Generalised NURBS interpolator with nonlinear feedrate scheduling and interpolation error compensation

Abstract

Current nonuniform rational B-spline interpolating methods encounter problems pertaining to the interpolating error, feedrate profile, and machining efficiency; the optimal feedrate profile may not be obtained owing to the complex kinematics of multi-axis machine tools with hybrid structures. To address these problems and obtain an optimal feedrate profile with minimum machining time, this paper establishes a generalised representation for the nonlinear feedrate scheduling model, with static and dynamic feedrate constraints, through a numerical convex transformation. Based on the generalised model representation, a time-optimal feedrate profile can then be solved globally for both series- and parallel-structured mechanisms without problems caused by profile linear simplification or imprecise feedrate evolution. Considering the feedrate fluctuation problem caused by the difference between the theoretical arc length of the curve interpolation and the actual tool path, this paper proposes a novel co-lateral triangle deviation (CTD)-based parameter compensation interpolation algorithm. With the CTD calculation, which is related to the actual feed motion in real time, the proposed interpolation algorithm can determine the interpolating compensation distance for each interpolating segment and obtain the interpolation points using a second-order Taylor series expansion with a minimal interpolating error. Carried on a hybrid mechanism with complex kinematic constraints, the experimental and comparison results validated the effectiveness of the proposed method in feedrate scheduling and feedrate fluctuation reduction.