Tolerance control and propagation for the product assembly modeller

Abstract

With the increasing use of computer-aided design (CAD) packages and modellers in engineering have come reduced product lead times and the incorporation of design for manufacturing (DFM) principles leading to concurrent engineering. Until recently, however, most CAD packages have been mainly concerned with accurate design representations in terms of nominal specifications, and the representation of tolerances on these systems in a manner that could be interpreted and used constructively in DFM and other manufacturability analyses have been ignored. This research develops a Tolerance Control and Propagation (TCP) engine for PAM, a product assembly modeller developed by the Automation and Robotics Laboratory. Tolerance control ensures that given individual dimensions, their tolerances and distributions, the designer specified functional dimension tolerance can be met with a specified level of confidence. Tolerance control is performed using Monte-Carlo simulation and the assumption of a beta distributed sum dimension. Although the Monte-Carlo simulation has been previously used for the solution of this problem, the assumption has been that the individual dimensions and their tolerances have been normally distributed. Our approach differs in that various distributions can be selected for each of the dimensions contributing to the sum dimension, thus giving a more accurate result. Tolerance propagation is the opposite of tolerance control, and determines the tolerances to be assigned to those dimensions contributing to a functional or sum dimension such that production cost is minimized. The TCP applies a simulated annealing algorithm to the continuous tolerance optimization problem, using a reciprocal cost function. Simulating annealing algorithms are traditionally applied to discrete optimization problems. Although the solutions obtained are not necessarily the minimum cost solution, the algorithm ensures that all constraints are met and that given the right parameters, a near-optimal solution is found.