关键词: 非均匀有理B样条, 插补, 数控系统, 速度波动, 进给速度

Abstract: Aim at the problems of feedrate fluctuation and computational efficiency in NURBS interpolation,a double secant interpolation algorithm of NURBS and a fast calculation and derivation algorithm of NURBS are proposed.In the double secant interpolation algorithm,based on the first interpolation by the second order Taylor method,the secant lines,which are generated by the required length for zero-feedrate fluctuation,are used to approximate the desired NURBS curve.In the fast calculation and derivation algorithm,all the nonzero derivatives of the numerators and denominators at knots in NURBS expression are calculated and stored in advance,then the any order derivative of NURBS can be fast calculated in real-time interpolation by Taylor formula,thus the computations of B-spline basis functions can be avoided,and the computational efficiency can be improved.Finally,a NURBS interpolator based on the proposed algorithms is implemented on a CNC platform developed by the authors,and the feasibility and applicability are verified by simulation analysis and experimental results.

Key words: NURBS, interpolation, CNC, feedrate fluctuation, feedrate