基于标准方程的等步长双曲线插补算法

Equal Step Length Interpolation Algorithm of Hyperbola Based on the Standard Equation

双曲线插补算法是数控加工双曲线轮廓的关键技术。文章从双曲线的标准方程出发,推导出不同象限不同插补方向的插补递推公式,推理出选择插补递推公式的判定方法,提出插补循环结束判断方法和确保插补终点与理论轮廓终点重合的方法,研究出双曲线的插补流程图,得到了双曲线等步长数据采样插补算法,并对插补轮廓误差进行分析。实例证明该算法计算简单,插补精度高,轮廓步长稳定,满足数控加工需求。

Interpolation algorithm of hyperbola is the pivotal technology of hyperbolic contour＇ s NC ma chining. Based on the hyperbolic standard equation, the interpolating recursion formulas of different quadrant and interpolating direct were deduced, the determinant method of choosing the interpolating re cursion formulas was reasoned, the judging method of interpolating cycle and the method of the interpo lating endpoint coinciding with the contour＇ s endpoint were put forward, the interpolating flow chart of hyperbola contour was researched, the equal step length interpolation algorithm of hyperbola was ob tained, and the interpolating contour error was analyzed. An example testifies that the interpolation algo rithm is simple, the interpolating precision is high, contour step lengths are steady, and so the interpola tion algorithm is satisfied with NC machining.