高精度数控机床非均匀有理B样条曲线插补控制研究

在复杂曲面数控加工中,经常应用非均匀有理B样条曲线。介绍了非均匀有理B样条曲线插补原理,分析了传统非均匀有理B样条曲线插补方法,即泰勒展开法,确认泰勒展开法在计算精度和时效性等方面存在不足。针对泰勒展开法存在的不足,提出采用割线法进行非均匀有理B样条曲线插补。介绍了割线法插补原理,分析了迭代运算初值及终止判定问题。通过对比确认,割线法求解时间短,精度较高,可以满足高精度数控机床非均匀有理B样条曲线的插补控制要求。

Research on Interpolation Control of Non-uniform Rational B-spline Curve of High Precision CNC Machine Tool

In NC machining of the complex surface,the NURBS curve is often used.The principle of NURBS curve interpolation was introduced.The traditional interpolation method for NURBS curve i.e.the Taylor expansion method was analyzed.It is confirmed that the Taylor expansion method has shortcomings in calculation accuracy and timeliness.In view of the shortcomings of the Taylor expansion method,it was proposed to adopt the secant method to carry out NURBS curve interpolation.The principle of secant interpolation was introduced,and the problems of the initial value and the termination judgment of iterative operation were analyzed.It is confirmed through comparison that the secant method has a short solution time and high accuracy,which can meet the interpolation control requirements for the NURBS curve in high precision NC machine tool.