Detection of a Rotor Crack Based on the Nonlinear Vibration Diagnosis Using Periodic Excitation

2005 ◽  
Author(s):  
Yukio Ishida ◽  
Tsuyoshi Inoue
Keyword(s):  
Nonlinear Vibration ◽  
Equations Of Motion ◽  
Frequency Component ◽  
Dominant Frequency ◽  
Vibration Characteristics ◽  
Periodic Excitation ◽  
Cracked Rotor ◽  
On Line ◽  
Linear And Nonlinear ◽  
Excitation Force

Detection of a rotor crack based on the nonlinear vibration diagnosis using periodic excitation force is investigated. Due to the open-close mechanism of the crack, the equations of motion of a cracked rotor have linear and nonlinear parametric terms. When a periodic excitation force is applied to the cracked rotor, various kinds of resonances due to the unique vibration characteristics of a crack. Furthermore, types of resonances, resonance points and dominant frequency component of these resonances are clarified theoretically and experimentally. These results enable us to detect a crack on-line without stopping the system.

Detection of a Rotor Crack Using a Harmonic Excitation and Nonlinear Vibration Analysis

2006 ◽  
Vol 128 (6) ◽  
pp. 741-749 ◽  
Author(s):  
Yukio Ishida ◽  
Tsuyoshi Inoue
Keyword(s):  
Power Series ◽  
Nonlinear Vibration ◽  
Piecewise Linear ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Crack Model ◽  
Cracked Rotor ◽  
Nonlinear Resonances ◽  
Excitation Force

Detection of a rotor crack based on the nonlinear vibration diagnosis using harmonic excitation force is investigated. The open-close mechanism of crack is firstly modeled by a piecewise linear function. In addition, another approximation crack model using a power series function that is convenient for the theoretical analysis is used. When the power series function crack model is used, the equations of motion of a cracked rotor have linear and nonlinear parametric terms. In this paper, a harmonic excitation force is applied to the cracked rotor and its excitation frequency is swept, and the nonlinear resonances due to crack are investigated. The occurrence of various types of nonlinear resonances due to crack are clarified, and types of these resonances, their resonance points, and dominant frequency component of these resonances are clarified numerically and experimentally. Furthermore, nonlinear theoretical analyses are performed for these nonlinear resonances, and it is clarified that the amplitudes of these nonlinear resonances depend on the nonlinear parametric characteristics of rotor crack. These results enable us to detect a rotor crack without stopping the system during on-line operation.

Analysis of Nonlinear Vibration for the Cracked Rotors With Unsymmetrical Viscoelastic Supported Conditions

2005 ◽  
Author(s):  
Changping Chen ◽  
Liming Dai ◽  
Yiming Fu
Keyword(s):  
Nonlinear Vibration ◽  
Nonlinear Vibrations ◽  
Equations Of Motion ◽  
Rotor System ◽  
Governing Equations ◽  
Response Curves ◽  
Disc Position ◽  
On Line ◽  
Cracked Rotor System ◽  
Line Crack

The nonlinear governing equations of motion for the cracked rotor system with unsymmetrical viscoelastic supported condition are derived and the nonlinear vibrations of the system are analyzed. The effects of the cracked depth, the cracked position and the disc position on the response curves of the rotational speed-the nonlinear vibration amplitude and the response curve of the nonlinear amplitude-frequency are discussed in detail. The results can be used for the on-line crack monitor of the rotor system.

Nonlinear Vibration Characteristics of Helical Spring

2010 ◽  
Vol 29-32 ◽  
pp. 1317-1322
Author(s):  
Nan Nan Wang ◽  
You Fu Hou ◽  
Zu Zhi Tian
Keyword(s):  
Nonlinear Vibration ◽  
Constitutive Relations ◽  
Low Frequency ◽  
Vibration Characteristics ◽  
Rigid Body Dynamics ◽  
Helical Spring ◽  
Low Frequency Vibration ◽  
Near Resonance ◽  
Finite Element Technology ◽  
Dynamics Response

A helical spring has large deformation under the condition of near resonance, in order to obtain the nonlinear vibration characteristics, the single-integral constitutive relations of helical spring based on nonlinear theory are discussed firstly, then nonlinear dynamic characteristics of helical spring are analyzed based on finite element technology. Finally, the dynamic simulation associated with flexible characteristics for helical spring is studied in ADAMS. The results show that the maximum stress of helical spring appears at transition region between different radius which is consistent with fracture position actually. Flexible dynamic response of helical spring mainly behaves low frequency vibration which is different from rigid body dynamics response.

Linear and Nonlinear Dynamics of Cantilevered Cylinders in Axial Flow

2014 ◽  
Author(s):  
Ahmad Jamal ◽  
Michael P. Païdoussis ◽  
Luc G. Mongeau
Keyword(s):  
Equations Of Motion ◽  
Axial Flow ◽  
Experimental System ◽  
Vital Role ◽  
Viscous Force ◽  
Flexible Cylinder ◽  
Force Coefficients ◽  
Precise Calculation ◽  
Linear And Nonlinear ◽  
Nonlinear Equations Of Motion

Understanding and prediction of the dynamics of slender flexible cylinders in axial flow is of interest for the design and safe operation of heat exchangers and nuclear reactors, specifically that of heat exchanger tubes, nuclear fuel elements, control rods, and monitoring tubes. In such fluid-structure interaction problems, the fluid forces acting on the flexible structure play a vital role in defining its dynamics. Therefore, a precise calculation of the coefficients associated to these forces, such as the longitudinal and normal viscous force coefficients, and base drag coefficient in the equation of motion is imperative. The present work is aimed at (i) calculating these force coefficients for a cantilevered slender flexible cylinder, fitted with an ogival end-piece, in axial flow and (ii) conducting experiments on the same system. In the calculation of these force coefficients, the parameters of the experimental system are used, so that the theoretically predicted dynamics would be representative of the actual physical system. These calculated force coefficients are then incorporated in the linear and nonlinear equations of motion and the predicted dynamics are compared with those of the experiments. The comparison shows good agreement between the theoretical and experimental results.

scholarly journals Oscillatory and steady streaming flow in the anterior chamber of the moving eye

2019 ◽  
Vol 863 ◽  
pp. 904-926 ◽  
Author(s):  
M. Dvoriashyna ◽  
R. Repetto ◽  
J. H. Tweedy
Keyword(s):  
Anterior Chamber ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Frequency Component ◽  
Dominant Frequency ◽  
Point Of View ◽  
Dimensional Structure ◽  
Steady Streaming ◽  
Constant Height ◽  
Angular Amplitude

We study the flow induced by eye rotations in the anterior chamber (AC) of the eye, the region between the cornea and the iris. We model the geometry of the AC as a thin domain sitting on the surface of a sphere, and study both the simpler case of a constant-height domain as well as a more realistic AC shape. We model eye rotations as harmonic in time with prescribed frequency $\unicode[STIX]{x1D714}_{f}$ and amplitude $\unicode[STIX]{x1D6FD}$, and use lubrication theory to simplify the governing equations. We write the equations in a reference frame moving with the domain and show that fluid motion is governed by three dimensionless parameters: the aspect ratio $\unicode[STIX]{x1D716}$ of the AC, the angular amplitude $\unicode[STIX]{x1D6FD}$ and the Womersley number $\unicode[STIX]{x1D6FC}$. We simplify the equations under the physiologically realistic assumptions that $\unicode[STIX]{x1D716}$ is small and $\unicode[STIX]{x1D6FC}$ large, leading to a linear system that can be decomposed into three harmonics: a dominant frequency component, with frequency $\unicode[STIX]{x1D714}_{f}$, and a steady streaming component and a third component with frequency $2\unicode[STIX]{x1D714}_{f}$. We solve the problem analytically for the constant-height domain and numerically as the solution of ordinary differential equations in the more realistic geometry. Both the primary flow and the steady streaming are shown to have a highly three-dimensional structure, which has not been highlighted in previous numerical works. We show that the steady streaming is particularly relevant from the clinical point of view, as it induces fluid mixing in the AC. Furthermore, the steady flow component is the dominant mixing mechanism during the night, when the thermal flow induced by temperature variations across the AC is suppressed.

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