Optimal selection of machining rate variables by geometric programming

Abstract

The selection of economically optimal machining rate variables, i.e. cutting speed and feed rate, is of major importance in the field of metal cutting. In this paper, apart from the conventional methods used for optimization in machining economics, geometric programming, a relatively new non-linear programming technique, is employed to optimize the constrained unit cost problem in turning. The cutting power available from the machine tool and the permissible CLA value of surface roughness are used as the forced constraints in the primal programme. Initially, the primal and dual programmes are formulated. Furthermore, a numerical example is presented to illustrate the application of geometric programming which has been proved successful. It is pointed out that geometric programming may be also used for optimization of unit cost in machining processes other than turning under the assumption that the imposed restrictions, discussed in this paper, are valid.