Roll Vibration Analysis of Planar Aerostatic Bearings through a Distributed Spring Model

Abstract

The aerostatic bearings used in guide ways in ultra precision motion stages can provide both normal stiffness and roll stiffness, which are critical to the dynamic characteristics and control of systems. The normal stiffness has been widely investigated so far, but the roll one has seldom been studied. A new method for analyzing the roll stiffness is proposed, in which the aerostatic bearing is modeled as a set of distributed springs. The stiffness distribution is obtained by using the derivate of the pressure distribution with respect to the air gap. All the distributed springs are then integrated by using the presented transformation and it leads to an equivalent spatial spring which contains both the normal stiffness and the roll stiffness. A planar aerostatic bearing is taken as an example to illustrate the procedure of the calculation. The proposed method can be used to predict the vibration characteristics of various kinds of aerostatic bearings under working conditions.