Modelling, Identification and Control of Thermal Deformation of Machine Tool Structures, Part 1: Concept of Generalized Modelling

With the increasing demand for improved machining accuracy in recent years, the problem of thermal deformation of machine tool structures is becoming more critical than ever. In spite of the effort for improving the thermal deformation characteristics of machine tools at the design stage, there are always some residual errors that have to be compensated for during machining. The design ofa generic multi-axis control system requires the development of two models to estimate the transient thermal load and to estimate the thermal deformation of the structure in real-time. To satisfy the stringent accuracy and stability requirements of these two models, a new concept of generalized modelling is introduced. It combines mathematical modelling with empirical calibration, and is based on the existence of a mathematical similarity between the real process and a simplified model, referred to as the fundamental generalized problem FGP. To obtain an analytical description of the heat transfer and thermal deformation processes in machine tool structures, an analytical solution of the FGP, which consists of an infinite plate with a central ring heat source, is derived using Hankel transformation. Computer-simulated test cases are presented to demonstrate the use of generalized modelling for predicting the transient thermal response in a complex machine tool structure. It was also shown how the generalized model can accurately extrapolate limited measurement data to predict the entire temperature field. The results confirmed that the generalized model can reproduce the accuracy of the finite-element solution, but two orders of magnitude faster.