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.

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.

scholarly journals Comparison of Common Methods in Dynamic Response Predictions of Rotor Systems with Malfunctions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongliang Yao ◽  
Qian Zhao ◽  
Qi Xu ◽  
Bangchun Wen
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Newmark Method ◽  
Incremental Harmonic Balance Method ◽  
Rotor Systems ◽  
Double Frequency ◽  
Frequency Domain Methods ◽  
Incremental Harmonic Balance

The efficiency and accuracy of common time and frequency domain methods that are used to simulate the response of a rotor system with malfunctions are compared and analyzed. The Newmark method and the incremental harmonic balance method are selected as typical representatives of time and frequency domain methods, respectively. To improve the simulation efficiency, the fixed interface component mode synthesis approach is combined with the Newmark method and the receptance approach is combined with the incremental harmonic balance method. Numerical simulations are performed for rotor systems with single and double frequency excitations. The inherent characteristic that determines the efficiency of the two methods is analyzed. The results of the analysis indicated that frequency domain methods are suitable single and double frequency excitation rotor systems, whereas time domain methods are more suitable for multifrequency excitation rotor systems.

scholarly journals DYNAMIC NON-LINEAR ANALYSIS OF A CRACKED BLADE

Aviation ◽  
2008 ◽  
Vol 12 (3) ◽  
pp. 66-79 ◽  
Author(s):  
Mykola Kulyk ◽  
Olexiy Kucher ◽  
Vsevolod Kharyton ◽  
Jean-Pierre Laine ◽  
Fabrice Thouverez
Keyword(s):  
Harmonic Balance ◽  
Linear Problem ◽  
Time Integration ◽  
Harmonic Balance Method ◽  
Problem Size ◽  
Crack Location ◽  
Equation Problem ◽  
Non Linear ◽  
Fixed Interface ◽  
Method Accuracy

A cracked blade non‐linear dynamic analysis was performed, taking into account contact interaction between crack sides. The contact‐induced non‐linear problem was solved by using the harmonic balance method. Accuracy and computational efficiency are demonstrated by comparing the results with the time integration of the system's motion equation Problem size reduction was performed using system fixed‐interface method. They suppose that a crack forms an interface between two sub‐structures and use a relative degree of freedom to describe the motion of crack sides. The influence of centrifugal forces was investigated in order to understand the necessity of problem non‐linear formulation depending on crack location and frequency of rotation. Santrauka Mentelės su įtrūkimu netiesinė dinamikos analizė atlikta įvertinant įtrūkimo kraštų kontaktinę sąveiką. Netiesinis uždavinys sprendžiamas harmoninės analizės metodu. Tokio metodo rezultatų tinkamumas ir efektyvumas demonstruojamas lyginant su sistemų dinaminių lygčių skaitinio sprendimo rezultatais. Sprendžiamo uždavinio eilė mažinama kraštų fiksavimo metodas. Šiuo atveju buvo laikoma, kad plyšys suformuoja ribą tarp dviejų konstrukcijos dalių ir plyšio ribų kitimo aprašymui naudojamos santykinės koordinatės. Buvo ištirta išcentrinių jėgų įtaka netiesiniam formulavimui, priklausomai nuo plyšio padėties ir kampinio greičio.

Relationship between harmonic balance method and non-linear output frequency response function approach

2007 ◽  
Vol 221 (12) ◽  
pp. 1533-1543 ◽  
Author(s):  
Z K Peng ◽  
Z Q Lang
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Harmonic Balance ◽  
Frequency Response Function ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Output Frequency ◽  
Non Linear ◽  
Harmonic Components ◽  
The Relationship

The current paper is concerned with the investigation of the relationship between the harmonic balance method (HBM) and the non-linear output frequency response function (NOFRF) approach in the analysis of non-linear systems. Both are applied to the Duffing's oscillator to demonstrate their relationships. The results reveal that, if the Volterra series representation of a non-linear system is convergent, the harmonic components calculated by the NOFRFs are a solution of the HBM. Moreover, the simulation studies show that, in the convergent cases, the NOFRF method can give more accurate results for the higher-harmonic components than the HBM. The relationship investigated in the current study between the two methods should help researchers and engineers to understand the HBM and the NOFRF methods.

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.

Computational Studies of the Unbalance Response of a Whole Aero-Engine Model With Squeeze-Film Bearings

2009 ◽  
Author(s):  
Philip Bonello ◽  
Pham Minh Hai
Keyword(s):  
Harmonic Balance ◽  
Linear Part ◽  
Harmonic Balance Method ◽  
Vibration Response ◽  
Squeeze Film ◽  
Engine Model ◽  
Nonlinear Solvers ◽  
Aero Engine ◽  
Receptance Method ◽  
First Time

The computation of the unbalance vibration response of aero-engine assemblies fitted with nonlinear bearings requires the retention of a very large number of modes for reliable results. This renders most previously proposed nonlinear solvers unsuitable for this application. This paper presents three methods for the efficient solution of the problem. The first method is the recently developed impulsive receptance method (IRM). The second method is a reformulation of the Newmark-Beta method. In addition to these two time-domain methods, a whole-engine receptance harmonic balance method (RHBM) is introduced that allows, for the first time, the frequency domain calculation of the periodic vibration response of a real engine. All three methods use modal data calculated from a one-off analysis of the linear part of the engine at zero speed. Simulations on a realistically-sized representative twin-spool engine model with squeeze-film damper bearings provide evidence that the popular Newmark-Beta method can be unreliable for large order nonlinear systems. The excellent correlation between the IRM and RHBM results demonstrates the efficacy of these two complementary tools in the computational analysis of realistic whole-engine models.

Comparison Between the Incremental Harmonic Balance Method and Alternating Frequency/Time-Domain Method

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
R. Ju ◽  
W. Fan ◽  
W. D. Zhu
Keyword(s):  
Fourier Transform ◽  
Time Domain ◽  
Harmonic Balance ◽  
Sampling Rate ◽  
Harmonic Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Acceptable Accuracy ◽  
Incremental Harmonic Balance ◽  
First Time ◽  
Ihb Method

Abstract Two widely used semi-analytical methods: the incremental harmonic balance (IHB) method and alternating frequency/time-domain (AFT) method are compared, and some long-standing discussions on frameworks of these two methods are cleared up. The IHB and AFT methods are proved for the first time to be theoretically equivalent when spectrum aliasing does not occur in the AFT method. Based on this equivalence, the minimal nonaliasing sampling rate for the AFT and fast Fourier transform (FFT)-based IHB methods can be obtained for a system with polynomial nonlinearities. While spectrum aliasing is theoretically inevitable for nonpolynomial nonlinearities, a sufficiently large sampling rate can be usually used with acceptable accuracy and efficiency for many systems. Convergence and efficiency of the IHB method, AFT method, and several FFT-based IHB methods are compared. Accuracy and convergence can be affected when the sampling rate is insufficient. This comparison can provide some insights to avoid misuse of these methods and choose which methods to use in engineering applications.

Computational Studies of the Unbalance Response of a Whole Aero-Engine Model With Squeeze-Film Bearings

2009 ◽  
Vol 132 (3) ◽  
Author(s):  
Philip Bonello ◽  
Pham Minh Hai
Keyword(s):  
Harmonic Balance ◽  
Linear Part ◽  
Harmonic Balance Method ◽  
Vibration Response ◽  
Squeeze Film ◽  
Engine Model ◽  
Nonlinear Solvers ◽  
Aero Engine ◽  
Receptance Method ◽  
First Time

The computation of the unbalance vibration response of aero-engine assemblies fitted with nonlinear bearings requires the retention of a very large number of modes for reliable results. This renders most previously proposed nonlinear solvers unsuitable for this application. This paper presents three methods for the efficient solution of the problem. The first method is the recently developed impulsive receptance method (IRM). The second method is a reformulation of the Newmark-beta method. In addition to these two time-domain methods, a whole-engine receptance harmonic balance method (RHBM) is introduced that allows, for the first time, the frequency domain calculation of the periodic vibration response of a real engine. All three methods use modal data calculated from a one-off analysis of the linear part of the engine at zero speed. Simulations on a realistically-sized representative twin-spool engine model with squeeze-film damper bearings provide evidence that the popular Newmark-beta method can be unreliable for large-order nonlinear systems. The excellent correlation between the IRM and RHBM results demonstrates the efficacy of these two complementary tools in the computational analysis of realistic whole-engine models.

Operational Deflection Shape for Crack Detection in Structures

2013 ◽  
Vol 569-570 ◽  
pp. 1085-1092 ◽  
Author(s):  
Erfan Asnaashari ◽  
Jyoti K. Sinha
Keyword(s):  
Crack Detection ◽  
Detection Methods ◽  
Laser Vibrometer ◽  
Higher Harmonics ◽  
Research Areas ◽  
Entire Structure ◽  
Exciting Frequency ◽  
Active Research ◽  
Harmonic Components ◽  
Cracked Structure

Crack detection in structures has been one of the active research areas for decades. Several crack detection methods have been suggested in the literature with their own advantages and limitations. In this paper, a very simplified method has been presented which assumes the vibration of entire structure can be scanned through a laser vibrometer. Therefore, measurement at a large number of locations in any structure is possible. Excitation of the cracked structure at a frequency always generates higher harmonic components of the exciting frequency due to the breathing of the crack. The deflection of the structure at higher harmonics of the exciting frequency is mapped by (a) amplitude of deflection (AOD) at higher harmonics as suggested in the literature, and (b) a new method based on the operational deflection shape (ODS) (both amplitude and phase) at higher harmonics for the crack detection. This paper presents the proposed method and the results through numerical examples.

Numerical and experimental investigation of crack in beams using frequency contour method

2018 ◽  
Vol 7 (2.1) ◽  
pp. 37
Author(s):  
Nancy Debora S ◽  
Antony Godwin I ◽  
Irish Nivitha R ◽  
Rishipal Reddy L
Keyword(s):  
Crack Detection ◽  
Crack Depth ◽  
Contour Method ◽  
Detection Methods ◽  
Crack Location ◽  
Depth Prediction ◽  
Sensing Systems ◽  
Contour Lines ◽  
Vibrational Characteristics ◽  
Support Conditions

Health monitoring of Structures is a vital tool for engineers to ensure the life of important structures like Dams and bridges, Stadiums and buildings and, Platforms and vessels, Wind turbines Airframes, and large machinery and equipments. SHM helps to detect damage at earlier stage before failure occurs by sensing systems. Various damage detection methods are available in accordance with vibrational characteristics of the structure. In this paper Frequency contour method which consumes less time is employed to detect, locate, and characterize damage in structural and mechanical systems.Experimental and Numerical modal analysis were carried out on cracked and healthy beams of steel with cantilever support conditions of size 20mmx20mm and of length 300mm using ABAQUS. Three natural frequencies are obtained as a basic criterion for crack detection. To locate the damage of the normalized frequency in terms of location and depth of the crack were designed using MATLAB. The intersection of three contour lines represents crack location and crack depth. Prediction ofdamage using frequency contour method gives good result

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