基于齐次坐标变换的带平面度零件装配误差分析

摘要

According to the flatness errors existing in actual manufacturing assembly,a method is proposed to analyze the error of plane coordination by using homogeneous coordinate transforma-tion.At first,with consideration of the irregular corrugate in surface of plane mating assembly, the reference coordinate system of plane mating assembly is established which helps to convent plane mating assembly to the mating between the relative coordinate system and the absolute co-ordinate system,and the mathematical model is also established.Euler angels inverse transform method is used to obtain the inclination which exists in corresponding axes between the relative coordinate system and the absolute coordinate system,and the general solution of the angle error is also obtained.By fitting and simulation of the known coordinate in rough surface on Matlab flat,the coordinate matrix is established and it is used to calculate the angle error.Subsequently, the rationality of the angle error analysis is verified by the component assembly surface of a cer-tain type of machine.%针对实际生产装配过程中存在的平面度误差，提出了一种运用齐次坐标变换方法分析平面配合误差的方法。首先考虑配合平面表面的不规则波纹状，通过建立平面配合参考坐标系，利用齐次坐标变换方法将平面配合关系转换成相对坐标系与绝对坐标系的配合关系，并建立其数学模型；利用欧拉角反变换方法得到了两坐标系对应的轴间倾角及角度误差的通解，通过 Matlab软件对实际粗糙平面上的已知坐标进行曲面拟合仿真，得到了配合坐标矩阵，代入通解后得到平面配合的角度误差。以某型机床床身组件装配表面为实例，验证了此角度误差分析方法的合理性。