Design and experimental validation of low stiffness aerostatic thrust bearings

Abstract

Linear aerostatic bearings are frequently used in high precision stages for their advantageous bearing properties, with low friction and absence of stick-slip being most notable. To improve relatively low out-of-plane stiffness of air bearings, pre-loading is applied. A common method of pre-loading is by utilizing vacuum, where a constant vacuum force decreases film height resulting in increased stiffness. Other methods for increasing stiffness are available, which is an active field of research. However, high stiffness results in strong coupling between bearing and running surface, transferring unwanted external vibrations. The amount of vibration transfer is quantified as transmissibility, which is the ratio of displacements between coupled surfaces. This property is frequency dependent. To reduce disturbance from external vibrations, this research focusses on reducing air bearing stiffness by combining pressurized and vacuum bearing pads, which to the knowledge of the author has not yet been researched. To analyse stiffness behaviour, air bearings have been modelled based on Reynolds equation. The effect of a vibrating running surface is modelled by linear perturbation of Reynolds equation. Resulting equations have been solved with a self developed finite volume method code, resulting in air film stiffness and damping as a function of frequency in an computationally efficient manner. Two combinations of thrust and vacuum bearings with a stable low stiffness operating point have been designed with the developed models. By offsetting vacuum and thrust surfaces or by using a micrometer pocket in the thrust bearing surface, vacuum and thrust stiffness cancel out, creating a range of low stiffness between regions with higher stiffness. To validate the models, air bearings have been manufactured. Measurements on restrictor properties have shown the literature model to be invalid for realistic pressure drops. Without taking the measured restrictor behaviour into account, model and measurement will not match. Also shown is that controlling surfaces flatness is essential for predictable bearing behaviour. Performance of available production methods is thoroughly researched. Model and measurement correspondence can only be achieved by taking surface properties into account. Also, the low tip-tilt stiffness of a single air bearing has been found to negatively effect measurements on film height. By using three bearings in the measurement set-up, tip-tilt stiffness has been significantly increased. This reduces measurement uncertainty. By taking these findings into account, excellent agreement between measurements and model has been achieved. This clears the way for development of a low stiffness prototype, combining thrust and vacuum bearings. Ideas on model improvement and prototype development are shared in the recommendations.