Asymmetrical pythagorean-hodograph spline-based C4 continuous local corner smoothing method with jerk continuous feedrate scheduling along linear toolpath

In computer numerical control systems, linear segments, which are generated by computer-aided manufacturing software, are the most widely used toolpath format. Since the linear toolpath is discontinuous at the junction of two adjacent segments, the fluctuations on velocity, acceleration and jerk are inevitable. Local corner smoothing is widely used to address this problem. However, most existing methods use symmetrical splines to smooth the corners. When any one of the linear segments at the corner is short, to avoid overlap, the inserted spline will be micro, thereby increasing the curvature extreme of the spline and reducing the feedrate along it. In this article, the corners are smoothed by a 𝐶4 continuous asymmetric Pythagorean-hodograph (PH) spline. The curvature extreme of the proposed spline is investigated first, and 𝐾=2.5 is determined as the threshold to constarin the asymmetry of the spline. Then a two-step strategy is used to generate a blended toolpath composed of asymmetric PH splines and linear segments. In the first step, the PH splines at the corners are generated under the premise that the transition lengths do not exceed half of the length of the linear segments. In the second step, the splines at the corners are re-planned to reduce the curvature extremes, if the transition error does not reach the given threshold and there are extra linear trajectories on both sides of the spline trajectory. Finally, the bilinear interpolation method is applied to determine the critical points of the smoothed toolpath, and a jerk-continuous feedrate scheduling scheme is presented to interpolate the smoothed toolpath. Simulations show that, under the condition of not affecting the machining quality, the proposed method can improve the machining efficiency by 7.84% to 23.98% compared to 𝐺3 and 𝐺4 methods.

Time-optimal Feedrate Scheduling with Actuator Constraints for 5-axis Machining

Cycle time minimization is one of the major goals that many manufacturers are eager to achieve. Maximizing feedrate is the direct solution, however, physical motions need to be under the specified motion limits to avoid high-frequency vibration, causing machining error. In this paper, a time-optimal feedrate scheduling approach for 5-axis G1 toolpath is presented for 5-axis machining. A quintic B-spline corner smoothing method is utilized to smoothen sharp corners in the toolpath. Then, the S-shape feedrate profile of each block is optimized under the actuator motion constraints, with the objective of minimizing the cycle time. Particle swarm optimization (PSO) is used to provide the optimized solution. Experiments are conducted to validate the proposed approach and the results are compared with two other existing approaches. It is found that the proposed method can achieve shorter cycle time and less contour errors, showing the effectiveness of the proposed approach.

Using Fuzzy Control for Feedrate Scheduling of Computer Numerical Control Machine Tools

In industrial processing, workpiece quality and processing time have become important issues lately. Fortunately, dynamic cutting feedrate scheduling has been proposed to improve machining accuracy and decrease cutting time. Studies have shown that the curvature and cutting feedrate significantly influence the machining accuracy. Therefore, the present study proposes a fuzzy control system for feedrate scheduling based on the curvature and curvature variation. The proposed system is implemented in actual cutting, and an optical three-dimensional scanner is performed as a verification to measure the cutting trajectory of the workpiece. Experimental results prove that the proposed fuzzy control system for dynamic cutting feedrate scheduling increases the cutting accuracy by 43% under the same cutting time; moreover, it decreases the cutting time by 49% under the same cutting accuracy.