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Dynamic MRR function optimization using calculus of variations. (English) Zbl 1213.49047
Summary: 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 an efficient tool to concretely optimize the profit of a cutting tool for operation planning and control in modern machining industry with profound insight.
MSC:
49N90 Applications of optimal control and differential games
49L20 Dynamic programming in optimal control and differential games
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