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.

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.

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.

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.

Measurement of Static and Dynamic Properties of a Tilting Pad Bearing and Comparison With Theory

1993 ◽  
Author(s):  
Thomas Bonner ◽  
John H. Vohr
Keyword(s):  
Dynamic Properties ◽  
Lubrication Theory ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Phase Angles ◽  
Good Agreement

Abstract Measurements were made of the static and dynamic properties of a seven inch diameter, four-pad, tilting pad bearing with both centrally pivoted and 60% offset pads. Data was recorded at 1500, 1800 and 3000 RPM and covered a range of Sommerfeld numbers from .055 to .625. Dynamic properties were measured by applying unbalance weights of various magnitudes to the rotor and measuring the synchronous response amplitudes and phase angles. Good agreement was obtained between measured properties and those predicted using linearized stiffness and damping coefficients obtained from isoviscous lubrication theory.

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.

Dynamic Properties of a Heliostat Structure Determined by Numerical and Experimental Modal Analysis

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
J. Felipe Vásquez-Arango ◽  
Reiner Buck ◽  
Robert Pitz-Paal
Keyword(s):  
Modal Analysis ◽  
Vortex Shedding ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Simple Approach ◽  
Operating Conditions ◽  
Mode Shapes ◽  
Fe Model ◽  
Damping Coefficients ◽  
Operating Points

An experimental and numerical modal analysis was performed on an 8 m2 T-shaped heliostat structure at different elevation angles. The experimental results were used to validate a finite element (FE) model by comparing natural frequencies and mode shapes. The agreement between experiments and simulations is good in all operating points investigated. In addition, damping coefficients were determined experimentally for each mode, in order to provide all necessary information for the development of a dynamic model. Furthermore, potentially critical operating conditions caused by vortex shedding were identified using a simple approach.

Stability and Damped Critical Speeds of a Flexible Rotor in Fluid-Film Bearings

1974 ◽  
Vol 96 (2) ◽  
pp. 509-517 ◽  
Author(s):  
J. W. Lund
Keyword(s):  
Dynamic Properties ◽  
Fluid Film ◽  
Internal Damping ◽  
Flexible Rotor ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Fluid Film Bearings ◽  
Multistage Compressor ◽  
Stiffness And Damping ◽  
Rotor Model

A method is described for calculating the threshold speed of instability and the damped critical speeds of a general flexible rotor in fluid-film journal bearings. It is analogous to the Myklestad-Prohl method for calculating critical speeds and is readily programmed for numerical computation. The rotor model can simulate any practical shaft geometry and support configuration. The bearings are represented by their linearized dynamic properties, also known as the stiffness and damping coefficients of the bearing, and the calculation includes hysteretic internal damping in the shaft and destabilizing aerodynamic forces. To demonstrate the application of the method, results are shown for an industrial, multistage compressor.

Response Analysis of a General Asymmetric Rotor-Bearing System

1980 ◽  
Vol 102 (1) ◽  
pp. 147-157 ◽  
Author(s):  
T. Inagaki ◽  
H. Kanki ◽  
K. Shiraki
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Field Measurements ◽  
Transverse Mass ◽  
Response Analysis ◽  
Mass Moment ◽  
Rotor Bearing ◽  
Asymmetric Rotor ◽  
Bearing System

This paper presents an analytical method for the evaluation of the synchronous response of a general asymmetric rotor-bearing system. In the analysis, slightly asymmetric shaft stiffness in bending and shearing, which distribute along the rotor, and asymmetric transverse mass moment of inertia are considered. The dynamic properties of bearings and pedestals are assumed to be anisotropic and coupled in each direction. The equations of motion with periodic time dependent coefficients are solved by the Harmonic Balance Method and formulated to the transfer matrix. These solutions include the “Modified Holzer-Myklestad-Prohl Method by Lund & Orcutt” as a special case. The results of the analysis are confirmed by a simple model test and field measurements of large turbosets.

Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part II: Effect of Tilt-Pad Bearings and Foundation Dynamics

1987 ◽  
Vol 109 (1) ◽  
pp. 8-14 ◽  
Author(s):  
J. M. Vance ◽  
B. T. Murphy ◽  
H. A. Tripp
Keyword(s):  
Critical Speed ◽  
Natural Frequencies ◽  
State Of The Art ◽  
Dynamic Properties ◽  
Experimental Measurements ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Speed Prediction ◽  
Bearing Stiffness ◽  
Stiffness And Damping

This is the second of two papers describing results of a research project directed at verifying computer programs used to calculate critical speeds of turbomachinery. This part describes measurements made to determine the characteristics of tilt-pad bearings and foundation dynamics. Critical speeds of a 166 kg laboratory rotor on tilt-pad bearings are then compared with predictions from a state-of-the-art damped eigenvalue computer program. Measured natural frequencies of a steam turbine are also compared with computer predictions. Accuracy of critical speed prediction is shown to depend on accuracy of 1) the “free-free” rotor models, 2) the bearing stiffness and damping coefficients, and 3) the dynamic properties of the foundation, which can be represented by an impedance that must be determined by experimental measurements.

Sign in / Sign up

Export Citation Format

Share Document