A new method for modeling edges of a toroidal cutting surface of solid ceramic end mills

Solid ceramic mills with a toroidal cutting surface are playing an important, steadily growing role in manufacturing products made of heat-resistant materials. However, properties of these mills have a drawback such as the low strength and, hence, their design requires the absence of zones with high concentration of stresses to reduce the probability of the brittle fracture. In this paper, a new approach to the formation of the cutting edge of solid ceramic end mills has been developed. Unlike the existing approaches, which are based on the shape of the helical groove on the periphery, the new approach is based on the shape of the cutting edge on the toroidal cutting surface determining the shape of the helical surface of the cutter on the radial section. The new method allows finding ranges, in which constant angle cutting edges in the toroidal region exist, and developing multiple new designs of solid end mills with varying combinations of geometric parameters. One of the most important advantages of this method is the ability to determine the ranges, where a smooth cutting edge in all areas of the cutting part of the cutter exists. The derived analytical dependencies can be used to develop new designs of tools of a special shape with a rational combination of geometric parameters of cutting edges with accounting for the radii of the torus surface and the radius of the cutter.