scholarly journals Analysis of the Response of a Rotor System Containing a Breathing Crack

2009 ◽  
Vol 413-414 ◽  
pp. 479-486
Author(s):  
Jean Jacques Sinou
Keyword(s):  
Crack Detection ◽  
Crack Depth ◽  
Harmonic Balance Method ◽  
Dynamical Behaviour ◽  
Rotor System ◽  
Harmonic Frequency ◽  
Transverse Cracks ◽  
Frequency Components ◽  
On Line ◽  
Truncated Fourier Series

The purpose of this paper is to investigate the influence of the presence of transverse cracks in rotors. The dynamic response of the cracked rotor is evaluated by expanding the changing stiffness of the crack (i.e. the breathing mechanism) as a truncated Fourier series and then using the Harmonic Balance Method. The crack detection is based on the use of the 2X and 3X super-harmonic frequency components of the non-linear dynamical behaviour at the associated sub-critical resonant peaks. Various parametric studies including the effects of the crack depth and location, and the crack–unbalance interaction on the dynamic of a crack rotor are undertaken. It will be illustrated that the emerging of super-harmonic frequency components and/or antiresonances can provide useful information on the presence of cracks and may be used on an on-line crack monitoring rotor system for small levels of damage.

On the Modeling of Open and Breathing Cracks of a Cracked Rotor System

2010 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Eric A. Butcher
Keyword(s):  
Finite Element ◽  
Crack Detection ◽  
Linear Time ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Crack Model ◽  
Open Crack ◽  
Cracked Rotor ◽  
Critical Rotational Speed ◽  
Cracked Rotor System

The modeling of a cracked rotor system with an open or breathing transverse crack is addressed here. The cracked rotor with an open crack model behaves as an asymmetric shaft. Hence, the time-varying area moments of inertia of the cracked section are employed in formulating the periodic finite element stiffness matrix for both crack models which yields a linear time-periodic system. The harmonic balance method (HB) is used in solving the finite element (FE) equations of motions for studying the dynamic behavior of the cracked rotor system. The unique behavior of the whirl orbits during the passage through the subcritical rotational speeds and the sensitivity of these orbits to the unbalance force direction can be used for early crack detection of the cracked rotor for both crack models. These whirl orbits were verified experimentally for the open crack model in the neighborhood of 1/2 of the first critical rotational speed where a good match with the theoretical whirl orbits was observed.

Developing a Generalized Harmonic Balance Method for Accurate Identification of Crack Depth in a Continuous Shaft-Disc System

2015 ◽  
Author(s):  
Hamid Khorrami ◽  
Ramin Sedaghati ◽  
Subhash Rakheja
Keyword(s):  
Harmonic Balance ◽  
Crack Detection ◽  
Crack Depth ◽  
Harmonic Component ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Vibrational Properties ◽  
Accurate Identification ◽  
Harmonic Components ◽  
Generalized Harmonic Balance Method

In this work, the effect of a crack on the vibrational properties of a shaft-disc system has been studied applying a generalized harmonic balance method. In the reviewed literature, the reported methods to find the unbalance response of a continuous shaft-disc system provide only the first harmonic component of the response; whereas, the presented method gives the super-harmonic components as well. The shaft-disk system consists of a flexible shaft with a single rigid disc mounted on rigid short bearing supports. The shaft contains a transverse breathing crack (fatigue crack). The main concept for crack detection in vibration-based methods is basically the investigation of crack-induced changes in the selected vibrational properties. Shaft critical speeds and harmonic and super-harmonic components of the unbalance lateral response have been used as typical vibrational properties for crack detection in a rotating shaft system. A generalized harmonic balance method has been developed to efficiently investigate changes in vibrational properties due to the effect of crack properties, depth and location. The results of the developed analytical model have been compared with those obtained from the finite element model and close agreement has been observed.

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 The Effects of Crack on the Transmission Matrix of Rotor Systems

2011 ◽  
Vol 18 (1-2) ◽  
pp. 91-103 ◽  
Author(s):  
Z.K. Peng ◽  
Z.Q. Lang ◽  
G. Meng ◽  
F.L. Chu
Keyword(s):  
Harmonic Balance ◽  
Crack Detection ◽  
Harmonic Balance Method ◽  
Detection Methods ◽  
Rotor Systems ◽  
Crack Location ◽  
Frequency Components ◽  
Harmonic Components ◽  
First Time ◽  
Method Analysis

The dynamic behavior of rotor containing crack is a subject of particular interest and has been extensively investigated by researchers. The effects of crack on the natural frequencies and modal shapes and motion orbits of rotor systems have already been well explored by researchers. In the present study, the infl uence of crack on the transmission matrices of the rotor systems is investigated by using the FEM (finite element method) analysis and the HBM (harmonic balance method) technique. It is for the first time revealed that there are differences between the transmission matrices for the fundamental frequency components and the transmission matrices for the super-harmonic components, and the differences are mainly determined by the crack location. The results are validated by numerical experiments where the system responses of a rotor system are obtained usingRunge-Kuttamethod. The results are of significance for the development of effective crack detection methods in practice.

scholarly journals Experimental Study on the Nonlinear Vibrations and n× Amplitudes of a Rotor With a Transverse Crack

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Jean-Jacques Sinou
Keyword(s):  
Experimental Study ◽  
Theoretical Analysis ◽  
Monitoring System ◽  
Nonlinear Response ◽  
Transverse Crack ◽  
Nonlinear Vibrations ◽  
Rotor System ◽  
Experimental Results ◽  
Frequency Components ◽  
On Line

In this paper, the nonlinear response of a rotor system containing a transverse crack is analyzed experimentally in order to propose a nondestructive detection of cracks in the rotor. More particularly, the evolutions of the n× superharmonic frequency components at the various subcritical resonant peaks and the decrease in the subcritical resonant speeds are investigated for various crack depths. The experimental results that are presented in this study confirm the theoretical analysis of many researchers and provide a possible basis for an on-line monitoring system.

scholarly journals Dynamic Characteristics of Rotor System with a Slant Crack Based on Fractional Damping

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Zhinong Li ◽  
Yunlong Li ◽  
Dong Wang ◽  
Zhike Peng ◽  
Haifeng Wang
Keyword(s):  
Fractional Order ◽  
Second Harmonic ◽  
Crack Depth ◽  
Excitation Frequency ◽  
Harmonic Component ◽  
Rotor System ◽  
Rotating Speed ◽  
Integer Order ◽  
Slant Crack ◽  
Frequency Components

AbstractThe traditional modeling method of rotor system with a slant crack considers only integer-order calculus. However, the model of rotor system based on integer-order calculus can merely describe local characteristics, not historical dependent process. The occur of fractional order calculus just makes up for the deficiency in integer-order calculus. Therefore, a new dynamic model with a slant crack based on fractional damping is proposed. Here, the stiffness of rotor system with a slant crack is solved by zero stress intensity factor method. The proposed model is simulated by Runge-Kutta method and continued fraction Euler method. The influence of the fractional order, rotating speed, and crack depth on the dynamic characteristics of rotor system is discussed. The simulation results show that the amplitude of torsional excitation frequency increases significantly with the increase of the fractional order. With the increase of the rotating speed, the amplitude of first harmonic component becomes gradually larger, the amplitude of the second harmonic becomes smaller, while the amplitude of the other frequency components is almost invariant. The shaft orbit changes gradually from an internal 8-type shape to an ellipse-type shape without overlapping. With the increase of the slant crack depth, the amplitude of the transverse response frequency in the rotor system with a slant crack increases, and the amplitude in the second harmonic component also increases significantly. In addition, the torsional excitation frequency and other coupling frequency components also occur. The proposed model is further verified by the experiment. The valuable conclusion can provide an important guideline for the fault diagnosis of rotor system with a slant crack.

Dynamic Analysis of a Slant-Cracked Functionally Graded Rotor-Bearing System

2021 ◽  
Author(s):  
Aneesh Batchu ◽  
Prabhakar Sathujoda
Keyword(s):  
Dynamic Response ◽  
Frequency Domain ◽  
Functionally Graded ◽  
Rotor System ◽  
Harmonic Frequency ◽  
Slant Crack ◽  
Rotor Bearing ◽  
State Frequency ◽  
Frequency Components ◽  
Bearing System

Abstract The dynamic response of a power law based functionally graded (FG) rotor-bearing system with a slant crack has been analysed in the present work. The vibration response of an FG rotor-bearing system with a slant crack has been simulated using the Houbolt time marching scheme for different crack depths. The time-domain vibration responses are converted into the frequency domain using Fast Fourier Transform (FFT) to identify the crack features in order to detect and monitor the cracks. The sub-harmonic frequency components of the steady-state frequency spectrum were centred on the FG rotor’s operating speed, separated by the interval frequency corresponding to the torsional frequency. The sub-harmonic frequency components of the transient state frequency domain were found to be centred on the critical speed of the FG rotor system. The subharmonic frequency components of the dynamic response confirm the existence of a crack in the FG rotor system, which could be used to detect the crack in an FG rotor system.

EXPERIMENTAL STUDY ON BREATHING CRACK DETECTION AND EVALUATION UNDER RANDOM LOADING WITH ENTROPY

2017 ◽  
Vol 41 (5) ◽  
pp. 669-680
Author(s):  
Buddhi Wimarshana ◽  
Felliphe Goes ◽  
Nan Wu* ◽  
Christine Wu
Keyword(s):  
Crack Detection ◽  
Crack Depth ◽  
Total Thickness ◽  
Breathing Crack ◽  
Random Loading ◽  
Beam Structure ◽  
Engineering Structures ◽  
Entropy Measures ◽  
Frequency Components ◽  
Random Frequency

Breathing crack detection and evaluation on a beam under random loading is experimentally studied and realized using entropy measures. During testing, the beam is subjected to random excitations which is the most evident excitation type experienced by most of the engineering structures. Frequency response function is employed to erase the random frequency components due to the excitation from the response of the structure to pick up the vibration characteristics of the beam structure itself with/without the breathing crack. Based on experimental results, the proposed methodology can clearly discriminate a crack with 25% depth of the total thickness of the beam from the healthy case. It is also capable of distinguishing a 50% crack depth from a 25% crack depth with distinct entropy values.

A Method of On-Line Analysis for Mechanical Dynamic Characteristic

1991 ◽  
Author(s):  
Fengquan Wang ◽  
Huixin Wu ◽  
Xiaolin Han ◽  
Haomin Fu
Keyword(s):  
Dynamic Characteristic ◽  
Rotor System ◽  
Repeated Sequences ◽  
Identification Error ◽  
Line Identification ◽  
On Line ◽  
Line Analysis

Abstract In this paper, a method of multipoint pseudorandom combined excitation with the orthogonal reciprocal repeated sequences (ORRS) is presented on the background of the on-line identification of the multivariate rotor system. The capacaty of the restraint to the identification error caused by the non-random D. C. drift of the multi-input excitation with the ORRS in the rotor system is also discussed. The validity of the method described in this paper is proved by the modelling tests of the multi-plate rotor system.

Sign in / Sign up

Export Citation Format

Share Document