1. Arne Thesen and Akachai Jantayavichit Slide 1 A new approach to tolerance improvement through real-time selective assembly Arne Thesen and Akachai Jantayavichit Department of Industrial Engineering University of Wisconsin-Madison 1513 University Ave, Madison, WI 53706, U.S.A. thesen@engr.wisc.edu

2. Arne Thesen and Akachai Jantayavichit Slide 2 Research Objective Pins Bushings Selective Assembly Process Assembly Station Tol. 10 -3 Tol. 10 -4 Tol. 10 -3 To develop and evaluate efficient algorithms for tolerance improvement of assembly parts through selective assembly 3 +10 -3 5x10 - 4

3. Arne Thesen and Akachai Jantayavichit Slide 3 Example: A SCROLL COMPRESSOR Needs close tolerances to maintain high pressure

4. Arne Thesen and Akachai Jantayavichit Slide 4 The compressor

5. Arne Thesen and Akachai Jantayavichit Slide 5 Example: An artificial heart valve Must avoid leakage

6. Arne Thesen and Akachai Jantayavichit Slide 6 Previous research focuses on batch process

7. Arne Thesen and Akachai Jantayavichit Slide 7 Previous work 1985 Boyer andA statistical selective assembly method Nasemetz(SSA) for a real time process 1990 MalmquistOMID heuristic: determine the batch size 1992PughSSA for a batch process 1993Robin and Multiple Regression modeling Mazharsolook 1996Zhang and Set theory and probability method Fang 1997 Coullard et al. Matching theory 1999 Chan and LinnBalanced probability and unequal tolerance zone 1999Thesen andEvaluate scroll compressor shells for Jantayavichit real time process

8. Arne Thesen and Akachai Jantayavichit Slide 8 Tolerance improvement Worst-case gap without selective assembly is  6  PIN BUSHING

9. Arne Thesen and Akachai Jantayavichit Slide 9 Tolerance improvement Classify components by size into tolerance classes Worst-case gap using 2 classes and matching identical classes is  3  –Resulting system is unstable PIN BUSHING

10. Arne Thesen and Akachai Jantayavichit Slide 10 Tolerance improvement Allow matching with component in neighbor class Worst case using 8 classes is 1.5  Resulting system is stable if most unlikely matches checked first

11. Arne Thesen and Akachai Jantayavichit Slide 11 Tolerance improvement Allowing matches with neighbor class  s 

12. Arne Thesen and Akachai Jantayavichit Slide 12 We focus on real-time applications in high- speed assembly systems (6 sec cycle times)

13. Arne Thesen and Akachai Jantayavichit Slide 13 A high-speed selective assembly station Note: This is presently a three-operator manual operation

14. Arne Thesen and Akachai Jantayavichit Slide 14 Establish required level of tolerance reduction From this set number of tolerance classes Establish algorithm for selecting components From neighborhood Decide how to deal with deadlock Discard Return Specify buffer capacity –More is better Designing a real-time assembly station

15. Arne Thesen and Akachai Jantayavichit Slide 15 Performance Analysis Performance measure: Yield Assuming that – All system states can be enumerated – Decisions in a given state are always made the same way Then we can compute steady state probability for – being in each state – making any state transition Decision rules for state space with 100,000 can be easily evaluated Simulation will be used for large models

16. Arne Thesen and Akachai Jantayavichit Slide 16 Unlimited buffer capacity, neighbor matches allowed Maximum population is unbounded when only matching components from identical classes.

17. Arne Thesen and Akachai Jantayavichit Slide 17 Limited buffer capacity Buffer Capacity = 48, Return upon deadlock

18. Arne Thesen and Akachai Jantayavichit Slide 18 Recommendations

19. Arne Thesen and Akachai Jantayavichit Slide 19 CONCLUSION Significant tolerance improvement is possible. Must use neighborhood matching rule. Results only valid for identical distributions. Extensions to unequal distributions under way.

20. Arne Thesen and Akachai Jantayavichit Slide 20 Any Questions ? Thank you Any Questions ?