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Closed-form solutions for multi-objective tolerance optimization
- Source :
- The International Journal of Advanced Manufacturing Technology. 70:1859-1866
- Publication Year :
- 2013
- Publisher :
- Springer Science and Business Media LLC, 2013.
-
Abstract
- Component tolerances have important influence on the cost and performance of products. In order to obtain suitable component tolerances, multi-objective tolerance optimization model is studied, in which the combined polynomial and exponential functions are used to model manufacturing cost. In this paper, analytical methods are proposed to solve the multi-objective optimization model. In this model, the objective function is not a monotone function, and it is possible that the assembly tolerance constraint, including worst-case method and root sum square method, is inactive. Therefore, two closed-form solutions are proposed for each component tolerance in terms of the Lambert W function. When the assembly tolerance constraint is not considered, the component tolerances are obtained and named as the initial closed-form solutions. If the initial solutions satisfy assembly tolerance constraint, it is the final value of optimal tolerances. Otherwise, constrained optimization model is established and Lagrange multiplier method is applied to obtain the new closed-form solution of component tolerances as the final value of optimal tolerances. Several simulation examples are used to demonstrate the proposed method.
- Subjects :
- Mathematical optimization
Polynomial
Mechanical Engineering
Constrained optimization
Multi-objective optimization
Industrial and Manufacturing Engineering
Manufacturing cost
Computer Science Applications
symbols.namesake
Control and Systems Engineering
Component (UML)
Lambert W function
Lagrange multiplier
symbols
Closed-form expression
Software
Mathematics
Subjects
Details
- ISSN :
- 14333015 and 02683768
- Volume :
- 70
- Database :
- OpenAIRE
- Journal :
- The International Journal of Advanced Manufacturing Technology
- Accession number :
- edsair.doi...........e7e75af8f5d80595be005ed23e0df6ae