A Real-Time C³ Continuous Local Corner Smoothing and Interpolation Algorithm for CNC Machine Tools

Linear tool path segments of computer numerical control (CNC) machine tools need to be smoothed and interpolated in order to guarantee continuous and steady machining. However, because of the highly nonlinear relation between arc lengths and spline parameters, it is difficult to develop algorithms to simultaneously achieve real-time corner smoothing and interpolation with high-order continuity, although it is important to guarantee both high calculation efficiency and good dynamic performance of high-speed CNC machining. This paper develops a computationally efficient real-time corner smoothing and interpolation algorithm with C³ continuous feature. The corners at the junction of linear segments are smoothed by inserting Pythagorean-hodograph (PH) splines under the constraints of user-defined tolerance limits. Analytical solutions of the arc length and curvature of the smoothed tool path are obtained by evaluating a polynomial function of the spline parameter. The smoothed tool path is interpolated in real time with continuous and peak-constrained jerk. Simulations and experimental results show that the proposed tool path smoothing and interpolation algorithm can be executed in real time with 0.5 ms control period. Acceleration and jerk continuity of each axis are achieved along the tool path. Comparisons with existing corner smoothing algorithms show that the proposed method has lower jerk than existing C² algorithms and the real-time interpolation algorithms based on the Taylor series expansion.