mentioned above, the knowledge on friction is more limited. That is why it has not been implemented in the actual system but it does play a role as a user constraint of possible remedies.

I POSSIBLE REMEDIES

fig.4

TRIBEXSY: general setup

4.3 TRIBEXSY a tribolopical emert system

The structure of the expert system is shown in fig. 4.Via a number of questions on the construction, the environment, the materials applied and the lubrication conditions, the chance of one or more failure mechanisms is determined. If one wants to use the system in the design stage, this is possible on the condition that a concrete elaboration of the system exists so that the answer need not often be too "Unknown",otherwise the probability of a correct outcome becomes very low. If the system is applied to find solutions for problems that have already occurred in practice, supplementary questions on the ambient conditions will be asked, while information must be given on the nature of the damage through comparison of the appearance of the actual damaged surfaceswithphotographsofsurfacesthat are representativeof thevarious types of wear. The knowledge has been so implemented that symptom solving is avoided as much as possible. If the diagnosis is, for instance, 3-body abrasive wear, the system will look for other wear mechanisms as a possible source of thud bodies, both in the contact to be considered

5. CONCLUSIONS

To render tribological knowledge usable for designers it will not only require systemization but also simplification. Since tribology contains a multitude of factual knowledge, it wiU be necessary to implement this knowledge in an automated system in view tf the accessibility. The tribological behaviour of a construction is subject to many external influences, thus rendering it virtually impossible to make forecasts with a 100%certainty. It is more a weighingof chances. An expert system is perfectly suited for laying down this type of knowledge. During the development of the expert system, it proved to be an advantage to be able to start from a certain d e f ~ t i o nof the problems. The system has been built for use within the Philips concern. As a result, a fairly good picture can be obtained of the conditions under which

499 tribological problems may occur and it is thus not necessary to model "the whole world". With the approach described in this paper, the most trivial wear problems can be avoided; in the case of very specific tribological problems the human tribological experts will have to be on stand-by to lend a hand. REFERENCES BAYER, R.G. and KU, T.C. 'Handbook of analyticaldesign for wear', 1964 (mcGregor, Plenum Press, New York). DOWSON, D. and HIGGINSON, G.R. 'Elastohydrodynamic Lubrication', 1966 (Pergamon Press, Oxford). DUDLEY, D.W. 'Wear Control Handbook', Chapter 'Gear Wear', 1980, A.S.M.E. 755-830. ERHARD, G. and STRICKLE, F. 'Gleitelemente aus Thermoplasten', Kunstoffe, 1972,a. HAMROCK, BJ. and DOWSON, D. 'Minimum Film Thickness in Elliptical Contacts for Different Regimes of Fluid Film Lubrication', N.A.S.A. Techn. Paper 1342, Oct. 1978. HOROWITZ, A. 'A contribution to the engineering design of machine elements involving contrashaped contacts', Israel Journal of Technology, 1971, Vo1.9, No.41. JOHNSON, K.L. 'Regimes of Elastohydrodynamic Lubrication', Journ. Mech. Eng. Science, 1970, Vo1.12, No.1. NIEMANN, G. 'Maschinenelemente', Zweiter Band 'Getriebe', 1960 (Springer Verlag, Berlin). R O W , C.N. and ARMSTRONG, E.L. 'Lubricant Effects in Rolling - Contact Fatigue', Lub. Eng., January 1982, Vo1.38, No.1. VERBEEK, H J . 'Tribological systems and wear factors', Wear 56,1979,81-92.


WRITTEN DISCUSSIONS AND CONTRIBUTIONS


503

WRITTEN DISCUSSIONS AND CONTRIBUTIONS

DISCUSSION

'Lubrication and Fatigue Analysis of a Cam and Roller Follower, B A GECIM

directions during these events. The position of sign change for the traction force is slightly after the top of the lift where the needle bearing torque is just enough to balance the inertia of the decelerating roller.

Mr H J van Leeuwen (Eindhoven University of Technology, The Netherlands)

'Prediction of Cam Wear Profiles' R H FRIES and C A ROGERS

This paper covers many interesting aspects of the tribological behaviour of a cam and roller follower contact, and I am looking forward to the release of the full paper. I would like to ask the following questions:

Dr J C Bell (Shell Research Ltd., Chester, UK)

SESSION Iv - CAHS

1. What is the origin of the very steep gradient in the film thickness at the transition between cam base circle and cam flanks? Can the author give some more information on the influence of the squeeze effect (how has it been modelled, what influence does it have)? 2.

The Johnson diagram for film thckness representations applies to entrainment effects only. When is it applicable for cam/follower EHD lubrication?

3.

At higher speeds the traction shows a sign change at Oo cam angle. Is it due to deceleration of the roller?

Reply by Dr B A Gecim (General Motors Research Labs, Warren, U S A )

I have a comment on the presentation of Dr Fries relating to the usefulness of the Archard wear model. At Thornton Research Centre we have been applying this model to automotive pivoted-follower valve train systems, and including a boundary/w, lubrication transition model. Some results for finger follower wear profiles were presented at a previous Symposium (Ref 1) showing good agreement of positions of wear maxim with those of experimental wear profiles. Recently Dr T A Colgan and I have applied this model to cam wear profiles with similarly g o d agreement with experimental wear maxima, and exhibiting similar features to those of Dr Fries. We conclude from this that:

1. The simple Archard wear model is proving to have validity for the prediction of cam and follower wear profiles. 2.

The most critical parameters appear to be the velocities of the contact over the cam (V,) and follower (V,) surfaces.

3.

Hydrodynamic factors can influence wear but are less important than Vc and VF for most operating conditions.

The author would like to thank Dr van Leeuwen for his interest in the paper. The steep change in film thickness at the transition points is caused by the change in load between that exerted by the hydraulic lash adjuster on the base circle and that exerted by the valve spring on the cam flanks. The squeeze film effects were predicted by solving the transient Reynolds equation in the inlet region of the Hertzian contact, at one degree intervals of the cam-shaft rotation. The transient solution and the quasistationary solution yielded almost identical results, except at the transition points. This indicated that the entrainment effects were dominant. Hence, the lubrication regimes chart was used to determine the elastic and viscous characteristics of the contact. At high speeds, roller inertia becomes dominant. The roller accelerates during valve opening and decelerates during valve closing, hence the traction forces act in opposite

These observations help to explain why maximum wear does not occur at the same points in the operating cycle for the cam and the follower, except under catastrophic conditions when damage is transferred from one surface to the other. Referring to Dr Willermet's paper in Session 11, it is suggested that Vc and vF could be of use as simple valve train wear criteria, though clearly not to be used in isolation. The selection of design geometries that minimise the periods over which Vc and vF have low values would be expected to lead to better wear performance on this basis.

504

Reference 1. J C Bell, P T Davies and W B Fur "Prediction of automotive valve train wear patterns with a simple mathematical model", Proc. 12th Leeds-Lyon Symposium on Tribology, Lyon, September 1985. Mr B A Shotter (Westland Helicopters, Yeovil, U K).

From your description it sounds as though your technique can be applied to conditions of abrasive wear, but I seem to remember seeing cam and follower degradation by contact fatigue. Could you please comment on the implications of such failure mechanisms. Reply by Professor R H Fries and C A Rogers (Virginia Polytechnic Institute and State University, Blacksburg, USA).

oversimplifcation of the competing modes of failure. It is (I think) normal in the catalogue selection of belts to specify a maximum centre distance for a given linear sped, presumably to avoid undesirable cyclical lateral belt vibrations excited by longitudinal fluctuations in belt tension, leading to fatigue. The problem is, however, an extremely complex one as the belt is moving laterally. Provided the belt satisfies the above criterion then Figure 1 would be valid for steady-state induced fatigue. Would the author like to comment? Reply by Professor B G Gerbert (Chalmers University of Technology), Gothenberg, Sweden) The simple natural frequency of lateral vibration of a moving belt is 1

The authors wish to thank Mr Shotter and Dr Bell for their comments and discussions. Our method is general in nature, and it can accodate virtually any wear model that can be described mathematically. We illustrated the method using an Archard wear model that is appropriate for abrasive wear. Had we elected to illustrate the method with a cam on a roller follower, then a fatigue wear model may have been more appropriate. Our wear prediction method is in no way restricted to the use of an Archard wear model.

~ - m $ f,'Zq F m where J

F = belt tension m = mass of belt per unit length v = belt velocity L, = length of free span of belt

Equation (A3) in the paper gives the bending frequency to be, f,

We have applied this method to the problem of wear profile prediction in rail vehicle wheels. In the wheel wear work, we have used both abrasive wear models and fatigue wear models (1). Interestingly, the predicted profiles are very insensitive to the selection of wear model. In addition, the predicted wear profiles closely resemble actual profiles of service worn wheels. In addition, the predicted wear profiles closely resemble actual profiles of service worn wheels. The cam wear prediction work is in its infancy, and we cannot yet draw similar conclusions about influence of the wear model on the predicted profiles. Citation of the experimental work by Dr Bell and his colleague, Dr Colgan, is gratifying to the authors. We made our predictions entirely without benefit of experimental work, and we are pleased to know that experimental work exists that exhibits features similar to our predictions. we expect to continue this work, and we hope to make comparisons between our wear profile predictions and the experimental work of others and ourselves. Reference 1. Fries, R H and Davila, C G., wheel Wear Predictions for Tangent Track Runningr,J Dynamic Systems, Measurement and Control, Vol 109, December 1987, pp 397-404. SESSION V - BELTS 'Power Rotating of Flat Belt Drives - A Wear Approach' B G GERBERT Dr D A Boffey (University of Edinburgh, UK)

Figure 1 in the Synopsis is perhaps an

=

z

vfi

The sum of the two is the resulting bending frequency f of a vibrating belt. Thus by substituting f by f, in equation (21) for the quantity B we are able to consider the influence of vibration on fatigue. In the diagrams in Figure 4 this implies that the "Fatigue" curve moves to the right. To my knowledge influence of vibration is not considered in the design procedure in the catalogues. SESSION VI - GEARS 'The Relationship between Uneven Tooth Contact Loading and Surface Durability in Flexible Gear Designs' J F HARROP and A TAM. Mr B A Shotter (Westland Helicopters, Yeovil, Somerset, UIo.

Concerning high contact ratio gears, whilst I accept that their noise can be less than conventional designs, I have always been uncertain about their load distribution. In aircraft engineering one has to be able to define loads as accurately as possible if one wants to achieve the very high reliabilities needed. Thus the uncertainties induced by trying to maintain a minimum of two teeth in contact seemed to be a retrograde step. You have demonstrated that the complexity of the problem is even greater with the rim flexural distortion. Thus I feel that you have justified my concern; would you agree with this point of view? A further comment concerns an aspect of the asymmetry induced by helical gears which could be relevant in this case. Because the instantaneous contact lines on the teeth sweep across the facewidth the oil tends to be swept

505

towards one face of the gearbox. With high speed, highly loaded gears, this can result in thermal distortion due to the combined energy losses from churning and contact sliding being passed to one end of the gear case. Did you considered this effect in your studies? Reply by Messrs J F Harrop and A Tam (Pratt and Whitney, Mississauga, Canada). High contact ratio (HCR) spur teeth are being used successfully in both engine and helicopter gearboxes. They provide increased tooth bending fatigue capacity, reduce the dynamic loads in the gear teeth and decrease noise and vibration. HOWeVeK, suitable tip modification to compensate for tooth flexing, edge relief and high quality surface finish ( < . 4 pm) are essential. Provided that the gear rim is designed to normal aircraft standards, rim flexing does not present a problem on HCR spur gears. Rim flexing/distortion of helical gears is more serious due to the effect of induced axial forces and moments at the gear teeth. It is the tangential deflection of the gear teeth that causes the problem. HCR teeth are probably more sensitive to these deflections than LCR teeth, i.e., the smooth transmission of loading, where more than two teeth are in contact, is perhaps lost. HCR teeth would probably be acceptable in a helical gear mesh if rim stiffness was sufficient to minimise distortion. The effect of possible thermal distortion due to energy losses was not included in our analysis. There has never been any sign of overheating in the gear teeth. Baffles, to prevent "oil hiding" in the gearbox, help retain oil mist in the gear mesh cavity and contribute towards uniform lubrication and cooling of the gear teeth. 'Temperature and Pressure Measurements in Gear Contacts with Thin-Film - Transducers' H PEEKEN and P AYANOGHU Mr H J van Leeuwen (Eindhoven University of Technology, The Netherlands).

To the discusser's knowledge, this is the first successful application of thin film micro-transducers in gear contacts. The authors are to be commended for their ingeneous testing device, which allows for sputtering processes on tooth flanks. I would like to address the following questions: (1)Why did the authors return to manganine pressure transducers? It was concluded in [I] that NiCr has to be preferred. ( 2 ) It appears that the pressure and

temperature distribution curves are presented in real time. As the radius of curvature and the load of the tooth flank is changing along the line of action, the maximum Hertzian stress will change accordingly. Hence, to be able to compare the measured pressure to the Hertzian stress distribution, the pressure data have to be transformed to the same point in time. This necessitates many TE%%&cers, OK a variable transducer position on the tooth flank. The time

dependency may also partly explain the difference between nominal and measured load. Another explanation could be misalignment of the flanks. If I am correctly informed, it amounts to 15 pm over a length of 20 mm, which is quite a bit. This can easily be checked by locating the transducers in different axial positions. Misalignment affects the temperature, film thickness and pressure distribution considerably (21. The best rig would improve from a self aligning device. IS the pressure zero or negative in the cavitating area (outlet)? and is the pressure gradient finite or zero at the onset of cavitation? This in interesting, because most theoretical treatments in EHD lubrication assume that the pressure gradient is zero (Reynolds' boundary condition).

Peeken H and Kohler A. "Determination of pressure and load distribution in a roller bearing with evaporated transducers", in Friction and Traction, Proceedings 7th Leeds-Lyon Symposium on Tribology, 1981, pp 186-191. Van Leeuwen H., Meyer H and Schouten M. 'Elastohydrodynamic Film Thickness and Temperature Measurements in Dynamically Loaded Concentrated Contacts: Eccentric Cam - Flat Follower", in: Fluid Film Lubrication - Osborne Reynolds Centenary, Proceedings 13th Leeds-Lyon Symposium on Tribology, 1987, pp 611-625. Reply by Professor Dr Ing H Peeken and Dr P A an0 lu (Institute fur Maschinenelemente und Masc inengestaltung, Aachen, West Germany).

-5+

(1) At the time the sputtering apparatus was delivered, the manganine target was the only one available. We have now acquired a NiCK target and are experimenting with it. Manganine transducers have nevertheless proven to be quite satisfactory, with pressure and temperature coefficients of 1.6 .10-6/ba~and 2 5.0 .10-6/K respectively. ( 2 ) For valid comparisons, the calculated and

measured values for the same point on the line of action are to be considered. In fact, the given nominal loads are those for the point on the line of action in which the transducer is positioned. The Hertzian distribution seen on Fig. 10 is calculated from the actual force on the transducer, this being the integral of the corresponding measured pressure curve, while the curvature is again that on the point of the transducer. The intention is in this case to compare the measured and Hertzian pressure distributions and not the magnitude of the curves. we intend to use differently positioned transducers to get the distributions for the whole line of action, but these have to be placed on the same tooth flank to avoid errors resulting from no two tooth flanks being exactly the same. ( 3 ) we in fact intent to produce laterally

506 offset transducers, or two of them alongside, to get an idea of the lateral load distribution. We are also working on a new test rig for much higher loads and with the provision for alignment. But the whole problem is not solved by aligning the axles, because there is still the misalignments of single teeth and not of the whole gear to be considered. ( 4 ) Recently taken pressure curves show a

negative value in the cavitating area with a finite gradient, but it is too early to make definite statements about it. For one thing, it could simply be an overshooting of the measuring system - we will first have to investigate its high frequency behaviour. What's more, the relative positions of the pressure and temperature curves are not known, so that this could only be the temperature influence on the transducer. This is on the other hand not so probable, as the temperature should have fallen in the outlet region. The curves were taken quite recently and such an effect was not noticeable in previous measurements, but rather a hysteresis of the transducer. We do not want to come to any conclusions about it yet.

SESSION VII - ROLLING ELEMENT BEARINGS (1) 'The Palmgren KAUZLARICH.

- Miner Rule Derived'

J J

Professor H Blok (Rijswijk, The Netherlands) In radially loaded rolling-element bearings one should distinguish between two kinds of duty cycles, here to be called the 'short' and the 'long, ones and which are imposed internally and externally, respectively. In such bearings the 'short' cycles relate to the variation of the load on each rolling element individually during it planetary motion. On the other hand, the 'long' cycles are associated with the variations of load and speed of the bearing in total during nonstationary operation, such as occurs in automobile practice. Now, the Palmgren-Miner role has long proved itself for stationary operation, such as that on test benches for routine fatigue testing where only the 'short, cycles will occur. But it would appear questionable whether this rule may still be considered reliable when it come to non-stationary operation. In fact, extensions of the present rule to non-stationary operation are usually made more or less tacitly subject to the assumption that the order or succession of severe and mild duty would be immaterial. However, from practice with aircraft structures this assumption has long been known to be invalid. The question may therefore be raised whether this assumption may nevertheless be justified for rolling-element bearings. If not, the application of the original Palmgren-Miner role, as well as that of the author's refinement thereof, would have to be limited to stationary operation only. Reply by Professor J J Kauzlarich (University of Virginia, Charlottesville, USA).

I certainly agree with Professor Blok that the order of succession of severe and mild duty is important, and that the Palmgren-Miner Rule set to a constant equal to 1 is incorrect. The simplicity of the Rule has led to continued use, and one way to correct the rule for a particular duty cycle is to determine a proper constant by experiment. As shown by Atkins and Mai (1, p 539), as well as others, fatigue crack growth can be divided into 3 stages, with Stage 1 concerned mainly with the initiation of crack growth, Stage 11 the continuum region of 'long crack' extension where fracture mechanics is rather successful, and Stage 111 a short time event where fracture takes place. Atkins and Mai (1, p 581) show that in Stage 11 the PalmgrenMiner rule may be 'proved', and that the Rule is independent of 'order of succession of severe and mild duty'. The difficulty lies with Stage 1 associated with crack initiation to the point of 'long crack' extension.

By modifying the P-M Rule based on L, life, as in the paper, this has the effec? of setting the Rule to a constant that has been determined by experiment. Collins ( 2 , p 242) points out that "If the various cyclic stress amplitudes are mixed in the sequence in a quasi-random way, the experimental Miner's sum more nearly approaches unity at the time of failure". Some experimental work on this subject is needed. [l] Atkins, A G and Mai Y W, 'Elastic and Plastic Fracture', Wiley, 1985. [ 2 ] Collins, J A, 'Failure of Materials in

Mechanical Design', Wiley, 1981. Dr J D Summers-Smith (Guisborough U K). The designer uses the concept of L, life as the basis for the application of rohing bearings. The definition of "life" in L,, calculation is based on the somewhat subjective idea of the "first detectable fatigue pit", though this is merely a point in a process that ultimately ends in failure collapse or seizure - that is the concern of the user rather than L,, life. "Life" in L,, sense can be detected in service by an increase in noise or vibration, but clearly this is a warning rather than an indication of immediately impending failure. Can any of the authors give guidance on how much of the ultimate life has been expended by the time the first fatigue pit has been detected? It is appreciated that this is not a simple question but depends on many factors; nevertheless, the user must take such a decision and any guidance that can improve the quality of the decision-making process must be of benefit. (This question was asked to all the authors in Session VII). Reply by Dr E IoaMides, Professor B Jacobson and Dr J H Tripe (SKF Engineering and Research Centre, Nieuwegein, The Netherlands). If this is a question, it certainly is "not a simple question", although one which is bound to arise in practice. Perhaps, with due deference to its asker, a re-statement will produce a question t o which an answer can be

507

supplied. The important issue is: how relevant is the manufacturer's definition of "failure", i.e. the first small spall, to the particular installation? This question has the following practical aspect. If the first spall is not taken as the criterion of failure but a given user can tolerate this spall, an appropriate extended LIg life can be considered for which failure suitable to the user's definition may occur. This will vary from application to application according to the precision and requirements of the application. The resulting extension of life should then be used to gauge the interval for planned maintenance, nothing more. Thus, the question turns on the relative costs of downtime and machine repair. If failure is catastrophic but maintenance is cheap, then the "appropriate" damage criterion should be a very slight one (first spall) and vice versa. The result clearly depends on the particular application. It is the kind of "rule of thumb" which the experienced engineer, perhaps unwittingly, already applies. SESSION VIII

- PLAIN BEARINGS

+

DO the authors anticipate extending the

anal sis of thermal transients to consider speci ic bearings quantitatively such as large sector pad thrust bearings and finite width journal bearings or do they consider their exponential correlation sufficient for treating thermal transients in design and practice?

120 110

-

100

-n

90

Y

j

E

I

I

!/

I

profile

80

70

E

.-7

60

2 r

(1)

'Axially Profiled Circular Bearings and Their Potential Application in High Speed Lubrication' S BASRI and D T GETHIN. Mr F A Martin (London,UK).

Dr Gethin has produced some interesting and useful information on his paper on axial profiled bearings. It is noticeable, however, that the effect of different profiles have generally been considered on the basis of the same eccentricity ratio. An alternative, and probably a more practical way of comparing results, is to consider performance on the basis of using the same load. This can either be accomplished on the computer with further reiteration or simply produced graphically as shown in the accompanying figure (developed from the authors paper). This figure (opposite) highlights the possible difference in trends which can occur, depending on the basis used. For the particular case considered, profile 3 has a higher m a x i m film temperature than profile 1 when using the same eccentricity ratio. However, the trends are reversed when using the same load (the latter being common practice in the design process). Reply by Drs S Basri and D T Gethin '(university College of Swansea, UK). The authors thank MK Martin for his kind remarks and are fully aware of the advantages of presenting the information in the way suggested. However, the presentation method in the paper readily enables the evaluation of bearing performance for a prescribed load which is the design practice commonly encountered. As pointed out, under this circumstance, profile 1 gives the highest operating temperature since the thinnest film will OCCUK with this profile (due to its inferior load carrvinq ability) which will be reflected in locally higher shear stress and reduced lubricant flow. 'Elapsed Time for the Decay of Thermal Transients in Fluid Film Bearings' C M M E'lTLES, H HESHMAT and K R BROCKWELL Professor J B Medley (University of Waterloo, Canada)

2.5

1 0.1

0.3

0.5

0.7

0.9

Eccentricity r a t i o H i g h e r temperatures with profile1 on a constant load basis

Can the authors give examples of cases where considerations for thermal transients are critically important? Reply by DK C M M Ettles (Rensselaer Polytechnic Institute, Troy, USA), Dr H Heshmat (Mechanical Technology Inc ,ynab,. USA) and MK K R Brockwell (National Research Council, Vancouver, Canada). We do not currently have plans to extend the analysis to finite width thrust bearings OK journal bearings. For the boundary conditions to be properly applied, we believe that the spatial coordinates in such an analysis should be three-dimensional, which would require extensive organization and, probably, long execution times. The two-dimensional analysis (Ref. 5 in the paper) gives the principal trends. In journal bearings thermal transients can have important effects on the clearance. This is discussed briefly in the paper. Suppose that a journal bearing m s satisfactorily under steady running conditions A and also satisfactorily under steady running conditions B. When changing from A to B, the clearance may temporily reduce to a value which is unstable. This could occur if the thermal

508

inertia of one of the components is much larger than the other, so that the thermal strain of one of the components lags significantly behind the other.

i'

Thermal transients in thrust bearings may be important in very large bearings where the support system is designed such that over a large portion of the shoe, deformation is in the opposite sense to elastic deformation. Disc supported shoes when the disc radius is large are an example. If the face temperature is suddenly reduced (following, for example, a restart with cold lubricant) both modes of deformation can act in the same sense, giving a concave film which will not balance about the pivot. This can lead to surface damage, since in severe cases the bearing has no load capacity.

3 60 0

SESSION XI - P W N BEARINGS (2) 'Dynamically Loaded Journal Bearings: A Modal Approach to M L Design Analysis' A KUMAR, J F BOOKER and P K GOENKA Mr F

A

Martin (London, LJIO

The authors are to be commended on their new modal approach. One of the problems with this type of work is how to present the results. It is difficult to present distorted bearing shapes without exaggerating or falsely distorting the real shape. An alternative method is to look at limiting clearance shapes. The discusser has shown this previously, relating to Dr GOenka's work (using the same connecting rod and operating conditions as in the present paper). These clearance shapes are shown in the accompanying figure (D1) for crank angle positions 18O and 386O.

It would be of interest to see some of this new work plotted on the same basis, for it gives an added visual dimension, showing for instance the stretching effect, the journal position, and minimum film thickness. What are the authors' views on this? Professor H Blok (Rijswijk, The Netherlands) In one of their slides the authors showed a set of three curves, all depicting the cyclic variation of minimum film thickness, hmin. As a datum line one of these curves has been made to relate to the hypothetical case of perfect rigidity of the surface of both the bearing and journal. Another curve results from the authors' "previous" numerical elastohydrodynamic evaluation, i.e. that to be considered their most realistic one. In any case, this evaluation is more accurate than their "present" one for the remaining, third curve which is primarily meant for quick estimates. NOW, the second curve, marked "previous", shows a smallest h which amounts to only about one half tha'fi%f the aforementioned curve for perfect rigidity. So, at least under the operating conditions concerned, the cyclic variation of the elastic distortion of the bearing surface, or say the "flapping action" (Ref. l), would appear to be rather detrimental as regards the risk of metallic contact.

,

\

1eo

180 a) 18 deg. crank angle Fig.

D1

b) 386 deg. crank angle

Limiting clearance shapes

In contrast, the third curve, marked "present", shows the quick estimate of the smallest h, to exceed that for perfect rigidity. h e n though the gain thus estimated amounts to a mere 10 or 15 percent, for design calculations it would appear unrealistic in that it is overoptimistic by over a factor of two. In other words, contrarily to the more accurate result of the second, "previous" curve the quick estimate is falsely indicative of a beneficial effect of the "flapping action". Finally, in view of the above-mentioned detrimental effect to be expected of the "flapping action" in the bearing of the present design and under the operating conditions concerned, it would appear worthwhile to redesign this bearing by optimization of its elastic compliance. In this connection it should be observed that, judging from the basic "flapping" model in the above-mentioned paper (Ref. 11, potentialities inherent in such optimizations even include the rather paradoxical case where during an increase of the load the minimum film thickness will increase too. Reference (1) Blok H. 1975, 'Full Journal Bearings under Dynamic Duty: Impulse Method of Solution and Flapping Action'; Trans. ASME, J. Lubric. Tech., Vol. 97, Series F, No 2, pp 168-179. For Errata, see Vol 99 (1977) of the same journal, page 223. Reply by Dr A Kumar, Professor J F Booker (Cornell University, Ithaca, USA) and Dr P K Goenka (General Motors Research Laboratories, Warren, USA). We certainly agree with Mr Martin that presentation is the unsolved problem for EHL of dynamically loaded journal bearings (in which both rigid body and elastic

509

displacements can vary circumferentially, axially and temporally). The "dynamics clearance space" concept proposed by Mr Martin seems both intuitively helpful and computationally feasible. (For example, determination of tool paths and cam contours are classic problems in computeraided design). As Mr Martin notes, the clearance space shape is one of the few graphic displays which is not distorted by an arbitrary change of scale(s). Unfortunately, the 3-D character of the clearance spaces in our problems requires a level of complexity somewhat beyond such 2-D presentations as those suggested in this Discussion. The same limitation applies to the excellent animated and narrated computergenerated video study of an elastic connecting rod bearing recently produced by B Fantino, J Frdne and J du Parquet. Effective presentation of the full dimensionality of transient EHL results will probably require future efforts much like this. It is unfortunate that Professor Blok did not have access to the full text of our paper at the time of preparing his Discussion, particularly since our Introduction opens with citation of his classic paper (Blok [19751) introducing the concept of "flapping action".

6

0.6

3

iz

4

0.4

0.2

0.0

10

5

0

15

20

'15 l

20 '

.

The table Below shows a steady external load without journal rotation for the idealistic bearing of Section 4.1.

I

35

30

40

t

loo

In his present Discussion Professor Blok notes that the effects of "flapping action" can be detrimental or beneficial, alluding to "the rather paradoxral case where during an increase of the load the minimum film thickness will increase too". We have previously observed a related phenomenon in the study of transient "squeeze films" (Kumar [ 19881 )

I

25

o

0

'

'

5

'

'

10

~

-

'

25 '

l

30 '

l

35 '

'

40 '

Time (83.3ps)

Idealistic bearing - (steady load Fig. 12 without rotation) film thickness and pressure transient extrema.

Idealistic Bearing - Steady State Without Rotation Figure 1 shows transient variation of film thickness and pressure extrema computed using modal subsets m = 2,6,8,10 to form the transformation matrix. In every case modal displacement 2 (loading axis rigid body eccentricity ratio) is initially 0.95, while all other (elastic) modal displacements are initially null. Figure 1 shows that (for rigid/elastic models m = 6,8,10) the resulting minimum film thickness actually increases for a time (though, presumably, the avera e film thickness always decfeasedqalitative result entirely consistent with elastic "wraparound"

.

We believe that modal re resentation (not necessarily coupled with m a co utation as here) can provide further insig t into this and other evidences of the "flapping action" mechanism(s). We hope to elaborate on this approach in a later publication. unfortunately, our present paper is already somewhat dated; more recent results suggest that it is probably unduly conservative as to the accuracy possible with the present modal approach. For example, in the realistic bearing example of Section 4.2, the accuracy at the critical extreme points for m = 8 is c h better than that shown in Figure 1 for m = 6. With this minor enhancement, results from the present program F-L are very nearly identical to previous results by Goenka and Oh [1986b], as we will report in a forthcoming publication examining the computing cost/ numerical accuracy trade-offs in some detail.

'

510

Professor Blok calls attention to the potential for optimization of elastic compliance in such cases as this. General interest in such an approach is also evidenced by a very recent trade journal article by Murray [ 1988I reviewing the previous structural optimization work of Goenka and Oh [1986b]. We believe that the increased computational speed and limited design space of the modal approach will assist in studies of this sort. Future Work. Other possibilities for future work are inclusion of structural inertia and damping, . temperature- and pressure-viscosity effects, and dynamic (mass-conserving) cavitation, as well as generalization of the mobility/ impedance method(s) for higher order systems via problemindependent (rather than problew dependent) modal transformation matrices. The list of such possible enhancements and extensions is nearly endless. Reference. (1) Murray, C J. (1988), 'Compliant Connecting Rod Reduces Bearing Stresses', Design News, 1988, 44, n 19, 278-279.

Pressure flow

a, Qh

Hydrodynamic or velocity flow

0

Index for plain bearings

f

Index for fully grooved bearings

d

Shaft diameter

b

Bearing length

E

Eccentricity ratio

U

Surface velocity of the journal diametral clearance

d'

h

lubricant dynamic viscosity

h

average film thickness

P

lubricant feed pressure into bearing

Pl

bearing power loss

2.

Introduction

'A Theoretical Investigation of Hybrid Journal Bearings Applied to High Speed Heavily Loaded Conditions Requiring Jacking Capabilities', D IVES, W WESTON, P G MORTON and W B ROWE.

it is necessary to make estimates of oil flow through engine bearings when specifying engine pump capacity. prediction of bearing power loss is important in order to estimate engine power lost in bearing friction. furthermore, bearing temperature rise and effective operating oil viscosity can be estimated when oil flow and power loss are known.

Professor J B Medley (University of Waterloo, Canada)

journal bearings used in internal combustion engines are normally:

SESSION XIV - HYDROSTATIC BEARINGS

.

How did you deal with thermal effects in your study?

- plain i.e. without grooves or - with a full central circumferential

Reply by Mr D Ives (Liverpool Polytechnic, UK), Mr W Weston (Huddersfield Polytechnic, UK), Mr P G Morton (General Electric Company, Stafford, UK) and Professor W B Rare (Liverpool polytechnic, UK).

- with a partial central circumferential

It is realised that thermal effects in large high speed bearings are of importance. For the work presented it was considered that an isothermal model would be adequate at this stage, the temperature rise through the bearing being accounted for by assuming an effective viscosity. An investigation into thermal aspects of the performance of slot entry hybrid journal bearings is presently in progress.

GENERAL DISCUSSION

+

Dr M Stano'evic (Vandervell Ltd., Maidenhead, A contribution to SESSION XI - PLAIN BEARINGS (2).

Oil flow and power loss models in dynamically loaded bearings

groove or groove

journal bearing oil flow models have been described in reference 1, section 7.9 for oil flow with central circumferential groove and section 7.10 for oil flow with single hole. these models based upon an average eccentricity ratio over the engine cycle have been used for dynamically loaded bearings and are described in reference 4 . a simple journal bearing power loss model has been described in reference 2, section 7. reference 3 , sections 12.16 to 12.18 considers similar models. these models based upon an average eccentricity ratio over an engine cycle have been adapted and used for engine bearings in references 4 and 5. the above simple models are sumarised below: oil flow through a plain bearing

(a)

Q = a,o

1. Notation (F - force, L

- length, T - time)

symbol

Name

Q

Bearing oil flow

=

Dim [L3fll

+

[ &$

Qh,

tan-'F]

]

(1 + 1.5 E*) + 7 u cd be

(b)Oil flow through a fully grooved or a partially grooved bearing

(1)

51 1

Q = $f

+

Qhf

3

nd (1 + 1.5 s 2 ) +4 u cd bs =mi6

and that the hydrodynamic flow is dominated by small clearances. Suppose that the partial groove is in the upper half of the bearing circumference. The following relationships are then deduced, refer to the Figure hielow. PLAIN Q = Qpo

it is seen that the total flow in the above formulae is a simple addition of pressure and hydrodynamic components. pressure flow component has been analysed in reference 6, and different total flow models have been discussed in reference 7 and 8.

+ Qho

c) power loss for plain and grooved bearings FULLY GROOVED

0 d3 b w2

Q=

PL =

Qpf

Qhf

Power loss defined above has been compared to several other models from different countries in reference 9. In equations (l), ( 2 ) and ( 3 ) average eccentricity ratio is calculated from average film thickness h by

PARTIALLY GROOVED [1 = Qpf + Qho

cd - 2h d'

Bearing length b is an effective length and it excludes groove width both for fully grooved and partially grooved bearings. The above formulae are characterised by the eccentricity ratio being averaged over the engine cycle. 3.

PARTIALLY GROOVED

Q =

Q p o + (Ihf

Improvements to Simple Models from References 4 and 5

The following improvements to the simple models described in references 4 and 5 have been carried out:

-

Oil flow and power loss are to be calculated at every crank angle increment and then averaged over the engine cycle instead of using the average eccentricity ratio in the equations (l), (2) and (3).

QPO

If the shaft centre locus is in the lower half of the clearance circle, the bearing oil flow consists of the following components: (a) fully grooved bearing pressure flow (b) plain bearing hydrodynamic flow, i.e.

-

It is possible to differentiate between fully grooved and partially grooved bearings by considering shaft locus during the engine cycle. 3.1

Improvements to the Bearing Oil Flow

Plain bearings without grooves have been considered in reference 10 where the improved method above has been compared to methods described in references 3 and 6. The feed hole diameter considered in reference 10 was small and the resulting ratios of velocity flows to pressure flows were large. The resulting differences in total flows were small for the models considered. Further work is required in this area, but this section concerns an improved method for oil flow calculations of partially grooved bearings. In the improved method it is assumed that the pressure flow is dominated by large clearances within the bearing circumference

-

If the shaft centre locus is in the upper half of the clearance circle, the flow consists of the following components: (a) plain bearing pressure flow (b) fully grooved bearing hydrodynamic flow, i.e =

$0

+

'hf

3.2 Improvements to the Bearing Power Loss

Improvements to the bearing power loss model as described in references 4 and 5 refer to partially grooved bearings. Again suppose that the partial groove is in the upper half of the bearing circumference.

- If the shaft centre locus is the lower half of the clearance circle, then the groove width is not subtracted from the bearing length b. -

If the shaft centre locus is in the upper

512

5. Discussion

half of the clearance circle, then the groove width is excluded from the bearing length b.

The new models of bearing oil flow and power loss are improved in relation to the models described in references 4 and 5 because oil flow and power loss are calculated at every crank angle increment and these models consider shaft locus in the engine cycle.

4. Some Results As an example a geometry of a main bearing of a four cylinder engine was analysed and the journal orbit was run for a plain, fully grooved and partially grooved bearing at two speeds. Results of oil flow and power loss using the improved models described above are shown in Table 1. Diametral clearances assumed in these calculations are 0.074 nun both for oil flow and power loss.

In the new model for the oil flow of partially grooved bearings, pressure flow is governed by large clearances within bearing circumference and velocity flow is governed by small clearances. In the new power loss model of partially

grooved bearings, power loss is governed by I I I small clearances within the bearing [Partially i Grooved IGrooved I

IPlain mlly

circumference.

I I+ k/min @ 2500 r/min10.37

I

kW @ 2500 r/min10.07 I

I

k/min

@

4500 r/min10.58

kw

@

4500 r/min10.24

Table 1

I

1.10

I

0.91

0.12

II

0.08

__+___I 1.20

I

1.03

I

Improved oil flow and power loss programs are run after the journal orbit programs and they use eccentricity-attitude data files as input. They may be incorporated into the journal orbit programs, so that oil flow and power loss are evaluated every time the orbit program is run.

0.39

I I

0.26

I I

References

I I

I

M C Shaw; E F Macks, 'Analysis and Lubrication of Bearings', McGraw-Hill, New York 1949.

Bearing Oil Flow and Power Loss Using the Improved Method

From Table 1 it is seen that partially grooved bearings have smaller flow rates and power losses than fully grooved bearings.

D D Fuller, 'Theory and Practice of Lubrication for Engineers', John Wiley, New York 1956.

Plain bearings have the smallest flow rates and power losses out of the three types of bearings considered.

A

Cameron, 'The Principles of Lubrication', Longmans, London 1966.

P E Vickery, 'Friction Losses in Automotive Plain Bearings - A Practial and Thoeretical Study', SAE Paper 750052.

The improved methods are compared to methods of references 4 and 5 in Table 2 .

Method of Improved Refs. 4 and 5 Method

I IPlainIFully PlainlFully

+Ti

I 0.40 I 1.13 Ii/min @ 2500 r/min

II

kW @ 2500 r/min 0.08

II

0.11

I

I

IR/min @ 4500 r/min 0.62

1.24

kW @ 4500 r/min 0.28

0.38

II

i I I II

I

Table 2

0.37 I 1.10 I

I

I

0.58 I

1.20 I

0071 I

0.24 I

I

I

0.39 I

I

Comparison of the oil flow and parer loss calculation methods of references 4 and 5 to the improved methods.

From Table 2 it follows that oil flow in the improved method is marginally laver for both fully grooved and plain bearings. Power loss of the improved method is marginally higher for fully grooved bearings whilst it is marginally lower for plain bearings. It is apparent that the differences between the two methods are small.

R H Spikes; S A Robinson, 'Engine Bearing Design Upto-Date', Instn. Mech Engrs Conference 'Tribology - Key to the Efficient Engine', Paper C1/82, Jan 1982. F A Martin; C S Lee, 'Feed-Pressure Flow in Plain Journal Bearings', ASLE Transactions, Vol. 26, No 3, pp 381-92, 1983. F A Martin, 'Developments in Engine Bearing Design', Tribology International, Volume 16, NO 3, pp 147-64, 1983. G J Jones; C S Lee; F A Martin, 'Crankshaft Bearings: Advances in Predictive Techniques Incorporation the Effects of Oil Holes and Grooving', Paper No 1, AE Symposium 1982. F A Martin, 'Friction in Internal Combustion Engine Bearings', IMechE Conference "Combustion Engines Reduction of Friction and Wear', Paper C67/85, 1985. (10) M Stanojevic, 'Oil Flow Through a Plain Bearing', Vandervell Internal mgineering Note, May 1987.

513

15th LEEDS-LYON SYMPOSrZlM ON TRIBOKIGY

THE TRIBouxiIcAL DESIGN OF MACHINE ELEMENTS 6th - 9th SEPTEMBER 1988 L l S OF AUTHORS TlTI.6 NAME -

EE

NAME

AFFILIATION/ADDRES

Mr

MAWolm&ki

RHP Industrial Bearings Ltd P 0 Box 18 Northern Road Newark Notts NG24 2JF U K

Dr

F Bremer

Philips Research Laboratories 5600 JA Eindhoven The Netherlands

Dr

DAshmm

Lucas Aerospace Ltd Engine Systems Division Hall Green Birmingham West Midlands B28 8SW U K

Dr

BJBrim

Department of Chemical Engineering & Technology, Imperial College of Science and Technology London SW7 2BX U K

PAyanoglu

Institute fur Maschinenelemente und Maschinengestaltung Technische Hochscule SchinkelstraBe 8 5100 Aachen West Germany

MI

Dr

KRBmcW

National Research Council 3650 Wesbrook Mall Vancouver B C V6S 2L2 Canada

Dr

H M Chen

Mechanical Technology Inc 968 Albany-Shaker Road Latham New York 12110 U S A

Mr

B Chen

Nanjing Institute of Technology Nanjing, Jiangsu The People's Republic of China

pmf

HSCheng

Northwestern University Technological Institute Evanston Illinois 60201 U S A

Dr

THCChilds

University of Bradford Postgraduate School of Mechanical & Manufacturing Systems Engineering Bradford BD7 1DP U K

R J Chittendeo

The University of Leeds Industrial Unit of Tribology Department of Mechanical Eng. Leeds LS2 9JT U K

Dr

TCChivers

CEGB Berkeley Nuclear Laboratories Berkeley Glos. GL13 9PB U K

Dr

Mr

Dr

prof

SBair

A D M

smri

DBerthe

Georgia Institute of Technology The George W Woodruff'School of Mechanical Engineering Atlanta Georgia 30332-0405 USA The University of Leeds Institute of Tribology Department of Mechanical Engineering Leeds LS2 9JT U K

University College of Swansea Department of Mechanical Engineering Singleton Park Swansea SA2 8PP U K Dr Institut National des Sciences Appliquees de Lyon, Laboratoire de Mecanique des Contacts atiment 113 20 Avenue Albert Einstein 69621 Villeurbanne Lyon, France

Dr

BBbushan

IBM, Almaden Research Centre K641802, 650 Harry Road San Jose CA 95120-6099 USA

Mr

G A Clayton

The University of Leeds Department of Mechanical Engineering Institute of Tribology Leeds LS2 9JT U K

Dr

PBoch

Ecole Nationale Superieure de Ceramique, Industrielle 47 & 73 Avenue Albert-Thomas 87065 Limoges Cedex France

Mr

E W Cowking

Friction, Lubrication & Wear Group GEC Engineering Research Centre Cambridge Road Whetstone Leicester LE8 3LH U K

Mr

SBOedo

Borg-Warner Automotive Inc Ithaca New York USA

Dr

ACckriey

Department of Mechanical Engineering Manufacturing & Machine Tools Division, U M I S T, P 0 Box 88 Manchester M60 1Q U K

Cornell University Dr Mechanical & Aerospace Engineering Upson Hall Ithaca New York 14853 USA

PEDale

Mechanical Research Department Ontario Hydro 800 Kipling Avenue, Toronto Ontario M8Z 5.9 Canada

514 TITLE NAME -

AFFILIATION/ADDRfSS

TlTI.6

NAME

AFFILIATION/ADDRESS

Dr

JADominy

Rolls-RoyCe PIC Manager - Transmissions Research POBox31 Derby DE28BJ U K

Dr

R J Gozdawa

Advanced Bearing Technology Ltd Brunel University Science Park Uxbridge Middlesex UB8 3PH U K

Dr

SSDoUgtas

Liverpool Polytechnic Faculty of Engineering Byrom Street Liverpool L3 3AF U K

Mr

RTCdEh

Birmingham Polytechnic Faculty of Computing and Information Studies Perry Barr Birmingham B42 2SU U K

Prof

DDavsw

The University of LeedS Institute of Tribology Department of Mechanical Eng. Leeds LS2 9JT U K

Mr

JCHamer

Dr

CMMEttles

Rensselaer Polytechnic Institute Department of Mechanical Eng. Troy N Y 12181 U S A

Imperial College of Science and Technology, Department of Mechanical Engineering Exhibition Road London SW7 2BX U K

Pmf

BJHamroct

The Ohio State University Department of Mechanical Eng 206 West 18th Avenue Columbus Ohio 43210 U S A

Dr

J F Harrop

Ecole Nationale Superieure des Mines de Paris, Centre de Mise en Forme des Materiaux, Sophia Antipolis 065M) Valbonne France

United Technologies Pratt and Witney Canada Inc Box 4080, Mississauga Ontario L5A 324 Canada

Dr

CJ J

Universite de Poitiers Laboratoire de Mecanique des Solides, 40 Avenue du Recteur Pineau, 86022 Poitiers Ceder France

Delft University of Technology Faculty of Mechanical Eng. and Marine Engineering Section Tribology Delft The Netherlands

Dr

H Heshmat

Project Manager Sr Project Engineer Mechanical Technology Inc 968 Albany-Shaker Road Latham, New York 12110 USA

Dr

PLHobter


Dr

E Ioannides

S K F Engineering & Research Centre

Dr

Dr

prof

Pmf

Mr

Dr

TSEyre

EFeldw

JFreoe

HFries

AGabelli

BAGeEim

Brunel University of Materials Technology, Department of Materials Technology Uxbridge Middlesex UB8 3PH UK

Virginia1 Polytechnic Institute and State University Department of Mechanical Eng. Blacksburg Virginia 24061 U S A SKF Engineering & Research Centre BV, Postbus 2350, 3430 DT Nieuwegein The Netherlands Senior Research Engineer Fluid Mechanics Department General Motors Research Labs. 30500 Mount Road, Warren MI 48090-9055 U S A

MII Aeijningen

B V, Postbus 2350, 3430 DT Nieuwegein The Netherlands

Mr

KIshii

The Ohio State University Department of Mechanical Eng. 206 West 18th Street Columbus Ohio 43210 U S A

Pmf

BGGerbert

Chalmers University of Tech. Division of Machine Elements 5-41296 Gteborg Sweden

D Iver

Liverpool Polytechnic Faculty of Engineering Byrom Street Liverpool W 3AF U K

Dr

DTGethin

University College of Swansea Department of Mechanical Engineering Singleton Park Swansea SA2 8PP U K

B Jacobson

SKF Engineering & Research Centre BV, Postbus 2350, 3430 DT, Nieuwegein The Netherlands

Mr

O G i

BW Mechanical Seals Long Beach, CA 90801 U S A

CMKrrlLer-Kslbnaa

Dr

PKGoenLa

General Motors Research Laboratories 30500 Mount Road Warren MI 48090-9055 USA

Delft University of Technology Faculty of Mechanical Engrg. and Marine Engineering Section Tribology Delft The Netherlands

Ir

515

AFFILIATION/ADDRESS

AFFIUATIONIADDRESS

PmfDr

EAMuijdermM


Mr

RAJvanOstayen

Technische Universiteit Eindhoven Instituut voor Aandrfil-en Tribolotechniek, W-HHOG 4,103 Postbus 513, 5600 MB Eindhoven The Netherlands

Dr

E W Parker

University of Virginia Mechanical Engineering Departlnent Thornton Hall Charlottesville VA 22903 U S A

Wolverhampton Polytechnic School of Engineering Wolverhainpton West Midlands WV1 1LY

Mr

I K Parker

University of Bradford Postgraduate School of Mechanical & Manufacturing Systems Engineering Bradford BD7 1DP UK

BW Mechanical Seals Teinecula CA 92390 U S A

Dr

TGPearce

British Railways Board Research Training Officer Research Division Railway Technical Centre London Road Derby DE2 8UP U K

Eindhoven University of Tech. Institute for Power Transmission and Tribology, W-HOOG 3.110 P 0 Box 513, 5600 MB Eindhoven The Netherlands Ecole National Superieure de Ceramique, lndustrielle 47 & 73 Avenue Albert Thomas 87065 Limoges Cedex France Prof

Mr

JJKaudarich

WEKey

R

JI(li0ger

The Ohio State University Department of Mechanical Eng 206 West 18th Avenue Columbus Ohio 43210 U S A

Mr

CNKo

S K F Engineering & Research

PmfDrIng H Peeken Centre B V, Postbus 2350, 3430 DT Nieuwegein The Netherlands

Prof Dr Eng H KneminsLi-Freda Politechnika Lodzka

Mr

F Platon

Ecole Nationale Superieure de Ceramique, lndustrielle 47 & 73 Avenue Albert-Thomas, 87065 Limoges Cedex France

Dr

C Pritchard

Materials Research Laboratory NTN Toyo Bearings Co Ltd Kuwana 511 Japan

British Railways Board Research Training Officer Research Division Railway Technical Centre London Road Derby DE28UP U K

Prof

CARogers

Tribology Research Institute Tsinghua University Beijing Peking The People's Republic of China

Virginia Polytechnic Institute and State University Department of Mechanical Eng. Blacksburg, Virginia 24061 USA

Dr

EWRoberts

National Centre of Tribology U K A E A, Risley, Warrington WA3 6AT U K

Prof

WBRowe

Liverpool Polytechnic Department of Mechanical Marine and Production Engineering Byroin Street Liverpool L3 3AF U K

Instvtvt Konstrukcii Maszyn 90-424 Lodz ul. B Stefanowskiego 1/15. Lodz Poland

Mr

Mr

Mr

Mr

Dr

Dr

Mr

AKumar

M Kuno

M U

PMaspeyrot

J 0M d d

A v Montfoortlaod

P G Morton

Institut fur Maschinenelemente und Maschinengestaltung Technische Hochscule SchinkelstraBe 8, 5100 Aachen West Germany

Cornell University Mechanical & Aerospace Engineering Upson Hall Ithaca New York 14853 U S A

Universite de Poitiers Laboratoire de Mecanique des Solides, 40 Avenue du Recteur Pineau, 86022 Poitiers Cedex France University College of Swansea Department of Mechanical Eng. Singleton Park Swansea SA2 8PP U K Philips Research Laboratories 5600 JA Eindhoven The Netherlands GEC Research Principal Research Associate Engineering Research Centre Mechanical Laboratory P 0 Box 36 Lichfield Road Stafford ST17 4LN

National Centre of Tribology U K A E A, Risley Warrington WA3 6AT U K Dr

Ph Sainsot

Institut National des Sciences Appliquees de Lyon, Laboratoire de Mecanique des Contacts Mtitnent 113 20 Avenue Albert Einstein 69621 Villeurbanne LYON France

516 TlTLE NAME -

AFFILLATION/ADDRESS

prof

RFSalaot

Georgia Institute of Technology The George W Woodruff School of Mechanical Engineering Atlanta Georgia 30332-0405 U S A

prof

ssasati

Mechanical Engineering Lab. Namiki 1-2, Sakura-Mura, Isukuba Sciencen city 305 Ibaraki 305 Japan

Dr

RSSayles

Imperial College of Science and Technology Department of Mechanical Eng. Exhibition Road London SW7 2BX U K

TITLE

NAME

AFFILIATION/ADDRGSS

Dr

C J Thijsse

Nederlandse Philips Bedrijven BV Postbus 218 5600 MD Eindhoven The Netherlands

Dr

Ph V e l a

lnstitut National des Sciences Appliquees de Lyon Laboratoire de Mecanique des Contacts, Gtiment 113 20 Avenue Albert Einstein 69621 Villeurbanne Cedex France

Ir

MVier

Eindhoven University of Tech. tnstitute for Power Transmission and Tribology W-HOOG 3.110, P 0 BOX513 5600 MB Eindhoven The Netherlands

Mr

A Skorin

RHP Industrial Bearings Ltd Northern Road Newark Notts NG24 2JF U K

Dr

B Warda

k

M J L Stakenborg

Technische Universiteit Eindhoven Instuut voor Aandrift-en Tribolotechniek, W-HOOG 4.103 Postbus 513, 5600 M B Eindhoven The Netherlands

Politechnika Lodzka Instytyt Konstrukcji Maszyn 90-924 Lodz ul. B Stefanowskiego 1/15 Loch Poland

Dr

F PWade

Brunel University of West London Department of Mechanical Eng. Uxbridge, Middlesex UB8 3PH UK

RHP Industrial Bearings Ltd Northern Road Newark Notts NG24 2JF U K

Dr

R B Waterhouse

Tribology Consultant Merlewood, The Avenue Guisborough, Cleveland TS14 8EE UK

The University of Nottingham Department of Metallurgy and Materials Science University Park Nottinghain NG7 2RD U K

Prof

swen

Pratt and Witney Canada Inc. Box 4080, Mississauga Ontario L5A 324 Canada

Tribology Research Institute Tsinghua University Beijing Peking The People's Republic of China

Mr

w wen00

Huddersfield Polytechnic Department of Mechanical Eng. Queens Gate Huddersfield HD1 3DH

Dr

P A Willerrnet

The Ford Motor Company Research Laboratory P 0 Box 2053, Dearborn MI 48121 U S A

prof

wowmer

The Georgia Institute of Technology The George W Woodruff School of Mechanical Engineering Atlanta Georgia 30332-0405 USA

Dr

M winfield

Birmingham Polytechnic Faculty of Computing and Information Studies Perry Barr Birmingham B42 2SU UK

MI

RA EW o o d

RHP Industrial Bearings Lid Northern Road Newark Notts NG24 2JF U K

Prof

s xu

Department of Mechanical Eng. Southwest University Nanjing The People's Republic of China

Dr

Dr

Mr

Dr

T A S m

J D Summerssmith

ATam

AGTangena

Philips Research Laboratories 5600 JA Eindhoven

The Netherlands

Dr

CMTaylor

The University of Leeds Institute of Tribology Department of Mechanical Eng. Leeds LS29JT UK

Mr

MJ T o d d

National Centre of Tribology U K A E A, Risley Warrington WA3 6AT UK

Dr

J HTr i p p

SKF Engineering & Research Centre BV, Postbus 2350 3430 DT, Nieuwegein The Netherlands

Ms

Dr

RTristani

PJlhdale

McMaster University Hamilton Ontario Canada Imperial College of Science and Technology Department of Chemical Eng. and Technology London SW7 2BX UK

517

15th LEEDS-LYON SYMPOSIUM ON TRIBOLOGY THE TRIBOLOGICAL DESIGN OF MACHINE ELEMENTS 6th

- 9th SEPTEMBER 1988

LIST OF DELEGATES AFFILIATION/ADDRESS

TITLE NAME -

Mr

MAbdolmaleti

RHP Bearings P 0 Box 18 Newark Notts U K

Mr

AAlberdi

Tekniker Asociacion de Investigacion c/lsasi s/n Eibar Guipbzcoa Spain

Mr

Dr

AFAUistonCreher

BSAndersson

Prof

H Blok

Consultant Dr H Colijnlaan 4, Fl 19, 2283 XM Rijswijk The Netherlands

Mr

s Boedo

Borg-Warner Automotive Inc 770 Warren Road Ithaca, New York 14850 USA

Plint 8r Partners Ltd Fishponds Road Wokingham RGll2QG U K Volvo Car Corporation Department 96320 PV3C S-40508 G6teborg Sweden

Dr

DAshman

Lucas Aerospace Ltd Engine Systems Division Shaftmoor Lane, Hall Green Birmingham B28 8SW U K

Mr

DAuger

The University of Waterloo Department of Mechanical Eng. Waterloo Ontario Canada N2L 3G1

Mr

PAyanOglu

Institut iiir Maschinenelemente und Maschinengestaltung RWTH Aachen Schinkelstr. 8, 5100 Aachen, W Germany

The University of Edinburgh Department of Mechanical Eng. Kings Buildings Mayfield Road Edinburgh EH9 3JL U K

Prof

JFBooker

Cornell University School of Mechanical & Aerospace Engineering, Ithaca. New York 14853 USA

Dr

B Bou-said

lnstitut National des Sciences Appliquees de Lyon Laboratoire &s MBcanique des Contacts, Biitiment 113 20 Avenue Albert Einstein 69621 Villeurbanne, Lyon, France

Mr

M Bouvier

Institut National des Sciences Appliquees de Lyon Laboratoire d6s Lyon Laboratoire dBs Mkanique des Contacts, Mtitnent 113 10 Avenue Albert Einstein 69621 Villeurbanne Lyon, France

Mr

ADBd

The University of Leeds Department of Mechanical Eng. Institute of Tribology Leeds LS2 9JT U K

Mr

TJBanLs

Ricardo Consulting Engineers plc Bridge Works Shoreham-by-Sea West Sussex BN4 614 U K

Ir

F Bremer

Philips Research Laboratories CFTlSAQ 2100 5600 MD Eindhoven The Netherlands

Mr

OBeaurepaire

SIC Ste Industrielle des Coussinets, B P 73-4 rue de la Liberte 74009 Annecy France

Mr

K R Bmckwell

National Research Council 3650 Wesbrook Mall Vancouver, BC V6S 2L2 Canada

Dr

JCBell

Shell Research Ltcl Thornton Research Centre P 0 Box 1 Chester CH1 3SH U K

Mr

A Burrows

Butterworth Scientific Ltd P 0 Box 63 Guildford Surrey GU2 5BH U K

Dr

PcaaO

Mr

CBerger

SEP Vernon France

Imperial College of Science and Technology, Tribology Section London SW7 2BX U K

Dr

WJBeswaricL

Hatfield Polytechnic Haffield Herts ALlO 9AB U K

Prof

HSCheng

Northwestern University Technological Institute Evanston, Illinois 60201 U S A

h

THCChilds

The University of Bradford Department of Mechanical and Manufacturing Engineering Bradford West Yorkshire BS7 1DP U K

h

BBbWbM

K64/802 IBM Almaden Research Center, 650 Harry Road San Jose, CA 95120-6099 USA 16 Clarence Street Bowburn Co Durham DH6 5BB U K

518

AFFILIATION/ADDRESS

AFFIUATlONIADDRESS

Industrial Unit of Tribology The University of Leeds Leeds LS2 9JT U K

Rensselaer Polytechnic Institute JEC 2034 Troy N Y 12180-3590 USA

h

TCChivers

Central Electricity Generating Board Berkeley Nuclear Laboratories Berkeley Glos GL13 9PB U K

Mr

cclayton

The University of Leeds Department of Mechanical Eng. Institute of Tribology Leeds LS2 9JT U K

Mr

SNCdlios

The University of Leeds Institute of Tribology Department of Mechanical Eng. Leeds LS2 9JT U K

Mr

Dr

h

EWCacvkhg

DACroILa

PDale

GEC Engineering Research Centre, Cambridge Road Whetstone Leicester LE8 3LH U K The University of Leeds Institute of Tribology Department of Mechanical Eng. Leeds LS2 9JT U K Ontario Hydro 800 Kipling Ave. Toronto Ontario M82 5S4 Canada

Mr

KDalgaao

The University of Bradford Department of Mechanical and Manufacturing Engineering Bradford W Yorks BD7 1DP U K

h

A J Day


Mr

PDeLaine

CLextral, B P 10 21 De Chazeau, 3270 Firminy Cedex France

Mrs

FdM Barragan De Ling

University CoUege Department of Mechanical Eng. Newprt Road CardiE CF2 1TA U K

h

Dr

Pmf

JDominy

SDoUgas

DDonsoo

Ars.PdDDuen

Ms

MCDubourg

Rolls-Royce plc POBox31 Derby DE2 8BJ U K Liverpool Polytechnic Department of Engineering & Technology Management Byrom Street Liverpool L3 3AF U K The University of Leeds Institute of Triboloev -. Department of Mechanical Eng. Leeds LS2 9JT U K Gear Research Institute Taiyuan University of Tech Taiyuan Shanxi People’s Republic of China lnstitut National Des Sciences Appliquees de Lyon. Laboratoire des Mecanique des Contacts Batiment 113 20 Avenue Albert Einstein 69621 Villeurbanne Lyon. France

Mr

D C Evans

The Glacier Metal Co Ltd Premier House 1 Canning Road Harrow Middlesex HA3 7TS U K

h

HPEvaos

University College Department of Mechanical Eng. Newprt Road Cardiff CF2 1TA U K

Dr

TSEyre

Brunel University Kingston Lane Uxbridge Middlesex UB8 3PH U K

Mr

FMHEzzat


Dr

E Felder

Ecole des Mines CEMEF Sophia Antipolis F 06560 Valbonne France

Dr

DNFenner

Kings CoUege Department of Mechanical Eng. The Strand London WC2R 2LS U K

Mr

J FKklbwse

Head of Department The Polytechnic Department of Mechanical and Production Engineering Queensgate Huddersfield GDl 3DH U K

Dr

J Fisber

The University of Leeds Department of Mechanical Eng Institute of Tribology Leeds LS2 9JT U K

Rof

JF&ne

University of Poitiers Laboratoire de Meanique des Solides 40 Ave du Recteur Pineau 86022 Poitiers Cedex France

Rof

RHFries

Virginia Polytechnic Institute and State University Department of Mechanical Eng Blacksburg Virginia 24061 USA

Dr. log. A Gabelti

SKF Engineering & Research Centre BV, Postbus 2350 3430 DT Nieuwegein The Netherlands

Dr

BACecim

General Motors Research Labs. Fluid Mechanics Department Warren, MI 48090-9055 USA

Pmf

BGGerbert

Chalmers University of Technology Division of Machine Elements 41296 GGteborg Sweden

Dr

DGethia

University College Department of Mechanical Eng. University Park Swansea SA28PP U K

519

TITLE NAME Prof

Mr

Mr

Mr

Dr

Mr

MGodet

RTGI~E~II

DHallgreo

CHamer

GMHdIon

RTHanlmg

NAME TITLE -

Institut National Des Sciences Appliquees de Lyon, Laboratoire des Mecanique des Contacts Batiment 113 20 Avenue Albert Einstein 69621 Villeurbanne Lyon, France

Mr

D Ives

Liverpool Polytechnic School of Engineering and Technology Management Byrom Street Liverpool L3 3AF, U K

m

Bo Jacobson

SKF Engineering & Research Centre POB 2350 3430 DT Nieuwegein The Netherlands

Mr

ZMJin

The University of Leeds Institute of Tribology Department of Mechanical Engrg Leeds LS2 9JT U K

Mr

B Jobbimr

The University of Leeds Institute of Tribology Department of Mechanical Engrg. Leeds LS2 9JT U K

Mr

D A Jones

The University of b e d s Institute of Tribology Department of Mechanical Eng. Leeds LS2 9JT U K

Dr

HPeterJostCBE

K S Paul Product Ltd Angle Lodge Laboratories Nobel Road London N18 3DB U K

Mrs

CMKalker

Technical University Delft Department of Mechanical Eng. Fac. der Werktuigbouwkunde en Maritieme Techniek Mekelweg 2 2628 CD Delti Holland

Mr

AFCKanters

Eindhoven University of Technology, Department of Mechanical Engineering, WH 03 110, P 0 Box 513 5600 MB, Eindhoven The Netherlands

Mr

GKapelski

E.N.S.C.I., 47a 73 Avenue Albert Thomas, 87065 Limoges Cedex France

Prof

J J Kauzlarich

University of Virginia Department of Mechanical Engineering, Thornton Hall Charlottesville, VA 22903 USA

City of Birmingham Polytechnic Department of Computing Perry Bar Birmingham B42 2SU UK Mobil Oil Box 502 S-18215 Danderyd Sweden Imperial College of Science and Technology, Tribology Section London SW7 2BX U K Reading University Department of Engineering Whiteknights Reading U K The University of Leeds Department of Mechanical Eng. lnstitute of Tribology Leeds LS2 9JT U K

Mr

JFHarrop

Pratt & Whitney Canada Box 4080, Mississauga Ontario L5A 324 Canada

Mr

SSHsssao


DrIr

G J J van Heijningen

Technical University Delft Fac det Werktuigbouwkunde en Maritieme Techniek Mekelweg 2, 2628 CD Delft Holland

Dr

WAWer

Esso Petroleum Company Ltd Esso Research Centre Milton Hill Abingdon Oxon OX13 6AE U K

P L Holster

Philips Research Laboratories POB 80.000 5600 JA Eindhoven The Netherlands

Mr

CNKo

SKF Engineering & Research Centre BV POB 2350 3430 DT Niewegein The Netherlands


Dr

E M Kopalinsky

The University of New South Wales Department of Mechanical Eng. Kensington N S W 2033 Australia

The University of Birmingham Department of Mechanical Engineering, P 0 Box 363, Birmingham B15 2TT U K

M D r

HKneminsLi-Freds

Instytut Konstrukcji Maseyn Politechnika Lhdska, 90-924 Lbdz, ul. Stefanowskiego 1/15 Poland

Michell Bearings Scotswood Road Newcastle upon Tyne NE15 6LL UK

Dr

M Kuno

NTN Toyo Bearing Co Ltd Material Research Laboratory Kuwana 511, Japan

SKF Engineering & Research Centre BV, POB 2350, 3430 DT Nieuwegein The Netherlands

Dr

C C Kweb

University College Department of Mechanical Eng. Newport Road Cardiff CF2 1TA U K

M Homapnieh

Dr

Dr

h

Dr

AFFLLIATIONIADDREjss

AFFILIATION/ADDRES

CJHooke

DHoroer

EOloannides

K

W

The Ohio State University Department of Mechanical Eng. 206 West 18th Avenue Columbus Ohio 43210 U S A

TITLE NAME -

AFFILIATION/ADDRESS

lTIzLi

NAME

Dr

AASMiranda

Universidade do Minho Av D. Afonso-Henriques 4800 GuimarAes Portugal

Dr

NKMishkh

Institute of Mechanics and Polymer Metals Minsk USSR

Dr

AJMoore

BP Research Centre Chertsey Road Sunbury-on-Thames Middlesex TW16 7LN U K

Dr

SLMoore

B P Research Centre Chertsey Road Sunbury on Thames Middlesex U K

Mr

P G Morton

G E C Engineering Research Centre P 0 Box 30 Lichfield Road Stafford ST17 4LN U K

DrIr

E A Muijderman


Mr

A J Munday

The University of Southainpton Department of Mechancal Eng. Southampton SO9 5NH U K

Dr

J P Naylor

CETIM, 52 Avenue Felix Louat 60304 Senlis France

Mr

D Nelias

Turbomeca Seirice Nisc au Point Bondes, 64320 Bizanos France

Prof

OKKnon

Director, Division of Mechanical Engineering and Electro-Physics, Kaist, P 0 Box 131, Cheongryang, Seoul, Korea

Mr

JLauciriCa

Tekniker Asociacion de Investigacion c/Isasi s/n Eibar Guipbzcoa Spain

Mr

RLee

Jaguar Cars Limited Advanced Engineering Group Jaguar Engineering Centre Abbey Road Whitley Coventry CV34LF U K

Mr

HJvanLeeuwea

Eindhoven University of Technology, Department of Mechanical Engineering, WH 04-102 P 0 Box 513, 5600 MB Eindhoven The Netherlands University of Toronto Department of Mechanical Eng. Toronto, Ontario M5S 1A4 Canada Institut National Des Sciences Appliquees de Lyon, Laboratoire des Mecanique des Contacts Batiment 113 20 Avenue Albert Einstein 69621 Villeurbanne Lyon, France Division of Machine Elements Chalmers University of Tech. 41296 Giiteborg Sweden Superintendent, Quality Engineering Test Establishment Department of Naval Defence Ottawa Ontario KIA OK2 Canada

Mr

JDCMcIwr

DipLIng N Madda

ProfDr.Sc. TUMAnh Nguyen

Hanoi Polytechnic Institute TrGng DaiHoc Bhch Khoa HB Noi Vietnam

Mr

D Nicholson


h

G

Mr

J Olsson

Chaliners University of Tech. Division of Machine Elements S-41296, Giiteborg Sweden

Kings College Department of Mechanical Eng. The Strand London WCZR 2LS U K

N-

Steyr-Bearings, P 0 Box 120, 44004teyr, Austria

Technical University Denmark Department of Machine Elements 2800 Lyngby Denmark

Mr

PMarchand

lnstitut Francais du Petrole BP 311, 92506 Rueil, Malmaison France

Mr

HMqimoo

Imperial College of Science and Technology, Tribology Section London SW72BX U K

Dr

AVOlver

Westland Helicopters Ltd Yeovil Somerset BA20 2YB U K

Consultant 98 Grove Avenue Hanwell London W7 3ES U K

Mr

B Osborne

Industrial Lubrication and Tri bology Peterson House Northhank Berryhill Industrial Estate Droitwich Worc WR9 9BL U K

Mr

IKParter


Dr

A Pannar

John Crane U K Ltd Crossbow House Liverpool Road Slough SL1 4QX U K

Mr

Dr

Mr

FAMartin

JBMedley

DMello

The University of Waterloo Department of Mechanical Eng. Waterloo Ontario Canada N2L 3G1

U S Department of Energy Office of Conservation Washington D C 20585 U S A

521

TFIzEi NAME -

TlTLE

NAM6

AFFILUTION/ADDRESS

Dr

T A StolarsLi

Brunel University Department of Mechanical Eng. Uxbridge, Middlesex UB8 3PH U K

Dr

J D Summers-Smith

Merlewood, The Avenue Guisborough Cleveland TS14 8EE U K

Mr

M Takeda

Technical Centre Europe Karkorstr 15, 4030 Ratingen West Germany

Dr

A G Tangena


Fiat Research Centre Strada Torino 50 10043 Orbassano Torino Italy

Dr

C M Taylor

The University of Leeds Institute of Tribology Department of Mechanical Engrg. Leeds LS2 9JT U K

National Centre of Tribology U K A E A Risley Warrington WA3 6AT U K

Ir

C J Thijsse

Nederlandse Philips Bedrigven B V Centre for Manufacturing Technology - Tribology Building SAQ-2113 5600 MD Eindhoven The Netherlands

Dr

J Trim

SKF Engineering & Research Centre BV POB 2350 3430 DT Nieuwegein The Netherlands

Dr

PJTweedale

Imperial College Department of Chemical Eng. and Technology, Prince Consort Road, South Kensington London SW7 2AZ, U K

Mr

JMValli

Or WP Ceramics Ltd Hameentie 135 D 00560 Helsinki Finland

MI

LCAVaodenat

GEC Avionics Ltd FARL, Airport Works, Rochester, Kent ME1 2XX U K

Dr

Ph V e l a

Institut National des Sciences Appliquees de Lyon, Laboratoire de Mecanique des Contacts Stiment 113, 20 Avenue Albert Einstein, 69621 Villeurbanne Lyon, France

Mr

M Vier

Eindhoven University of Tech. Department of Mechanical Eng. WH 03.110, P 0 Box 513 5600 MB, Eindhoven The Netherlands

Mr

DJWdl

C.E.G.B., Bedminster Down Bridgwater Road Bristol BS13 SAN, U K

Dr

FPWardle

RHP Industrial Bearings Ltd P 0 Box 18 Northern Road Newark Notts NG24 2JF U K

Dr

w WeSam

Head of Department The Polytechnic Queensgate Huddersfield HD1 3DH U K

Dr

PAWikmet

Ford Motor Company Research Laboratory Mail Drop 3179, P 0 Box 2053 Dearborn, MI 48121, U S A

Dr

CPritChard

B R Research Division Room 305 K. Railway Technical Centre, London Road, Derby DE2 SUP U K

Mr

SJRaddi&

Central Electricity Generating Board, Tribology Section Berkeley Nuclear Labs. Berkeley Glos GL13 9PB U K

Mr

Dr

Dr

Mr

Prof

Mr

BRigaut

WHRobeas

RARowntnx?

PhSainsot

RFSalent

ssasaki

CETIM 52 Av. Felix Louat 60304 Senlis France

UK Atomic Energy Authority Risley Technical Centre Risley Warrington Cheshire WA3 6AT U K

Laboratoire de Mkanique des Contacts - Bitiment 113, 20 Avenue Albert Einstein 69621 Villeurbanne, Lyon France Georgia Institute of Technology School of Mechanical Engineering Atlanta, Georgia 30332-0405 USA Mechanical Engineering Lab. Namiki 1-2, Tsuluba-shi Ibaraki 305 Japan

Dr

RSSayh


Dr

PAJblt

Pilgrim Engineering Developments Balinoral House Longmore Avenue Bentley Mill Walsall WS2 ODA Staffs U K

Mrs

ASeyed-Harraf

The University of Leeds Institute of Tribology Department of Mechanical Eng. b e d s LS2 9JT U K

Mr

NPSheldrake


Prof

Mr

Dr

wenshizhu

BAShotter

MStawjevic

Tsinghua University Tribology Research Institute Beijing People's Republic of China Westland Helicopters (Box 245) Engineering Division Yeovil Somerset BA20 2YD U K Vandervell Ltd VanwaU Business Park Maidenhead Berks SL6 4BG U K

522

TlTLE NAME -

AFFJllATION/~DRESS

Mr

wwilsoo

SEPCO Unit9 Surburton Street Attercliffe Coininon Shefield S9 2DN U K

pmt

WOW-

Georgia Institute of Technology George W Woodruss School of Mechanical Engineering Atlanta, GA 30332-0405, U S A

Mr

A J W m


Dr

HXu

Lancashire Polytechnic School of Mechanical and Production Engineering Preston PR1 2TQ U K

pmt

sxu

South East University Department of Mechanical Eng Nanjing People's Republic of China

Mr

JQYm

The University of Leeds Institute of Tribology Department of Mechanical Eng. Leeds LS29JT U K

Mr

M Zarrebini-EMnhani

The University of Leeds Institute of Tribology Department of Mechanical Eng. Leeds LS29JT U K

Mr

RZecbd

Technische Akademie Esslingen Postfach 12 69, D-7302 Osfildern

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Standard Handbook of Machine Design

Standard handbook of machine design

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Textbook of Machine Design (M.E.)

Schaum's Outline of Machine Design

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Electrical Machine Design

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Mark's Calculations For Machine Design

design of abrasive cut off machine

Design Elements for the Workshop

Nonlinear Problems in Machine Design

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