The improved NURBS-based C2 PH spline curve contour following task with PDFF controller

Abstract

In this paper, using the specifications of nodal points on a nonuniform rational B-spline (NURBS) curve of three degrees with respect to NURBS curve parameter and defining the coefficients for the velocity and acceleration vectors on these points, a new method is presented to design a tool path via C2 PH spline curves. Values of the velocity/acceleration vector coefficients corresponding to the nodal points on the original NURBS curve are computed by pattern search algorithm. To this end, the normal distance between the constructed C2 PH spline curve and its corresponding original NURBS curve is considered as the objective function. Using combination of the time-dependent feed rate interpolation in the acceleration/deceleration phase of the motion and the constant feed rate interpolation in the middle region of the motion, the position commands of the designed NURBS-based C2 PH spline curve are generated. Several improved NURBS-based C2 PH spline curve following tasks were implemented with pseudo-derivative feedback feed forward (PDFF) controller. The experimental and simulation results confirm that the devised interpolator with designed PDFF controller is not only feasible for machining the complicated tool path represented in the improved NURBS-based C2 PH spline form but also yields satisfactory contouring performance under variable feed rate.