scholarly journals Dynamics Investigation on Axial-Groove Gas Bearing-Rotor System with Rod-Fastened Structure

2021 ◽  
Vol 12 (1) ◽  
pp. 250
Author(s):  
Sha Li ◽  
Yanjun Lu ◽  
Yongfang Zhang ◽  
Di Hei ◽  
Xiaowei Zhao
Keyword(s):  
Degrees Of Freedom ◽  
Reynolds Equation ◽  
Position Angle ◽  
Transformation Method ◽  
Rotor System ◽  
Research Report ◽  
Nonlinear Characteristics ◽  
Gas Bearings ◽  
Computing Error ◽  
Gas Bearing

This research report discusses the dynamic behaviors of an axial-groove gas bearings-rotor system with rod-fastened structure. The time-based dependency-compressible Reynolds equation in the gas bearing nonlinear system is solved by the differential transformation method, and the continuous gas film forces of a three-axial-groove gas bearing are obtained. A dynamic mathematical model of the rotor system with rod-fastened structure supported in two- and three-axial-groove gas bearings with eight degrees of freedom is established. The dynamic motion equation of the rod-fastened rotor system is solved by the modified Newmark-β method based on disturbance compensation, which can reduce the computing error and improve computing stability. The dynamic characteristics of the rod-fastened rotor-gas bearing system are analyzed efficiently by the diversiform unbalance responses. The influence of the position angle of the pad on the nonlinear characteristics of the rod-fastened rotor system is also studied.

scholarly journals Numerical and Experimental Investigation on Axial Rub Impact Dynamic Characteristics of Flexible Rotor Supported by Hybrid Gas Bearings

2021 ◽  
pp. 146134842098664
Author(s):  
Long Hao ◽  
Dongjiang Han ◽  
Wei Zhao ◽  
Qingjun Zhao ◽  
Jinfu Yang
Keyword(s):  
Dynamic Characteristics ◽  
Radial Direction ◽  
High Efficiency ◽  
Load Capacity ◽  
Rotor System ◽  
Dynamic Responses ◽  
Flexible Rotor ◽  
Test Rig ◽  
Gas Bearings ◽  
Gas Bearing

Gas bearings are widely used in micro- and small turbomachinery. Because of the pursuit of high efficiency, turbomachinery adopts small clearance of rotor and stator. The gas bearing rotor system easily suffers from rub impact due to the inherently low damping and load capacity of gas film. Axial rub impact may lead to catastrophic failure of gas bearing rotor system. Previous work put emphasis on radial rub, and only a few papers researched on the axial rub impact by simulation method. In this paper, dynamic responses of full annular axial rub are investigated numerically and experimentally. A single span flexible rotor test rig is established to support this research. Dynamic characteristics of full annular axial rub of this gas bearing rotor system are obtained with finite element language-APDL. Dynamic characteristics within full speed range are experimentally researched based on the test rig. The dynamic behaviors are analyzed by means of waterfall diagrams, frequency spectrums, orbit trails, and vibration amplitude waveforms. During speed up, half speed whirl and gas film oscillation occur in radial direction. During speed down, the full annular axial rub between rotor thrust disk and gas bearing occurs. When lightly axial rub impact happens, the vibration patterns in the radial direction change barely, and 0 Hz component appears in the axial direction. When serious full annular axial rub impact happens, 0 Hz component occurs in both radial and axial directions and rotor orbit shows transverse motion in radial direction. These forms of dynamic characteristics can be effectively used to diagnose the full annular axial rub impact.

Numerical Analysis Method and Bifurcation of Gas-Lubricated Journal Bearing-Rotor System with Gyroscopic Effect

2011 ◽  
Vol 230-232 ◽  
pp. 197-201
Author(s):  
Yong Fang Zhang ◽  
Xiao Lei Shi ◽  
Yan Jun Lu ◽  
Lie Yu
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Transformation Method ◽  
Rotor System ◽  
Time Dependent ◽  
Analysis Method ◽  
Gyroscopic Effect ◽  
Dynamic Motion ◽  
Nonlinear Behaviors ◽  
Gas Journal Bearing

Based on the nonlinear theory, the unbalanced responses of the gas-lubricated journal bearing-rotor system are investigated. A time-dependent mathematical model is established to describe the pressure distribution of gas-lubricated journal bearing with nonlinearity. The rigid rotor with gyroscopic effect supported by self-acting gas journal bearing with three axial grooves is modeled. The differential transformation method is employed to solve the time-dependent gas-lubricated Reynolds equation, and the dynamic motion equation is solved by Newmark-β method. The unbalanced responses of the rotor system supported by finite gas-lubricated journal bearings are analyzed by bifurcation diagram, orbit diagram, Poincaré map. The numerical results reveal periodic, period-4 motion of nonlinear behaviors of the system.

Investigation of Train Dynamics in Passing Through Curves Using a Full Model

Joint Rail ◽  
2004 ◽  
Author(s):  
Mohammad Durali ◽  
Mohammad Mehdi Jalili Bahabadi
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Full Model ◽  
Bogie Frame ◽  
Nonlinear Characteristics ◽  
Train Derailment ◽  
Train Dynamics

In this article a train model is developed for studying train derailment in passing through bends. The model is three dimensional, nonlinear, and considers 43 degrees of freedom for each wagon. All nonlinear characteristics of suspension elements as well as flexibilities of wagon body and bogie frame, and the effect of coupler forces are included in the model. The equations of motion for the train are solved numerically for different train conditions. A neural network was constructed as an element in solution loop for determination of wheel-rail contact geometry. Derailment factor was calculated for each case. The results are presented and show the major role of coupler forces on possible train derailment.

An Assessment of the Value of Theory in Predicting Gas-Bearing Performance

1961 ◽  
Vol 83 (2) ◽  
pp. 195-200 ◽  
Author(s):  
S. Cooper
Keyword(s):  
Steady State ◽  
Slip Velocity ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Experimental Methods ◽  
Experimental Results ◽  
Theoretical Investigations ◽  
Gas Bearing ◽  
Theoretical Results

The object of the paper is to indicate the value of theoretical investigations of hydrodynamic finite bearings under steady-state conditions. Methods of solution of Reynolds equation by both desk and digital computing, and methods of stabilizing the processes of solution, are described. The nondimensional data available from the solutions are stated. The outcome of an attempted solution of the energy equation is discussed. A comparison between some theoretical and experimental results is shown. Experimental methods employed and some difficulties encountered are discussed. Some theoretical results are given to indicate the effects of the inclusion of slip velocity, stabilizing slots, and a simple case of whirl.

Externally pressurized gas bearings in a mixed configuration

2002 ◽  
Vol 216 (2) ◽  
pp. 181-189
Author(s):  
A Cazan ◽  
R Gohar ◽  
M M A Safa
Keyword(s):  
Full Length ◽  
The Other ◽  
Gas Bearings ◽  
High Stiffness ◽  
Parallel Arrangement ◽  
Gas Bearing

This paper analyses the stabilityof an externally pressurized gas bearing (EPB) in a series-parallel arrangement. This mixed con. guration is an alternative to the rigidly mounted single bearing with no external damping, yielding, as one extreme, a high stiffness, but a low whirl threshold speed. The other extreme is a series bearing arrangement with a full-length externally pressurized sleeve between the journal and the housing, yielding a lower stiffness but a higher whirl threshold speed. The paper shows that a mixed con. guration allows for an increase in whirl threshold speed above that for an equivalent rigidly mounted single bearing but below that for a series arrangement. However, the mixed con. guration is stiffer than the series arrangement.

Dynamic Characteristics of a Hydrostatic Gas Bearing Driven by Oscillating Exhaust Pressure

1984 ◽  
Vol 106 (4) ◽  
pp. 477-483 ◽  
Author(s):  
C. B. Watkins ◽  
H. D. Branch ◽  
I. E. Eronini
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Source Model ◽  
Regular Perturbation ◽  
Response Characteristics ◽  
Finite Difference Approximations ◽  
Bode Plots ◽  
Gas Bearing

Vibration of a statically loaded, inherently compensated hydrostatic journal bearing due to oscillating exhaust pressure is investigated. Both angular and radial vibration modes are analyzed. The time-dependent Reynolds equation governing the pressure distribution between the oscillating journal and sleeve is solved together with the journal equation of motion to obtain the response characteristics of the bearing. The Reynolds equation and the equation of motion are simplified by applying regular perturbation theory for small displacements. The numerical solutions of the perturbation equations are obtained by discretizing the pressure field using finite-difference approximations with a discrete, nonuniform line-source model which excludes effects due to feeding hole volume. An iterative scheme is used to simultaneously satisfy the equations of motion for the journal. The results presented include Bode plots of bearing-oscillation gain and phase for a particular bearing configuration for various combinations of parameters over a range of frequencies, including the resonant frequency.

Experimental Identification of Dynamic Force Coefficients for a 110 mm Compliantly Damped Hybrid Gas Bearing

2014 ◽  
Author(s):  
Adolfo Delgado
Keyword(s):  
Load Capacity ◽  
Excitation Frequency ◽  
Dynamic Test ◽  
Inlet Pressure ◽  
Dynamic Force ◽  
Metal Mesh ◽  
Gas Bearings ◽  
Force Coefficients ◽  
Test Parameters ◽  
Gas Bearing

Compliant hybrid gas bearings combine key enabling features from both fixed geometry externally pressurized gas bearings and compliant foil bearings. The compliant hybrid bearing relies on both hydrostatic and hydrodynamic film pressures to generate load capacity and stiffness to the rotor system, while providing damping through integrally mounted metal mesh bearing support dampers. This paper presents experimentally identified force coefficients for a 110 mm compliantly damped gas bearing using a controlled-motion test rig. Test parameters include hydrostatic inlet pressure, excitation frequency, and rotor speed. The experiments were structured to evaluate the feasibility of implementing these bearings in large size turbomachinery. Dynamic test results indicate weak dependency of equivalent direct stiffness coefficients to most test parameters except for frequency and speed, where higher speeds and excitation frequency decreased equivalent bearing stiffness values. The bearing system equivalent direct damping was negatively impacted by increased inlet pressure and excitation frequency, while the cross-coupled force coefficients showed values an order of magnitude lower than the direct coefficients. The experiments also include orbital excitations to simulate unbalance response representative of a target machine while synchronously traversing a critical speed. The results indicate that the gas bearing can accommodate vibration levels larger than the set bore clearance while maintaining satisfactory damping levels.

Effect of a Planetary Gearbox on the Dynamics of a Rotor System

2018 ◽  
Author(s):  
Ali Tatar ◽  
Christoph W. Schwingshackl
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Rotor System ◽  
Mode Shapes ◽  
Rotating System ◽  
Planetary Gearbox ◽  
Finite Element Software ◽  
Gyroscopic Effects ◽  
The Masses ◽  
Parameter Values

The dynamic analysis of rotors with bladed disks has been investigated in detail over many decades and is reasonably well understood today. In contrast, the dynamic behaviour of two rotors that are coupled via a planetary gearbox is much less well understood. The planetary gearbox adds inertia, mass, stiffness, damping and gyroscopic moments to the system and can strongly affect the modal properties and the dynamic behaviour of the global rotating system. The main objective of this paper is to create a six degrees of freedom numerical model of a rotor system with a planetary gearbox and to investigate its effect on the coupled rotor system. The analysis is based on the newly developed finite element software “GEAROT” which provides axial, torsional and lateral deflections of the two shafts at different speeds via Timoshenko beam elements and also takes gyroscopic effects into account. The disks are currently considered as rigid and the bearings are modelled with isotropic stiffness elements in the translational and rotational directions. A novel planetary gearbox model has been developed, which takes the translational and rotational stiffness and the damping of the gearbox, as well as the masses and inertias of the sun gear, ring gear, planet gears and carrier into account. A rotating system with a planetary gearbox has been investigated with GEAROT. The gearbox mass and stiffness parameters are identified as having a significant effect on the modal behaviour of the rotor system, affecting its natural frequencies and mode shapes. The higher frequency modes are found to be more sensitive to the parameter changes as well as the modes which have a higher deflection at the location of the gearbox on the rotor system. Compared with a single shaft system, the presence of a gearbox introduces new global modes to the rotor system and decouples the mode shapes of the two shafts. The introduction of a planetary gearbox may also lead to an increase or a reduction of the frequency response of the rotor system based on gear parameter values.

Optimization of Nonlinear Unbalanced Flexible Rotating Shaft Passing Through Critical Speeds

2021 ◽  
Author(s):  
Sadegh Amirzadegan ◽  
Mohammad Rokn-Abadi ◽  
R. D. Firouz-Abadi
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Oscillations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Beam Theory ◽  
Rotor System ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Applied Torque

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for this work. The shaft is modeled as a beam and the Euler–Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6 degrees of freedom. In order to solve these equations numerically, the finite element method (FEM) is used. Furthermore, for different bearing properties, rotor responses are examined and curves of passing through critical speeds with angular acceleration due to applied torque are plotted. Then the optimal values of bearing stiffness and damping are calculated to achieve the minimum vibration amplitude, which causes to pass easier through critical speeds. It is concluded that the value of damping and stiffness of bearing change the rotor critical speeds and also significantly affect the dynamic behavior of the rotor system. These effects are also presented graphically and discussed.

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