Kriging Approach Dedicated to Represent Hydrodynamic Bearings

Abstract

The mathematical modeling of journal bearings has advanced significantly since the Reynolds equation was first proposed. Advances in the processing capacity of computers and numerical techniques led to multi-physical models that are able to describe the behavior of hydrodynamic bearings. However, many researchers prefer to apply simple models of these components in rotor-bearing analyses due to the computational effort that complex models require. Surrogate modeling techniques are statistical procedures that can be applied to represent complex models. In the present work, Kriging models are formulated to substitute the thermohydrodynamic (THD) models of three different bearings found in a Francis hydropower unit, namely a cylindrical journal (CJ) bearing, a tilting-pad journal bearing (TPJ) bearing, and a tilting-pad thrust (TPT) bearing. The results determined by using the proposed approach reveal that Kriging models can be satisfactorily used as surrogate THD-models of hydrodynamic bearings.

A state-of-the-art review on uncertainty analysis of rotor systems

“…It should be noted that the Kriging surrogate is a method of interpolation based on the Gaussian process, but it can also be used for epistemic uncertainties, which is superior to the response surface method when non-linear behaviors and/or when functions with discontinuities or strong variations must be approximated. The method has been used in UQ, optimizations and parameter identifications [12,36,108,[159][160][161]. For a predefined input vector x, the system output y(x), i.e., QoI, can be metamodeled by…”

“…The dynamics of rotor systems under the fuzzy or random uncertainties associated with different kinds of bearings are the most heated research topics [53][54][55]60,103,104,108,111,117,195,[217][218][219][220][221][222][223], among which the journal bearings are major focuses of many researchers. For uncertainties in journal bearings, three main points were generally investigated, i.e., the rough surfaces, radial clearance and lubricant viscosity (caused by lubricant temperature variations).…”

“…Envelopes of the uncertain transient responses of a flexible rotor supported by journal bearings were discussed by Cavalini et al [104] based on fuzzy analysis. Kriging metamodel was used to represent the thermohydrodynamic models of three kinds of bearings in a Francis hydropower unit [108], i.e., a cylindrical journal bearing, a tilting-pad journal bearing and a tilting-pad thrust bearing.…”

Advanced Meta-Modelling Techniques and Sensitivity Analysis for Rotordynamics in an Uncertain Context

“…When many uncertain parameters are present, an efficient strategy consists in the creation of a surrogate model that mimics the behaviour of the full model. Recent strategies have been based on the use of a single method, as PCE [1,2,3] or kriging [4,5,6] to predict the critical speeds of uncertain rotors. However, none of them is able to deal with both nature of uncertainty at this step.…”