虚轴机床磁力研磨刀具轨迹点的空间插补

3D Space Interpolations for Magnetic Abrasive Finishing by Virtual Axis Machine Tool

基于东北大学研制的三杆五坐标并联虚轴机床的双摆动刀具结构 ,建立数学模型 ,对磁力研磨的刀具轨迹点的空间直线插补、圆弧插补进行了研究 ,推导出插补点的计算公式·采用了一种新的圆弧分类方法 ,对不同种类的圆弧建立不同形式的辅助坐标系 ,通过坐标变换将原坐标系中圆弧插补转换为辅助坐标系中圆弧插补 ,利用辅助坐标系的不同设置及改变步长的正负号处理了圆弧过象限情况 ,解决了圆弧插补问题 。

Based on the structure of the double oscillation axis cutting tool of the 3 legged 5 DOF virtual axis machine tool in parallel, the interpolation mathematic model was set up. Space line interpolations and circular arc interpolations of the tool path for magnetic abrasive finishing were researched. The interpolations formulae was derived. A new method was presented to classify the circular arcs. For different kinds of circular arcs, different auxiliary coordinate systems were set up. The circular arcs interpolations in the original coordinate system were transformed into the arcs interpolation in the auxiliary coordinate systems. The circular arcs quadrant transitions were solved by the application of different coordinate systems, positive stepper and negative stepper. The different circular arcs interpolations were solved. The virtual axis machine tool can be used in magnetic abrasive finishing for finishing the free form surface mould.