Planar tool radius compensation for CNC systems based on NURBS interpolation

This paper introduces the realization of a tool radius compensation algorithm for NURBS trajectory. First, a single-segment NURBS trajectory tool radius compensation algorithm is developed. Different from the straight line and arc trajectory, the self-intersection phenomenon is prone to happen when calculating a single NURBS tool center trajectory, and the self-intersection will cause the overcut of workpiece. To avoid this situation, the algorithm introduced in this paper can detect whether the NURBS tool center track has caused overcut, and deal with the self-processing. Second, the tool radius compensation algorithm with multi-segment NURBS trajectory is implemented. The focus of this part is the tool radius compensation of the trajectory transfer, and the trajectory transfer is divided into two types: the extension type and the shortened type. For the shortened type transfer, cross-processing is needed to avoid the overcut of workpiece at the transfer. When calculating the tool radius compensation of the shortened type, we not only need to find the intersection of the tool center trajectory of two adjacent NURBS curves, but also need to select the intersection we need when a number of intersections exist. For the extension type transfer, in order to ensure the continuity of the tool center trajectory, we need to extend the tool center trajectory or add arc-segment at the transfer. The proposed algorithm can automatically decide where to extend the tool center trajectory or add arc-segment to achieve the best efficiency. Finally, the algorithm can output the calculated NURBS tool center trajectory in the form of linear segment interpolation G code or NURBS interpolation G code according to the processing needs. Simulations on VERICUT and experiments on three-axis CNC machine tool shows the effectiveness and validation of the tool path compensation algorithm.