A Tracking-Based Numerical Algorithm for Efficiently Constructing the Feasible Space of Tool Axis of a Conical Ball-End Cutter in Five-Axis Machining. (December 2019) - Li, Xiangyu; Ren, Junxue; Tang, Kai; Zhou, Yuke
Abstract: To meet the high requirement on cutter stiffness in five-axis machining of complex parts with deep channels, such as an aero-engine blisk, conical ball-end cutter is preferred over the traditional cylindrical cutter as the former can increase the stiffness ten folds or more over the latter of a same size. However, because the shank of conical ball-end cutter is a cone instead of a cylinder, when calculating the feasible space of tool axis (FSTA) for any given center of the ball-end, the line-visibility, which is critically utilized in the case of cylindrical ball-end cutter, is no longer applicable. Currently in practice, the calculation of FSTA for the conical ball-end cutter has to resort to the simplest brute-force approach of checking for collision for every sampled tool axis. This process of exhaustive collision checking is extremely time-consuming and lacks accuracy, as there are typically thousands of center points of ball-end on a five-axis tool path, and for each of them there can be again thousands of sampled tool axes to check for collision, which is itself a very time-consuming task. In this paper, we propose a tracking-based numerical algorithm for constructing FSTA of the conical ball-end cutter amid an obstacle environment defined by freeform surfaces. Our algorithm avoids the time-consuming collision checking by directly tracing out the characteristic curves on the boundary surfaces of obstacles. As a result, it not only tremendously reduces the computing time by only searching around the boundary of FSTA, but also substantially improves the accuracy of the final constructed FSTA as the step size of tracing can be set sufficiently small without increasing much on the computing time. Simulation tests of the proposed algorithm are also reported to validate its time efficiency and accuracy. Highlights: The concept of characteristic points of critical tool axis for conical ball-end tool. An efficient and tracking-based method for finding the characteristic points. A merging method on the Gaussian sphere for constructing FSTA. High efficiency and accuracy in computing FSTA as shown by the experiments.