Tilting Pad Journal Bearings Research Articles

Transient lubrication performance of tilting-pad journal bearings under dynamic load considering bi-directional misalignment and mixing temperature behavior

Tilting-pad journal bearings (TPJBs) are highly self-adaptive for serving as support bearings in marine gas turbines. However, the research on the transient lubrication performance of TPJBs during ship navigation is limited, especially under misalignment and complex heat exchange. A transient tribo-dynamic model considering the bi-directional misalignment and mixing temperature behavior of TPJBs has been built. The time-varying oil film characteristics are comparatively analyzed among different misalignments. Moreover, the influence of mixing temperature behavior on transient responses is further revealed. The results indicate that the interaction effect of mixing behavior and misalignment has a substantial impact on the transient characteristics of TPJBs with dynamic load. It is significant to forecast the lubrication performance of TPJBs of marine gas turbines.

Experimental study on the influence of flexible structure and gas supply method on the characteristics of aerostatic tilting-pad bearing

Purpose This paper aims to propose novel flexible structure-supported tilting-pad aerostatic bearings and to improve operational stability and vibration reduction of aerostatic bearings. Design/methodology/approach The authors established an aerostatic bearing-rotor test rig and designed two aerostatic tilting-pad bearings with different flexible support structure and an ordinary aerostatic tilting-pad bearing and then examined their effects in dynamic performance to assess the vibration reduction performance of different flexible structures. Furthermore, the authors proposed three gas supply methods and conducted experiments to study the influence of gas supply methods in the performance of bearings. Findings The experimental results show that among the three structures, the double-layer flexible structure-supported tilting-pad bearing demonstrates outstanding vibration damping performance and it significantly enhances the operational stability of the bearing-rotor system. Furthermore, the experimental results indicate that the gas supply method has a significant impact on the performance of the aerostatic bearing. There is a certain pressure difference between the gas supply pressure for the loading pads and that for the nonloading pads, which is advantageous for increasing the operational stability and reducing system vibration. Originality/value The authors designed novel flexible aerostatic tilting-pad journal bearing structures, which can enhance the operational stability and reduce vibrations of the bearing. Additionally, this article proposes an air supply method advantageous for increasing the stability of the bearing and reducing system vibrations.

The impact of installation deviation on the lubricating characteristics of a 1000 MW giant hydropower unit’s tilting-pad journal bearing

Abstract With the trend towards larger and higher capacity units, tilting-pad journal bearings are being increasingly used in hydropower units. Through thermo-hydrodynamic (THD) analysis, it is possible to establish pressure differential equations that consider the change in oil viscosity with temperature, which is essential to ensure safe operation of the bearing. Further research on the flowing characteristics of tilting-pad journal bearings, especially about installation deviations, is essential for giant hydropower unit. This study establishes a three-dimensional model of a 1000 MW hydropower unit’s turbine journal bearing to investigate temperature, pressure distribution, and load under various installation deviation scenarios. The findings aim to optimize the design and engineering practices of tilting-pad bearings in rotating machinery, meeting the evolving needs of the power industry.

Series solution of the Reynolds equation in finite-length tilting-pad journal bearing including pad deformation

This paper applies the variable separation method to the hydrodynamic pressure calculation of finite-length tilting pad journal bearings under Reynolds boundary conditions, and a series solution of the Reynolds equation is obtained based on the Sturm-Liouville theory, which considers pad deformation. The thermal effect is also taken into account. A comparison of the present solutions is made with the results obtained by other applied methods, as well as past and recent published data, and good agreement is noted. The steady-state and dynamic performance of a four-pad tilting pad journal bearing are investigated by the load capacity, pressure distribution, friction force, lubricant effective viscosity, journal center velocity, journal center orbits, and phase portrait under the proposed series solution of the Reynolds equation. This study contributes to quickly evaluating the nonlinear dynamic performance of a tilting pad journal bearing rotor system and supporting the nonlinear dynamic design of the system.

A Numerical Investigation of Mixed Thermal Elastohydrodynamic Lubrication in Tilting-Pad Journal Bearing

Abstract The tilting-pad journal bearing in the cooling system of the nuclear power plant is equipped below the ground and vertically positioned to accomplish its function for water transfer. Usually, the loading conditions are relatively stable since the required water volume almost remains the same level during the operation, but the loading direction cannot be known in advance. Furthermore, the bearing is designed with several separate pads, which allows the bearing to support the loading flexibly. The safety application of nuclear energy requires the bearing to have a reliable ability to maintain the rotating motion of gear sets. This study develops a numerical model to simulate the mixed thermo-elastohydrodynamic lubrication for the tilting-pad journal bearing in the nuclear plant. The elastic and thermal fields are properly determined, and the induced displacement is taken into account for an accurate description of film thickness. The asperity contact due to misaligned journal is well evaluated in the local area where the lubrication film cannot separate the surfaces. A parametric study is undertaken in detail to reveal the aspects that influence bearing lubrication. The conclusions potentially provide fundamentals for further lubrication optimization of the bearing system.

Dynamic performances of novel misaligned non-uniform distributed tilting-pad bearing

The non-uniform distributed tilting-pad journal bearings (NDTPJB) in large wind turbine main shafting has become an important development trend for high-power wind turbines due to the advantages of improving reliability and reducing maintenance costs. However, studies involving NDTPJB have not been reported under specific conditions such as low speed, wide range variable direction and magnitude of heavy-load in wind turbine. A new transient mixed elastohydrodynamic lubrication (mixed EHL) model for NDTPJB is established, taking into account the misalignment effect of the shaft tilt and the swinging of pads in the circumferential and axial directions, as well as the influence of pivot friction and elastic deformation effects. Based on the mathematical model, the dynamic characteristics and structural parameter effects of NDTPJB are systematically studied under low speed, wide range variable direction and magnitude of heavy-load. The results indicate that the NDTPJB exhibits a more significant sensitivity to the heavy load direction due to the different functional roles of the above distributed pads (ADP) and bottom distributed pads (BDP). The modified mixed EHL model can more accurately evaluate the lubrication performance of NDTPJB, and combine the characteristics in individual pad swing and the overall effect of the pads to comprehensively analyze the dynamic lubrication behavior of NDTPJB. By setting the pivot coefficient to 0.55, reducing the distribution angle of BDP, and increasing the distribution angle of ADP, a better load-carrying capacity can be achieved. The research results have guiding significance for further monitoring and analyzing the experimental performance of NDTPJB, as well as designing and optimizing such bearing structures.

Tilting Pad Journal Bearing Computational Fluid Dynamic Parametric Modeling for New Energy Transition Challenges

Abstract The necessity of increasing the efficiency and reducing the carbon foot-print of machines is pushing centrifugal compressor bearings design to higher and higher peripheral speed and lower oil consumptions especially in the new energy transition fields, resulting in an increase in the bearing temperatures. Therefore, the bearing thermal management starts to play a major role in extending the machine operability and reducing the maintenance frequency. A full three-dimensional (3D) parametric conjugate heat transfer computational fluid dynamic (CFD) model for tilting pad journal bearings (TPJBs) is introduced in this paper to address the temperature aspects of oil-film bearings. The parametric geometry of the model and the automatic mesh update, allow the equilibrium position search to be obtained without adopting any dynamic mesh algorithms. The tilting pad and rotating shaft equilibrium position are automatically calculated with a Newton–Raphson algorithm. The static performance of the TPJB is investigated for different journal diameters, bearing clearance, and operating conditions. The numerical results obtained are compared with experimental data from compressor mechanical running tests to demonstrate the reliability of the model presented. The 3D distributions of the oil pressure, velocity, and temperature given by the CFD model, can be locally optimized to face the new energy transition challenges.

Effect of Reduced Oil Flow Rate on the Performance of a Load on Pad Journal Bearing: Flooded Versus Evacuated Conditions

Abstract Means to decrease the energy consumption of tilting pad journal bearings (TPJBs) without affecting their performance and structural integrity are mandatory in a cost efficient operation. Reducing the lubricant flow supplied to a bearing is a distinct method to diminish drag power losses along with savings in oil storage and pump equipment. However, a too low flow remains questionable in industrial practice. Starved flow conditions produce hot pad surfaces that could lead to Babbitt failure; and under certain loads, generate subsynchronous vibrations (SSV). This paper aims to resolve some of the issues above via measurements of the load performance conducted with a four-pad TPJB configured as load-on-pad (LOP) and having its ends sealed or open to make flooded and evacuated conditions. Prior measurements were conducted with the same bearing under load-between-pads (LBP); see Refs. [1] and [2]. The nominal supplied flow (Q) of ISO VG 46 oil at 60 °C is proportional to shaft speed (max. 12 krpm: 62.8 m/s surface speed). In the tests, the flow Qs ranges from 1.5 Q to just ¼ Q, and the applied units load reaches 2.07 MPa. Compared to the flooded bearing, the evacuated bearing produces a slightly larger eccentricity across the range of flow rates. For a unit load = 2.07 MPa and shaft speed of 6 or 12 krpm, the highest pad subsurface temperature reaches ∼130 °C for Qs below 50% nominal. For both bearings, flooded or evacuated, drag power losses decrease to ∼30% as the oil flow drops from 100% to 50% Q. As the oil flow increases to 1.5 Q, the drag power increases ∼10% for both bearing types at 6 krpm and for the flooded one at 12 krpm, while the evacuated bearing shows a reduction of ∼7%. The drag power grows as the static load increases; the evacuated bearing producing up to ∼ 40% lesser power loss than the flooded bearing. Both bearings produce similar size direct stiffnesses though largely orthotropic, Kyy ≫ Kxx. Direct damping coefficients Cxx ∼ Cyy increase with shaft speed and unit load but dramatically decrease as Qs drops, in particular for the evacuated bearing. The current measurements and those in Refs. [1] and [2] demonstrate that LOP and LBP bearings can safely operate with 50% of nominal flow thus saving drag power, and without too large pad, temperature rises. Alas, too low Qs produces a significant reduction in the damping coefficient orthogonal to the applied load direction. The effect is most evident in the LOP evacuated bearing, which is most prone to show SSV Hash.

A genetic-continuation algorithm for bifurcation analysis of nonlinear rotordynamic systems

This study presents a combined numerical scheme with genetic algorithm and continuation method for analysing nonlinear vibrations in rotor-bearing systems. A modified genetic algorithm is developed for solving multiple coexisting roots in nonlinear rotordynamic problem. Here, the genetic objective is the completion of periodicity for the boundary values of journal/pad phase states during the consecutive generations. The arc-length continuation takes the role to extend the solutions with respect to operating parameters such as the shaft spin speed and disc mass eccentricity. The resulting bifurcation diagrams, then, can comprehensively show the emergences and disappearances of multiple response states and their stability conditions in detail, which is unlike with the commonly applied numerical integration method. A finite model of heavily loaded Jeffcott rotor supported by six-pad tilting pad journal bearing is utilized to evaluate the developed algorithm. The 150 initial states for the journal and pad are generated, and the 8 optimal results are selected and inbreeded for evolution; it repeats for 15 generations. As results, multiple coexisting responses are identified at the same condition, and various bifurcation events such as periodic doubling, saddle-node are discovered from the solution manifolds.

Machine Learning-Based Optimizer for Tilting Pad Journal Bearing Inlet Flowrate

Abstract In view of the green economy and energy transition, the reduction of the environmental impact of the power generation sector plays a key role. Fluid film bearings are the most common bearing for industrial turbomachinery and new design requirements have a direct impact on bearings operation. In fact, to achieve higher levels of efficiency, bearings must support higher specific loads and higher peripheral speeds. Furthermore, there is great interest in reducing the oil flowrate required for the bearing operation as much as possible. In this work, an optimization strategy for reducing the flowrate fed to tilting pad journal bearings (TPJBs) is proposed. An artificial neural network (ANN) is trained to estimate the static and dynamic performance of the bearings. The training dataset is built with a Reynolds-based thermo-hydrodynamic model. The trained ANN is then used in a constrained optimization that has the goal of minimizing the oil flowrate while ensuring safe bearing operation. Predictions are compared with experimental data from compressor mechanical running tests. The proposed model is an effective tool that can help industry achieve the goals required by the energy transition and can help in the development of optimized fluid film bearings.

The Impact of Thermal Load and Turbulent Flow on Minimum Film Thickness of a Large Tilting-Pad Journal Bearing

Abstract Thermal loads induced by internal fluid friction significantly influence the operating behavior of high-speed journal bearings. These loads increase on average if critical Reynolds numbers are exceeded. This paper presents a detailed thermo-elasto-hydrodynamic (TEHD) analysis of a large five-pad tilting-pad journal bearing operating up to surface speeds of 94 m/s. The structure mechanical analysis is conducted by a FE-Code that is implemented as a submodule of the bearing code to improve computational efficiency. The nonlinear structure model includes the pads, their aligning ring, and the housing while the journal's thermal expansion is approximated analytically. The contact of pads and ring is modeled with a contact algorithm. Validation with test data from literature indicates the relevance of structure model's complexity. Besides the pad deflection, in particular, the consideration of the ring and housing thermal expansion is decisive in predicting the effective clearance properly. Furthermore, comparisons between measurement and simulation show that the experimentally identified nonlinear speed-dependent characteristic of minimum film thickness that features an increase due to turbulent flow is well predicted by the theoretical model. Generally, results provide an insight on the impact of the different effects dominating the behavior of the bearing in the respective speed ranges, and therefore, improve the understanding of complex bearing systems. Finally, the quality of results of approximation formulas that are easier to implement and more time efficient than the complex FE-code is investigated.

A Contribution to Experimental Identification of Frequency-Dependent Dynamic Coefficients of Tilting-Pad Journal Bearings with Centered and Off-Centered Pivot

Linearized dynamic bearing parameters and models are of essential interest for rotordynamic analyses in machine design. This paper experimentally studies the impact of pad preload and pivot offset on the frequency-dependent characteristics of dynamic stiffness (K) and damping coefficients (C) of a KC-model for tilting-pad journal bearings. For this purpose, two four-pad test bearing configurations (preload m=0.17, pivot offset 0.5 and preload m=0.47, pivot offset 0.6) that differ highly with respect to the pad design parameters are investigated. Contributing effects on the results due to geometric differences are excluded as far as possible, as only one aligning ring and one pivot support design is used. The tests are conducted on a high-performance test rig for surface speeds up to 140 m/s and excitation frequencies of 500 Hz. Significant deviations between the two bearings are identified that generally match theoretically predicted differences and, therefore, contribute to the validation of dynamic bearing modeling.

Theoretical analysis and experimental tests of tilting pad journal bearings with shoes made of polymer material and low-boiling liquid lubrication

Selecting the appropriate bearing system for the rotor requires a good knowledge of the available solutions and the operating conditions of the machine. For newly designed machinery operating in adverse conditions, selecting bearings that ensure correct and long-lasting operation can be extremely challenging. Difficulties increase when the machine's operating parameters are beyond the technical capabilities of available technical solutions. This article presents the course of the design process and results of numerical and experimental research of a prototype microturbine that uses an innovative rotor-bearing system. Due to the adverse operating conditions, new tilting pad journal bearings were designed, in which the sliding surfaces of the tilting pads were made of polymeric material and a low-viscosity medium in liquid form was used as the lubricating medium. The basic bearing parameters were selected and pre-checked by numerical calculations. The oil-free turbomachinery design thus developed was subjected to experimental testing under near-real conditions. The results of these tests confirmed that the developed bearings performed very well, ensuring stable operation of the high-speed rotor of the microturbine over a wide speed range. Despite the unfavourable lubrication conditions, no signs of bearing wear were observed. The results obtained indicate a new, promising direction for the development of bearing systems for turbomachinery, in which, with a suitable design of the bearings, a low-boiling working medium in liquid form can be used as a lubricating medium.

Optimization Numerically for Five-Pad Tilting-Pad Journal Bearings Design Based on Particle Swarm

The design of five-pad tilting-pad journal bearings (TPJB) is complicated because of the uncertainty of design parameters that greatly affects the performance of TPJB. In this study, the numerical lubrication model is established to predict the performance of TPJB. Furthermore, a new optimal method combining the lubrication model and particle swarm method with a comprehensive target is brought out, which can obtain the optimal design parameters correctly and rapidly compared with the enumeration method. The performance of TPJB is better after optimization, especially the when the temperature and frictional coefficient decreased by about 31.1% and 35.8%, respectively. Moreover, different application scenarios of TPJB need different weight factor combinations in the comprehensive target, which is valuable for different design requirements.

Simplified transformation matrices of journal bearings in vertical application

Rotodynamic simulation of complex or/and large systems, for instance hydropower machines, may consist of models with many degrees of freedom and require multidisciplinary computations such as fluid-thermal-structure interactions or rotor-stator interactions due to electromagnetic forces. Simulating such systems is often computationally heavy and impractical, especially in the case of optimization or parametric study, where many iterations are required. This has, therefore, created a need for simplified dynamic models to improve computational efficiency without significantly affecting the accuracy of the simulation result. The purpose of this paper is to present simplified coordinate transformation matrices for journal bearings in vertical rotors, which require less computational effort. Matrix multiplications, which appear during coordinate transformation, were eliminated, and the bearing stiffness and damping matrices in the fixed reference frame were represented by local coefficients instead. The dynamic response of a vertical rotor with eight-shoe Tilting pad journal bearings was simulated using the proposed model for two operational conditions, i.e., when the rotor was spinning at constant and variable speeds. The results from the proposed model were compared to those from the original model and validated through experiments. The conclusion was that the presented simulation model is time efficient and can effectively be used in rotordynamic simulations and analyses.

Artificial neural network for tilting pad journal bearing characterization

Tilting pad journal bearings (TPJBs) are modeled with Reynold-based models or computational fluid dynamics (CFD) approach. In both cases, the estimation of the dynamic coefficients of the oil-film forces and the static characteristic, can be computationally expensive and time consuming. Artificial Intelligence (AI) is assuming a key role in engineering but is rarely applied in fluid film bearing analysis. A properly trained Deep Learning (DL) model can perform very fast predictions of TPJB behavior with accuracy comparable to more time-consuming models. In this case, the main drawback is the time required to build the training dataset. In this work, an Artificial Neural Network (ANN) is trained to predict the dynamic stiffness and damping coefficients along with the main static quantities of TPJBs, such as minimum oil-film thickness and inlet flowrate. At first, a design of experiment is performed to build an appropriate training dataset. Secondly, a Reynolds-based thermo-hydrodynamic (THD) model is used to populate the training dataset and an appropriate test dataset. Then, a feed-forward ANN is trained with Levenberg–Marquardt backpropagation and its architecture is optimized to increase accuracy. Finally, the accuracy of the ANN is tested using the test dataset and experimental data. The time and computational effort required by the ANN regression are much less than those required by the THD model. Therefore, the trained ANN is an effective and efficient tool for the characterization of TPJBs.

Numerical analysis of the effect of texture on the steady-state characteristics of tilting pad journal bearings

This work aims to study the effect of semi-ellipsoid texture on the bearing load capacity and maximum oil film temperature of tilting pad journal bearings. It has been shown that surface texture can improve the steady-state performance of bearings, but there are few studies on tilting pad journal bearings. A thermal elastohydrodynamic model of tilting pad journal bearings have been developed to support the analysis and solved by the finite difference method. The calculation results of the model are in good agreement with the simulation results of MADYN 2000 software, which proves the validity of the model. The effects of texture distribution, depth, radius, and density on the characteristics of tilting pad journal bearings were studied and compared with those of untextured tilting pad journal bearings. The results show that texture can significantly enhance or weaken the steady-state characteristics of tilting pad journal bearings, which is related to the texture parameters. This work provides a reference for the design of tilting pad journal bearings.

Dynamic of a Flexible Rotor-Bearing System Supported by Worn Tilting Journal Bearings Experiencing Rub-Impact

Wear usually occurs in the loaded part of hydrodynamic bearings and leads to bearing geometry imperfections. This paper investigates the effects of wear-induced geometric imperfections of tilting pad journal bearings (TPJBs) on the dynamic behavior of the system. Furthermore, the effect of wear on the journal-bearing rub-induced contact pressure severity is investigated. A novel tribo-dynamic model is proposed for a flexible rotor-worn TPJB which integrates a mixed elastohydrodynamic model with a rotor-worn TPJB thermal and dynamic model to assess the effects of the bearing wear progression on rotor-TPJB behavior. Based on the results, wear changes the temperature distribution of the pads and oil film as well as the dynamic behavior of the system. Dynamic simulations reveal a higher vibration level and contact pressure for the worn TPJBs near the system’s critical speed and service speed. Finally, thermal and dynamic condition indicators are suggested to detect TPJB wear severity at its early stages.

Investigation on Pivot Rolling Motion Effect on the Behavior of Rocker Back Tilting Pad Journal Bearings

The rolling motion of the pads with rocker back (RB) and ball and socket pivots is normally neglected in common software programs for the study of the rotor dynamic behavior of tilting pad journal bearings (TPJB). In other words, the theoretical contact point of the pivot is considered fixed. The aim of this work is to provide a novel way to implement in commercial software the effect of the variation of the circumferential coordinate of the theoretical contact point due to the pad rolling motion in RB TPJB. This is done by introducing an equivalent pivot rotational stiffness evaluated with an analytically derived formula, validated through finite element analysis. Such a stiffness is a function of the pad load and the radii of the contact pair, increasing with the load, the radii, and the degree of conformity of the contact. The static and dynamic characteristics of a five pad RB TPJB are then evaluated with a commercial software with and without the rotational stiffness contribution for two different pivot geometries. Non-negligible differences were found, particularly regarding the cross-coupled dynamic coefficients that show the higher sensitivity to the rotational stiffness. The inclusion of a pivot rotational stiffness among the data of commercial software for simulation of RB TPJB could contribute to fill the gap between numerical and experimental results.

Tilting-Pad Bearings—The Contact Flexibility of the Pivot

The modeling of tilting-pad journal and thrust bearings presents a level of complexity beyond that of bearings with a fixed-arc geometry, particularly with regard to their dynamic influences. With tilting-pad bearings, the theory surrounding their fluid film must be complemented with the representative modeling of the pad dynamics. What has been recognized in recent decades is the significance of the pad support, in particular the flexibility of the pivot region of the pad. The typical model for including the stiffness of the pivot is based on the Hertzian contact theory. Some researchers have noted that the Hertzian theory does not permit sufficient flexibility in the pivot region. It has been suggested that the contact mechanics at the pivot would be better represented as a pairing of rough surfaces. The modeling used here is based on a statistical asperity micro-contact theory for rough surface line contact that has been extended to include contact stiffness. This model has been applied to the determination of the effective dynamic properties of tilting-pad bearings. The results show that pivot stiffness can be as low as one third of the stiffness determined by the Hertzian theory. A comparison to published experimental results confirms the significance of the rough surface modeling, particularly for the line contacts associated with rocker-back tilting pads.