Harmonic Transfer Function Based Damage Identification of Breathing Cracked Jeffcott Rotor

This paper proposes a vibration-based damage identification method based on 6-dof Jeffcott rotor system, which is based on harmonic balance and Newton-Raphson methods. First, the equations of motion are derived by using energy method and Lagrange principle. The crack model is based on strain energy release rate (SERR) in fracture mechanics and modified to accommodate 6-dof Jeffcott rotor model. Then, Gear’s method is used to solve the vibration responses of nominal and damaged rotor systems. By processing vibration responses, the transfer function shifts between nominal and damaged systems are taken as the input of damage identification algorithm. Finally, damage severity can be correlated with the damage parameter estimated via developed damage identification model. Numerical examples are shown to demonstrate the effectiveness in identifying the breathing crack in the rotor system.

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Roll-Yaw Coupling Effect of Jeffcott Rotor With Breathing Crack

Volume 4B: Dynamics, Vibration, and Control ◽

10.1115/imece2015-52412 ◽

2015 ◽

Author(s):

J. Zhao ◽

H. A. DeSmidt ◽

M. Peng ◽

W. Yao

Keyword(s):

Coupling Effect ◽

Rotor System ◽

Crack Model ◽

Breathing Crack ◽

Cracked Rotor ◽

Lagrange Principle ◽

Jeffcott Rotor ◽

Vibration Responses ◽

Cracked Rotor System ◽

Rotor Model

A new rotor model is developed in this paper to explore the dynamic coupling effect of roll-yaw motion. The rotor model employs a 6 degree-of-freedom Jeffcott rotor with a breathing crack. Based on the energy method and Lagrange principle, equation of motion is derived in yawing coordinate system with consideration of unbalance mass. The breathing crack model is established by Zero Stress Intensity Factor (SIF) method based on the crack released strain energy concept in fracture mechanics. SIF method is used to determine the crack closure line by computing SIF for opening mode. The vibration responses of the cracked rotor system are solved by Gear’s method. The coupling effect of yawing and rolling motion is studied in this paper to investigate vibration response of cracked rotor system. With the yawing motion, the dynamics of the rotor-bearing system is changed by additional stiffness and force terms. The parametric study is conducted to analyze the effect of yawing rate and acceleration on the crack breathing behavior. Finally, the vibration responses of the nominal and damaged rotor systems are analyzed to find out the indication for the damage detection and health monitoring.

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Nonlinear Breathing Behavior Study of Transverse Crack on a Jeffcott Rotor Under Torsional Excitation

Volume 2: Dynamic Modeling and Diagnostics in Biomedical Systems; Dynamics and Control of Wind Energy Systems; Vehicle Energy Management Optimization; Energy Storage, Optimization; Transportation and Grid Applications; Estimation and Identification Methods, Tracking, Detection, Alternative Propulsion Systems; Ground and Space Vehicle Dynamics; Intelligent Transportation Systems and Control; Energy Harvesting; Modeling and Control for Thermo-Fluid Applications, IC Engines, Manufacturing ◽

10.1115/dscc2014-5824 ◽

2014 ◽

Cited By ~ 2

Author(s):

J. Zhao ◽

H. A. DeSmidt ◽

W. Yao

Keyword(s):

Damage Detection ◽

Stiffness Matrix ◽

Strain Energy Release ◽

Vibration Response ◽

Crack Model ◽

Open Area ◽

Lagrange Principle ◽

Time Step ◽

Crack Open ◽

Jeffcott Rotor

In this paper, Jeffcott rotor model is employed to explore the vibration response of breathing cracked system with unbalance mass. Based on the energy method and Lagrange principle, 6 degree-of-freedom equation of motion is derived in fixed coordinate system. The crack model is established using strain energy release theory of facture mechanics. The stiffness matrix induced by the crack is changing with the variation of crack open area. Zero stress intensity factor (SIF) method is used to determine the crack closure line by computing the SIF for opening mode. By integrating compliant coefficients over newly determined crack open area, the stiffness matrix is updated and vibration response is solved for every time step by Gear’s method. In addition, the breathing behavior of the crack is studied for multiple eccentricity phases and rotation speeds in order to provide effective guidance for damage detection. The paper explores the effect of external torsional loading on the crack breathing behavior. Finally, the coupling of lateral and torsional vibration is investigated to be used as an indicator of damage detection and health monitoring.

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Roll-Yaw Coupled Vibration of the Rotor System With Breathing Crack and Unbalance Mass

Volume 4A: Dynamics, Vibration, and Control ◽

10.1115/imece2015-52469 ◽

2015 ◽

Author(s):

J. Zhao ◽

H. A. DeSmidt ◽

M. Peng ◽

W. Yao

Keyword(s):

Coupling Effect ◽

Rotor System ◽

Crack Model ◽

Clear Understanding ◽

Coupled Vibration ◽

Breathing Crack ◽

Energy Concept ◽

Vibration Responses ◽

Rolling Rate ◽

Rotor Model

This paper develops a new finite element rotor model with consideration of the coupling effect of rolling and yawing motion. The crack model is built using released strain energy concept in fracture mechanics. The nonlinear breathing behavior of cracks on the rotor shaft is simulated through Zero Stress Intensity Factor (SIF) method. The vibration responses of rotor system are solved by Newmark Integration method for both nominal and damaged system. With the yawing motion, the additional force will be induced for beam element and center disk. Incorporated with breathing crack model, the breathing behavior of crack is comprehensively studied in terms of the rolling rate, yawing rate and yawing acceleration. The clear understanding of crack breathing behavior is beneficial for the damage detection and health monitoring of the rotor system.

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Damage Identification Using Sensitivity-Enhancing Control and Identified Models

Journal of Vibration and Acoustics ◽

10.1115/1.2159037 ◽

2005 ◽

Vol 128 (2) ◽

pp. 210-220 ◽

Cited By ~ 14

Author(s):

Jason A. Solbeck ◽

Laura R. Ray

Keyword(s):

Transfer Function ◽

Closed Loop ◽

Damage Identification ◽

Structural Models ◽

Damage Parameter ◽

Measured Parameter ◽

Parameter Vector ◽

Input Output ◽

Output Data ◽

Torsional System

This paper investigates a coherence approach for locating structural damage using modal frequencies and transfer function parameters identified from input-output data using Observer/Kalman filter identification (OKID). Autonomous damage identification using such forward methods generally require (i) a structural model by which to relate measured and predicted modal properties induced by damage, and (ii) good sensitivity of modal parameter changes to damage states. Using the coherence approach, a damage parameter vector comprised of a finite set of modal frequencies and transfer function parameters is hypothesized for each damage case using either identified or analytic structural models. Measured parameter vectors are extracted from experimental input-output data for a damaged structure using OKID and are compared to hypotheses to determine the most likely damage state. The richness of the parameter vector set, which is comprised of high-quality frequency measurements and lower-quality transfer function parameters, is evaluated in order to determine the ability to uniquely localize damage. The method is evaluated experimentally using a three-degree-of-freedom torsional system and a space-frame truss. Damage parameter hypotheses are generated from a model of the healthy structure developed by system identification in the torsional system, and an analytic model is used to generate damage hypotheses for the truss structure. Feedback control laws enhance the parameter vectors by including closed-loop modal frequencies in order to reduce noise sensitivity and improve uniqueness of parameter vector hypotheses to each damage case. Results show improvements in damage identification using damage parameter vectors comprised of open- and closed-loop modal frequencies, even when model error exists in structural models used to form damage parameter vector hypotheses.

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Rub-Impact Detection of Rotor Systems Using Time-Frequency Techniques

Volume 4B: Dynamics, Vibration, and Control ◽

10.1115/imece2016-65412 ◽

2016 ◽

Cited By ~ 2

Author(s):

Laihao Yang ◽

Xuefeng Chen ◽

Shibin Wang ◽

Hao Zuo

Keyword(s):

Contact Force ◽

High Speed ◽

High Efficiency ◽

Rotor System ◽

Fast Time ◽

Time Varying ◽

Rotor Systems ◽

Time Frequency ◽

Jeffcott Rotor ◽

Vibration Responses

Since increasing demands for high efficiency of high speed rotating machines in recent years, the clearance between rotor and stator becomes smaller and smaller. Consequently, rub-impact fault is more likely to occur. It has become one of the most common and serious malfunctions for rotor system in practical engineering. Because the rub-impact severely induces the rotor dynamic instability, it will finally result in catastrophic failures and great economic loss if undetected in time. The occurrence of the rub-impact leads to a contact force between rotating shaft and stator which can be regarded as an additional support on the rotor system. The contact force will further result in the stiffening effect. As a result, some fast time-varying phenomena of vibration responses including the fast time-varying transient stiffness and the fast oscillated instantaneous frequency (IF) may appear. These phenomena may offer abundant characteristics to diagnose the rub-impact fault of rotor system. In this paper, an effective method based on the fast oscillated characteristics of IF for vibration responses is proposed to detect rub-impact fault of rotor bearing system. First of all, the fast time-varying transient stiffness of rub-impact rotor system is qualitatively formulated based on the Jeffcott rotor model and the fast oscillated characteristics of IF is presented and theoretically analyzed. Second, a time-frequency technique called nonlinear squeezing time-frequency transform (NSTFT) is introduced to extract the fast oscillated IF resulting from the rub-impact fault of rotor systems. Numerical simulations are respectively conducted on the Jeffcott rotor system with linear stiffness and oil film bearings. And then the oscillated characteristics of the IF are analyzed. The analysis results suggest that the IF of the vibration responses remains constant at the rotating frequency if there is no rub-impact fault. However, if rub-impact fault occurs, the IF of the vibration responses will oscillate periodically around the basic harmonic frequency. Furthermore, the oscillation law of the IF of vibration responses for rub-impact rotor systems is also numerically investigated. It is found that the oscillation frequency is the 1/k (k = 1, 2, 3, ...) of the rotating frequency if the rotor system operates at periodic-k motion. Finally, rub-impact fault experiments are performed under different operating regimes. The experimental results are consistent with the numerical results, thus demonstrating the validity and the practicability of the proposed method.

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Cracked Shaft Damage Identification via Symmetry Breaking Active Magnetic Bearing Control and Interrogation

Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B ◽

10.1115/detc2011-48738 ◽

2011 ◽

Author(s):

J. Zhao ◽

H. A. DeSmidt

Keyword(s):

Symmetry Breaking ◽

Structural Damage ◽

Damage Identification ◽

Magnetic Bearing ◽

Active Magnetic Bearing ◽

Crack Model ◽

Lagrange Principle ◽

Disk System ◽

Data Set ◽

Loop Control

A new vibration-based damage identification methodology for cracked rotor systems with periodically time-varying dynamics is developed and demonstrated on a shaft-disk system. This approach is based Floquet theory and utilizes measured changes in the system natural frequencies to estimate the severity and location of shaft structural cracks during operation. The damage identification is enhanced through the use of an Active Magnetic Bearing with adjustable support stiffness and acceleration feedback. Here, a novel symmetry-breaking closed-loop control is employed during the iterative damage identification process to enrich the data set by removing the Eigen degeneracy of the symmetric shaft structure. This approach enables full damage identification from a single sensor and hence without requiring measured modeshape information. The dynamical model of system is built based on the Lagrange principle and the assumed mode method while the crack model is based on fracture mechanics. The method is synthesized via harmonic balance and numerical examples for a shaft/disk system demonstrate the effectiveness in detecting both location and severity of the structural damage.

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Time-delayed positive-position and velocity fefe edback controller to suppress the lateral vibrations in nonlinear Jeffcott-rotor system

Menoufia Journal of Electronic Engineering Research ◽

10.21608/mjeer.2018.64548 ◽

2018 ◽

Vol 27 (1) ◽

pp. 261-278 ◽

Cited By ~ 1

Author(s):

M. Eissa ◽

M. Kamel ◽

N. A. Saeed ◽

W. A. El-Ganaini ◽

H. A. El-Gohary

Keyword(s):

Rotor System ◽

Lateral Vibrations ◽

Jeffcott Rotor

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Analytical and experimental study on Van der Pol-type and Rayleigh-type equations for modeling nonlinear aeroelastic instabilities

Advances in Structural Engineering ◽

10.1177/13694332211022056 ◽

2021 ◽

pp. 136943322110220

Author(s):

Guangzhong Gao ◽

Ledong Zhu ◽

Hua Bai ◽

Wanshui Han ◽

Feng Wang

Keyword(s):

Aerodynamic Force ◽

Early Stage ◽

Higher Order ◽

Empirical Modeling ◽

Identification Algorithm ◽

Van Der Pol ◽

Single Degree Of Freedom ◽

Section Shape ◽

Vibration Responses ◽

Aerodynamic Parameters

An empirical modeling of nonlinear aerodynamic force during aeroelastic instabilities, that is, vortex-induced vibration (VIV), galloping and flutter, is necessary in the estimation of vibration responses. Previous works on single-degree-of-freedom (SDOF) models suggest that nonlinear forms (Van der Pol or Rayleigh types) differ from section to section, which causes difficulty in practical application. Analytical evidences in this study have clarified that Van der Pol-type and Rayleigh-type models are equivalent in the amplitude-dependent aerodynamic damping; their difference lies in the higher-order harmonic responses. An identification algorithm of aerodynamic parameters is proposed to improve the robustness of aerodynamic parameters and guarantee the equivalence of both model types. Wind-tunnel tests of typical aeroelastic instabilities indicate that higher-order harmonic responses are small for VIV, galloping, and early-stage flutter instability when compared with the fundamental components due to weak nonlinearity. Van der Pol-type and Rayleigh-type models are both applicable until the flutter amplitude grows excessively large. It is clear that both model types are suitable for any section shape when use the proposed method of aerodynamic identification, and thus can be treated as a universal model for estimating the vibration amplitudes of nonlinear aeroelastic instabilities.

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