Dynamic Modelling and Nonlinear Characteristics of a Cracked Bolt-Disc Combined Rotor System

2021 ◽  
Author(s):  
Yi Liu ◽  
Heng Liu ◽  
Yuan Li ◽  
Nanshan Wang
Keyword(s):  
Stiffness Matrix ◽  
Crack Depth ◽  
Dynamic Modelling ◽  
Rotor System ◽  
Correction Coefficient ◽  
Local Defect ◽  
Open Crack ◽  
Rotating Shaft ◽  
Dynamic Behaviors ◽  
Crack Location

Abstract Different from the crack on the rotating shaft, the crack on the bolt which is a connecting part of the bolt-disc combined rotor is a kind of local defect. The local crack on the bolt under high pretension is always in open state, and it increases the overall vibration of the combined rotor significantly in practice. This paper studies the modelling of the crack on the bolt and nonlinear dynamic behaviors of the cracked bolt-disc rotor system. The circumferential bolts with a transverse open crack are treated as several bar elements under the assumption that each bolt has the same original tensile extension length. The cracked correction coefficient is introduced to describe the decreasing amount of bolt's tension due to crack. After this coefficient is obtained according to finite element method, the stiffness matrix of circumferential bolts with crack is built based on total potential energy. The dynamic model consists of a time-independent stiffness matrix for perfect bolts, a time-variant reductive stiffness and an additional moment. As a result, the crack in bolt reduces rotor's nonlinear stability and leads to greater vibration and fluctuation. In addition, crack depth has much larger influence than crack location on the dynamic behaviors.

In-Plane Vibration and Crack Detection of a Rotating Shaft-Disk Containing a Transverse Crack

1998 ◽  
Vol 120 (2) ◽  
pp. 551-556 ◽  
Author(s):  
Ming-Chuan Wu ◽  
Shyh-Chin Huang
Keyword(s):  
Crack Detection ◽  
Transverse Crack ◽  
Rotation Speed ◽  
Crack Depth ◽  
Multiple Scale ◽  
Crack Identification ◽  
Response Curves ◽  
Rotating Shaft ◽  
Crack Location ◽  
Depth Rotation

Dynamic response and stability of a rotating shaft-disk containing a transverse crack is investigated. FFT analysis of response amplitudes showed that the 2Ω component (Ω: rotation speed) was excited by crack breathing and could serve as a good index for crack identification. Intensive numerical studies of crack location, crack depth, rotation speed, and sensing position on response amplitudes displayed a feasible technique for the identification of crack depth and crack location. It is achieved by intersecting the two equi-amplitude response curves of two separated sensing probes. Finally, the instability of the system caused by a crack is examined via Floquet theory and the multiple scale method. The stability diagrams, illustrated as functions of crack depth, rotation speed, and damping, are shown and discussed.

Detection of Cracks in Stationary Rotors via the Modal Frequency Changes Induced by a Roving Disc

2014 ◽  
Author(s):  
Z. N. Haji ◽  
S. O. Oyadiji
Keyword(s):  
Natural Frequencies ◽  
Crack Depth ◽  
Mode Shapes ◽  
Crack Identification ◽  
Open Crack ◽  
Suggested Approach ◽  
Rotor Systems ◽  
Crack Location ◽  
High Crack ◽  
Frequency Changes

In this study, a crack identification approach based on a finite element cracked model is presented to identify the location and depth ratios of a crack in rotor systems. A Bernoulli-Euler rotor carrying an auxiliary roving disc has been used to model the cracked rotor, in which the effect of a transverse open crack is modelled as a time-varying stiffness matrix. In order to predict the crack location in the rotor-disc-bearing system, the suggested approach utilises the variation of the normalized natural frequency curves versus the non-dimensional location of a roving disc which traverses along the rotor span. The merit of the suggested approach is to identify the location and sizes of a crack in a rotor by determining only the natural frequencies of the stationary rotor system. The first four natural frequencies are employed for the identification and localisation of a crack in the stationary rotor. Furthermore, this approach is not only efficient and practicable for high crack depth ratios but also for small crack depth ratios and for a crack close to or at the node of mode shapes, where natural frequencies are unaffected.

A novel geometric model of breathing crack and its influence on rotor dynamics

2021 ◽  
pp. 107754632110328
Author(s):  
Krishanu Ganguly ◽  
Haraprasad Roy
Keyword(s):  
Stiffness Matrix ◽  
Search Algorithm ◽  
Random Search ◽  
Geometric Model ◽  
Crack Depth ◽  
Mathematical Formulation ◽  
Viscoelastic Model ◽  
Mode Shapes ◽  
Rotating Shaft ◽  
Full Rotation

The present research focuses on performing the dynamic study of a cracked, internally damped, composite rotating shaft system with journal bearing end supports. A novel mathematical formulation is proposed to introduce a time-varying stiffness matrix for simulating the breathing behaviour of the crack. The random search algorithm is used as one of the metaheuristic processes to carry out the optimization and generate time-dependent geometric parameters of the cracked surface for one full rotation. The derived stiffness matrix is used in the composite shaft’s higher order motion equation obtained through equivalent modulus theory, whose internal damping properties are incorporated using operator-based viscoelastic model. Eigenanalysis is carried out to perform a thorough study of dynamic characteristics of cracked shaft considering the crack depth and crack position as two important parameters. The effect of crack on stacking sequence as well as mode shapes of the heterogeneous laminated shaft is also studied.

FEM Modelling and Experimental Verification of a Rotor System With a Open Crack

2009 ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Nobuhiro Nagata ◽  
Yukio Ishida
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Natural Frequencies ◽  
Experimental System ◽  
Element Model ◽  
Rotor System ◽  
Open Crack ◽  
Rotating Shaft ◽  
Risk Condition ◽  
Resonance Curves

Continuous operation of rotating machinery with a rotor crack is a risk condition since the rotor crack grows rapidly and may fail causing a catastrophic accident. This paper develops the finite element model of the rotating shaft with an open crack. The natural frequencies and the resonance curves of such a rotor system with an open crack is investigated, and the concise and accurate modeling of the open crack element is discussed. The natural frequencies and the resonance curves of the experimental system are measured for various positions and depths of the open crack. By comparing both the theoretical and experimental results, the accuracy of the developed simple finite element model of the rotating shaft with an open crack is clarified.

scholarly journals Numerical and experimental studies for crack detection of a beam-like structure using element stiffness index distribution method

2017 ◽  
Vol 39 (3) ◽  
pp. 203-214
Author(s):  
Nguyen Viet Khoa ◽  
Quang Van Nguyen ◽  
Nguyen Dinh Kien ◽  
Cao Van Mai ◽  
Dao Thi Bich Thao
Keyword(s):  
Stiffness Matrix ◽  
Crack Detection ◽  
Crack Depth ◽  
Experimental Studies ◽  
Mode Shapes ◽  
Stiffness Index ◽  
Distribution Method ◽  
Crack Location ◽  
Index Distribution ◽  
Global Stiffness Matrix

In this paper, numerical and experimental studies for crack detection of structures using "element stiffness index distribution" are presented. The element stiffness index distribution is defined as a vector of norms of sub-matrices corresponding to element stiffness matrices calculated from the reconstructed global stiffness matrix of the beam. When there is a crack at an element, the element stiffness index of that element will be changed. By inspecting the change in the element stiffness index distribution, the crack can be detected. A significant peak in the element stiffness index distribution is the indicator of the crack existence. The crack location is determined by the location of the peak and the crack depth can be determined from the height of the peak. The global stiffness matrix is calculated from the measured frequency response functions instead of mode shapes to avoid limitations of the mode shape-based methods for crack detection. Numerical simulation results for the cases of beam-like structures are provided. The experiment is carried out to justify the efficiency of the proposed method.

scholarly journals Bifurcation Study of Thin Plate with an All-Over Breathing Crack

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
Lihua Chen ◽  
Jian Xue ◽  
Zhijie Zhang ◽  
Wei Zhang
Keyword(s):  
Boundary Conditions ◽  
Thin Plate ◽  
Nonlinear Dynamic ◽  
Crack Depth ◽  
Dynamic Responses ◽  
Phase Portraits ◽  
Open Crack ◽  
Breathing Crack ◽  
Dynamic Behaviors ◽  
Cracked Plate

An all-over breathing crack on the plate surface having arbitrary depth and location is assumed to be nonpropagating and parallel to one side of the plate. Based on a piecewise model, the nonlinear dynamic behaviors of thin plate with the all-over breathing crack are studied to analyze the effect of external excitation amplitudes and frequencies on cracked plate with different crack parameters (crack depth and crack location). Firstly, the mode shape functions of cracked thin plate are obtained by using the simply supported boundary conditions and the boundary conditions along the crack line. Then, natural frequencies and mode functions of the cracked plate are calculated, which are assessed with FEM results. The stress functions of thin plate with large deflection are obtained by the equations of compatibility in the status of opening and closing of crack, respectively. To compare with the effect of breathing crack on the plate, the nonlinear dynamic responses of open-crack plate and intact plate are analyzed too. Lastly, the waveforms, bifurcation diagrams, and phase portraits of the model are gained by the Runge-Kutta method. It is found that complex nonlinear dynamic behaviors, such as quasi-periodic motion, bifurcation, and chaotic motion, appear in the breathing crack plate.

scholarly journals Monitoring breathing cracks of a beam-like bridge subjected to moving vehicle using wavelet spectrum

2013 ◽  
Vol 35 (2) ◽  
pp. 131-145
Author(s):  
Khoa Viet Nguyen
Keyword(s):  
Stiffness Matrix ◽  
Crack Depth ◽  
Wavelet Spectrum ◽  
Accurate Estimation ◽  
Open Crack ◽  
The Finite Element Method ◽  
Breathing Crack ◽  
Moving Vehicle ◽  
Beam Height ◽  
Crack Position

In this paper a wavelet spectrum technique for monitoring the breathing crack phenomenon of a beam-like bridge subjected to moving vehicle is presented. The stiffness of element with a breathing crack is modeled as a time dependent stiffness matrix using the finite element method. The stiffness matrix of the structure at each moment depends on the curvature of the structure at the crack position. The breathing crack phenomenon can be detected by analysing the instantaneous frequency (IF) of the system using the wavelet spectrum. When the crack depth is large, the crack area might be determined by the significant peak in the IF. The simulation results show that when the crack “breaths” the amplitude of the vibration obtained from the vehicle is smaller than in the case of an open crack. This is a warning when using the amplitude of the dynamic response to estimate the crack depth when there is a breathing crack in the structure. Therefore, it is important to distinguish the open crack and breathing crack to obtain a more accurate estimation of the crack depth. The results showed that crack with a depth as small as 10% of the beam height can be detected by the method. The proposed method can be applied with a noise level up to 10%.

Rotordynamic Crack Diagnosis: Distinguishing Crack Depth and Location

2013 ◽  
Author(s):  
Philip Varney ◽  
Itzhak Green
Keyword(s):  
Fatigue Crack ◽  
Condition Monitoring ◽  
Crack Depth ◽  
Forced Response ◽  
System Response ◽  
Contour Plot ◽  
Crack Model ◽  
Finite Width ◽  
Angular Response ◽  
Crack Location

The goal of this work is to establish a condition monitoring regimen capable of diagnosing the depth and location of a transverse fatigue crack in a rotordynamic system. The success of an on-line crack diagnosis regimen hinges on the accuracy of the crack model used. The model should account for the depth of the crack and the localization of the crack along the shaft. Negating the influence of crack location on system response ignores a crucial component of real cracks. Two gaping crack models are presented; the first simulates a finite-width manufactured notch, while the second models an open fatigue crack. An overhung rotordynamic system is modeled, imitating an available rotordynamic test rig. Four degree-of-freedom equations of motion for both crack models are presented and discussed, along with corresponding transfer matrix techniques. Free and forced response analyses are performed, with emphasis placed on results applicable to condition monitoring. It is demonstrated that two identifiers are necessary to diagnose the crack parameters: the 2X resonance frequency and the magnitude of the 2X component of the rotor angular response at resonance. First, a contour plot of the 2X resonant shaft speed versus crack depth and location is generated. The magnitude of the 2X component of the rotor’s angular response along the desired contour is obtained, narrowing the possible pairs of crack location/depth to either one or two possibilities. Practical aspects of the diagnosis procedure are then discussed.

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