Modelling, identification and control of thermal deformation of machine tool structures, part 2: Generalized transfer function

With the ever increasing demand for higher machining accuracy at lower cost, thermal deformation of machine tool structures has to be minimized at the design stage, and compensated for during operation. To compensate for this type of error, two real-time process models are required to identify the magnitude of the transient thermal load and to estimate the relative thermal displacement between the tool and the work piece. Special considerations should be given to the solution of the first ill-posed inverse heat conduction model IHCP. In this paper, the concept of generalized modelling is extended to the thermal deformation problem. The results of this analysis is used to develop expressions for the generalized transfer functions of the thermal, and thermal deformation response of the machine tool structure. These transfer functions are the basic building blocks for real-time solution of the IHCP and then the deformation problem. The latter acts as a feed-back signal to the control system. Finite element simulation of the temperature field and the thermal deformation of a machine tool structure confirmed that the generalized transfer function approach cart reproduce the accuracy of the finite element model but two orders of magnitude faster.