A cracked beam finite element for rotating shaft dynamics and stability analysis

Arem, Saber El; Maïtournam, Habibou

doi:10.2140/jomms.2008.3.893

Cited by 11 publications

(25 citation statements)

References 34 publications

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“…This change of the whirl orbit shape during the passage through one-half and one-third of the first critical rotating frequency has been experimentally observed in [32,29,16]. Also, in previous works ( [11,13,12,8]), we have made similar observation with a more realistic breathing mechanism of the crack. When looking at the phase diagrams of Fig.7, we can easily notice the velocity jumps at each opening/closing of the crack.…”

Section: Saber El Aremsupporting

confidence: 85%

“…It opens totally (lowest stiffness) at ϕ = 3π 2 . This approach was first presented by Andrieux and Varé [2] and experimentally validated by Stoisser and Audebert [30] then largely discussed and improved in [8,12,9]. This variation of the stiffness of the nodal element representing the cracked transverse section will be, in the next part of this paper, adapted to be used in a two-Degrees-Of-Freedom (2−DOF) dynamical system describing a rotating shaft with a cracked transverse section.…”

Section: A Brief Review Of the Edf−lms Approachmentioning

confidence: 99%

“…1. the phenomenon of crack closure is taken into account in an exact way by setting the system global stiffness to its value for a non-cracked shaft, 2. the resort to the penalization technique when the crack closes totally is avoided and the numerical simulations cost is reduced by 20 to 100 times as noticed by El Arem and Maitournam [12].…”

Section: Saber El Aremmentioning

confidence: 99%

“…This method has been intensively used [14,22,8,13] for the stability analysis of cracked rotors and more generally for systems governed by linear ordinary differential equations with periodic coefficients [24]. The simplifying condition (12) will no longer be considered in what follows: the system stiffness is henceforth response-dependent causing the equilibrium equations to be nonlinear. The HHT method is used for the time integration of the system.…”

Section: Linear Stability Analysis: Floquet Theorymentioning

confidence: 99%

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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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Section: Saber El Aremsupporting

confidence: 85%

Section: A Brief Review Of the Edf−lms Approachmentioning

confidence: 99%

Section: Saber El Aremmentioning

confidence: 99%

Section: Linear Stability Analysis: Floquet Theorymentioning

confidence: 99%

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

Arem

2019

Nonlinear Dyn

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“…Varé and Andrieux [7] extended this method in order to show how shear effects can be implemented in the model of a cracked section. Arem und Maitournam [8] presented stiffness variations deduced from three-dimensional FE calculations accounting for the unilateral contact between the crack lips as originally developed by Andrieux and Varé [6].…”

Section: Introductionmentioning

confidence: 99%

A Cohesive Zone Model for the Investigation of the Breathing Mechanism of Transversal Cracks in Rotors

Liong¹,

Proppe²

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. The presence of a crack reduces the mean stiffness of the rotor system and introduces a stiffness variation during the revolution of the shaft. How the variable part of the rotor stiffness varies between a minimum (for a closed crack) and a maximum (for an open crack), depends on the so-called breathing mechanism. The breathing mechanism is known when the open and closed parts of the cracked area are known for all angular positions of the rotor. Here, finite element (FE) and multi-body simulation (MBS) is introduced. It is based on a representation of the fracture process zone by a cohesive zone model (CZM). First, the cracked elastic shaft with various relative crack depths is modelled by FE. As a second step, the FE model of the shaft is transferred into an MBS model in order to

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

Arem

Zid

2017

Nonlinear Dyn

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We present a systematic approach to deal with the modeling and analysis of the cracked rotating shafts behaviour. We begin by revisiting the problem of modelling the breathing mechanism of the crack. Here we consider an original approach based on the form we give to the energy of the system and then identify the mechanism parameters using 3D computations with unilateral contact conditions on the crack lips. A dimensionless flexibility is identified which makes the application of the approach to similar problems straightforward. The additional flexibility due to the crack is then introduced in a simple and comprehensive dynamical system (2 DOF) to characterize the crack effects on the dynamical response of a rotating shaft. Many results could help in early crack detection.

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A cracked beam finite element for rotating shaft dynamics and stability analysis

Cited by 11 publications

References 34 publications

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

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

A Cohesive Zone Model for the Investigation of the Breathing Mechanism of Transversal Cracks in Rotors

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

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