A deterministic method of robust design (previously described and summarized here) has been applied to the problem of determining optimum nominal dimensions of manufactured components which are subject to dimensional tolerances. The optimum sought is that for which an assembly of the components shows least variability, as measured by one or more relevant parameters (e.g. a clearance) for a fixed set of tolerances. The aim of the method is demonstrated by an example of a multiparameter assembly problem. The method provides a potential means of improving assembly quality without tightening tolerances, when nominal dimensions can be adjusted subject to other requirements of the design. [S1050-0472(00)00802-3]
Issue Section:
Technical Papers
1.
Gladman, C. A., 1959, “Techniques for Applying Probability to the Tolerancing of Machined Dimensions,” CSIRO, Australian National Standards Laboratory, Technical Paper II, pp. 1–5.
2.
Mansoor
, E. M.
, 1963
, “The Application of Probability to Tolerances Used in Engineering Design
,” Proc. Inst. Mech. Eng.
178
, No. 1
, pp. 29
–51
.3.
Pheil
, G. D.
, 1957
, “Probability Applied to Assembly Fits
,” Prod. Eng.
, 28
, No. 21
, p. 88
88
.4.
Parkinson
, D. B.
, 1982
, “The Application of Reliability Methods to Tolerancing
,” ASME J. Mech. Des.
, 104
, pp. 612
–618
.5.
Parkinson
, D. B.
, 1984
, “Tolerancing of Component Dimensions in CAD
,” Computer-Aided Des.
, 16
, No. 1
, pp. 25
–32
.6.
Parkinson
, D. B.
, 1985
, “Assessment and Optimization of Dimensional Tolerances
,” Computer-Aided Des.
, 17
, No. 4
, pp. 191
–199
.7.
Parkinson
, D. B.
, 1987
, “Control and Optimization of Variability
,” Reliab. Eng.
, 19
, pp. 211
–236
.8.
Parkinson
, D. B.
, 1993
, “Quality Based Design by Probability Optimization
,” Quality Reliab. Eng. Int.
, 9
, pp. 29
–37
.9.
Requicha
, A.
, 1983
, “Towards a Theory of Geometric Tolerancing
,” Int J. Robo. Res.
, 2
, No. 4
, pp 45
–60
.10.
Srinivasan, R., and Word, K., 1992, “A Computational Investigation Into Structure of Form and Size Errors Based on Machining Mechanics,” Proc. Advances in Design Automation Conf., Scottsdale, AZ, pp. 161–171.
11.
Smith, B., 1993, “Six Sigma Design,” IEEE Spect., pp. 43–47.
12.
Vasseur
, H.
, Kurfess
, T. R.
, and Cagan
, J.
, 1997
, “Use of a Quality Loss Function to Select Statistical Tolerances
,” ASME J. Manuf. Sci. Eng.
, 119
, pp. 410
–416
.13.
Bjorke, O., Computer-Aided Tolerancing 1989, 2nd ed., ASME, NY.
14.
Cagan, J., and Kurfess, T. R., 1992, “Optimal Tolerance Allocation Over Multiple Manufacturing Alternatives,” Proc. Advances in Design Automation Conf., Phoenix, AZ, pp. 165–172.
15.
Nigan
, S. D.
, and Turner
, J. U.
, 1995
, “Review of Statistical Approaches to Tolerance Analysis
,” Computer-Aided Des.
, 27
, No. 1
, pp. 6
–15
.16.
D’Errico
, J. R.
, and Zaino
, N. A.
, 1988
, “Statistical Tolerancing Using a Modification of Taguchi’s Method
,” Technometrics
, 30
, No. 4
, pp. 397
–405
.17.
Jeang
, A.
, 1997
, “An Approach of Tolerance Design for Quality Improvement and Cost Reduction
,” Int. J. Prod. Res.
, 35
, No. 5
, pp. 1193
–1211
.18.
Chen
, M.-S.
, 1995
, “Optimizing Tolerance Allocation for a Mechanical Assembly, With Non-linear Multiple Constraints
,” J. Chinese Soc. of Mech. Eng.
, 16
, No. 4
, pp. 349
–361
.19.
Gadallah, M. H., and El Maraghy, H. A., 1994, “The Tolerance Optimization Problem, Using a System of Experimental Design,” ASME, DE-Vol 69- Advances in Design Automation –1994. 1, pp. 251–265.
20.
Lee
, J.
, and Johnson
, G. E.
, 1993
, “Optimal Tolerance Allotment Using a Genetic Algorithm and Truncated Monte-Carlo Simulation
,” Computer-Aided Des.
, 25
, No. 9
, pp. 601
–611
.21.
Skowronski
, J.
, and Turner
, J. U.
, 1997
, “Using Monte-Carlo Variance Reduction in Statistical Tolerance Synthesis
,” Computer-Aided Des.
, 29
, No. 1
, pp. 63
–69
.22.
Otto
, K. N.
, and Antonsson
, E. K.
, 1993
, “Extensions to the Taguchi Method of Product Design
,” ASME J. Mech. Des.
, 115
, pp. 5
–13
.23.
Belegundu
, A. D.
, and Zhang
, S.
, 1992
, “Robustness of Design Through Minimum Sensitivity
,” ASME J. Mech. Des.
, 114
, pp. 213
–217
.24.
Iyer
, R. K.
, and Downs
, T.
, 1980
, “A Variance Minimization Approach to Tolerance Design
,” IEEE. Trans. Circuits Syst.
, 27
, pp. 737
–747
.25.
Shenoi
, B. A.
, 1974
, “Optimum Variability Design and Comparative Evaluation of Thin Film RC Active Filters
,” IEEE Trans. Circuits. Syst.
, 211
, pp. 263
–267
.26.
Ilumoka, A., Spence, R., and Soin, R. S., 1980, “The Tolerance Design of Circuits by Statistical Exploration,” Proc. 1980 IEEE ISCAS, Houston, pp. 882–885.
27.
Ilumoka
, A.
, and Spence
, R.
, 1988
, “Parametric Tolerance Design for Electrical Circuits
,” Quality Reliab. Eng. Int.
, 4
, pp. 87
–94
.28.
Parkinson
, D. B.
, 1997
, “Robust Design by Variability Optimization
,” Quality Reliab. Eng. Int.
, 13
, pp. 97
–102
.29.
Logothetis
, N.
, and Haigh
, A.
, 1988
, “Characterising and Optimizing Multi-response Processes by the Taguchi Method
,” Quality Reliab. Eng. Int.
, 4
, pp. 159
–169
.30.
Parkinson
, D. B.
, 1998
, “Simulated Variance Optimization for Robust Design
,” Quality Reliab. Eng. Int.
, 14
, pp. 15
–21
.31.
Greig, D. M., 1980, Optimization, Longman, pp. 63–64.
32.
Bertsekas, D. P., 1982, Constrained Optimization and Lagrange Multiplier Methods, Academic, pp. 104–165.
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