圆柱刀五轴数控侧铣直纹面的直线插补误差分析

Linear Interpolation Error Analysis for Cylindrical Cutter of Five-axis CNC Flank Milling Ruled Surface

在五轴联动数控系统中,相邻刀位点间的运动通过直线、圆弧或样条曲线进行插补运动,其中直线插补方法最具典型性。以圆柱刀侧铣加工直纹面时因线性插补引起的非线性误差为研究对象,首先,在被加工曲面上采用最佳一致逼近法规划圆柱刀侧铣直纹面的刀具位置;然后,利用包络原理建立刀具线性插补时所形成的包络面解析表达式;以理想曲面为基准面,利用牛顿迭代法求取点到曲面的最小距离,从而建立刀具包络面与理论曲面的误差模型,以此得到刀具线性插补时产生的非线性误差;最后,利用MATLAB软件通过数值算例对影响非线性误差的规律、大小以及其影响因素进行了分析。

Linear, circular, and spline interpolation are used for interpolation motion in the five-axis CNC system, and the line interpolation method is most typical one. Aiming at the nonlinear errors due to the linear interpolating during the rule surfaces flank milling by using cylindrical milling cutter, the cutter position and orientation were determined by using the best uniform approximation method firstly. Then, the cylindrical cutter＇s envelope surface which was generated by cutter＇s linear interpolation motion between adjacent cutter location points was builded by the envelope principle. The nonlinear errors between the envelope surface and designed surface were obtained based on the minimum distance calculation between a point of envelope surface and the designed surface by using Newton iteration method. The pattern, scale and influence factors of the nonlinear error were analyzed via numerical examples by MATLAB software.