NURBS Interpolator with Adaptive Smooth Feedrate Scheduling and Minimal Feedrate Fluctuation

Abstract

For an effective NURBS interpolator, generating the smooth feedrate profile and minimizing the feedrate fluctuation are two main tasks, which have a great influence on the machining quality. In this paper, a NURBS interpolator is proposed to solve the problem with offline-online two stages, which contain curving splitting, feedrate scheduling, and real-time interpolation modules. At first, in offline module, the limited feedrate of the curve is calculated with consideration of geometric characteristics and dynamic constraints, and the curve is split into several segments according to the key regions. Thus the necessary information is stored. Then the feedrate scheduling algorithm is applied with constant feedrate scheduling method at each segment, where tangential acceleration and jerk are taken into consideration to generate an adaptive smooth S-type feedrate profile. Moreover, in real-time interpolation module, an average feedrate calculation method is proposed to determine the sampling step size. And to minimize the feedrate fluctuation, a double interpolation algorithm based on the cosine theorem is presented, which use the second-order Taylor’s expansion method two times in one interpolation period. Finally, simulations and experiments are conducted to verify the performance of the proposed interpolator.