scholarly journals Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

2021 ◽  
Author(s):  
T. A. El-Sayed ◽  
Hussein Sayed
Keyword(s):  
Equations Of Motion ◽  
Journal Bearings ◽  
Third Order ◽  
Damping Coefficients ◽  
The Third ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Rotor Stiffness ◽  
Stiffness And Damping ◽  
Bearing System

AbstractHydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they are susceptible to oil whirl instability, which may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical journal bearings is used to investigate the stability and bifurcations of rotor bearing system. Since a closed form for the finite bearing forces is not exist, nonlinear bearing stiffness and damping coefficients are used to represent the bearing forces. The bearing forces are approximated to the third order using Taylor expansion, and infinitesimal perturbation method is used to evaluate the nonlinear bearing coefficients. The mesh sensitivity on the bearing coefficients is investigated. Then, the equations of motion based on bearing coefficients are used to investigate the dynamics and stability of the rotor-bearing system. The effect of rotor stiffness ratio and applied load on the Hopf bifurcation stability and limit cycle continuation of the system are investigated. The results of this work show that evaluating the bearing forces using Taylor’s expansion up to the third-order bearing coefficients can be used to profoundly investigate the rich dynamics of rotor-bearing systems.

scholarly journals Bifurcation Analysis of Rotor/Bearing System using Third Order Journal Bearings Stiffness and Damping Coefficients

2021 ◽  
Author(s):  
Tamer Elsayed ◽  
Hussein Sayed
Keyword(s):  
Journal Bearing ◽  
Journal Bearings ◽  
Third Order ◽  
The Third ◽  
Bifurcation Stability ◽  
Jeffcott Rotor ◽  
Load Carrying ◽  
Proper Design ◽  
Rotor Stiffness ◽  
Stiffness And Damping

Abstract Journal bearings have many applications in industry due to its high load carrying capacity. In addition proper design of journal bearings enables safe operation at very high speeds. However, they are susceptible to oil whirl instability which may cause bearing failure. The fluid film pressure distribution inside the journal bearing is described by Reynolds equation. Many studies had been done to approximate the bearing performance using first order bearing coefficients. Although this analysis is stable for evaluating the threshold speed but it is insensitive to limit cycles above the threshold speed. Mush literature show that above the threshold speed, subcritical or supercritical bifurcations may be observed. Therefore, the aim of the present paper is to evaluate the third order bearing coefficients for a finite length journal bearing using finite perturbation method. The values of these coefficients are evaluated using infinitesimal perturbation analysis. These values are used to investigate the bifurcation stability of flexible Jeffcott rotor supported by two symmetric journal bearings. The effect of rotor stiffness ratio on the bifurcation stability of the system is investigated. The results of this work show that the third order parameters can be used to evaluate the type of bifurcation above the threshold speed.

An Experimental Investigation on the Static and Dynamic Characteristics of Journal Bearings Under the Influence of Twisting Misalignment

1997 ◽  
Vol 119 (1) ◽  
pp. 188-192 ◽  
Author(s):  
P. Arumugam ◽  
S. Swarnamani ◽  
B. S. Prabhu
Keyword(s):  
Finite Element Method ◽  
Vertical Direction ◽  
Journal Bearings ◽  
Response Functions ◽  
The Finite Element Method ◽  
Static And Dynamic Characteristics ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Different Levels ◽  
Bearing System

The misalignment between the journal and the bearing in a rotor-bearing system may be due to manufacturing error, elastic deflection, thermal expansion etc. In the present work, the eight linearized stiffness and damping coefficients of the cylindrical and three lobe bearings are identified at different levels of bearing misalignment (twisting misalignment) and at different speeds of the rotor. The identification method used here needs FRFs (Frequency Response Functions) obtained by the measurements and the finite element method. The twisting misalignment changes the stiffness and damping coefficients in the vertical and horizontal directions. In the case of three lobe bearings, for 0.7 degree of misalignment, the stiffness in the vertical direction is increased by about 12 percent.

scholarly journals Numerical Simulation of Nonlinear Oil Film Forces of Tilting-Pad Guide Bearing in Large Hydro-unit

2000 ◽  
Vol 6 (5) ◽  
pp. 345-353 ◽  
Author(s):  
Li-Feng Ma ◽  
Xin-Zhi Zhang
Keyword(s):  
Reynolds Equation ◽  
Nonlinear Simulation ◽  
Motion Patterns ◽  
Damping Coefficients ◽  
Nonlinear Motion ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Angular Velocities ◽  
Stiffness And Damping ◽  
Bearing System

A new numerical method is proposed for predicting the nonlinearity of tilting-pad guide bearing oilfilm force in the rotor-bearing system in a large hydro-unit. Nonlinear displacement and velocity of the journal center, as well as nonlinear tilting angles and angular velocities of the pads in non-stationary Reynolds equation are taken into account. This method is also suited for other small rotor-bearing system. As an example, the response due to a momentarily created unbalance is Calculated. The nonlinear motion patterns of the pad and journal whirling orbit are obtained. Finally, the nonlinear orbit is compared to the linear one that could be calculated from linear stiffness and damping coefficients. It is shown that there are important differences between those two orbits and that the nonlinear simulation is more accurate.

On the Dynamic Behavior of Hybrid Journal Bearings

1976 ◽  
Vol 98 (1) ◽  
pp. 90-94 ◽  
Author(s):  
S. M. Rohde ◽  
H. A. Ezzat
Keyword(s):  
Dynamic Behavior ◽  
High Frequency ◽  
Journal Bearings ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Bearing Stiffness ◽  
Coupling Stiffness ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
Stiffness And Damping

An analysis of the dynamic behavior of hybrid journal bearings is presented. The analysis accounts for the compressibility of the lubricant in the bearing recesses and supply line. Results show that when the journal is subjected to high frequency excitation the bearing stiffness and damping can change drastically. The behavior is characterized by a “break frequency” beyond which the bearing stiffness increases sharply. This is accompanied by a rapid decrease in bearing damping. It is also shown that the cross-coupling stiffness coefficients are reduced at high excitation frequencies. The asymptotic behavior of the stiffness and damping coefficients is examined at both ends of the frequency spectrum.

Stability of Multirecess Hybrid-Operating Oil Journal Bearings

1985 ◽  
Vol 107 (1) ◽  
pp. 116-121 ◽  
Author(s):  
Y. S. Chen ◽  
H. Y. Wu ◽  
P. L. Xie
Keyword(s):  
Finite Difference Method ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Design Parameters ◽  
Stability Threshold ◽  
Damping Coefficients ◽  
Hybrid Bearing ◽  
The Stability ◽  
Stiffness And Damping ◽  
Bearing System

An analysis and a numerical solution using finite difference method to predict the dynamic performance of multirecess hybrid-operating oil journal bearings are presented. The linearized stiffness and damping coefficients of a typical capillary-compensated bearing with four recesses are computed for various design parameters. The corresponding stiffness and the stability threshold of the bearing are then obtained, and the opposite influences of the hydrodynamic action on them are demonstrated. The effect of rotor flexibility on the onset of self-excited whirl is discussed, and a method is given to determine the stability threshold of a rotor-hybrid bearing system.

Modal Analysis of Rotor on Piecewise Linear Journal Bearings Under Seismic Excitation

1999 ◽  
Vol 121 (2) ◽  
pp. 190-196 ◽  
Author(s):  
B. J. Gaganis ◽  
A. K. Zisimopoulos ◽  
P. G. Nikolakopoulos ◽  
C. A. Papadopoulos
Keyword(s):  
Modal Analysis ◽  
Dynamic Properties ◽  
Piecewise Linear ◽  
Computer Time ◽  
Seismic Excitation ◽  
Damping Coefficients ◽  
Highly Nonlinear ◽  
Rotor Bearing ◽  
Stiffness And Damping ◽  
Bearing System

A rotor bearing system is expected to exhibit large vibration amplitudes when subjected to a large seismic excitation. It is possible that these vibrations can lead to large values the eccentricity of the bearings. Then the bearing is operated in highly nonlinear region because the stiffness and the damping coefficients are nonlinear as functions of the eccentricity. To solve this problem numerical integration must be performed with high cost in computer time. The idea of this paper was to divide the nonlinear area into more areas where the stiffness and damping coefficients could be considered to be constants. In other words the bearing coefficients are considered to be piecewise constant. The excitation due to the earthquake is modelled as a movement of the base of the bearings using the El Centro data for the acceleration. Then a simplified modal analysis for each of these piecewise linear regions can be performed. The equation of motion of the rotor contains rotational speed depended terms, known as gyroscopic terms, and terms due to base excitation. The response and the variation of the dynamic properties of this complicated rotor bearing system are investigated and presented.

Rotor-Bearing Dynamics With Emphasis on Attenuation

1962 ◽  
Vol 84 (4) ◽  
pp. 491-498 ◽  
Author(s):  
J. W. Lund ◽  
B. Sternlicht
Keyword(s):  
Critical Speed ◽  
Reynolds Equation ◽  
Journal Bearings ◽  
Dimensionless Form ◽  
Damping Coefficients ◽  
Transmitted Force ◽  
Rotor Bearing ◽  
Bearing Dynamics ◽  
Rotor Mass ◽  
Bearing System

This paper presents a theoretical analysis of the dynamics of a rotor-bearing system. The analysis is quite general but because of space limitations only the symmetrical rotor supported in two plain cylindrical journal bearings is considered. Furthermore, the rotor mass is concentrated at midspan giving the rotor only one degree of freedom. Limiting the analysis to small amplitudes of rotor motion the components of the fluid film force are made linear with respect to journal amplitude and velocity. The resulting 8 coefficients, denoted spring and damping coefficients, are calculated from Reynolds equation and by coupling them with the rotor, the motion and the force transmitted to the bearing pedestal are obtained. Results are presented in dimensionless form for transmitted force and for critical speed.

Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part I: Analytical Bearing Model

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Mohammad Miraskari ◽  
Farzad Hemmati ◽  
Mohamed S. Gadala
Keyword(s):  
Journal Bearing ◽  
Nonlinear Coefficient ◽  
Journal Bearings ◽  
Flexible Rotor ◽  
Dynamic Coefficients ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Bearing Force ◽  
Derivatives Of ◽  
Bearing System

To determine the bifurcation types in a rotor-bearing system, it is required to find higher order derivatives of the bearing forces with respect to journal velocity and position. As closed-form expressions for journal bearing force are not generally available, Hopf bifurcation studies of rotor-bearing systems have been limited to simple geometries and cavitation models. To solve this problem, an alternative nonlinear coefficient-based method for representing the bearing force is presented in this study. A flexible rotor-bearing system is presented for which bearing force is modeled with linear and nonlinear dynamic coefficients. The proposed nonlinear coefficient-based model was found to be successful in predicting the bifurcation types of the system as well as predicting the system dynamics and trajectories at spin speeds below and above the threshold speed of instability.

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