Tolerance synthesis by neural learning and nonlinear programming

The tolerance design directly in#uences the functionality of products and related production costs. Tolerance synthesis is a procedure that distributes assembly tolerances between components or distributes "nal part design tolerances between related tolerances. In order to make a reliable trade-o! between design tolerances and costs, it is necessary to obtain the cost}tolerance relationships. Various operations such as turning, milling, drilling, grinding, casting, etc., have di!erent cost}tolerance relationships. Previous studies have usually established cost}tolerance functions for various manufacturing operations by regression analysis using the empirical data. Using traditional methods of regression analysis, people must make assumptions about the form of the regression equation or its parameters, which may not be valid. The neural network recently has been reported to be an e!ective statistical tool for determining the relationships between input factors and output responses. This study deals with the optimal tolerance design for an assembly simultaneously considering manufacturing cost and quality loss. In this paper, a backpropagation (BP) network is applied to "t the cost}tolerance relationship. Once the cost}tolerance functions have been generated, mathematical models for tolerance synthesis can be built. By solving the formulated mathematical models, the optimal tolerance allocation can be generated. An optimization method based on simulated annealing (SA) is then used to locate the combination of controllable factors (tolerances) to optimize the output response (manufacturing cost plus quality loss) using the equations stemming from the trained network. A tolerance synthesis problem for a motor assembly is used to investigate the e!ectiveness and e$ciency of the proposed methodology. ( 2001 Elsevier Science B.V. All rights reserved.