Fluid Film Journal Bearings Research Articles

Finite Element Method Applied to the Eigenvalue Analysis of Flexible Rotors Supported by Journal Bearings

This work deals with a finite element procedure developed to perform the eigenvalue analysis of damped gyroscopic systems, represented by flexible rotors supported on fluid film journal bearings. The rotor finite element model is based on the Timoshenko beam theory, accounting for the shaft rotary inertia and gyroscopic moments. The governing equations for the hydrodynamic journal bearing are obtained through the Galerkin weighted residual method applied to the classical Reynolds equation. A perturbation scheme on the fluid film governing equation permits to obtain the zero-th and first order lubrication equations for the bearings, which allow the computation of the dynamic force coefficients associated with the bearing stiffness and damping. The rotor-bearing system equation, which consists of a case of damped gyroscopic equation, is rewritten on state form to compute the complex eigenvalues. The natural frequencies at several operating conditions are obtained and compared to the technical literature data. The influence of the effective damping on the eigenvalue real part sign is analyzed for some examples of rotor-bearing systems, showing how the stability conditions can be predicted by the eigenvalue analysis. The procedure implemented in this work can provide useful guidelines and technical data about the selection of the more appropriate set of bearing parameters for rotating machines operating at stringent conditions.

Lateral Vibration Analysis of Flexible Shafts Supported on Elliptical Journal Bearings

This paper presents the development of a finite element procedure for the dynamic analysis of flexible rotors supported on fluid-film elliptical journal bearings operating under several operating conditions. The rotating shaft is modeled by using Timoshenko beam theory and the coupled rotating components, such as disks and impellers, are modeled by using lumped masses. The modeling of the elliptical journal bearings is performed by solving the lubrication equations generated from the application of a linearized perturbation method on the classical Reynolds equation. The bearing carrying-load capacity and the linearized dynamic force coefficients can be predicted for elliptical bearings with different preloads and journal eccentricities. The rotor transient whirling unbalance response is estimated by performing the time integration of the finite element equations using Newmark method. Experimental whirling unbalance response of a rotating shaft supported at two identical journal bearings is used to validate the finite element procedure. A comparative analysis of the dynamic response of flexible rotors supported on both cylindrical and elliptical journal bearings is performed to show that some elliptical bearings are capable of attenuating the rotor unbalance response more efficiently than cylindrical bearings are.

Fuzzy Based Decision Making for Selection of Fluid Film Journal Bearing

This paper presents a theoretical prediction of selection procedure for fluid film journal bearing by incorporating fuzzy approach. In this paper a fuzzy model is proposed for selection of hydrostatic, hydrodynamic and hybrid journal bearing. Selection criteria is formulated for the choice of space requirement, total cost of bearing and load bearing capacity of the related journal bearing. This method provides a third dimension to the existing method of selection of bearing, which is dynamic and may be further refined to address to every individual needs. Therefore a fuzz y logic approach is used for decision making for selection of correct fluid film bearing

Nonlinear effects caused by coupling misalignment in rotors equipped with journal bearings

Misalignment is one of the most common sources of trouble of rotating machinery when rigid couplings connect the shafts. Ideal alignment of the shafts is difficult to be obtained and rotors may present angular and/or parallel misalignment (defined also as radial misalignment or offset). During a complete shaft revolution, a periodical change of the bearings load occurs in hyperstatic shaft-lines, if coupling misalignment between the shafts is excessive. If the rotating machine is equipped with fluid-film journal bearings, the change of the loads on the bearing causes also the variation of their instantaneous dynamic characteristics, i.e. damping and stiffness, and the complete system cannot be considered any longer as linear.Despite misalignment is often observed in the practice, there are relatively few studies about this phenomenon in literature and their results are sometimes conflicting. The authors aim at modeling accurately this phenomenon, for the first time in this paper, and giving pertinent diagnostic information. The proposed method is suitable for every type of shaft-line supported by journal bearings. A finite element model is used for the hyperstatic shaft-line, while bearing characteristics are calculated by integrating Reynolds equation as a function of the instantaneous load acting on the bearings, caused also by the coupling misalignment. The results obtained by applying the proposed method are shown by means of the simulation, in the time domain, of the dynamical response of a hyperstatic shaft-line. Nonlinear effects are highlighted and the spectral components of the system response are analyzed, in order to give diagnostic information about the signature of this type of fault.

Model Based Analysis of Coupled Vibrations Due to the Combi-Bearing in Vertical Hydroturbogenerator Rotors

The studies presented in this paper focus on analyzing how the combined thrust-journal bearing (commonly called combi-bearing) influences the dynamics of hydropower rotors. Thrust bearing is a component used in vertical rotating machinery and shafts designed to transmit thrust. The total axial load is carried by the single thrust bearing. Any design, manufacture, or assembly error in this component (thrust bearing) would certainly influence the functionality of the entire machine. The analyzed combi-bearing is an existing machine component used in the hydropower unit Porjus U9 situated in northern Sweden. This combi-bearing is a fluid-film lubricated tilting-pad thrust and journal bearings combined together. Only linear fluid-film stiffness was taken into account in the model while fluid-film damping and pads inertia effects were not taken into account. The linearized model shows that the combi-bearing couples the rotor’s lateral and angular motions. However, if the thrust bearing’s pads arrangement is not symmetrical or if all the pads are not angularly equidistant the rotor axial and angular motions are also coupled. This last case of coupling will also occur if the thrust bearing equivalent total stiffness is not evenly distributed over the thrust bearing. A defective pad or unequal hydrodynamic pressure distribution on the pads’ surfaces may be the cause. The Porjus U9’s simulation results show that the combi-bearing influences the dynamic behavior of the machine. The rotor motions’ coupling due to combi-bearing changes the system’s natural frequencies and vibration modes.

Effect of turbulence on the static performance of a misaligned externally adjustable fluid film bearing lubricated with couple stress fluids

Static analysis of a misaligned externally adjustable fluid-film bearing is carried out thereby including turbulence and couple-stress effects in lubricants blended with polymer additives. A modified form of Reynolds equation, incorporated with the theory of micro-continuum and the concept of adjustability, is solved numerically, for various simulated operating conditions. The effects of turbulence and couple-stress on key performance parameters are presented. This study predicts that, an externally adjustable fluid-film journal bearing operating with negative adjustment configuration and lubricants with couple-stress, results in superior load carrying capacity with reduced friction and end leakage, as compared to a conventional partial arc bearing.

On the modelling of hybrid aerostatic-gas journal bearings

Gas journal bearings have been increasingly adopted in modern turbo-machinery applications as they meet the demands of operation at high rotational speeds, in clean environment, and with great efficiency. Due to the fact that gaseous lubricants, typically air, have much lower viscosity than more conventional oils, carrying capacity and dynamic characteristics of passive systems are generally poorer. In order to enhance these characteristics, one solution is used to combine the aerodynamic effect with the addition of external pressurization. This study presents a detailed mathematical model for hybrid lubrication of a compressible fluid-film journal bearing. Additional forces are generated by injecting pressurized air into the bearing gap through orifices located on the bearing walls. A modified form of the compressible Reynolds equation for active lubrication is derived. By solving this equation, stiffness and damping coefficients can be determined. A multibody dynamics model of a global system comprised of rotor and hybrid journal bearing is built in order to study the lateral dynamics of the system. Campbell diagrams and stability maps are presented, showing the main advantages and drawbacks of this special kind of hybrid fluid-film bearing.

Static, Dynamic, and Thermal Properties of Compressible Fluid Film Journal Bearings

Modern turbo-machinery applications, high-speed machine tools, and laboratory equipment require ever-growing rotational speeds and high degree of precision and reliability. Gas journal bearings are often employed because they meet the demands of high-speed performance, in a clean environment, and work great efficiency. A great deal of literature has concentrated on the analysis and prediction of the static and dynamic performance of gas bearings, assuming isothermal conditions. The present contribution presents a detailed mathematical modeling for nonisothermal lubrication of a compressible fluid film journal bearing, in order to identify when this type of analysis should be of concern. Load capacity, stiffness, and damping coefficients are determined by the solution of the standard Reynolds equation coupled to the energy equation. Numerical investigations show how bearing geometry, rotational speed and load influence the bearing performance. Comparisons between isothermal and thermohydrodynamic models and discrepancies are quantified for three different types of bearing geometries.

Transient CFD Analysis of Multi-Lobe Bearings at 60000RPM for A Gas Turbine

Transient CFD Analysis of Multi-Lobe Bearings at 60000RPM for A Gas Turbine

Mass Conserving Cavitation Effects in Squeeze-Film Journal Bearings Subjected to Sinusoidal Loads

This article presents a study of cavitation effects associated with the performance of fluid-film journal bearings subjected to fully reversing sinusoidal loading. Employing an established mass-conserving cavitation algorithm, it is observed that periodic time histories of journal eccentricity and maximum film pressure are strongly influenced by the process of cavitation formation and collapse. A new set of design charts for the prediction of cyclic-minimum film thickness is provided over a range of nondimensional loads, bearing geometric parameters, feed hole orientations, and cavitation threshold pressures typically found in practice. Good agreement of numerical and experimental results is obtained over a large range of loads for cavitation threshold pressure values typically associated with vaporous cavitation.

Couple stress fluid improve rub-impact rotor-bearing system – Nonlinear dynamic analysis

This study performs a dynamic analysis of the rub-impact rotor supported by two couple stress fluid film journal bearings. The strong nonlinear couple stress fluid film force, nonlinear rub-impact force and nonlinear suspension (hard spring) are presented and coupled together in this study. The displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The numerical results show that the dynamic behaviors of the system vary with the dimensionless speed ratios, the dimensionless unbalance parameters and the dimensionless parameter, l ∗. Inclusive of the periodic, sub-harmonic, quasi-periodic and chaotic motions are found in this analysis. The results of this study contribute to a further understanding of the nonlinear dynamics of a rotor-bearing system considering rub-impact force existing between rotor and stator, nonlinear couple stress fluid film force and nonlinear suspension. We also prove that couple stress fluid used to be lubricant do improve dynamics of rotor-bearing system.

Bifurcation and chaos for porous squeeze film damper mounted rotor–bearing system lubricated with micropolar fluid

This study presents a dynamic analysis of a flexible rotor supported by two porous squeeze micropolar fluid-film journal bearings with nonlinear suspension. The dynamics of the rotor center and bearing center are studied. The analysis of the rotor–bearing system is investigated under the assumptions of non-Newtonian fluid and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various nondimensional speed ratios. The dynamic equations are solved using the Runge–Kutta method. The methods of analysis employed in this study are inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincare maps, and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the dynamic system varies with the nondimensional speed ratios, the nondimensional parameter, and permeability. The modeling results obtained by using the method proposed in this paper can be employed to predict the dynamics of the rotor–bearing system, and the undesirable behavior of the rotor and bearing centers can be avoided.

Identification methods and test results for tilting pad and fixed geometry journal bearing dynamic coefficients – A review

Fluid film journal bearings (FFBs) are used to support high-speed rotors in turbomachinery which often operate above the rotor first bending critical speed. The FFBs provide both lateral support and dynamic coefficients: stiffness, damping, and mass terms, related to machine vibrations. Detailed numerical values of the bearing dynamic characteristics are necessary for proper design and operation of rotating machinery. The methods of the identification of fluid film journal bearing static and dynamic characteristics, particularly the bearing stiffness, damping, and mass coefficients, from measured data, obtained from different measurement systems, is reviewed. Many bearing tests have been performed to validate a number of different theoretical models, including the classical Reynolds isoviscous model. More advanced bearing models include the thermohydrodynamic (THD), and thermoelastohydrodynamic (TEHD) approaches. The advanced models also include turbulence effects which are important as rotor speeds continue to increase. The range of measured bearing data no longer includes current operational conditions. The various approaches to the bearing identification problem are discussed, including the different force excitation methods of incremental loading, sinusoidal, pseudorandom, impulse, known/additional unbalance, and non-contact excitation. Also bearing excitation and rotor excitation approaches are discussed. Data processing methods in the time and frequency domains are presented. Methods of evaluating the effects of measurement uncertainty on overall bearing coefficient confidence levels are reviewed. In this review, the relative strengths and weaknesses of bearing identification methods are presented, and developments and trends in improving bearing measurements are documented. Future trends in journal bearing identification improvement are discussed.

Identification Methods and Test Results for Tilting Pad and Fixed Geometry Journal Bearing Dynamic Coefficients – A Review

Fluid film journal bearings (FFBs) are used to support high-speed rotors in turbomachinery which often operate above the rotor first bending critical speed. The FFBs provide both lateral support and dynamic coefficients: stiffness, damping, and mass terms, related to machine vibrations. Detailed numerical values of the bearing dynamic characteristics are necessary for proper design and operation of rotating machinery.The methods of the identification of fluid film journal bearing static and dynamic characteristics, particularly the bearing stiffness, damping, and mass coefficients, from measured data, obtained from different measurement systems, is reviewed. Many bearing tests have been performed to validate a number of different theoretical models, including the classical Reynolds isoviscous model. More advanced bearing models include the thermohydrodynamic (THD), and thermoelastohydrodynamic (TEHD) approaches. The advanced models also include turbulence effects which are important as rotor speeds continue to increase. The range of measured bearing data no longer includes current operational conditions.The various approaches to the bearing identification problem are discussed, including the different force excitation methods of incremental loading, sinusoidal, pseudorandom, impulse, known/additional unbalance, and non-contact excitation. Also bearing excitation and rotor excitation approaches are discussed. Data processing methods in the time and frequency domains are presented. Methods of evaluating the effects of measurement uncertainty on overall bearing coefficient confidence levels are reviewed.In this review, the relative strengths and weaknesses of bearing identification methods are presented, and developments and trends in improving bearing measurements are documented. Future trends in journal bearing identification improvement are discussed.

Non-linear dynamic analysis of bearing—rotor system lubricating with couple stress fluid

The current study performs a dynamic analysis of a rotor supported by two couple stress fluid film journal bearings with non-linear suspension. The dynamics of the rotor centre and bearing centre are studied. The analysis of the rotor—bearing system is investigated under the assumptions of a couple-stress lubricant and a short journal bearing approximation. The displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The analysis methods employed in this study include the dynamic trajectories of the rotor centre and the bearing centre, Poincaré maps, and bifurcation diagrams. The Lyapunov exponent analysis is also used to identify the onset of chaotic motion. Numerical results show that the stability of the system varies with the non-dimensional speed ratios. Specifically, it is found that the system is quasi-periodic at a small speed ratio ( s = 0.5). At speed ratios of s = 0.6–0.7, the system is periodic. At s = 0.8–1.9, the system is quasi-periodic, but the system is periodic at s = 2.0–2.6. However, the system exhibits chaotic motion at the speed ratios s = 2.7–2.74. At the speed ratios s = 2.75–3.16, the system becomes periodic. At s = 3.17–3.30, the system is unstable. The Poincaré map has a particular form at s = 3.17, indicative of a chaotic motion. At s = 3.31–6.0, the system finally becomes periodic. The results also confirm that the stability of the system varies with the non-dimensional speed ratios s and l∗. The results of this study allow suitable system parameters to be defined such that undesirable behaviour of the rotor centre can be avoided and the bearing system life extended as a result.

Nonlinear numerical analysis of a flexible rotor equipped with squeeze couple stress fluid film journal bearings

This study performs a dynamic analysis of a rotor supported by two squeeze couple stress fluid film journal bearings with nonlinear suspension. The numerical results show that the stability of the system varies with the non-dimensional speed ratios and the dimensionless parameter l*. It is found that the system is more stable with higher dimensionless parameter l*. Thus it can conclude that the rotor-bearing system lubricated with the couple stress fluid is more stable than that with the conventional Newtonian fluid. The modeling results thus obtained by using the method proposed in this paper can be used to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided.

Bifurcation analysis of flexible rotor supported by couple-stress fluid film bearings with non-linear suspension systems

This study analyzes the dynamic behavior of a flexible rotor supported by two couple-stress fluid film journal bearings with non-linear suspension systems. The analysis employs a short journal bearing assumption and considers the respective effects on the dynamic response of the system of the lubricant type (i.e. Newtonian or non-Newtonian), the bearing housing suspension system (i.e. linear or non-linear), the rotor speed and the degree of rotor unbalance. The behavior of the system is analyzed by reference to bifurcation diagrams, dynamic trajectory diagrams and Poincaré maps, respectively. In general, the results show that the dynamics of the system are significantly dependent on the rotor speed and the degree of rotor unbalance. Furthermore, it is found that the use of a couple-stress fluid lubricant enhances the dynamic stability of the rotor-bearing system considerably compared to that obtained when using a traditional Newtonian lubricant. Finally, the results show that the common assumption of a linear journal housing suspension system results in a significant underestimation of the vibrational amplitudes of both the rotor and the bearing and should therefore be replaced by a non-linear assumption.

Misalignment in rigidly coupled rotors

Misalignment of multibearing rotor systems is one of the most common fault conditions yet it is still not fully understood. There are numerous (and sometimes confusing) accounts in the literature asserting the presence of harmonics in the vibration signal, but no quantitative descriptions are offered. Harmonics may arise, of course, from the nonlinearities in fluid film journal bearings or from the kinematics of flexible couplings, but in this paper only rigidly coupled rotors mounted on idealised linear bearings are considered. It is shown that even for this case, excitation at twice synchronous speed is developed and an expression for the magnitude and phase of the response is derived. Several examples are then studied to give some insight into the magnitude of these harmonic terms which can arise. It is argued that it is precisely because the harmonic terms can arise from diverse sources, that a full description of the phenomena has proved somewhat elusive.

Studies on Misalignment in Coupled Rotors

Misalignment of multi-bearing rotor systems is one of the most common fault conditions yet it is still not fully understood. There are numerous (and sometimes confusing) accounts in the literature asserting the presence of harmonics in the vibration signal, but no quantitative descriptions are offered. Harmonics may arise, of course, from the nonlinearities in fluid film journal bearings or from the kinematics of flexible couplings, but in this paper only rigidly coupled rotors mounted on idealised linear bearings. It is shown that even for this case, excitation at twice synchronous speed is developed and an expression for the magnitude and phase of the response is derived. Several examples are then studied to give some insight into the magnitude of these harmonic terms which can arise. It is argued that it is precisely because the harmonic terms can arise from diverse sources, a full description of the phenomena has proved somewhat elusive. A brief discussion of the type of rig required to validate the model is given. There is a need to separate the phenomena discussed here from the nonlinearities found in real machines. Some features of the new facility are described.

Nonlinear dynamic analysis of a flexible rotor supported by micropolar fluid film journal bearings

The bifurcation and chaos of dynamic response of a rotor–bearing system with nonlinear suspension are investigated on the basis of assumptions of the micropolar lubricant together with short bearing approximation. The dynamics of the rotor center and bearing center are studied. The spatial displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The dynamic equations are solved using the Runge–Kutta method. The analysis methods employed in this study is inclusive of the dynamic trajectories of the rotor center and bearing center, Poincaré maps and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the system varies with the non-dimensional speed ratios. Specifically, it is found that the dynamic behaviors of the system include periodic, quasi-periodic and chaotic motions. Thus it is concluded that the bearing and rotor center trajectory had undesirable vibrations. Understanding the dynamic behaviors of these parameters provides theoretical and practical ideas for controlling rotor–bearing systems and optimizing their operation.