Abstract
Designing the optimal control for a machine tool necessitates a mathematical model of the cutting process. In the present paper, a flank-wear model was developed for a carbide tool used in steel turning. It yields the relation between the process parameters (cutting speed, feed and depth of cut) on the one hand, and the width of the wear land on the other. In the second stage—the optimization proper—the problem consists of optimizing a non-linear system with the initial, and part of the final, conditions known, and the terminal time not given explicitly. Complexity was reduced by converting from time- to path-derivatives, and the problem was solved using the gradient method, yielding cost differences which are negligible compared with the conventional method. To complete the picture, a motor control system was sought minimizing the error in obeying the speed change command on the one hand, and the path error during simultaneous operation of several feed spindles on the other.
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