新一代GPS标准中非理想表面模型的建模方法

Modeling method for the skin model in new-generation geometrical product specifications

本文重点研究在新一代产品几何技术规范标准下如何将非理想表面模型以离散数学的方法表达出来。利用马尔科夫链蒙特卡洛仿真技术(MCMC)和基于主成分分析(PCA)的全局建模法来实现考虑几何约束和公差规范的具有随机误差的非理想表面模型的仿真分析;利用统计形状分析方法(SSA)和基于广义Darboux结构的局部建模法来实现在制造过程中产生的系统误差的非理想表面模型的仿真分析;并引入平均非理想表面模型概念及其统计分析方法对产品变形趋势进行预测。最后以实际工件为对象,通过本文提出的方法得到了其非理想表面模型的仿真结果,并对其仿真效果进行了综合分析,分析结果证明了本文提出方法的正确性和可行性。

Against the background of new-generation geometrical product specifications（GPS） ,the respresentaion of skin model by using discrete mathematics is focused in this paper. Considering geometric constraint requirements and tolerance specification, to achieve skin model simulation with random deviations, Markov chain Monte carlo （MCMC） simulation techniques and a global-modeling approach based on principal component analysis （PCA） are investigated. Statistical shape analysis （SSA） model and a local-modeling approach based on augmented Darboux frame are utilized here for the simulation of the skin model with systematic deviations which are produced in the manufacturing process. The concept of the mean skin model and its robust statistics are also introduced. In the end, a case study based on a part is applied here and simulation results of its skin model validate the correctness and applicability of the proposed method.