Capillary Forces in Microassembly

Modeling, Simulation, Experiments, and Case Study

By: Pierre Lambert

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Hardcover | 25 October 2007

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288 Pages

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Capillary Forces in Microassembly discusses the use of capillary forces as a gripping principle in microscale assembly. Clearly written and well-organized, this text brings together physical concepts at the microscale with practical applications in micromanipulation. Throughout this work, the reader will find a review of the existing gripping principles, elements to model capillary forces as well as descriptions of the simulation and experimental test bench developed to study the design parameters. Using well-known concepts from surface science (such as surface tension, capillary effects, wettability, and contact angles) as inputs to mechanical models, the amount of effort required to handle micro-components is then predicted.

Researchers and engineers involved in micromanipulation and precision assembly will find this a highly useful reference for microassembly system design and analysis.

Industry Reviews

From the reviews:

"Presented in five parts this text considers the use of capillary forces as a means to grip and assemble micrometre scale structures. ... This book reads easily and is well presented in terms of technical figures and mathematical detail. ... topics discussed are illustrated via a number of examples and, ultimately a thorough case study involving a watch bearing. ... serves best as a reference for those specialists working in the field or for a postgraduate researcher looking for a clear explanation of microassembly principles." (Matthew R. Foreman, Contemporary Physics, Vol. 51 (6), 2010)

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Preface	p. IX
Context	p. IX
Contributions of this Book	p. XII
What this Book Does Not Tell	p. XV
Reading Suggestion	p. XVI
Microassembly Specificities
From Conventional Assembly to Microassembly	p. 3
Introduction	p. 3
Design of Monolithic Products for Microassembly	p. 4
Combined Part Manufacturing and Assembly	p. 6
Product External Assembly Functions	p. 6
Product Internal Assembly Functions	p. 6
Stochastic or Self-Assembly	p. 7
Parallel Assembly	p. 8
Conclusions	p. 8
Classification of Forces Acting in the Microworld	p. 9
Introduction	p. 9
Classification Schemes of the Forces	p. 10
Conclusions	p. 12
Handling Principles for Microassembly	p. 13
Introduction	p. 13
Presentation of Gripping Principles	p. 13
Classification of Gripping Principles	p. 25
Comparison between Gripping Principles	p. 28
Conclusions	p. 29
Conclusions	p. 35
Modeling and Simulation of Capillary Forces
Introduction	p. 39
First Set of Parameters	p. 41
Introduction	p. 41
Surface Tension	p. 41
Young-Dupre Equation and Static Contact Angle	p. 42
Laplace Equation	p. 43
Effects of a Liquid Bridge on the Adhesion Between Two Solids	p. 45
A Priori Justification of a Capillary Gripper	p. 47
Conclusions	p. 49
State of the Art on the Capillary Force Models at Equilibrium	p. 51
Introduction	p. 51
Energetic Approach: Interaction Between Two Parallel Plates	p. 51
Energetic Approach: Other Configurations	p. 55
Geometrical Approach: Circle Approximation	p. 57
Geometrical Approach: Parabolic Approximation	p. 61
Comparisons and Summary	p. 61
Static Simulation at Constant Volume of Liquid	p. 65
Introduction	p. 65
Description of the Problem	p. 65
Assumptions	p. 66
Equations and Numerical Simulation	p. 67
Discussion and Conclusions	p. 71
Comparisons Between the Capillary Force Models	p. 73
Introduction	p. 73
Qualitative Arguments	p. 73
Analytical Arguments	p. 75
Definition of the Case Study	p. 75
Preliminary Computations	p. 76
Determination of the Immersion Height h	p. 77
Laplace Equation Based Formulation of the Capillary Force	p. 79
Energetic Formulation of the Capillary Force	p. 79
Equivalence of Both Formulations	p. 80
Conclusions	p. 81
Example 1: Application to the Modeling of a Microgripper for Watch Bearings	p. 83
Introduction	p. 83
Presentation of the Case Study	p. 83
Analytical Model Based on the Circle Approximation	p. 86
Numerical Model Based on the Laplace Equation	p. 89
Benchmark	p. 93
Pressure Difference Saturation	p. 94
Conclusions	p. 96
Second Set of Parameters	p. 97
Introduction	p. 97
Surface Heterogeneities and Surface Impurities	p. 97
Surface Roughness	p. 98
Static Contact Angle Hysteresis	p. 99
Dynamic Spreading	p. 100
Conclusions	p. 101
Limits of the Static Simulation	p. 103
Introduction	p. 103
Performances of the Assembly Machines	p. 103
Nondimensional Numbers and Buckingham [pi] Theorem	p. 103
Another Approach: Use of a ID Analytical Model	p. 106
Limitations of the Static Model	p. 108
Conclusions	p. 110
Approaching and Rupture Distances	p. 111
Introduction	p. 111
Approaching Contact Distance	p. 111
Rupture Distance and Residual Volume of Liquid	p. 113
Mathematical and Notation Preliminaries	p. 114
Volume Repartition	p. 115
Rupture Condition and Rupture Gap	p. 117
Analytical Benchmarks	p. 119
Summary of the Methods	p. 120
Comparison between the Methods	p. 122
Conclusions	p. 124
Example 2: Numerical Implementation of the Proposed Models	p. 127
Introduction	p. 127
Liquid Bridge Simulation for the Analysis of a Meniscus	p. 127
Evaluation of the Double Iterative Scheme	p. 131
Pseudodynamic Simulation	p. 133
Conclusions	p. 135
Conclusions of the Theoretical Study of Capillary Forces	p. 137
Experimental Aspects
Introduction	p. 141
Test Bed and Characterization	p. 143
Introduction	p. 143
Requirements	p. 143
Test Bed Principles	p. 145
Force Measurement	p. 145
Drop Dispensing	p. 146
Vision	p. 148
CAD Model and Drawings	p. 148
Characteristics of the Force Measurement Set Up	p. 151
Typical Calibration	p. 151
Linearity	p. 151
Accuracy	p. 152
Influence of a Misalignment on the Force Measurement	p. 152
Characteristics of the Contact Angles Measurements	p. 154
Surface Tension Measurement	p. 155
Modus Operandi	p. 155
Characterization	p. 158
Set of Available Grippers	p. 158
Set of Available Components	p. 159
Set of Available Blades	p. 160
Available Liquids	p. 161
Contact Angles Characterization	p. 161
Conclusions	p. 162
Results	p. 163
Introduction	p. 163
Preliminary Results: Validation of the Simulation Code	p. 163
Meniscus Profile	p. 163
Comparison with the Analytical Expressions	p. 164
Experimental Validation	p. 166
Advancing vs Receding Contact Angle	p. 168
Influence of the Gap	p. 170
Force-Distance Curve	p. 170
Tension Force vs. Laplace Force	p. 171
Influence of the Gripper Geometry	p. 171
Influence of the Surface Tension	p. 172
Influence of the Contact Angle [theta subscript 1]	p. 174
Influence of the Relative Orientation	p. 174
Auxiliary PTFE Tip	p. 176
Dynamical Release	p. 177
Simulation Results	p. 177
Experimental Results	p. 182
Approaching Contact and Rupture Distances	p. 185
Shear Force	p. 186
Conclusions	p. 187
Example 3: Application to the Watch Bearing Case Study	p. 189
Introduction	p. 189
Available Grippers	p. 189
Available Components	p. 191
Liquid Properties	p. 191
Liquid Dispensing	p. 192
Contact Angles	p. 195
Example 4: Application to the Watch Bearing Case Study: Results	p. 199
Introduction	p. 199
Picking	p. 199
Introduction	p. 199
Errors	p. 200
Solutions	p. 201
Automated Control	p. 202
Placing	p. 204
Compliance Effect	p. 205
Force Measurement	p. 206
Introduction	p. 206
Modification of the Force Measurement Test Bed	p. 206
Comparison Between Models and Experiments	p. 206
Ongoing Experimental Study	p. 208
Conclusions	p. 209
Conclusions	p. 211
Introduction	p. 211
Picking Operations	p. 211
Releasing Strategies	p. 213
Design Aspects	p. 215
General Conclusions and Perspectives
Conclusions and Perspectives	p. 221
Conclusions	p. 221
Perspectives	p. 223
Appendices
Modeling Complements	p. 227
Analytical Approximations of the Capillary Forces	p. 227
Preliminary	p. 227
Between a Sphere and a Plane	p. 228
Between Two Spheres	p. 230
Volume Repartition by the Energetic Approach	p. 233
Assumptions, Notations, and Mathematical Preliminaries	p. 233
L-V Interfacial Energy	p. 234
Total Interfacial Energy	p. 235
Geometry Complements	p. 237
Area and Volume of a Spherical Cap	p. 237
Differential Geometry of Surfaces	p. 238
Mean Curvature of a Surface	p. 238
Mean Curvature of an Axially Symmetric Surface	p. 239
Catenary Curve	p. 240
Comparison Between Both Approaches	p. 243
Symbols	p. 247
References	p. 251
Index	p. 261
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Capillary Forces in Microassembly

Modeling, Simulation, Experiments, and Case Study

At a Glance

Hardcover

Industry Reviews

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