微线段高速加工的圆锥截线拐角插补算法

针对数控高速加工时微小线段拐角过渡的平滑问题，建立基于二次有理Bézier形式的圆锥截线拐角过渡矢量模型，推导三种类型的园锥截线过渡曲线的最大轮廓偏差和最大曲率计算公式，提出一种微小线段间圆锥截线拐角过渡的插补算法。算法可在满足轮廓加工精度和相邻小线段长度的条件下选择圆锥截线的权因子，确定圆锥截线拐角过渡曲线的类型；根据数控系统的动态响应能力、弓高误差和过渡曲线多步转接的要求，确定拐角曲线过渡的最大加工速度；进一步提出通过修改圆锥截线的权因子实现拐角曲线的加工速度与各直线段路径的进给速度衔接过渡的前瞻处理方法。与圆弧拐角过渡的对比结果表明，算法可有效提高微小线段间的拐角加工速度，缩短数控加工时间。

A Micro-line Corner Curve Interpolation Algorithm Based on Conic Section for High-speed Machining

The issue of smoothing sharp corners between consecutive small line blocks in high-speed machining was discussed. According to the characteristics of the rational quadratic Bézier curve, the vector model of conic section transition was constructed. The formulas of the maximum contour error and the maximum curvature of conic segments were derived. Subsequently, a corner curve transition interpolation algorithm based on conic section was proposed. On the basis of this algorithm, the conic section type was defined by the weight which could satisfy the prescribed contour machining accuracy and the adjacent line segment length. At the same time, the maximum velocity limited by chord error, interpolation distance and dynamic response of machine tool was calculated. Moreover, an improved look-ahead method, which could adjust the corner velocity between two trajectories by modifying the weight of the transition curve, was presented. The comparison between the arc transition results and the conic section transition results showed that the proposed algorithm could improve transition velocity and reduce machining time.