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Influence des défauts sur le comportement vibratoire linéaire des systèmes tournant

Arnaud Lazarus 1, 2
2 DYN - Laboratoire d'études de DYNamique
SEMT - Service d'Etudes Mécaniques et Thermiques : DEN/DM2S/SEMT
Abstract : In the case of many rotating machines (turbomachines, power pump unit...), modelling of "imperfections" such as anisotropic bearings or cracked rotors lead naturally to specific governing equations called linear periodic time-varying systems. Studying the dynamic behavior of parametric oscillators governing by this type of equations is usually simple thanks to the well-known Floquet's theory but can be more difficult for complex model with a lot of degrees of freedom...

By writing the Floquet's solutions in the frequency domain, we extend the modal analysis used for the classical oscillators to the parametric oscillators. The concept of parametric eigenmode is also introduced and described through several academic examples. Thus, the vibratory behavior of the parametric pendulum with one degree of freedom governing by the well-known Mathieu's equation is investigated. In the same manner, various 2 degrees of freedom rotating systems with non symmetrical stiffnesses are studied (simplified models of cracked rotors).

Like classic eigenmodes, parametric ones can be easily adapted to complex systems with n degrees of freedom thanks to the finite element method. However, these modes being poly-harmonic, the modal basis of the whole system is obtained through the component synthesis method where each substructure is naturally associated with each harmonic. These ideas are implemented in the finite element software Cast3m to predict the three-dimensional dynamic behavior of large rotating machines with imperfections. The numerical method efficiency is finally tested by comparing numerical and experimental results coming from a test rig composed of a vertical anisotropic shaft rotating on anisotropic supports (academic model of a horizontal open cracked rotor).
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Submitted on : Monday, March 23, 2009 - 11:50:33 PM
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  • HAL Id : tel-00370228, version 1

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Arnaud Lazarus. Influence des défauts sur le comportement vibratoire linéaire des systèmes tournant. Mécanique [physics.med-ph]. Ecole Polytechnique X, 2008. Français. ⟨tel-00370228⟩

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