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Variation Modeling and Design in Compliant Assemblies

Professor S. Jack Hu and Dr. Kaushik Iyer, University of Michigan
Presented June 15, 2000 at the ADCATS 2000 Conference

Component fixturing variations, tooling location and force variations, and component material compliance all contribute to variability in the overall dimensions and performance of multi-component assemblies. Traditionally, treatments for predicting and controlling undesired variations at the system level have assumed rigid material properties for each component. However, omission of component compliances has been shown to provide unrealistic predictions of variation stack-ups for entire assemblies. This and other inadequacies of the rigid-component assumption have been particularly evident in automotive and aircraft assemblies that contain flexible metal sheets and large numbers of connections (welds or rivets).

A recently developed model for predicting variations in such compliant assemblies (CAVA) will be presented. The model relates the dimensional deviations of an assembly to individual component deformations, which can be varied statistically according to variations in non-component factors (machining, fixturing and tooling). Additional variations can arise from the configuration of the assembly system (series, parallel or hybrid lines). An extension of CAVA to evaluate the robustness of compliant assembly systems will also be discussed. The analytical technique will be demonstrated through one or two robustness evaluation examples.

The surfaces of assembled components are commonly regarded as being flat or smooth. However, machining processes and material microstructure together impart local, small deviations to actual surface profiles. Deviations in the profile of a component surface from the nominal surface are widely believed to influence fretting fatigue and wear life (e.g. in airframe riveted lap joints, automotive and turbine engine components, etc.), electrical contact resistance, etc. In this case, the relevant length scales lie in the asperity-contact width range and are associated with surface roughness, waviness and form. Recent exploratory work directed towards the development of analytical solutions for the assembly of parts with realistic (non-flat) surface profiles will also be discussed.

Dr. Jack Hu received his B.S. from Tianjin University in 1983, M.S. and Ph.D. from the University of Michigan in 1986 and 1990 respectively. He has been on the faculty at the University of Michigan since 1992.

Dr. Hu's teaching and research interests are in assembly and joining, engineering statistics, and manufacturing system design and analysis, with specific applications to automotive body assembly systems. He has published more than 80 papers in ASME, SME and other international journals and referenced conference proceedings. He has also developed various innovative approaches for designing and controlling variation in assembly systems. These approaches have been widely used by U.S. auto manufacturers in their design and production. 

Currently, Dr. Hu serves as the Director of the U.S. NSF sponsored Industry-University Cooperative Research Center for Dimensional Measurement and Control in Manufacturing, and the Deputy Director of the S. M. Wu Manufacturing Research Center. He also co-directs the General Motors Satellite Laboratory at the University of Michigan. He served as the Technical Director for the "2 mm Program" and the "Intelligent Resistance Welding Program", both sponsored by the Advanced Technology Program and the Auto Body Consortium.
Dr. Hu is the recipient of various awards, including the Outstanding Young Manufacturing Engineer Award from the Society of Manufacturing Engineers in 1993, the National Science Foundation CAREER Award in 1996, the Robert Caddell Faculty Achievement Award from the College of Engineering at the University of Michigan in 1997, and the Faculty Achievement Award from the Department of Mechanical Engineering at the University of Michigan in 2000.

Dr. Kaushik Iyer, Vis. Research Investigator, University of Michigan, Ann Arbor, MI. Dr. Iyer obtained his B. Tech. from the Indian Institute of Technology in 1991, M.S. from the Oregon Graduate Institute of Science and Technology in 1993 and Ph.D. from Vanderbilt University in 1997. His doctoral dissertation was on the local mechanical behavior and fretting fatigue of airframe riveted lap joints (Adviser: G. T. Hahn). Since then, his areas of research activity have broadened to include roughness origins in machined surfaces, high-cycle fretting fatigue in turbine engines, automotive engine wear and contact mechanics of non-flat surfaces. He has written over 15 articles relating to riveted connections, contact fatigue and quenching process modeling.


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