基于离散化几何形状误差模型的产品规范建模理论研究

项目名称： 基于离散化几何形状误差模型的产品规范建模理论研究

项目编号： No.51305006

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 机械、仪表工业

项目作者： 张敏

作者单位： 北京工业大学

项目金额： 25万元

中文摘要： 产品几何技术规范（Geometrical Product Specification，GPS）是所有机电产品功能设计与计量规范的基础，被认为是实现制造业信息化的关键技术。然而，由于其数字化描述及计算机集成方面还不完善，阻碍了其在现代制造业中的应用。本项目以能反映加工误差的非理想几何形状模型为对象，以离散几何和统计形状分析等现代数学工具为基础，开展产品几何技术规范与认证体系的数字化设计方法研究。在分析GPS原理框架的基础上，建立能够反映产品规范设计信息的规范表面模型，提出将传统基于文本的公差设计要求体现为规范表面模型的几何要素变动量的转化关系；推导统计形状分析在多目标模型中的数值解法；探讨GPS中各类操作算子算法，设计和开发出完整的能够与CAx无缝集成的产品几何规范与认证系统。本研究将在产品设计阶段体现并实现对最终产品几何行为的预测，保证产品数字化设计过程的连续性，有重要的理论和实用意义。

中文关键词： 产品几何技术规范；几何形状误差模型；小波分析；离散几何；齿面接触分析

英文摘要： Geometrical product specifications (Geometrical Product Specification, GPS) is a standardized basis for the functional design and metrology of all the mechanical and electrical products as well as is considered to be the key technology to achieve manufacturing informationalization. However, due to its digitized description and computer integration are ambiguous, its application in modern manufacturing is hindered. This project based on non-ideal geometrical model and discrete geometry, statistical shape analysis and other modern mathematical tools carry out the digital design methods of geometrical product specifications and verifications.Based on analysis of the framework of GPS, derived the mathematical description of discrete GPS system, established the surface model to reflect the specifications requirement, proposed embodying in the geometric elements of the specification surface model relationship instead of the traditional text-based tolerance design method, deduced statistical shape analysis algorithms in the numerical solution of multi-objective models, studied different operator algorithms on GPS system, designed and development a complete geometrical product specification and certification system integrated within CAx context. In this study, geometrical behaviors of the final products can be reflecte

英文关键词： Geometrical Product Specification；non-ideal surface model；wavelet analysis；discrete geomety；tooth contact analysis