On the B-spline interpolated tool trajectories for five-axis sculptured surface machining

Abstract

B-spline interpolation scheme is now available on modern five-axis Computer Numerical Control (CNC) machine tools. With this newly implemented interpolation scheme, a cutting tool can be directly commanded to trace B-spline trajectories, which approximate ideal 3D curved trajectories, in sculptured surface machining. The approximation of ideal tool trajectories by B-spline interpolated tool trajectories inevitably leads to machining errors, referred to as the geometry-based errors in the present work. It is essential to ensure synchronisation of the movements of the three translational and two rotational joints of a five-axis machine tool to reduce the geometry-based errors. This paper presents an effective method to achieve synchronisation of the machine joint movements. It first fits a 3D B-spline for the three translational joints and then uses a knot inheriting procedure to fit a 2D B-spline for the two rotational joints. Evaluation of the presented method was made through the machining of a typical bi-cubic Bezier surface on a five-axis machine tool capable of performing non-uniform B-spline interpolation. It was found that the resulting geometry-based errors, which were varying along the given isoparametric tool paths, were able to be maintained below 25m.