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 Arne Thesen and Akachai Jantayavichit

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

Previous research focuses on batch process Arne Thesen and Akachai Jantayavichit

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

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

Arne Thesen and Akachai Jantayavichit The production system Arne Thesen and Akachai Jantayavichit

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

Arne Thesen and Akachai Jantayavichit The compressor Arne Thesen and Akachai Jantayavichit

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

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

Tolerance improvement Worst-case gap without selective assembly is 6s PIN BUSHING Arne Thesen and Akachai Jantayavichit

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

Tolerance improvement with direct matching s s s Arne Thesen and Akachai Jantayavichit

Tolerance improvement Direct matching Buffer utilization Yield 8 tolerance classes Arne Thesen and Akachai Jantayavichit

Tolerance improvement Direct matching For reject rates less than 1% Very large buffer capacities needed Very high buffer utilizations expected Arne Thesen and Akachai Jantayavichit

Tolerance improvement with neighbor search Allow matching with component in neighbor class Worst case using 8 classes is 1.5s Arne Thesen and Akachai Jantayavichit

Tolerance improvement Allowing matches with neighbor class Arne Thesen and Akachai Jantayavichit

Neighbor search Matching strategies Random Direct match first Least likely first Most likely first Arne Thesen and Akachai Jantayavichit

Arne Thesen and Akachai Jantayavichit 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 Arne Thesen and Akachai Jantayavichit

Neighbor search: Yield Arne Thesen and Akachai Jantayavichit

Neighbor search: Buffer utilization Arne Thesen and Akachai Jantayavichit

Arne Thesen and Akachai Jantayavichit Neighbor search, least likely first Buffer Capacity = 48, Discard upon deadlock Arne Thesen and Akachai Jantayavichit

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

Recommendations Use neighbor search with most unlikely first Arne Thesen and Akachai Jantayavichit

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

Thank you Any Questions ? Arne Thesen and Akachai Jantayavichit