An efficient and accurate interpolation method for parametric curve machining

Abstract

A subsection interpolation method based on the curve curvature threshold is proposed to resolve the incompatible problem of machining accuracy and machining efficiency in parametric curve machining. In the pre-interpolation stage, the curve curvature threshold is calculated based on geometric and kinematic constraints. The subsection interpolation key points and their nominal velocities are then determined from the curvature threshold points and the start and end points of the curve, and the arc length of each subsegment can be calculated based on the adaptive Simpson method. As a result, the S-type speed planning algorithm and the bidirectional speed scanning algorithm are used to update and realize the global speed curve to reduce the speed fluctuation. In the real-time interpolation stage, the curve interpolation parameters are calculated using the parametric modified second-order Runge–Kutta method, which could improve the interpolation accuracy significantly and also shorten the interpolation time. Finally, it is found using numerical cases that the proposed method can smooth the overall interpolation speed, reduce the speed fluctuation effectively and improve the real-time performance of the interpolation.