A closed-form solution to the problem of optimal tool-path generation for sculptured surface machining on multi-axis NC machine

The topic of the paper is in the field of sculptured surface machining (SSM) on multi-axis NC machines. It presents novel results of investigation of tool-path generation for sculptured surface machining on multi-axis NC machines. The purpose of the paper is to develop an integral form of solution to the problem of optimal tool-path generation. The concept of time-minimal tool-paths is introduced, as well as the optimization problem being formulated analytically. The problem of optimization is subdivided into the following three partial sub-problems: (a) the problem of local tool-path generation; (b) the problem of regional tool-path generation, and finally, (c) the problem of global tool-path generation. The paper presents a closed-form solution to the first two sub-problems. A solution to the problem of optimal tool-path generation is given in the form of an integral equation. The obtained solution enables one to retain the optimal cutter configuration (i.e., the cutter position, and the cutter orientation), as well as the optimal instant direction of feed-rate at every cutter location-point (further, CC-point).