Accounting uncertainties in the optimal design of multi-stage hot forging

Abstract

Today, most of product designs employ sophisticated computer models and finite element analysis in their design. Most of these models are based on physical models without taking into account the uncertainties that occur during manufacturing. Forging is an industrial process extensively used in metal forming. Process uncertainties can cause defective parts and so incorporating uncertainty analysis on an optimization model will diminish rejected parts. On one hand a very narrow tolerance on the process parameters would increase productions costs and on the other hand large tolerances would induce a high percentage of part rejection. Thus, controlling the tolerance limits on the process parameters would lead to an improvement on the product quality and to a reduction of the production costs of hot forged parts. Using a finite element thermal mechanical analysis coupled with a genetic algorithm an optimisation method has been developed for shape design of multi-stage forging processes. The design objective is to optimise the pre-form die shape and the initial temperature of the billet in order to make the achieved final forging product to approach the desired one as much as possible. The computational efficiency of the method simulating two-stage hot forging processes has been demonstrated earlier. The main purposes of this work are to identify, quantify and control uncertainties during the forming process based on a reasonable number of data sets acquired with a finite element analysis computer model. Initial temperature of the billet, friction between dies and billet and variations in the forging set up together with cooling rate are the main factors affecting the final part dimensions. Considering temperatures and friction to be random variables, an attempt is made to fit a reasonable probability distribution to the different data sets. The analysis of the parameters uncertainties on the optimal pre-form die shape will drive to the robust design of the forging parameters.