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Tolerance optimization of a lower arm by using genetic algorithm and process capability index

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Abstract

Tolerance optimization that considers variances of design variables should be performed before beginning the manufacturing process from a cost-effective perspective in the design process. The authors used a genetic algorithm and the process capability index (Cpk) to solve the robust objectives and probability constraints and to formulate a constrained optimization problem into an unconstrained one. The design space provided by the Cpk-values of weight and stress on the lower arm of a vehicle’s suspension was explored by using the central composite design method and the 2nd order Taylor series expansion. The optimal solutions were found via the genetic algorithm, in which the Cpk-values took into account the variances occurring in a design variable’s tolerances. The mean and standard deviation of Mass and Smax were predicted by using the 2nd order Taylor series expansion and the 2nd order polynomial response surface models generated from the central composite design method. The Cpk of Mass and Smax were calculated, where the Pareto set was generated by maximizing the Cpk-values via the MOGA (Multi-Objective Genetic Algorithm). From the Pareto set, optimal alternatives were selected and verified by simulated results from FE (Finite Element) analysis and Monte-Carlo simulation.

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Abbreviations

C pk :

process capability index

DV_SD :

objective function

LSL :

lower specification limit

USL :

upper specification limit

R Square :

coefficient of determination

R SquareAdj :

adjusted coefficient of determination

g(x) :

constraints

x(x) :

design variables

y(x) :

objective functions(responses)

µ(x) :

mean value of design variables

σ(x) :

standard deviation value of design variables

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Authors and Affiliations

  1. Consulting Team, VP Korea, 3F Core B/D 8-1, Sunae-dong, Bundang-gu, Gyeonggi-do, South Korea, 463-825

    Kwang-Ki Lee

  2. Dept. of Mechanical Engineering, Dong-A University, 37 Nakdong-daero 550 beon-gil saha-gu, Busan, South Korea, 604-714

    Yun-Cheol Ro & Seung-Ho Han

Authors
  1. Kwang-Ki Lee
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  2. Yun-Cheol Ro
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  3. Seung-Ho Han
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Correspondence to Seung-Ho Han.

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Lee, KK., Ro, YC. & Han, SH. Tolerance optimization of a lower arm by using genetic algorithm and process capability index. Int. J. Precis. Eng. Manuf. 15, 1001–1007 (2014). https://doi.org/10.1007/s12541-014-0428-4

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  • DOI: https://doi.org/10.1007/s12541-014-0428-4

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