曲面匹配方法在刀具加工轨迹优化中的应用

为减小非可展直纹面侧铣过程中产生的原理误差,提出一种新的刀具加工轨迹优化方法,将曲面匹配方法应用于初始刀具加工轨迹的优化过程,并使用序列二次规划算法求解曲面匹配问题。首先,采用现有的刀具加工轨迹生成方法得到刀轴轨迹曲面;其次,对刀轴轨迹曲面进行法向偏移得到对应的刀具加工包络面并进行原理误差计算,使用基于序列二次规划算法的曲面匹配方法对加工包络面与设计曲面进行曲面逼近,得到空间变换矩阵;再次,通过空间变换和法向偏移,得到优化后的刀轴轨迹曲面及其对应的刀具加工包络面,以及对应的优化刀具加工轨迹及加工误差分布数据;最后,使用MATLAB进行仿真,并与基于最小二乘法的曲面匹配方法进行对比验证。仿真结果表明该优化方法有效地减小了初始刀具加工轨迹产生的原理误差,这说明提出的方法能够用于减小非可展直纹面侧铣加工时产生的原理误差。研究成果为提高非可展直纹面侧铣的精度提供了新的技术支持。

Application of surface matching method in tool path optimization

In order to reduce the principle error generated in the flank milling process of undevelopable ruled surface, a new optimization method for tool path was proposed. Surface matching method was applied to optimize the initial tool path, and the sequential quadratic programming algorithm was used to solve the surface matching problem. Firstly, the existing tool path generation method was used to obtain the tool axis trajectory surface. Secondly, the envelope surface was achieved by offsetting the tool axis trajectory surface along its normal vector, and the principle error was calculated. The surface matching method based on the sequential quadratic programming algorithm was operated to match the envelope surface with the design surface and a spatial transformation matrix was obtained. Thirdly, an optimized tool axis trajectory surface and its corresponding envelope surface were generated, and the corresponding optimized tool path and the error distribution data were obtained. Finally， the simulation was performed by MATLAB and compared with the surface matching method based on least square method. The simulation result showed that the proposed method reduced the principle error of the initial tool path effectively, which indicated that the proposed method could apply to reduce the principle error in the flank milling process of the undevelopable ruled surface. The research results provide a new technical way to improve the accuracy of undevelopable ruled surface flank milling.