Tilting Pad Journal Bearings Research Articles

Computational Model Development for Hybrid Tilting Pad Journal Bearings Lubricated with Supercritical Carbon Dioxide

Fluid film bearings lubricated with supercritical carbon dioxide (sCO2) eliminate the infrastructural requirement for oil lubricant supply and sealing in turbomachinery for sCO2 power systems. However, sCO2’s thermohydrodynamic properties, which depend on pressure and temperature, pose a challenge, particularly with computational model development for such bearings. This study develops a computational model for analyzing sCO2-lubricated tilting pad journal bearings (TPJBs) with external pressurization. Treating sCO2 as a real gas, the Reynolds equation for compressible turbulent flows solves the pressure distribution using the finite element method, and the Newton−Raphson method determines the static equilibrium position by simultaneously calculating forces, moments, flow rates of externally pressurized sCO2, and pressure drop due to flow inertia. The finite difference method solves the energy equation for temperature distribution. The density and viscosity of sCO2 are converged using the successive substitution method. The obtained predictions agree with the previous and authors’ computational fluid dynamics predictions, thus validating the developed model. Hybrid lubrication increases the minimum film thickness and stiffness up to 80% and 65%, respectively, and decreases the eccentricity ratio by up to 65% compared to those of pure hydrodynamic TPJB, indicating significant improvement in the load capacity. The bearing performance is further improved with increasing sCO2 supply pressure.

Tilting Pad Journal Bearing Ball and Socket Pivots: Experimental Determination of Stiffness

Tilting pad journal bearings (TPJB) are used in turbomachinery for their stability at high speeds. For design purposes, it is necessary to preliminarily investigate the turbomachine rotor dynamic behavior by simulation. The dynamic characteristics of all components must be known as precisely as possible and experimental validation of each single model is required. While a lot of work has been carried out on bearings, the ball-and-socket stiffness is still estimated by means of Hertzian formulas. Recently, some authors have used the finite element method, but it seems that nothing has been done experimentally to date. This paper describes the test rig designed to determine the stiffness of a TPJB ball-and-socket pivot by equipping the grippers of a tensile universal testing machine with specifically designed interfaces. A methodology for evaluating the stiffness from the experimental results is reported. Preliminary compression results are presented and compared with the analytical ones obtained using Hertz’s formula showing significant differences for the ball-and-socket conformal contact.

A novel framework for relationship of manufacturing tolerance and component-level performance of journal bearings

This work proposes a mathematical framework to identify the relationship between the manufacturing tolerance of a component and the expected variations on its mechanical performance with focus on journal bearing applications. The manufacturing tolerance is described through probability density functions, while its effect on performance is addressed via stochastic simulations. The procedure underlies the adoption of a surrogate model under local and global training (based on adaptive Kriging interpolation) to predict the probability to exceed a certain performance metric. The proposed framework is illustrated and validated studying a tilting pad journal bearing in terms of minimum and maximum dynamic coefficient values. Results show a significant saving in terms of computational time, making this framework attractive for the selection and assessment of acceptable manufacturing tolerances.

Internal flow and bearing characteristics in tilting pad journal bearing with fluid structure intersection

Journal bearings have the advantage of being damped. However, at high rotational speeds, self-excited oscillations called oil whip occur, leading to damage of bearing and shafts. Tilting Pad Journal Bearings are used in high-speed rotating machinery as they are effective against oil whip. The Reynolds equation has been used as a typical calculation method to investigate bearing characteristics, but it is difficult to apply when the bearing is complex. In this paper, a prediction method of bearing characteristics of Tilting Pad Journal Bearing using CFD was constructed. To simulate the motion of the pad as it oscillates against the fluid force, Dynamic Fluid Body Intersection was studied. In order to compare with the calculation results, an active oscillating rotor using magnetic bearings was constructed. As a result, the calculation results were roughly consistent with the experimental results, and a prediction method by CFD was constructed.

Analysis of mixed lubrication performance of water-lubricated rubber tilting pad journal bearing

Water-lubricated rubber bearing (WLRB) often operate in mixed lubrication. Friction and wear are their common failure modes. In present study, the tilting-pad structure is employed to improve the conventional WLRB. A mixed lubrication model of water-lubricated rubber tilting-pad journal bearing (WLRTPJB) is developed to reveal the mixed elastohydrodynamic (Mixed-EHD) performance. The influence of structure and operating parameters on the tribological properties and pad swing characteristics are studied. The results show a lower contact load of a WLRTPJB, especially under heavy load conditions. The studies also give the optimum pivot offset and preload factor that can minimize the contact pressure. Moreover, the equilibrium tilting-pad angle is sensitive to changes in design and operating parameters. This study would provide certain guiding significance for design optimization of WLRB.

Prediction of nonlinear dynamic coefficients of tilting-pad journal bearings with pad perturbation

In this paper, a modified partial derivative method is developed to predict the linear and nonlinear dynamic coefficients of tilting-pad journal bearings with journal and pad perturbation. To this end, Reynolds equation and its boundary conditions along with equilibrium equations of the pad are used. Finite difference, partial derivative method, and perturbation technique have been employed simultaneously for solving these equations. The accuracy of the results is investigated by comparing the linear dynamic coefficients of three types of tilting-pad journal bearings with those published the literature. It is shown that the nonlinear dynamic coefficients depend on Sommerfeld number, eccentricity ratio, and length to diameter ratio. Similar to the case of linear dynamic coefficients of TPJB, it is observed that the eccentricity ratio effects on nonlinear dynamic coefficients are more notable when the eccentricity ratio is higher than 0.8 or less than 0.2.

Effect of Pad Material, Copper Versus Steel, on the Performance of a Tilting Pad Journal Bearing: Measurements and Predictions

Abstract High-temperature operation limits the life of fluid film bearings; hence the need to quantify the effect of pad material on the performance of tilting pad journal bearings (TPJBs). The paper presents measurements of performance conducted on a copper-pads bearing (C-PB) and a steel-pads bearing (S-PB). Both bearings have the same geometry and differ on the pads' backing material, copper versus steel, and slightly in the assembled cold clearance. The journal diameter D = 102 mm, and a bearing has five pads with length L = 0.4D, nominal radial clearance 0.064 mm, and pad preload of 0.42. The pads are 12.3 mm in thickness and have a 50% offset pivot, ball-in-socket type. The bearings operate at four shaft speeds ranging from 6 krpm (32 m/s surface speed) to 14 krpm (74 m/s) and under multiple specific loads ranging from 0.17 MPa to 2.1 MPa. ISO VG 32 oil, at a supply temperature of 49 °C, lubricates a test bearing configured with end seals (flooded bearing). At the highest load (on pad) and low shaft speed, the S-PB static eccentricity is up to 37% higher than that for the C-PB. The oil exit temperature rise is similar for both bearings, the maximum difference reaches 6 °C. For all operating conditions, the pads' peak temperature rise, having a maximum difference of 5 °C–16 °C, is larger for the S-PB. The S-PB produces a ∼5% lower drag power loss than that in the C-PB. Drag power in both bearings increases with shaft speed and is largely independent of the applied load. From dynamic load tests with multiple excitation frequencies to 250 Hz, the C-PB direct stiffness KYY (along the load direction) is up to 30% higher than the S-PB stiffness, while the difference in KXX between the C-PB and the S-PB ranges from 60% to 90%. Similar to the stiffness results, the C-PB produces larger direct damping coefficients; CYY and CXX are up to 25% and 40% larger than those for the S-PB. Both bearings, however, show symmetry in the damping coefficients, i.e., CXX ∼ CYY. Virtual mass coefficients (MXX, MYY) are significant in magnitude though having a large uncertainty. A computational physics model predicts the TPJB performance under identical conditions. The exhaustive comparison conducted with a sound dimensional characterization of parameters reveals that predictions agree well with measurements of journal eccentricity, oil exit temperature, pad surface temperatures, and stiffness and damping force coefficients. The differences amount to 20% or less. The model relies on specifying the material properties for pads and pivots and the operating (hot) clearance to produce accurate thermomechanically induced deformations that affect bearing performance at high loads and high surface speed operation.

Experimental Characterization of Large Turbomachinery Tilting Pad Journal Bearings

The paper deals with the experimental characterization of different 280 mm diameter tilting pad journal bearings for turbomachines using a dedicated test rig. The test articles were a 5-pad Direct Lube Rocker Pivot bearing, a 5-pad Flooded Rocker Pivot bearing, and a 4-pad Flooded Ball and Socket Pivot bearing. The three bearings were tested in their specific design range of operating conditions. Their static and dynamic behavior was investigated as a function of different operating parameters. In particular, the assumed journal center eccentricity and pads temperature were measured, and the power loss determined as a function of angular speed for different static loads. Dynamic stiffness and damping coefficients were determined as a function of excitation frequency for different speeds and loads. The experimental results were compared showing the influence of the operating parameters, configuration, and oil supply.

Dynamic Response Analysis of Tilting Pad Journal Bearing Considering Fluid-Structure Interaction

The transient hydrodynamic lubrication model of tilting pad journal bearings (TPJBs) was established by the computational fluid dynamics (CFD) method and the self-developed dynamic grid program. The fluid-structure interaction between the flow field and the rotor motion, the pads rotations was realized. The feasibility of the model is proved by comparing with the experimental data. The dynamic response of TPJBs under the various unbalance, the loading modes and the rotating speeds was studied. The dynamic response of TPJBs is further analyzed through a research of the relationships among the shaft whirl orbits, transient force acting on the shaft, rotation angles of the pads and transient oil film force of the pads. With the increase of unbalance, the whirl orbits expand and whirl orbits centers rise continuously. The whirl orbits and orbit center attitude angles of TPJBs are smaller than those of fixed-pad journal bearings. Compare with the load between pads, the whirl orbits are smaller and whirl orbits centers drop slightly under the load on pads. With the increase of rotating speed, the whirl orbits expand nonlinearly, whirl orbit center rises nonlinearly. The transient force acting on the shaft, the rotation angles of the pads and the transient oil film force of the pads change periodically, and the period and frequency of these changes are the same as that of the shaft rotation. The maximum force acting on the shaft appear before the maximum shaft center position (the vertexes of the whirl orbit).

Numerical and experimental study on dynamic characteristics of tilting-pad journal bearings considering pivot stiffness in a vertical rotor system

Purpose The purpose of this paper is to study the influence of pivot stiffness on the dynamic characteristics of tilting-pad journal bearings (TPJBs) and the stability of the bearing-rotor system. Design/methodology/approach A theoretical numerical model is established, and the influences of pivot stiffness on TPJBs and a bearing-rotor system are analyzed. Then, two kinds of pivot structures with different stiffness are designed and the vibration characteristics are tested on the vertical rotor bearing test bench. Findings The pivot stiffness has an obvious effect on the dynamic characteristics of the TPJBs and the stability of the bearing-rotor system. As a result of appropriate pivot stiffness, the critical speed and the vibration amplification factor can be reduced, the logarithmic decay rate and the stability of the rotor system can be effectively increased. While the journal whirl orbit is smoother and the rubbing is obviously reduced when the bearings have flexible pivots. Originality/value The influence of pivot stiffness on TPJBs and a vertical rotor-bearing system is studied by theoretical and experimental methods.

Numerical Evaluation and High-Speed Rotating Test on Circular Arc Spring Dampers for Centrifugal Compressors

Abstract A circular arc spring damper (CASD) is a recently proposed fluid-film damper that has two or more arc-shaped centering springs and dual radial clearances formed by wire electric discharge machining (WEDM). CASD requires less space and weight than a conventional cage-centered squeeze-film damper (SFD). It provides linear stiffness and stable damping force in rotor-bearing systems to attenuate vibration due to imbalance or to improve rotordynamic stability. The authors have been investigated the dynamic characteristics of CASD in component-level experiments. However, their performance and applicability to real machines have not been confirmed in system-level experiments. Additionally, a theoretical means of evaluation for CASD should be established to predict its dynamic coefficients and to understand the mechanism of dynamic force generation. In the first part of this study, a numerical evaluation method using two-way fluid–structure interaction (FSI) analysis and its theoretical background is presented. Transient structural analysis and fluid-film flow analysis with a simple homogeneous cavitation model are coupled in the commercial multiphysics platform ansys. The accuracy of the method was validated by comparing the damping and added-mass coefficients with results from previous experiments. Furthermore, several aspects of the force generation mechanism and the difference from conventional SFD were studied numerically. The second part of the study addresses the application of CASD in a multistage centrifugal compressor. A combined 4-in. diameter, five-pad tilting pad journal bearing (TPJB) with four-arc type CASD was newly designed and manufactured. To prove the applicability of the developed damper bearing, a series of rotating tests were conducted at a high-speed balancing facility with a full-scale dummy rotor with a critical speed ratio (CSR) of approximately 3.1. The measured unbalance response showed a much lower amplification factor (AF) than that of the conventional TPJB without the damper, which infers a significant improvement in the stability. The measured responses agreed with the rotordynamic analysis, which uses the dynamic coefficients of CASD derived from the proposed numerical evaluation method.

Optimization analysis of an energy harvester for smart tilting pad journal bearings considering higher vibration modes

In the light of Industry 4.0, ambient energy harvesting has been used to substitute electrical batteries and power condition monitoring sensors installed on industrial equipment. In this work, piezoelectric energy harvesters are assembled to a tilting pad journal bearing in order to harness energy from its vibration. The main contributions of this work are related to the development of a harvester model excited by its tip considering n-vibrational modes, thus allowing the determination of how many vibrational modes should be used in the computational analysis in order to achieve a balance between precision and simulation time. For this, a test rig was built to simulate this harvesting condition and validate the mathematical model developed. Finally, an optimization analysis was made to determine the best number of harvesters that should be assembled to each tilting pad as well as their geometry, in order to maximize the energy harnessed from this component without impairing the dynamic behavior of the rotating machine. The results showed an improvement of 35% on harvested energy of the optimized bearing, which contributes to the development of an independent smart bearing applied to rotating machines, capable of monitoring itself without using an external power source.

Measurements to Quantify the Effect of a Reduced Flow Rate on the Performance of a Tilting Pad Journal Bearing With Flooded Ends

Abstract Operation of tilting pad journal bearings (TPJBs) with a reduced flow decreases pumping costs and oil sump storage. A low supplied oil flow improves system energy efficiency by reducing drag power losses, albeit the temperature rise in both the bearing pads and the lubricating oil become a concern. This paper presents measurements of the static and dynamic load performance of a flooded ends TPJB lubricated with an ISO VG 46 oil supplied at 60 °C, and with a flow rate ranging from 150% to just ∼5% of a nominal supply condition. The flow range covers both over-flooded and starved flow conditions. The test bearing is a four-pad, 102 mm diameter, center pivot, with single orifice feeds, and configured with end seals to flood the bearing housing. The experiments include operation at two shaft speeds = 6 krpm and 12 krpm (= 64 m/s surface speed) and under three specific loads = 0.345 MPa, 1.03 MPa, and 2.07 MPa applied in between pads (LBP). The measurements show the bearing drag power loss decreases by nearly 20% when the flow rate drops to 50% of nominal. However, halving the flow produces a raise in pad subsurface temperatures, ∼7 °C for operation at 12 krpm. Flow reduction below 50% does result in even more substantial power savings; however, it also produces too hot pad temperatures that approach 130 °C, a known limit for Babbitt material safe operation. The bearing static eccentricity (e) and direct stiffnesses Kxx < Kyy (load direction) do not show a significant dependency on the supplied flow, either above or below the nominal condition. A minor stiffness hardening does occur for very low flow conditions, 5% or so of nominal. Damping coefficients (Cxx ∼ Cyy) decrease by ∼30% as the flow rate decreases from 150% to just a few % of the nominal flow. The experimental results are first to quantify the operation of a TPJB supplied with minute amounts of lubricant flow. A test with a very low flow rate at ∼2% of nominal and under a light load produced the emergence of a broadband subsynchronous vibration (SSV) frequency, albeit with a very small amplitude.

Tilt Pad Bearing Distributed Pad Inlet Temperature With Machine Learning—Part I: Static and Dynamic Characteristics

AbstractUncertainty in mixing coefficients (MCs) for estimating pad leading-edge film temperature in tilt pad journal bearings reduces the reliability of predicted characteristics. A three-dimensional hybrid between pad (HBP) model, utilizing computational fluid dynamics (CFD) and machine learning (ML), is developed to provide the radial and axial temperature distributions at the leading edge. This provides an ML derived, two-dimensional film temperature distribution in place of a single uniform temperature. This has a significant influence on predicted journal temperature, dynamic coefficients, and Morton effect response. An innovative finite volume method (FVM) solver significantly increases computational speed, while maintaining comparable accuracy with CFD. Part I provides methodology and simulation results for static and dynamic characteristics, while Part II applies this to Morton effect response.

Numerical and Experimental Study on the Dynamic Bearing Properties of a Four-Pad and Eight-Pad Tilting Pad Journal Bearings in a Vertical Rotor

Abstract In this paper, the dynamics of tilting pad journal bearings (TPJB) with four and eight pads are studied and compared experimentally and numerically. The experiments are performed on a rigid vertical rotor supported by two identical bearings. Two sets of experiments are carried out under a similar test setup. One set is performed on a rigid rotor with two four-pad bearings, while the other is on a rigid rotor with two eight-pad bearings. The dynamic properties of the two bearing types are compared with each other by studying the unbalance response of the system at different rotor speeds. Numerically, the test rig is modeled as a rigid rotor and the bearing coefficients are calculated based on Navier–Stokes equation. A nonlinear bearing model is developed and used in the steady-state response simulation. The measured and simulated displacement and force orbits show similar patterns for both bearing types. Compared to the measurement, the simulated mean value and range (peak-to-peak amplitude) of the bearing force deviate with a maximum of 16% and 38%, respectively. It is concluded that, unlike the eight-pad TPJB, the four-pad TPJB excites the system at the third- and fifth-order frequencies, which are due to the number of pads, and the amplitudes of these frequencies increase with the rotor speed.

A full 3D computational model for tilting-pad journal bearings and comparing it to 2D models

In this paper, a new model is developed to analyze a tilting pad bearing with 5 pads in a load-between-pad configuration in three dimensions. Isothermal Navier-Stokes equations with phase fraction equation for cavitation model are solved for 3D steady state simulation using the OpenFOAM package. Results show that with decrease in eccentricity, the difference between the 3D and 2D simulations increases. This is mainly due to the fluid inertia effects when entering the pads. Although applying the inertial boundary condition to the 2D model reduces the discrepancy, the difference in pressure distribution remains. Thus, at the lower eccentricity ratio, it is highly recommended to use 3D model in order to calculate pressure distribution precisely in tilting pad journal bearing.

A new gaseous cavitation model in a tilting-pad journal bearing.

With the higher rotational speeds and loads in bearings, the gaseous cavitation becomes more and cannot be ignorable in the bearing designs. However, there is no enough research in non-equilibrium gaseous cavitation model. This paper builds a new gaseous cavitation model based on the Bunsen solubility and bubble dynamics. The equilibrium pressure is calculated by the Bunsen solubility based on the local pressure and its pressure difference with the local pressure decides the cavitation mass transfer rate in this new model for gaseous cavitation. A titling-pad journal bearing at 3000 rpm and under 299 kN load is chosen as the research object with this new model and an original equilibrium model applied. As for the minimum film thickness and bearing force balance, this new model performs in better accordance with the experiment than the equilibrium model. According to the multiphase distributions in the bearing film, the gaseous cavitation rate in this new model can simulate the non-equilibrium processes of dissolution and cavitation under the high rotational speed, which is close to the physical gaseous cavitation process. This new model is developed and applied successfully in tilting-pad journal bearings for simulating the non-equilibrium gaseous cavitation.

A method for the experimental estimation of direct and cross-coupled dynamic coefficients of tilting-pad journal bearings of vertical hydro-generators

This article presents a method to experimentally estimate the direct and cross-coupled dynamic coefficients of tilting-pad journal bearings of vertical hydro-generators and other similar rotating machinery for damage detection purposes. Based on a simplified second-order model of a journal bearing in the state-space, the method employs only the usually monitored vibrations, the shaft radial relative, and the bearing radial absolute vibrations originated by the hydro-generator residual unbalance or by hydraulic excitations in the turbine rotor. This article shows that the method was successfully tested using the shaft and bearing vibration signals synthesized by a mathematical model of a 700 MW hydro-generator, even when these signals are contaminated with random noise. This article also shows the method’s performance when applied to real vibration signals acquired from the modeled hydro-generator. Finally, it discusses the possible measures to improve the method’s efficiency.

Nonlinear Vibration Analysis of a Flexible Rotor Supported by a Flexure Pivot Tilting Pad Journal Bearing in Comparison to a Fixed Profile Journal Bearing With Experimental Verification

Abstract In this paper, an efficient numerical method consisting of the real mode component mode synthesis (CMS) model reduction, shooting method with parallel computing, and Floquet analysis was developed for nonlinear rotordynamics analysis of a flexible rotor supported by a four-lobe flexure pivot tilting pad journal bearing (FPTPJB) in load-on-pad (LOP) and load-between-pad (LBP) orientations in comparison to a fixed profile journal bearing (JB) of the same pad geometry. The method used the rotor's finite elements and bearing forces obtained from directly solving the Reynolds equation to determine the limit cycles and Hopf bifurcation types. For the investigated rotor and bearing parameters, the numerical results indicated that the onset speed of instability (OSI) of FPTPJB is considerably higher than that of JB of the same orientation. Also, FPTPJB in LOP orientation yielded substantially higher OSI than the LBP one, whereas the OSI of JB in LOBP orientation was higher than the LOP counterpart. Nonlinear calculation results indicated that all bearing types and orientations gave subcritical Hopf bifurcation. The FPTPJB in LOP orientation produced the largest stable operating region, whereas the JB in LBP configuration yielded the smallest one. The experiment showed subcritical Hopf bifurcation occurred at speed close to the calculated OSI in all cases except FPTPJB in LOP orientation that the OSI is higher than the maximum test rig speed. The whirling orbit had the same frequency as the first critical speed and was precessed in the shaft rotation direction.

Theoretical and Experimental Investigations on Directly Lubricated Tilting Pad Journal Bearing under Starved Lubrication

In this study, a comprehensive thermoelastohydrodynamic model considering turbulence and cavitation is developed. After comparing the Reynolds-Rayleigh-Plesset and Elrod and Adams models, the Elrod and Adams model is adopted to consider cavitation effects. To validate the developed model, a series of novel two-phase flow or mixed bubble experiments is designed by extracting the characteristics of actual operating conditions. Experiments are performed on a high-speed test rig. The oil film pressure and pad surface temperature of a loaded pad under various preset gas volume fractions are measured. The experimental and simulation results show reasonable agreement, and the developed model can successfully predict the bearing performance under starved conditions.