Non-ideal surface modelling approach for enabling uncertainty representation

Abstract

Non-ideal models have gained considerable attention in the design stage for evaluating product functionality and performance considering the realistic conditions of the product surface. The performance evaluation generally involves deriving the statistical distributions of certain key characteristics, such as gaps and distances, based on numerous assembly process simulations, thus necessitating a large number of samples of non-ideal surfaces. The traditional practice for generating such samples is to model the systematic and random deviations of each point on the part surface. It is difficult, however, to represent the randomness of the real surface formation mechanism using this point-wise approach, thus leading to significant computational cost. As a result, this technique hinders the wider adoption of specified surface randomness representations in performance simulation and analysis.The deviation modes that feature non-ideal surfaces are dominated by manufacturing error factors, which could be systematically represented by corresponding mode functions. Furthermore, the variations in the manufacturing process inevitably cause randomness in surface deviations. In this paper, this randomness is defined as the uncertainty of non-ideal surfaces and reflected by the randomness of deviation mode function coefficients. A conceptual non-ideal surface error model that characterises the uncertainty of non-ideal surfaces through the random distributions of mode function coefficients as represented in phase space is therefore proposed. The phase space is a multi-dimensional space, in which each point denotes a group of mode function coefficients that determines a certain non-ideal surface sample. Following the distribution law of coefficients, a number of non-ideal surface samples can be generated by phase space sampling. This method reduces the problem from modelling an infinite number of surface points to modelling a finite coefficient dimension of points in the compact phase space. It thus enables the efficient modelling of non-ideal surfaces that reflect realistic errors resulting from the manufacturing process and facilitates the product performance analysis under the effect of surface randomness. To verify the method, a case study involving a tapered surface manufactured by the taper-turning process is presented. The phase space and error model are discussed with respect to typical manufacturing error factors in this process.