GEOMETRICAL DESIGN OF CUTTING TOOLS WITH SURFACES OF REVOLUTION FOR HELICAL SURFACES

Machining of helical surfaces of constant pitch with tools bounded by surfaces of revolution is accompanied by generation errors due to impe rfections of the effective cutting edge, relative positioning errors o r kinematics of the machine tool. Therefore, the development of algori thms for the geometrical modelling of helical surfaces could be very u seful. In fact, it is possible to model geometrically the effective ge nerated surface on the workpiece when the cutting edge is known at dis crete points, for instance, by physical measurement. Based on the prin ciple of minimal distance first proposed in a previous work of the fir st author, a numerical method is developed that provides a very simple , yet very accurate, means to resolve both the direct and the inverse problem in the machining of helical surfaces with milling cutters and end mills. Thus, the profile of the cutting tool can be determined eve n for surfaces on the workpiece of arbitrary shape known either analyt ically or at discrete points. More importantly, it can be established either in the design or the exploitation stage what the accepted error s on the tool are (due to sharpening or wear), such that the tolerance s on the surface to be machined are still met.