On a systematic approach for cracked rotating shaft study: breathing mechanism, dynamics and instability

Arem, Saber El; Zid, Maha Ben

doi:10.1007/s11071-017-3367-7

Cited by 12 publications

(16 citation statements)

References 25 publications

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“…In this article, we continue to improve the EDF − LMS approach to make it a more comprehensive and generic methodology in dealing with beams and shafts with cracks. We already have started the generalization of the approach in a recent article ((El Arem and Ben Zid, 2017)) where the problem was formulated to write the total elastic energy of the system as a function of the applied forces instead of bending moments. By giving an approximate formula of the extracted additional flexibility due to the crack breathing, we have shown that the procedure of identification could be skipped which would allow a significant effort saving for those who would have adopted the approach.…”

Section: Aim and Plan Of The Articlementioning

confidence: 99%

“…In fact, in addition to being able to consider a crack of any shape, the possibility of having a crack located at any position along the shaft axis will be given. We are not limited by a crack at mid − span of the shaft like in (El Arem and Ben Zid, 2017). This becomes possible by constructing a CBFE that could be assembled with other beam finite elements (cracked or not) to model a beam or a shaft with cracks.…”

Section: Aim and Plan Of The Articlementioning

confidence: 99%

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On the mechanics of beams and shafts with cracks: A standard and generic approach

Arem

2021

European Journal of Mechanics - A/Solids

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A generic methodology to deal with the mechanics of beams and shafts with cracks is presented. The elastic energy of the system under static loading is written in a comprehensive manner to remarkably reduce the 3D computations indispensable to the identification of the crack breathing mechanism. With a new reformulation of the problem, the breathing mechanism identification is distilled down to the computation of a dimensionless function that gives a fine and precise description of the system flexibility evolution when the crack breathes. This breathing function is exclusively inherent to the crack geometry and completely independent of the 3D model parameters which makes the approach more universal and could be applied straightforward to similar problems. This standard and generic methodology is completed by a detailed description of the technique of construction of a Cracked Beam Finite Element. Moreover, we give a nonlinear fitting formula of the identified function that all the process of identification could be skipped when a cracked transverse section is to be inserted in a beam-like model of a cracked shaft. A validation of the approach under static loading is given for a cantilever beam with one, then two cracked transverse sections. We also show, for a simple cracked shaft, common features of its vibrational behavior.

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Section: Aim and Plan Of The Articlementioning

confidence: 99%

Section: Aim and Plan Of The Articlementioning

confidence: 99%

On the mechanics of beams and shafts with cracks: A standard and generic approach

Arem

2021

European Journal of Mechanics - A/Solids

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“…Dimarogonas's SERR crack model clearly reveals the impact of the regular opening and closing of the crack on rotor stiffness. However, the calculation process of solving the generated equation of motion of the cracked rotor is complex and not suitable for engineering practice [18]. In this paper, the model of cracked rotor is proposed by Papadopoulos and Dimarogonas [1], which can reveal changes in stiffness of the cracked rotor better, to create a crack model that can help in solving the equation of the rotor motion simply.…”

Section: Stiffness Model Of Cracked Rotormentioning

confidence: 99%

“…By using the inverse matrix of each softness matrix, the stiffness matrix KOP, KUC ,KHc are calculated, and the stiffness matrix Kc of cracked shaft element are obtained from formula (8). In formula (18), E, G, I, l and R are the elastic modulus, shear modulus, moment of inertia, length and radius of the axis, respectively.…”

Section: Stiffness Model Of Cracked Rotormentioning

confidence: 99%

Analysis of Vibration Characteristics of PD Control Active Magnetic Bearing and Cracked Rotor System

Zhang

Bolong

Wang

et al. 2019

IJE

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A B S T R A C TCrack fault of rotor is one of the most prominent problems faced by magnetic bearing rotor system. In order to improve the safety performance of this kind of machinery, it is necessary to research the vibration characteristics of magnetic bearing cracked rotor system. In this paper, the stiffness model of the crack shaft element was established by the strain energy release rate (SERR) theory. The mathematical model of PD controller of AMBs cracked rotor system is based on the finite element method. The vibration characteristics of PD controller of AMBs rotor system were examined in the test rig under crack depth of rotor. The spectrum of vibration characteristics were detected in the AMBs cracked rotor system. T he results of experiments showed that the 2× and 3× harmonic components can be used for fault diagnosis of crack fault of AMBs rotor systems under PD controller of AMB.

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“…In this article, we continue to advance a family of models and discussions we have started developing nearly twenty years ago at Electricité De France (EDF) and the Solid Mechanics Laboratory (LMS) ofÉcole Polytechnique in France. All these models belong to what we have called the EDF−LMS approach as described in [10]. It provides means to overcome the difficulties and imprecisions ([25, 5]) inherent to the first and oldest approach initiated in the 1970s by Dimarogonas and his coworkers and based on the linear fracture mechanics principles [26].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear analysis, instability and routes to chaos of a cracked rotating shaft

Arem

2019

Nonlinear Dyn

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This is an author-deposited version published in: https://sam.ensam.eu Handle IDAbstract The aim of this paper is to explore the dynamical response of a rotating shaft with a cracked transverse section. This complex problem is distilled down to the study of a very comprehensive mechanical system composed of two non-cracked rigid bars connected with a nonlinear bending spring that concentrates the global stiffness of the cracked shaft. The switching crack model is presented as a specific case of the EDF-LMS family of models and adopted to describe the breathing mechanism of the crack. By analyzing the system equilibrium equations, we show that the stiffness change when the crack breathes leads to shocks with velocity jumps and coupling between the transverse oscillations. The linear stability of the periodic solutions is examined based on the Floquet's theory. Nonlinear dynamics tools such as Poincaré maps and bifurcation diagrams are used to unveil the system oscillations characteristics. Many well-known features due to the crack presence have been observed, but some unexpected responses are noticed like chaotic behavior. This can be confidently attributed to the abrupt change of the structure stiffness with the breathing crack. It has also been observed that with the super-harmonic resonance phenomenon, the increase of static deflection accompanied by that of the first two harmonics amplitudes are good indicators of a propagating crack presence.

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On a systematic approach for cracked rotating shaft study: breathing mechanism, dynamics and instability

Cited by 12 publications

References 25 publications

On the mechanics of beams and shafts with cracks: A standard and generic approach

On the mechanics of beams and shafts with cracks: A standard and generic approach

Analysis of Vibration Characteristics of PD Control Active Magnetic Bearing and Cracked Rotor System

Nonlinear analysis, instability and routes to chaos of a cracked rotating shaft

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