Control of the Thermal Deformation of a Machine Tool

The study concerns the control of the temperature distribution of a machine tool structure containing several varying heat sources and control sources. For this purpose, the state equations of the machine tool temperature are formulated by utilising the finite element method, and an optimal control sequence is obtained by the linear programming method as a time-optimal control problem. In the case of a very complicated structure of a machine tool, computing time to obtain the control sequence is considerably shortened by limiting reference points in the computation without affecting the accuracy. This method can be applied to a case for shortening the warming-up period of a machine tool as well as for varying heat sources. The validity of the control is experimentally confirmed.