Uncertainty analysis of hydrostatic bearing working conditions with experimental, CFD, and analytical approach

Abstract The design and real-time control of hydrostatic bearings (HS) require precise models capable of accurately predicting bearing behaviour under diverse operational conditions. Traditional analytical models have been found to be inadequate to simultaneously estimating critical parameters, including carrying capacity, recess pressure, film thickness, and flow rate. To overcome these limitations, Computational Fluid Dynamics (CFD) has emerged as a powerful tool in recent years. However, the accuracy of operational data used to calibrate the numerical and analytical models significantly influences the propagation of uncertainty. This study focusses on an experimental campaign and the development of a CFD model within the OpenFOAM® environment. Numerical and analytical models were calibrated using various input parameters, such as flow rate and recess pressure, to replicate experimental conditions while accounting for extreme operational scenarios and the inherent uncertainties in the experimental data. The results indicate that although average CFD predictions exhibit consistent errors in estimating operational parameters, the uncertainty ranges of the experimental and numerical data overlap under the conditions examined. On the contrary, analytical predictions show notable discrepancies, even when measurement uncertainties are considered. In particular, recess pressure emerged as the most effective input parameter to accurately estimating carrying capacity. These findings highlight the critical importance of incorporating measurement uncertainties into the calibration of numerical and analytical models for HS bearings, offering valuable information for their precise design and effective real-time control. Moreover, this paper demonstrates how CFD enables the consideration of misalignments measured during experimentation, a factor that is not accounted for in current analytical models.