非可展直纹面侧铣加工的最小二乘刀位规划方法

Least square positioning method of flank milling for non-developable ruled surface

将圆柱刀和圆锥刀侧铣非可展直纹面的理论模型归结为刀具曲面与设计曲面的最佳平方逼近问题。该方法从刀具轴线出发,以被加工曲面的刀位规划误差为纽带,得到刀具曲面上的一条映射曲线,该曲线能够表征刀具曲面与被加工曲面的贴近程度,进而提出了确定刀具位置的最小二乘逼近模型和解算方法。通过数值算例与两点偏置法、三点偏置法和UG数控加工模块加工的结果进行比较,分析了其误差分布规律。结果表明,所提方法的几何残留误差较小,可为非可展直纹面的侧铣加工提供一定的参考依据。

The theoretical model of flank milling non-developable ruled surface of cylindrical cutter and conical cutter was summarized as the best square approximation problem for the tool surface and surface designed.Based on the tool path planning errors of processed surface,a mapping curve of the tool axis was obtained on the tool surface,which could be used to express the closeness between the tool surface and the surface to be machined.Further,the Least Square（LS）approximation model and corresponding solving methods for the determination of tool position were presented.Experimental results showed that the geometrical errors related to the proposed method significantly lower than that associated with Double Point Offset（DPO）method,Three Point Offset（TPO）method and CNC machining module of UG.The methods provided a theoretical reference for the flank milling of non-developable ruled surface.