NURBS曲线泰勒展开插补法的平稳性与改进研究

Research on Stability and Improvement of Taylor-Expansion-Based Approach for NURBS Curve Interpolation

泰勒1阶或2阶级数展开是NURBS曲线迭代插补的常用方法,这种方法会导致弦长误差,从而导致速度波动与运动冲击。为此,分析了泰勒展开插补法的3种误差来源,提出了在1阶泰勒展开法基础上通过界定搜索邻域并采用二分插值搜索方法来精确求取插补点参数的改进方法。该方法充分利用了泰勒展开法的初始精度和NURBS曲线的局部线性特征。试验表明,平均位移相对误差降低至6.46×10-11,且每个插补周期的搜索不多于3次,从而有效抑制了速度波动,实现了高速平稳加工。

The first or the second order Taylor expansion is an usual approach for NURBS curve iterative interpolation.The approach always resulted in chord errors and consequent feedrate fluctuation and motion impact.Therefore,after analyzing the three reasons that cause Taylor-expansion-based interpolation errors,an improved approach was proposed to deriving accurate interpolation points by means of search neighborhood determination and binary interpolation search based on the first Taylor expansion.The proposed approach made full use of both origin accuracy of the first Taylor expansion and the local linear characteristics of NURBS curve.The interpolation test shows the average relative displacement error is decreased to 6.46×10-11.Moreover,the search times are no more than three in every interpolation period.Thus,feedrate fluctuation is greatly suppressed and high speed and high stability machining is realized.