Paper:

# Compensation of Thermo-Dependent Machine Tool Deformations Due to Spindle Load Based on Reduced Modeling Effort

## Christian Brecher and Adam Wissmann

Laboratory for Machine Tools and Production Engineering, RWTH Aachen University, Manfred-Weck Haus, 19 Steinbachstrasse, Aachen 52074, Germany

This paper presents the continuance of the scientific work on compensation of thermo-dependent machine tool deformations due to spindle load in consideration of rough machining. After the development of an indirect compensation method, based on a transfer function using a third order time delay element, further works have been focused on the reduction of the modeling effort. The reduction of the modeling effort makes the developed compensation approach suitable for the industry. The thermo-dependent behavior of machine tools is strongly non-linear. Hence, modeling in several operating points is essential. Primarily, the investigated machine tool wasmodeled by using six spindle speed levels. Due to different possible torques at every speed level, the power spectrum of the spindle was divided into four power levels. Thus, the starting point was the modeling of thermo-dependent machine tool deformation by executing 24 experiments. The appropriate compensation results were very satisfactory. The aim of the presented work is a compensation result of similar performance achieved by noticeable lower modeling effort. In the first step, the thermal behavior of the investigated milling machine is analyzed. The analysis affects the choice of adequate speed and power levels for modeling. According to previous results, the chosen transfer function is a third order time delay element. The performance of the compensation method based on a reduced number of models is validated on two different speed / power spectra. The final comparison of the compensation results regarding root mean square errors presents the benefit.

*Int. J. Automation Technol.*, Vol.5, No.5, pp. 679-687, 2011.

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