Tilting-pad Bearings Research Articles

프로세스 대형 모터-발전기의 저어널 베어링 설계 개선 - Part I : 베어링 성능해석

In this study, with the purpose of fundamentally improving the unbalance response vibration of a large PRT motor-generator rotor by design, a performance improvement design analysis is carried-out by retrofitting tilting pad bearings, replacing the plain partial journal bearings that were originally applied for operation at a rated speed of 1,800 rpm. In this process, a goal of the design analysis is to obtain a design solution for maximizing the direct stiffness of the bearings while satisfying the key basic lubrication performance requirements such as the minimum lift-off speed and maximum oil-film temperature. The results show that with a careful design application of tilting pad journal bearings for operation at such a relatively low speed of 1,800 rpm, direct stiffness increment of the bearings by about two times can be effectively achieved. Prevention of pad unloading is also considered in the analysis. Moreover, the designs of elliptical and offset half journal bearings are also analyzed and reviewed.

Steady state characteristics of a tilting pad journal bearing with controllable lubrication: Comparison between theoretical and experimental results

This paper is aimed at presenting results regarding the static and thermal behavior of a tilting-pad journal bearing operating under controllable regime. The bearing is rendered controllable by injecting high pressure oil into the clearance using holes drilled across the bearing pads in the radial direction. The modification of the injection pressure enables to modify the bearing static and dynamic properties according to the operational needs. The results presented are obtained using a theoretical model, which considers all the effects that determine the bearing behavior (controllable elastothermohydrodynamic lubrication regime), as well as using a test rig designed and built to this effect. The comparison between experimental and theoretical results provides solid ground to determine the accuracy of the available model for the the prediction of the steady-state behavior of the tilting-pad bearing with controllable lubrication. Among the parameters considered for the study are: oil film temperature field, resulting forces over rotor and pads, and rotor equilibrium position. The results obtained show good agreement between theory and experiment, as long as the assumptions on which the model is based are respected. Also, it is shown that some improvements are possible when it comes to model the steady-state behavior of the controllable bearing with the injection system turned off.

Analytical Techniques of Case and Pad for 5-Pad Tilting Pad Bearing

As the pad of a tilting pad bearing has invisible, three dimensional complicated movements around its pivot point inside the bearing case, its contact surface is difficult to establish. The loading points inside the bearing case are also not easy to predict accurately. This paper presents practical analysis techniques and loading conditions for the pad and bearing case of a tilting pad bearing in the structural analysis to meet the actual operating conditions. The analysis for the pad is conducted by applying the pressure of lubricant to the whole pad surface and constraining the circumferential degrees of freedom at nodes around the pivot. Part of the pad of boundary condition is hydraulic of practically applied lubricant and contact area of pivot and the rotational degree of freedom in line with circumferential. It is proposed to using of external case boundary condition 4 pads and 5 pads. Points of the case, combined with the pad are applied to the actual load. The result of analysis, the reliability of the pad and the case was obtained, because stress distribution is nearly identical with the actual phenomenon.

Measured Static and Rotordynamic Coefficient Results for a Rocker-Pivot, Tilting-Pad Bearing With 50 and 60% Offsets

Static and rotordynamic coefficients are measured for a rocker-pivot, tilting-pad journal bearing (TPJB) with 50 and 60% offset pads in a load-between-pad (LBP) configuration. The bearing uses leading-edge-groove direct lubrication and has the following characteristics: 5-pads, 101.6 mm (4.0 in) nominal diameter,0.0814 -0.0837 mm (0.0032–0.0033 in) radial bearing clearance, 0.25 to 0.27 preload, and 60.325 mm (2.375 in) axial pad length. Tests were performed on a floating bearing test rig with unit loads from 0 to 3101 kPa (450 psi) and speeds from 7 to 16 krpm. Dynamic tests were conducted over a range of frequencies (20 to 320 Hz) to obtain complex dynamic stiffness coefficients as functions of excitation frequency. For most test conditions, the real dynamic stiffness functions were well fitted with a quadratic function with respect to frequency. This curve fit allowed for the stiffness frequency dependency to be captured by including an added mass matrix [M] to a conventional [K][C] model, yielding a frequency independent [K][C][M] model. The imaginary dynamic stiffness coefficients increased linearly with frequency, producing frequency-independent direct damping coefficients. Direct stiffness coefficients were larger for the 60% offset bearing at light unit loads. At high loads, the 50% offset configuration had a larger stiffness in the loaded direction, while the unloaded direct stiffness was approximately the same for both pivot offsets. Cross-coupled stiffness coefficients were positive and significantly smaller than direct stiffness coefficients. Negative direct added-mass coefficients were obtained for both offsets, especially in the unloaded direction. Cross-coupled added-mass coefficients are generally positive and of the same sign. Direct damping coefficients were mostly independent of load and speed, showing no appreciable difference between pivot offsets. Cross-coupled damping coefficients had the same sign and were much smaller than direct coefficients. Measured static eccentricities suggested cross coupling stiffness exists for both pivot offsets, agreeing with dynamic measurements. Static stiffness measurements showed good agreement with the loaded, direct dynamic stiffness coefficients.

The Effect of Tilting Pad Journal Bearing Dynamic Models on the Linear Stability Analysis of an 8-Stage Compressor

Rotordynamic instability, a self-excited vibration phenomenon, can lead to equipment failures, reduced production rates, and expensive redesign. Properly characterizing the stability response of flexible rotors on tilting pad bearings is therefore vital. Typically, this must be first considered during the design stage with computer modeling. Previous studies have demonstrated that non-synchronous bearing coefficients give a lower estimate of bearing stability than the eight synchronously reduced tiling pad bearing coefficients. However, a study of a reduced order non-synchronous stiffness-damping-mass (KCM) model and the effect on stability estimates has not been done previously for the same rotor model. In this paper, four load-between-pad tilting pad bearing designs, two four-pad and two five-pad, are considered. The stability margin for an eight-stage gas reinjection compressor is estimated for the four bearings, using a full KC representation, the KCM representation, and synchronously reduced bearing coefficients. The full KC representation gave the lowest estimate of stability margin, with up to 18% difference between full KC and KCM and up to 109% difference between full KC and synchronously reduced bearing coefficients. The results indicate that the KCM bearing representation does not necessarily result in the lowest estimate of rotordynamic stability margin, which is of significant interest to rotating machinery designers.

Active control of unbalance response of rotor systems supported by tilting-pad gas bearings

This article establishes an optimal control model using piezoelectric actuators, proportional–derivative (PD) compensation, and gap sensors to control the vibration of rotor systems supported by tilting-pad gas bearings with active pads. The optimal control law between the voltage applied on the actuator and dynamic displacement of rotor is obtained by means of conventional optimal control theory. Using this active control model, the unbalance responses of rotor system are numerically controlled. Results show that the unbalance responses of system can be effectively suppressed by this optimal control system. This article provides a theoretical basis for further improving the stability of rotor systems supported by tilting-pad gas bearings.

Phenomena of Stability Loss of Rotor Rotation at Tilting Pad Bearings

It is experimentally observed and studied the phenomena of stability loss of rotor rotation in tilting pad bearings of different designs. The trends of changing by stability limiting rotational speed of rotor depending on its unbalance and type of journal bearing are obtained. The results of spectral analysis and phase paths of rotor motion are presented, features of rotor dynamics in range of unstable rotational speed are analyzed. The methods of building and identification of discrete non-linear mathematical models of rotor are developed, permitting to analyze polyharmonic vibrations.

Rotor stability estimation with competing tilting pad bearing models

When predicting the stability of rotors supported by tilting pad journal bearings, it is currently debated whether or not the bearings should be represented with frequency dependent dynamics. Using an experimental apparatus, measurements of pad temperatures, unbalance response and stability are compared with modeling predictions for two tilting pad bearing designs. Predictions based on frequency dependent tilting pad bearing dynamics exhibited significantly better correlation with the stability measurements than those assuming frequency independent dynamics.

Stability Analysis of an Industrial Gas Compressor Supported by Tilting-Pad Bearings Under Different Lubrication Regimes

This work is aimed at a theoretical study of the dynamic behavior of a rotor-tilting pad journal bearing (TPJB) system under different lubrication regimes, namely, thermohydrodynamic (THD), elastohydrodynamic (EHD), and hybrid lubrication regime. The rotor modeled corresponds to an industrial compressor. Special emphasis is put on analyzing the stability map of the rotor when the different lubrication regimes are included into the TPJB modeling. Results show that, for the studied rotor, the inclusion of a THD model is more relevant when compared to an EHD model, as it implies a reduction on the instability onset speed for the rotor. Also, results show the feasibility of extending the stable operating range of the rotor by implementing a hybrid lubrication regime.

Research on the Complete Dynamical Model of Tilting-Pad Bearings Considering the Coupling Moving of Shaft and Pads with Turbulent Oil Film

Considering the coupling moving of shaft and pads, a theoretical model for calculating the complete dynamic coefficients of tilting-pad bearing is described in this paper. The model includes the influence of turbulence. Based on this model, the effect of turbulence on journal equilibrium position, pads inclinations, and complete dynamic coefficients is investigated for given load cases. The numerical results indicate that the effect of turbulence is not neglected for higher Reynolds number.

5패드 틸팅 패드 베어링의 설계 조건 변화가 소형 가스터빈의 횡진동 특성에 미치는 영향

In tilting pad bearing design process, the selection of the proper configuration type of either a load-between-pad(LBP) or load-on-pad(LOP) as well as preload and pivot offset conditions is to be carefully considered. Also the bearing needs to be designed in order to be suited for the rotor-bearing system and operating condition. In this paper, it is observed that the dynamic characteristics in a five pad tilting pad bearing for the LBP and the LOP configurations are influenced by the variation of preload and pivot offset. In this context, rotor dynamic analysis of the 5 MW industrial gas turbine supported by the tilting pad bearing at the front and roller bearing at the rear is carried out based on the dynamic coefficients of the tilting pad bearing investigated. The result shows that two rigid body critical modes experience various changes according to the influence of the tilting pad bearing uniquely applied to one side of this machine. Mainly, the second critical speed, the rigid body mode of conical shape with high whirling in the tilting pad bearing, is significantly changed by preload and pivot offset regardless of the LBP and LOP configurations. And, the first critical mode, the rigid body mode of conical shape with high whirling in the roller bearing, is sensitively affected by preload applied to the LOP configuration and by its asymmetric dynamic properties.

Discontinuity effects in dynamically loaded tilting pad journal bearings

This article describes two discontinuity effects that can occur when modelling radial tilting pad bearings subjected to high dynamic loads. The first effect to be treated is a pressure build-up discontinuity effect. The second effect is a contact-related discontinuity that disappears when a contact force is included in the theoretical model. Methods for avoiding the pressure build-up discontinuity effect are proposed.

Dynamic characteristics of a single pad externally adjustable fluid film bearing

Purpose – The paper aims to devise an externally adjustable fluid film bearing whereby the hydrodynamic conditions can be changed as required in a controlled manner. Unlike a tilting pad bearing, in this bearing film thickness can be varied by providing radial and tilt adjustments to the pad, irrespective of the operating conditions. This variation in film thickness in‐turn varies the stiffness and damping coefficients.

Identification and Prediction of Force Coefficients in a Five-Pad and Four-Pad Tilting Pad Bearing for Load-on-Pad and Load-Between-Pad Configurations

This paper presents the identification of the rotordynamic force coefficients for direct lubrication five-pad and four-pad tilting pad bearings. The bearing is 110 mm in diameter with a L/D of 0.4 pad axial length (44 mm). The experiments include load-on-pad and load-between-pad configurations, with 0.5 and 0.6 pivot offsets, for rotor speeds ranging from 7500 rpm to 15,000 rpm. The bearing force coefficients are identified from multiple frequency excitations (20–300 Hz) exerted on the bearing housing by a pair of hydraulic shakers and are presented as a function of the excitation frequency and rotor speed for a 300 kPa unit load. The experimental results also include temperatures at the trailing edge of three pads. The direct force coefficients, identified from curve-fits of the complex dynamic stiffness, are frequency independent if considering an added mass term much smaller than the test device modal mass. The force coefficients from the four-pad bearing load-between-pad configuration show similar coefficients in the loaded and orthogonal directions. On the other hand, as expected, the five-pad bearing load-on-pad shows larger coefficients (∼25%) in the loaded direction. The maximum pad temperature recorded for the 0.5 pivot offset configurations is up to 20°C higher than those associated to the 0.6 offset configuration. Results from a predictive code are within 50% of the experimental results for the direct stiffness coefficients and within 30% for the direct damping coefficients.

Rotordynamic Characteristics of a Five Pad, Rocker-Pivot, Tilting Pad Bearing in a Load-on-Pad Configuration; Comparisons to Predictions and Load-Between-Pad Results

Rotordynamic data are presented for a rocker-pivot tilting pad bearing in load-on-pad (LOP) configuration for (345–3101 kPa) unit loads and speeds from 4000 rpm to 13,000 rpm. The bearing was directly lubricated through a leading edge groove with five pads, 0.282 preload, 60% offset, 57.87 deg pad arc angle, 101.587 mm (3.9995 in.) rotor diameter, 0.1575 mm (0.0062 in.) diametral clearance, and 60.325 mm (2.375 in.) pad length. Measured results were reported for this bearing by Carter and Childs (2008, “Measurements Versus Predictions for the Rotordynamic Characteristics of a 5-Pad, Rocker-Pivot, Tilting-Pad Bearing in Load Between Pad Configuration,” ASME Paper No. GT2008-50069) in the load-between-pad (LBP) configuration. Results for the LOP are compared with predictions from a bulk-flow Navier–Stokes model (as utilized by San Andres (1991, “Effect of Eccentricity on the Force Response of a Hybrid Bearing,” STLE Tribol. Trans., 34, pp. 537–544)) and to the prior LBP results. Frequency effects on the dynamic-stiffness coefficients were investigated by applying dynamic-force excitation over a range of excitation frequencies. Generally, the direct real parts of the dynamic-stiffness coefficients could be modeled as quadratic functions of the excitation frequency, and accounted for by adding a mass matrix to the conventional [K][C] model to produce a frequency-independent [K][C][M] model. Measured added-mass terms in the loaded direction approached 60 kg. The static load direction in the tests was y. The direct stiffness coefficients Kyy and Kxx depend strongly on the applied unit load, more so than speed. They generally increased linearly with load, shifting to a quadratic dependence at higher unit loads. At lower unit loads, Kyy and Kxx increase monotonically with running speed. The experimental results were compared with predictions from a bulk-flow computational fluid dynamics analysis. Stiffness orthotropy was apparent in test results, significantly more than predicted, and it became more pronounced at the heavier unit loads. Measured Kyy values were consistently higher than predicted, and measured Kxx values were lower. Comparing the LOP results to prior measured LBP results for the same bearing, at higher loads, Kyy is significantly larger for the LOP configuration than LBP. Measured values for Kxx are about the same for LOP and LBP. At low unit loads, stiffness orthotropy defined as Kyy/Kxx is the same for LOP and LBP, progressively increasing with increasing unit loads. At the highest unit load, Kyy/Kxx=2.1 for LOP and 1.7 for LBP. Measured direct damping coefficients Cxx and Cyy were insensitive to changes in either load or speed, in contrast to predictions of marked Cyy sensitivity for changes in the load. Only at the highest test speed of 13,000 rpm were the direct damping coefficients adequately predicted. No frequency dependency was observed for the direct damping coefficients.

A Review of Tilting Pad Bearing Theory

A theoretical basis for static and dynamic operation of tilting pad journal bearings (TPJBs) has evolved over the last 50 years. Originally demonstrated by Lund using the pad assembly method and a classic Reynolds equation solution, the current state of the art includes full thermoelastohydrodynamic solutions of the generalized Reynolds equation that include fluid convective inertia effects, pad motions; and thermal and mechanical deformations of the pads and shaft. The development of TPJB theory is reviewed, emphasizing dynamic modeling. The paper begins with the early analyses of fixed geometry bearings and continues to modern analyses that include pad motion and stiffness and damping effects. The development of thermohydrodynamic, thermoelastohydrodynamic, and bulk-flow analyses is reviewed. The theories of TPJB dynamics, including synchronous and nonsynchronous models, are reviewed. A discussion of temporal inertia effects in tilting pad bearing is considered. Future trends are discussed, and a path for experimental verification is proposed.

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

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

Constrained Design Optimization of Rotor-Tilting Pad Bearing Systems

Design of a rotor-bearing system is a challenging task due to various conflicting design requirements, which should be fulfilled. This study considers an automatic optimization approach for the design of a rotor supported on tilting-pad bearings. A numerical example of a rotor-bearing system is employed to demonstrate the merits of the proposed design approach. The finite element method is used to model the rotor-bearing system, and the dynamic speed-dependent coefficients of the bearing are calculated using a bulk flow code. A number of geometrical characteristics of the rotor simultaneously with the parameters defining the configuration of tilting pad bearings are considered as design variables into the automatic optimization process. The power loss in bearings, stability criteria, and unbalance responses are defined as a set of objective functions and constraints. The complex design optimization problem is solved using heuristic optimization algorithms, such as genetic, and particle-swarm optimization. Whereas both algorithms found better design solutions than the initial design, the genetic algorithms exhibited the fastest convergence. A statistical approach was used to identify the influence of the design variables on the objective function and constraint measures. The bearing clearances, preloads and lengths showed to have the highest influence on the power loss in the chosen design space. The high performance of the best solution obtained in the optimization design suggests that the proposed approach has good potential for improving design of rotor-bearing systems encountered in industrial applications.

Simplified Morton Effect Analysis for Synchronous Spiral Instability

A simplified analytical approach for modeling the synchronous instability phenomenon known as the Morton effect is presented. The analysis is straightforward and easily applied to any rotor supported on fluid film bearings. The analysis clarifies the interaction of three distinct machine characteristics, which combine to create a case of the Morton effect. Some example calculations are shown illustrating the possible types of spiral vibration. In addition, an analytical approach is described for estimating the magnitude of the shaft temperature difference in a journal bearing as a direct function of the shaft orbit. It is significant that this method can readily be applied to any type of journal bearing, from plain sleeve bearings to tilting pad bearings. Example calculations using the method are shown.

A New Active Tilting-Pad Bearing: Nonlinear Modeling and Feedback Control

This article introduces a new type of active fluid film bearing and its feedback control. In particular, the active adjustment of the angular velocity of the pads of a tilting-pad bearing in response to changes in the operating conditions of the rotating machine is proposed. This is motivated by the observation that there is more control authority in the pad tilting motion than in its radial translation. To this end, a dynamic model for the bearing system is first developed, inclusive of the nonlinear hydrodynamic force for the infinitely short bearing case. A model-based controller is then constructed, based on measurements of the journal position and velocity and pad tilting angles, to ensure that the journal is asymptotically regulated to the bearing center. Numerical simulations illustrate the performance of the active bearing under the proposed control in comparison with the bearing's standard passive mode of operation.