Robust Optimization And Tolerance Analysis Of Autobody Panel Stamping

In practical forming process, the fluctuations of material properties of sheet metal and processing parameters are the key aspects which result in the scrap rate of auto-body panel staying at a high level. In recent years, CAE-based robust optimization and tolerance analysis have been received increasing attention. However, the traditional method of coupling of iteration optimization and random simulation requires a great many numerical simulations, so it is difficult to apply in industry. Although many domestic and foreign researchers have presented some surrogate models and non-random simulation methods to reduce the computational cost, the number of numerical simulation increases rapidly in the case of multiple design variables and design parameters. Therefore, actual methods of robust optimization and tolerance analysis are limited to solve simple models. Funded by National Natural Science Foundation of China through grant #50475020, and co-funded by the High-Technology Research & Development Program of the Ministry of Science & Technology of China through grant #2007AA04Z130, the research work established efficient robust optimization and tolerance analysis models, which were successfully applied in complex auto-body panel stamping process. The main research content is as follows:(1) Reduced collocation response surface model (RCRSM) is constructed using polynomial chaos expansion (PCE) with points of monomial cubature rule (MCR). Weighted residual method is used to establish integration for the orthogonal form of the residual and the base function of RCRSM, and the corresponding collocation method is given. Since that the number of Gauss quadrature points is exponential growth of the number of model's dimension, MCR is used to replace Gauss quadrature in solving the integration for reducing the number of collocation points and improving the efficiency of the construction of RCRSM. When the number of input variables increases, MCR requires points far less than those of Gauss quadrature according to the same degree and meets the precision demanded for practical engineering. This theory plays a key role in the research work.(2) It is important for robust optimization to utilize the interactions between design variables and design parameters and the nonlinear effect of response to design variables. In order to deal with problems with regard to robust optimization, RCRSM is built over both design variables and design parameters and their interactions. This procedure has advantages over dual response surface method, which only considers the first-order interactions between design variables and design parameters and assumes that the responses follow normal distributions. Furthermore, the procedure allows design variables fluctuate around their means, so the application is extensive.(3) In order to avoid the adverse effect of exceptional responses, a robust regression method which allows for outliers in sample points is presented to construct RCRSM. When the range of input variable is large, exceptional response may be occurring in the simulation of a complex stamping process due to numerical instable. Therefore, the adverse effect of exceptional responses should be considered when robust optimization and tolerance analysis models are constructed. The approach is applied successfully to tolerance analysis of the scrap rate of the stamping part of a car deck-lid outer panel.(4) For strongly nonlinear problems, the ranges of design variables are cut step by step during the optimization process to improve the fitting precision of PCE and the adaptation of RCRSM. It is shown that the procedure is able to find optimum values of design variables in wide range. The method is applied to the robust optimization of a car deck-lid outer panel to demonstrate the availability.(5) Experiments of a cylindrical cup drawing and material tensile are performed to measure probability density functions of the sheet metal material properties, friction coefficient, blank holder force and forming quality. Robust optimization and tolerance analysis are performed and their validity is proved.