中文摘要：

在分析各类尺寸和位置公差对应的公差域形状、大小及公差域局部坐标系的基础上，提出以公差域的边界表达及其对几何要素的约束作用为核心、以几何面数学方程组形式表达公差域的边界、以约束方向向量和偏差向量表达公差域对几何要素的约束作用的尺寸公差与位置公差统一的公差域模型，并运用该模型实现了圆柱域、同轴圆柱域及两平行平面域的公差域约束几何变动范围的求解。借助ACIS几何造型工具开发了原型系统，实现了虚拟环境下的公差域构建和可视性显示，相关模型和算法也通过实例进行了验证。

英文摘要：

Tolerance zone modeling plays a fundamental role in error propagation analysis, assembly precision predicting and assembly simulation with geometric precision. By analyzing the shape, size and local coordinate systems of various tolerance zones corresponding with different tolerances, a synthetic tolerance zone model integrating size and position tolerances was presented, in which the representation of virtual boundary and its constraint to geometrical element were central part, besides mathematic equation groups were built to represent tolerance boundary and geometric constraints were characterized by direction vector and error vector. The model was applied to find the range of tolerance zone constrained geometric variation among cylinder, concentric cylinder and two parallel planes. A prototype system was developed by using ACIS geometric modeling tool to perform the construction and display of typical tolerance zones in virtual environment, and related models and algorithms were verified by examples.