Steady-state response of a rotor excited by combined rotational and translational base motions

International audienceIn the transportation domain, the on-board rotor in bending is subjected not only to rotating mass unbalance but also to support movements. The equations of motion in bending of the rotating rotor take into account the geometric asymmetry of disks and/or shaft and consider six types of deterministic support motions. The application of Lagrange's equations using the finite element method based on the theory of Timoshenko leads to the equations of motion which highlight periodic parametric terms due to the asymmetry of the rotor and time-varying parametric terms due to the rotational base excitations. When the rotor base is subjected to combined rotation and sinusoidal translation, analytical solutions are derived and analyzed by means of Campbell diagrams and steady-state responses

Prediction of the non-linear dynamic behavior of on-board rotors under extreme solicitations

International audienc

Effect of support sinusoidal motions on the vibration of an on-board rotor-bearing system

International audienceIn generator and pump rotors installed in power plants, the rotating mass unbalance and the different motions of the rotor support are among the main sources of flexural vibrations. This work aims to observe the dynamic behavior of an on-board rotor subject to rigid support movements. The modeling takes into account six types of support deterministic motions (rotational and translational motions) when the kinetic and strain energies in addition to the virtual work of the rotating flexible rotor components are calculated. The finite element method is applied using the Timoshenko beam theory. The proposed on-board rotor model considers the rotary inertia, the gyroscopic inertia, the shear deformation of shaft as well as the geometric asymmetry of shaft and/or rigid disk of the rotor. By computing the Rayleigh damping coefficients, the effect of rotor internal damping is included in the study. The Lagrange's equations are used to obtain the differential equations of the rotor in bending relative to the rigid support which forms a noninertial reference frame. The equations of motion exhibit periodic parametric coefficients due to the asymmetry of the rotor and time-varying parametric coefficients due to the support rotations. In the presented applications, the rotor mounted on rigid/elastic linear bearings is excited by a rotating mass unbalance combined with sinusoidal oscillations of the rigid support. The dynamic behavior of the rotor is analyzed by means of rotor orbits and fast Fourier transforms (FFTs)

Investigation on the Dynamics of an On-Board Rotor-Bearing System

International audienceIn ship and aircraft turbine rotors, the rotating mass unbalance and the different movements of the rotor base are among the main causes of vibrations in bending. The goal of this paper is to investigate the dynamic behavior of an on-board rotor under rigid base excitations. The modeling takes into consideration six types of base deterministic motions (rotations and translations) when the kinetic and strain energies in addition to the virtual work of the rotating flexible rotor components are computed. The finite element method is used in the rotor modeling by employing the Timoshenko beam theory. The proposed on-board rotor model takes into account the rotary inertia, the gyroscopic inertia, the shear deformation of shaft as well as the geometric asymmetry of shaft and/or rigid disk. The Lagrange's equations are applied to establish the differential equations of the rotor in bending with respect to the rigid base which represents a noninertial reference frame. The linear equations of motion display periodic parametric coefficients due to the asymmetry of the rotor and time-varying parametric coefficients due to the base rotational motions. In the proposed applications, the rotor mounted on rigid/elastic bearings is excited by a rotating mass unbalance associated with sinusoidal vibrations of the rigid base. The dynamic behavior of the rotor is analyzed by means of orbits of the rotor as well as fast Fourier transforms (FFTs)

Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings

International audienceThe major purpose of this study is to predict the dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings in the presence of rigid support movements, the target application being turbochargers of vehicles or rotating machines subject to seismic excitation. The proposed on-board rotor model is based on Timoshenko beam finite elements. The dynamic modeling takes into account the geometric asymmetry of shaft and/or rigid disk as well as the six deterministic translations and rotations of the rotor rigid support. Depending on the type of analysis used for the bearing, the fluid film forces computed with the Reynolds equation are linear/nonlinear. Thus the application of Lagrange's equations yields the linear/nonlinear equations of motion of the rotating rotor in bending with respect to the moving rigid support which represents a non-inertial frame of reference. These equations are solved using the implicit Newmark time-step integration scheme. Due to the geometric asymmetry of the rotor and to the rotational motions of the support, the equations of motion include time-varying parametric terms which can lead to lateral dynamic instability. The influence of sinusoidal rotational or translational motions of the support, the accuracy of the linear 8-coefficient bearing model and the interest of the nonlinear model for a hydrodynamic journal bearing are examined and discussed by means of stability charts, orbits of the rotor, time history responses, fast Fourier transforms, bifurcation diagrams as well as Poincaré maps

Chaotic motion of an on-board rotor mounted on fluid-film bearings

National audienc

Bifurcation Analysis of a Non-linear On-Board Rotor-Bearing System

International audienceThe non-linear dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings and subject to rigid base excitations is investigated in this work. The proposed finite element rotor model takes into account the geometric asymmetry of shaft and/or rigid disk and considers six types of base deterministic motions (rotations and translations) and non-linear fluid film forces obtained from the Reynoldsequation. The equations of motion contain time-varying parametric coefficients because of the geometric asymmetry of the rotor and the base rotations. In the case when sinusoidal excitations of the rotor base lead to periodic (harmonic and sub-harmonic) responses, an optimized shooting algorithm based on the non-linear Newmark time integration scheme is employed to solve the equations of motion. The non-linear phenomena observed in the on-board rotor-bearing system, such as period-doubling motion and chaos, are characterized by means of bifurcation diagrams, rotor orbits and Poincaré maps

Steady-state dynamic behavior of an on-board rotor under combined base motions.

International audienceIn the transportation domain, on-board rotors in bending are subjected not only to rotating mass unbalance but also to several movements of their base. The main objective of this article is to predict the dynamic behavior of a rotor in the presence of base excitations. The proposed on-board rotor model is based on the Timoshenko beam finite element. It takes into account the effects corresponding to rotary inertia, gyroscopic inertia, and shear deformation of shaft as well as the geometric asymmetry of disk and/or shaft and considers six types of deterministic motions (rotations and translations) of the rotor's rigid base. The use of Lagrange's equations associated with the finite element method yields the linear second-order differential equations of vibratory motion of the rotating rotor in bending relative to the moving rigid base which forms a non-inertial frame of reference. The linear equations of motion highlight periodic parametric terms due to the geometric asymmetry of the rotor components and time-varying parametric terms due to the rotational motions of the rotor rigid base. These parametric terms are considered as sources of internal excitation and can lead to lateral dynamic instability. In the presented applications, the rotor is excited by a rotating mass unbalance combined with constant rotation and sinusoidal translation of the base. Quasi-analytical and numerical solutions for two different rotor configurations (symmetric and asymmetric) are analyzed by means of stability charts, Campbell diagrams, steady-state responses as well as orbits of the rotor

Modal Reduction Technique for On-Board Rotor-bearing system with time varying Parameters

International audienc

Laboratoire Commun AdViTAM : Advanced Vibration Tests for the Analysis of rotating Machines

International audienc