Title: A precise direct parametric interpolation method for NURBS-toolpath generation

Authors: De-ning Song; Zhen-yuan Jia; Jian-wei Ma; Ning Zhang; Li-kun Si

Addresses: Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China ' Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China ' Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China ' Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China ' Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China

Abstract: Non-uniform rational B-spline (NURBS) interpolator has many advantages over conventional linear/circular interpolator. However, as there is a nonlinear corresponding relation between the curve parameter and the arc displacement of the NURBS curve, it is hard to accurately calculate the parameter of the next interpolation point, thus resulting in a deviation between the desired and the actual feed rate, i.e., feed rate fluctuation. A large feed rate fluctuation may cause machine-tool vibration, which is bad for the cutter life and the machining quality. Therefore, aiming at reducing the feed rate fluctuation, this paper presents a high-precision parametric interpolation method, which features a second-order Runge-Kutta algorithm with parameter compensation. First, a second-order Runge-Kutta method is employed to compute the initial interpolation-point parameter. After that, the parameter is compensated using first-order Taylor's expansion of the feed rate-fluctuation function, thus enhancing the calculation precision of the next interpolation point parameter. Experimental results demonstrate the advantage of the presented method.

Keywords: parametric interpolation; NURBS interpolator; feed rate fluctuation; high-precision machining.

DOI: 10.1504/IJISE.2019.097743

International Journal of Industrial and Systems Engineering, 2019 Vol.31 No.2, pp.278 - 286

Received: 08 Feb 2017
Accepted: 02 Jun 2017
Published online: 07 Feb 2019 *

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