Mathematical and Physical Simulation of the Properties of Hot Rolled Products

This book had its origins in "Thermal-Mechanical Modelling of the Flat Rolling Process", by Pietrzyk and Lenard, Springer-Verlag, 1991. The advances in modeling and computing ability allowed the improvement of the models in the 1991 manuscript. The objective was to explore the possibilities of producing steels with pre-determined attributes, called designer steels. Writing would have been impossible without the help of colleagues, co-workers, students and funding agencies. The authors wish to thank NATO, for funding "Microstructure Control During Hot Strip Rolling", Collaborative Research Grants Programme, CRG 930112. J.G.Lenard is grateful for the financial assistance received from the Natural Sciences and Engineering Research Council of Canada, the Manufacturing Research Corporation of Ontario, Imperial Oil, Dofasco Inc. and Alcan International. The research studies of Drs. P. Munther, J. Biglou, S. Zhang, A. Karagiozis and Y-J Hwu in addition to the work of B. Hum and H. Calquhoun were invaluable and no publication could have resulted without their contributions. M. Pietrzyk is grateful for the assistance received from KEN (Polish Committee for Scientific Research), British Council, and the Maria Sklodowska-Curie Fund. Thanks are also due to Drs. M. Glowacki, Z. Kedzierski, J. Kusiak, R. Kuziak, J. Majta and Z. Malinowski. L. Cser wishes to acknowledge the assistance of Mr. L. Arvai and Dr. K. Farkas. Thanks are due to Dr Pekka Mantyla of Rautaruukki Steel and Prof Antti Korhonen of Helsinki University of Technology for their helpfiil advice. The patience and the assistance of our families must be mentioned. These include Harriet and Patti; Alina, Marta and Wojtek and Lengyel Veronika, Adrienn and Adam. John Wiley and Sons, Inc. is acknowledged for permission to reproduce Figs 4.6, 4.9, 4.12 and 4.14 from "Friction and Wear of Materials", 2°** edition, by E. Rabinowicz. The Iron and Steel Institute of Japan is acknowledged for permission to reproduce Figs 2, 3 and 4 of "Thermo-mechanical Treatment of a High Nb - High V Bearing Microalloyed Steel, 1995, by Tajima and Lenard. Permission to reproduce Figs 3, 4, 5, 10, 12, and 13 from "Modelling the Thermomechanical and Microstructural Evolution During Rolling of a Nb HSLA Steel", by Pietrzyk, Roucoules and Hodgson, ISIJ, 1995, is acknowledged. R. Wusatowski is thanked for permission to reproduce Figs 3.56, 3.57, 3.58 and 3.59fi-omZ. Wusatowski's "Fundamentals of Rolling". The CRC Press is acknowledged for permission to reproduce Tables 3 and 13 from Booser: "Handbook of Lubrication", 2"'' edition. Dr. J. Bartecek is thanked for permission to reproduce Table 3 of "Heat Exchange Between the Workpiece and the Tool in Metal Forming Processes", by Pietrzyk et al. McGraw-Hill is acknowledged for permission to reproduce Figure 4-24 of the text by Schey, "Introduction to Manufacturing Processes", 2"*^ edition. The Japan Society for Technology of Plasticity is thanked for permission to reproduce Fig. 2 of "A Mathematical Model of Cold Rolling - Experimental Substantiation" by Roychoudhury and Lenard. MUNKSGAARD International Publishers Ltd. is acknowledged for permission to reproduce Fig. 5 of "Tribology in Metalforming", by Lenard, in Scand. J. of Metall., 1998, vol. 26, Supplement 1. Springer-Verlag is acknowledged for permission to reproduce Fig. 1.1 of "Thermal-mechanical Modelling of the Flat Rolling Process" by Pietrzyk and Lenard. Profs

VI D.RJ. Owen, E. Onate and E. Hinton are thanked for permission to reproduce Figs 10 and 11 of "Application of the Finite Element Technique to the Interpretation of the Plane Strain Compression Test", by Pietrzyk and Tibballs, Proc. COMPLAS 4. Profs J. Huetink and F.P.T. Baaijens are thanked for permission to reproduce Figs 1 - 7 of "Inverse Analysis Applied to the Evaluation of Rheological and Microstructutral Parameters in Hot Forming of Steels", by Pietrzyk, et al., published in the Proc. NUMIFORM'98. Prof J.H. Beynon and the other editors of the Proc. of the 2"^ Conf on Modelling of Metal Rolling Processes are thanked for permission to reproduce Figs 1 and 10 of "Validation of Finite-Element Models for Asymmetric Rolling", by Pietrzyk, et al. The authors are grateful to Hitachi Review for permission to reproduce Fig. 2 of "New Control Techniques for Cold Rolling Mills" by Hishikawa et al, 1990 and to JSME International for Figs 4 and 5 of "The Development of a Die Sensor" by Yoneyama and Hatamura, 1987. Publisher SIGMA is thanked for permission to reproduce Fig. 9 of "Model profilu blach grubych, przystosowany do systemu sterowania on-line w walcowni blach grubych", Dyja et al., Hutnik, 1998. Publisher AKAPIT is acknowledged for permission to reproduce Figs 4 - 1 1 from the paper by Pietrzyk, et al, "Wykorzystanie komputerowej symulacji do oceny wrazliwosci mikrostruktury i wlasnosci blach na zmiany parametrow technologicznych procesu walcowania na goraco", Proc. KomPlasTech'98. WYDAWNICTWA AGH is thanked for permission to reproduce Fig. 1 of'TSlumerical Aspects of the Simulation of Hot Metal Forming Using Internal Variable Method", by Pietrzyk, Metall Foundry Eng., 1998. Thanks are due to A.A. Balkema for permission to reproduce figures from "Dislocation model for work hardening and recrystallization appUed to the finite-element simulation of hot forming", Pietrzyk, et al, and from "Application of FE simulation of the compression test to the evaluation of constitutive equation for steels at elevated temperatures", Kusiak, et al., both appearing in Simulation of Materials Processing: Theory, Methods and Applications", eds Shen and Dawson. The permission to reproduce figures from the Journal of Materials Processing Technology, received from Elsevier must mentioned. These include the work of Hum, B., Colquhoun, H.W. and Lenard, J.G., 1996, "Measurement? of Friction During Hot Rolling of Aluminum Alloys", J. Mat. Proc. Techn., 60, 331-338; Karagiozis, AN. and Lenard, J.G., 1985, "The Effect of Material Properties on the Coefficient of Friction in Cold Rolling", Proc. Eurotrib'95, Lyon, 17; Zhang, S. and Lenard, J.G., 1996, "Reduction of the Roll Force during Lubricated Cold Rolling of Aluminum Strips", J. Synthetic Lubrication, 12, 303-321; and Lenard, J.G. and Zhang, S., 1997, "A Study of Friction During Lubricated Cold Rolling of an Aluminum Alloy", J. Mat. Proc. Techn., 72, 293-301. Thanks are due for permission to reproduce Figs 2 - 10, from the paper by Majta, et al "A study of the effect of the thermomechanlcal history on the mechanical properties of a high niobium steel". Mat. Sc. & Eng., 1996. The University of Miskolc is thanked for permission to reproduce figures from "Investigation of parameters influencing the accuracy of artificial neural networks in modelling stress-strain curves", Farkas and Arvai. Prof Korhonen is thanked for permission to reproduce figures from the Ph.D. dissertation of P. Myllykoski and from "Application of neural networks in rolling of steel", by Larkiola and Korhonen, Proc. IPMM Conf, 1997. DOFASCO Inc. is thanked for the photograph of their strip mill, pictured on thefrontcover. The expert help in the preparation of the manuscript of Ms. Barbara Krzemien-Kotula and Ms. Halina Kusiak is gratefully acknowledged. Special thanks are extended to Ms. Patti Lenard for the excellent job of proofreading. h4A THEMA TICAL AND PHYSICAL SIMULA TION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

Chapter 1 Introduction The contribution of manufacturing to the gross national product in an industrialized country is a good, albeit not exclusive, indication of its rank among the developed or developing nations. Schey shows some interesting information in his text Introduction to Manufacturing Processes, 2"** ed. (Schey, 1987) by plotting the contribution of manufacturing to the GNP as a fimction of the gross national product per capita. The figure indicates Germany as the leader, followed by Switzeriand and Japan, Italy, France and the USA. The Canadian contribution, in 1982, was near 20%. At the low end of the scale arp the developing nations, including Bangladesh, Zaire and Ethiopia. Using data from the Worid Development Report 1997, published by the Worid Bank (1997), the situation in 1995 is indicated in Figure 1.1. Singapore and China have become major manufacturing nations. As well, Japan has the highest gross domestic product (GDP) per capita income of all nations. At the lower end, developing countries indicate fairly low contributionfi-ommanufacturing to their GDP.

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Figure 1.1 The contribution of manufacturing to the GDP, 1995 In this chapter, the steel industry, a major contributor to the wealth, is discussed in terms of its capabilities and production. Data concerning raw steel capacity and raw steel production are included and discussed. The current concerns of the major steel producers are mentioned. These include the protection of the environment, competition from minimills, upgrading the

quality of the product by improving the adaptive control systems, introducing tool steel rolls to reduce roll wear and investigating the possibilities of direct casting and rolling thin strips. In the words of the former Director of Research of The Steel Company of Canada, Mr. J.C. McKay (1988) ..."there is no material like steel". Its strength, ductility and formability are unmatched by others and Mr. McKay did not think that the competition from aluminum or ceramics is to be taken as a threat at the present time. While the last comment is arguable, it is true that as of now, the formability of aluminum does not approach that of steel, nor does the ductility of ceramics.

1.1

STEEL PRODUCTION

It is of some interest to examine the international situation in terms of raw steel production by steel grade, method of casting and amounts of production. These data are shown in Figures 1.2 and 1.3, giving the total amount of steel production by selected countries and the breakdown by type and method of casting. 1 UULf UUU -

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Figure 1.2 Production of raw steel in the world

It is quite apparent that while total steel production has been declining during the last five years, this decline was limited to approximately 6%. Minor increases are observable in the amount of steel produced in North America and in Western Europe. There is a very serious drop in the steel production data of the former USSR; from a high of 170 million tons in 1990 to 86 million tons in 1994. Surprisingly, this drop was not filled in by the steel companies of the West. Hungary's steel production showed a drop from 1990 when the total was 3.2 million tons, to a low of 1.9 million tons in 1993. There is a marginal increase evident in 1994, to 2.1 million tons. MA THEMA TICAL AND PHYSICAL SIMULA JION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

The breakdown of the production data indicates several changes in the way steel is produced. Figure 1.3 shows some of the trends, presenting information on the types of steel produced and the favoured method of preparing the slabs for hot rolling. The data refers to steel production in the United States only.

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Figure 1.3 Raw steel production by steel type and by billet preparation

There was significant evidence up to the middle of the 1980s that industrialized nations produced and rolled less carbon steels and more alloy steels, reflecting a concentration on the value added product of the higher priced steels. At the same time, less developed nations were increasing their share of the carbon steel markets but did not have the technology necessary to produce the steels requiring careful thermal-mechanical treatment, or in other words, controlled rolling. Figure 1.3 above shows a deviationfi-omthis trend. The amount of carbon steel produced has been growing over the last few years, while the amounts of alloy and stainless steels produced have not changed in a very significant manner. The data do not show the current concerns of customers, however. Among the carbon steels, two new types are involved: the coated steels, especially galvanized steels, which reduce the effects of corrosion, produced for the automotive market, and the extra low carbon steels, containing 0.002 0.004% C, necessitating rolling in the two-phase or the ferrite temperature ranges. Both of these steel types need the extra skill and technology possessed by the companies of the industrialized nations. As well, the method of producing billets has changed drastically. In 1985 almost 50 million tons of steel were prepared from ingots and about 40 million tons by continuous casting. In 1994, the situation is reversed and continuous casting is used in almost 95% of production, indicating the cost saving introduced by the technology change. As mentioned above, the

INTRODUCTION

information in Figure 1.3 refers to the United States only. It may be assumed with some assurance, however, that the trends are universal.

1.2

FUTURE CHANGES IN PERSONNEL

The Canadian Steel Trade and Employment Congress is a joint initiative of the United Steelworkers of America and Canada's steel companies. In a recent brochure (Steel in Our Future, 1995) the Congress stated its views on the future of steel in North America, referring to the United States, Canada and Mexico. The brochure discusses the changing face of the steel trade. It comments on the "customerdriven" and "environmentally-conscious" technologies one must use. As well, while the basic ideas of steel making and steel producing have not changed, the details of the processes have. The people and the products are vastly different. A direct quotation from the brochure is especially interesting: *'By 1980, you needed a high school education to get a job in the mill. As we approach the year 2000, you will require a post-secondary education *\ In the opinion of the authors and considering the introduction of high technology in the steel industry and the requirement for increasing the value-added component of the product, the statement may be applied universally. The recent cover story in The Economist (The Economist, 1998) also indicates that the nature of manufacturing has changed and now demands highly qualified workers, able to deal with the increased complexities of production.

1.3

COMPETITION FROM OTHER MATERIALS

Steel competes with aluminum, plastics, composites and ceramics and this competition is the fiercest in the automotive industry as over the last decade the pressure for increased fuel economy resulted in the need for lighter weight cars. The competition is not over as the pressure for even lower fiiel consumption has not abated. While there was a considerable change in the amount of steel and iron used in vehicles in favor of the alternatives, there is some evidence that in the recent past, steel has been enjoying increased use. Steel's ease in manufacturability, advances in optimizing techniques and complete recyclability are the reasons for this comeback (Driving Your Future, 1995). Some examples indicate the trend. While the original design for the 1996 Sable and Taurus included an aluminum hood and fender, the cars were introduced into the market with steel for those parts. The roof of the 1996 Saturn is made of steel instead of a combination of steel and plastic. The rear subframe of the 1997 Corvette is manufactured from hydroformed steel tubing, instead of aluminum extrusions. Some of these facts are illustrated in Figure 1.4. It is apparent that while steel usage has increased, the amount of the other materials has remained largely unchanged. The efforts in the aluminum industry, toward making aluminum competitive with steel, are not to be underestimated. Considerable research is being devoted to studies of the formability MA THEMA JJCAL AND PHYSICAL SIMULA TION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

of aluminum sheets. The work considers, among others, the process of forming, the tribology problems at the die/metal interface, the development of new alloys in addition to a constant search for improved productivity. The steel engineers are, of course, aware of the necessary trends toward lighter weight vehicles, as evidenced by the development of the ultra light weight car frame whose performance has exceeded the original specifications. 2000.0

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1.4

CURRENT CONCERNS

Minimills: Dominance of the integrated steel producers is increasingly challenged by the minimills with lower costs of production. Minimill technology emerged in the 1970s, originally used for the production of specialty steels. The small mills have expanded their operations to produce carbon steels in a very short time period. The cost reduction was obtained mostly from producing liquid steel from scrap, using an electric furnace, lowering capital costs per ton of annual steelmaking capacity to one third that of a new integrated mill. Initially, minimills produced no more than half a million tons per year. This amount increased fast, however, and many of them now produce over one million tons. Protection of the environment: The need for the protection of the environment is realized by steel producers and environmental management is now an integral part of plant management at all modem steel mills. Recycling is built into the steelmaking process. Examples of environmental innovations include several processes. The development of pulverized coal injection reduces the need for coke. This process is expected to replace about 15% of coal consumption by the year 2000. Electric arc furnace technologies, including new direct current furnaces, which consume about 350 kWh per ton, compared to 500 kWh per ton of the older models, will reduce energy consumption, which in INTRODUCTION

turn will reduce pollution. Waste recycling is, of course, also used in the plants. Finally, steel is acknowledged as the most recycled material. Cost reduction: Mr. R. Ackert (Algoma Steel Corp., Sault Ste. Marie, Canada, private communication, 1994) indicated that the current trend in the industry is toward cost reduction by eliminating non-essential process steps, many of which are energy intensive. He also identified problems associated with direct rolling, eliminating the reheating process. As examples, he mentioned the NUCOR plants, the SMS technology and the efforts of Voest Alpine. Further, the post-roUmg heat treatment may also be eliminated by careful planning of the thermo-mechanical process during rolling and accelerated cooling. Quality improvements: In order to address the demands of customers for increased quality of the product, new control systems are being planned. These include the possibility of introducing some elements of artificial intelligence m the adaptive control schemes of hot strip mills and cold rolling mills. Tool steel rolls: Roll wear costs are about 10% of the cost of steel production. Introducing tool steels for the work rolls of hot strip mills appears to reduce roll wear by a substantial amount. Direct casting and rolling: The Projet Bessemer, located in Boucherville, Quebec, deals with the possibility of minimizing the rolling process during the production of thin strips, directly usable for fiirther cold rolling. The prototype mill, now in operation, can produce thickness as low as 2 millimeters. One rolling stand is located downstream fi-om the tundish. The aim is to refine the technology such that the mechanical, metallurgical and geometrical quality of the direct cast and rolled strip is as good or better than the one obtained by the present techniques. The mill is operated by a consortium of Canadian steel companies. The possibility of dynamic reaystaUizaiion during strip rolling: In continuous rod and bar rolling processes, extremely high strain rates (100-1000 s'*) and short ihterpass times (between few tens of milliseconds to few hundreds of milliseconds) are bang employed. Typical strains per pass (0.4-0.6) are lower than the critical strain for the onset of dynamic recrystallization at high strain rates. However, due to the very short interpass times, there is not enou^ time for complete static recrystallization of deformed austenite at rolling temperatures, especially in microalloyed steels. Consequently, the strain is retained to the next pass and this strain accumulation may exceed the level of the critical strain. In this case, dynamic recrystallization may occur during rolling, and wiU be followed by metadynamic recrystallization. Until recently, it was generally accepted that in plate and strip rolling with longer interpass times, there is no possibility of pass to pass strain accumulation, which is required for the initiation of dynamic recrystallization. The retarding effects of microalloying elements on the recrystallization kkietics are well known. Recently, it has been proposed that under appropriate conditions (low temperatures, high strains per pass and some limited precipitation), it is possible to accumulate large enough strains to initiate dynamic recrystallization during strip rolling of niobium microaUoyed steels. The possibility of the occurrence of dynamic recrystallization during strip roUmg has major industrial implications. Ignoring the possibility of dynamic recrystallization during strip rolling may lead to errors in roll force predictions. For nearly all practical deformation conditions at moderate to high strain rates, dynamic recrystallization is expected to produce significant grain refinement resulting in monotonic stress-strain curves. Another advantage is a reduction in rolling loads.

MATHEMATICAL AND PHYSICAL SIMULATION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

1.5

THE ROLLING PROCESS

In what follows, the rolling process will be discussed in terms of hot and cold rolling of flat products. The concept of the process is simple and well known. Strips or plates are passed through two hardened steel cylinders, rotating in opposite directions. During the pass the thickness of the work piece is reduced, its length is increased while its width remains largely unchanged. The usual practice is to roll first at high temperatures, followed by cold rolling. The billets have been prepared by the continuous casting process. They are reheated in the soaking pits and are hot rolled next, in hot strip mills. The layers of scale are removed by pickling and further reductions are obtained by cold rolling. One of the traditional aims of hot rolling is to reduce the size of slab at as high a temperature as possible, thereby reducing the mill loads and increasing the tonnage. During the past 40 years, the technologies of process control have been widely developed in order to satisfy the demand for highly accurate dimensions, for closely controlled mechanical/physical properties and for high productivity. For a modem hot strip mill, process control is fiilly computerized, so the properties of the final product may be precisely controlled. The objectives of subsequent cold rolling include the production of sheets possessing high quality surfaces and accurate and consistent dimensions in addition to high speeds, required by the increasing demands for high rates of production.

L5.1 The hot rolling process A schematic diagram of a hot strip mill is depicted in Figure 1.5.

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There are five major parts in the hot strip rolling process. They are: •

Reheating: The slab is heated up to 1200~1250°C in a fiimace to remove the cast dendrite structures and dissolve most of the alloying elements.

INTRODUCTION

•

•

• •

1.5.2

Rough rolling: Before rolling, the scale is removed by a high pressure water spray in the descaling box. The slab is rolled in the roughing stands. The thickness of the slab is reduced from approximately 270 mm to about 50 mm. The width is controlled by edge rolling. At the end of rough rolling, the strip is sent to the finishing mill along the transfer table. Finish rolling: The finishing mill is composed of five to seven tandem stands. The strip is continuously rolled in the finishing mill. At the entry to the finishing mill, the temperature of the strip is measured and at the exit, both temperature and thickness are measured. The Automatic Gauge Control (AGC) system uses the feedback signal from the gauge meter to control the exit thickness of the strip. The finishing temperature is controlled by changing the rolling speed. Cooling: After rolling, the strip is cooled by a water curtain on the runout table. Coiling: At the exit of the runout table, the temperature of the strip is measured and the strip is coiled by the coiler. The cold rolling process

The layer of scales are removed from the surfaces of the strips and fiirther reduction of the thickness is produced by cold rolling.

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Figure 1.6 A schematic diagram of a modem cold rolling mill for aluminum (Hishikawa et al., 1990, reproduced with permission) MA THEMA TICAL AND PHYSICAL SIMULA TION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

A large variation of configurations are possible in this process. An example of a modem cold rolling mill, for aluminum, is shown in Figure 1.6. The mill is six-high; having two small diameter work rolls of 470 mm diameter and two sets of backup rolls. The diameter of the intermediate backup roll is 510 mm and the third backup roll is of 1300 mm diameter. The mill is capable of producing strips of 0.08 mm thickness at speeds up to 1800 meters per minute.

1.6 IMPROVEMENTS OF THE ROLLING PROCESS The process of rolling has been around for some time and it is well known. The basic ideas have not changed; the thickness of a piece of metal is reduced while its length is increased. The possibilities of improvements are to be considered in terms of the mechanical, metallurgical and geometrical attributes on the product, by increasing its value-added product. This implies that the control of the process must be enhanced. This is possible by examining the components of the rolling system and devising ways of changing them to reach the desired improvements. Providing the information necessary for those improvements is the objective of this book. Realizing that control of the rolling process relies on mathematical and physical simulation, these form the major focus of the study. The components are reviewed, discussed and applied to various forms of the process. Mathematical predictions are made, always with a parallel set of measurements. The conclusions regarding the ability of a model to predict the variables are arrived at only after successful comparisons.

1.7

THE CONTENTS OF THE BOOK

There are ten chapters in this book. In the present chapter, Introduction, the economics of steel making and the rolling of flat products, both hot and cold, are considered. The argument is made that improvements of product quality and productivity are necessary to maintain competitiveness. In a process, such as flat rolling, in which the basic idea has not changed for a considerable time, successful improvements require a very complete, thorough understanding of the physics and the mechanics of the phenomena. This is possible through physical and mathematical modeling and that is the major concern of the book. The topics of the following chapters are concerned with the components that are needed in building up a physical or a mathematical model of the rolling process. In each case, mathematical modeling and the substantiation of the predictions of the model are presented in parallel. Tribology, including friction, lubrication, heat transfer and wear, is discussed in Chapter 2. A brief introduction to the basic ideas of friction is first. This is followed by a presentation of the background necessary for an understanding of the principles of lubrication, including the thickness of lubricant films, the various lubricating regimes, and the effect of lubrication on the mill loads. A look at the effects of heat transfer on the rolling process is next. The last topic, before Case Studies, is the wear of work rolls. In the Case Studies, recent experimental resuhs, concerning tribological problems, are reviewed. These include measurements of frictional and heat transfer coefficients and the ability of oils to lower the forces and torques on the mill. The resistance of the material to deformation is treated in Chapter 3. The methods and the difficulties in obtaining true stress-true strain curves, under isothermal conditions, at constant, INTRODUCTION

22 true strain rates, are described. The types of mathematical models, applicable to represent the constitutive behavior of the metals, at high and at low temperatures, are shown. Specific examples of stress-strain curves are demonstrated in the Case Studies. The boundary conditions, connected with tribology, and the initial conditions, connected with the material's flow strength, are put to use in Chapter 4, dealing with modeling the rolling process. An empirical model and several one-dimensional models are presented, all of which are designed to calculate one or more of the rolling parameters: the roll separating force, the roll torque, the roll pressure, the power, the temperature rise and the forward slip The detailed derivations are not given, instead, the readers are asked to consult the appropriate references. The sensitivity of the predictions of the models to various parameters is considered. The chapter closes with an examination of the predictive capabilities of the models, applicable for both hot and cold rolling. Thefinite-elementmodel is analyzed next, in Chapter 5, as appHed to the flat rolling process. The basic ideas of the finite-element approach are described and are applied to several examples. Rigid-plastic and elastic-plastic formulations are considered. Symmetric and non-symmetric rolling are examined. The possibilities of modeling the microstructural phenomena during hot forming and subsequent cooling are reviewed in Chapter 6. The critical temperatures are listed and discussed. The metallurgical events, such as the hardening and restoration mechanisms, are presented. The models developed by others and by the present writers are given next. The predictions of the models are compared to experimental results as well as information, obtained fi-om industry. Shape rolling is described in Chapter 7. The usual method to deal with the threedimensional aspects of shape rolling is to use three-dimensional models. The disadvantages of this approach include the long computing times and the large memory requirements. An alternative technique is introduced, in which the two-dimensional FE approach can be used to calculate the three-dimensional distribution of the variables. The calculations are coupled with the relations, describing the evolution of the microstructure, and the predictions are compared to data, developed under closely controlled circumstances. One-dimensional models and their predictive abilities are also given in the chapter. The inverse method, designed to take advantage of the non-homogeneous nature of plastic deformation, is presented in Chapter 8. The method is applied to determine the behavior of metals, subjected to large plastic flow. Knowledge based modeling, including the use of artificial intelligence, expert systems, fiizzy sets and logic and neural networks, is an exciting approach to analyze the rolling process. The possibilities are given in Chapter 9, starting with several definitions of terms, not commonly used in engineering. Acquisition of knowledge and its storage are considered. Data mining and the use of self organizing maps in the hot rolling process are demonstrated. In the case studies, the use of these techniques is discussed and applied to several problems associated with the rolling process. Afi-amework, to allow the use of neural networks in the prediction of the grain size in hot rolling, is the first example. This is followed by the application of neural networks to the prediction of constitutive behavior of steels and aluminum and to the prediction of the roll separating force during hot rolling of strips of the two alloys. Conclusions are listed in Chapter 10. These are given chapter by chapter, recapitulating the major points in each. MA THEMA TICAL AND PHYSICAL SIMULA TION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

n Chapter 2 Tribology of Flat Rolling and the Boundary Conditions Tribology is defined as the study of contacting surfaces in relative motion. In metal forming, these surfaces refer to the contact between the workpiece and the forming die and in the present context of flat rolling the contacting surfaces involve the work roll and the rolled metal. Traditionally, tribology has been taken to be concerned with fiiction, lubrication and wear. The transfer of heat at the contacting surfaces must also be included in the phenomena, since it is the transfer of forces aw^heat at the surfaces of contact that contributes to fiictional resistance, creates wear of the rolls and hence, causes surface damage to the rolled product. During flat rolling, the transfer of forces at the roll/workpiece interface is accomplished by the normal stresses and by the shear stresses. It is the usual practice to define the average, over the roll gap, of their ratio as the coefficient of fiiction. The transfer of heat is described most conveniently in terms of the proportionality of the heat flux to the diflference of the average temperatures of the contacting surfaces, with the factor of proportionality defined as the heat transfer coefficient. Knowledge of the manner of the dependence of these coefficients on process and material parameters is necessary for successfiil process and product design. As well, accurate and consistent modeling - both predictive and adaptive - of the phenomena in the roll gap and the boundary conditions of the deformation zone in flat rolling requires the same information. Understanding the dependence of// and a on the parameters would lead to an appreciation of their attendant influence on roll wear, reported to cost as much as 10% of total processing costs. Further, product surface quality, of prime concern to customers, and because of that, to the engineers of the steel industry, would be improved. As written by Roberts (1997): *'Ofall the variables associated with rolling, none is more important than friction in the roll bite. Friction in rolling, as in many other mechanical processes can be a best friend or a mortal enemy, and its control within an optimum range for each process is essential. " While Roberts wrote about fiiction in the roll bite, it is appropriate to suggest a change to his quote and replace the term "fiiction" with "tribology", including all its four components fiiction, lubrication, heat transfer and wear. These concerns are currently of special significance as the traditional cast iron and high Cr rolls are being replaced by tool steel rolls in hot strip mills, making the study of tribology an important research priority. The first objective of this chapter is to present a brief discussion of the essential components of tribology as a "tribological system" and the adhesion hypothesis, as applied to metal forming and especially to flat rolling of metals. This discussion is followed by a compilation and review of the background and recent technical literature on fiiction, lubrication, heat

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^

,

transfer and roll wear, in terms of the effects of the important parameters on the roll forces, the roll torques, the forward slip and the coefficients of friction and heat transfer. Experimental techniques used to determine them are given. Published values of the coefficients of friction and heat transfer are also shown, indicating the difficulties in measurements, contradictions and the missing information. Results of flat rolling experiments using aluminum and steel strips are then presented, with the reduction per pass, the temperature, the rolling speed and the lubricant and its additives chosen as the process parameters. While some of the case studies deal with cold rolling, the information presented and the trends observed are helpful when dealing with high temperature phenomena. As pointed out by reseeirchers, data on friction, obtained using a bench machine, have not been found to correlate well with industrial experience. The authors agree with this observation and are convinced that the statement is equally valid for all aspects of tribology. In the experimental work reported below, two laboratory scale rolling mills were employed. As far as possible, the process parameters were chosen to be close to industrial conditions.

2.1

THE TRTOOLOGICAL SYSTEM

Several researchers define the "tribological system" in terms of the process and material parameters. Since both coefficients of heat transfer and fiiction depend on surface interactions, both are affected by essentially the same set of parameters. Perhaps the best definition of a tribological system is given by Schey (1983), who identified the components and the parameters of the system and indicated their interactions in an easy-to-read flowchart. In the rolling process the three components are the work roll, the lubricant and the workpiece, which is the rolled strip. The parameters, which are listed for the die, the lubricant, the workpiece and the process, operate together to create the final product. Three regimes of lubrication are also identified. These are the boundary, hydrodynamic and plastohydrodynamic regimes. The interactions of the parameters in each of these regimes are indicated, as well. These interactions are influenced by a large number of material and process parameters, affecting the mechanical and thermal phenomena at the contact (Rabinowicz, 1965, 1995; Schey, 1983; Bowden and Tabor, 1950). Process parameters include the temperature, speed, and reduction. In addition, the attributes of the mill affect tribology: roll diameter, hardness, surface roughness, roll cooling, bearing design, mill stiffiiess, lubricant delivery systems, including the locations of the nozzles, all contribute here. Mechanical properties of the rolls and the rolled material, including the yield stress, resistance to deformation, penetration hardness - that is, surface and bulk hardness - Young's modulus, shear modulus, density and stored elastic energy as well as the thermo-physical properties - heat transfer coefficient, heat conduction coefficient, specific heat, thermal expansion - also affect the interactions. Surface parameters, such as the chemical reactivity, defined as the tendency to acquire a film of different chemical composition than that of the rolls or rolled material, the tendency to adsorb molecules from the environment, the adsorption of water vapor and oxygen and surface energy need to be understood. Further, the random nature of scale formation, the chemical composition of the scale and the strength of the adhesive forces between the layer of scale and the parent metal must be accounted for in the studies. This indicates that the chemical MATHEMATICAL AND PHYSICAL SIMULATION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

13 composition of the hot metal and that of the layer of scale, will also influence surface interactions. Lubricants affect surface interactions in a very significant manner and their properties must be precisely described. The chemical composition, the additives and their concentration in the base oil, the chain length, density, viscosity, viscosity - temperature, viscosity - pressure characteristics need to be known. A schematic diagram of a four-high mill, the rolled strip, lubricant delivery and some of the significant phenomena are shown in Figure 2.1.

Roll separating force Back-up roil Emulsion spray Roll torque" Work roll

Roll flattening Friction Normal stresses Heat transfer Roll wear

Rolled strip Surface defects

Figure 2.1 Rolling a strip in a four-high mill

2.1.1

The adhesion hypothesis

The hypothesis, presented by Bowden and Tabor (1950), explains the origins of resistance to motion in terms of adhesive bonds formed between the two contacting surfaces that are an interatomic distance apart. In a later publication, Bowden and Tabor (1973) credit the French scientist Desaguliers, living and working in the 18*^ century, with this idea and reproduce his account of an experiment with two lead balls which, when pressed and twisted together by hand, created adhesive bonds and were able to hold a load of 16 lbs. It is understood that engineering surfaces are never completely smooth and that they contain asperities and valleys, observable when viewed under suitable magnification. Contact occurs at the asperities, implying that the real contact area is significantly smaller than the apparent area Thus, when the two surfaces come in contact, one must distinguish between the apparent area of contact and the true area, the second of which indicating the totality of contact spots at the asperities. If the surfaces are clean, the atoms are close enough such that in order to separate them the force of attraction between them must be overcome. Cleanliness of the surface, such as the one needed for the adhesion hypothesis to be fiiUy operative, is obtained when new surfaces are created, either by plastic forming or by machining. The adhesive bond must be TRIBOLOGY OF FLAT ROLLING AND THE BOUNDARY CONDITIONS

^4 separated if relative motion is to occur. This separation may take place at the junction itself or one of the contacting metals may shear. In fact, the weakest component will give. If that is the forming die, the roll, roll wear is enhanced. If the rolled metal gives, as it often does, surface damage may result. As the load increases, the asperities flatten and the real area contact approaches that of the apparent area. The number of contacting asperities also grows and it follows that, as long as no lubricants are used, frictional resistance to relative motion would also increase, pointing out the dependence of friction on material properties, specifically on the resistance of the metals to deformation. As will be argued later, increasing loads may lead to increasing or decreasing coefficients of fhction, depending on the interaction of the parameters. Formation of the bonds takes time, indicating that the magnitude of the relative velocity of the interacting bodies, as well as the rate sensitivity of their resistance to deformation, may play important roles in determining the magnitude of the fiictional forces. Heat is transferred at the contact points, affecting the mechanical and thermal properties at the surface. As implied by the adhesion hypothesis, many of these parameters interact with and affect each other. Lubricants are used in the metal forming industry to control friction, to reduce the loads on the forming machinery, that is, on the rollmg mill, and to minimize the wear of the work rolls and the back-up rolls. As well, lubricants, through these actions, contribute to the production of high quality rolled surfaces, of prime importance to the producers. Four phenomena are of special interest when the flat rolling process is considered. The first is the type of lubricating regime - boundary, mixed, hydrodynamic - in existence in the contact zone. The second is the lubricant itself its chemical composition, including the anti-fiiction, extreme pressure, boundary and anti-oxidant additives; the viscosity of the oil and its dependence on the pressure and the temperature. The roughness of the roll and the rolled metal and the direction of the grooves - around the roll, created by a slow moving grinding wheel along the roll, or in a random direction, possibly manufactured by electrical discharge machining - are also of importance as is the thickness of the oil film. Lubricants may be applied neat as done during cold rolling of aluminum strips or in an emulsion, as is the practice when steel strips are rolled, either hot or cold. Emulsions are also employed during hot rolling of aluminum strips and slabs. The emulsions are often made up of water as the carrier, to which the oil, mixed with a suitable emulsifier and other additives, is added, in various concentrations. In that case, static and dynamic droplet size, flow rate, pressure, the type of the nozzles, their location and the location of where the spray is aimed at may also affect the events at the interface in a significant manner.

2.2

INTERACTIONS AT THE SURFACE OF CONTACT

As mentioned above, the phenomena at the surface of contact include fiictional events, lubrication, the transfer of heat and their result, the wear of the work rolls and surface defects of the rolled product. In what follows, these will be reviewed briefly, with reference to the process of flat rolling of metals, both hot and cold. In these processes, the surface of contact refers to the region between the roll and the workpiece. Friction is treated first, followed by a presentation of the effects of lubrication on the rolling process. Heat transfer is next. The last topic is the wear of work rolls. MATHEMAHCAL AND PHYSICAL SIMULATION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

15 2.2.1

Friction

The basic idea is, of course, well known: when an object, in contact with another, is to be moved relative to the other, some resistance must be overcome. This resistance is caused by the interaction of the two bodies and is referred to as the interfacial friction. Overcoming it requires some effort and adds to the total work expended in starting and maintaining the relative movement of the parts. In the flat rolling process, friction at the roll - rolled metal interface is of immediate concern in this chapter. It is noted, however, that when the mill is designed and the driving motor, the spindles, bearings and the joints are sized, frictional resistance in all components of the mill must be considered. The traditional theory of friction has been suggested by Amonton who stated it 1699. As given by Hutchings (1992), the first law states that the fiiction force and the normal force are proportional, with the constant of proportionality defined as the coefficient of friction. The second observation concerns the independence of the fHctional resistance on the apparent area of contact. The third postulate considers the independence of the magnitude of the friction force on the sliding velocity. Rabinowicz (1995), in his new edition of the original text on friction and wear of materials (Rabinowicz, 1965), also discusses these three postulates. He indicates that while the first two postulates are close to actual events, experimental evidence shows that the third one is not. 2.2,1,1

Techniques of measurements for the coefficient of friction in flat rolling

Several methods for measuring interfacial fiiction during plastic deformation have been developed, some of which have been listed by Wang and Lenard (1992). A more comprehensive list, applicable to other metal forming processes, including bulk and sheet metal forming, has been presented by Schey (1983). In summary, they may be divided into the following categories: Direct measurement methods: The most typical in this group is the embedded pin transducer technique. Originally suggested by Siebel and Lueg (1933) and adapted by van Rooyen and Backofen (1960) and Al-Salehi et al. (1973), the method has been applied to measure interfacial conditions in cold rolling (Karagiozis and Lenard, 1985; Lenard and Malinowski, 1993; Lim and Lenard, 1984). Variations of this procedure have been presented by Lenard (1990, 1991) and Yoneyama and Hatamura (1987). A cantilever, machined out of the roll such that its tip is in the contact zone and fitted with straingauges, and its various refinements were presented by Banerji and Rice (1972) and Jeswiet (1991). Detailed information of the distributions of interfacial fiictional shear stresses and die - that is, the work roll - pressures may be obtained by these methods, but the experimental setup and the data acquisition are elaborate and costly. Since the major criticism concerns the possibility of some metal or oxide intruding into the clearance between the pins and their housing, it is necessary to substantiate the resulting coefficients of fiiction by independent means. This substantiation has been performed successfully in several instances (see, for example, Hum, Colquhoun and Lenard, 1996), demonstrating that the technique leads to reliable data. Measuring the average frictional shear stresses or the average coefficient of friction at the interface: Examples of methods belonging to this group are plane-strain drawing Pawelski TRIBOLOGY OF FLAT ROLLING AND THE BOUNDARY CONDITIONS

^6

^__

^

(1964), plane-strain compression with parted dies (Nagamatsu et al., 1970), and the draw-bead test, pull-out test or the twist-compression test (Schey, 1983). The draw-bead test, when performed with care, has been shown to give consistent results. A powerful and often used method is the ring-compression test, yielding the friction faaor. The relationship of the coefficient offriction,obtained by these techniques, to that in the flat rolling process, has not beenfiiUyestablished as yet. Deriving the constant friction factor or coefficient of friction front the measured deformation load: This method may be applied to various processes, such as uniaxial compression (Schroeder and Webster, 1949), extrusion, drawing and rolling (Evans and Avitzur, 1968). The resulting magnitude of the coefficient of friction will depend on the completeness of the model used for its determination. Determining the constant friction shear factor or coefficient of friction by measurements of deformation or other indirect indices: Examples involve uniaxial compression with a tapered punch (Wang, 1983); measuring the forward slip or the bite angle inflatrolling (Roberts, 1983; Reid and Schey, 1978); monitoring the fold-over in plane-strain compression (Avitzur and Kohser, 1978); or the extrusion-forging test, proposed by Gunasekera and Mahadeva (1988). The most popular and most widely used technique, however, is theringcompression test (Male and Cockroft, 1964; DePierre and Gumey, 1974). Calculating the coefficient of friction from measured values of the forward slip: Several formulae relating the coeflfident offrictionto the forward slip in terms of geometry or other parameters (Lenard, 1992) have been published in the literature. As will be discussed below, best results are obtained when all parameters - the forward slip, roll force and roll torque - are taken into account (Lenard and Zhang, 1997). Caution is needed, as the results depend, in a very significant manner, on the mathematical model used in the computations. Two of these approaches are usefiil when determining the coefficient of friction in the flat rolling process. One involves direct measurements, while the other is an inverse analysis, in which a parameter, such as the roll force, is measured and a model, in which ju is treated as a free parameter, is used to match the measured force. In the second approach the quality of the results depends on the quality and therigorof the mathematical model used. Direct measurements of the coefficient offrictionmflatrolling are possible by following the suggestions of Pavlov, quoted in Underwood's text (Underwood, 1950). By applying a large tension to the strip, the neutral point is moved to the exit, allowing the iniference of the magnitude of the coefficient from the measured roll force and torque. In another technique, the minimum coefficient offrictionis identified at the reduction at which no roll bite occurs. Both techniques lead to an average value of the coefficient. Transducers embedded in the roll, first used by Siebel and Lueg (1933) and their refinements, give the roll pressure, the interfacial shear stress and the coefficient offriction,which has been shown not to remain constant in the roll gap. Two close-up pictures of a four-pin-transducer combination are shown in Figures 2.2 and 2.3, below, reproducedfromHum et al., (1996). As shown, there are four transducers and pins. Two of these are positioned in the radial direction, while two are tilted at 25° from the radial. The transducers in the radial direction are expected to yield identical or nearly identical MA THEMA TICAL AND PHYSICAL SIMULA TION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

data. When this is the case, the test is successful. Force analysis of the pins, each of which are loaded by the normal and shear forces at the contact surface, leads to the roll pressure and the shear stress distribution along the roll gap. The average of their ratio is reported as the actual coefficient of friction in the deformation zone. As mentioned above, the usual critique of the embedded pin - transducer technique is possibility that some of the rolled metal will enter the clearance between the pin and its housing. This is true, of course. However, a properly formulated model, used to extract the coefficient of friction from the collected data, must account for the effect of the resistance to movement of the pins in their carefiiUy drilled and honed holes on fiiction at the roll surface. Further, data produced using the technique may and should be substantiated in several independent ways. The roll force, measured independently by the force transducers located under or over the work roll bearing blocks, should equal the result of integration of the measured roll pressure distribution over the contact length. As well, the roll torque should be close to the resuh of the integration, again over the surface of contact, of the shear force, multiplied by the roll radius. Mathematical models, using the experimentally obtained coefficient of friction, should also yield roll forces, torques and forward slip of the correct magnitudes. Another variation of the embedded pin - transducer method was presented by Yoneyama and co-workers and used to measure the stresses and the temperatures at the roll - strip contact (Yoneyama and Hatamura, 1989; Hatamura and Yoneyama, 1988). The structure of the three-dimensional stress detector and the die-sensor used by Yoneyama and Hatamura is reproduced in Figure 2.4.

Figure 2.2 The embedded transducers Figure 2.3 The pins (Hum, Colquhoun and Lenard, 1996, reproduced with permission) TRIBOLOGY OF FLAT ROLLING AND THE BOUNDARY CONDITIONS

18

Deformation part for z-direction

Pin diameter: 3.0 rm Hole diameter: 3.1 mm Case Detective pin 3-dlrectlonal stress detector Parallel circular Plate Tight fit

Figure 2.4 The sensor of Yoneyama and Hatamura (1987), reproduced with permission

The inverse method has also been used to infer what the coefficient of friction must have been in a particular rolling pass (Lenard and Zhang, 1997). As mentioned above, the technique is useful but its results depend on the quality and rigor of the model. Implications of the choice of the mathematical model will be discussed below. 2,2. /. 2

Calculating the coefficient of friction

Relationships connecting the coefficient of friction to several parameters, have been published in the technical literature. Most of these rely on matching the measured and calculated roll separating force and choosing the coefficient of friction to allow that match. Cold rolling: The equation, given by Hill, is quoted by Hoffman and Sachs (1953), in the form: 1.08+1.02 r-y/R'Ah

K h^

/' = " 1.79 1 -

i^^

MATHEMATICAL AND PHYSICAL SIMULATION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

(2.1)

^^^^

19

where Pr is the roll separating force per unit width, a is the average flow strength in the pass and R' is the radius of the flattened roll, calculated by Hitchcock's relation, (see Eq. 4.6 in Chapter 4, One-dimensional Models). This formula has been used in several instances. Roberts (1967) derived a relationship for the coefficient of fiiction in terms of the roll separating force Pr, the radius of theflattenedroll R \ the reduction r, the average of the tensile stresses at the entry and exit GI, the average flow strength of the metal in the pass, a, and the entry thickness of the strip, hemry'-

. = = %

PM-r) r~i cr-J\J\J\J

[

I

+ 20000 - O n [A

T = 300°C ^ p = 30 MPa p = 50 MPa P = 70 MPa p = 90MPaj

^

I

A A A

20000

A

(D O

A

15000-

T = 500*C ] P = 30 MPa o P = 50 MPa D P = 70 MPa A P = 90 MPa J

+

.«> 15000

A A

1

^AAAAAAAAAA

10000-

8 A^^

^, 10000 H

n° °

0° ° 5000-

%

^/^^^"^^^ n -1 1

10

5000

++++^++ * 1

1 20 30 time of contact (s)

1 40

Figure 2.8 The coefficient of heat transfer; 300X

50

10

I 1 I 20 30 40 time of contact (s)

50

Figure 2.9 The coefficient of heat transfer; 500°C

The heat transfer coefficients, as computed by the inverse technique described above, vary in a broad range from 50 to 20000 W/Km^ For the first 2 - 5 seconds, a increases at a reasonably fast rate but its magnitude is not very large, indicating that the combined effects of the developing mechanisms cause those changes. These include the rate of rise of the pressure, reaching its full magnitude, typically in less than 0.8 seconds; the corresponding increase of the heat flux and the decrease of the difference of the temperatures of the two contacting surfaces, the ratio of which defines the coefficient of heat transfer. After approximately 5 seconds of contact, a much slower rise of the coefficient or steady-state conditions are observed. The slow rise of a appears to be connected to higher interfacial pressures, regardless of the MA THEMA TICAL AND PHYSICAL SIMULA TION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

35 temperatures. The heat transfer coefficient then remains constant at pressures below 70 MPa. The exception is indicated by the data for the experiments in which the initial workpiece temperature was 900°C. Fast initial rise of a is still noted but the rate of rise of the heat transfer coefficient at the higher pressures is lower than before. Steady-state condition is achieved noticeably later. The heat transfer coefficient appears to be strongly dependent on the interfacial pressures at all of the test temperatures. It does not appear however, to be as strongly dependent on the temperature. 20000

^ t

16000

20000 T = 700*^ 1 + P = 30 MPa o P = 60 MPa n P = 70 MPa A P = 90 MPa

12000

fc

1 i

A~ «nnDD 0 0 0 0 0 0 0

8000 >

ooo%4

4000

1

10

I

\

1—

20 30 40 time of contact (s)

Figure 2.10 The coefficient of heat transfer; 700°C

50

"T 20 30 time of contact (s)

Figure 2.11 The coefficient of heat transfer; 900°C

Steady-state conditions are reached in most of the experiments, indicating that the ratio of the heat flux and the interfacial temperature diffisrence remains reasonably constant. The transfer of heat is not expected to be effected by the flattening of the asperities as this phenomenon must happen at the beginning of the test. Beyond the first few seconds of contact, the true area is expected to remain unchanged. Non-linear regression analysis: The experiments conducted were designed to simulate bulk forming of metals using a cold die. Upset forging is the process that is most closely simulated by the tests. In order to ease the choice of the interfacial heat transfer coefficient when mathematical modeling of that process is contemplated, empirical relations were developed, giving a as afiinctionof time and three parameters, A, B and Q, each of which is expressed as a fiinction of the non-dimensionalized pressure and temperature. The equation given below may then be used to estimate the coefficient of heat transfer:

a = l000[{A-2BQ)t-Bt^\

(2.26)

TRIBOLOGY OF FLAT ROLLING AND THE BOUNDARY CONDITIONS

^6

^_^_

where the coefficients A, B and Q are given in terms of the non-dimensional pressure/? = P/100 and the temperature, T = TVIOOO. The time is designated by t in seconds, P is the pressure in MPa and T* is the temperature in °C. For t in between Q and 0, the coefficients are given by: A = [ -0.99861 + 1.39288/7 + 4.162827'- 1.93378/? ^ - 7.58453r^ + 4.855247 Y B = [ -1.40191 + 1.50341/7 + 5.513427- 0.8955/? ^ - 5.718637^ + 1.199367^ Q = [18.81105 - 24.37649/7 - 55.55337+ 35.30695/7 ^ + 45.073177^ + 40.672357^ 16.59242/7 ^ - 42.087327*f + 4 Eq. (2.26) is vahd up to 700°C and pressures below 90 MPa. It is emphasised that these relations were obtained in a compression process in which the effect of the relative velocity is not very large. Calculations using Eq. (2.26) give values of the heat transfer coefficient quite close to the measured data of Figures 2.8 - 2.10. The applicability of Eq. (2.26) in the flat rolling process remains unanswered. The predictions, however, appear to be in the right ball park.

2.3

THE DEPENDENCE OF INTERFACIAL PHENOMENA ON PROCESS AND MATERIAL PARAMETERS

As mentioned above, the tribological system involves a very large number of parameters, the interaction of which determines the success of the rolling process. In what follows, a judicial decision is taken to limit the discussion to only those parameters deemed most important. The process parameters in the flat rolling process, of prime importance, are then taken to be the reduction, the speed, the temperature and the surface roughness. The material parameters include the resistance of the metal to deformation, its surface hardness and its parameters of anisotropy. The effects of each of these on the phenomena at the roll/strip contact will be considered below, in light of how they affect the flat rolling process. 2.3.1

The effect of the reduction

As the reduction is increased, the loads on the rolled metal and thus, the roll pressures, increase. The asperities are flattened and the real area of contact approaches the apparent area, at a rate that depends on the contacting metals' elastic and plastic strengths. The number of adhesive bonds formed also increases, and the strength of these bonds will depend on the two materials, including their chemical affinity for each other. Using no lubricants and well cleaned surfaces, the frictional resistance will likely increase. The roughness of the rolled surface will be reduced with the roll's surface imprinted on the metal. Rabinowicz (1995) presents data on the coefficient of friction, measured using steel sliding on aluminum, under a large range of loads, from a low of 10"^ grams to 1000 grams. His data are reproduced here as Figure 2.12, indicating that the coefficient is independent of the load. These results contradict the data obtained during unlubricated cold rolling of aluminum alloy MA THEMA TICAL AND PHYSICAL SIMULA TION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

37

strips using steel rolls (Lim and Lenard, 1984), in which the coefficient of friction, measured using the first version of the embedded transducer - pin combination (employing two sets of pins), clearly mcreased with the loads. The contradiction is more apparent than real, however, as Rabinowicz uses a best-fit line through the data points to draw his conclusions. T 1.5 h-

o o

8

1.0K

C

^—•_• • • •

•

o data of Whitehead (1950) steel on aluminum uniubricated

0.5 h

10"

10-'

10 load, g

10^

10-^

lO**

Figure 2.12 The coefficient of friction is shown to be independent of the load; steel on aluminum (Rabinowicz, 1995; reproduced with permission) A different picture emerges when the sliding of copper on copper with no lubricants is considered in Figure 2.13, showing a large change of the fnctional resistance as the interfacial load is increased. Recent experimental studies, obtained when rolling aluminum strips indicate that the reduction, and thus the load, is a significant contributor tofrictionalresistance. 1

1

1

1

1

^j

y^^

1.5

1

o a>

8 c

1.0

—

0.5

—

/

o

n 10-^

9

copper on copper uniubricated

1

1

10-^

1

1 10 load, g

1

1

10^

103

—\

Figure 2.13 Friction, observed with copper sliding on copper, shows a marked dependence on the load (Rabinowicz, 1995; reproduced with permission) TRIBOLOGY OF FLAT ROLLING AND THE BOUNDARY CONDITIONS

38 Further, the coefficients are significantly higher than the measurements of more recent experiments, conducted under actual conditions, indicate. These reflect the difficulty and the importance of surface cleanliness, probably not fiilly achieved in industry or in the laboratory. Figure 2.14 shows the data, plotting the coefficient of fiiction against the reduction. 0.24

0.20

£

Alloy . speed (rpmj + 1100-HO o 1100-H14 5052-H34 J

I°

0.16

jg 0.12 H

0.08

0.04

1

5

1

1

10 15 reduction (%)

1

20

25

Figure 2.14 The dependence of the coefficient of fiiction on the reduction during cold rolling of aluminum alloys, with no lubrication (Karagiozis and Lenard, 1985, reproduced with permission) At this point, all one can conclude is that the coeffident of fiiction is definitely dependent on the normal loads. The exact nature of that dependence is not yet clear, but is likely connected to the attributes of the contacting materials, their elastic and plastic strength, roughness, relative velocity, etc. In fact, it is the interaction of these parameters that will determine thefirictionalbehavior of the contacting materials. Introducing lubricants into the contact surface changes the reaction of the rolled metal to the reduction, as indicated above when the Stribeck curve was introduced. The number of operating mechanisms also increases and these involve the composition of the oil, the presence of anti-fiiction and extreme pressure additives, its viscosity and its viscosity - pressure and viscosity - temperature coefficient. During a particular rolling pass the following competing mechanisms are active: • • • • • •

the rate at which the pressure on the lubricant increases; the rate at which the viscosity of the oil increases, leading to lower fiiction; the rate at which the number of contacting asperities grows, leading to higher fiiction; the pressure at which the lubricant layer breaks up, leading to higher fiiction; the relative velocity and the amount of lubricant drawn into the contact region and the orientation of the grooves formed by the asperities, aiding or impeding the spread of the lubricant within the contact zone. MATHEMAHCAL AND PHYSICAL SIMULATION OF THE PROPERHES OF HOT ROLLED PRODUCTS

39 2.3.2

The effect of the velocity

The coefficient offrictiondecreases as the velocity increases (Zhang and Lenard, 1996), at least in the boundary and in the mixed lubrication regimes, defined according to the ratio of the oil fiilm thickness to the asperity height. As shown by the Stribeck diagram, beyond the transition to hydrodynamic lubrication, fiictional resistance increases with relative velocity, caused by the increasing fiictional resistance within the layer of oil, separating the two surfaces. Among others, there are several competmg mechanisms that affect the velocity dependence offiictionalresistance, in the boundary and in the mixed lubricating regimes. One is the potential increase of the resistance of the material as the rate of straining is increased. Another is the availability of less time for the adhesion of the contacting asperities. As well, the increasing oil volume, drawn into the deformation zone affects thefiictionalphenomena. Referring to the data given by Rabmowicz (1995) the relative velocity affects frictional resistance in a very significant manner. Ti sliding on ti at progressively increasing velocity indicates that the coefficient of fiiction decreases as the velocity grows, see Figure 2.15.

10

10"

-3

10""

1 0,-1'

10

1000

sliding velocity, mm/sec

Figure 2.15 The velocity dependence of fiiction when Ti is slidmg against Ti (Rabinowicz, 1995; reproduced with permission) 2.3.3

The effect of the temperature

Of the process parameters, the least researched one is the temperature at the contacting surfaces, no doubt because of the difficulties associated with its measurements. The temperatures at the contacting surfaces should be reported, and while there have been attempts to measure them, they are still rather elusive. Measuring the temperature of the center of the rolled sample using embedded thermocouples has also been done and in that case a mathematical model is needed to estimate the temperature at the surface. The model also TRIBOLOGY OF FLAT ROLLING AND THE BOUNDARY CONDITIONS

40

_^

would require the heat transfer coefficient in the contact zone and that introduces another level of complexity. The heat transfer coefficient and its dependence on the significant process and material parameters will be discussed later. Explicit data on the dependence of the coefficient of friction on temperature, measured in actual situations, are difficult to find. Probably the most comprehensive data are given by Male (1964), who used the ring compression test to measure the coefficient for a number of materials and temperatures. The data indicate that, in general, as the temperature increases so does the coefficient offriction.The deviations from this trend are small and they appear at the high temperature ranges. The data of Devenpeck and Rigo (1983), also obtained in the ring compression test, indicate a very significant dependence of the fiiction factor on the temperature, felt as the effect of the presence or absence of scaling. The authors used a C-Mn steel and a temperature range of 865°C to 880''C. The fiiction factor was found to varyfroma high of 0.915, when dry, scaled surface was present to a low of 0.162, when no scales were present but a lubricant was used. Wang and Lenard (1992), considering hot ring tests, compared the results of Venugopal et al, (1989), Pawleski et al., (1988) to data they produced. Venugopal et al. used ARMCO iron which scaled heavily, as did the steels, employed by Wang and Lenard. Pawelski et al. used a carbon steel as well as a Cr steel. The data obtained show some contradictions. Wang and Lenard (1992) observed that the temperature had no effect on fiiction. Venugopal et al., (1989) found the fiiction factor decreases as the temperature is increased. Pawelski et al., (1988) found that fiiction increased a little with the temperature when the carbon steel was used and that it increased much faster when a steel with low rate of scaling was employed. Data, indicating the temperature dependence offiictionalresistance, have also been given in Wusatowski (1965). The coefficients of fiiction, obtained by matching the measured and calculated roll separating forces, indicate a very strong dependence on the rolling speed, as expected and indicated by others. However, the downward trend is not obeyed at low speeds where there is an increase of the fiictional resistance. It is difficuh to separate the temperature and the speed effects on the coefficient at this point. The data for five different carbon steels (indicated by the numbers, 1 to 5), reproduced m Figure 2.16, below, show that the coefficient of fiiction during hot rolling of steels first rises with increasing temperature, reaches a plateau and falls. The velocity effect on fiiction is also observable in Figure 2.16; as the velocity increases, fiictional resistance decreases. In part a) the roll surface velocity is 3 m/s; in b) it is 2 m/s; in c) it is 1 m/s while in d) it is lowered to 0.5 m/s. As Schey (1983) writes, and as the above review suggests, the effect of temperature on fiiction is a fianction of the condition of the surface, including the presence or absence of lubrication or scaling, its thickness, its behavior - whether brittle or viscoplastic - in addition to the strength of the adhesion of the scale to the parent material. He also points out the fact that much of the information, concerning mostly hot and warm rolling of steel, is contradictory. Rabinowicz (1995) separates the effect of temperature changes, caused by external heating or cooling or by high speed sliding, on the coefficient of fiiction. It is the former case that is applicable here. In the cases presented in (Rabinowicz, 1995) the fiictional coefficient appears to be insensitive to those changes. There are exceptions to this general observation, however. The coefficient of fiiction between stainless steel 304 and nickel, stainless steel and cobalt and graphite and aluminum is shown to be strongly temperature dependent. Evidently, there is a contribution to these changes by material properties. MATHEMATICAL AND PHYSICAL SIMULATION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

41

a)

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temperature, "^C

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temperature, **C

800

1000

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temperature, **C

Figure 2.16 The coefficient offriction,inferred while hot rolling five carbon steels at different temperatures and roll surface velocities (Wusatowski, 1965; reproduced with permission) Evidently, the effect of the temperature on the magnitude of the coefficient of fiiction in hot rolling should not be separated from other phenomena. Chemical composition, scale TRIBOLOGY OF FLAT ROLLING AND THE BOUNDARY CONDITIONS

42

breakers, time in the furnace, etc. should be taken into account when the coefficient is chosen for modeling. 2.3.4 The effect of the surface roughness Figure 2.17 shows the variation of the coefficient of friction as a function of the RMS roughness, in microinches (Rabinowicz, 1995). The author's conclusion is that except in the case of very low and very high surface roughness, friction is independent of the surface roughness. The same conclusion is reached by Booser (1984) who writes .. ."surface roughness has little or no consistent effect on the coefficient of friction of clean, dry surfaces. "...Current results appear to contradict this conclusion, no doubt because of the lack of clean, dry surfaces in practice. 1.5

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copper on copper unlubricated L=1000g, u=0.1 mm/sec

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Roll forces, lubricant A Roll forces, lubricant F Roll torque, lubricant A Roll torque, lubricant F

0.50

0.00 0

a A o ^

1 \ 1 1— 2500 500 1000 1500 2000 roll surface speed (mm/s)

Figure 2.28 The accuracy of the computations; lubricants A and F Further computations were performed to test how the choice of the model may affect the results. The objective was to match not only the measured and calculated forces and torques but the forward slip as well. In what follows, the model was described briefly first. An extended version of the mathematical model of the flat rolling process, developed by Roychoudhury and Lenard (1984), was used in the present study. The model was based on the original technique of Orowan (1943). Assuming that planes remain planes, the roll gap was divided TRIBOLOGYOFFLATROLUNGAND THE BOUNDARY CONDITIONS

52

_ _ — .

into slabs and the equation of equilibrium was integrated for each slab. Assembling the slabs leads to the roll pressure and in turn, to the roll separating force and roll torque. Additional steps include the use of the theory of elasticity to analyze the elastic entry and exit regions of the rolled strip and the integration of the biharmonic equation to account for the deformation of the work roll. As was well known, Orowan's model uses thefrictionhill, in which the location of the neutral point was obtained at the intersection of the roU pressure curves, extendingfromentry and exit. In the present refinement, only one equation of equilibrium was employed. An assumption for the variation of the coefficient offrictionin the roll gap was made with some guidancefromprevious experience. This assumption includes the location of the neutral point. The equation of equilibrium was then integrated, starting with the known initial condition at the entry. Satisfaction of the boundary condition at exit drives the iterative process. (The full details of the model are given below, in Chapter 4 "One-dimensional Models of the Flat Rolling Process") .The results are shown in Figure 2.29, for lubricant A and 50% nominal reduction. 0.25

2.00 Lubricant A Nominal reduction = 50"

J

0.20 t5

n

0.15

Model + Coldraj O Hill [ D varying friction

5 ^ 1 g 0)

In the nr^odel the coefficient of friction] varies from entry to exit 1.50

1.00

0.10 0.50

0.05

0.00

0.00 500 1000 1500 2000 roll surface speed (mm/s)

2500

Figure 2.29 The coefficient of friction, calculated by three methods - oil A, 50% reduction

Lubricant A Nominal reduction = 50% + roll force O roll torque A forward slip "T T" T" 500 1000 1500 2000 roll surface speed (mm/s)

2500

Figure 2.30 The accuracy of the onedimensional model

The data obtained using Hill's formula, indicated by the diamonds, and with the first model, designated by the squares, are also included. The crosses show the current values of the coefficient of friction. The message is clear: the inferred values of the coefficient of friction are strongly dependent on which model is used. The trends are similar in most of the cases and if relative magnitudes are wanted. Hill's formula is completely adequate. If more exact results, that are to be used in the predictive-adaptive scheme of the mill, are needed, a model that allows matching the roll force, the torque and the forward slip may be necessary. The accuracy of the last set of calculations is shown in Figure 2.30, indicating results similar to that given in Figure 2.28. Again, the roll forces, as measured and predicted, are close, as are most of the forward slip values. The torque needed to cause plastic deformation is about 20% lower than the experimental data, indicating the magnitude of the losses in the drive train. MATHEMATICAL AND PHYSICAL SIMULATION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

53 2.5.2

Cold roUing of aluminum with lubricants

One mm thick, 25 mm wide 1100 H14 aluminum alloy strips were rolled using the two-high mill, described above (Lenard and Zhang, 1996). SAE 5 lubricant, with no additives, was used for lubrication. After cleaning the strips using n-heptane, a neutral cleaner, 10 drops of the lubricant was put on each side of the strip. The oil was then spread carefixlly and evenly on the surfaces. The roll separating forces, roll torques and the forward slip were measured for a range of reductions arid rolling speeds. The mathematical model, referred to above and given in detail in Chapter 4, was used to infer the magnitudes of the coefficient of friction. The results of the computations with the proposed model are given in terms of the calculated and measured roll forces, torques and forward slip, in Figure 2.31. The facility of the model was evident in the figure. All three parameters are predicted with good accuracy, provided the coefficient of friction was chosen with care. In general, the measured roll torques are larger than the computed values, as before. The proper choice of the coefficient of friction in the mathematical model led to the data given in Figure 2.31, indicating that the ratios of all three of the computed and measured parameters are consistent. The magnitudes of the coefficient may therefore be considered to be quite accurate, since they are based on matching all three parameters. 0.15 + Roll force o Roll torque A Fonvard slip

1.60-

8

1.20-

0.80-

o

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0.10 H > o

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1100-H14 Aluminum SAE 5 lubricant 6 - 4 0 rpm rolling speed 10-60% reduction

0.40-

n nn

1

1 1 8 12 test number

1 16

0.00 20

Figure 2.31 The accuracy of the model 1100 H14 aluminum was rolled (Zhang and Lenard, 1997; reproduced with permission)

20.0 40.0 reduction (%)

60.0

Figure 2.32 The coeflScient of friction; 1100 HI4 aluminum (Zhang and Lenard, 1997; reproduced with permission)

The values of the coefficient are plotted in Figure 2.32, for a range of rolling speeds, against the reduction, for the strips lubricated with the SAE 5 oil. The experiments with the light oil indicate values of the coefficient of friction that are as expected. In general, the magnitudes increase with increasing reductions and decrease with increasing speeds. The velocity TRIBOLOGY OF FLAT ROLLING AND THE BOUNDARY CONDITIONS

54

dependence was not linear. At the lower speeds the coefficient was not highly sensitive to changes. At higher speeds a large drop in magnitudes was found, beyond which no more significant changes were demonstrated. Extending the speed range would certainly lead to a better appreciation of the effect of relative velocity. There was an exception to the load dependence offriction,demonstrated at 10 rpm, where \i appeared to drop with the reduction. However, the drop was not large and was not considered to change the general conclusions. The speed and load effects became much more dominant at higher velocities. The magnitudes of the coefficient offrictionvariedfroma low of 0.025 to a high of 0.12.

0.15

•

•

•

•

•

I 0-10

§ o

0.05-

1100-H14 Aluminum SAE 5 lubricant 5-40 rpm 10-50% reduction

0.00 i.OOE-ll

•

1

1

1

I

1

1

« l l

l.OOE-10

1

1 1 1 Mll|

l.OOE-9

1 1 1 I1I I 1

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Figure 2.33 The Stribeck curve, obtained while cold rolling 1100 H14 aluminum with SAE 5 (Zhang and Lenard, 1997; reproduced with permission)

The Stribeck curve: Using the values of \x, determined above, the Stribeck curve was given in Figure 2.33. In calculating the Sommerfeld number, the lubricant's dynamic viscosity should be corrected for the effects of the pressure and the temperature. The formula used in the present case was a variation of the one employed by Sa and Wilson (1994). In the computations the pressureviscosity coefficient was taken to be 0.0217 MPa"^. No specific data for the temperature-viscoaty coefficient was available and its magnitude was taken to be 0.03 K'^ (Booser, 1984). The mean roll pressure was obtained by dividing roll separating force by the projected contact area. The temperature of the oil was assumed to be identical to the average strip temperature during the pass. In plotting the Stribeck curve, its sensitivity to various values of the two coefficients was found to be low. The Stribeck curve confirms the conclusions drawnfromthe calculated oil-film thickness. Using the SAE 5 oil, the lubricating regime just enters the mixed range. When a metal is rolled, the mill loads - that is, the roll separating forces and the roll torques - increase with increasing reduction. The majority of research studies indicate that as the MATHEMATICAL AND PHYSICAL SIMULATION OF THE PROPERTIES OF HOT ROLLED PRODUCTS

J5 reduction is increased, the coefficient of friction grows when aluminum is rolled (Lim and Lenard, 1984; Karagiozis and Lenard, 1985), and decreases when steel is rolled (Lin et al., 1991). The tendency to transfer aluminum oxide to the rolls is expected to be the cause for the apparent contradiction. 2.5.3

Hot rolling of low carbon steel (Laboratory data)

AISI 1018 (0.19% C, 0.7% Mn) carbon steel slabs were used in all experiments. The steel was delivered in the form of cold rolled bars. The samples were machined to 12.7 mm thickness, 50.8 mm width and 305 mm length. Three reductions were investigated! 10, 20, and 30% at temperatures from 825°C to 1125°C. The roll speed was 25 rpm in all experiments, giving a roll surface velocity of 196 mm/s. The specimens were rolled with the scale which acted both as an insulator and as a lubricant during the rolling operation, even though it was eventually broken off. Each experiment was repeated three to five times and average values of the roll separating forces, roll torques and the forward slip were reported. A rigid-plastic finite element model, presented in (Pietrzyk and Lenard, 1991), was used to correlate the measured values of the forward slip and the coefficient of friction. Shida's equations (1971), which give the steel's resistance to deformation in terms of the strain, rate of strain, the temperature and the carbon content, are used for estimation of the mean plane-strain flow stress. In the calculations, the magnitude of the coefficient of friction was inferred by matching the measured and calculated values of the forward slip, roll force and torque. The results are given in Figure 2.34.

0.28 Nominal reduction + 10% 20% 0 D 30%

0.24 H

£

0.20 H

S

0.16 H

t

0.12 0.08 800

900 1000 1100 entry surfg.ce temperature (°C)

1200

Figure 2.34 The coefficient of fiiction inferred, using a two dimensional finite element model, during hot rolling of a low carbon steel (Munther and Lenard, 1995; reproduced with permission)

TRIBOLOGY OF FLAT ROLLING AND THE BOUNDARY CONDITIONS

J6 The data indicate that the coefficient of fhction drops as the temperature of the rolled sample increases, clearly contradicting the information provided by Wusatoski (1969). The trend of the present data follow that of Geleji. As well, the magnitudes of the coefficient of friction are significantly lower than indicated by others. Further, they are far from the sticking friction, usually assumed to exist in hot rolling situations. These changes are generally thought to be the result of the mathematical models used in the inverse calculations. In previous studies, only the roll separating forces were matched and an empirical formula or at most a simple one-dimensional model, was used. In producing the data below, an advanced model and three parameters were matched. The current results on the coefficient of friction therefore are expected to be closer to realistic magnitudes. 2.5.4

Hot rolling of steel (Industrial data)

Data obtained from the logbooks of Dofasco Inc. were utilized in order to gain an insight into the magnitudes of the coeflScient of friction on the stands of the finishing train of an industrial hot strip mill. Low carbon steel was rolled. The necessary data concerning the chemical composition of the steel, the thickness at each stand, the reduction, the temperature, the roll speed and the roll radius, were taken from the logbooks. The empirical formula of Ekelund, given for cold rolling, was adapted for use in the hot rolling process (see Eq. 2.3).

0.5 o

0.4

pi

ti ^ 0.3

low carbon steel Dofasco's#2 hot strip mill

0^

)0 0

o

Q> O

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