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Nonlinear dynamic journal bearing modeling within rotordynamic analyses requires the calculation of the nonlinear bearing forces particularly depending on shaft eccentricity and velocity. The bearing forces can be calculated properly using Reynolds differential equation and mass conserving cavitation algorithms, based for example on Elrod’s cavitation algorithm. This approach achieves high model accuracy and allows the consideration of additional effects like misalignment, variable viscosity and transient local oil distribution in the lubricant film. However, despite rising calculating capacity dynamic bearing analyses are still very CPU-time consuming and, consequently, approximation methods are commonly applied in multibody or rotordynamic analyses, especially in day-to-day business. While many approximation procedures are limited to special bearing geometries Glienicke et al. describe a method which is flexible to model different journal bearing geometries, as well as to consider many additional effects like oil supply pressure or starved lubrication conditions in a time averaged manner. It can be applied for both fixed-pad and tilting-pad journal bearings and its characteristic data is included in an a priori calculated map enabling a time-efficient call up of characteristic parameters of the bearing forces from a look-up table in dynamic simulations. Further, the data can be transferred to any other bearing if the requirements of the theory of similarity are supposed to be valid. In this investigation, the method is first successfully extended by the authors to consider misalignment. Secondly, the general idea of the procedure is transferred and applied to thrust bearings in order to enable a six degree of freedom rotordynamic modeling. In case of a simply lateral movement and rotation-symmetric bearing design the procedure is simple, though, in case of tilting movements it becomes more complicated. A misaligned thrust bearing provides tilting and cross-coupling moments. Cross coupling moments are smaller than the main moments, but have similar orders of magnitude and should therefore be considered. Strategies are investigated for a proper approximation of the nonlinear thrust bearing main and cross-coupling forces and moments. All steps are verified using a direct solution of Reynolds differential equation based on an extended mass conserving algorithm adapted from Elrod’s numerical implementation for the stationary case. Finally, the whole procedure and its application to rotordynamic analysis is verified by comparisons with results gained using direct online solution of Reynolds equation in rotordynamic simulation. While good simulation quality of this approximation approach is documented for selected rotor-bearing-systems in literature the range of validity is not clearly defined. Here, the influences of different parameters on the simulation error are investigated conducting different variation calculations for an overhung rotor with documented vibrational behavior from literature. It is shown that the simulation quality depends on the cavitation zone and decreases with rising vibrational velocity. The root cause for this upcoming error and a possible modification for the elimination of this limitation are presented.

Improving efficiency is a general task in the design process of high-speed journal bearings. A specific fixed-pad bearing geometry featuring reduced pad length and additional design measures with the intention of reducing frictional power loss is investigated, experimentally and theoretically, for a journal diameter of 500 mm up to surface speeds of 94 m/s and unit loads of 5.0 MPa. To model fluid flow in the bearing outside the lubricant gap, an extension to Elrod’s cavitation algorithm based on assuming the inertia of fluid flow is proposed. Validation of the extended thermo-elasto-hydrodynamic lubrication (TEHL) model shows good agreement between measurement and prediction in wide operating ranges, however, with systematic tendencies of the remaining deviations. Furthermore, measured local pressure and film thickness distributions indicate a complex formation of cavitation with an influence of axial flow that is not covered by pure Couette-flow in the cavitation region. Measured as well as predicted data prove increased bearing efficiency for high rotor speeds. To provide understanding on the impact of the applied design measures improving efficiency, their combination is separated into the individual ones. Reduced axial and peripheral pad length both contribute almost equally to the reduction in power loss and improve its value by 37% compared to the standard design. Finally, further steps to deeper identify the behavior of the bearing are comprehensively discussed.

Dynamic analyses of vertical hydro power plant rotors require the consideration of the non-linear bearing characteristics. This study investigates the vibrational behavior of a typical vertical machine using a time integration method that considers non-linear bearing forces. Thereby, the influence of support stiffness and unbalance magnitude is examined. The results show a rising influence of unbalance on resonance speed with increasing support stiffness. Furthermore, simulations reveal that the shaft orbit in the bearing is nearly circular for typical design constellations. This property is applied to derive a novel approximation procedure enabling the examination of non-linear resonance behavior, using linear rotor dynamic theory. The procedure considers the dynamic film pressure for determining the pad position. In addition, it is time-efficient compared to a time integration method, especially at high amplitudes when damping becomes small.

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