MODELING, IDENTIFICATION AND CONTROL OF THERMAL DEFORMATION OF MACHINE-TOOL STRUCTURES, PART 1 - CONCEPT OF GENERALIZED MODELING

With the increasing demand for improved machining accuracy in recent y ears, the problem of thermal deformation of machine tool structures is becoming more critical than ever. In spite of the effort for improvin g the thermal deformation characteristics of machine tools at the desi gn stage, there are always some residual errors that have to be compen sated for during machining. The design of a generic multi-axis control system requires the development of two models to estimate the transie nt thermal load and to estimate the thermal deformation of the structu re in real-time. To satisfy the stringent accuracy and stability requi rements of these two models, a new concept of ''generalized modelling' ' is introduced It combines mathematical modelling with empirical cali bration, and is based on the existence of a mathematical similarity be tween the real process and a simplified model, referred to as the fund amental generalized problem FGP. To obtain an analytical description o f the heat transfer and thermal deformation processes in machine tool structures, an analytical solution of the FGP, which consists of an in finite plate with a central ring heat source, is derived using Hankel transformation. Computer-simulated test cases are presented to demonst rate the use of generalized modelling for predicting the transient the rmal response in a complex machine tool structure. It was also shown h ow the generalized model can accurately extrapolate limited measuremen t data to predict the entire temperature field The results confirmed t hat the generalized model can reproduce the accuracy of the finite-ele ment solution, but two orders of magnitude faster.