Upper bound analysis of oblique cutting with nose radius tools

Abstract

A generalized upper bound model for calculating the chip flow angle in oblique cutting using flat-faced nose radius tools is described. The projection of the uncut chip area on the rake face is divided into a number of elements parallel to an assumed chip flow direction. The length of each of these elements is used to find the length of the corresponding element on the shear surface using the ratio of the shear velocity to the chip velocity. The area of each element is found as the cross product of the length and its width along the cutting edge. Summing up the area of the elements along the shear surface, the total shear surface area is obtained. The friction area is calculated using the similarity between orthogonal and oblique cutting in the ‘equivalent’ plane that includes both the cutting velocity and chip velocity. The cutting power is obtained by summing the shear power and the friction power. The actual chip flow angle and chip velocity are obtained by minimizing the cutting power with respect to both these variables. The shape of the curved shear surface, the chip cross section and the cutting force obtained from this model are presented.