中文摘要：

为全面表征拓扑修形斜齿轮的齿面误差信息,针对数控成形磨齿机的运动功能和修形齿面形成的机理,依据极坐标法测量的数学模型提出了在机拓扑测量方法。根据砂轮廓形与工件的接触迹线通过坐标变换推导出拓扑修形齿面理论点的数学方程,并对修形齿面进行网格划分。利用数控成形磨齿机的回转运动（C轴）、径向进给运动（X轴）和轴向进给运动（Z轴）形成理论渐开线点到点的拓扑测量。最后在成形磨齿机上进行测量实验,表征出齿面误差等值图。

英文摘要：

For fully characterizing the tooth surface errors information of the topological modification helical gear,the method on- machine topology measurement is proposed by a mathematical model of the polar coordinate,based on CNC form grinding motion function and formation mechanism of the tooth surface modification. According to the contact trace of the outline shape of grinding wheel and the workpiece,the mathematical equation of tooth flank modification theory point is derived through coordinate conversion,and the tooth surface grids are divided. The point to point topology measurement of theoretical involute is completed by using the rotary（ C axis） and radial feeding motion（ X axis） and axial motion（ Z axis） of CNC form grinding machine. Finally,on the form grinding the topology measurement experiment is carried out,and the tooth surface errors are characterized by contour map.