A Preliminary Nonlinear Analysis of the Axial Transient Response of the Sector-Shaped Hydrodynamic Thrust Bearing-Rotor System

2003 ◽  
Vol 125 (4) ◽  
pp. 854-858 ◽  
Author(s):  
Q. Zhu ◽  
W. J. Zhang
Keyword(s):  
Nonlinear Analysis ◽  
Transient Response ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Rotor System ◽  
Time Dependent ◽  
Vibration Equation ◽  
Oil Film ◽  
Dependent Form ◽  
Turbo Expander

This paper describes a nonlinear model and analysis of the axial transient response of the sector-shaped hydrodynamic thrust bearing-rotor system in a turbo-expander under a suddenly applied step load. The model is comprised of a time-dependent Reynolds Equation for oil film forces, and a vibration equation for the axial shaft system. The time-dependent form of the Reynolds Equation is solved by a finite difference method with a successive over-relaxation scheme, and the vibration equation is solved by the fourth-order Runge-Kutta method and the Adams method. In addition, a linear analysis is attempted in order to evaluate its suitability for the situation under consideration. The result of the analysis has shown that the linear model is unsuited, while the nonlinear analysis appears reasonable. Two system parameters, the initial oil film thickness and the angle of the inclination of the tapered land in a thrust bearing, are shown to have significant impacts on the transient response under consideration, and to be possibly optimized to achieve a minimum axial transient response.

A Nonlinear Analysis of the Axial Steady State Response of the Hydrodynamic Thrust Bearing-Rotor System Subjected to a Harmonic Excitation

2005 ◽  
Author(s):  
T. N. Shiau ◽  
W. C. Hsu
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Harmonic Excitation ◽  
Rotor System ◽  
Time Dependent ◽  
Steady State Response ◽  
Harmonic Force ◽  
Oil Film ◽  
State Response

The purpose of this study is to investigate the nonlinear axial response of a thrust bearing-rotor system, which is subjected to an axial harmonic force. For the axial vibration of the rotor, the system forces include the external axial harmonic force and the reacting oil film forces, which are obtained by solving a time-dependent Reynolds Equation within the thrust pads of the thrust bearing. The time-dependent Reynolds Equation is solved by a finite difference method, and the system equation of motion is solved by the fourth-order Runge-Kutta method. A linear analysis is attempted in to evaluate its suitability for the situation under consideration. And the bearing stiffness and damping coefficients are investigated with parameters including the dimensionless wedge thickness, the initial oil film thickness and the rotor spin speed. The results show that the average steady state response will decrease as the harmonic axial force intensifies its fluctuating magnitude. The results also indicate that it will induce ultra-super harmonics when the axial harmonic force intensifies its fluctuating magnitude.

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.

On the Influence of Thrust Bearings on the Nonlinear Rotor Vibrations of Turbochargers

2016 ◽  
Author(s):  
Ioannis Chatzisavvas ◽  
Aydin Boyaci ◽  
Andreas Lehn ◽  
Marcel Mahner ◽  
Bernhard Schweizer ◽  
...  
Keyword(s):  
Hydrodynamic Model ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Oil Viscosity ◽  
Oil Film ◽  
Thrust Bearings ◽  
Run Up ◽  
Generalized Reynolds Equation

This work investigates the influence of hydrodynamic thrust bearings on the lateral rotor oscillations. Four thrust bearing models are compared in terms of their predictions of the oil-film pressure (Reynolds equation), the oil-film temperature (energy equation) and the load capacity. A detailed thrust bearing model using the generalized Reynolds equation and the 3D energy equation, a model using the standard Reynolds equation with a 2D energy equation, a model where the standard Reynolds equation and the 2D energy equation are decoupled and finally an isothermal thrust bearing model are presented. It is shown that in lower rotational speeds, the four models produce almost the same results. However, as the rotational speed is increased, the necessity for a thermo-hydrodynamic model is demonstrated. Run-up simulations of a turbocharger rotor/bearing system are performed, using an isothermal thrust bearing model with different inlet oil-temperatures. The influence of the oil-temperature of the thrust bearing on the subsynchronous rotor oscillations is investigated. Finally, a thermo-hydrodynamic model is compared with an isothermal in run-up simulations, where the influence of the variable oil-viscosity is discussed.

The Numerical Analysis of the Velocity and Pressure Distribution of the Oil Film in Heavy Hydrostatic Thrust Bearing

2014 ◽  
Vol 541-542 ◽  
pp. 658-662
Author(s):  
Jian Li ◽  
Yuan Chen ◽  
Yang Chun Yu ◽  
Zhu Xin Tian ◽  
Yu Huang
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Pressure Distribution ◽  
Working Conditions ◽  
Thrust Bearing ◽  
Rotation Speed ◽  
The Other ◽  
Surface Load ◽  
Oil Film ◽  
Volume Method

To study the velocity and pressure distribution of the oil film in a heavy hydrostatic thrust bearing, a mathematical model of the velocity is proposed and the finite volume method (FVM) has been used to simulate the flow field under different working conditions. Some pressure experiments were carried out and the results verified the correctness of the simulation. It is concluded that the pressure distribution varies small under different rotation speed when the surface load on the workbench is constant. But the velocity of the oil film is influenced greatly by the rotation speed. When the rotation speed of the workbench is as quick as enough, the velocity of the oil film on one radial side of the pad will be zero, that is to say the lubrication oil will be drained from the other three sides of the recess.

scholarly journals Run-Up Simulation of a Semi-Floating Ring Supported Turbocharger Rotor Considering Thrust Bearing and Mass-Conserving Cavitation

Lubricants ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 44
Author(s):  
Christian Ziese ◽  
Cornelius Irmscher ◽  
Steffen Nitzschke ◽  
Christian Daniel ◽  
Elmar Woschke
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Thrust Bearing ◽  
Three Dimensional ◽  
Reliable Prediction ◽  
Two Phase ◽  
Hydrodynamic Bearings ◽  
Thrust Bearings ◽  
Run Up ◽  
The Impact

The vibration behaviour of turbocharger rotors is influenced by the acting loads as well as by the type and arrangement of the hydrodynamic bearings and their operating condition. Due to the highly non-linear bearing behaviour, lubricant film-induced excitations can occur, which lead to sub-synchronous rotor vibrations. A significant impact on the oscillation behaviour is attributed to the pressure distribution in the hydrodynamic bearings, which is influenced by the thermo-hydrodynamic conditions and the occurrence of outgassing processes. This contribution investigates the vibration behaviour of a floating ring supported turbocharger rotor. For detailed modelling of the bearings, the Reynolds equation with mass-conserving cavitation, the three-dimensional energy equation and the heat conduction equation are solved. To examine the impact of outgassing processes and thrust bearing on the occurrence of sub-synchronous rotor vibrations separately, a variation of the bearing model is made. This includes run-up simulations considering or neglecting thrust bearings and two-phase flow in the lubrication gap. It is shown that, for a reliable prediction of sub-synchronous vibrations, both the modelling of outgassing processes in hydrodynamic bearings and the consideration of thrust bearing are necessary.

Transient Vibration of High-Speed, Lightweight Rotors Due to Sudden Imbalance

1983 ◽  
Vol 105 (3) ◽  
pp. 480-486 ◽  
Author(s):  
M. Sakata ◽  
T. Aiba ◽  
H. Ohnabe
Keyword(s):  
Transient Response ◽  
High Speed ◽  
Rotor System ◽  
Response Analysis ◽  
Transient Vibration ◽  
Flexible Shaft ◽  
Shaft System ◽  
Transient Response Analysis ◽  
Flexible Disk ◽  
Blade Loss

In the field of rotor dynamics, increased attention is being given to the transient response analysis of the rotor, since the effects of impact loading and vibrations of the rotor arising from blade loss can be studied by a time transient solution of the rotor system. As recent trends in rotating machinery have been directed towards lightweight, high-speed flexible rotors, the effect of flexibility on transient response analysis is becoming of increasing importance. In the present paper, a transient vibration analysis is carried out on a flexible-disk/flexible-shaft system or rigid-disk flexible-shaft system subjected to a sudden imbalance that is assumed to represent the effect of blade loss. To solve the basic equation governing a rotating flexible disk the Galerkin’s method is used, and the equation of motion of the rotor system is numerically solved by employing the Runge-Kutta-Gill’s method. Experiments were conducted on a model rotor having a blade loss simulator; the shaft vibrations were also measured. The validity of the anaytical results was demonstrated by comparison with the experimental results.

Dynamic Stability of an Axially Moving Yarn with Time-Dependent Tension

2014 ◽  
Vol 900 ◽  
pp. 753-756 ◽  
Author(s):  
You Guo Li
Keyword(s):  
Differential Equation ◽  
Homotopy Perturbation Method ◽  
Time Dependent ◽  
Second Law ◽  
Order Ordinary Differential Equation ◽  
Vibration Equation ◽  
Transversal Vibration ◽  
First Order ◽  
Homotopy Perturbation ◽  
Axially Moving

In this paper the nonlinear transversal vibration of axially moving yarn with time-dependent tension is investigated. Yarn material is modeled as Kelvin element. A partial differential equation governing the transversal vibration is derived from Newtons second law. Galerkin method is used to truncate the governing nonlinear differential equation, and thus first-order ordinary differential equation is obtained. The periodic vibration equation and the natural frequency of moving yarn are received by applying homotopy perturbation method. As a result, the condition which should be avoided in the weaving process for resonance is obtained.

Effect of recess depth on lubrication performance of annular recess hydrostatic thrust bearing by constant rate flow

2018 ◽  
Vol 70 (1) ◽  
pp. 68-75 ◽  
Author(s):  
Jun-peng Shao ◽  
Guang-dong Liu ◽  
Xiao-dong Yu ◽  
Yan-qin Zhang ◽  
Xiu-li Meng ◽  
...  
Keyword(s):  
Thrust Bearing ◽  
Simulation Method ◽  
Content Type ◽  
Oil Film ◽  
Constant Rate ◽  
Lubrication Performance ◽  
Optimal Value ◽  
Improved Performance ◽  
Lubrication Characteristics ◽  
Volume Method

Purpose The purpose of this paper is to describe a simulation and experimental research concerning the effect of recess depth on the lubrication performance of a hydrostatic thrust bearing by constant rate flow. Design/methodology/approach The computational fluid dynamics and finite volume method have been used to compute the lubrication characteristics of an annular recess hydrostatic thrust bearing with different recess depths. The performances are oil recess pressure, oil recess temperature and oil film velocity. The recess depth has been optimized. A test rig is established for testing the pressure field of the structure of hydrostatic thrust bearing after recess depth optimization, and experimental results show that experimental data are basically identical with the simulation results, which demonstrates the validity of the proposed numerical simulation method. Findings The results demonstrate that the oil film temperature decreases and the oil film pressure first increases and then decreases with an increase in the recess depth, but oil film velocity is constant. To sum up comprehensive lubrication performance, the recess depth of 3.5 mm is its optimal value for the annular recess hydrostatic thrust bearing. Originality/value The computed results indicate that to get an improved performance from a constant flow hydrostatic thrust bearing, a proper selection of the recess depth is essential.

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