Tilting Pad Journal Bearings Research Articles

An efficient method for establishing the static equilibrium position of the hydrodynamic tilting-pad journal bearings

Establishing the static equilibrium position of the tilting-pad journal bearing is key to determining the bearing performance. Methods for establishing the equilibrium were divided into three groups and compared. The fastest convergence was achieved using the quasi-Newton methods, namely the Anderson mixing scheme and Broyden's methods. Root-finding boundaries and the Armijo rule were implemented into these methods to obtain the globally convergent efficient methods. To test the methods, the two-dimensional computational model of the tilting-pad journal bearing based on the thermo-elasto-hydrodynamic lubrication theory was proposed. The results of the equilibrium for two bearings operating in laminar and transition flow regimes under different loads and speeds were shown. These results were validated with two sets of published experimental data.

Tilting Pad Journal Bearing Misalignment Effect on Thermally Induced Synchronous Instability (Morton Effect)

Abstract This paper investigates the influence of misaligned journal bearing effects on the thermally induced rotor instability (Morton effect “ME”) problem. The Morton effect is caused by uneven viscous heating of the journal in a fluid film bearing, which causes thermal bending, especially in rotors with an overhung disc or coupling weight. The thermally induced bending in the shaft may cause a vibration instability, which results in an excessive level of synchronous vibration. Previous research focused on parametric studies of the rotor and bearing design parameters, including overhung mass, bearing radial clearance, and lubricant viscosity. The present study investigates the influence of journal misalignment on the Morton effect. A coupled fluid-thermal-structural, three-dimensional finite element model (FEM) is developed to simulate fluid film pressures and temperatures, and shaft temperatures and vibrations. Simulations were conducted with different ratios of journal misalignment, and different pad-pivot types to determine their effect on the phenomenon. The simulation results indicate that the amplitude of the misalignment angle affects the instability speed range (ISR) caused by the Morton effect under certain conditions.

Static Characteristics of a Tilting Five-Pad Journal Bearing with an Asymmetric Geometry

In this paper, static characteristics of a tilting five-pad rocker-backed journal bearing with an asymmetric geometry, i.e., different clearance for each pad, are investigated. A thermo-elasto-hydrodynamic (TEHD) model considering the elasticity of the pad and pivot is used for the simulation. The pivot stiffness of each pad obtained by experiment is also introduced in the model. The experimental tests were carried out on a tilting pad journal bearing (TPJB) with a nominal diameter of 100 mm and a length-to-diameter (L/D) ratio of 0.7 with load-between-pad (LBP) and load-on-pad (LOP) arrangements. Several analyses, including numerical simulations and experimental measurements, are implemented in order to obtain the static behaviors of the tilting-pad bearing under variations of rotational speed, amplitude and direction of applied static load, such as clearance distribution profile, static eccentricity, temperature and pressure distribution. The results show that the effect of asymmetric geometry on the static characteristics is not negligible.

Effects of Tilting Pad Journal Bearing Design Parameters on the Pad-Pivot Friction and Nonlinear Rotordynamic Bifurcations

This study numerically analyzes and investigates the effects of the bearing design parameters of a tilting pad journal bearing (TPJB) on the pad-pivot friction-induced nonlinear rotordynamic phenomena and bifurcations. The bearing parameters were set to the pad preload, pivot offset, spherical pivot radius, and bearing length to diameter (L/D) ratio. The Stribeck curve model (SCM) model was applied at the contact surface between the pad and the pivot, which varied to the boundary-mixed-fluid friction state depending on the friction condition. The rotor-bearing model was set up with a symmetrical five-pad TPJB system supporting a Jeffcott type rigid rotor. The fluid repelling force generated in the oil film between each pad and the shaft was calculated using a finite element method. The simulation recurrently conducted the transient numerical integration to obtain the Poincaré maps and phase states of the journal and pad with various bearing design variables, then the nonlinear properties of each condition were analyzed by expressing the bifurcation diagrams. As a result, the original findings of this study are: (1) The pad preload and pivot offset significantly influenced the emergence of Hopf bifurcations and the associated limit cycles. In contrast, (2) the pivot radius and L/D ratio contributed relatively less to the friction-induced instability. Resultantly, (3) all the effects diminished when the rotor operated under the larger mass eccentricity of the disc.

Computational Fluid Dynamics Based Mixing Prediction for Tilt Pad Journal Bearing TEHD Modeling—Part I: TEHD-CFD Model Validation and Improvements

AbstractThe core contributions of Part I (1) present a computational fluid dynamics (CFD)-based approach for tilting pad journal bearing (TPJB) modeling including thermo-elasto hydrodynamic (TEHD) effects with multi-mode pad flexibility, (2) validate the model by comparison with experimental work, and (3) investigate the limitations of the conventional approach by contrasting it with the new approach. The modeling technique is advanced from the author’s previous work by including pad flexibility. The results demonstrate that the conventional approach of disregarding the three-dimensional flow physics between pads (BP) can generate significantly different pressure, temperature, heat flux, dynamic viscosity, and film thickness distributions, relative to the high-fidelity CFD model. The uncertainty of the assumed mixing coefficient (MC) may be a serious weakness when using a conventional, TPJB Reynolds model, leading to prediction errors in static and dynamic performance. The advanced mixing prediction method for “BP” thermal flow developed in Part I will be implemented with machine learning techniques in Part II to provide a means to enhance the accuracy of conventional Reynolds based TPJB models.

Computational Fluid Dynamics Based Mixing Prediction for Tilt Pad Journal Bearing TEHD Modeling—Part II: Implementation With Machine Learning

Abstract Reynolds based thermo-elasto-hydrodynamic (TEHD) simulations of tilting pad journal bearings (TPJBs) generally provide accurate results; however, the uncertainty of the pad’s leading edge thermal boundary conditions causes uncertainty of the results. The highly complex thermal-flow mixing action between pads (BPs) results from the oil supply nozzle jets and geometric features. The conventional Reynolds approach employs mixing coefficients (MCs), estimated from experience, to approximate a uniform inlet temperature for each pad. Part I utilized complex computational fluid dynamics (CFD) flow modeling to illustrate that temperature distributions at the pad inlets may deviate strongly from being uniform. The present work retains the uniform MC model but obtains the MC from detailed three-dimensional CFD modeling and machine learning, which could be extended to the radially and axially varying MC case. The steps for implementing an artificial neural network (ANN) approach for MC regression are provided as follows: (1) utilize a design of experiment step for obtaining an adaptable training set, (2) conduct CFD simulations on the BP to obtain the outputs of the training set, (3) apply an ANN learning process by Levenverg–Mardquart backpropagation with the Bayesian regularization, and (4) couple the ANN MC results with conventional TEHD Reynolds models. An approximate log fitting method provides a simplified approach for MC regression. The effectiveness of the Reynolds TEHD TPJB model with ANN regression-based MC distributions is confirmed by comparison with CFD based TEHD TPJB model results. The method obtains an accuracy nearly the same as the complete CFD model, but with the computational economy of a Reynolds approach.

Fractional modeling applied to tilting-pad journal bearings

Tilting-pad journal bearings can be found in a variety of industrial applications due to their stabilizing effects and damping behavior. Reliable mathematical modeling is demanded to analyze and control those dynamical systems. This paper adopts a fractional approach to extend an extant mathematical model of test rig for active tilting-pad bearings. Along with related results, the theoretical framework here presented may contribute to better understand such dynamic behavior, possibly supporting the development of more efficient control strategies for this important mechanical system.

Performance of Tilting Pad Journal Bearings with the Same Sommerfeld Number

This paper presents the change of non-dimensional characteristics and thermal behavior of different sized tilting pad journal bearings (TPJBs) with the same Sommerfeld number. A three-dimensional (3D) TPJB numerical model is provided considering the thermo-elastic hydro-dynamic (TEHD) lubrication model with pad thermal-elastic deformation. The pivot stiffness is assumed to be the combination of linear and cubic stiffness based on the Hertzian contact theory. The TPJBs in a configuration of load between pad (LBP) with the same Sommerfeld number having seven different sizes are simulated, and their non-dimensional dynamic and static characteristics and thermal behavior are compared. Pad thermal and elastic deformation are both taken into account. If the changes in lubricant viscosity, thermal deformation, and elastic deformation of journal/pads due to viscous shearing are ignored, the bearings with identical Sommerfeld numbers should show the same performance characteristics. However, the heat generation at the bearing clearance during operation (a) induces a decrease in viscosity and heat transfer to journal/pads and (b) results in a thermal deformation. Furthermore, the elastic deformation of the tilting pads and pivots also affects the bearing dynamic performance. For the same Sommerfeld number, the numerical analyses provide how the viscous shearing and elastic deformation lead to a change in bearing performance. For the small bearings with the same Sommerfeld number, the non-dimensional characteristics did not change significantly, where the heat generation was small being compared to the large sized bearing. The largest change in non-dimensional characteristics occurred when the maximum temperature of the oil film increased by 30 °C or more compared to the lubricant supply temperature. The root cause of the change in the non-dimensional characteristics is the viscous shearing in the oil film, and the thermal deformation of the structures surrounding the oil film acts in combination. These results provide insight into the Sommerfeld number, which can be used for the early stage of bearing design.

Experimental analysis of the thermal unbalance effect of a flexible rotor supported by a flexure pivot tilting pad bearing

The Morton effect is a thermally induced increase of synchronous vibrations amplitudes of rotors. The shearing of the fluid film in a journal bearing produces an asymmetric heating of the rotor which causes its thermal bending and increases the unbalance. The vector of synchronous vibrations describes a spiral with slowly increasing amplitude and phase change. The thermal bending is also enlightened by a hysteresis effect of the synchronous vibrations during start-up and coast-down. The purpose of this study is to highlight experimentally the signature of Morton effect in a flexible rotor supported by a flexure pivot tilting pad journal bearing. A dedicated test rig has been built. It consists of a flexible rotor guided at one end by a ball bearing and at the other end by a flexure pivot tilting pad bearing. The tests consist of controlled start-ups to a speed close to the critical speed of the first rotor flexible mode, followed by controlled coast-downs. They show a hysteresis of the amplitudes and phases of the synchronous vibrations. Other tests performed at constant speeds show amplitude and phase variations corresponding to spiral vibrations. The results are explained by the non-uniform distribution of the rotor temperature.

Analytical Method for Hydrodynamic Force in Finite-Length Tilting-Pad Journal Bearing Including Turbulence Effect

Abstract To improve the efficiency in nonlinear dynamic calculation of finite-length tilting-pad journal bearings (TPJBs) under dynamic loads, an analytical method for hydrodynamic bearing forces, which considers the turbulence effect, is proposed using the method of separation of variables under the dynamic Gümbel boundary condition. No thermal effects are considered because this method is designed for the low viscosity case. The infinitely long bearing pressure is introduced as the circumferential pressure, and a general solution of the nonhomogeneous Reynolds equation is derived as the axial pressure. The turbulence model of Ng and Pan is characterized by a linear function of film thicknesses. A complete analytical expression of hydrodynamic bearing forces is derived. The analytical simulation shows slight differences and extremely low time expense in lubricating and dynamic performance compared to published data and finite difference method (FDM) simulation. The analytical method could be used to fast evaluate the nonlinear dynamic performance of a TPJB-rotor system in the low viscosity environment, supporting the nonlinear dynamic design of the system.

Performance analysis of tilting pad journal bearing using COMSOL Multiphysics and Neural Networks

The objective of this paper is to study the effect of geometrical parameters on the performance of tilting pad journal bearing. COMSOL Multiphysics software is used to simulate the tilting pad journal bearing at different eccentricity ratios and pad clearances. The effect of changing pad numbers (from 3 to 6 pads) and the pads clearance angles (from 2° to 6°) on the performance parameters such as the load carrying capacity, frictional torque and attitude angle was analyzed. It was found that as the number of pads increases the load carrying capacity and the friction coefficient increase, while the attitude angle decreases. Decreasing the clearance between pads leads to an increase in the load carrying capacity of the bearing while it has minor effect on the other performance parameters. The characteristic data obtained from COMSOL program is used to train three suggested neural networks. The first is a feed-forward Neural Network which consists of three layers with {80 sigmoid, 5 sigmoid and 1 linear} neurons. The second is a radial bases Neural Network and the third is a generalized regression Neural Network. Applying the three trained Neural Networks (Feed forward, Radial basis, and Generalized regression) to predict the performance of tilting pad bearing at values not used in the training process. The results show a high accuracy to predict the attitude angle, the coefficient of friction and the load carrying capacity. The percentage relative errors between the predicted values and that obtained by COMSOL are between (0 and 0.98) %. The neural networks model show high capacity in predicting the output variables correctly for both the training data and that which was not included.

Effect of pivot stiffness on nonlinear dynamic characteristics of tilting pad journal bearings

The role of pivot stiffness on dynamic response is explored in a large stiffness range for tilting pad journal bearings in vertical and horizontal rotors. Two designs are compared: rigid pivot and disc spring set pivot. The latter is adjustable to vary from completely soft to almost rigid. Effect of journal unbalance is also discussed. It is shown that two threshold points of 0.1 and 10 are discovered for pivot stiffness ratio. Specific pivot stiffness at different intervals has totally different effects on orbits. In addition, another point exists as turning point for pivot stiffness ratio and results in the significant orbit peak. Further, pivot stiffness effect is sensitive to journal unbalance, particularly at the peak point.

Multi-domain stability and modal analysis applied to Gas Foil Bearings: Three approaches

The dynamic characteristics of rotors supported by Gas Foil Bearings (GFBs) are commonly assessed using linear force coefficients, which are usually derived from an analytical perturbation in combination with an implicit compliance model. This remains common practice even though discrepancies have been reported between the Onset Speed of Instability (OSI) predicted using such linear coefficients and observations from non-linear time integration. For the first time, the present paper pinpoints the root cause of this discrepancy by demonstrating an extended perturbation, akin to that used for tilting pad journal bearings, to predict exactly the same OSIs as obtained from an eigenvalue analysis based on the Jacobian of the full non-linear system of equations. To demonstrate this, the OSIs predicted using (i) the classical perturbation, (ii) the extended perturbation, and (iii) the Jacobian eigenvalues are compared over a range of compliance levels covering essentially rigid bearings to modern heavily loaded industrial GFBs. Using carefully aligned implementations, the deficiency of the classical method is demonstrated to increase with the compliance level (up to 13% for the benchmark case), while the extended perturbation provides OSIs in agreement with the Jacobian eigenvalues for all compliance levels. Furthermore, the mode shapes attainable from the three approaches, encompassing only the rotor, the rotor and foil, and the rotor, foil and pressure respectively, are compared.

Research on rotary system with tilting-pad journal bearings

Research on rotary system with tilting-pad journal bearings

Piezoelectric harvester for smart tilting pad journal bearings

Piezoelectric harvesters have been the object of constant research due to the increasing need for smart and independent sensors. The main contribution of the present work to this field is the development of a new approach: to harness the vibrational energy from tilting pad journal bearings using piezoelectric harvesters and use it to power typical condition monitoring sensors. The goal of this work is to verify if it is possible to assemble the harvester on the bearing without impairing its dynamic behavior and to ascertain that the energy harvested is enough to power the condition monitoring sensor. In order to achieve it, the electric and mechanical harvester models were developed and coupled with the bearing model using the full coefficients approach. It was possible to verify that the harvester may produce up to 2.25 mW of energy, enough to power a typical wireless sensor without impairing the bearing’s stability. These results indicate that it is possible to develop an independent smart bearing for rotating machines, fully capable of monitoring itself without an external power source.

Cooled Pads for Tilting-Pad Journal Bearings

Tilting-pad journal bearings (TPJBs) are widely installed in rotating machines owing to their high stability, but some drawbacks can be noted, such as higher cost with respect to cylindrical journal bearings and thermal issues. High temperatures in the pads correspond to low oil-film thicknesses and large thermal deformations in the pads. Therefore, the restriction of the maximum temperature of the bearing is a key aspect for oil-film bearings. The temperature reduction is generally obtained by adopting higher oil inlet flowrates or suitable oil nozzles. In this paper, the idea of using cooled pads with internal channels in which an external cooling fluid is circulated will be applied to a TPJB for the first time. The three-dimensional TEHD model of the TPJB, equipped with a cooled pad, will be introduced, and the results of the numerical simulations will be discussed. Several analyses have been performed in order to investigate the influence of cooling conditions, such as the type, flowrate, inlet temperature and number of cooled pads. Two types of pad geometry with different cross-sections of the cooling circuit, namely, circular and six-square multi-channel sections, have been compared to the reference bearing with solid pads. Simple experimental tests were performed by means of a test rig equipped with a cooled pad bearing obtained with the additive manufacturing process, thus showing the effectiveness of the solution and the agreement with the predictions.

Nonlinear dynamic analysis of low viscosity fluid-lubricated tilting-pad journal bearing for different design parameters

To reveal nonlinear dynamic rules of low viscosity fluid-lubricated tilting-pad journal bearings (TPJBs), the effects of design parameters on journal center orbits and dynamic minimum film thicknesses of water-lubricated TPJBs with and without static loads are investigated. The hydrodynamic bearing force used in the nonlinear dynamic analysis is an approximate analytical solution including the turbulence effect. The results reveal the methods for vibration suppression and load capacity improvement and give an optimal pivot offset and clearance ratio that can maximize the minimum film thickness. The results also show that four-pad TPJBs with loads between pads are preferred due to good dynamic performance and load capacity. This study would provide some guidance for nonlinear design of low viscosity fluid-lubricated TPJBs under dynamic loads.

A 3D Approach for THD Lubrication in Tilting Pad Journal Bearing—Theory and Experiment

The study of rotating machines stands out in the context of systems and structures due to the significant number of typical phenomena that may be present during the operation of such equipment. Rotating systems play an important role in industrial environments, with a wide range of application, namely, pumps, turbines, generators and compressors, and turbochargers, among others. Given this context, tilting pad journal bearings (TPJBs) can offer considerable stability to the rotor system due to its damping and stiffness characteristics, especially under high rotation speeds, whereas journal bearings with a fixed geometry may be subjected to fluid-induced instability. Consequently, thermal effects are significant in rotating machines to evaluate the behavior of hydrodynamic bearings due to the increase in shear effects in the lubricant caused by the rotation speed, leading to excessive temperature increase under specific operational conditions and, therefore, significant changes in lubricant viscosity. These effects may influence the dynamic characteristics of bearings, affecting the dynamic response of the entire system. From this perspective, a specific test rig was designed to perform the characteristic uncoupled motion of the shaft when supported by this kind of bearing. Experimental tests were directly compared with numerical models, showing promising results. In addition, the thermohydrodynamic (THD) lubrication was numerically solved by a finite volume method, considering an approach for a 3D THD model and the pivot flexibility.

Experimental and theoretical investigations on transition of lubrication conditions for a five-pad tilting-pad journal bearing with eccentric pivot up to highest surface speeds

Abstract Lubrication conditions of tilting-pad journal bearings strongly depend on the combination of bearing design, lubricant flow rate, and operating boundary conditions. A five-pad tilting-pad journal bearing is investigated experimentally for surface speeds ranging from 25 to 140 m/s and specific bearing loads between 1.0 and 4.0 MPa at different fresh oil flow rates. Comparisons to theoretical analyses indicate speed-dependent transition from fully flooded to partially filled conditions in certain space between pad regions. These conditions are discussed in detail and a semi-empirical model to approximate this behavior is proposed and validated with the test data.

Tilting-Pad Journal Bearing Subjected to Fuzzy Type-2 Uncertain Parameters

Abstract This paper evaluates the effects of uncertainties on the load capacity of a four-pad tilting-pad journal bearing, in which the pad radius, oil viscosity, and radial clearance are considered as uncertain information. The hydrodynamic supporting forces at the bearing pads are obtained by solving the Reynolds equation. In this case, the uncertain parameters are modeled as fuzzy type-2 variables. Fuzzy type-2 sets have been widely used due to their ability to model higher orders of uncertainties as compared with the fuzzy type-1 approach. They allow for inaccurate knowledge to be included in the membership functions used to describe the uncertain parameters. In the present contribution, the so-called α-level optimization was associated with the fuzzy type-2 technique for uncertainty analysis purposes. A sensitivity analysis was also carried out as an additional assessment of the considered uncertain parameters. The numerical results allowed to understand how the uncertain parameters affect the bearing supporting forces for three shaft speeds, namely, 3000, 9000, and 15,000 rpm. It was demonstrated that the effect of the uncertain parameters on the supporting forces increases according to the shaft speed. Additionally, the load capacity revealed to be more sensitive to variations on the oil viscosity and radial clearance than to the pad radius concerning the adopted uncertain interval. Consequently, the obtained results can provide suitable information for the design, manufacturing, and maintenance of tilting-pad journal bearings.