The Mechanics of Three-Dimensional Cutting Operations

Abstract The oblique tool, which has a cutting edge that is inclined to the direction of motion of the workpiece at an angle other than 90 deg, represents the most general type of cutting tool. The more complex three-dimensional tools of production may be related to an equivalent oblique tool having a given inclination angle and a corresponding effective rake angle. In this investigation the chip-flow direction and the velocity and force relations for an oblique cutting tool were compared with experimental results. The angle between the direction of chip flow and a normal to the cutting edge was found to be approximately equal to the inclination angle for ordinary friction conditions, but to be progressively larger than the inclination angle as the friction decreased. The effective rake angle for an oblique tool is found to increase without a corresponding decrease in the included tool angle. The direction of the force component in the tool face was found to deviate considerably from the chip-flow direction, particularly for larger values of inclination angle. However, the directions of maximum shear stress and shear strain on the shear plane were found to be nearly colinear for values of inclination up to 30 deg. The analytical consequences of these observations are discussed. The method of applying the oblique-tool results to three-dimensional tools is illustrated by three examples involving a lathe tool, a face-milling cutter, and a drill point. The drill-point discussion is extended to illustrate the value to be derived from a qualitative application of basic oblique-tool mechanics to the interpretation of drill test data.