Optimal tolerance allocation using a multiobjective particle swarm optimizer

Particle swarm optimizers are routinely utilized in engineering design problems, but much work remains to take advantage of their full potential in the combined areas of sensitivity analysis and tolerance synthesis. In this paper, a novel Pareto-based multiobjective formulation is proposed to enhance the operations of a particle swarm optimizer and systematically distribute tolerances among various components of a mechanical assembly. The enhanced algorithm relies on nonlinear sensitivity analysis and the statistical root sum squares model to simultaneously optimize product performance criteria, the manufacturing cost, and the stack-up tolerance. It is shown that the proposed algorithm can accomplish its optimization task by successfully shifting nominal values of design parameters instead of the expensive tightening of component tolerances. Several numerical experiments for optimal design of a stepped bar assembly were conducted, which highlight the advantages of the proposed methodology.