Shaping quasi-helical surfaces by means of disk tools

Abstract

The machining of chip channels in conical cutting tools with helical teeth (face mills, countersinks, or reamers) by means of disk tools (mills and grinding wheels) involves the formation of quasihelical sur� faces with variation in the face cross section over the length of the part. Shaping these surfaces is very diffi� cult. One possibility is to produce an acceptable chan� nel profile directly in the machine tool by trial passes, with change in the setup and with selection of the shape of the machining tool. Standard biangular asymmetric mills are most often used as the last tool. Analytical methods permitting the determination of the resulting cross section of the machined surface at the design stage are not sufficiently developed for practical purposes. In the present work, we consider the iterative shaping of quasihelical surfaces, for the example of the machining of chip channels in conical cutting tools with helical teeth by means of a biangular asymmetric mill. In this approach, two conjugate surfaces are formed in the relative helical motion of a disk tool: the tool's machining surface; and the machined surface of the part. These surfaces touch along the contact line, any point of which is simultaneously on the surface of the tool and the part. Each conjugate point is charac� terized by a common normal and a common tangent. In machining, when any point of the tool surface is on the contact line, its trajectory is tangential to the tool surface. Hence, if the trajectory of some point of the tool surface at a given time is tangential to that sur� face, this point belongs to the track left by the tool as a result of its specified helical motion. For a quasihelical surface, the next point on that track will be formed by another point of the tool sur� face. The section of the track bounded by the surface of the part (in the present case, its conical section) is the conical quasihelical surface obtained. If we describe the working section of the tool surface in dis� crete (point) form and we find the conjugate points, we may determine the contact line at each instant of rela� tive tool motion.