Error localization and updating of junction properties for an engine cradle model

Extending the bandwidth of validity of FEM models used in vibroacoustic design is a generic objective of model generation processes. Achieving this objective requires a critical review of both testing and modeling processes. Using the case study of an engine cradle, tools used to detect modal test inconsistencies are first illustrated. On the modeling side, weld spots and lines and variations of thickness due to press forming are shown to have relatively minor impact when compared to the contact surfaces. Usual junction simplifications are also shown to play a major role particularly at higher frequencies where more localized modeshapes occur

Qualitative Analysis of Forced Response of Blisks With Friction Ring Dampers

A damping strategy for blisks (integrally bladed disks) of turbomachinery involving a friction ring is investigated. These rings, located in grooves underside the wheel of the blisks, are held in contact by centrifugal loads and the energy is dissipated when relative motions between the ring and the disk occur. A representative lumped parameter model of the system is introduced and the steady-state nonlinear response is derived using a multi-harmonic balance method combined with an AFT procedure where the friction force is calculated in the time domain. Numerical simulations are presented for several damper characteristics and several excitation configurations. From these results, the performance of this damping strategy is discussed and some design guidelines are given

Modélisation du frottement en pied d'aube par une approche fréquentielle

This thesis considers the dynamics of structural systems with dry friction damping, usingCoulomb's law for the friction force model.An indirect method is proposed to impose constraints. Also, a new frequency-time domain method, the Dynamic Lagrangian mixed Frequency-Time method (DLFT), is defined to get the steady-state forced response. The dynamic Lagrangians are a new formulation for Lagrangians in frequency domain. Note that dynamic Lagrangians may also be used in frequency domain. This new formulation is more convenient than augmented Lagrangians when a nonlinear solver is used to get the frequency response in frequency domain. The use of dynamic Lagrangians allow one to solve for the nonlinear forces between two finite element nodes of the structure without using artifacts such as a contact stiffness similar to a penalty coefficient. Hence the finite element model does not have to be degraded at the contact interface. Furthermore, a new reduction of the nonlinear system is proposed to decrease the required computation time. Also, an adaptive reduction is proposed to avoid ill-conditioning problems when structural damping is weak. Several numerical systems with different difficulties are studied. For example, case of a friction damped beam with a flexible element when the friction.A set of numerical examples is presented for a beam in contact with a flexible dry friction element, for frictional constraints that feature two-dimensional relative motion, for a large-scale system with many friction dampers, and for a simple system with a clearance.A test rig is designed to study effects of dry friction damping on the first resonance mode. The main feature of this rig is to lay out two blade's attachments. The test rig was studied numerically to validate the DLFT.Dans cette thèse, la dynamique de systèmes amortis par frottement sec est étudiée en utilisantune loi de Coulomb pour modéliser les forces de frottement.Une méthode indirecte de prise en compte des contraintes est proposée. De plus, une nouvelle méthode alternant le domaine fréquentiel et le domaine temporel, la DLFT (Dynamic Lagrangian mixed Frequency-Time method), est définie pour déterminer la réponse stationnaire du système en régime forcé. Les Lagrangiens Dynamiques sont une nouvelle formulation des Lagrangiens dans le domaine fréquentiel. A noter que les Lagrangiens dynamiques peuvent aussi être utilisés dans le domaine temporel.Cette nouvelle formulation est plus adaptée que les Lagrangiens augmentés dans le cadre d'une méthode d'optimisation afin d'estimer la réponse fréquentielle d'un système non linéaire. L'utilisation des Lagrangiens dynamiques nous permet de déterminer les forces non linéaires entre les nœuds du modèle éléments finis de la structure sans utiliser d'artifices tels que l'introduction d'une raideur de contact servant de pénalité.Une nouvelle réduction du système non linéaire est aussi proposée pour réduire les temps de calcul. De plus, une réduction adaptative du système a été définie pour éviter les problèmes de mauvais conditionnement lorsque l'amortissement structural est faible.Plusieurs modèles numériques présentant des difficultés divers seront étudiés. On s'intéressera par exemple au cas d'une poutre amortie par frottement sec avec un élément flexible lorsque le frottement se caractérise par un mouvement relatif 2D. On montrera également que la DLFT permet de résoudre des systèmes éléments finis de grande taille tels que des roues aubagées désaccordées. Un système avec jeu sera aussi étudié.Un banc expérimental a été conçu afin d'étudier les effets de l'amortissement par frottement sec sur le premier mode de résonance. La caractéristique principale de ce banc est de disposer de pieds d'aube réels. Il a été étudié numériquement afin de valider la DLFT

On the influence of multiple contact conditions on brake squeal

This study focuses on squeal noise prediction for an automotive brake system. For this purpose, a stability study of a finite element model of the brake system is carried out. For the determination of the squeal propensity of a brake system via finite element models, the commonly used approach consists in considering only a friction coefficient at the pad-disc interface. However, numerous other contacts exist in a brake system. In the present study, the influence of several contacts between the caliper, the bracket, the pad and the piston is studied. It turns out that the consideration of these numerous contacts has a real impact on the stability results and can not therefore be neglected. Indeed, a high dispersion of results for the system’s eigenvalues indicating strong modifications of the stability behavior and thus of the squeal propensity is observed when different contact conditions are considered. This study insights the necessity to take into account of all contact conditions during the design process of brake systems

Modélisation du frottement en pied d'aube par une approche fréquentielle

Dans cette thèse, la dynamique de systèmes amortis par frottement sec est étudiée en utilisant une loi de Coulomb pour modéliser les forces de frottement. Une méthode indirecte de prise en compte des contraintes est proposée et une nouvelle méthode alternant le domaine fréquentiel et le domaine temporel, la DLFT (Dynamic Lagrangian mixed Frequency-Time method), est définie pour déterminer la réponse stationnaire du système en régime forcé. Les lagrangiens dynamiques sont une nouvelle formulation des Lagrangiens dans le domaine fréquentiel. A noter que les Lagrangiens dynamiques peuvent aussi être utilisés dans le domaine temporel. Cette nouvelle formulation est plus adaptée que les Lagrangiens augmentés dans le cadre d'une méthode d'optimisation afin d'estimer la réponse fréquentielle d'un système non linéaire. Une nouvelle réduction du système non linéaire est aussi proposée pour réduire les temps de calcul. La méthode proposée a été validée numériquement et expérimentalement.This thesis considers the dynamics of structural systems with dry friction damping, using Coulomb's law for the friction force model. An indirect method is proposed to impose constraints and a new frequency-time domain method, the Dynamic Lagrangian mixed Frequency-Time method (DLFT), is defined to get the steady-state forced response. The dynamic Lagrangians are a new formulation for Lagrangains in frequency domain. Note that dynamic Lagrangians may also be used in frequency domain. This new formulation is more convenient than augmented Lagrangians when a nonlinear solver is used to get the frequential response in frequency domain. Also, an adaptative reduction is proposed to avoid ill-conditionning problems when structural damping is weak. The new method has been validated numerically and experimentally.LYON-Ecole Centrale (690812301) / SudocSudocFranceF

Prediction and analysis of quasi-periodic solution for friction-induced vibration of an industrial brake system with the Generalized Modal Amplitude Stability Analysis

Brake squeal is a major issue for car manufacturers as it is the reason for the return of many vehicles to customer services, representing high costs for the companies. To meet customer’s expectations, squeal must be accurately predicted during the design process. In the context of the automotive industry, squeal usually refers to friction-induced vibrations that generate noise. The main methodology employed nowadays for friction-induced vibrations prediction of industrial systems is the well-known complex eigenvalue analysis (CEA) despite its limitations. The latter suffers from an under- or over-predictive aspect and the vibration amplitudes cannot be estimated. A recent approach, called the generalised modal amplitude stability analysis (GMASA), has been developed as a complementary approach of the CEA to identify the modes involved in the nonlinear dynamic response of systems subjected to friction-induced vibrations and to approximate the quasi-periodic oscillations. The objective of this paper is to predict the nonlinear dynamic response of a full industrial automotive brake system. The GMASA is employed to predict its nonlinear dynamic response. It is demonstrated that when the CEA predicts a single unstable mode, two are actually involved in the nonlinear dynamic response. The quasi-periodic oscillations are analysed, as well as the evolution of the contact conditions at the pad/disc interface and exhibits the presence of micro-impacts

Study of the nonlinear stationary dynamic of single and multi-instabilities for disk brake squeal

International audienceThe focus of this paper is to show and discuss the nonlinear dynamical behaviours of brake system subjected to friction-induced vibration that can be generated due to the co-existence of multi-unstable modes. A finite element model with friction coupling is used to analyse the stability of the brake system and the stationary nonlinear oscillations for squeal noise prediction. The mechanism of squeal instability considers a mode coupling phenomenon that is classically referred to as coalescence

Mise en place d’une technique numérique pour l’estimation de vibrations non-linéaires auto-entretenues avec frottement: Application à la prédiction du crissement de frein automobile

International audienceCe papier présente une approche non-linéaire permettant d'approximer le comportement vibratoire non-linéaire dans le cas où plusieurs instabilités sont impliquées dans la réponse du système. Cette méthode dénommée MASA (Modal Amplitude Stability Analysis) est complémentaire de l'ana-lyse aux valeurs propres complexes. Dans un premier temps, les aspects théoriques de la méthode sont présentés. Puis, le modèle éléments finis du frein servant d'illustration est présenté. Enfin, la méthode non-linéaire est appliquée sur le modèle afin de prédire la réponse dynamique de celui-ci

A new treatment for predicting the self-excited vibrations of nonlinear systems with frictional interfaces: The Constrained Harmonic Balance Method, with application to disc brake squeal

International audienceBrake squeal noise is still an issue since it generates high warranty costs for the automotive industry and irritation for customers. Key parameters must be known in order to reduce it. Stability analysis is a common method of studying nonlinear phenomena and has been widely used by the scientific and the engineering communities for solving disc brake squeal problems. This type of analysis provides areas of stability versus instability for driven parameters, thereby making it possible to define design criteria. Nevertheless, this technique does not permit obtaining the vibrating state of the brake system and nonlinear methods have to be employed. Temporal integration is a well-known method for computing the dynamic solution but as it is time consuming, nonlinear methods such as the Harmonic Balance Method (HBM) are preferred. This paper presents a novel nonlinear method called the Constrained Harmonic Balance Method (CHBM) that works for nonlinear systems subject to flutter instability. An additional constraint-based condition is proposed that omits the static equilibrium point (i.e. the trivial static solution of the nonlinear problem that would be obtained by applying the classical HBM) and therefore focuses on predicting both the Fourier coefficients and the fundamental frequency of the stationary nonlinear system. The effectiveness of the proposed nonlinear approach is illustrated by an analysis of disc brake squeal. The brake system under consideration is a reduced finite element model of a pad and a disc. Both stability and nonlinear analyses are performed and the results are compared with a classical variable order solver integration algorithm. Therefore, the objectives of the following paper are to present not only an extension of the HBM (CHBM) but also to demonstrate an application to the specific problem of disc brake squeal with extensively parametric studies that investigate the effects of the friction coefficient, piston pressure, nonlinear stiffness and structural damping

Periodic and quasi-periodic solutions for multi-instabilities involved in brake squeal

International audienceThis paper is devoted to the computation of nonlinear dynamic steady-state solutions of autonomous systems subjected to multi-instabilities and proposes a new nonlinear method for predicting periodic and quasi-periodic solutions intended for application to the disc brake squeal phenomenon. Firstly, finite element models of a pad and a disc are reduced to include only their contact nodes by using a Craig and Bampton strategy. Secondly, a complex eigenvalue analysis is performed showing two unstable modes for a wide range of friction coefficients, after which a Generalized Constrained Harmonic Balance Method (GCHBM) is presented. This method can compute nonlinear periodic or pseudo-periodic responses depending on the number of unstable frequencies. The numerical results are in good agreement with those of time marching methods