Lubrication-film height imaging for hydrostatic bearings with fluorescence

Abstract

The performance of hydrostatic bearings is in part decided by their lubrication-film height shape. Imaging the shape can be done by dissolving fluorescent dyes in the layer. However, current imaging techniques are rooted in heuristics, and as such, their physics, design parameters, and error sources are not quantitively understood. To fully grasp and consequently design the ultimate measurement system, the governing equation—the fluorescent radiative transfer equation—is solved analytically for a plane-parallel system. The new solution method assumes that fluorescent radiative transfer is well-described by the first two photon generations. Verification is done experimentally and by a concurrent Monte Carlo method. The model also successfully predicted the response of a real measurement setup. Further model analysis led to the understanding of factors such as: camera positioning; light source design; and the effect of the reflective background on which the lubrication layer lays. The insights suggest a practical implementation for a dynamic imaging setup.