Upper Bound Analysis of Turning Using Sharp Corner Tools

Abstract

A generalized upper bound model of turning operations using flat-faced sharp corner tools with both the side and end cutting edges engaged in cutting is described. The projection of the uncut chip area on the rake face plane is divided into a few regions separated by lines parallel to the chip flow direction at transition points. The area of each of these regions is transformed to the area of the corresponding regions of the shear surface using the ratio of the shear speed to the chip speed. Summing up the area of these regions, the total shear surface area is obtained. The tool-chip contact length at vertices is obtained from the length along the shear surface using the similarity between orthogonal and oblique cutting in the “equivalent” plane (the plane formed by the cutting velocity and chip velocity). Knowing the tool-chip contact length, the friction area is calculated. The chip flow angle and chip speed are obtained by minimizing the cutting power with respect to both these variables. Comparison of the chip flow angle predicted by the current model with the chip flow angle measured by direct high speed photography of the chip motion over the tool rake face shows good correlation between the two for various tool geometries and cutting conditions. The shape of the shear surface and the chip cross section predicted by the model are also presented.

Keywords:

• Upper bound analysis
• Chip flow angle
• Sharp corner tools
• Triangular form cutting tools

Acknowledgment

The authors would like to thank Sandeep Sachidanandan and Rajesh Singh for help in conducting the experiments used in this study. This material is based partly upon work supported by the National Science Foundation under Grant No. EPS-0236913 and matching support from the State of Kansas through Kansas Technology Enterprise Corporation.