中文摘要：

通过对空间凸轮非等价加工方式下理论刀轴轨迹曲面微分几何特性的研究，表明加工空间凸轮工作廓面必然存在法矢异向误差。为寻求加工误差最小的最佳刀轴矢量，提出了数控侧铣加工空间凸轮廓面的方法。根据实际刀轴轨迹面是直纹面的性质，以NURBS直纹面重构理论刀轴轨迹面，采用最小二乘优化方法确定侧铣加工刀位，给出了理论加工误差模型，并通过实例的数值计算和加工实验结果证明了该方法的有效性。

英文摘要：

A new optimized positioning method of a cutter with smaller diameter than that ot the cam follower for milling the spatial cam was presented. According to the differential geometrical structure of theoretical surface of tool axis trajectory, errors caused by the different directions of normal vector along the contact were unavoidable. In order to find the best tool axis vector to minimize the machining error, this paper realized the non-quivalent machining of spatial cam surfaces using the NC side milling method. The practical surface of tool axis trajectory was a ruled surface, so the theoretical surface of tool axis trajectory was reconstructed by the NURBS ruled surface. The cutter position for NC side milling the spatial cam was confirmed based on the least square optimization method and the machining error was given. At last, a numerical simulation and machining example was described, and the results show the effectiveness of side milling spatial cam.