A circumscribed corner rounding method based on double cubic B-splines for a five-axis linear tool path

Linear segments are widely used to describe the tool path in five-axis NC machining. However, the geometrical discontinuity of adjacent segments will inevitably result in the feedrate fluctuation and excessive acceleration, thus deteriorating the machining accuracy and machining quality. In this paper, a new circumscribed corner rounding method for a five-axis linear tool path is proposed based on double cubic B-splines. Compared with commonly used inscribed corner rounding method, the transition curves generated by the circumscribed method have smaller curvatures, which is benefit of improving the feedrate of the corner regions of the tool path. A configuration of control points for the circumscribed corner transition spline is first given, and double cubic B-splines are subsequently employed to smooth the trajectories of the tool tip point and the second point on the tool axis according to the maximum approximation error. Then, based on the parametric synchronization between the bottom and top B-splines, the first and second geometrical derivative continuous conditions of the tool orientation are derived at the junctions between the remaining linear tool path and the transition curves. The proposed corner rounding method is capable of achieving tool orientation continuous change without any iteration, which can be used in a high-efficiency way. Simulations are performed to show the feasibility and efficiency of the proposed method.