Machine parameter selection for turning with constraints: an analytical approach based on geometric programming

This paper describes the design and development of an analytical tool for the selection of machine parameters in turning. The problem is to determine values for machine speed and feed that minimize the total cost of machining; specifically the costs associated with machining time and cutting tool wear. Geometric programming is used as the basic methodology, and the solution approach for the selection of machine parameters is based on an analysis of the complementary slackness conditions and realistic machining conditions. The quality of the solution is illustrated on several examples and compared to solutions obtained by some optimization methods proposed in the literature. In general, our technique is simple and straightforward and indicates how sensitive the solution is to the machine power consumed and surface finish attained.