Linear Stability Analysis of a Tilting-Pad Journal Bearing System

2006 ◽  
Vol 129 (2) ◽  
pp. 348-353 ◽  
Author(s):  
Guang Qiao ◽  
Liping Wang ◽  
Tiesheng Zheng
Keyword(s):  
Linear Stability ◽  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Critical Mass ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Assembly Technique ◽  
The Stability ◽  
Tilting Pad Journal Bearing ◽  
Bearing System

This paper describes a mathematical model to study the linear stability of a tilting-pad journal bearing system. By employing the Newton-Raphson method and the pad assembly technique, the full dynamic coefficients involving the shaft degrees of freedom as well as the pad degrees of freedom are determined. Based on these dynamic coefficients, the perturbation equations including self-excited motion of the rotor and rotational motion of the pads are derived. The complex eigenvalues of the equations are computed and the pad critical mass identified by eigenvalues can be used to determine the stability zone of the system. The results show that some factors, such as the preload coefficient, the pivot position, and the rotor speed, significantly affect the stability of tilting-pad journal bearing system. Correctly adjusting those parameter values can enhance the stability of the system. Furthermore, various stability charts for the system can be plotted.

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

2011 ◽  
Author(s):  
Alejandro Cerda Varela ◽  
Ilmar Ferreira Santos
Keyword(s):  
Stability Analysis ◽  
Dynamic Behavior ◽  
Journal Bearing ◽  
Lubrication Regimes ◽  
Lubrication Regime ◽  
Stable Operating ◽  
Tilting Pad ◽  
The Stability ◽  
Tilting Pad Journal Bearing ◽  
Bearing System

This work is aimed at theoretically study the dynamic behavior of a rotor-tilting pad journal bearing 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.

Tilting Pad Journal Bearings: A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot Flexibility

2012 ◽  
Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Operating Temperature ◽  
Excitation Frequency ◽  
Full Model ◽  
Stability Calculation ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients. The current work presents recent test data for a 100 mm (4 in) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency dependent stiffness and damping. Measured hot bearing clearances are approximately 30% smaller than measured cold bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons. The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.

Non-linear stability analysis of micropolar fluid lubricated journal bearings with turbulent effect

2019 ◽  
Vol 71 (1) ◽  
pp. 31-39
Author(s):  
Subrata Das ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Micropolar Fluid ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Turbulent Regime ◽  
Content Type ◽  
Non Linear ◽  
The Stability ◽  
Bearing System

Purpose The purpose of this paper is to investigate the effect of turbulence on the stability characteristics of finite hydrodynamic journal bearing lubricated with micropolar fluid. Design/methodology/approach The non-dimensional transient Reynolds equation has been solved to obtain the non-dimensional pressure field which in turn used to obtain the load carrying capacity of the bearing. The second-order equations of motion applicable for journal bearing system have been solved using fourth-order Runge–Kutta method to obtain the stability characteristics. Findings It has been observed that turbulence has adverse effect on stability and the whirl ratio at laminar flow condition has the lowest value. Practical implications The paper provides the stability characteristics of the finite journal bearing lubricated with micropolar fluid operating in turbulent regime which is very common in practical applications. Originality/value Non-linear stability analysis of micropolar fluid lubricated journal bearing operating in turbulent regime has not been reported in literatures so far. This paper is an effort to address the problem of non-linear stability of journal bearings under micropolar lubrication with turbulent effect. The results obtained provide useful information for designing the journal bearing system for high speed applications.

An Analytical Complete Model of Tilting-Pad Journal Bearing Considering Pivot Stiffness and Damping

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Zhiyong Yan ◽  
Yi Lu ◽  
Tiesheng Zheng
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Local Coordinate System ◽  
Dynamical Behavior ◽  
Complete Model ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Generalized Force ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Considering the freedom of pad tilting and pad translation along preload orientation, an analytical complete model, as well as mathematical method, which contains 2n+2 degrees of freedom, is presented for calculating the dynamical characteristics of tilting-pad journal bearing. Based on the motion relationship of shaft and pad, the local coordinate system, the generalized displacement, and the generalized force vector are chosen. The concise transformation of generalized displacement, generalized force, and its Jacobian matrix between the local and global coordinate systems are built up in matrix form. A fast algorithm using the Newton–Raphson method for calculating the equilibrium position of journal and pads is proposed. The eight reduced stiffness and damping coefficients can be obtained assuming that the journal and all pads are subject to harmonic vibration. Numerical results show that the reduced damping coefficients and the threshold speed can be effectively enhanced by giving suitable pad pivot stiffness and damping simultaneously, and this analytical method can be applied to analyze dynamical behavior of the tilting-pad journal bearing rotor system.

scholarly journals Nonlinear Dynamics Analysis of Tilting Pad Journal Bearing-Rotor System

2011 ◽  
Vol 18 (1-2) ◽  
pp. 45-52 ◽  
Author(s):  
Jiayang Ying ◽  
Yinghou Jiao ◽  
Zhaobo Chen
Keyword(s):  
Nonlinear Dynamics ◽  
System Dynamics ◽  
Journal Bearing ◽  
Rotor System ◽  
Moment Of Inertia ◽  
Dynamics Analysis ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Tilting Pad Journal Bearing ◽  
Bearing System

The nonlinear dynamics theory is increasingly applied in the dynamics analysis of tilting pad journal bearing-rotor system. However, extensive work on system dynamics done previously neglects the influence caused by the moment of inertia of the pad. In this paper, a comparison is made between the responses of the rotor in the bearings with and without pad inertia effect. Taking the Jeffcott rotor system as an example, the characteristics of bearing-rotor system, such as bifurcation diagram, cycle response, frequency spectrum, phase trajectories, and Poincaré maps, were attained within a certain rotation rate range. The pivotal oil-film force of tilting pad journal bearing was calculated by database method. The results directly demonstrate that considering the influence of the pad moment of inertia, system dynamics characteristics are found more complicated when rotor-bearing system works around natural frequency and system bifurcation is observed forward when rotor-bearing system works on high-speed range.

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

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Alejandro Cerda Varela ◽  
Ilmar Ferreira Santos
Keyword(s):  
Stability Analysis ◽  
Dynamic Behavior ◽  
Theoretical Study ◽  
Journal Bearing ◽  
Lubrication Regimes ◽  
Lubrication Regime ◽  
Stable Operating ◽  
Tilting Pad ◽  
The Stability ◽  
Tilting Pad Journal Bearing

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.

Identification of Dynamic Coefficients of a Five-Pad Tilting Pad Journal Bearing up to Highest Surface Speeds

2020 ◽  
Author(s):  
Philipp Zemella ◽  
Thomas Hagemann ◽  
Bastian Pfau ◽  
Hubert Schwarze
Keyword(s):  
Flow Rate ◽  
Time Domain ◽  
Static Load ◽  
Journal Bearing ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Oil Flow ◽  
Tilting Pad Journal Bearing ◽  
The Impact

Abstract Tilting-pad journal bearings are widely used in turbomachinery industry due to their positive dynamic properties at high rotor speeds. However, the exact description of this dynamic behavior is still part of current research. This paper presents measurement results for a five-pad tilting-pad journal bearing in load between pivot configuration. The bearing is characterized by a nominal diameter of 100 mm, a length of 90 mm, and a pivot offset of 0.6. Investigations include results for surface speeds between 25 and 120 m/s and specific bearing loads ranging from 0.0 to 3.0 MPa. Results of theoretical predictions are commonly derived from perturbation of stationary operation under static load. Therefore, experimental results for stationary operation including pad deflection under static load are presented first to characterize the investigated bearing. Measured results indicate considerable non-laminar flow in the upper region of the investigated range of rotor speeds. Second, dynamic excitation test are performed with excitation frequencies up to 400 Hz to evaluate dynamic coefficients of a stiffness (K) and damping (C) KC-model, and additionally, a KCM-model using additional virtual mass (M) coefficients. KCM-coefficients are obtained by fitting frequency dependent KC-characteristics to the KCM-model structure using least square approach. The wide range of rotating and excitation frequencies leads to subsynchronous as well as supersynchronous vibrations. Excitation forces are applied with multi-sinus and single-sinus characteristics. The latter one allows evaluation of KC-coefficients at the particular frequency ratio in the time domain. Here, frequency and time domain evaluation algorithms for dynamic coefficients are used in order to assess their special properties and quality. The impact of surface speed, bearing load, and oil flow rate on measured and predicted KCM-coefficients is investigated. Measured and predicted results can be well fitted to a KCM-model and show a significant influence of the ratio between fluid film and pivot support stiffness on the speed dependent characteristic of bearing stiffness coefficients. However, the impact of this ratio on damping coefficients is considerably lower. Further investigations on the impact of oil flow rates indicate that a significant decrease of direct damping coefficients exists below a certain level of starvation. Above this limit, direct damping coefficients are nearly independent of oil flow rate. Results are analyzed in detail and demands on improvements for predictions are derived.

Research on the Complete Dynamic Model of Tilting-Pad Journal Bearings Including Fluid Film Temperature Effect

2012 ◽  
Vol 157-158 ◽  
pp. 589-594
Author(s):  
Zhen Shan Zhang ◽  
Xu Dong Dai
Keyword(s):  
Journal Bearing ◽  
Dynamic Properties ◽  
Fluid Film ◽  
Effect Of Temperature ◽  
Rotor Systems ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Precise Prediction ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings

Considering the coupling moving of shaft and pads, a theoretical model for calculating the complete dynamic coefficients (CDCs) of tilting-pad journal bearing (TPJB) is described in this paper. The model includes the influence of fluid film temperature. Based on this model, the effect of fluid film temperature on journal equilibrium position, pads inclinations, and complete dynamic coefficients is investigated for given load cases. The numerical results indicate that the effect of temperature is not neglected for the dynamic properties of TPJB. The solution will provide useful tool for precise prediction of dynamic behavior of the rotor systems supported by TPJB.

Frequency Effects in Tilting-Pad Journal Bearing Dynamic Coefficients

1983 ◽  
Vol 26 (2) ◽  
pp. 222-227 ◽  
Author(s):  
J. K. Parsell ◽  
P. E. Allaire ◽  
L. E. Barrett
Keyword(s):  
Journal Bearing ◽  
Frequency Effects ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Tilting Pad Journal Bearing
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