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Research Papers

Application of Quasi-Monte Carlo Method Based on Good Point Set in Tolerance Analysis

[+] Author and Article Information
Yanlong Cao

State Key Laboratory of Fluid Power
and Mechatronic Systems,
College of Mechanical Engineering,
Zhejiang University,
Zheda Road 38,
Hangzhou 310027, China;
Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
College of Mechanical Engineering,
Zhejiang University,
Zheda Road 38,
Hangzhou 310027, China
e-mail: sdcaoyl@zju.edu.cn

Huiwen Yan

Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
College of Mechanical Engineering,
Zhejiang University,
Zheda Road 38,
Hangzhou 310027, China
e-mail: 969848190@qq.com

Ting Liu

Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
College of Mechanical Engineering,
Zhejiang University,
Zheda Road 38,
Hangzhou 310027, China
e-mail: 1197857467@qq.com

Jiangxin Yang

Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
College of Mechanical Engineering,
Zhejiang University,
Zheda Road 38,
Hangzhou 310027, China
e-mail: yangjx@zju.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received April 23, 2015; final manuscript received February 16, 2016; published online May 10, 2016. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 16(2), 021008 (May 10, 2016) (7 pages) Paper No: JCISE-15-1147; doi: 10.1115/1.4032909 History: Received April 23, 2015; Revised February 16, 2016

Tolerance analysis is increasingly becoming an important tool for mechanical design, process planning, manufacturing, and inspection. It provides a quantitative analysis tool for evaluating the effects of manufacturing variations on performance and overall cost of the final assembly. It boosts concurrent engineering by bringing engineering design requirements and manufacturing capabilities together in a common model. It can be either worst-case or statistical. It may involve linear or nonlinear behavior. Monte Carlo simulation is the simplest and the most popular method for nonlinear statistical tolerance analysis. Monte Carlo simulation offers a powerful analytical method for predicting the effects of manufacturing variations on design performance and production cost. However, the main drawbacks of this method are that it is necessary to generate very large samples to assure calculation accuracy, and that the results of analysis contain errors of probability. In this paper, a quasi-Monte Carlo method based on good point (GP) set is proposed. The difference between the method proposed and Monte Carlo simulation lies in that the quasi-random numbers generated by Monte Carlo simulation method are replaced by ones generated by the method proposed in this paper. Compared with Monte Carlo simulation method, the proposed method provides analysis results with less calculation amount and higher precision.

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References

Figures

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Fig. 1

Three sets of two-dimensional points for size 1597: (a) random numbers, (b) GP set, and (c) GLP set

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Fig. 2

Flow chart of GP method and GLP method

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Fig. 3

The relationships between the means and sample size obtained by different methods: (a) Y1, (b) Y2, (c) Y3, (d) Y4, (e) Y5, and (f) Y6

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Fig. 4

The relationships between the standard deviations and sample size obtained by different methods: (a) Y1, (b) Y2, (c) Y3, (d) Y4, (e) Y5, and (f) Y6

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Fig. 5

An example assembly applied to the case study

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Fig. 6

The relationships between mean and standard deviation of function requirement g and sample size n : (a) mean of g versus sample size n and (b) standard deviation of g versus sample size n

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