A precise direct parametric interpolation method for NURBS-toolpath generation

Non-uniform rational B-spline (NURBS) interpolator has many advantages over conventional linear/circular interpolator. However, as there is a nonlinear corresponding relation between the curve parameter and the arc displacement of the NURBS curve, it is hard to accurately calculate the parameter of the next interpolation point, thus resulting in a deviation between the desired and the actual feed rate, i.e., feed rate fluctuation. A large feed rate fluctuation may cause machine-tool vibration, which is bad for the cutter life and the machining quality. Therefore, aiming at reducing the feed rate fluctuation, this paper presents a high-precision parametric interpolation method, which features a second-order Runge-Kutta algorithm with parameter compensation. First, a second-order Runge-Kutta method is employed to compute the initial interpolation-point parameter. After that, the parameter is compensated using first-order Taylor's expansion of the feed rate-fluctuation function, thus enhancing the calculatio...