Non-linear dynamic of rotor-stator system with non-linear bearing clearance

The study deals with a rotor-stator contact inducing vibration in rotating machinery. A numerical rotor-stator system, including a non-linear bearing with Hertz contact and clearance is considered. To determine the non-linear responses of this system, non-linear dynamic equations can be integrated numerically. However, this procedure is both time consuming and costly to perform. The aim of this Note is to apply the Alternate Frequency/Time Method and the 'path following continuation' in order to obtain the non-linear responses to this problem. Then the orbits of rotor and stator responses at various speeds are investigated

Anisotropic behaviour law for sheets used in stamping: A comparative study of steel and aluminium

For a car manufacturer, reducing the weight of vehicles is an obvious aim. Replacing steel by aluminium moves towards that goal. Unfortunately, aluminium's stamping numerical simulation results are not yet as reliable as those of steel. Punch-strength and spring-back phenomena are not correctly described. This study on aluminium validates the behaviour law Hill 48 quadratic yield criterion with both isotropic and kinematic hardening. It is based on the yield surface and on associated experimental tests (uniaxial test, plane tensile test, plane compression and tensile shearing)

Stabilité des systèmes incertains via une méthode MEgPC et développements - application à un modèle éléments finis de frein

National audienceLa difficulté à caractériser finement certains organes pousse à introduire dans les modèles une forme de méconnaissance à leur sujet. Cette incertitude peut être introduite et traduite de différentes façons. Nous avons choisi ici une approche stochastique, reposant sur l'introduction de variables aléatoires pour représenter l'incertitude liée à des paramètres choisis du système. Le système cible est un couple disque-plaquette de frein dont on cherche à étudier le crissement pouvant apparaître lors du couplage de deux modes et une perte de stabilité. Pour repérer ces plages de fonctionnement instable pouvant donner lieu à des vibrations auto-entretenues (crissement), il faut étudier le système aux valeurs propres tangent à l'équilibre. C'est ainsi un problème aux valeurs propres stochastique que l'on se propose de résoudre ici. La démarche s'appuie sur une décomposition sur le chaos polynomial pour traduire la dispersion des éléments propres ainsi qu'une partition de l'espace stochastique (famille des méthodes MEgPC). Trois développements sont proposés pour rendre plus efficace la méthode : une sélection des modes propres déterministes utilisés pour représenter les modes stochastiques, un critère de qualité de l'approximation polynomiale pour chaque élément de la partition basé sur le coefficient de Rayleigh et enfin, une construction dynamique de la partition empruntant des principes aux méthodes de continuation. La propagation d'une incertitude relative au coefficient de frottement entre le disque et la plaquette sera présentée. Ce paramètre est en effet difficile à caractériser dans l'environnement de fonctionnement et au cours de la vie d'un frein alors qu'il est à l'origine même du phénomène engendrant les vibration auto-entretenues

Non-Linear Periodic and Quasi-Periodic Vibrations in Mechanical Systems - On the use of the Harmonic Balance Methods

Available freely from: http://www.intechopen.com/books/advances-in-vibration-analysis-research/non-linear-periodic-and-quasi-periodic-vibrations-in-mechanical-systems-on-the-use-of-the-harmonic-bInternational audienceIn this chapter, the general formulation and extensions of the harmonic balance method will be presented. The chapter is divided into four parts. Firstly we propose to present the general formulation and the basic concept of the harmonic balance method to find periodic oscillations of non-linear systems. Secondly a generalization of the method is exposed to treat quasi-periodic solutions. Thirdly, a condensation procedure that keeps only the non-linear degrees of freedom of the mechanical system is described. This technique may be of great interest to reduce the original non-linear system and to calculate the dynamical behaviour of non-linear systems with many degrees of freedom. The last part presents the classical continuation procedures that let us follow the evolution of a solution as a system parameter varies

Stochastic Analysis of the Eigenvalue Problem for Mechanical Systems Using Polynomial Chaos Expansion: Application to a Finite Element Rotor

International audienceThis paper proposes to use a polynomial chaos expansion approach to compute stochastic complex eigenvalues and eigenvectors of structures including damping or gyroscopic effects. Its application to a finite element rotor model is compared to Monte Carlo simulations. This lets us validate the method and emphasize its advantages. Three different uncertain configurations are studied. For each, a stochastic Campbell diagram is proposed and interpreted and critical speeds dispersion is evaluated. Furthermore, an adaptation of the Modal Accordance Criterion is proposed in order to monitor the eigenvectors dispersion

The invariant manifold approach applied to nonlinear dynamics of a rotor-bearing system

The invariant manifold approach is used to explore the dynamics of a nonlinear rotor, by determining the nonlinear normal modes, constructing a reduced order model and evaluating its performance in the case of response to an initial condition. The procedure to determine the approximation of the invariant manifolds is discussed and a strategy to retain the speed dependent effects on the manifolds without solving the eigenvalue problem for each spin speed is presented. The performance of the reduced system is analysed in function of the spin speed

Advanced Meta-Modelling Techniques and Sensitivity Analysis for Rotordynamics in an Uncertain Context

International audienceIt is essential to predict accurately the critical speeds and associated vibration amplitudes of rotating machineries to ensure a correct design to limit noise nuisance and fatigue failure. However, numerous uncertainties are present, due to environmental variations or manufacturing tolerances for e.g., and must be taken into consideration in the design stage to limit their impact on the system dynamics. These uncertainties are usually modelled with a probability law and the dynamic response becomes stochastic. On the other side, during the design stage, a few key parameters, often called design parameters, are identified and tuned to ensure a robust conception of the rotor w.r.t to the uncertain model parameters. In this context, one must tackle a high-dimension parametric problem but numerous parameters of different nature. The efficiency of an advanced meta-modelling technique that couple polynomial chaos expansion and kriging is demonstrated here. The kriging efficiency is improved by introducing physical properties of the rotor. A finite element model of a rotor subjected to nine uncertain parameters is studied. The hybrid surrogate model gives a direct access to the Sobol indices, exploited to conduct an extensive sensitivity analysis

Non-linear dynamic of rotor–stator system with non-linear bearing clearance

International audienceThe study deals with a rotor-stator contact inducing vibration in rotating machinery. A numerical rotor-stator system, including a non-linear bearing with Hertz contact and clearance is considered. To determine the non-linear responses of this system, non-linear dynamic equations can be integrated numerically. However, this procedure is both time consuming and costly to perform. The aim of this Note is to apply the Alternate Frequency/Time Method and the 'path following continuation' in order to obtain the non-linear responses to this problem. Then the orbits of rotor and stator responses at various speeds are investigated

Stability and nonlinear self-excited friction-induced vibrations for a minimal model subjected to multiple coalescence patterns

In certain industrial applications with frictional interfaces such as brake systems, the friction-induced vibrations created by coupled modes can lead to a dynamic instability and thus to an important deterioration in the operating condition. As a result, they are considered as a source of critical engineering problem. In addition, the presence of the nonlinearity makes necessary the consideration of the nonlinear dynamic analysis in order to explain clearly the complexity of the contribution of different frequency components due to unstable modes in the self-excited friction-induced vibrations, to get a design as reliable as possible and to avoid catastrophic failure during the operation phase of the mechanism. The present paper is based on previous works of Sinou and Jézéquel and extends them to include a developed damped four-degree-of-freedom system with frictional contact and spring cubic nonlinearities. Its essential goals are to analyze numerically the mode-coupling instability of the four-degree-of-freedom system owing to the friction between the surfaces of contact and to predict its nonlinear dynamic behavior. The numerical study of stability for the static solution of the mechanical system is performed by applying the complex eigenvalue analysis of the linearized differential equations of motion and by identifying the Hopf bifurcation points as a function of the coefficient of kinetic friction. Depending on the Runge-Kutta time-step integration scheme and the fast Fourier transforms, quantitative and qualitative nonlinear phenomena related to self-excited friction-induced oscillations and limit cycle evolutions are observed and discussed for various friction coefficients

Analysis of squeal noise and mode coupling instabilities including damping and gyroscopic effects

This paper deals with an audible disturbance known as automotive clutch squeal noise from the viewpoint of friction-induced mode coupling instability. Firstly, an auto-coupling model is presented showing a non-conservative circulatory effect originating from friction forces. Secondly, the stability of an equilibrium is investigated by determining the eigenvalues of the system linearized equations. The effects of the circulatory and gyroscopic actions are examined analytically and numerically to determine their influence on the stability region. Separate and combined effects are analysed with and without structural damping and important information is obtained on the role of each parameter and their interactions regarding overall stability. Not only is structural damping shown to be of primary importance, as reported in many previous works, this article also highlights a particular relationship with gyroscopic effects. A method of optimizing both the stability range and its robustness with respect to uncertainty on system parameters is discussed after which practical design recommendations are given