A common problem in transient rotordynamic simulations is the numerical effort necessary for the computation of hydrodynamic bearing forces. Due to the nonlinear interaction between the rotordynamic and hydrodynamic systems, an adequate prediction of shaft oscillations requires a solution of the Reynolds equation at every time step. Since closed-form analytical solutions are only known for highly simplified models, numerical methods or look-up table techniques are usually employed. Numerical solutions provide excellent accuracy and allow a consideration of various physical influences that may affect the pressure generation in the bearing (e.g., cavitation or shaft tilting), but they are computationally expensive. Look-up tables are less universal because the interpolation effort and the database size increase significantly with every considered physical effect that introduces additional independent variables. In recent studies, the Reynolds equation was solved semianalytically by means of the scaled boundary finite element method (SBFEM). Compared to the finite element method (FEM), this solution is relatively fast if a small discretization error is desired or if the slenderness ratio of the bearing is large. The accuracy and efficiency of this approach, which have already been investigated for single calls of the Reynolds equation, are now examined in the context of rotordynamic simulations. For comparison of the simulation results and the computational effort, two numerical reference solutions based on the FEM and the finite volume method (FVM) are also analyzed.

In the present theoretical analysis, the combined effects of slider curvature and non-Newtonian pseudoplastic and dilatant lubricants (lubricant blended with viscosity index improver) on the steady and dynamic characteristics of pivoted curved slider bearings have been investigated for Rabinowitsch fluid model. The modified Reynolds equations have been obtained for steady and damping states of bearing. To solve the modified Reynolds equations, perturbation theory has been adopted. The results for the steady state characteristics (steady state film pressure, load carrying capacity and centre of pressure) and dynamic characteristics (dynamic damping and dynamic stiffness) have been calculated numerically for various values of viscosity index improver using Mathematica. In comparison with the Newtonian lubricants, higher values of film pressure, load carrying capacity, dynamic damping and dynamic stiffness have been obtained for dilatant lubricants, while the case was reversed for pseudoplastic lubricants. Significant variations in the bearing characteristics have been observed for even small values of pseudoplastic parameter, that is, with the non-Newtonian dilatant and pseudoplastic behaviour of the fluid.

Rotors of rotating machines are often mounted in hydrodynamic bearings. Loading alternating between the idling and full load magnitudes leads to the rotor journal eccentricity variation in the bearing gap. To avoid taking undesirable operating regimes, its magnitude must be kept in a certain interval. This is offered by the hydrodynamic bearings lubricated with smart oils, the viscosity of which can be changed by the action of a magnetic field. A new design of a hydrodynamic bearing lubricated with magnetically sensitive composite fluid is presented in this paper. Generated in the electric coil, the magnetic flux passes through the bearing housing and the lubricant layer and then returns to the coil core. The action of the magnetic field on the lubricant affects the apparent fluid viscosity and thus the position of the rotor journal in the bearing gap. The developed mathematical model of the bearing is based on applying the Reynolds equation adapted for the case of lubricants exhibiting the yielding shear stress. The results of the performed simulations confirmed that the change of magnetic induction makes it possible to change the bearing load capacity and thus to keep the rotor journal eccentricity in the required range. The extent of control has its limitations. A high increase in the loading capacity can arrive at the rotor forced vibration’s loss of stability and induce large amplitude oscillation.