Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 671062, 12 pages
Research Article

Dynamic MRR Function Optimization Using Calculus of Variations

Department of Information Management, Yu Da University, Miaoli County 361, Taiwan

Received 19 February 2010; Accepted 22 April 2010

Academic Editor: Jyh Horng Chou

Copyright © 2010 Tian-Syung Lan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A dynamic machining model to optimize the control of material removal rate (MRR) for a cutting tool undergoing the considerations of fixed tool life and maximum machining rate is established in this paper. This study not only applies material removal rate mathematically into the objective function, but also implements Calculus of Variations to comprehensively optimize the control of material removal rate. In addition, the optimal solution for the dynamic machining model to gain the maximum profit is provided, and the decision criteria for selecting the optimal solution of the dynamic machining model are then recommended. Moreover, the computerized analyses to simulate both the dynamic and traditional machining models for a numerical example are also promoted. This study definitely contributes an applicable approach to the dynamic function of material removal rate and provides the efficient tool to concretely optimize the profit of a cutting tool for operation planning and control in modern machining industry with profound insight.