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.

A Method for Solving Stiffness of Finite Length Self-Acting Gas-Lubricated Journal Bearing

2012 ◽  
Vol 562-564 ◽  
pp. 643-649
Author(s):  
Jian Lu Wang ◽  
Yan Jun Lu ◽  
Hui Ma ◽  
Yong Fang Zhang ◽  
Yong Hui Chen
Keyword(s):  
Finite Length ◽  
Efficient Method ◽  
Partial Derivative ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Transformation Method ◽  
The Self ◽  
Time Dependent ◽  
Dynamic Design ◽  
Derivative Method

Based on the differential transformation method, an efficient method is proposed to calculate stiffness of finite length self-acting gas-lubricated journal bearing. Time dependent Reynolds equation in gas lubrication of the self-acting journal bearing is solved, gas film pressure distribution and stiffness of the bearing are obtained. In comparison with the partial derivative method, the proposed method for solving stiffness of self-acting gas-lubricated journal bearing is verified. The proposed method can provide the theoretical reference to the dynamic design of self-acting gas-lubricated journal bearing-rotor system.

Nonlinear Dynamic Behaviors and Bifurcation of Symmetrical Rotor System Supported by Self-Acting Gas Jounal Bearings

2010 ◽  
Vol 97-101 ◽  
pp. 2634-2638 ◽  
Author(s):  
Wei Min Wang ◽  
Yan Jun Lu ◽  
Zhi Jun Cao ◽  
Yong Fang Zhang ◽  
Lie Yu
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Period Doubling ◽  
Journal Bearings ◽  
Time Dependent ◽  
Jeffcott Rotor ◽  
Successive Over Relaxation ◽  
Rotor Dynamic ◽  
Gas Journal Bearing ◽  
Bifurcation Behavior

The unbalanced response and corresponding bifurcation behavior of the rotor dynamic system supported by gas journal bearings are investigated. A time-dependent mathematical model is used to describe the pressure distribution of gas journal bearing with nonlinearity. The rigid Jeffcott rotor with self-acting gas journal bearing supports is modeled. The finite difference method and the Successive Over Relaxation (S.O.R.) method are employed to solve the time-dependent Reynolds equation of gas journal bearings. The bifurcation of unbalanced responses of the rotor is analyzed by a Poincaré map. The numerical results reveal periodic, period-doubling, quasi-periodic, and chaotic motion of rich and complex non-linear behaviors of the system.

Static and Dynamic Characteristics of Self-Acting, Partial-Arc, Gas Journal Bearings

1964 ◽  
Vol 86 (2) ◽  
pp. 405-413 ◽  
Author(s):  
R. J. Wernick ◽  
C. H. T. Pan
Keyword(s):  
Power Series ◽  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Standard Form ◽  
Journal Bearings ◽  
Static And Dynamic Characteristics ◽  
Stability Derivatives ◽  
Bearing Loads ◽  
Gas Journal Bearing

The Reynolds equation applicable to a self-acting partial-arc gas journal bearing is perturbed in terms of the compressibility number Λ. The resulting set of equations is then put into a standard form and Galerkin’s method is used to obtain bearing loads and stability derivatives. These results are expressed in a power series in Λ.

Static and Dynamic Characteristics of Externally Pressurized Porous Gas Journal Bearing With Four Degrees-of-Freedom

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Shuyun Jiang ◽  
Shengye Lin ◽  
Chundong Xu
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Reynolds Equation ◽  
Static Load ◽  
Journal Bearing ◽  
Load Capacity ◽  
Linear Perturbation ◽  
Static And Dynamic Characteristics ◽  
Bearing Number ◽  
Gas Journal Bearing

This paper studies the static and dynamic coefficients of an externally pressurized porous gas journal bearing. The finite difference method is used to solve the Reynolds equation of the bearing to obtain the static load capacity. The linear perturbation method is adopted to derive the perturbation equations considering four degrees-of-freedom (4DOF), namely, the translational movements in x and y directions and the rotational movements around x and y directions. The effects of various parameters on the dynamic behaviors of the journal bearing are studied. These parameters include the bearing number, the supply pressure, the feeding parameter, the length-to-diameter ratio, the porosity parameter, the eccentricity ratio, and tilting angles. Simulated results prove that the proposed method is valid in estimating the static and dynamic characteristics of a porous gas journal bearing with 4DOF.

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.

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.

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.

Analysis of the Stiffness and Damping Characteristics of an Externally Pressurized Porous Gas Journal Bearing

1977 ◽  
Vol 99 (2) ◽  
pp. 295-301 ◽  
Author(s):  
N. S. Rao
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Dynamic Pressure ◽  
Porous Wall ◽  
Small Perturbations ◽  
One Dimensional ◽  
Damping Characteristics ◽  
Flow Through ◽  
Stiffness And Damping ◽  
Gas Journal Bearing

The dynamic behavior of an externally pressurized porous gas journal bearing is analyzed by assuming one dimensional flow through porous wall. A periodic (displacement) disturbance is imposed on the bearing, and the dynamic pressure distribution is determined by small perturbations of the Reynolds equation. Stiffness and damping for various design conditions are calculated numerically using a digital computer and presented in the form of design charts and tables.

Extension of the Patir-Cheng Flow Simulation of a Rough Surface Bearing to a Compressible Lubricant

1982 ◽  
Vol 24 (4) ◽  
pp. 209-214
Author(s):  
B. C. Majumdar ◽  
B. J. Hamrock
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Roughness Parameter ◽  
Flow Simulation ◽  
Surface Structures ◽  
Surface Pattern ◽  
Hydrodynamic Load ◽  
Gas Journal Bearing ◽  
Compressible Lubricant

It is shown that the average Reynolds equation for rough surfaces using an incompressible lubricant derived by Patir and Cheng (1)§ can be used for a compressible lubricant if the surface structures of both surfaces are the same. The average Reynolds equation is applied to an infinitely long gas journal bearing to find the hydrodynamic load capacity. The effect of the roughness parameter and the surface pattern parameter on the hydrodynamic load is also investigated.

Hybrid Reduced Model of Rotor

2013 ◽  
Vol 60 (3) ◽  
pp. 319-333
Author(s):  
Rafał Hein ◽  
Cezary Orlikowski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hybrid Model ◽  
Rotor System ◽  
Reduced Model ◽  
Order Model ◽  
Gyroscopic Effect ◽  
Reduced Models ◽  
Rigid Finite Element Method ◽  
Low Order

Abstract In the paper, the authors describe the method of reduction of a model of rotor system. The proposed approach makes it possible to obtain a low order model including e.g. non-proportional damping or the gyroscopic effect. This method is illustrated using an example of a rotor system. First, a model of the system is built without gyroscopic and damping effects by using the rigid finite element method. Next, this model is reduced. Finally, two identical, low order, reduced models in two perpendicular planes are coupled together by means of gyroscopic and damping interaction to form one model of the system. Thus a hybrid model is obtained. The advantage of the presented method is that the number of gyroscopic and damping interactions does not affect the model range

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