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Tolerance analysis and yield estimation using Monte Carlo simulation – case study on linear and nonlinear mechanical systems

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Abstract

Dimensions of individual components give rise to a critical dimension in an assembly, called the assembly dimension(s) or the assembly response(s). This concept is applicable to any engineering system. Thus, a variation in the individual dimension/characteristics directly affects the assembly response or the performance of the system. The random assembly of the individual dimensions gives rise to a statistical distribution of assembly response. Tolerance analysis is the estimation of resultant variation of the assembly response, for a given set of tolerances associated with individual dimensions, and the functional relationship between the individual dimensions and the assembly response. Several methods for tolerance analysis have been reported over the decades. The Monte Carlo simulation still remains the benchmark approach for testing of the precision obtained by any other method. This paper presents two case studies to explore the insight of the methodology for tolerance analysis. The first case study is on a linear assembly while the second one is the nonlinear assembly. Three sub-studies considering (a) uniform distribution, (b) normal distribution, and (c) beta distribution, of individual dimensions have been attempted in each of the two cases. Further, in each sub-study, the tolerance analysis and the yield estimation has been carried out for the worst-case criteria, followed by analysis of the estimated yield due to reduction of assembly tolerance. The results have been presented in the form of histograms for all 2 × 3 × 3 cases.

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Acknowledgments

Authors are highly grateful to the anonymous reviewer for pointing out important issues to be addressed for improvement of the manuscript.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Sant Longowal Institute of Engineering and Technology, Longowal, 148 106, India

    Pradeep K Singh & Vaibhav Gulati

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  1. Pradeep K Singh
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  2. Vaibhav Gulati
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Correspondence to Pradeep K Singh.

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Singh, P.K., Gulati, V. Tolerance analysis and yield estimation using Monte Carlo simulation – case study on linear and nonlinear mechanical systems. Sādhanā 46, 34 (2021). https://doi.org/10.1007/s12046-020-01545-5

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  • DOI: https://doi.org/10.1007/s12046-020-01545-5

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