中文摘要：

传统的公差分析以平面尺寸链为基础,只能进行尺寸公差的分析,无法考虑形位公差的影响,在零件的制造过程中,受各种加工条件及外界因素的影响,不可避免的存在形位误差,这些形位误差对装配体的功能要求起着重要作用。为了解决此问题,利用雅可比旋量理论建立了装配功能要求与零件公差之间的三维公差数学模型,将该模型融入蒙特卡洛算法中,实现了装配体三维公差统计分析。最后以机床尾座为例,对比了极值法与统计法的分析结果,验证了所述方法的实用性。

英文摘要：

Based on the planar dimension chain,the traditional tolerance analysis is only used for dimensional tolerance analysis,which can not consider the influence of geometric tolerance. Parts is affected by various processing conditions and external factors in the manufacturing process,which cannot avoid the existence of geometrical error,These geometrical errors play an important role to the functional requirement of the assembly. In order to solve this problem,the 3D mathematical model of tolerance between assembly functional requirement and component tolerance was established by using jocobian-torsor theory. This model was involved in monte carlo algorithm,and the 3D tolerance statistical analysis of assembly was realized. Finally,a machine tailstock was taken as an example,the result of worst case method and statistical method was compared,and practicability of the proposed method was verified.