The Shear-Angle Relationship in Metal Cutting

Abstract The several analytical solutions that have been presented for the shear angle in metal cutting are described briefly and the underlying assumptions critically discussed. The friction process that obtains in cutting is considered in detail and it is shown that a variable restraint and accompanying variation in the effective hardness of the metal cut constitute a major difference between ordinary friction and that between chip and tool. This variation in relative restraint and effective hardness accounts for the wide variation of coefficient of friction with rake angle observed in metal cutting. Furthermore, this variable restraint constitutes a significant connecting link between shear and friction processes, and is responsible for the shear plane not being in the direction of maximum shear stress in the general case. These new concepts are incorporated with the best features of previous work, and an equation is presented, in which the angle between the shear plane and direction of maximum shear stress figures prominently. The new equation for shear angle is illustrated and discussed with the aid of experimental cutting data covering a wide range of operating conditions.