Numerical investigation on the mode coupling contact dynamic instabilities.

When dealing with complex mechanical systems, the frictional contact is at the origin of significant changes in the dynamic behavior of systems. The presence of frictional contact can give rise to mode-coupling instabilities that produce harmonic "friction induced vibrations". Unstable vibrations can reach large amplitude that could compromise the structural integrity of the system and are often associated with annoying noise emission. The study of this kind of dynamic instability has been object of many studies ranging from both theoretical and numerical study of simple lumped models to numerical and experimental study on real mechanical systems, such as automotive brakes, typically affected by such issue. In this paper the numerical analysis of a lumped system constituted by several degrees of freedom in frictional contact with a slider is presented, where the introduction of friction gives rise to an unstable dynamic behavior. Two different approaches are used to investigate the effects of friction forces. The linear Complex Eigenvalue Analysis (CEA) allows for calculating of the complex eigenvalues of the system that can be characterized by a positive real part (i.e. negative apparent modal damping). The effects of the main parameters on the system stability are investigated. In the second approach a non linear model has been developed that takes into account the stick slip behavior at the interface to solve the time-history solution and analyze the unstable vibration. The mode selection mechanism occurring in transient nonlinear analysis, when several unstable modes are predicted by the linear CEA, and driving the selection of the frequency of the unstable vibrations, is investigated. Furthermore, by means of the transient analysis, the influence of the type of perturbation at the equilibrium position on the time history of the system vibrations is analyzed. Results comparison between the two different approaches highlights how nonlinearities affect the time-history solution and how stable and unstable behavior can be predicted by the linear CEA. The obtained results have been extended to the finite element model of a simple mechanical system

Selection of Interface DoFs in Hub-blade(s) Coupling of Ampair Wind Turbine Test Bed

International audienceSubstructure coupling is an important tool in several applications ofmodal analysis. It is particularly relevant in virtual prototyping of complex systems and responds to actual industrial needs, especially in an experimental context. Furthermore, the reverse problem, the decoupling of a substructure from an assembled system, arises when a substructure cannot be tested separately but only when coupled to neighboring substructures, a situation often encountered in practice. In this paper, the dynamic behavior of the Ampair test bed wind turbine rotor, made by three blades - each one bolted to the hub at three points - is analyzed. The aim is both to identify the dynamic behavior of the rotor starting from the frequency response functions (FRFs) of blades and hub, and to select a reduced set of relevant DoFs to represent the interface between blades and hub. FRFs to be used in the coupling procedure are obtained starting from FE model of each substructure, by using a super-element based computational approach. The decoupling problem, with the aim of identifying the dynamic behavior of each blade from the FRFs of the assembled rotor and of the hub, is also considered

Identification of bolted joint properties through substructure decoupling

Substructure decoupling techniques, defined in the frame of Frequency Based Substructuring, allow to identify the dynamic behaviour of a structural subsystem starting from the known dynamics of the coupled system and from information about the remaining components. The problem of joint identification can be approached in the substructuring framework by decoupling jointed substructures from the assembled system. In this case, information about the coupling DoFs of the assembled structure is necessary and this could be a problem if the interface is inaccessible for measurements. Expansion techniques can be used to obtain the dynamics on inaccessible (interface) DoFs starting from accessible (internal) DoFs. A promising technique is the System Equivalent Model Mixing (SEMM) that combines numerical and experimental models of the same component to obtain a hybrid model. This technique has been already used in an iterative coupling–decoupling procedure to identify the linear dynamic behaviour of a joint, with a Virtual Point description of the interface. In this work, a similar identification procedure is applied to the Brake Reus Beam benchmark to identify the linear dynamic behaviour of a three bolted connection at low levels of excitation. The joint is considered as a third independent substructure that accounts for the mass and stiffness properties of the three bolts, thus avoiding singularity in the decoupling process. Instead of using the Virtual Point Transformation, the interface is modelled by performing a modal condensation on remote points allowing deformation of the connecting surfaces between subcomponents. The purpose of the study is to highlight numerical and ill-conditioning problems that may arise in this kind of identification

Towards a Fine-Grained Theory of Focus

This paper investigates the roles of focus, arguing that such a notion is too wide and can be applied to several phenomena. I show that focus needs to be further specified for (at least) another feature and is therefore made of smaller primitive traits. These can combine to create bundles of features, which give rise to the several types of foci we know. Moreover, these features are subject to parametrization and can thus account for cross-linguistic differences

Measurement of the very rare K+→π+ννˉK^+ \to \pi^+ \nu \bar\nu decay

The decay K+→π+νν¯ , with a very precisely predicted branching ratio of less than 10−10 , is among the best processes to reveal indirect effects of new physics. The NA62 experiment at CERN SPS is designed to study the K+→π+νν¯ decay and to measure its branching ratio using a decay-in-flight technique. NA62 took data in 2016, 2017 and 2018, reaching the sensitivity of the Standard Model for the K+→π+νν¯ decay by the analysis of the 2016 and 2017 data, and providing the most precise measurement of the branching ratio to date by the analysis of the 2018 data. This measurement is also used to set limits on BR(K+→π+X ), where X is a scalar or pseudo-scalar particle. The final result of the BR(K+→π+νν¯ ) measurement and its interpretation in terms of the K+→π+X decay from the analysis of the full 2016-2018 data set is presented, and future plans and prospects are reviewed

Bilan énergétique mécanique de contacts frottants en présence d'instabilités dynamiques de contact; de la dissipation surfacique à la dissipation volumique

Whenever relative motion between two system components occurs, through a dry contact interface, vibrations are induced by the frictional contact. The local dynamics at the contact (ruptures and wave generation) couples with the system dynamics, giving origin to vibrations and affecting the macroscopic frictional behavior of the system. In this thesis, in order to develop an overall approach to the investigation of the multi-physic phenomenon, the energy has been pointed out as a coupling physical characteristic among the several phenomena at the different scales. The formulation of a mechanical energy balance is used for distinguishing between two different dissipative terms, i.e. the dissipation by material/system damping and the dissipation at the contact. The energy flows coming from the frictional surfaces, by friction induced vibrations, excites the dynamic response of the system, and vice versa the influence of the system dynamic response on the local energy dissipation at the contact interface affects the related tribological phenomena. The friction-induced vibrations have been analyzed using three different approaches: the finite element approach, to investigate the coupling between the contact and system dynamics by the analysis of the energy flows; the experimental approach to validate the numerical results and observe the influence of phenomena not still included into the numerical model; a lumped parameter model approach to quickly investigate the effects of the system parameters. The numerical analysis by the 2D finite element model allowed investigating the repartition of the energy introduced into the mechanical system between the two dissipative terms (material damping and contact) during both stable and unstable friction-induced vibrations. In particular, it has been shown how the friction-induced vibrations modify the overall capacity of the system to absorb and dissipate energy; an estimation of the power dissipated at the contact, without considering the dynamic behavior of the system (energy flows by friction induced vibrations) can lead to significant error in the quantification of the dissipated energy at the contact, which affects directly several tribological phenomena. The experimental squeal measurements show how the same unstable modes are recovered both experimentally and numerically, validating the use of the 2D transient simulations for the reproduction of the unstable friction-induced vibrations. Once the energy balance formulated, it has been used on the lumped model to approach the instability over-prediction issue characteristic of the complex eigenvalue analysis. By energy considerations, a newer instability index (MAI) has been defined to compare the different unstable modes and to select the mode that becomes effectively unstable during the transient response. The Modal Absorption Index allows quantifying the capability of each mode to exchange energy with the external environment.Chaque fois que se produit un mouvement relatif entre deux systèmes, avec une interface à contact sec, le contact frottant induit des vibrations. La dynamique locale au contact (ruptures et la génération d'ondes) se couple avec la dynamique du système, donnant origine à des vibrations et affectant le comportement frictionnel macroscopique du système. Dans cette thèse, afin de développer une approche globale pour l'investigation des phénomènes multi-physiques, l'énergie a été utilisée comme une caractéristique physique universelle du couplage. La formulation de un bilan énergétique mécanique est utilisé pour identifier deux termes dissipatifs différents, i.e. la dissipation par amortissement matériel/système et la dissipation au contact. Les flux d'énergie, provenant des surfaces en contact et dus aux vibrations induites par frottement, excitent la réponse dynamique du système et, vice versa, l'influence de la réponse dynamique du système sur la dissipation d'énergie locale à l'interface de contact affecte les phénomènes tribologiques connexes. Dans cette thèse, les vibrations induites par le frottement ont été analysées en utilisant: l'approche par éléments finis pour étudier, par l'analyse des flux d'énergie, le couplage entre le contact et la dynamique du système; l'approche expérimentale pour valider les résultats numériques et observer l'influence des phénomènes pas encore inclus dans les modèles numériques; une approche avec une modèle à paramètres concentrés pour évaluer rapidement les effets des paramètres du système. L'analyse numérique par le modèle éléments finis 2D permet une répartition de l’énergie introduite dans le système mécanique entre les deux termes dissipatifs (amortissement matériau et contact), au cours de la réponse transitoire aussi bien en conditions stables qu’instables. En particulier, les vibrations induites par frottement modifient la capacité globale du système à absorber et dissiper l’énergie; une estimation de la puissance dissipée au contact, sans prendre en compte le comportement dynamique du système (flux d’énergie par les vibrations induites par frottement) peut conduire à des erreurs significatives dans la quantification de l’énergie dissipée au contact, ce qui affecte directement plusieurs phénomènes tribologiques. Les mesures expérimentales de crissement montrent comment les mêmes modes instables sont reproduits soit expérimentalement soit numériquement, validant l’utilisation de la simulation 2D transitoires pour l’analyse des vibrations instables induites par le frottement. L’équilibre énergétique a été utilisé sur le modèle à paramétrés concentrés, pour approcher le problème de la surestimation d’instabilité, qui est caractéristique d’une analyse des valeurs propres complexes. Un nouvel indice d’instabilité (MAI) a été défini, par des considérations énergétiques, pour comparer les différents modes instables et pour sélectionner le mode qui devient effectivement instable pendant le crissement

Evaluation of Different Contact Assumptions in the Analysis of Friction-Induced Vibrations Using Dynamic Substructuring

Dynamic substructuring methods are initially developed for time-invariant systems to evaluate the dynamic behavior of a complex structure by coupling the component substructures. Sometimes, the component substructures change their position over time, affecting the dynamics of the entire structure. This family of problems can be tackled using substructuring techniques by isolating the time dependency in the coupling conditions among the time-invariant substructures. Mechanical systems, composed of subsystems in relative motion with a sliding interface, can be analyzed using this approach. In previous work, the authors proposed a solution method in the time and frequency domain using this approach under the assumption that the relative sliding motion at the contact interfaces is a-priori known, at least approximately. This assumption implies that the perturbation generated by the friction-induced vibration is neglected. In subsequent work, a more realistic contact assumption was considered to account also for the local vibration of the contact point and the geometric nonlinearity due to the elastic deformation. In this paper, a simplification with respect to the realistic contact assumption is introduced, which neglects the angular variation of the direction normal to the contact interface. The simplified approach is advantageous because it is equally able to highlight the occurrence of friction-induced instabilities, and it reduces the computational burden. The results of the substructuring methods using different contact assumptions are compared with those of a reference numerical method to show how the choice of the contact algorithm allows for tackling a wide range of operating conditions, from simple position-dependent problems up to complex friction-induced vibration phenomena

Evaluation of Different Contact Assumptions in the Analysis of Friction-Induced Vibrations Using Dynamic Substructuring

Dynamic substructuring methods are initially developed for time-invariant systems to evaluate the dynamic behavior of a complex structure by coupling the component substructures. Sometimes, the component substructures change their position over time, affecting the dynamics of the entire structure. This family of problems can be tackled using substructuring techniques by isolating the time dependency in the coupling conditions among the time-invariant substructures. Mechanical systems, composed of subsystems in relative motion with a sliding interface, can be analyzed using this approach. In previous work, the authors proposed a solution method in the time and frequency domain using this approach under the assumption that the relative sliding motion at the contact interfaces is a-priori known, at least approximately. This assumption implies that the perturbation generated by the friction-induced vibration is neglected. In subsequent work, a more realistic contact assumption was considered to account also for the local vibration of the contact point and the geometric nonlinearity due to the elastic deformation. In this paper, a simplification with respect to the realistic contact assumption is introduced, which neglects the angular variation of the direction normal to the contact interface. The simplified approach is advantageous because it is equally able to highlight the occurrence of friction-induced instabilities, and it reduces the computational burden. The results of the substructuring methods using different contact assumptions are compared with those of a reference numerical method to show how the choice of the contact algorithm allows for tackling a wide range of operating conditions, from simple position-dependent problems up to complex friction-induced vibration phenomena

La permanenza dell’Antichità. Dal laboratorio bolognese: Alexandre, Thèbes, Troie, Merlin

Il contributo espone i risultati e le prospettive future di alcuni percorsi di ricerca attorno al tema della permanenza e della rielaborazione dei classici nel Medioevo. Sono presentate alcune considerazioni sul Roman de Thèbes, specialmente per quanto riguarda la posizione stemmatica dei frammenti conservati ad Angers; segue una panoramica sulla singolare commistione tra romanzo arturiano e materia antica nella silloge del codice Cologny, Fondation Martin Bodmer, Bodmer 147. In conclusione è valutata la presenza di un progetto culturale di matrice storiografica alla base della prosificazione franco-italiana (Prose 2) del Roman de Troie.The essay relates the results and the expected developments of research coordinated by Brunetti at the University of Bologna, concerning texts and themes from classical antiquity to the Middle Ages. The authors discuss the Roman de Thèbes, in particular the controversial stemmatic position of the fragments preserved in Angers; and the compilation of the MS. Cologny, Fondation Martin Bodmer, Bodmer 147, a remarkable blend of Arthurian novel and Matter of Rome. The paper also discusses the outcome of research aimed at proving the existence of a specific cultural project as premise to the composition of the Franco-Italian mise en prose (Prose 2) of the Roman de Troie

Configuration-Dependent Substructuring as a Tool to Predict the Vibrational Response of Mechanisms

Dynamic substructuring allows us to predict the dynamic behavior of mechanical systems built by linking together several subsystems, whose dynamic behavior is known. The classical formulation, originally conceived for invariant systems, was extended by the authors to include mechanical systems made by invariant subsystems that may be coupled in different configurations. A mechanism is a typical example of a mechanical system built by coupling together invariant subsystems; during its motion, it can take several configurations that significantly affect its vibrational behavior. Therefore, the configuration-dependent substructuring approach can provide meaningful insights into the dynamic behavior of the mechanism. In this paper, the proposed approach is exploited to evaluate the vibrational behavior of a three-point linkage, a widely used mechanism to connect agricultural tractors to operating machines, considering a significant range of operative configurations. The proposed substructuring approach is able to predict the frequency response functions, the natural frequencies and the mode shapes of the mechanism in a wide range of configurations