An Analytical Representation of Chip Area for Corner-Radiused Tools Under Both Depth-of-Cut and Feed Variations

Abstract

The operation of corner-radiused tools under both depth-of-cut and feed variation is a situation that occurs for many processes (e.g., straight turning, contour turning, boring, and face-milling) and under many practical conditions. A new chip-area expression is formulated by applying a rotational transformation to the chip-area geometry. Results obtained with this new representation are compared to an exact area computation algorithm based on geometric shapes. The new representation and its associated expressions are far more simple than those of the exact area representation. The errors introduced by the new representation have been analyzed and found to be very small. To increase the accuracy of the expressions for numerical applications, numerical and analytical error-compensation functions have been developed. The latter makes the expressions exact, at the expense of increased algorithmic content, whereas the former is less algorithmic with negligible errors even under extreme conditions. [S1087-1357(00)00404-4]