1. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Variation Modeling and Design for Compliant Assemblies Prof. S. Jack Hu and Dr. K. Iyer Department of Mechanical Engineering and Applied Mechanics The University of Michigan

2. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Compliant Sheet Metal Assembly

3. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Variation Simulation Methods Worst Case: (Conway, 1948; Chase and Parkinson, 1991) Root Sum Squares (RSS): (Spotts, 1978, Lee and Woo, 1990) Monte Carlo Simulation: (Craig, 1989)

4. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Problem with Conventional Variation Simulation Using Rigid Body Assumption (Takezawa, 1980) N=64

5. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Example of Variation Stackup

6. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN PC Based Compliant Assembly Variation Analysis Introduction B) Unique Properties of Compliant Assembly Assembly Mechanism Locating Principle Variation Propagation Type Properties Rigid Body AssemblyCompliant Assembly Deformation and Spring- back “3-2-1” Rigid-body Motion Force & Geometry Closure “N-2-1” Geometry Closure Assembly Examples Assembly Characteristics

7. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Understanding Variation “Stack-up” in Compliant Sheet Metal Assembly (Simple 1D model) Clamping forces Springback:

8. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN When 1 and 2 are independent, Characteristics: (1) The assembly variation can be less than that of individual components, (2) The assembly variation is dominated by the variation of the more rigid component. Part 1 10 1 100 Part 2 10 2 100 WhLWhL (mm) same material Example

9. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Variation Simulation Using FEM - Direct Monte Carlo

10. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Linearized Sensitivity Approach

11. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Compliant Assembly Variation Analysis ( CAVA ): Overview (Liu and Hu, 1997; Long and Hu, 1998)

12. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Experimental Verification of CAVA

13. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Comparison between Experiments and CAVA Correlation 

14. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN CAVA Operating Procedures Create model Calculate Evaluate Modify the model

15. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN CAVA Interface

16. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Process for Sheet Metal Assembly The “3-2-1” fixture elements are closed The additional “N-3” clamps and weld guns are closed Welding. Then fixtures & clamps released, and sheet metal spring-back

17. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Variation Characteristics in Sheet Metal Assembly (a) Rigid body motion by “3-2-1” fixture (b) Deformed part held by additional clamps and weld guns (c) Spring-back after tooling release V a = [S 1 ] V p + [S 2 ] V t = [S] V s

18. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Robustness Evaluation R2R2 Variation Transmission Ratio C Sensitivity Index Robustness Index K = N (Lee, Long and Hu; 2000)

19. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN CAVA Applications: Joint Design Measure Variation Sources Node Di r. 413763233247255313309335505519527 2742 0.58100.02450.0549-0.12300.00880.18604.2300-0.04730.4400-0.83900.01301.2800 2762 0.8090-0.08590.0432-0.0608-0.0096-0.00265.9000-0.43400.3650-0.5840-0.02070.1420 3092 0.27800.21300.2540-0.0091-0.00020.00902.18000.55502.0000-0.0717-0.00270.0717 4982 -0.0026-0.0096-0.06080.0432-0.08580.80900.1420-0.0207-0.58400.3650-0.43405.9000 5002 0.18600.0088-0.12300.05490.02450.58101.28000.0130-0.83900.4400-0.04734.2300 5192 0.0090-0.0002-0.00910.25400.21300.27800.0717-0.0027-0.07172.00000.55502.1800

20. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN 1) Parts variations are absorbed in lap joints 2) Parts variations are magnified in butt joints Lap JointButt JointLap-Butt Joint K8.5627.6111.98 Average Deviation (mm) 1.459.643.70 Joint Design: Robustness vs. Architecture

21. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN CAVA Applications: Fixture Configuration Design Case #1234 Locations of clamps C1, C2, C3 C1, C2, C3, C4 C1, C2, C3, C5 C1, C2, C3, C4, C5 K0.846 5 0.842 9 0.753 6 0.7110

22. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Evolution of Variation and Stiffness (Hu, 1997)

23. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN CAVA Applications: Assembly Line Configuration Serial Line Configuration Parallel Line Configuration

24. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Assembly With 2 Joining Operations

25. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Line Configuration Variation Single Assembly StationSerial Line Assembly

26. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Line Configuration Robustness RobustnessKpKt Station 10.948014.8973 Station 20.70070.2774 System0.6610.70 1)Contributions of tooling and part variations can be different in different stations and joint designs. 2)A parallel configuration should be avoided with a station for which K t > 1

27. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN A new methodology and variation simulation software, CAVA, has been developed which can be used to Evaluate the dimensional capability of product architectures – Joint structure – The number and location of welds Evaluate the dimensional capability of processes – Fixture schemes – Assembly sequence Work Impact

28. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Assembly of Parts with Non-Flat Surfaces Relevance –Fatigue crack initiation –Fretting –Wear –Leakage –Electrical contact resistance –…any situation where the integrity of a contact interface is important

29. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Bolted Joint Model 3 1 1 2

30. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN 2-D FEA of Surface Waviness 32mm16mm24mm 16mm Abaqus software Axisymmetric model plates (CAX4 elements) Bolt in plane stress (CPS4 elements) Bolt thickness (3-direction) varies to simulate circular cross section Hole properties “smeared” Sliding between plates possible Stick conditions assumed at all bolt- plate interfaces

31. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Surface Waviness (Profile) Examples I. Perfectly Flat II. Sinusoidal gap with amplitude of 100  m. III. Arbitrarily shaped gap from contact of sinusoid surfaces with amplitudes of 50  m and 100  m. IV. Arbitrarily shaped gap from contact of sinusoid surfaces with amplitudes of 25  m, 50  m and 100  m.

32. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Contact Pressure and Gap Distributions I. IV. III. II.

33. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Preliminary Indications Joint compliance: –176 mm/GN (II) > 30 mm/GN (IV) > 26 mm/GN (III) > 8.5 mm/GN (I) Peak contact pressure, total gap and compliance are all related to each other. Contact pressure distribution is non-“elliptical”.  Local bending at the contact surfaces is significant and affects the contact pressure and slip distributions. Gap closure has may have a complex relationship to waviness –more wavy can mean more closure (compare III and IV) Friction coefficient appears to have no effect on the contact pressure and slip distributions.

34. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Shear Stress, Slip and Bulk Stresses I. IV. II. III.

35. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Preliminary Parametric Study Models I and IV considered Material property change: steel vs. Al –T= 20  C,  = 0.4 Temperature rise: 20  C  150  C –Al (material properties),  = 0.4 Friction coefficient change:  =0 and 0.4 –Steel (material properties), T = 20  C

36. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Effects of Material: Steel vs. Aluminum I IV I

37. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Effects of Temperature Rise: 20  C  150  C I IV I

38. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Effect of Friction Coefficient:  = 0 and  = 0.4 I IV I

39. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Results Effect of material property: –For perfectly flat contact, the effects on contact pressure and gap distribution are negligible –For wavy contact, the total gap and maximum gap increase dramatically with decreasing material stiffness (Al)  The machining tolerances applied to steel are not directly transferable to Aluminum Effect of temperature rise: –Possibly complex alteration of the contact area, pressure and gap distributions in flat and wavy contacts Effect of friction coefficient: –Does not alter contact pressure distribution –Can affect the gap distribution if waviness is significant Inverse relationship with initial contact area indicated higher  promotes gap closure.

40. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Additional Results Increase in compliance with Al is ~ 3X: –8.5 mm/GN to 25 mm/GN in model I –30 mm/GN to 82.2 mm/GN in model IV Thermal springback: –539 mm/GN in model I (64.7 mm) –480 mm/GN in model IV (57.6 mm) Effect of  on compliance is negligible

41. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN Work in Progress A) Inclusion of gasket –Solution for perfectly flat contact (model I) has been obtained. –Modeling the highly localized, non-linear deformation of gasket material in the presence of surface waviness is currently receiving attention. Gasket

42. NATIONAL SCIENCE FOUNDATION– INDUSTRY/UNIVERSITY COOPERATIVE RESEARCH CENTER Dimensional Measurement and Control in Manufacturing COLLEGE OF ENGINEERING, THE UNIVERSITY OF MICHIGAN B) Multi-rivet joints –effects of clamping sequence C) Closed-form solution for wavy contact P E 1, 1 E 2, 2