球头铣刀余摆线加工表面形貌的建模与仿真研究

Research on Modeling and Simulation of Surface Topography Obtained by Trochoidal Milling Mode with Ball End Milling Cutter

余摆线铣削因切削力小、表面质量和生产率高,而广泛应用于高速加工中。球头铣刀因适应性好,且姿态可灵活调整,而成为多轴加工复杂表面的常用刀具。然而,球头铣刀齿形复杂,余摆线铣削的运动轨迹方向不断变化,工件的材料去除和表面形貌的创成过程异常复杂,传统方法建模困难。提出一种球头铣刀余摆线加工表面形貌的数值仿真方法,根据齐次坐标矩阵变换原理建立刀齿的运动轨迹方程,通过改进Z-MAP算法完成了加工表面形貌的仿真。该算法通过建立刀齿微元的随动矩形包围圈和瞬时扫掠四边形,使用角度累加法快速地获取刀齿微元在单位时间步长内扫掠到的工件网格点,根据多元函数的泰勒公式,用线性插值的方法求出该网格点的高度坐标。仿真结果表明球头铣刀余摆线铣削的表面形貌整体上优于普通直线铣削。试验结果表明,在垂直和倾斜加工条件下,球头铣刀余摆线铣削获得的表面形貌与仿真结果具有较高的一致性,说明所提出的方法可以预测球头铣刀余摆线的加工表面形貌。

Trochoidal milling mode has small cutting force, high surface quality and productivity, which is widely used in the high speed and velocity machining. Due to a good adaptability and flexible adjustment of orientation, ball end milling cutter is commonly used for multi-axis machining complex surface. However, the processes of part material removal and the machined surface formation is very complicated and difficult to describe because the tooth profile of ball end milling cutter is complex and the direction of cutter trajectory changes continuously in trochoidal milling process. A numerical simulation method is put forward to simulate the surface topography milled with ball end milling cutter which is based on the principle of homogeneous coordinate transformation matrix to establish the locus equation of cutter tooth, and finish the surface topography simulation by improving Z-MAP algorithm. The algorithm quickly obtain the part grid nodes perhaps swept by the cutter tooth within unit time step through the establishment of servo rectangular encirclement and instantaneous scanning quadrilateral of the basic unit of the cutter tooth, and on these bases the part grid node really swept is determined through the angle sum method, and the height coordinate is calculated using the method of linear interpolation according to Taylor formula of multivariate function. The results show that ball end milling surface topography obtained by trochoidal milling is superior to the ordinary straight line milling on the whole. Experimental validation results show that no matter in the case of vertical or tilting machining, surface topography of trochoidal milling with ball end cutter is high consistency with the simulated ones, and the proposed method can predict the surface topography in practical manufacturing.