A novel time-optimal linear toolpath smoothing method based on airthoid and circular splines for CNC machining

Linear commands need to be smoothed by inserting high-order continuous splines at corners to eliminate the tangential discontinuities of connection points. Although several local smoothing methods have been developed, it is still a challenge to improve the machining efficiency further, when following the transition spline with the predefined fixed proportion constraints. In fact, the curvature distribution of the transition spline has a direct impact on the transition velocity and machining efficiency. This article presents a real-time local smoothing method with curvature-optimized transition splines to smooth linear commands. The designed transition spline, composed of a biairthoid spline and a circular segment, is analytically determined by maximizing the allowable velocity and staying within the predefined geometric constraints. As a result, the curvature increment induced by only biairthoid splines is significantly prevented, and thus, faster transition motion is gracefully attained. With the analytical expression of the arc length and curvature extreme, it is friendlier to the CNC system for real-time executing smooth motion. Simulations and experiments demonstrate that the proposed method can shorten the machining time by more than 8% when compared to the traditional only biairthoid splines.