Particle Swarm Optimization for Simultaneous Optimization of Design and Machining Tolerances

Tolerance assignment in product design and process planning (machining) affects both the quality and the cost of the overall product cycle. It is a crucial issue to determine how much the tolerance should be relaxed during the assignment process, since a tight tolerance implies a high manufacturing cost and a loose tolerance results in low manufacturing cost. Hence, during tolerance assignment, a balance between a reduction in quality loss and a reduction in manufacturing cost must be considered. Traditionally, in the two stages (product design and process planning) tolerances (Ngoi & Teck, 1997) are often conducted separately. This is probably due to the fact that they deal with different type of tolerances. Product design is concerned with related component tolerances, whereas process designing focus on the process tolerance according to the process specification. However, this separated approach in tolerance design always suffers from several drawbacks. First of all, it is difficult to obtain optimal design tolerance because the designer can not determine the exact manufacturing cost without the specified manufacturing information. Therefore, the manufacturing engineer must frequently communicate with the designer to adjust the design tolerances and obtain the appropriate process planning. However, this task is timeconsuming and painstaking. In addition, design tolerances are further distributed for machining tolerances. Nevertheless, the machining tolerances commonly can not occupy the design tolerances space. Thus the final tolerance distribution is suboptimal and accordingly, the actual cost will be inevitably higher than the desired cost. Moreover, due to the specified procedure, the manufacturing engineer is not informed the design details and does not have the overview of the whole product. To overcome the above drawbacks, we need to develop a simultaneous tolerance design. Zhang (Zhang, 1996) presented the concept of simultaneous tolerance, proposed a general mathematical model for tolerance optimization in concurrent engineering context, and then introduced a new concept of interim tolerances that help determine appropriate manufacturing processes. Singh (Singh et al., 2003) utilized genetic algorithms and penalty function approach to solve the problem of simultaneous selection of design and manufacturing tolerances based on the minimization of the total manufacturing cost. Gao and Huang (Gao & Huang, 2003) utilized a nonlinear programming model for optimal