Mathematical modeling and experimental testing of high-speed spindle behavior

Abstract

The prediction of thermo-mechanical behavior of the spindle is essential for machining precision. Particularly, the characteristics of high-speed spindles depend on their thermal behavior. The heat generated on the bearings transfers to the spindle and surrounding air, thus causing the thermal expansion of spindle elements. This paper presents the thermo-mechanical model of the spindle with ball bearings with angular contact. In this paper, the main source of heat on the spindle occurs due to friction torque on bearings with angular contact. The presented model is based on the mechanical model of the bearing and the numerical model (FEM) of the spindle. The proposed solution considers non-stationary change of temperature, thermal deformation, and bearing stiffness, based on the angular position of the ball. Predicting of bearing characteristics has been used to establish the change in static stiffness of the spindle nose as well as the effect of thermal expansion on the machining accuracy. In order to validate the model, experiments have been performed for different speeds. The paper establishes that the predicted temperatures on the spindle and spindle nose stiffness under different speeds correspond to those measured experimentally. The results of the experiment have shown that the increase of spindle speed causes the increase of bearing temperature, thus leading to the expansion of bearing elements. Additionally, these changes cause increased stiffness of the bearing, which in turn increases the stiffness of the spindle nose.