Dynamic Modeling of Aerostatic Spindle With Shaft Tilt Deformation

Abstract

This paper presents a new dynamic model of aerostatic spindle including the journal and thrust bearings. Reynolds equations are used to model the dynamics of a 4-degree-of-freedom (DOF) aerostatic journal bearing and a 3-DOF aerostatic thrust bearing. Finite element model of the spindle shaft is developed based on the Timoshenko beam theory considering the centrifugal and gyroscopic effects and is coupled with the bearing to construct the dynamic model of the whole aerostatic spindle. The effect of shaft tilt motion due to elastic deformation on the dynamic characteristics of the aerostatic bearing is considered for the first time. The finite difference method is used to determine the load capacity and moments provided by the bearings with changing air film thickness due to shaft vibration, and Newmark-β method is used to obtain the dynamic response of the spindle shaft. The simulated natural frequencies of the aerostatic spindle are verified through impact experiments under static and rotating conditions. Based on the developed model, the effects of tool overhang length, rotating speed, air film thickness, and supply air pressure on the frequency response function of the spindle are investigated comprehensively. The proposed dynamic model of the aerostatic spindle is able to provide useful guidance for structure design and process planning for micro-machining.