Constrained Cutting Rate-Tool Life Characteristic Curve, Part 1: Theory and General Case

[+] Author and Article Information
C. L. Hough

Dept. of Mechanical Engineering, Texas A&M University, College Station, Texas

Y. Chang

Dept. of Mechanical Engineering, The University of Suwon, Korea

J. Manuf. Sci. Eng 120(1), 156-159 (Feb 01, 1998) (4 pages) doi:10.1115/1.2830092 History: Received October 01, 1993; Revised January 01, 1997; Online January 17, 2008


The concept of a cutting rate-tool life (R-T) characteristic curve is extended to the general machining economics problem (MEP) with a quadratic-logarithmic tool life and constraint equations. The R-T characteristic curve presents the general loci of optima, which is useful in selecting optimal parameters for multiple machining conditions. The necessary and sufficient conditions for the global optimum of the unconstrained MEP are presented. These conditions are equivalently applied to the concept of the constrained R-T characteristic curve. In terms of quadratic geometric programming the objective function and constraints of the general MEP are called as quadratic posylognomials (QPL). The QPL problems are classified as convex and nonconvex and the convexity is determined by the second order terms of the tool life model. Nonlinear programming and an exhaustive method are demonstrated to determine the R-T characteristic curve for three cases of posynomial, convex QPL, and non-convex QPL problems.

Copyright © 1998 by The American Society of Mechanical Engineers
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