Capillary Forces in Microassembly: Modeling, Simulation, Experiments, and Case Study

microtechnology and mems

microtechnology and mems Series Editor: H. Fujita D. Liepmann The series Microtechnology and MEMS comprises text books, monographs, and state-of-the-art reports in the very active field of microsystems and microtechnology. Written by leading physicists and engineers, the books describe the basic science, device design, and applications. They will appeal to researchers, engineers, and advanced students. Mechanical Microsensors By M. Elwenspoek and R. Wiegerink CMOS Cantilever Sensor Systems Atomic Force Microscopy and Gas Sensing Applications By D. Lange, O. Brand, and H. Baltes Modelling of Microfabrication Systems By R. Nassar and W. Dai Micromachines as Tools for Nanotechnology Editor: H. Fujita Laser Diode Microsystems By H. Zappe Silicon Microchannel Heat Sinks Theories and Phenomena By L. Zhang, K.E. Goodson, and T.W. Kenny Shape Memory Microactuators By M. Kohl Force Sensors for Microelectronic Packaging Applications By J. Schwizer, M. Mayer and O. Brand Integrated Chemical Microsensor Systems in CMOS Technology By A. Hierlemann

CCD Image Sensors in Deep-Ultraviolet Degradation Behavior and Damage Mechanisms By F.M. Li and A. Nathan Micromechanical Photonics By H. Ukita Fast Simulation of Electro-Thermal MEMS Efficient Dynamic Compact Models By T. Bechtold, E.B. Rudnyi, and J.G. Korvink Piezoelectric Multilayer Beam-Bending Actuators Static and Dynamic Behavior and Aspects of Sensor Integration By R. Ballas CMOS Hotplate Chemical Microsensors By M. Graf, D. Barrettino, A. Hierlemann, and H.P. Baltes Capillary Forces in Microassembly Modeling, Simulation, Experiments, and Case Study By P. Lambert

P. Lambert

Capillary Forces in Microassembly Modeling, Simulation, Experiments, and Case Study

123

Professor Pierre Lambert Université Libre de Bruxelles (ULB) BEAMS Department (CP165/14) Avenue F.D. Roosevelt 50 1050 Bruxelles, Belgium Series Editors: Professor Dr. Hiroyuki Fujita University of Tokyo Institute of Industrial Science 4-6-1 Komaba, Meguro-ku Tokyo 153-8505, Japan Professor Dr. Dorian Liepmann University of California Department of Bioengineering 6117 Echteverry Hall Berkeley, CA 94720-1740, USA

Library of Congress Control Number: 2007927260 ISBN 978-0-387-71088-4

e-ISBN 978-0-387-71089-1

Printed on acid-free paper. © 2007 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com

I dedicate this book to those whose time I devoted to writing it. Je d´edie ce livre `a ceux a` qui j’ai pris le temps de l’´ecrire.

Foreword

Within the field of microassembly, this book crosses a bridge between the world of surface science and chemistry on the one hand and the world of mechanical engineering on the other hand. Indeed, the mechanical devices produced at a scale ranging from a few micrometer up to a few millimeter are brought face to face with the effects of downscaling, and in particular with the predominance of surface tension effects over the gravity effects. Many illustrations of this trend can be found in the literature and in emerging industrial products based on surface tension effects such as the fluid lens patented by B. Berge and produced by Philips, the emergence of capillary stop drives or, with other words, surface tension based micro-valves, the use of surface tension combined with electrostatic effects in the manufacturing of liquid handling systems such as the EWOD (i.e., electro-wetting on dielectric) devices, and so on. To focus on microassembly, two approaches are currently considered. The self-assembly paradigm, in which surface effects are used to organize and assemble micrometric structures (mainly up to a few micrometer), and the microrobotic assembly, based on the miniaturization of the actuation, high resolution micromanipulators, and gripping devices, more dedicated to mesoscopic sized components (mainly down to about 10 µm). Self-assembly is clearly not the subject of this book, even if some obvious links relate the proposed models to this field. As a scientific knowledge, microrobotics focuses on active structures, able to produce motions and to interact mechanically, i.e., produce efforts, with their environment at the microscale (between a few micrometer and a few millimeter). One of the main challenging issues of it concerns the handling of small components, in order to precisely position, assemble, characterize, or modify them. The research in this field covers a wide area of interesting topics, including the exploration of new phenomena (i.e., which are new from the point of view of microrobotics) and the development of an adequate scientific background (step 1), the development of demonstrators illustrating new strategies to pick up, to handle, and to release microcomponents, and which

VIII

Foreword

try to minimize or take benefit from the new physical effects of the miniaturization (step 2), and finally, the set up of efficient and reliable industrial products addressing specific needs (step 3). Step 1 is fundamental in that sense that new efficient micromanipulation systems can only be developed bearing in mind the specificities of the micro-world and take advantage of it through new approaches. Precisely, this book proposes a physical understanding of the surface tension phenomena, builds models that can be used in simulations and in the design of a surface tension based gripping demonstrator. The author uses wellknown concepts from surface science (like surface tension, capillary effects, wettability, contact angles) and efficiently uses them as outputs of chemists models (which explain whether a liquid will wet or not a surface), but as inputs of mechanical models predicting the amount of effort that can be used to handle microcomponents. The book is unique in that sense that this is the first in this direction and it proves that the microrobotic approach can lead to very efficient systems. It is very well organized and the content is presented in a very rigorous, pleasant, and pedagogical manner by a real expert of the addressed issues. We strongly recommend to all persons, students, engineers, researchers who are interested in micromanipulation and microassembly to read it.

Besan¸con Brussels Lausanne April 2007

Prof. N. Chaillet Prof. A. Delchambre Prof. J. Jacot

Preface

0.1 Context In the current context of trend to miniaturization, the main goal defined at the very beginning of this work was to study the influence of miniaturization on the manipulation tasks performed in microassembly, because for a few years, most papers dealing with microassembly have referred to overviews that mentioned the importance of forces related to the microworld. The reader can have a quick overview on the scales covered by the term microworld in Fig. 0.1. In this figure, several domains can be distinguished: 1. The “macro” domain, related to conventional manufacturing and assembly technologies 2. The “micro” domain where the limits of conventional means can be undergone and new strategies arise. Sometimes the upper area of the micro domain is called “meso” domain 3. The “nano” domain fills the gap between the micro domain and the atoms and molecules world. It is the ultimate domain of mechanical engineers As a comparison, the accuracy of conventional manufacturing is about 10 µm and the size of hair is between 10 and 100 µm. This book deals with components

meso nano

micro

macro

L(m) 10-9

10-6 µ-accuracy

Fig. 0.1. Sizes and scales

10-3 µ-components

1

X

Preface

ranging from 10 µm to a few millimeter, with part features that can reach the micron: The chosen case study consists in a watch ball bearing with 0.3 and 0.5 mm diameter balls. More generally, the current breakthrough of the miniaturization of electronic components and the development of their related production equipment make it possible today to produce cheap components integrating a lot of functionalities. These production techniques allow the 2D manufacturing to use several materials: glass, silicon, metals. Beside these applications from the semiconductor industry, the conventional mechanical design also tries to reduce the size of the products and the emergence of micromechatronics develops new miniaturized robots with a lot of functionalities (sensing, actuation, guiding). This trend does not spare assembly and the products are not only reduced in size but also the assembly and production equipment are downscaled, giving rise to several concepts like microfactory or new assembly strategies such as parallel assembly. The pieces of equipment and especially the grippers are downscaled, but new grippers based on microworld related physics are now commercially offered by a lot of industries and laboratories. The first representation that crosses the mind when talking about micro is that it surely must be “small.” The prefix micro can of course be understood as defining the size of a component (10−6 m), but a microproduct has not to be understood as a product with a size of a few microns. Let us give an overview of some definitions that can help us better define the concepts of micropart, microcomponent, microproduct, microsystem, microassembly. Benmayour [19] proposes a general definition of a microproduct using an analogy with the term “microscopic” object. In the same way as a microscopic object cannot be seen with bare eye, a microproduct is a product that can neither be manufactured nor assembled with bare hand: The production of a microproduct requires adapted manufacturing and assembly equipment. Unfortunately, this definition is quite general and some conventional products like cars cannot be considered as microproducts even when assembled with dedicated equipment. Moreover, this definition can give us an upper boundary but cannot provide any indications about the lower limit of a microproduct. However, it conveys the idea that the size criterion alone cannot be taken into account. We consider in this book microproducts like a watch ball bearing made of microparts or microcomponents (like balls). Roughly speaking, we will consider that microproducts have sizes ranging from a few cm3 to a few dm3 . For example, we use to speak about a micropump for a product that has external dimensions of a cylinder with a 8 cm diameter and 2 cm height. These microproducts are made of several microparts or microcomponents that have a size ranging from 10 µm to a few millimeter, but they can have some features with a size reaching 1 µm. For example, the pumping mechanism of a micropump can be smaller than a cube with 10 mm edge, having at least one dimension smaller than 100 µm. Nelson [130] generally refers to 1 µm– 100 µm as “microscale” and 100 µm to 1 mm as “mesoscale.”

0.1 Context

XI

As far as assembly equipment is concerned, most microfactories are actually desktop factories, that is having external dimensions of 1 m2 ×40 cm. Bohringer et al. [22] locates the field of microassembly between conventional assembly, dealing with part dimensions higher than 1 mm and what they call “the emerging field of nanoassembly” (with part dimensions ≤1 µm). A microgripper can be a gripper to handle microcomponents, even if the whole gripping mechanism is still quite big compared to the handled part, or it can refer to the terminal tip(s) of the gripper that is(are) in contact with the microcomponent (for example, a particular kind of micromanipulation tool is the Atomic Force Microscope (AFM): This equipment is not designed like a gripper but several laboratories try to use it to push microcomponents. In this case, the AFM tip can be considered as a gripper, made of a cantilever (100 × 10 × 2 µm3 ) with a tip of conical or pyramidal shape of 10 µm height and a tip radius of about 10 nm). Other criteria can be considered to characterize microcomponents, such as, for example, the required tolerances and clearances in order to ensure the function (the pumping mechanism of the micropump cannot show clearances bigger than a few micron in order to guarantee that drug can be transferred from the tank to the patient). A less quantifiable way to define a micropart is to verify whether the models and the techniques used in the macroworld are still valid. For example, macroassembly is clearly based on the mechanical grip force to pick up and the own weight of the component to release, while microassembly has to turn to other techniques due to relative decrease of the gravity force compared to surface forces (see Fig. 0.2). As the main goal of this work is to consider the modeling of the forces acting in the manipulation of a micropart, we consider that the use of these forces make sense in our microcomponents. We prefer to refer to model assumptions and compare the sizes of a part or the roughness of a component with several cut-off lengths arising from model assumptions. We consequently identify a domain between a “van der Waals” cut-off length of a few tens of nanometer

Forces exerted on the component [N]

10

10

Classical gripping

Capillary gripping

5

10

Vacuum gripping

A

0

10

C

-5

B

10

-10

10

Weight ~ L3 10

-15

Vacuum force ~ L2 Capillary force ~ L

-20

10

-8

10

-6

10

-4

-2

10 10 Size of the component [m]

Fig. 0.2. Scaling laws and micromanipulation

0

10

XII

Preface

Table 0.1. Comparison between micro and macroproducts Criterion Size

Macroproduct

Microproduct Below 1 mm Below 500 µm Accuracy 0.1–10 µm 5 µm Clearances Very small Complexity Made of several Multifunctional, complex elementary components products, few components Compact design products Maintenance Maintenance and replacement No maintenance, replacement of the defective components of the product in case of failure Heterogeneousness Several parts from different technological domains involving new joining techniques

Ref. [166] [41] [166] [91] [166]

[154]

[166]

Table 0.2. Comparison between micro and macroassembly Criterion Automation Batch size Resource consumption Response time

Macroassembly Microassembly Automatic Manual and semiautomatic, to be automated. Single parts, Batches of parts, serial assembly parallel assembly Expected to be lower

Ref. [65, 166], [159, 185]

[6]

Expected to be shorter because of lower inertia

(limit of the nonretardated van der Waals forces, see page 10) and a capillary cut-off length of a few millimeter (see (8.1)): This domain will be considered as our microworld. To give the reader a broader overview, we summarize some criteria related to micro/macroproducts and to micro/macroassembly (Tables 0.1 and 0.2).

0.2 Contributions of this Book This book falls into five parts whose main contributions are summarized in Fig. 0.3 (the fifth part containing the appendices is not shown in this figure). The first part introduces the concept of microassembly (Chap. 1), proposes in Chap. 2 a classification of the forces acting in microworld (which has been defined in the previous section), and summaries in Chap. 3 the numerous gripping principles proposed in the scientific literature. This summary (which is essentially a review of the literature) serves as a basis for a gripping principles classification from which it turns out that the forces generated by surface tension can suit the microgripping task.

0.2 Contributions of this Book

XIII

Part I: Microassembly Specificities • Different kinds of microassembly • What are the forces in action • What are the possible handling principles -- classification of the handling principles -- proposal: the capillary gripper

Part II: Modeling and simulation of Capillary Forces • Parameters involved in a gripping based on surface tension • Classical methods for capillary forces computing: energy derivation method, geometrical approximations, resolution of the Laplace equation at equilibrium -- Proof of equivalence between the energy derivation and the Laplace equation based methods -- Implementation of a double iterative numerical scheme to compute forces in the axially symmetric case, based on the solving of the Laplace equation -- Determination of the limits of this static simulation -- Determination of approaching contact distance, rupture distance and residual volumes after rupture -- Approximation of cycle times -- Application to the watch ball bearing case study

Part III: Experimental Aspects Testbench: -- Set up of a force measurement testbench (from 10µN to 10mN) -- Set up of a contact angles measurement testbench -- Tested liquid: water, isopropanol and silicone oil, from 0.1µL to 1µL -- Tested materials: steel, silicon, PTFE, zirconium -- Tested geometries: concave and convex cones, spheres, cylinders

Studied parameters and phenomena: -- Inputs: gap, geometries, contact angles, surface tension, dynamic release, volume, relative orientation, evaporation -- Outputs: forces and liquid bridges profiles

Watch ball bearing case study: -- Study of the picking errors and solutions -- Study of the releasing reliability -- Measurement of the picking force and reliability study

Answered questions: -- Advancing vs receding contact angle, tension term vs. Laplace term -- Quantified comparison between picking principles -- Quantified comparison between releasing strategies -- Design rules for a surface tension based gripper

Part IV: Perspectives Modelling and Simulation - Dynamic simulation - Capillary condensation simulation

Design and manufacturing perspectives - Surface tension control (i.e. electrowetting) - Design and manufacturing of a surface tension based gripper prototype for SMD components

Fig. 0.3. Contributions of this book

XIV

Preface

The second part concerns the modeling aspects. Therefore, Chap. 6 presents the underlying parameters (such as surface tension and contact angles) and models (Young-Dupr´e and Laplace equations), which rule the surface tension forces (also called capillary forces). This chapter explains the action of these forces on a solid, thanks to two terms: the so-called “Laplace” or pressure term and the so-called “interfacial tension” term (see Sect. 6.5). Based on these parameters, Chap. 7 reviews some approximations to compute capillary forces at equilibrium: energy differentiation methods, geometrical methods assuming a given shape of the meniscus (typically arc or parabola). Chapter 8 details how to implement a numerical resolution of the so-called Laplace equation to determine the meniscus shape in axially symmetric cases. This allows the computation of the capillary forces linking a component and a gripper, relying on the following assumptions: equilibrium, vanishing Bond number (i.e., gravity is neglected), axial symmetry, constant contact angles, constant volume of liquid. The originality of this model relies on the fact that the volume of liquid can be imposed, which leads to a double iterative scheme for the resolution. Another contribution of this book is to prove analytically the equivalence of this approach and the energy minimization method (in the case of a prism–plane interaction, see Chap. 9). The proposed model is applied to the case study of a watch ball bearing, showing the interest for a gripper geometry conforming with that of the component (Chap. 10). This model is then enriched, thanks to a second set of parameters (Chap. 11), showing how surface roughness and surface impurities can be included in the model through the value of the contact angle. The contact angle hysteresis is introduced in this chapter; however, it will be shown (thanks to experiment) how to chose between both. Finally, this chapter illustrates with a figure from the literature an interesting damping effect, which prevents high contact forces. The limits of the proposed model are discussed in Chap. 12, showing the suitability of this model even in the case of highly accelerated components. This chapter provides some approximations of the damping time of the oscillations of the meniscus, which indicates a first order of magnitude of the cycle time of a surface tension based picking task. Some conditions of meniscus rupture are given in Chap. 13. To conclude this second part, a detailed implementation of the proposed models is given in Chap. 14. The third part of this book focuses on experimental aspects. First, we detail in Chap. 17 the set up of an experimental test bed allowing the measure of the models inputs (contact angles, volumes of liquid) and outputs (forces and meniscus shapes). Then, Chap. 18 provides numerous model validation and exhaustive results concerning the influence of the gap, the gripper geometry, the surface tension, the contact angles (including the choice between the advancing and the receding contact angles), the relative orientation of the gripper with respect to the component, the conditions of dynamical release, and the rupture distance of the meniscus. Theses results are discussed in Chap. 21 in terms of picking and releasing strategies; therefore, we introduce the concept of adhesion ratio φ:

0.3 What this Book Does Not Tell

φ=

Fmin , Fmax

XV

(0.1)

where Fmin and Fmax are, respectively, the minimal and the maximal values of the capillary force, which is assumed to be tuned between the picking stage (Fmax ) and the releasing stage (Fmin ). Ratios tending to zero indicate a very flexible gripping strategy (components with a large mass range can be picked), while a ratio tending to 1 indicates a nonsuitable gripping strategy. These results have been then applied in a final illustration of the surface tension gripping based on a watch ball bearing case study. The characterization of the underlying parameters is led in Chap. 19 while Chap. 20 presents the results of picking and releasing tasks of the 0.3 and 0.5 mm diameter balls of this bearing. The conclusions presented in Chap. 21 discuss the results of Chaps. 18, 19, and 20. The fourth part contains the general conclusions and the perspectives of this work (Chap. 22). Finally, the fifth part contains the appendices, which includes modeling and geometry complements, some elements of the proof of equivalence of both capillary force models, some tracks toward a dynamical simulation, and finally, a list of the main symbols and abbreviations used in this book. The book is ended by a list of references and an index.

0.3 What this Book Does Not Tell This book is an attempt to present on a comprehensive way the elements ruling a reliable surface tension based gripping of a small component with a gripper (typically a sub-millimeter sized component), in gaseous environment (typically ambient atmosphere). However, the analysis proposed to understand the role of the underlying parameters ruling capillary forces is very general, and the proposed model is only valid for axially symmetric cases. In a whatever geometrical configuration, the reader will have to turn himself (herself) toward an energy minimization tool such as, for example, the well-known Surface Evolver software. The case of lateral capillary forces is hardly treated in the experimental part, and we refer the interested reader to the work of Peter A. Kralchevsky [105]. On the same way, the so-called self-assembly or auto-assembly is not treated in this book: These aspects of self-assembly, which are not restricted to capillary forces, are presented, for example, in the work of Karl F. B¨ ohringer. It will be shown that a static modeling is quite sufficient for our purpose; nevertheless, the reader will find additional information concerning dynamical simulation in [156]. Finally, the case of immersed environments is treated in [64]. Let us note that the example treated in this book concerns the case of watch bearing balls with a diameter ranging from 0.3 to 0.5 mm. The use of surface tension has an upper limit (the so-called capillary length equal to a

XVI

Preface

few millimeter for water), it is not limited in terms of miniaturization. Nevertheless, the manufacturing of micron-sized grippers would require adapted manufacturing techniques that have not been considered in this book, but this is more a perspective than a limitation.

0.4 Reading Suggestion For a quick reading, the chapters and sections listed in Table 0.3 are essential for a good understanding of this book. Let us emphasize the presentation of four examples (Table 0.4). Table 0.3. Quick reading suggestions Chapter/Section Title Page Preface 3 Handling Principles for Microassembly 13 6 First Set of Parameters 41 7.1 Introduction to the State of the Art 51 on the Capillary Forces Models 8 Static Simulation at Constant Volume of Liquid 65 17 Test bed and Characterization 143 21 Final discussion of Part III 211 22 Conclusions and Perspectives 221 Appendix D List of symbols 247

Table 0.4. Examples Chapter 10 14 19 20

Title Page Application to the Modeling of Microgripper for Watch Bearings 83 Numerical Implementation of the Proposed Models 127 Watch Bearing Case Study: Characterization 189 Watch Bearing Case Study: Results 199

Brussels April 2007

P. Lambert

Contents

Preface 0.1 0.2 0.3 0.4

..................................................... Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contributions of this Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . What this Book Does Not Tell . . . . . . . . . . . . . . . . . . . . . . . . . Reading Suggestion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

IX IX XII XV XVI

Part I Microassembly Specificities 1

From Conventional Assembly to Microassembly . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Design of Monolithic Products for Microassembly . . . . . . . . . 1.3 Combined Part Manufacturing and Assembly . . . . . . . . . . . . 1.4 Product External Assembly Functions . . . . . . . . . . . . . . . . . . . 1.5 Product Internal Assembly Functions . . . . . . . . . . . . . . . . . . . 1.6 Stochastic or Self-Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Parallel Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 3 4 6 6 6 7 8 8

2

Classification of Forces Acting in the Microworld . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Classification Schemes of the Forces . . . . . . . . . . . . . . . . . . . . . 2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 9 10 12

3

Handling Principles for Microassembly . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Presentation of Gripping Principles . . . . . . . . . . . . . . . . . . . . . 3.3 Classification of Gripping Principles . . . . . . . . . . . . . . . . . . . . 3.4 Comparison between Gripping Principles . . . . . . . . . . . . . . . . 3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13 13 13 25 28 29

4

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

XVIII Contents

Part II Modeling and Simulation of Capillary Forces 5

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

6

First Set of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Young–Dupr´e Equation and Static Contact Angle . . . . . . . . 6.4 Laplace Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Effects of a Liquid Bridge on the Adhesion Between Two Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 A Priori Justification of a Capillary Gripper . . . . . . . . . . . . . 6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41 41 41 42 43

7

45 47 49

State of the Art on the Capillary Force Models at Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Energetic Approach: Interaction Between Two Parallel Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Energetic Approach: Other Configurations . . . . . . . . . . . . . . . 7.4 Geometrical Approach: Circle Approximation . . . . . . . . . . . . 7.5 Geometrical Approach: Parabolic Approximation . . . . . . . . . 7.6 Comparisons and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51 55 57 61 61

8

Static Simulation at Constant Volume of Liquid . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Description of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Equations and Numerical Simulation . . . . . . . . . . . . . . . . . . . . 8.5 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65 65 65 66 67 71

9

Comparisons Between the Capillary Force Models . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Qualitative Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Analytical Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Definition of the Case Study . . . . . . . . . . . . . . . . . . . . . 9.3.2 Preliminary Computations . . . . . . . . . . . . . . . . . . . . . . . 9.3.3 Determination of the Immersion Height h . . . . . . . . . 9.3.4 Laplace Equation Based Formulation of the Capillary Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.5 Energetic Formulation of the Capillary Force . . . . . . . 9.3.6 Equivalence of Both Formulations . . . . . . . . . . . . . . . . 9.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73 73 73 75 75 76 77

51 51

79 79 80 81

Contents

10 Example 1: Application to the Modeling of a Microgripper for Watch Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Presentation of the Case Study . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Analytical Model Based on the Circle Approximation . . . . . 10.4 Numerical Model Based on the Laplace Equation . . . . . . . . . 10.5 Benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Pressure Difference Saturation . . . . . . . . . . . . . . . . . . . . . . . . . 10.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

XIX

83 83 83 86 89 93 94 96

11 Second Set of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Surface Heterogeneities and Surface Impurities . . . . . . . . . . . 11.3 Surface Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Static Contact Angle Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . 11.5 Dynamic Spreading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97 97 97 98 99 100 101

12 Limits of the Static Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Performances of the Assembly Machines . . . . . . . . . . . . . . . . . 12.3 Nondimensional Numbers and Buckingham π Theorem . . . . 12.4 Another Approach: Use of a 1D Analytical Model . . . . . . . . 12.5 Limitations of the Static Model . . . . . . . . . . . . . . . . . . . . . . . . 12.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

103 103 103 103 106 108 110

13 Approaching and Rupture Distances . . . . . . . . . . . . . . . . . . . . 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Approaching Contact Distance . . . . . . . . . . . . . . . . . . . . . . . . . 13.3 Rupture Distance and Residual Volume of Liquid . . . . . . . . . 13.4 Mathematical and Notation Preliminaries . . . . . . . . . . . . . . . . 13.5 Volume Repartition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.6 Rupture Condition and Rupture Gap . . . . . . . . . . . . . . . . . . . 13.7 Analytical Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.8 Summary of the Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.9 Comparison between the Methods . . . . . . . . . . . . . . . . . . . . . . 13.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

111 111 111 113 114 115 117 119 120 122 124

14 Example 2: Numerical Implementation of the Proposed Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2 Liquid Bridge Simulation for the Analysis of a Meniscus . . . 14.3 Evaluation of the Double Iterative Scheme . . . . . . . . . . . . . . . 14.4 Pseudodynamic Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

127 127 127 131 133 135

XX

Contents

15 Conclusions of the Theoretical Study of Capillary Forces

137

Part III Experimental Aspects 16 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

141

17 Test Bed and Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.2 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.3 Test Bed Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.3.1 Force Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.3.2 Drop Dispensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.3.3 Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.4 CAD Model and Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.5 Characteristics of the Force Measurement Set Up . . . . . . . . . 17.5.1 Typical Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.5.2 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.5.3 Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.5.4 Influence of a Misalignment on the Force Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.6 Characteristics of the Contact Angles Measurements . . . . . . 17.7 Surface Tension Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 17.8 Modus Operandi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.9 Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.9.1 Set of Available Grippers . . . . . . . . . . . . . . . . . . . . . . . . 17.9.2 Set of Available Components . . . . . . . . . . . . . . . . . . . . 17.9.3 Set of Available Blades . . . . . . . . . . . . . . . . . . . . . . . . . . 17.9.4 Available Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.9.5 Contact Angles Characterization . . . . . . . . . . . . . . . . . 17.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

143 143 143 145 145 146 148 148 151 151 151 152 152 154 155 155 158 158 159 160 161 161 162

18 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2 Preliminary Results: Validation of the Simulation Code . . . 18.2.1 Meniscus Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2.2 Comparison with the Analytical Expressions . . . . . . . 18.2.3 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . 18.3 Advancing vs Receding Contact Angle . . . . . . . . . . . . . . . . . . 18.4 Influence of the Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.4.1 Force–Distance Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.4.2 Tension Force vs. Laplace Force . . . . . . . . . . . . . . . . . . 18.5 Influence of the Gripper Geometry . . . . . . . . . . . . . . . . . . . . . . 18.6 Influence of the Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . 18.7 Influence of the Contact Angle θ1 . . . . . . . . . . . . . . . . . . . . . . .

163 163 163 163 164 166 168 170 170 171 171 172 174

Contents

XXI

18.8 Influence of the Relative Orientation . . . . . . . . . . . . . . . . . . . . 18.9 Auxiliary PTFE Tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.10 Dynamical Release . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.10.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.10.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 18.11 Approaching Contact and Rupture Distances . . . . . . . . . . . . 18.12 Shear Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.13 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

174 176 177 177 182 185 186 187

19 Example 3: Application to the Watch Bearing Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.2 Available Grippers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.3 Available Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.4 Liquid Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.5 Liquid Dispensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.6 Contact Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

189 189 189 191 191 192 195

20 Example 4: Application to the Watch Bearing Case Study: Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.2 Picking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.2.2 Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.2.3 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.2.4 Automated Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.3 Placing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.4 Compliance Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.5 Force Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.5.2 Modification of the Force Measurement Test Bed . . . 20.5.3 Comparison Between Models and Experiments . . . . . 20.5.4 Ongoing Experimental Study . . . . . . . . . . . . . . . . . . . . 20.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

199 199 199 199 200 201 202 204 205 206 206 206 206 208 209

21 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Picking Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Releasing Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Design Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

211 211 211 213 215

XXII

Contents

Part IV General Conclusions and Perspectives 22 Conclusions and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

221 221 223

Part V Appendices A

Modeling Complements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Analytical Approximations of the Capillary Forces . . . . . . . . A.1.1 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1.2 Between a Sphere and a Plane . . . . . . . . . . . . . . . . . . . A.1.3 Between Two Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Volume Repartition by the Energetic Approach . . . . . . . . . . A.2.1 Assumptions, Notations, and Mathematical Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2.2 L–V Interfacial Energy . . . . . . . . . . . . . . . . . . . . . . . . . . A.2.3 Total Interfacial Energy . . . . . . . . . . . . . . . . . . . . . . . . .

227 227 227 228 230 233

B

Geometry Complements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.1 Area and Volume of a Spherical Cap . . . . . . . . . . . . . . . . . . . . B.2 Differential Geometry of Surfaces . . . . . . . . . . . . . . . . . . . . . . . B.2.1 Mean Curvature of a Surface . . . . . . . . . . . . . . . . . . . . . B.2.2 Mean Curvature of an Axially Symmetric Surface . . B.3 Catenary Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

237 237 238 238 239 240

C

Comparison Between Both Approaches . . . . . . . . . . . . . . . . .

243

D

Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

247

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

251

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

261

233 234 235

1 From Conventional Assembly to Microassembly

1.1 Introduction The goal of this chapter is to give an overview of different assembly strategies that can be used at the considered scale from 10 µm to 10 mm. Indeed, even in the field of microproducts, components have to be assembled. The production of microsystems integrating many functionalities, many components made of different materials require flexible, modular, accurate mechanisms, which can finely feed, pick, orientate, move, and release different types of objects at the right place. The assembling and packaging operations that achieve the microcomponents’ fusion into a hybrid microsystem is usually considered a bottleneck in the manufacturing process more than the manufacturing of components itself. This is particularly true for very small components that require high positioning tolerances leading to high manufacturing cost. High cost gripping solutions for various applications concerning the handling and the assembling of microcomponents have been developed but they do not offer satisfying economical solutions yet. According to Breguet et al. [30], the main three challenges characterizing microassembly are the following: • • •

Precise alignment (submicron) of the components in several degrees of freedom and in a large workspace (a few cm3 ) Grasping and releasing of these delicate components Attaching them together

We present a taxonomy of microassembly in this chapter. To produce a miniaturized multifunctional system, we distinguish the following criteria: • •

Do we have to assemble a composed product or can we design it to avoid (or at least reduce) assembly tasks? Do we assemble a lot of loose components or can we combine assembly and manufacturing in situ? [167]

4

1 From Conventional Assembly to Microassembly Multifunctional product

Monolithic product

Composed product

Combined part manufacturing and assembly

Product external assembly functions

Assembly of loose components

Self-Assembly or stochastic assembly

Product internal assembly functions

Fig. 1.1. Taxonomy of microassembly

• •

Is the assembly equipment inside or outside the product? Can we use selfassembly (also called stochastic assembly)? [167] Finally, is the assembly required to be serial or can the throughput be increased by using parallel assembly? [22]

This classification is shown in Fig. 1.1.

1.2 Design of Monolithic Products for Microassembly The first and most basic approach for microassembly consists in downscaling the conventional approach. The use of miniaturized grippers (mainly downscaled tweezers or vacuum grippers, but an exhaustive description of the suitable gripping principles is presented in Chap. 3) allows to pick, move, orientate, and release microcomponents; however, the word gripper explicitly refers to a two finger tool used to grip an object, it must be understood here as any device allowing to pick a component, such as, for example, a vacuum gripper with only one finger. The most often associated strategy consists in serial pick and place of components. The main drawbacks of such an approach consist in physical limits (sticking problems at release) and in nonoptimal solutions (all efforts for accurate positioning must be repeated for each component). Some authors [65] propose to improve this situation by combining design for both microassembly and microworld adapted assembly equipment. The design for microassembly is supposed to reduce the number of assembly tasks or at least to improve the suitability of design for automated assembly. To illustrate this, let us consider the design of a rotational joint with a one-way actuation and an elastic force to get the system back to the equilibrium. This example is illustrated in Fig. 1.2. In the conventional design, the rotational joint is made of a small ball bearing (SKF produces reduced ball bearing with

1.2 Design of Monolithic Products for Microassembly

5

Spring

Moving part

Moving part

Notch hinge

Ball bearing

Fig. 1.2. Conventional design vs micro-driven design: case of a rotational joint (the actuator is not shown)

outer diameter of about 2 mm. As a comparison, one of the smallest ball bearing with an outer diameter of 0.9 mm has been assembled by the researchers of the MEL1 (Japan) with their microfactory [6, 135]. Once both parts and the ball bearing are assembled, they still need to be put together with the actuator and the elastic element allowing the backward motion. Several elements have to be manufactured and assembled. Besides the hardness of the task, the different tolerances lead to a low-effective system with clearances. Moreover, if the moving part has to guarantee watertightness with an antagonist counterpart, the system will probably not meet the requirements. An alternative design could replace the ball bearing and the elastic element by an elastic flexure hinge, combining both functionalities in one component. The maximal deflection of the notch hinge – a notch hinge is a flexure hinge with a circular profile – depends on the Young’s modulus and the elastic limit of the material, and on the width and thickness of the hinge [35]. With titanium and wire electro-discharge machined2 hinges with 5 mm thickness and 100 µm width, the angular range can reach 15◦ . This new design reduces the number of parts, highly simplifies the assembly task, and enhances the functionality of the system: no clearance, no friction, no wear, and consequently no scraps, making this kind of design particularly suitable for biocompatible applications.

1

2

MEL = Mechanical Engineering Laboratory, see National Institute of Advanced Industrial Science and Technology http://www.aist.go.jp. EDM = Electro Discharge Machining is “a machining method using a free electrical discharge between an electrode and a workpiece to generate heat flow with high energy density, so that contact force and chatter vibration can be avoided during machining” [87].

6

1 From Conventional Assembly to Microassembly Micro electro-discharge machining (drilling)

Insert of the pin

Twist for breakage Removal of neck material by of the neck micro-electro discharge machining

Workpiece Pin produced with wire electro discharge grinding

Ultrasonic vibration of the worktable

Fig. 1.3. Pin-in-hole combination produced by part manufacturing and assembly steps [115] (Copyrights CIRP.)

1.3 Combined Part Manufacturing and Assembly According to Tichem and Karpuschewski [166], “the goal of this method is to minimize the assembly content of composed products by creating products on basis of a combination of part manufacturing and assembly operations. This reduces the amount of part handling operations and delicate joining operations. Clearly, this method is not a pure assembly method. It recognises the fact that, in the microdomain, part manufacturing and assembly can in certain cases be integrated. The separation between part manufacturing and assembly as visible in the macrodomain vanishes.” An example of this approach can be found in [115], dealing with a pin-in-hole combination performed by part manufacturing and assembly steps. More recently, Jing-Dae Huang and Chia-Lung Kuo[87] have improved this method combining micro-EDM and laser welding to manufacture and achieve pin-plate assembly of 50 µm diameter pins with a large aspect ratio.

1.4 Product External Assembly Functions This approach is the most conventional one, often based on the use of accuracy positioning systems and microgrippers. This method can be improved by adding visualization systems and imaging processing. We will not focus on this method because it is not micro-oriented. Nevertheless, it has to be mentioned because it can lead to a micro-specific assembly method when coupled with a parallel assembly approach, which is also presented in this section.

1.5 Product Internal Assembly Functions The principle of internal assembly is to provide a microproduct with additional functionalities such as, for example, internal actuators. The assem-

1.6 Stochastic or Self-Assembly

7

Fiber holding groove Bimorph

Passive spring Silicon wafer surface

Fiber

V-beam (thermal actuation)

Fig. 1.4. Example of internal adjustment of optic fibers (Reprinted with permission from [82]. Copyrights 2006 Institute of Physics.)

bly of this product with another component can then be performed in two steps: A first coarse positioning of the component on the product is performed with a conventional, whether miniaturized or not, handling tool. The ultimate positioning with the required accuracy is performed inside the product, thanks to the internal actuators. This way to perform assembly provides final microproducts with a higher complexity and more internal functionalities. The cost aspects of such a method must be analyzed carefully. The example of internal assembly given in [175] includes the following functions for a self-adjusting microsystem: a controlled actuation of the component, the sensing of the position of the component, and the freezing of the component in the final position. The studied example consists in interconnecting optical fibers with each other. The fine positioning is performed by using a piezoelectric plate glued on a passive silicon layer, allowing a bending motion of the actuator when voltage is supplied to the piezoelectric electrodes. This bending motion is used for the fine positioning of the fibers. Two ways can be used to keep the alignment: The first way is to use active control, the second one consists in permanently freezing the alignment, but nowadays, no technical solution has been proposed yet for this application. Recently, an adaptation of this principle has been proposed in [82], which is illustrated in Fig. 1.4.

1.6 Stochastic or Self-Assembly The underlying idea of stochastic assembly is to avoid any deterministic interaction and control of the part position during the assembly task. The components to be assembled are jumbled in close distance before applying a force field that will perform the assembly. An example of stochastic assembly

8

1 From Conventional Assembly to Microassembly

Fig. 1.5. Example of stochastic assembly illustrated in [23]: capillary forces in the adhesive (black) cause self-assembly

is cited in [166] and consists in using the capillary force of an adhesive drop to align two parts (information on lateral forces modeling can be found in [105]). This principle taken from [23] is illustrated in Fig. 1.5. Other effects are cited in [22] and have been applied by several authors to proceed stochastic assembly: • • • •

Fluidic agitation and mating part shapes Vibratory agitation and electrostatics force fields Vibratory agitation and mating part shapes Colloidal self-assembly [106]

1.7 Parallel Assembly Unlike the sequential process, parallel assembly is the assembly of more than two devices at the same time. As a comparison, batch fabrication is widely used in microelectronic where the same parallel concept is applied for silicon chip fabrications. Parallel assembly avoids the drawbacks of a sequential one for small devices: time consuming and low throughput. The drawback of parallel assembly is less flexibility compared to sequential assembly. An example of parallel microassembly with electrostatic force fields is given in [22].

1.8 Conclusions These different strategies for microassembly are logistic approaches for assembly (we have not discussed technology yet). It is now essential to focus on the ways to perform the assembly tasks: feeding, positioning, pick, and place. More specifically, we intend to focus on microgripping. Therefore, the following chapters are devoted to the forces acting at the envisaged scale (10 µm to 10 mm) and the related handling principles.

2 Classification of Forces Acting in the Microworld

2.1 Introduction When downscaled, volumic forces (e.g., the gravity1 ) tend to decrease faster than other kinds of forces such as the capillary force or the viscous force. Although they still exist on a macroscopic scale, these forces are often negligible (and neglected) in macroscopic assembly. A reduced system is consequently brought face-to-face with the relative increase of these so-called surface forces. According to the literature on microassembly, these forces are mainly the electrostatic forces, the van der Waals forces, the liquid bridge (also called capillary or surface tension) forces, the forces due to the mechanical clamping (contact forces) and deformation (pull-off forces), and viscous drag. The term surface force is misleading since all these forces does not really depend on the square of the characteristic length. Nevertheless, this term conveys the idea that these forces decrease more slowly than the weight, which leads to some cut-off sizes below which these forces disturb the handling task because they generate the sticking of the microcomponent to the tip of the gripper (the weight is no longer sufficient to overcome them and ensure release). There are several ways to tackle this problem: These forces can be reduced, overcome, or exploited as a gripping principle. The choice will be different according to the manipulation strategy (see Fig. 2.1): The parameters (materials, environment, geometries) will be chosen to maximize the force used as a gripping principle (for example by choosing hydrophilic materials in a manipulation based on the capillary force) and to minimize the disturbing forces (use of hydrophobic materials in a manipulation based on a mechanical gripper). This chapter presents some general classifications of the forces according to their range and introduces the most often cited forces in microassembly literature.

1

From one point of view, inertia forces also involve the mass of the component, but the possible high dynamics at small scales compensate this effect, as illustrated by the dynamical release proposed in [77].

10

2 Classification of Forces Acting in the Microworld Forces

Gripping principles

Fig. 2.1. Forces and gripping principles: The force underlying in a gripping principle must be maximized, all the others should be decreased

2.2 Classification Schemes of the Forces According to Lee [118], we go over the first simplified classification of the different forces in four main categories: • • • •

Gravity, with an infinite range Electromagnetic force, with an infinite range Weak force, with a range smaller than 10−18 m Strong force, with a range smaller than 10−15 m

These last two forces are outside the scope of this work due to their very short range (inside the nucleus). Electromagnetic forces represent the source of all intermolecular interactions and their influence can be combined to that of gravity in some phenomena such as the rise of a liquid in small capillaries. The interaction between atoms, molecules, and solids is characterized by the following: • •

Chemical forces and covalent bonding, with a range over the order of an interatomic separation (typically 0.1–0.2 nm) Coulomb force and ionic (or partially ionic) bond

Moreover, the interaction between microscopic bodies also depends on the Lifshitz–van der Waals (VDW) forces, which can be classified into four categories: •

Dispersion forces, also called London forces [120], are due to a Coulomb interaction. They represent one third of the Lifshitz–van der Waals forces, are long range (more than 10 nm), can be attractive or repulsive, and act between all atoms and molecules, even between neutral ones. These forces are nonadditive, which means that the interaction between two molecules is affected by the presence of other bodies. The interaction energy of the dispersion forces decreases as a function of the separation distance to the sixth power ( r16 )

2.2 Classification Schemes of the Forces

•

•

11

Orientation forces, also called Keesom forces, coming from the interaction between two permanent dipoles. Their energy also depends on the separation distance as r16 Induction forces, also called Debye forces, due to the interaction between a permanent dipole and an induced dipole, with an energy decreasing as 1 r6

•

Retardation forces, described by Casimir and Polder, due to the nonnegligible propagation time of the electromagnetic wave between the dipoles when their separation distance becomes higher than typically 10 nm. Because of this propagation time, the relative orientation of the dipoles are less favorable and the interaction energy decreases faster than for the other terms ( r17 )

A detailed description of these four terms can be found in [118] (Table 3, p10) or in [88]. At this stage of reading, it seems that the fast decrease of the van der Waals with the separation distance put them aside as far as microsystems are concerned. However, a more subtle investigation shows that this decrease complies with another power law in the case of two macroscopic bodies interacting with each other [89]. Still mentioned in [118], the Coulomb and Lifshitz–van der Waals forces are not sufficient to explain the adhesion between two solids: the molecular interactions (also called donor–acceptor interactions by physicists or acid–base interactions by chemists) also play a role in adhesion, but as their range is limited to the interatomic separation (typically smaller than 0.3 nm), we will not consider them in what follows even if a more detailed study concerning the close contact of two bodies should probably involve their effects. Finally, we cannot conclude this section without mentioning the role of capillary forces [48], [80]. These forces play an important role in a lot of surrounding phenomena and applications: They allow children to build up sand castles and everyone to collect the crumbs more easily, provoke adhesion between microcomponents, cause reliability failure in MEMS2 applications [104, 125, 176, 179, 184], and are of the utmost importance in microassembly. As a first conclusion, we propose the schematic summary presented in Table 2.1. Table 2.1. Forces summary according to the interaction distance Interaction distance Up to infinite range From a few nm up to 1 mm >0.3 nm 0.3 nm < separation distance V , decrease r • Otherwise, increase r With this geometrical shape, the switch from a convex to a concave meniscus smoothly occurs when a passes through zero before changing its sign.

7.6 Comparisons and Summary Comparisons between the different formulations of the energetic method have already been proposed in the ad hoc section. In conclusion of this section devoted to the approximations, we propose the graphical comparison (Fig. 7.12) of the meniscus shapes between the geometrical methods. The impact on the pressure difference and the force is plotted in Fig. 7.13. As the difference between the “arc” and the “parabolic” approximations must be explained (the “better” approximation must be determined), we will turn ourselves to numerical solutions: According to the Laplace equation, we will compute the shape of a meniscus at equilibrium for a given volume. These simulations are of the highest interest as far as the use of capillary force as

62

7 State of the Art on the Capillary Force Models at Equilibrium −4

x 10

z [m]

6

4

2

0 2

4

6 r [m]

8

10

12 −4 x 10

Fig. 7.12. Comparison between the arc (solid line) and the parabolic (dashed line) approximations (Reprinted with permission from [108]. Copyright 2005 American Chemical Society). 500

8

0 Force [mN]

6 ∆p

−500 −1000 −1500

4 2

−2000 −2500 0

200

400 Gap [µm]

(a)

600

800

0 0

200

400 Gap [µm]

600

800

(b)

Fig. 7.13. Comparison between the meniscus shape models: arc (Open square) and parabola (Open triangle) models. (a) Pressure difference ∆p across the LV interface; (b) Force (Both reprinted with permission from [108]. Copyright 2005 American Chemical Society).

gripping principle is concerned. These simulations will consequently directly be related to the problematics of microgripping and microassembly presented in the state of the art of this work. Table 7.1 summarizes several classical approximations found in the literature and gives the corresponding references and assumptions (see Fig. 6.6 and Appendix A.1 for more details). The considered assumptions are as follows: 1. 2. 3. 4. 5.

Parallel plates Spherical tip (radius R) near a plate Arc approximation of the interface (where ρ = constant is the radius) Energetic formulation The radii r1 and r2 of the two circular contact lines are very small compared to R

7.6 Comparisons and Summary

63

Table 7.1. Summary of the capillary forces (sign “−” has been omitted) (Reprinted with permission from [111], Copyrights 2006 Koninklijke Brill N.V.) Ref. [124] [124] Eq.7.10 Eq.7.14 [89] [161] [71] [70] [48]

6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

Force F = 4πRγ cos θ (r1 /R)2 r1 /R F = 4πRγ cos θ{ 12 [ z/R+1−(1−(r 2 1/2 ] − [ 4 cos θ ]} 1 /R) ) πγ 2 2 F = z (r1 cos θ1 + r2 cos θ2 ) F = 2πγ r2 cos θ + 2πrγ z 4πRγ cos θ F = 1+(z/h) F = πγρ’2 ( ρ1 − ρ1
) F = 2πγρ + γρ πρ2 z F = 2πγρ + γρ π 2 sin θ F = 2πr2 γ sin(θ2 + φ) + πr22 γ( ρ1 − r12 )

Assumptions 2,5,6,7,8,9 2,3,6,7,15 1,4,7,8,10,11 1,4,7,8,11,12 2,4,7,10,13,14 2,3,15 1,3,8,9 1,3,7,9 2,3

r1 = r2 = r (“symmetric case”) The contact angles are equal: θ1 = θ2 = θ The gap z is very small compared to the radius r of the contact line The curvature of the interface in the horizontal plane is negligible | ρ1
|