球头铣刀曲面加工的刀具切触区域解析建模

Analytical Modeling of Cutter Engagement Regions in Ball-end Milling of Curved Surface

针对球头铣刀三维曲面加工,提出一种刀具切触区域仿真的通用解析模型。采用微分方法,将曲面加工过程离散为一系列连续的微小斜平面稳态加工。以每一小斜面切削过程为研究对象,建立描述刀具进给方向变化的数学模型,针对不同的进给方向并基于空间坐标系旋转变换,提出一组确定刀具切触边界曲线及各边界交点的解析公式,以精确界定刀具切触区域的封闭几何。通过与Z-Map模型的切触区域仿真对比,验证了本文模型的有效性及其精确高效的特点。

This paper presents a generalized analytical model of cutter engagement region simulations for ball - end milling of 3D curved surface. With differential method, the curved surface machining is treated as a series of sequential small inclined surfaces steady state milling. According to the cutting process of each small inclined surface, the mathemati- cal models which are used to describe the variation of cutter feed direction are established. Through space coordinate sys- tem rotation transformation, a set of analytic formula of cutter contact boundaries and the intersection points are proposed, in order to exactly determine the closed geometry of engagement regions for different feed directions. The effectiveness and characteristics of accuracy and high - efficiency of the model presented in this paper are verified by the comparison of engagement region simulations with Z - Map model.