中文摘要：

针对自由曲面五轴加工的刀位规划问题,提出回转刀具二次曲面与自由曲面切触时刀轴矢量的计算方法。通过分析曲面间高阶切触性质,建立了曲面切触阶与曲面几何不变量之间的对应关系;通过建立回转刀具加工自由曲面的运动学模型,推导出在离散刀位处刀具包络面与自由曲面二阶切触时的刀轴倾角函数关系,并解析求解该状态下的刀具姿态方程。加工实例表明,该模型能很好地描述刀具包络面与自由曲面间的切触关系,并保证加工过程中刀轴矢量变化的平稳顺滑性,从而获得较高的加工表面质量。

英文摘要：

Aiming at the tool path planning of five-axis machining in free-form curved surface, the method of compu- ting cutter-axis vector for revolving cutters was proposed in the scenario of single-point contact between the curved surface of revolving cutters and free-form curved surface. With analysis on properties of surfaces in higher-order contact, the relationship between order of surface contact and surface geometric invariant was established. Through simulating the kinematic model for machining free-form curved surface with revolving cutters, the function relation- ship of cutter axis angle was deduced and the attitude equation in the dispersed cutter position was formulated, while the enveloping cutter surface and the free-form curved surface were in second-order contact. By instance of machi- ning practice, this simulation model was with persuasion to illustrate the contact relationship of cutter＇s enveloping surface and free-form curved surface, and the variation smoothness of cutter＇s vector in the process of machining was guaranteed to achieve higher machining surface quality.