A polynomial equation-based interpolation method of NURBS tool path with minimal feed fluctuation for high-quality machining

Due to the approximation errors of interpolation methods in non-uniform rational b-spline (NURBS) interpolation, feed fluctuation is inevitable, which has great effects on the machining quality and should be minimized. Based on the idea of zero feed fluctuation, a polynomial equation-based interpolation method of NURBS tool path is proposed in this paper. Firstly, a polynomial equation with respect to the curve parameter increment is formulized according to the sampling step size, which is determined by the scheduled feedrate, acceleration, and jerk. Then, Newton’s method is utilized to solve the high-degree polynomial equation with taking both convergence rate and computational load. In order to improve the computing efficiency in real-time interpolation, a fast-evaluation and derivation algorithm is proposed, which uses the Taylor series expansion to accelerate the calculation of any order derivatives of NURBS. Simulations are conducted among the proposed method and the chord-tracking algorithm (CTA) method, and the results of each method are compared on the basis of computing time and feed fluctuation, which shows that the proposed method is better than the CTA method. Experiment is also conducted to verify the feasibility and applicability of the proposed method in practical application.