Non-isometric dual-spline interpolation for five-axis machine tools by FIR filtering-based feedrate scheduling using pseudo curvature under axial drive constraint

Abstract

Due to the nonlinear relationship between workpiece-space and joint-space motions of five-axis machine tools, feedrate scheduling for dual-spline interpolation is acknowledged as a challenging task. Existing methods mainly employ iterative computation, repetitive toolpath discretization, or large feedrate margin, to solve the nonlinear problem. To avoid them, this paper presents a FIR (finite-impulse-response) filtering-based dual-spline interpolation algorithm using pseudo curves. A 3D translational-axis pseudo curve and a 2D rotary-axis pseudo curve are proposed as intermediaries to reduce the dimension of five-axis feedrate-scheduling problem thus figuring out partial nonlinear matters. The FIR filtering is employed to smooth the low-order continuous or even discontinuous axis velocities, to the jerk bounded ones, which further tackles the rest of the nonlinear matters. Although above methods solve the nonlinear issue, they induce new problems which are defined as the filtering-induced-tooltip-contour-error (FITCE) and the filtering-induced-tool-orientation-contour-error (FIOCE) here. To deal with these new problems, two extra constraints, namely the FITCE/FIOCE limitation and a frequency limitation, are added into the interpolation process beyond routine axis drive limitations. Additionally, the presented method does not require constant distance between two splines of the toolpath, which indicates that it is suitable for non-isometric dual-spline toolpath as well. Illustration and experimental tests demonstrate that the presented method merely conducts one-step toolpath discretization without iteration, and performs well in both motion efficiency and smoothness, as well as in real-time capability.