Tolerance allocation: A reliability based optimisation approach

Abstract

Tolerance analysis and allocation are two activities of great importance in product development. The mathematical formulation of the latter concerns the establishment and solution of a constraint optimisation problem. In this work, making one step forward, a probabilistic framework is developed and the tolerance synthesis problem is reformulated to a reliability based optimisation one introducing probabilistic constraints. Advanced reliability methods are merged with professional computer aided tolerance tools to estimate the distribution of the assembly key characteristic. Cost-tolerance relationships based on the variability of the manufacturing resources rather than on empirical formulas were adopted in a process based cost modelling methodology. The suggested framework is compared to the classical tolerance allocation approaches of the worst case scenario and the root sum square. It was found that despite the increased computational cost, further relaxation in the design tolerance can be achieved using reliability based optimisation techniques driving down the product cost.