Evaluation of machine tool dynamics in dry gear hobbing considering time-varying thermal effects

Effective stability analysis strongly depends on accurately predicting machine tool dynamics. However, the nonlinear thermal effects during the machining operations present a significant challenge to accurately modeling the machine tool dynamics. To this end, the evolution of the machine tool dynamics under the thermal growth during the dry gear hobbing process is investigated, and a rapid evaluation model of the temperature-dependent dynamics is developed. Firstly, a preliminary test was conducted to explore thermal effects on the machine tool dynamics. Then, the free vibrations at the spindle nose during the hobbing operations were filtered, and the corresponding modal parameters were estimated. Subsequently, the influence of temperature rise on the modal parameters is analyzed. The results show that the first- and third-order natural frequencies increase by 142 and 95 Hz, respectively, and the damping ratios for all modes are reduced with the machine tool temperature rise. Finally, the relationship between the feature temperatures and modal parameters is described using the multi-output Gaussian Process regression (MOGPR) model. The overall prediction accuracy is 95.6 %, and the relative errors in the test data set are within 10 %. The findings can provide an essential basis for the machining stability analysis of dry gear hobbing.