汽车覆盖件成形工艺的稳健优化与容差分析
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摘要
在实际生产中,板料性能和工艺参数的波动是汽车覆盖件废品率居高不下的关键因素。近年来,基于数值模拟的稳健优化与容差分析逐渐得到重视,然而稳健优化过程中随机模拟与反复迭代优化相结合的传统方法需要大量的数值模拟,还难以应用。虽然许多国内外学者已提出一些响应面模型与非随机模拟方法以降低模拟次数,但是当设计变量和参数个数增多时模拟次数激增,导致稳健优化与容差分析仍然局限于分析和优化简单零件。本文在国家自然科学基金项目(编号:50475020)和科技部863项目(编号:2007AA04Z130)的资助下,研究和建立了高效的稳健优化与容差分析模型,并成功应用于复杂汽车覆盖件成形工艺的优化。主要研究内容如下:
(1)基于单项式容积法和混沌多项式展开,构造了简约配点响应面模型。采用加权余量法建立响应面模型残差与基函数正交的积分形式,并给出与积分形式等价的配点法。针对高斯积分点个数随变量维数增加而呈幂次递增的特性,采用单项式容积法代替高斯积分法,减少并合理配置了配点个数,提高了响应曲面模型的建模效率。研究结果表明,当变量维数增加时同等阶次的单项式容积法积分点个数远远少于高斯积分点个数,而且计算精度满足工程要求。该方法是本文的核心理论,在此基础上针对汽车覆盖件成形工艺的特点建立了稳健优化与容差分析模型。
(2)稳健优化的关键是利用设计变量与设计参数的相互作用以及设计变量与响应量之间的非线性效应。为了应用简约配点响应面模型求解稳健优化问题,提出在简约配点响应面模型中同时包含设计变量和设计参数以及它们之间的交叉项。研究结果表明,该方法可以避免双响应面法只考虑设计变量与设计参数之间的一阶交互作用以及假设响应量为正态分布的局限。此外,该方法还允许设计变量围绕均值波动,具有更广的应用范围。
(3)当输入参数波动比较大时,复杂汽车覆盖件成形的数值模拟可能产生数值不稳定,容易导致异常响应,所以在建立稳健优化和容差分析模型时需要考虑异常点的影响。为了降低和消除样本点的异常响应对响应面模型精度的影响,提出了一种构造简约配点响应面模型的稳健回归方法,从而允许在响应量中存在异常响应。将该方法应用于汽车行李箱外板成形工艺的容差分析,成功预测了冲压件拉裂的概率。
(4)针对设计变量与响应量呈强非线性关系的问题,建立了逐步缩小设计变量取值范围的优化搜索方法,提高了混沌多项式的拟合精度和简约配点响应面模型的自适应性。研究结果表明,该方法允许设计变量在大区间内寻求工艺参数的最优值。将该方法应用于汽车行李箱外板成形工艺的稳健优化,验证了其求解强非线性稳健优化问题的可行性。
(5)通过圆筒件拉深实验测量了压边力、摩擦系数、板料性能参数以及成形质量的概率分布,验证了基于简约配点响应面模型的稳健优化和容差分析的有效性。
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.
(1)基于单项式容积法和混沌多项式展开,构造了简约配点响应面模型。采用加权余量法建立响应面模型残差与基函数正交的积分形式,并给出与积分形式等价的配点法。针对高斯积分点个数随变量维数增加而呈幂次递增的特性,采用单项式容积法代替高斯积分法,减少并合理配置了配点个数,提高了响应曲面模型的建模效率。研究结果表明,当变量维数增加时同等阶次的单项式容积法积分点个数远远少于高斯积分点个数,而且计算精度满足工程要求。该方法是本文的核心理论,在此基础上针对汽车覆盖件成形工艺的特点建立了稳健优化与容差分析模型。
(2)稳健优化的关键是利用设计变量与设计参数的相互作用以及设计变量与响应量之间的非线性效应。为了应用简约配点响应面模型求解稳健优化问题,提出在简约配点响应面模型中同时包含设计变量和设计参数以及它们之间的交叉项。研究结果表明,该方法可以避免双响应面法只考虑设计变量与设计参数之间的一阶交互作用以及假设响应量为正态分布的局限。此外,该方法还允许设计变量围绕均值波动,具有更广的应用范围。
(3)当输入参数波动比较大时,复杂汽车覆盖件成形的数值模拟可能产生数值不稳定,容易导致异常响应,所以在建立稳健优化和容差分析模型时需要考虑异常点的影响。为了降低和消除样本点的异常响应对响应面模型精度的影响,提出了一种构造简约配点响应面模型的稳健回归方法,从而允许在响应量中存在异常响应。将该方法应用于汽车行李箱外板成形工艺的容差分析,成功预测了冲压件拉裂的概率。
(4)针对设计变量与响应量呈强非线性关系的问题,建立了逐步缩小设计变量取值范围的优化搜索方法,提高了混沌多项式的拟合精度和简约配点响应面模型的自适应性。研究结果表明,该方法允许设计变量在大区间内寻求工艺参数的最优值。将该方法应用于汽车行李箱外板成形工艺的稳健优化,验证了其求解强非线性稳健优化问题的可行性。
(5)通过圆筒件拉深实验测量了压边力、摩擦系数、板料性能参数以及成形质量的概率分布,验证了基于简约配点响应面模型的稳健优化和容差分析的有效性。
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.
引文
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[1] Belytschko T., Liu W. K., Moran B., Nonlinear finite elements for continua and structures, John Wiley & Sons Inc, 2000
[2] Rousseeuw P. J., Leroy A. M., Robust regression and outlier detection, Hoboken, NJ, Wiley-Interscience, 2003
[3] Box G. E. P., Non-normality and test on variances, Biometrika, 1953, 40: 318-335
[4] Myers R. H., Montgomery D. C., Response surface methodology: process and product optimization using designed experiments, J. Wiley, New York, 2002
[5] Rousseeuw P. J., Wagner J., Robust regression with a distributed intercept using least median of squares, Computational Statistics & Data Analysis, 1994, 17 (1): 65
[6] Rousseeuw P. J., Katrien V. D., Computing LTS regression for large data sets, Data Mining and Knowledge Discovery, 2006, 12 (1): 29-45
[7] Maronna R. A., Bustos O., Yohai V., Bias and efficiency robustness of general M-estimators for regression with random carriers, New York, Springer Verlag, 1979
[8]王彤,何大卫, LTS回归与M估计稳健性的比较,中国卫生统计, 1999, 16 (2): 79-81
[9]陈立周,稳健设计,北京,机械工业出版社, 2000
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[6] Mian L., Shapour A., Vikrant A., A multi-objective genetic algorithm for robust design optimization, GECCO’05, 2005, 771-778
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[8] Lawrence C. T., Zhou J. L., Tits A. L., User's guide for CFSQP Version 2.5: A C code for solving (large scale) constrained nonlinear (minimax) optimization problems, generating iterates satisfying all Inequality constraints, College Park, Maryland, 1998
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[1] Belytschko T., Liu W. K., Moran B., Nonlinear finite elements for continua and structures, John Wiley & Sons Inc, 2000
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[6] Rousseeuw P. J., Katrien V. D., Computing LTS regression for large data sets, Data Mining and Knowledge Discovery, 2006, 12 (1): 29-45
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[9]陈立周,稳健设计,北京,机械工业出版社, 2000
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[3] Phadke M. S., Quality engineering using robust design, New Jersey, Prentice-Hall, 1989
[4]康立山,非数值并行算法(第一册),模拟退火算法,北京,科学出版社, 1994
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