面向系统的平面公差语义及其数学模型

摘要

According to the requirements of digital precision analysis and tolerance design for a ma-chine tool system,taking the plane as an example,the system-oriented tolerance semantics and its mathematical model were proposed.This tolerance semantics was defined as the 6-DOF output of which the tolerance on a part surface acted on its associated part.Conforming to the modeling principle proposed herein,the mathematical description for tolerance area was based on the feature points of the part's three-dimensional contouring,and was applicable in part lay out and assembly.The six output parameters of plane tolerance were calculated and expressed as a homogenous coordinate conversion matrix,then,it was realized that the mathematical model of tolerance is compatible with the error model of machine tool system.In the end,an application demonstration about tolerance adj ustment was provided.%针对机床系统的数字化精度分析及公差设计需求，以平面为例，提出了面向系统的公差语义并给出了其数学模型。面向系统的公差语义被定义为零件几何要素的公差对其广义配合件在6个自由度上的作用输出。遵循所提出的建模原则，公差域的数学描述基于零件的三维造型特征点，并适用于零件和装配两个层面。推导出了平面公差的6个输出参数并表示为齐次坐标变换矩阵的形式，实现了公差数学模型与机床系统误差模型的兼容。最后给出了一个在公差调整中的应用示例。