螺旋锥齿轮齿面离散点空间坐标及法矢的计算

根据螺旋锥齿轮的切齿加工方法和齿轮啮合原理,运用矢量运算的方法建立了大轮成形法加工和小轮刀倾法加工的理论齿面方程并规划了齿面计算网格点区域.运用Visual Studi0 2008编程环境,编写了理论齿面各离散点空间坐标及法矢的计算软件,通过该软件可计算得到螺旋锥齿轮理论齿面各离散点在齿轮坐标系中的坐标值和单位法矢.将得到的理论齿面坐标点及法矢导入到三坐标测量机中进行测量获得各离散点的齿形误差,然后将获得该理论齿面坐标点及法矢的参数输入到CNC3906齿轮测量中心进行齿形误差测量,获得齿面上各离散点的齿形误差.将两组齿形误差测量数据进行对比分析,论证了所开发的计算软件的正确性,为螺旋锥齿轮齿面偏差的测量以及螺旋锥齿轮数字化闭环制造提供了正确的理论齿面数据.

Calculation of Spatial Coordinates and Normal Vector for Spiral Bevel Gear Tooth Surface

According to the processing methods and gear meshing theory of spiral bevel gear. vector operations method is used to establish theoretical tooth equations of formate gear and tilt cutter pinion,and the tooth surface area of grid point is planed. Using visual studio 2008 programming environment, a calculation software is written for getting the theoretical tooth surface spatial coordinates and normals of discrete point in the gear coordinates system. The resulting theoretical tooth surface coordinates and normals are imported into the eoordinate measuring machine to measure and get profile errors of the discrete points. Then, the corresponding parameters are imported into CNC3906 gear measuring center to calculate and measure, and get profile errors of the diserete points. The two kinds of profile error are compared to demonstrate the correctness of calculation software. The method provides a correct theoretical tooth surface data for the three-coordinates measurement of tooth surface deviation and digital closed-loop manufacturing of spiral bevel gear.