研究了五轴机床铣磨高次离轴非球面技术, 分析了B-C双转台五轴机床的运动学原理, 得到了刀轴矢量与B、C轴转角的数学映射, 建立了刀具轨迹算法模型。针对高陡度高次离轴非球面矢高变化率太大等问题, 对其进行坐标系变换使其近轴端和远轴端等高, 将离轴非球面由母镜坐标系位置转化到子镜坐标系位置, 坐标变换后高次离轴非球面在子镜坐标系下的方程求解困难, 提出一种新的求解旋转后高次离轴非球面坐标的方法, 最后通过Matlab仿真和实例分析, 利用五轴机床加工等高处理的高次离轴非球面, 经三坐标测量仪测量, 结果为面型PV值5.92μm, RMS值为0.893μm, 验证了刀具轨迹算法和坐标变换算法的正确性。

The technology of milling high order off-axis aspheric surface with five-axis machine tool studied and the kinematics principle of B-C double turntable five-axis machine tool analyzed, the mathematical mapping between tool axis vector and rotation angles of B and C axis is obtained, and the algorithm model of tool path is established. Aiming at the problem of high steepness and high order off-axis aspheric surface with large vector height change rate, coordinate system transformation is carried out to make its paraxial and off-axis ends equal. The off-axis aspheric surface is transformed from the parent mirror coordinate system to the sub-mirror coordinate system. After coordinate transformation, it is difficult to solve the equation of high order off-axis aspheric surface in the sub-mirror coordinate system. A new method for solving the coordinates of high order off-axis aspheric surface after rotation is proposed, finally, through the simulation of Matlab and an example analysis, machining of contoured high-order off-axis aspheric surface with five-axis machine tool, the results measured by a three-axis measuring instrument show that the surface-type PV value is 5.92μm and the RMS value is 0.893μm, which verifies the correctness of trace algorithm of the tool path and coordinate transformation algorithm.