Stochastic collocation approach for evaluation of journal bearings dynamic coefficients

Gabriel Garoli¹; Helio Castro¹

¹ University of Campinas

doi:10.20906/CPS/USM-2016-0044

Resumo

Rotordynamics is an important field of study due to the vastly applicability of rotating machines. A crucial component of these machines is the bearing that connects the rotating shaft with the static foundation of the machine. Therefore, it is important this component does not transmit the shaft's vibration to the base. One way to minimize that transference is the use of fluid journal bearings, which absorbs part of the energy of the vibration. Mathematical models of rotor-bearing systems were develop to predict it behavior and design it. A common approach used for bearing modelling is the consideration of a linear model, which takes into account the damping and stiffness coefficients of each element. In order to evaluate these coefficients, a numerical solution of the Reynolds equation can be applied, considering bearing's geometry and the fluid properties. However, these parameters have some uncertainties, which can be modeled using probability distributions. Therefore, the deterministic problem to evaluate the damping and stiffness coefficients of the bearing should become a stochastic problem. Thus, this work presents a Stochastic Collocation method for performing damping and stiffness coefficients evaluation of a fluid journal bearing. Generalized polynomial chaos is adopt to approach the probability distributions functions of the random parameters. The Stochastic Collocation is a non-intrusive method, like the Monte Carlo Methods, so it needs a deterministic solver. To obtain the solution of the Reynolds equation, which model the fluid flow inside the bearing, a finite-volume method was used. Through the pressure distribution on the lubricant and the gap between the journal and the bearing, the damping and stiffness coefficients are evaluated. The application of the Stochastic Collocation method allows statistical post-processing, thus the uncertainties of the bearing can be propagated to the damping and stiffness coefficients and then, for example, can be used in the modelling of a rotor-bearing system. T

Palavras-chave: Stochastic collocation; generalized polynomial chaos; journal bearing; rotordynamics