数控加工曲线的等弧长圆弧拟合方法

数控加工中,只有直线和圆弧才能直接进行加工,对其他任何曲线的加工都必须首先用直线或圆弧进行拟合.用圆弧拟合曲线的方法很多,但都存在不同程度的不足.为此提出了用曲线段长度作为圆弧长度,按照曲线段斜率变化规律判定圆心方位,以凸弧代替凸曲线的曲线圆弧拟合方法;用级数展开简化超越三角方程,避免了迭代求解的麻烦,提高了曲线拟合效率.计算结果表明:所提出的方法其曲线拟合精度较高,计算便捷,是实际应用中曲线轮廓加工的有效曲线拟合方法.

The Method of Curve Fitting with Equal Length Arc Used for NC Processing

In NC processing, only the straight line and circle arc can be processed directly , and the others must be fitted with them before processed. There are many methods of fitting curves with arc, but different shortage exists. An are is built based on its length equal to the segment length of the curve approached , the direction of the eircinal center is judged according to the variety inclined of curve segment slope, so that convex curve is replaced with a convex arc. The overstep equation of triangle is simplified with expanding series to improve computing efficiency. The computation result shows the method is not only very simple to calculate, but also has high accuracy to approach the processed curve by an equal length arc.