A generalized modelling methodology for optimized real-time compensation of thermal deformation of machine tools and CMM structures

Abstract

Thermal deformation of the machine tool structure plays a critical role in controlling the level of machining accuracy. Since thermally-induced errors cannot completely be eliminated at the design stage, the use of indirect compensation systems emerges as the most economical and inevitable course of action. These systems are based on two different, but yet complimentary, approaches; the use of empirical compensation function and the on-line execution of numerical simulation models. Recognizing the existence of a mathematical similarity between the real process and a simplified dynamic model, the generalized modelling approach is proposed to resolve the main problems associated with existing indirect compensation methods. It is demonstrated that the proposed methodology can be used to identify the true global optimum position and minimum number of the temperature sensors with the highest contribution to the compensation function. These issues have been the focus of a recent research activity world-wide and remain the main obstacles limiting the acceptance of the empirical compensation approach by industry. The use of the generalized modelling method to improve the thermal deformation predictions, through filtering out random temperature measurement errors, is also demonstrated. The application of the generalized modelling method to compensation systems based on numerical simulation is discussed. It is shown that the method can reproduce the accuracy of the finite-element solution, but two orders of magnitude faster, for on-line prediction of the transient temperature field in the machine tool structure. The use of the generalized modelling method to test and to improve the accuracy of finite-element models is also discussed.