Tilting-pad Bearings Research Articles

Friction and Lubrication of Large Tilting-Pad Thrust Bearings

Fluid film bearings have been extensively used in the industry because of their unbeatable durability and extremely low friction coefficient, despite a very low coefficient of friction dissipation of energy being noticeable, especially in large bearings. Lubricating systems of large tilting pad thrust bearings utilized in large, vertical shaft hydrogenerators are presented in this paper. A large amount of heat is generated due to viscous shearing of the lubricant large tilting pad thrust bearings, and this requires systems for forced cooling of the lubricant. In the dominant bath lubrication systems, cooling is realized by internal coolers or external cooling systems, with the latter showing some important advantages at the cost of complexity and also, potentially, lower reliability. Substantial losses in the bearings, reaching 1 MW in extreme cases, are a good motivation for the research and development aimed at reducing them. Some possible methods and their potential efficiency, along with some effects already documented, are also described in the paper.

Establishment of Approximate Analytical Model of Oil Film Force for Finite Length Tilting Pad Journal Bearings

Tilting pad bearings offer unique dynamic stability enabling successful deployment of high-speed rotating machinery. The model of dynamic stiffness, damping, and added mass coefficients is often used for rotordynamic analyses, and this method does not suffice to describe the dynamic behaviour due to the nonlinear effects of oil film force under larger shaft vibration or vertical rotor conditions. The objective of this paper is to present a nonlinear oil force model for finite length tilting pad journal bearings. An approximate analytic oil film force model was established by analysing the dynamic characteristic of oil film of a single pad journal bearing using variable separation method under the dynamicπoil film boundary condition. And an oil film force model of a four-tilting-pad journal bearing was established by using the pad assembly technique and considering pad tilting angle. The validity of the model established was proved by analyzing the distribution of oil film pressure and the locus of journal centre for tilting pad journal bearings and by comparing the model established in this paper with the model established using finite difference method.

유한 요소 해석을 통해 계산된 틸팅 패드 베어링의 피봇 강성과 Hertzian 접촉 모델 해석 결과 비교

Recent studies emphasize the importance of pivot stiffness in the analysis of tilting pad bearings (TPBs). The present paper develops a finite element model of the pad pivot and compares the predicted pivot stiffness to the results of Hertzian contact model calculations. Specifically, a finite element analysis generates tetrahedral mesh models with ~40,000 nodes for a ball-socket pivot and ~50,000 nodes for a rocker-back pivot. These models assume a frictionless boundary condition in the contact area. Increasing the applied loads on the pad in conjunction with increasing time steps ensures rapid convergence during the nonlinear numerical analysis. Predictions are performed using the developed finite element model for increasing the differential diameters between the pad pivot (or ball) and the bearing housing (or socket). The predictions show that the pivot contact area increases with decreasing differential diameters and increasing applied loads. Further, the maximum deformation occurring at the pivot center increases with increasing differential diameters and increasing applied loads. The pivot stiffness increases nonlinearly with decreasing differential diameters and increasing applied loads. Comparisons of results of the developed finite element model to those of Hertzian contact model calculations assuming a small contact area show that the latter model underestimates the pivot stiffnesses predicted by the finite element models of the ball-socket and rocker-back pivots, particularly for small differential diameters. This result implies the need for cautionduring the design of pivot stiffness by the Hertzian contact model.

Analysis of tilting-pad thrust bearing static instability and lubrication performance under the bistability

Purpose – The purpose of this paper is to analyze the problems of tilting-pad thrust bearing static instability and lubrication performance under static bistability. Design/methodology/approach – The static equilibrium state of tilting-pad thrust bearing is analyzed, and key parameters are extracted from the general lubrication model. Then, a distribution area of bearing static equilibrium points is achieved by solving the model. The area is divided into three sub-areas which represent monostabillity, bistability and instability, and an unstable boundary of the area is discovered. By these findings, a reversible lubrication failure phenomenon is explained. A calculation method is proposed to obtain bearing lubrication performance under the bistability. Findings – The variation of working conditions can lead to migration of unstable boundary and static instability. After resuming the working conditions, unstable boundary will resume in situ, and the bearing will operate steadily again. Moreover, there is a big difference between the two groups of lubrication performance solutions under the bistability. Practical implications – The static stability acceptance test of tilting-pad thrust bearing should be implemented under start–stop, accidental excitation and other conditions before service to prevent such lubrication failure phenomenon. Moreover, fulcrum position of the bearing pad should be kept away from the bistable area. Originality/value – This paper has preliminarily revealed a static instability mechanism of tilting-pad thrust bearing, analyzed bistability lubrication performance and proposed some suggestions to improve the bearing stability.

Two-scale EHL: Three-dimensional topography in tilted-pad bearings

Derived from the Heterogeneous Multiscale Methods (HMM), a two-scale method is developed for the analysis of Elastohydrodynamic Lubrication (EHL) and micro-EHL in tilted-pad bearings with three-dimensional topography. A relationship linking the pressure gradient to mass flow rate is derived and represented in the bearing domain through homogenisation of near-periodic simulations describing the Fluid Structure Interaction (FSI) of topographical features. For the parameters investigated the influence of compressibility and piezoviscosity was found to be more significant than that of non-Newtonian (shear-thinning) behaviour on textured bearing performance. As the size of topography increased two-scale solutions demonstrated that at constant load the coefficient of friction increased and the minimum film thickness decreased over a range of pad lengths and tilt angles.

Performance of hydrostatic tilted thrust pad bearings of various recess shapes operating with non-Newtonian lubricant

Hydrostatic thrust bearings are an integral part of hydroelectric power stations. These bearings are usually designed to work under parallel operation, but tilt is inevitable due to manufacturing errors, assembly errors, structural vibrations and structural deformations. Owing to the advent of latest advancements in manufacturing techniques, any geometric shape of recess can be easily manufactured and the designer has a greater flexibility. The geometric shape of recess significantly affects the performance of a bearing. Therefore, the present study is aimed to numerically analyze the influence of the tilt and recess shape on the static and dynamic performance characteristics of the hydrostatic thrust pad bearing system having Rabinowitsch fluid model lubricant. The lubricant obeying Rabinowitsch fluid model with tilt makes the Reynolds equation highly non-linear therefore, finite element method is used to analyze. Three different types of recess shapes of equal area A¯b/A¯oc=4 have been analyzed to model hydrostatic thrust pad compensated by orifice compensator. The numerically simulated results indicate that the tilt angle significantly affects the dynamic and static characteristic parameters. The value of pocket pressure and fluid film reaction of a hydrostatic thrust pad bearing has been found to significantly decrease with tilt whereas the value of lubricant flow, fluid film stiffness coefficient and fluid damping coefficient increase with tilt.

프로세스 고속 경량 원심 압축기의 로터다이나믹 안정성 강화를 위한 설계해석 - Part II: 로터다이나믹 안정성 개선

In this Part II study, rotordynamic stability analyses were carried out to confirm improvements to the stability of a process high-speed lightweight centrifugal compressor, depending on the effects of tilting pad journal bearing designs. The bearing design variables considered were the clearances, LBPs, LOPs, and preloads. The results showed that the rotordynamic stability of the subject compressor rotor-bearing system improves exactly in accordance with the effects of the bearing design variables, which were determined in the preceding Part I study, owing to reduced bearing stiffnesses. Specifically, it was confirmed that the stability of the rotor system can be greatly improved by increasing both the machined and assembled bearing clearances, but there were no stability improvements by simply changing from an LBP to an LOP design. In addition, it was confirmed that for given fixed machined bearing clearances, the stability can be additionally improved by decreasing the preloads, i.e., by increasing the assembled clearances. In conclusion, it may be necessary to improve the designs of the original tilting pad bearings to obtain a sufficient margin of rotordynamic stability against a possible aerodynamic cross-coupled stiffness in a process high-speed centrifugal compressor. Thus, increasing the machined and assembled bearing clearances and decreasing the preload could be effective solutions.

Numerical and Experimental Research on Dynamic Characteristics of Tilting-pad Journal Bearing of Pivot Stiffness and Damping

In view of the characteristic of the tile which swings and slightly vibrates through geometric direction of preload, an analytical model for vibration of entire dynamic characteristics of tilting pad bearing and its corresponding simplified dynamic model of 8 parameters are made. Based on this theory, the tilting-pad journal bearing of pivot stiffness and damping is designed. The resilient pads are set between the tiles and the bearings, thus, the pivots of the tiles are put on the resilient pads and a small clearance is left between the resilient pads and the bearings. Therefore, the oil can be shared by the small clearance and the bearing lubrication system, and that can cause squeeze film damping effect which improves the damping coefficient of the system. According to different processing technic, two kinds of tilting-pad journal bearing of pivot stiffness and damping are designed, and their dynamic characteristics are worked out by numercial and experimental research. The result shows that the tilting-pad journal bearing of pivot stiffness and damping can increase the first-order damping of rotor-bearing system and thus improve system's stability obviously.

Experimental and Numerical Simulation of Unbalance Response in Vertical Test Rig with Tilting-Pad Bearings

In vertically oriented machines with journal bearing, there are no predefined static radial loads, such as dead weight for horizontal rotor. Most of the commercial software is designed to calculate rotordynamic and bearing properties based on machines with a horizontally oriented rotor; that is, the bearing properties are calculated at a static eccentricity. For tilting-pad bearings, there are no existing analytical expressions for bearing parameters and the bearing parameters are dependent on eccentricity and load angle. The objective of this paper is to present a simplified method to perform numerical simulations on vertical rotors including bearing parameters. Instead of recalculating the bearing parameters in each time step polynomials are used to represent the bearing parameters for present eccentricities and load angles. Numerical results are compared with results from tests performed in a test rig. The test rig consists of two guide bearings and a midspan rotor. The guide bearings are 4-pad tilting-pad bearings. Shaft displacement and strains in the bearing bracket are measured to determine the test rig’s properties. The comparison between measurements and simulated results shows small deviations in absolute displacement and load levels, which can be expected due to difficulties in calculating exact bearing parameters.

Rotordynamic Evaluation of Full Scale Rotor on Tilting Pad Bearings with 0.1 and 0.3 Preload

A system identification method for rotating machinery stability evaluation is investigated based on sine sweep excitation testing with electromagnetic actuator. The traditional MIMO FRF is transformed into dFRF from real number field to complex field with a transformation matrix, eliminating the influence of forward and backward modal overlap and providing higher accuracy to identify rotor’s first forward modal parameters using the rational polynomial method. The modal parameters are acquired for stability estimation. Furthermore, two sets of bearing with preloads of 0.1 and 0.3 under both load-on-pad (LOP) and load-between-pad (LBP) conditions are investigated. The effects of oil inlet pressure (1.0 bar–1.75 bar) and temperature (43°C–51°C) on the stability of rotor are investigated in detail. Results indicate that the stability of rotor will be improved by increasing the oil inlet temperature and pressure. It is found that the rotor is more stable on bearing with 0.1 preload than that of 0.3 preload. Load-on-pad provides more damping to rotor than load-between-pad. The method and outcomes of this paper can provide both theory basis and technology foundation for improving the rotor stability of centrifugal compressors.

Swing Characteristic of Pads in Four-pad Tilting Pad Bearing

The swing characteristic of pads on four-pad tilting pad bearing is studied systematically with the guide bearing for helim circulator in fourth generation nuclear power units HTR as object. Theoretical derivation reveals that dimensionless pad pendulum angle depends on structural parameters, preload and eccentricity, but independent of viscosity of lubrication oil film, shaft rotating speed and clearance. Numerical analysis shows that: pad pendulum angle is determined by pad circumferential position relative to the load, preload and eccentricity. When the structural parameters of tilting pad bearing are constant, pendulum angle curve of pad facing the load was depend on preload, its pendulum angle increases first and then decreases with the eccentricity ratio increase while the preload less than 0.5, when the preload is greater than 0.5 its pendulum angle decreases gradually with the eccentricity ratio increase; pendulum angle curve of pad side of the load increases or decreases with the eccentricity ratio increase when the preload is smaller, and remains constant first and then decreases with the eccentricity ratio increase when the preload is greater. Pad pendulum angle has great influence on minimum oil film thickness; its value maybe negative thus leads to the minimum oil film thickness greater than fixed pad. The study results provides basis for safety operation analysis of the helim circulator.

Numerical and Experimental Stability Investigation of a Flexible Rotor on Two Different Tilting Pad Bearing Configurations

Rotordynamic stability is crucial for high performance centrifugal compressors. In this paper, the weighted instrumental variable (WIV) based system identification method for rotating machinery stability is investigated based on a sine sweep forward excitation with an electromagnetic actuator. The traditional multiple input multiple output (MIMO) frequency response function (FRF) is transformed into a directional frequency response function (dFRF). The rational polynomial method (RPM) combined with WIV is developed to identify the rotor’s first forward mode parameters. This new approach is called the COMDYN method. Experimental work using the COMDYN method is carried out under different rotating speeds, oil inlet temperatures, and pressure conditions. Two sets of bearings with preloads 0.1 and 0.3 are investigated. A numerical rotor-bearing model is also built. The numerical results correlate reasonably well with the experimental results. The investigation results indicate that the new method satisfies the desired features of rotating machine stability identification. Furthermore, the system log decrement was improved somewhat with the increase of oil inlet temperature. The increase of oil supply pressure affects the rotor-bearing system stability very slightly. The results of this paper provide new and useful insights for potentially avoiding instability faults in centrifugal compressors.

Theoretical and Experimental Study on the Dynamic Characteristics of Tilting Pad Thrust Bearing Considering Excitation Frequency

A modeling and testing method of dynamic characteristics considering excitation frequency of tilting pad trust bearing are proposed to study the effect of the excitation frequency on its dynamic characteristics. The excitation frequency is introduced into calculation process of dynamic coefficients of tilting pad thrust bearing according to the definition of stiffness and damping of tilting pad bearings. The mathematical model of its dynamic characteristics containing excitation frequency is deduced through establishing fluid film thickness equation, Reynolds equation and equation of tile motion under the condition of axial disturbance. The variation of stiffness and damping with perturbation frequency, that is, the ratio of excitation frequency to spindle rotation frequency, speed and load are analyzed. Test results of stiffness and damping in different excitation frequency, rotation speeds and loads are obtained in the test rig of tilting pad trust bearing by using impulse excitation method. The following conclusions are obtained through analyzing the theoretical and test results. When the perturbation frequency is small, the stiffness of tilting pad thrust bearing increases gradually with its enlargement, the damping is just the opposite. While the stiffness and damping tend to be stable gradually after perturbation frequency increases to a certain degree. In addition, the amplitude of variation of stiffness and damping with perturbation frequency is little affected by speed and load.

프로세스 고속 경량 원심 압축기의 로터다이나믹 안정성 강화를 위한 설계해석 - Part I: 베어링 설계의 영향

Part I of this study analyzed the effects of tilting pad bearing designs to reduce the stiffness of the bearings used in a process high-speed lightweight centrifugal compressor intended for a domestic refinery use. This was done in an attempt to enhance the robustness of its rotordynamic stability against possible aerodynamic cross-coupled stiffness. The bearing design variables reviewed were the clearances, LBPs, LOPs , and preloads. The results showed that there was practically no difference between the LBP and LOP designs in terms of the bearing stiffness, because the compressor rotor was lightweight and the bearings had relatively high preloads. Increasing both the machined and assembled clearances in bearing designs has resulted in the bearing stiffness being greatly reduced. In addition, it has been confirmed that an additional reduction in the bearing stiffness can be obtained for given fixed machined clearances by decreasing the preloads, i.e., by increasing the assembled clearances. Keywordsprocess compressor (프로세스 압축기), rotordynamic stability (로터다이나믹 안정성), effects of bearing design (베어링 설계의 영향), tilting pad bearing (틸팅 패드 베어링), reducing bearing stiffness (베어 링 강성 감소), bearing clearance (베어링 틈새)

Lateral Vibration Attenuation of Shafts Supported by Tilting-Pad Journal Bearing With Embedded Electromagnetic Actuators

Hydrodynamic tilting-pad bearings with electromagnetic actuators are designed to take advantage of the load-carrying capacity of the hydrodynamic bearing together with the actuation capacity of the electromagnets. Hence, actuators can be downsized because they do not work as bearings as it is the case of magnetic bearings. In this work, one presents the numerical and experimental analysis of rotor vibration attenuation using a tilting-pad journal bearing with embedded electromagnetic actuators when proportional-derivative (PD) control is implemented. Experimental results in the frequency domain show reductions in shaft-vibration amplitude of 11% for the rotating speed of 600 rpm and 18% for the rotating speed of 1100 rpm, with good agreement of the mathematical model. The actuation capacity of the bearing in study is compared to the capacity of other active bearings in literature, showing that the present bearing is competitive in terms of specific control capacity.

Tilting pad gas bearing design for micro gas turbines

This paper presents the results of a dynamic stability investigation of a micro gas turbine supported by two flexible tilting pad bearings. The pad flexibility allows centrifugal and thermal shaft growth of the rotor but can also introduce undesirable rotor instabilities. An eigenvalue analysis on the linearised rotor-bearing dynamics is performed to estimate the required pad stiffness and damping for stability. Results of the eigenvalue analysis are evaluated by fully nonlinear orbit simulations.

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness, and Different Pad Preloads

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to nonsynchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are compared to a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced nonsynchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two-degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

Evaluation of the Thermal Effects in Tilting Pad Bearing

The analysis of thermal effects is of expressive importance in the context of rotordynamics to evaluate the behavior of hydrodynamic bearings because these effects can influence their dynamic characteristics under specific operational conditions. For this reason, a thermohydrodynamic model is developed in this work, in which the pressure distribution in the oil film and the temperature distribution are calculated together. From the pressure distribution, the velocity distribution field is determined, as well as the viscous dissipation, and consequently, the temperature distribution. The finite volume method is applied to solve the Reynolds equation and the energy equation in the thermohydrodynamic model (THD). The results show that the temperature is higher as the rotational speed increases due to the shear rate of the oil film. The maximum temperature in the bearing occurs in the overloaded pad, near the outlet boundary. The experimental tests were performed in a tilting pad journal bearing operating in a steam turbine to validate the model. The comparison between the experimental and numerical results provides a good correlation. The thermohydrodynamic lubrication developed in this assignment is promising to consistently evaluate the behavior of the tilting pad journal bearing operating in relatively high rotational speeds.

Numerical modelling of hydrostatic lift pockets in hydrodynamic journal bearings – Application to low speed working conditions of highly loaded tilting pad journal bearings

Hydrodynamic journal bearings supporting high mass rotating machinery are subjected to low rotational speeds during start-up or idling phases. These working conditions need a hydrostatic pressure contribution to ensure a correct load capacity when the hydrodynamic pressure is not established yet. This is possible by means of hydrostatic lift pockets. These pockets avoid mechanical damages via sufficient film thickness from start-up to hydrodynamic working conditions. In a first part, it is showed how an existing isothermal 3D hydrodynamic numerical modelling of tilting pad bearing has been adapted to take into account the lift pocket impact on static bearing performance. This approach is only valid for low rotational speeds, when inertia step pressure effects (rises or drops) at the film-pocket edge can be neglected compared to the total bearing pressure pattern. Then, numerical simulations have been performed, from 1 to 200 rpm with pockets and from 75 to 200 rpm without pockets. The results have been compared and discussed in terms of pressure fields and bearing static performance such minimum film thickness, friction torque or rotor center position. Therefore, the interest of such lift pockets has been highlighted. Finally, calculations with and without pockets have been carried out in case of a strong bearing misalignment. As a result, the benefits of the lift pockets in this configuration are also significant in terms of static performance.

Morton Effect Cyclic Vibration Amplitude Determination for Tilt Pad Bearing Supported Machinery

This paper presents theoretical models and simulation results for the synchronous, thermal transient, instability phenomenon known as the Morton effect. A transient analysis of the rotor supported by tilting pad journal bearing is performed to obtain the transient asymmetric temperature distribution of the journal by solving the variable viscosity Reynolds equation, a 2D energy equation, the heat conduction equation, and the equations of motion for the rotor. The asymmetric temperature causes the rotor to bow at the journal, inducing a mass imbalance of overhung components such as impellers, which changes the synchronous vibrations and the journal's asymmetric temperature. Modeling and simulation of the cyclic amplitude, synchronous vibration due to the Morton effect for tilting pad bearing supported machinery is the subject of this paper. The tilting pad bearing model is general and nonlinear, and thermal modes and staggered integration approaches are utilized in order to reduce computation time. The simulation results indicate that the temperature of the journal varies sinusoidally along the circumferential direction and linearly across the diameter. The vibration amplitude is demonstrated to vary slowly with time due to the transient asymmetric heating of the shaft. The approach's novelty is the determination of the large motion, cyclic synchronous amplitude behavior shown by experimental results in the literature, unlike other approaches that treat the phenomenon as a linear instability. The approach is benchmarked against the experiment of de Jongh.