Abstract: In order to solve the difficult machining problems， the diamond turning of toric surfaces was discussed. In the tool path generating processes， an integrated discretization method was proposed for the discretization of cutting contact points. Besides， the distances in Z direction of adjacent cutting contact points were set up to reduce the tool movements resulting in the decrease of discretization errors. For the interpolation of cutting location points， the three bending moment method was proposed to realize the continuous of second order derivative. The simulation results indicate that the integrated discretization method may reduce discretization errors and the interpolation errors were decreased from 0.35 μm to 0.001 2 μm. The experimental results show that the tool path generation is practicable and the surface quality of workpiece will be improved.

Key words: toric surface, diamond turning, tool path, Hermite interpolation, three bending moment method

摘要： 为解决环曲面加工困难的问题，对环曲面金刚石切削方法进行研究。在刀具路径规划中，使用了刀触点综合离散方法，该方法结合了等角度离散与等弧长离散的优点；提出了通过控制相邻刀触点间Z向距离以减小刀具的Z向移动从而提高离散精度的方法。根据加工时刀位点插补的特点，应用三弯矩法计算插补入口参数，实现插值函数的二阶导数连续。仿真分析表明，综合离散方法能够减小离散误差，使用三弯矩法进行插补计算可将最大插值误差由Hermite插值的0.35 μm减小至0.001 2 μm，效果明显。加工试验结果表明，该路径规划方法可用于环曲面的加工，且能改善工件的加工质量。

关键词: 环曲面, 金刚石切削, 刀具路径, Hermite插补, 三弯矩法