Geometric definition, rapid prototyping, and cutting force analysis of cylindrical milling tools with arbitrary helix angle variations

Abstract

In this work, a method is developed for geometric definition and analysis of cylindrical milling tools having various free-form variations of helix angle. The method is based on replicating a position vector on each cutting edge to generate a point set for the whole tool envelope using piece-wise rotation and magnification matrices which are varied according to mathematical laws describing the intended variable shape of the tool. The computed point sets are applied in additive manufacturing of samples of such tools having non-conventional shape features by transforming the point sets to stereolithography formats that are sliced to guide the 3D-printing processes. This manufacturing route that simplifies the realization of arbitrary helix profiles on milling tools is a major contribution of this work since such tools are gaining popularity for their passive damping of vibrations and reduction of cutting forces but are notoriously difficult to manufacture, limiting their exploitation. Analyses are shown about the effects of the considered variable profiles on milling cutting force. These suggest that cutting forces can be greatly suppressed by the proposed free-form helix angle variations. For example, relative to a conventional fixed helix tool of same mean helix angle, the innovative tools recorded 40.33%–84.42% and 60.53%–67.81% force reductions at axial depths of cut of 1 and 5 mm. This demonstrates that innovative variable tool profiles which can be realized through the simplified rapid prototyping technique are promising for advanced sustainable manufacturing of parts with preferred surface conditions.