Optimal Statistical Tolerance Allocation of Assemblies for Minimum Manufacturing Cost

Kuo Ming Cheng; Jhy Cherng Tsai

doi:10.4028/www.scientific.net/AMM.52-54.1818

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 52-54Optimal Statistical Tolerance Allocation of...

Optimal Statistical Tolerance Allocation of Assemblies for Minimum Manufacturing Cost

Abstract:

This paper explores a systematic method for optimal statistical tolerance allocation using the Lagrange multiplier method for minimizing manufacturing cost subject to constraints on dimensional chains and machining capabilities. The reciprocal power and exponential cost-tolerance models for statistical tolerancing are investigated for employing this method. The optimization problem is solved by applying the algorithmic approach. Especially, we further derive a closed-form expression of the tolerance optimization problem for reciprocal exponential cost-tolerance model by introducing the Lambert W function. For constrained minimization problems with only equality constraints, the optimum tolerance allocation can be obtained by solving simultaneous equations without further differentiating. An example is illustrated to demonstrate this approach. The result also shows that tolerances can be allocated quickly, economically and accurately using this method.

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Periodical:

Applied Mechanics and Materials (Volumes 52-54)

Pages:

1818-1823

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.52-54.1818

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Cite this paper

Online since:

March 2011

Authors:

Kuo Ming Cheng, Jhy Cherng Tsai

Keywords:

Cost-Tolerance Function, Lagrange Multipliers, Optimal Tolerance Allocation, Statistical Tolerancing

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