基于制造误差形态的装配性仿真表面几何误差建模理论研究

As an important aspect of product design, product assemblability aims at the evaluation of product function/capability and the difficulty of assembly. The most effective approach to analyzing product function/capability and assemblability is the application of assembly simulation methods. However, the assembly simulation considering non-ideal part surfaces resulting from manufacturing errors remains a novel and challenging topic, which differs from normal assembly simulation methods considering only the ideal condition of parts in that, it aims basically at the appropriate prediction of the uncertainties of the mating part surfaces in an assembly to be simulated. In another word, the problem can be seen as a tolerance modelling problem, which involves not only the completeness of non-ideal surface representation and its convenience for computation, but also the consideration of invariance and randomness of the representation under different manufacturing circumstances. From the view of information theory, based on the basic definition of non-ideal surface, this project puts forward the theory of deviation modes. At the same time, through analysis into the intrinsic cause of manufacturing errors, the error spectrum theory is newly proposed to represent surface error. With related mathematical methods, following the principles of Manufacturing Engineering theories, methods for mapping and transformation between different concepts are proposed. Under the guidance of the proposed theory, corresponding enabling technologies that support the consideration of manufacturing errors in assembly simulations are developed, which strikes a firm basis for the realization of assembly design based on non-ideal surfaces.

保证包括产品功能/性能和装配难易程度在内的产品装配性问题是产品设计的重要内容。利用装配仿真对产品装配性进行分析是当今最精确有效的方法。而考虑制造因素造成的零件表面非理想条件下的装配性仿真分析是一项具有学术挑战性和新颖性的研究课题。与仅考虑零件理想状态的装配仿真不同，其基础问题是零件配合表面的不确定性“预测”的准确描述问题，即误差模型问题。它不仅涉及对非理想表面表达完备性，还涉及在不同制造误差因素不变性与随机性条件下的表达和计算的方便性等难题。本项目从信息论的角度，由非理想表面的基本概念的定义出发，提出偏差模态理论。并基于制造产生误差的内在因素分析，提出新的表达表面误差的误差谱理论。利用数学手段，解决相关概念之间的映射、变换和求解运算。在所建理论的指导下，研究相应的支持数字化制造中考虑制造误差的装配仿真分析使能技术，为实现基于非理想表面的装配性设计奠定基础。

预先分析产品功能、性能、可装配性等装配性问题是产品设计的重要内容。当今基于理想几何模型的仿真方法已广泛应用于装配性问题的分析。而考虑制造误差造成的零件表面非理想状态下的装配性仿真分析仍是一项具有学术挑战性的研究课题。其中，如何建立误差模型对“预测的”非理想表面及其不确定性进行准确的描述是基础问题。本项目从制造角度出发研究非理想表面误差建模理论及其关键技术，主要研究了四项内容。.（1）从非理想表面是理想表面的偏离等概念出发，提出基于曲线坐标系构建偏差坐标系，进而建立偏差函数的建模方法实现非理想表面偏差的表达。.（2）分析多种制造误差对表面偏差的影响模式，建立相应偏差模态函数和总表面偏差函数，提出相空间概念，给出非理想表面的参数化表达。.（3）从制造误差随机性是引起表面不确定性的事实出发，利用相空间中“点”的分布（也就是制造参数的随机联合分布）表达非理想表面不确定性的分布，建立了非理想表面的误差表达模型。.（4）开展非理想表面误差建模理论的应用研究。给出产品密封性分析、面向非理想平面装配的位姿偏差统计分析、面向柱面装配的可装配性评价分析等研究示例。开发了支持非理想表面配合装配性分析的原型系统。.本项目由非理想表面基本概念出发，提出了偏差模态理论，并基于制造误差内在因素分析，提出了误差谱理论，进而形成了一整套关于非理想表面偏差及误差的表达理论和模型。经过研究考虑非理想表面配合的装配仿真分析相关使能技术，验证了该模型不仅方便表面的表达，还能从制造的角度反映出非理想表面不确定误差的因素和真实状况，为实现基于非理想表面的装配性设计奠定了基础。