Abstract: Tolerance modeling and analysis using ideal surface model or without considering shape deviation often leads to interference risk in part assembly or assembly accuracy cannot be guaranteed.To solve the problem,the geometric deviations of part features were expressed in vectors based on the definitions of half space and polyhedron.The tolerance polyhedron inequalities of part layer were constructed according to the dimensional tolerance constraints.The tolerance polyhedron inequalities of assembly layer were constructed based on ideal surface model.The tolerance polyhedron inequalities based on non-ideal surface model were constructed by adjusting the parameters of assembly contact surfaces using assembly optimization functions,and the surface shape deviations were incorporated into the tolerance mode.The milling cutter seat assembly was taken as an example to establish the tolerance polyhedron convex hulls of each deviation transfer path of the assembly,which solved by Minkowski sum.The deviation value of the target ring was obtained by intersection operation.The tolerance values were adjusted manually and recalculated until the target ring deviation met the initial precision design requirement.

Key words: tolerance modeling, tolerance analysis, polyhedron, convex hull, shape deviation, milling cutter seat

摘要： 采用理想表面模型或未考虑形状偏差进行公差建模与分析往往导致零件装配产生干涉风险或装配精度得不到保证。针对该问题,首先基于半空间和多面体的定义将零件特征几何偏差以向量的形式表示,根据尺寸公差带约束构建了零件层的公差多面体不等式组。其次,以理想表面构建装配层公差多面体不等式组,通过使用装配优化函数对装配接触面参数进行调整,将形状偏差纳入公差模型中,从而构建了基于非理想表面的公差多面体不等式组。最后,以铣刀座装配体进行了实例研究,建立了该装配体的各偏差传递路径的公差多面体凸包,并使用闵可夫斯基和依次求解,然后进行交集运算得出目标环偏差值;手工调整公差值并重新计算,直至分析出的目标环偏差值满足初始精度设计需求。

关键词: 公差建模, 公差分析, 多面体, 凸包, 形状偏差, 铣刀座