scholarly journals Vibration and Stability Analysis of a Bearing–Rotor System with Transverse Breathing Crack and Initial Bending

Machines ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 79
Author(s):  
Yuehua Wang ◽  
Xin Xiong ◽  
Xiong Hu
Keyword(s):  
Nonlinear Response ◽  
Crack Depth ◽  
Rotor System ◽  
Frequency Change ◽  
Breathing Crack ◽  
Cracked Rotor ◽  
Rotor Systems ◽  
Vibrational Characteristics ◽  
The Stability ◽  
Cracked Shaft

This paper focuses on the stability and nonlinear response of a bearing-rotor system affected by a transverse crack and initial bending which was thought to be part of an unbalance or had been neglected before. The differences of breathing functions for the transverse breathing crack caused by initial bending is presented here, and the calculation of time-varying finite elements stiffness matrix of the cracked shaft is improved by replacing traditional the approximate crack segment with an exact area. After establishing the dynamic model of the cracked rotor with initial bending, vibrational characteristics such as amplitude-speed diagram, frequency spectrogram and bifurcations are investigated in detail. The eigenvalues of the transition matrix are calculated and analyzed as an indicator of dynamic stability with the growths of crack depth and initial bending. Many differences are found between the two cases of dynamic response of rotor system by numerical simulation. The frequency change with the growth of initial bending is opposite to the change with the growth of crack depth, and the shapes of amplitude-speed also having great different features. Stable regions are reduced and extended laterally by initial bending. All these results obtained in this paper will contribute to identify the bending fault and assess the stability of the bearing-rotor systems.

Numerical Investigation on the Nonlinear Dynamics of Anisotropic Breathing Cracked Rotor Systems

2020 ◽  
Author(s):  
Zhaoli Zheng ◽  
Zixuan Li ◽  
Di Zhang ◽  
Yonghui Xie ◽  
Zheyuan Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Breathing Crack ◽  
Cracked Rotor ◽  
Tangent Stiffness Matrix ◽  
Rotor Systems ◽  
Relative Angle

Abstract The nonlinear breathing crack behaviors and anisotropy of the bearing are important sources of severe vibration of rotor systems. However, the rotor system considering both of these factors has not gained sufficient attention in the existing studies. In this paper, the nonlinear dynamics of such anisotropic breathing cracked rotor system is investigated based on three-dimensional finite element model (FEM). Firstly, the equations of motion of the rotor system are established in the rotating frame to facilitate the modeling of the breathing crack. The fixed-interface component mode synthesis (CMS) is used to reduce the system’s degrees of freedom (DOFs). Then, in the process of solving the equations by harmonic balance method (HBM) and Newton-Raphson method, an original method for fast calculating tangent stiffness matrix is proposed. Finally, the effects of the crack depth, the anisotropy of bearing and relative angle between bearings on the nonlinear dynamics of the system are studied. The results show that the breathing behavior will complicate the vibration and introduce additional transverse stiffness. The increase of crack depth will deteriorate the vibration. The anisotropy and relative angle of bearing will lead to the splitting and merging of the resonant peaks, respectively.

scholarly journals EFFECT OF FRICTION ON VIBRATIONAL CHARACTERISTICS OF ROTOR SYSTEM DURING ROTOR-STATOR INTERACTION

2020 ◽  
pp. 22-31
Author(s):  
Anton Kurakin ◽  
Keyword(s):  
Experimental Data ◽  
Experimental Investigation ◽  
Friction Coefficient ◽  
Rotor System ◽  
Aluminum Bronze ◽  
Rotor Systems ◽  
Vibrational Characteristics ◽  
Rotor Stator Interaction ◽  
Intermediate Value ◽  
Impact Motion

Systems operation which include rotating elements in certain cases is associated with occurrence of contact between the rotating parts (rotor) and the stationary parts (stator). There were cases then rotor-stator interaction led to damage or to complete unit destruction. For this reason, rotor-stator interaction is one of the main problem of rotor systems exploitation. The main aim of the work is to gather detail data about effect of friction on vibrational characteristics of rotor system during rotor-stator interaction. In this article the experimental investigation method and experimental investigation of dynamic behavior of rotor during rotor-stator interaction is presented. The analysis of experimental data obtained during interaction between steel rotor and stator made of aluminum, bronze and PTFE is presented. All results with rotor-stator contact and without were compared by using Campbell diagrams, orbits and frequency responses. Analysis of experimental data shows that friction has strong effect on vibrational characteristics of rotor system during rotor-stator interaction. According to friction ratio three kinds of vibrational characteristics of rotor system are distinguished: forward slipping if friction coefficient is small, backward rolling if friction coefficient is big, vibratory impact motion if friction coefficient has intermediate value. Created experimental method and gathered data about rotor dynamics during rotor-stator contact can be used for verification and tuning of mathematical models.

Nonlinear Response Characteristics of a Cracked Rotor in Maneuvering Aircraft

2003 ◽  
Author(s):  
Fu-Sheng Lin ◽  
Guang Meng ◽  
Eric Hahn
Keyword(s):  
Fault Diagnosis ◽  
Constant Velocity ◽  
Nonlinear Response ◽  
Nonlinear Behavior ◽  
Rotor System ◽  
Parameter Range ◽  
Cracked Rotor ◽  
Periodic Response ◽  
Response Characteristics ◽  
Cracked Rotor System

This paper investigates numerically the nonlinear response of a simple cracked rotor in moving supports, as may occur in aircraft rotors when the aircraft is maneuvering with constant velocity or acceleration. Of particular interest is the influence of the aircraft climb angle. Results show that the climb angle can markedly affect the parameter range for which the system is stable; and over which there results bifurcation, quasi-periodic response or chaotic response. It is shown that aircraft acceleration can also significantly affect the nonlinear behavior of the cracked rotor system, illustrating the possibility for online rotor crack fault diagnosis.

Negative Effective Stiffness Content in Cracked Rotors

2018 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Fatima K. Alhammadi
Keyword(s):  
Equations Of Motion ◽  
Rotor System ◽  
Effective Stiffness ◽  
Cracked Rotor ◽  
Force Vector ◽  
Rotor Systems ◽  
Wide Range ◽  
Unbalance Force ◽  
Time Periodic ◽  
Cracked Rotor System

The appearance of cracks in rotor systems affects the whirl response in the neighborhood of the critical whirl rotational speeds. The combined effect of the crack depth and the unbalance force vector angle orientation with respect to the crack opening direction on the effective stiffness content of the cracked rotor system in the neighborhood of the critical rotational speed is addressed here. The effective stiffness expression of the cracked system can be obtained from the direct integration of the equations of motion of the cracked rotor system. The cracked rotor equations of motion can be expressed by the Jeffcott rotor or the finite element models. The appearance of cracks in rotor systems converts them into parametrically excited dynamical systems with time-periodic stiffness components. The interaction between the time-periodic stiffness and the external periodic forcing function of the unbalance force significantly alters the effective stiffness content in the system at both transient and steady state operations. For wide range of crack depths and unbalance force vector angles, the effective stiffness has been found to be of negative values. This means that the cracked rotor system tends to have more resistance to deflect towards the center of its whirl orbit and less resistance to deflect away under the unbalance force excitation effect. Consequently, in the negative stiffness content zone of the unbalance force vector angles, the cracked rotor system tends to exhibit a sharp growth in the vibration whirl amplitudes. However, for positive effective stiffness values, the shaft has more resistance to deflect away from its whirl orbit center. Therefore, the cracked rotor system is at higher risk of failure in the negative effective stiffness zone of unbalance force vector angles than the positive effective stiffness zone of these angles.

Roll-Yaw Coupling Effect of Jeffcott Rotor With Breathing Crack

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.

Nonlinear Dynamic Analysis of a Cracked Rotor-Bearing System With Fractional Order Damping

2011 ◽  
Author(s):  
Shiming Xue ◽  
Junyi Cao ◽  
Yangquan Chen
Keyword(s):  
Fractional Order ◽  
Crack Depth ◽  
Nonlinear Dynamic Analysis ◽  
Orientation Angle ◽  
Rotor System ◽  
Speed Ratio ◽  
Crack Model ◽  
Cracked Rotor ◽  
Mass Eccentricity ◽  
Cracked Rotor System

Fatigue cracking of the rotor shaft is an important fault observed in rotating machinery of key industry, which can lead to catastrophic failure. Nonlinear dynamics of a cracked rotor system with fractional order damping is investigated by using a response-dependent breathing crack model. The four-th order Runge-Kutta method and ten-th order CFE-Euler (Continued Fraction Expansion-Euler) method are introduced to simulate the proposed system equation of fractional order cracked rotors. The effects of derivative order of damping, rotating speed ratio, crack depth, orientation angle of imbalance relative to the crack direction and mass eccentricity on the system dynamics are demonstrated by using bifurcation diagram, Poincare map and rotor trajectory diagram. The results show that the rotor system displays chaotic, quasi-periodic and periodic motions as the fractional order increases. It is also found that the imbalance eccentricity level, crack depth, rotational speed, fractional damping and crack angle all have considerable influence on the nonlinear behavior of the cracked rotor system.

Nonlinear Dynamic Analysis of a Cracked Rotor-Bearing System With Fractional Order Damping

2012 ◽  
Vol 8 (3) ◽  
Author(s):  
Junyi Cao ◽  
Shiming Xue ◽  
Jing Lin ◽  
Yangquan Chen
Keyword(s):  
Fractional Order ◽  
Crack Depth ◽  
Nonlinear Dynamic Analysis ◽  
Orientation Angle ◽  
Rotor System ◽  
Speed Ratio ◽  
Crack Model ◽  
Cracked Rotor ◽  
Mass Eccentricity ◽  
Cracked Rotor System

Fatigue cracking of the rotor shaft is an important fault observed in the rotating machinery of key industries, which can lead to catastrophic failure. Nonlinear dynamics of a cracked rotor system with fractional order damping is investigated by using a response-dependent breathing crack model. The fourth-order Runge–Kutta method and tenth-order continued fraction expansion-Euler (CFE-Euler) method are introduced to simulate the proposed system equation of fractional order cracked rotors. The effects of the derivative order of damping, rotating speed ratio, crack depth, orientation angle of imbalance relative to the crack direction, and mass eccentricity on the system dynamics are demonstrated by using a bifurcation diagram, Poincaré map, and rotor trajectory diagram. The simulation results show that the rotor system displays chaotic, quasi-periodic, and periodic motions as the fractional order increases. It is also observed that the imbalance eccentricity level, crack depth, rotational speed, fractional damping, and crack angle all have considerable influence on the nonlinear behavior of the cracked rotor system. Finally, the experimental results verify the effectiveness of the theoretical analysis.

scholarly journals Identification of Bearing Dynamic Parameters and Unbalanced Forces in a Flexible Rotor System Supported by Oil-Film Bearings and Active Magnetic Devices

Actuators ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 216
Author(s):  
Yinsi Chen ◽  
Ren Yang ◽  
Naohiro Sugita ◽  
Junhong Mao ◽  
Tadahiko Shinshi
Keyword(s):  
Variable Stiffness ◽  
Rotor System ◽  
Unknown Parameters ◽  
Oil Film ◽  
Rotor Systems ◽  
Response Characteristics ◽  
Unbalanced Force ◽  
Displacement Force ◽  
The Stability ◽  
And Control

As the rotational speed of conventional rotor systems supported by oil-film bearings has increased, vibration problems such as oil whip and oil whirl have become apparent. Our group proposed the use of active magnetic bearings (AMBs)/bearingless motors (BELMs) to stabilize these systems. In such a system, measuring the variable stiffness and damping of the oil-film bearings, the current-force and displacement-force parameters of the AMBs/BELMs, and the residual unbalanced force is necessary to satisfy the stability of the rotor system. These parameters are the foundation for the rotor dynamics analysis and optimization of the control strategy. In this paper, we propose a method to simultaneously identify the parameters of the oil-film bearings and AMBs/BELMs along with the residual unbalanced forces during the unbalanced vibration of the rotor. The proposed method requires independent rotor responses and control currents to form a regression equation to estimate all the unknown parameters. Independent rotor responses are realized by changing the PID control parameters of the AMBs/BELMs. Numerical simulation results show that the proposed method is highly accurate and has good robustness to measurement noise. The experimental results show that the unknown parameters identified by the responses generated by different controller parameters are similar. To confirm that the identification results are correct, verification experiments were carried out. The vibration amplitude of the rotor was successfully suppressed by applying a force to the rotor in the opposite direction to the residual unbalanced force. The frequency response characteristics and unbalanced responses of the rotor estimated by the values of the parameters identified show good consistency with the measured results.

Stability Analysis on a Crack Rotor System in the Special Speeds

2013 ◽  
Vol 675 ◽  
pp. 116-120 ◽  
Author(s):  
Feng Lan Wang
Keyword(s):  
Experimental Study ◽  
Stability Analysis ◽  
Theoretical Analysis ◽  
Stability Problem ◽  
Critical Speed ◽  
Transverse Crack ◽  
Crack Depth ◽  
Rotor System ◽  
Single Disk ◽  
The Stability

In this paper, the single disk rotor system with a transverse open and close crack has been taken as an example; the stability problem on the system in the special speeds has been discussed by theoretical analysis and experimental study. First, the conditions, positions and areas of the stable vibrations and the unstable vibrations on a rotor system with a transverse crack have been studied quantitatively theoretically. Not only the conclusions of other authors are verified，but also that the unstable vibrations are found in the regions near the rotational speed at 2/5and 2/7 of the critical speed in the large crack and the small damping case. Then the influence of some factors such as the crack depth parameters and the damping on stability of the system is qualitatively discussed.

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