scholarly journals An Algebraic Approach for Identification of Rotordynamic Parameters in Bearings with Linearized Force Coefficients

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2747
Author(s):  
José Gabriel Mendoza-Larios ◽  
Eduardo Barredo ◽  
Manuel Arias-Montiel ◽  
Luis Alberto Baltazar-Tadeo ◽  
Saulo Jesús Landa-Damas ◽  
...  
Keyword(s):  
Rotational Speed ◽  
Algebraic Approach ◽  
Rotational Inertia ◽  
Fe Model ◽  
Rotordynamic Coefficients ◽  
Rotor Bearing ◽  
Identification Technique ◽  
Stiffness And Damping ◽  
The Mathematical Model ◽  
Bearing System

In this work, a novel methodology for the identification of stiffness and damping rotordynamic coefficients in a rotor-bearing system is proposed. The mathematical model for the identification process is based on the algebraic identification technique applied to a finite element (FE) model of a rotor-bearing system with multiple degree-of-freedom (DOF). This model considers the effects of rotational inertia, gyroscopic moments, shear deformations, external damping and linear forces attributable to stiffness and damping parameters of the supports. The proposed identifier only requires the system’s vibration response as input data. The performance of the proposed identifier is evaluated and analyzed for both schemes, constant and variable rotational speed of the rotor-bearing system, and numerical results are obtained. In the presented results, it can be observed that the proposed identifier accurately determines the stiffness and damping parameters of the bearings in less than 0.06 s. Moreover, the identification procedure rapidly converges to the estimated values in both tested conditions, constant and variable rotational speed.

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.

Modal and Transient Response Analysis for Complex Gear-Bearing System

2011 ◽  
Vol 130-134 ◽  
pp. 1152-1155 ◽  
Author(s):  
Jian Li Ge ◽  
Guo Lai Yang ◽  
Jian Wei Hao
Keyword(s):  
Numerical Solutions ◽  
Impact Load ◽  
Response Analysis ◽  
Fe Model ◽  
Similar System ◽  
Shell Elements ◽  
Hexahedral Elements ◽  
Stress And Deformation ◽  
Stiffness And Damping ◽  
Bearing System

The radar antenna pedestal is a complex gear-bearing system including three rotary motions, i.e. horizontal rolling, pitching rotation and azimuth rotation. In this paper, spring-dashpot elements and connection elements are applied to simulate gear meshing and bearing connection respectively. Moreover, the equivalent average stiffness and damping of teeth meshing and bearing connection are calculated. Then, quadrilateral shell elements, hexahedral elements, wedgy elements, connection elements and spring-dashpot elements are employed to build the finite element (FE) model of the gear-bearing system in Hypermesh software. Via intermediate file, the model is imported into ABAQUS software for modal analysis whose solutions agree well with experimental data. Then, impact acceleration is imposed on the three bolts of the underpan along the x-axis, y-axis and z-axis respectively. Dynamic stress distribution and regulation changing with time under impact load are obtained. From the numerical solutions, the regions where stress and deformation is lager are found. The method can provide significant reference to analysis and optimum design of the similar system.

Coupled Lateral and Torsional Nonlinear Transient Rotor–Bearing System Analysis With Applications

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Jianming Cao ◽  
Paul Allaire ◽  
Timothy Dimond
Keyword(s):  
Rotational Speed ◽  
System Analysis ◽  
Equations Of Motion ◽  
Squeeze Film ◽  
Rotor Bearing ◽  
Nonlinear Transient ◽  
Gyroscopic Effects ◽  
Nonlinear Equations Of Motion ◽  
Torsional Analysis ◽  
Bearing System

This paper provides a time transient method for solving coupled lateral and torsional analysis of a flexible rotor–bearing system including gyroscopic effects, nonlinear short journal bearings, nonlinear short squeeze film dampers (SFDs), and external nonlinear forces/torques. The rotor is modeled as linear, and the supporting components, including bearings and dampers, are modeled as nonlinear. An implicit Runge–Kutta method is developed to solve the nonlinear equations of motion with nonconstant operating speed since the unbalance force and the gyroscopic effect are related to both the rotational speed and the acceleration. The developed method is compared with a previous torsional analysis first to verify the nonlinear transient solver. Then the coupled lateral and torsional analysis of an example flexible three-disk rotor, perhaps representing a compressor, with nonlinear bearings and nonlinear dampers driven by a synchronous motor is approached. The acceleration effects on lateral and torsional amplitudes of vibration are presented in the analysis. The developed method can be used to study the rotor motion with nonconstant rotational speed such as during startup, shutdown, going through critical speeds, blade loss force, or other sudden loading.

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.

Development of Herringbon-Grooved Aerodynamic Journal Bearing Systems for Ultra-High-Speed Rotations

2015 ◽  
Vol 656-657 ◽  
pp. 652-657 ◽  
Author(s):  
Norifumi Miyanaga ◽  
Jun Tomioka
Keyword(s):  
Rotational Speed ◽  
High Speed ◽  
Journal Bearing ◽  
Damping Properties ◽  
Shaft Rotation ◽  
Ultra High Speed ◽  
The Difference ◽  
The Stability ◽  
Stiffness And Damping ◽  
Bearing System

It is absolutely important for ultra-compact rotational machineries to achieve sable shaft rotation at ultra-high-speed. This paper discussed herringbone-grooved aerodynamic journal bearing systems developed for the purpose. In this system, the bearings are supported by rubber-O-rings for accurate and stable operations. To grasp the possibility for stabilization, two types of O-rings with different stiffness and damping properties under bearing supporting were tested in the experiment. As the results, the bearing system demonstrated the maximum rotational speed over 460,000 rpm without unstable phenomenon called whirl. However, the difference in rubber O-rings definitely affected the stability of the bearing system.

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.

Based on One-Dimensional Model to Calculate the Critical Speed

2012 ◽  
Vol 203 ◽  
pp. 427-431
Author(s):  
Jun Feng Wang ◽  
Kang Sun
Keyword(s):  
Critical Speed ◽  
Early Stage ◽  
Reference Value ◽  
Dimensional Model ◽  
Lumped Mass ◽  
One Dimensional ◽  
Rotor Bearing ◽  
Continuous Mass ◽  
Stiffness And Damping ◽  
Bearing System

Use the simple geometric features of a one-dimensional model to calculate the rotor critical speed, the shaft use the beam element to simulate, considering the shear deformation, continuous mass, the rotation inertia and gyro effect, bearing simplified as linear stiffness and damping element, disc use the lumped mass element to simulate, considering the mass and the effect of inertia, finite element method is applied, established the rotor-bearing system dynamics model, through the example to validate, the results show that the model is the advantage of calculation on a smaller scale, solution speed and high precision, easy to adjust the parameters for the model, suitable for large needs to adjust the parameters in the early stage of design and analysis of the rotor-bearing system, it has great reference value for the design and analysis of rotor dynamics.

Measurement of Rotordynamic Coefficients for a Hydrostatic Radial Bearing

1991 ◽  
Vol 113 (3) ◽  
pp. 518-525 ◽  
Author(s):  
B. T. Murphy ◽  
M. N. Wagner
Keyword(s):  
Reynolds Number ◽  
Hydrostatic Pressure ◽  
Rotational Speed ◽  
Sole Source ◽  
Working Fluid ◽  
Test Apparatus ◽  
Matrix Solution ◽  
Rotordynamic Coefficients ◽  
Direct Stiffness ◽  
Stiffness And Damping

Measurement of rotordynamic coefficients is presented for a pair of hydrostatic radial bearings, including direct and cross-coupled stiffness and damping. Two different hydrostatic configurations were tested: (1) an externally fed bearing 74.7 mm (2.95 in.) in diameter with a nominal direct stiffness of approximately 210 MN/m (1.2 million lb/in.) and (2) an internally fed bearing 54.6 mm (2.15 in.) in diameter with a nominal direct stiffness of approximately 88 MN/m (0.5 million lb/in.). Each bearing had 6 equally spaced hydrostatic pressure pockets, stationary for the externally fed bearing and rotating for the internally fed bearing. Also, both bearings had extended exit regions to provide additional damping. The top rotational speed was 22,700 rpm and the maximum axial Reynolds number was 50,000 using a freon derivative, Freon-113, as the working fluid. The test apparatus was a “synchronous rig” as an intentionally eccentric journal was used as the sole source of excitation. Data reduction was done by performing a matrix solution to separate damping from stiffness. Results show the internally fed bearing to be 20 percent less stiff than predicted, and to have a significant amount of damping which agrees well with predictions. The internally fed bearing was found to be approximately 60 percent less stiff than predicted, and to be roughly neutral in terms of damping, as predicted.

Finite Element and Modal Analyses of Rotor-Bearing Systems Under Stochastic Loading Conditions

1984 ◽  
Vol 106 (1) ◽  
pp. 80-89 ◽  
Author(s):  
E. Hashish ◽  
T. S. Sankar
Keyword(s):  
Finite Element ◽  
Simple Procedure ◽  
Stochastic Loading ◽  
Rotor Bearing ◽  
Random Disturbances ◽  
Element Technique ◽  
Stiffness And Damping ◽  
The Mathematical Model ◽  
Rotor Dynamic ◽  
Spatial Support

A flexible rotor bearing system is represented in detail utilizing the state of the art finite element technique. The mathematical model takes into account the gyroscopic moments, rotary inertia, shear deformation, internal viscous damping, hysteretic damping, linear as well as nonlinear stiffness, and damping for the finite bearing and the bearing support flexibility. Using a simple Timoshenko element and recognizing an analogy between the motion planes, a procedure is given that requires a construction of only three symmetric 4×4 matrices. As an application, the different effects of the bearing lining flexibility and the bearing support flexibility on the rotor stability behavior is studied and discussed. The necessary relation for general modal analysis is simply restated and integrated into the conventional spectral approach, thus developing a simple procedure for the calculation of the stochastic response of a general rotor dynamic system. An application to a light rotor bearing featuring a general spatial support and subjected to random disturbances is illustrated.

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