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.

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.

scholarly journals Structural Damage Detection Using Slopes of Longitudinal Vibration Shapes

2015 ◽  
Author(s):  
W. Xu ◽  
W. D. Zhu ◽  
S. A. Smith
Keyword(s):  
Steady State ◽  
Damage Detection ◽  
Structural Damage ◽  
Longitudinal Vibration ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Noise Robustness ◽  
Steady State Response ◽  
Structural Damage Detection ◽  
State Response

While structural damage detection based on flexural vibration shapes, such as mode shapes and steady-state response shapes under harmonic excitation, has been well developed, little attention is paid to that based on longitudinal vibration shapes that also contain damage information. This study originally formulates a slope vibration shape for damage detection in bars using longitudinal vibration shapes. To enhance noise robustness of the method, a slope vibration shape is transformed to a multiscale slope vibration shape in a multiscale domain using wavelet transform, which has explicit physical implication, high damage sensitivity, and noise robustness. These advantages are demonstrated in numerical cases of damaged bars, and results show that multiscale slope vibration shapes can be used for identifying and locating damage in a noisy environment. A three-dimensional (3D) scanning laser vibrometer is used to measure the longitudinal steady-state response shape of an aluminum bar with damage due to reduced cross-sectional dimensions under harmonic excitation, and results show that the method can successfully identify and locate the damage. Slopes of longitudinal vibration shapes are shown to be suitable for damage detection in bars and have potential for applications in noisy environments.

Stability and steady-state response analysis of a single rub-impact rotor system

2014 ◽  
Vol 85 (1) ◽  
pp. 133-148 ◽  
Author(s):  
Xingyu Tai ◽  
Hui Ma ◽  
Fuhao Liu ◽  
Yang Liu ◽  
Bangchun Wen
Keyword(s):  
Steady State ◽  
Rotor System ◽  
Response Analysis ◽  
Steady State Response ◽  
State Response

scholarly journals Structural Damage Detection Using Slopes of Longitudinal Vibration Shapes

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
W. Xu ◽  
W. D. Zhu ◽  
S. A. Smith ◽  
M. S. Cao
Keyword(s):  
Steady State ◽  
Damage Detection ◽  
Structural Damage ◽  
Longitudinal Vibration ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Noise Robustness ◽  
Steady State Response ◽  
Structural Damage Detection ◽  
State Response

While structural damage detection based on flexural vibration shapes, such as mode shapes and steady-state response shapes under harmonic excitation, has been well developed, little attention is paid to that based on longitudinal vibration shapes that also contain damage information. This study originally formulates a slope vibration shape (SVS) for damage detection in bars using longitudinal vibration shapes. To enhance noise robustness of the method, an SVS is transformed to a multiscale slope vibration shape (MSVS) in a multiscale domain using wavelet transform, which has explicit physical implication, high damage sensitivity, and noise robustness. These advantages are demonstrated in numerical cases of damaged bars, and results show that MSVSs can be used for identifying and locating damage in a noisy environment. A three-dimensional (3D) scanning laser vibrometer (SLV) is used to measure the longitudinal steady-state response shape of an aluminum bar with damage due to reduced cross-sectional dimensions under harmonic excitation, and results show that the method can successfully identify and locate the damage. Slopes of longitudinal vibration shapes are shown to be suitable for damage detection in bars and have potential for applications in noisy environments.

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