Aimed at the AFR specified in the stage of design, a mathematic model that can be used to tolerance synthesis simulation in CAT was established based on the geometric features' variations of DOF. Two steps were involved in the course of tolerance synthesis modeling: the relationships among each feature's DOFs with AFRs were explicitly formulated with homogeneous matrix transforms and the synthesis equations were obtained with the matrix inversion technique. An engineering example, gear pump, was introduced to test the proposed method. The synthesis equations between the backlash spacing and the corresponding features' DOFs were obtained, and the distribution of each feature's DOFs was calculated by the method of Monte Carlo. The results show the validity and practicability of the method proposed.

针对产品设计阶段规定的装配功能要求,在特征自由度公差表示模型的基础上,利用齐次坐标变换的知识分析并推导了装配功能要求与零件配合特征自由度变动的关系矩阵,通过矩阵求逆的方法得到公差综合仿真等式,由此建立了基于特征自由度变动的公差综合模型。以齿轮泵为例,研究并建立了两齿轮装配后的侧向间隙（装配功能要求）与泵体及齿轮相应配合特征自由度变动的公差综合模型,运用Monte Carlo方法进行了仿真实验,得到各配合特征自由度在公差范围内的变动量及分布统计结果,验证了建立的公差综合模型及仿真方法的有效性和实用性。

特征几何变动, 自由度(DOFs), 公差综合, 建模与仿真, 装配功能要求