基于数论的复杂装配体公差分析理论与方法

Currently, many shortages and limitations exist in the field of tolerance analysis of complex assembly, based on both assembability and functionality. Three main problems are as follow: 1) the tolerance analysis model are inconsistent with the new generation of the geometrical product specification; 2) the generation of the 3-D tolerance chain combined with both dimensional and geometrical tolerance is still lacking; 3) accuracy and efficiency in common statistical tolerance method need to be improved. To cope with these problems, this project has proposed a novel tolerance analysis theory and method based on number theory and discrete surface. Firstly, based on the principle of skin model, non-ideal functional feature surface model including form error, waviness and roughness is to be built from the parts’ error surfaces, therefore forming multiple-scale point cloud represented skin model under the constraints of separate tolerance principles, in order to incorporate tolerance information into geometrical model of the error parts; then, on the study of assembly tolerance information expression, tolerance chain generation method and tolerance representation within the CAD environment, comprehensive 3-D tolerance chain model in service of the overall process of tolerance analysis is to be constructed; after that, rapid sampling strategy of error parts will be considered based on number theory and assessing technique of functional dimensional tolerance will be carried out, to realize the of 3-D statistical tolerance analysis of complex assembly; finally, the computer aid tolerance prototype built in the 3D CAD system will be developed to facilitate the integration of CAx system and the new generation of the geometrical product specification.

复杂装配体基于可装配性及功能性的公差分析仍存在较大局限，主要体现在公差分析模型与新一代产品几何规范与认证标准体系不相符、综合考虑尺寸与几何公差的三维公差链的自动生成方法欠缺及常用统计公差方法的精度与效率有待提高。为此本申请提出一种新的基于数论和离散表面相结合的复杂装配体公差分析理论和方法。以零件肤面模型为基础，构建包含几何误差、波纹度及粗糙度的非理想特征功能表面模型，建立不同公差原则约束下的误差零件多尺度点云肤面模型；结合装配体公差信息表达、公差链生成方法，构建服务于公差分析全过程的三维公差链综合模型；基于数论方法建立误差零件样本快速抽样策略，实现复杂装配体三维公差的统计分析，开发集成于三维CAD系统的CAT原型系统。旨在基于新一代产品几何规范与认证标准体系，扩展并完善统计公差分析的理论与方法，实现公差设计的高效高精度的统计分析，并促进CAx系统与新一代GPS标准体系的融合。

复杂装配体基于可装配性及功能性的公差分析仍存在较大局限，主要体现在公差分析模型与新一代产品几何规范与认证标准体系不相符、综合考虑尺寸与几何公差的三维公差链的自动生成方法欠缺及常用统计公差方法的精度与效率有待提高。为此本申请提出一种新的基于数论和离散表面相结合的复杂装配体公差分析理论和方法。以零件肤面模型为基础，构建包含几何误差、波纹度及粗糙度的非理想特征功能表面模型，建立不同公差原则约束下的误差零件多尺度点云肤面模型；结合装配体公差信息表达、公差链生成方法，构建服务于公差分析全过程的三维公差链综合模型；基于数论方法建立误差零件样本快速抽样策略，实现复杂装配体三维公差的统计分析，开发集成于三维CAD系统的CAT原型系统。旨在基于新一代产品几何规范与认证标准体系，扩展并完善统计公差分析的理论与方法，实现公差设计的高效高精度的统计分析，并促进CAx系统与新一代GPS标准体系的融合。