Contour Machining Performance Improvement by Smoothing Spatial Piecewise Linear Toolpath and Quasi-Optimal Feed Rate Planning

Currently, not all control systems of multi-axis machine tools and industrial robots are capable of efficiently machining the products with a complex surface shape. The toolpath for such products is usually described by blocks using G01 operator frames, which are short segments. To machine such a contour, it is necessary to periodically decrease the feed rate at the conjugation points of the segments, which leads to a decrease in performance and a lower quality of machining. The study introduces a method to solve the problem: smoothing the toolpath by including spline segments in it. When smoothing, we used a cubic B-spline with five control points, which made it possible for the entire path to have geometric continuity G2. The smoothing scheme enabled us to analytically express the maximum curvature, take into account the specified error in the approximation of the spline construction and the mutual intersection of adjacent curves. Contour machining performance was improved by using a bidirectional frame preview algorithm, which accounted for the specified geometric constraints and chordal spline construction error, as well as limits of the contour rate, acceleration and jerk in each segment of the path. The second-order Runge-Kutta method with a compensation approximation scheme was used for parametric interpolation, which made it possible to reduce fluctuations in the feed rate and positively affected the quality of the machined product surface. The experimental results confirm the correctness of the chosen approach and its validity in the control system for high-speed machining of products with complex surfaces.

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