a new approach to tolerance improvement through real-time selective assembly
DESCRIPTION
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. [email protected]. Research Objective. - PowerPoint PPT PresentationTRANSCRIPT
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 EngineeringUniversity of Wisconsin-Madison
1513 University Ave, Madison, WI 53706, U.S.A.
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 3 +10-3
5x10- 4
Arne Thesen and Akachai Jantayavichit Slide 3
Previous research focuses on batch process
Arne Thesen and Akachai Jantayavichit Slide 4
Example: An artificial heart valveMust avoid leakage
Arne Thesen and Akachai Jantayavichit Slide 5
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 Slide 6
The production system
Arne Thesen and Akachai Jantayavichit Slide 7
We focus on real-time applications in high-speed assembly systems (6 sec cycle times)
Arne Thesen and Akachai Jantayavichit Slide 8
The compressor
Arne Thesen and Akachai Jantayavichit Slide 9
Example: A SCROLL COMPRESSORNeeds close tolerances to maintain high pressure
Arne Thesen and Akachai Jantayavichit Slide 10
A high-speed selective assembly stationNote: This is presently a three-operator manual operation
Robot
Rejects
FIFO Input buffersMeasuring
stationRandom accessassembly buffe r
Tops
Bottoms
Arne Thesen and Akachai Jantayavichit Slide 11
Tolerance improvement
-3 -2.3 -1.5 -0.8 0 0.75 1.5 2.25 3 -3 -2.25 -1.5 -0.75 0 0.75 1.5 2.25 3
• Worst-case gap without selective assembly is 6
PIN BUSHING
Arne Thesen and Akachai Jantayavichit Slide 12
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
Arne Thesen and Akachai Jantayavichit Slide 13
Tolerance improvement withdirect matching
s
Tolerance classes
Class coverage
Largest gap
Relative size of gap
Tolerance improvement
1 6 6 100.00 % 0 2 3 3 50.00 % ½ 4 1.5 1.5 25.00 % 1/4 8 0.75 0.75 12.50 % 1/8
16 0.38 0.38 6.25 % 1/16 32 0.19 0.19 3.62% 1/32
Arne Thesen and Akachai Jantayavichit Slide 14
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
0 20 40 60 80 100
Buffer capacity
Per
cent
Tolerance improvement Direct matching
Buffer utilization
Yield
8 tolerance classes
Arne Thesen and Akachai Jantayavichit Slide 15
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 Slide 16
Tolerance improvement with neighbor search
• Allow matching with component in neighbor class• Worst case using 8 classes is 1.5
Arne Thesen and Akachai Jantayavichit Slide 17
Tolerance improvement Allowing matches with neighbor class
s
Tolerance classes
Class coverage
Largest gap
Relative size of gap
Tolerance improvement
1 6 2 3 6 100.00 % 0 4 1.5 3 50.00 % ½ 8 0.75 1.5 25.00 % 1/4
16 0.38 0.75 12.50 % 1/8 32 0.19 0.38 6.25 % 1/16
Arne Thesen and Akachai Jantayavichit Slide 18
Neighbor search Matching strategies
• Random• Direct match first• Least likely first• Most likely first
Arne Thesen and Akachai Jantayavichit Slide 19
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 Slide 20
Neighbor search: Yield
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10 20 30 40 50
Buffer Capacity
Yie
ld (
%)
Least Likely
Random
Reverse
DirectFirst
Arne Thesen and Akachai Jantayavichit Slide 21
Neighbor search: Buffer utilization
0
10
20
30
40
50
0 5 10 15 20 25 30 35 40 45 50
Buffer Capacity
Avg
bu
ffe
r p
op
ula
tio
n
Least Likely
Random
Reverse
DirectFirst
Arne Thesen and Akachai Jantayavichit Slide 22
Neighbor search, least likely first Buffer Capacity = 48, Discard upon deadlock
0
10
20
30
40
50
60
70
10 15 20 25 30 35 40 45 50
Tolerance classes
Av
era
ge
Bu
ffe
r P
op
ula
tio
n
Discard rate Average populationunlimited capacity
Averagepopulation
0.03
0.04
0.05
0.02
0.01
0.06
Ret
urn
Rat
e
Arne Thesen and Akachai Jantayavichit Slide 23
Establish required level of tolerance reduction
From this set number of tolerance classes
Establish algorithm for selecting componentsNeighborhood
Decide how to deal with deadlock Discard
Return
Specify buffer capacity
Designing a real-time assembly station
Arne Thesen and Akachai Jantayavichit Slide 24
RecommendationsUse neighbor search with most unlikely first
Tolerance improve-
ment
Buffer capacity
Expected population
Discard rate (%)
Return rate (%)
1/4 12 3.1 0.01 0.4
1/8 28 12.5 0.29 0.6
1/12 48 24.3 0.16 0.8
1/16 60 36.3 0.29 0.8
1/20 72 45.0 0.29 1.0
Arne Thesen and Akachai Jantayavichit Slide 25
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 Slide 26
Thank you
Any Questions ?Any Questions ?