Modeling Stiffness and Damping in Rotational Degrees of Freedom Using Multibond Graphs

A contribution is proposed for the modeling of mechanical systems using multibond graphs. When modeling a physical system, it may be needed to catch the dynamic behavior contribution of the joints between bodies of the system and therefore to characterize the stiffness and damping of the links between them. The visibility of where dissipative or capacitive elements need to be implemented to represent stiffness and damping in multibond graphs is not obvious and will be explained. A multibond graph architecture is then proposed to add stiffness and damping in hree rotational degrees of freedom. The resulting joint combines the spherical joint multibond graph relaxed causal constraints while physically representing three concatenated revolute joints. The mathematical foundations are presented, and then illustrated through the modeling and simulation of an inertial navigation system; in which stiffness and damping between the gimbals are taken into account. This method is particularly useful when modeling and simulating multibody systems using Newton-Euler formalism in multibond graphs. Future work will show how this method can be extended to more complex systems such as rotorcraft blades' connections with its rotor hub.Fondation Airbus Grou

Bioaéroelasticité d’aéronefs à voilure tournante par bond graphs

Under certain flight conditions, rotorcrafts might suffer from the emergence of undesirable oscillations, potentially unstable phenomena, known as aeroelastic Rotorcraft-Pilot Couplings (RPCs). These phenomena critically affect the safety and performance of rotorcraft designs. Therefore, there is an important interest in being able to predict the emergence of such dynamic phenomena, as soon as possible during the design process of helicopters. A review of the state-of-the-art reveals that these phenomena are the result of interactions between pilots’ biodynamics and helicopters’ aeroelastic behaviors. In order to provide more modularity and granularity in the modeling of complex systems, a bond graph based approach is used. A helicopter aeromechanical model and a pilot upper limb neuromusculoskeletal model are developed using bond graphs. Three original bond graph representations are proposed, to model: quasi-steady aerodynamic forces, lag-flap-pitch joint at blades’ roots, and a Hill-type muscle force model that accounts for muscle reflexive feedback. Encouraging results are found when comparing the pilot biodynamic model transmissibility cyclic lever angle to lateral cockpit accelerations computations to literature experimental results. A linear model of the coupled human-machine bioaeroelastic system around hover is analyzed in terms of stability. It reveals not only the regressing lag mode, as conjectured in literature, but also the advancing lag mode can be destabilized during a lateral-roll aeroelastic RPC. Furthermore, a criterion to assess the stability of the equilibrium of a dynamic system from a linear model limits the possibility to take into account nonlinear physical behaviors, reducing the design space. The first blocks towards a method based on Chetaev functions is proposed, to determine if an equilibrium is unstable, directly from its large nonlinear mathematical model, at a potentially interesting computational cost. The helicopter ‘ground resonance’ case illustrates the soundness of the proposal.Dans certaines conditions de vol, les aéronefs à voilure tournante souffrent parfois de l’émergence d’oscillations indésirables, phénomènes potentiellement instables connus sous le nom de Couplages Pilote-Aéronef aéroélastiques (CPA). Ces phénomènes affectent de manière critique la sécurité et la performance des aéronefs. Par conséquent, il est important d’être capable de prédire l’émergence de tels phénomènes dynamiques, le plus tôt possible dans le processus de conception des hélicoptères. Une revue de la littérature révèle que ces phénomènes sont le résultat d’interactions entre les comportements biodynamique du pilote et aéroélastique des hélicoptères. Afin d’avoir une plus grande modularité et granularité dans le processus de modélisation de systèmes complexes, une approche par bond graphs est adoptée. Un modèle aéromécanique d’hélicoptère et un modèle neuro-musculo-squelettique d’un des membres supérieurs du pilote sont développés en bond graphs. Parmi les représentations proposées, trois sont originales, notamment afin de modéliser : des efforts aérodynamiques quasi-statiques, la liaison traînée-battement-pas entre pale et moyeu rotor, et les efforts musculaires à partir d’un modèle de Hill qui tient compte d’une boucle de rétroaction neuromusculaire. Des résultats encourageants sont obtenus lorsque l’on compare la transmissibilité, entre l’angle de manche de pas cyclique imposé par le pilote et des accélérations latérales de la cabine, calculée à partir du modèle biodynamique, et à partir des résultats expérimentaux tirés de la littérature. Un modèle du système bioaéroélastique homme-machine est linéarisé, au voisinage d’un vol stationnaire, et analysé en termes de stabilité. L’étude révèle, comme conjecturé dans la littérature, que le mode régressif de traînée peut être déstabilisé. De plus, il apparaît que le mode progressif de traînée peut également être déstabilisé lors d’un CPA sur l’axe latéral-roulis. Un critère d’analyse de la stabilité d’un équilibre d’un système dynamique à partir d’un modèle linéaire limite la possibilité de prendre en compte certains comportements non-linéaires et donc réduit l’espace de conception. Les premières pierres vers une méthode basée sur des fonctions de Chetaev sont posées, afin de déterminer si l’équilibre d’un système dynamique est instable, directement à partir d’un modèle mathématique non-linéaire de grande dimension, à un coût de calcul potentiellement intéressant. Afin d’illustrer la pertinence de la proposition, le cas de la résonance sol d’un hélicoptère est présentée

A convolutional neural network aided physical model improvement for AC solenoid valves diagnosis

This paper focuses on the development of a physics-based diagnostic tool for alternating current (AC) solenoid valves which are categorized as critical components of many machines used in the process industry. Signal processing and machine learning based approaches have been proposed in the literature to diagnose the health state of solenoid valves. However, the approaches do not give a physical explanation of the failure modes. In this work, being capable of diagnosing failure modes while using a physically interpretable model is proposed. Feature attribution methods are applied to CNN on a large data set of the current signals acquired from accelerated life tests of several AC solenoid valves. The results reveal important regions of interest on current signals that guide the modeling of the main missing component of an existing physical model. Two model parameters, which are the shading ring and kinetic coulomb forces, are then identified using current measurements along the lifetime of valves. Consistent trends are found for both parameters allowing to diagnose the failure modes of the solenoid valves. Future work will consist of not only diagnosing the failure modes, but also of predicting the remaining useful life

An improved first-principle model of AC powered solenoid operated valves for maintenance applications

Solenoid operated valves (SOVs) are critical components in many industrial applications. There has been a continuing interest in the industry to have robust condition monitoring, prognostics and health management tools to support the condition based maintenance and predictive maintenance program for such valves. For critical assets like SOVs, it is of paramount interest to understand why a component might be declared as defective. In such a situation, a first principle-model based approach will always be preferred to a purely data-driven approach, because of its inherent interpretability. Furthermore, first principle-models typically have less free parameters than their data driven counterparts and will require less data to identify their parameters. In this paper, we present the improvement of a first-principle model of alternating current (AC) powered SOVs taking into account two important degradation effects. Using this model, we show that the state of degradation can be estimated from current and input voltage measurement signals on the solenoids. Our method is validated using data from an accelerated life test campaign on 48 identical AC-powered SOVs

Modeling Stiffness and Damping in Rotational Degrees of Freedom Using Multibond Graphs

Abstract-a contribution is proposed for the modeling of mechanical systems using multibond graphs. When modeling a physical system, it may be needed to catch the dynamic behavior contribution of the joints between bodies of the system and therefore to characterize the stiffness and damping of the links between them. The visibility of where dissipative or capacitive elements need to be implemented to represent stiffness and damping in multibond graphs is not obvious and will be explained. A multibond graph architecture is then proposed to add stiffness and damping in three rotational degrees of freedom. The resulting joint combines the spherical joint multibond graph relaxed causal constraints while physically representing three concatenated revolute joints. The mathematical foundations are presented, and then illustrated through the modeling and simulation of an inertial navigation system; in which stiffness and damping between the gimbals are taken into account. This method is particularly useful when modeling and simulating multibody systems using Newton-Euler formalism in multibond graphs. Future work will show how this method can be extended to more complex systems such as rotorcraft blades' connections with its rotor hub

An Energetic Approach to Aeroelastic Rotorcraft-Pilot Couplings Analysis

This paper describes an energetic method using multibond graphs to model multi-physical systems. Its potential in building physical meaningful graphs that represent equivalent mathematical models of classic analytical approaches is shown. An application to the study of an aeroelastic rotorcraft-pilot coupling is studied by analyzing the passive pilot behavior in the cyclic control loop. A rotorcraft in hover flight is simulated and perturbed on its rolling motion axis. Depending on the rotorcraft characteristics air resonance may occur, and the pilot may involuntarily excite the cyclic lever, increasing the rolling motion of the fuselage to an unstable point. Future work will explore eventual alternative solutions to notch filters to avoid passive pilot reinjection at low fuselage frequency modes by controlling for example the actuators of the swashplate through model inversion using the bond graph metho

Instability Mechanism of Roll/Lateral Biodynamic Rotorcraft–Pilot Couplings

The paper investigates the basic mechanism of aeroservoelastic pilot-assisted oscillation about the roll axis due to the interaction with pilot's arm biomechanics. The motivation stems from the observation that a rotor imbalance may occur as a consequence of rotor cyclic lead–lag modes excitation. The work shows that the instability mechanism is analogous to air resonance, in which the pilot's involuntary action plays the role of the automatic flight control system. Using robust stability analysis, the paper shows how the pilot's biodynamics may involuntarily lead to a roll/lateral instability. The mechanism of instability proves that the pilot biodynamics is participating in the destabilization of the system by transferring energy, i.e., by producing forces that do work for the energetically conjugated displacement, directly into the flapping mode. This destabilizes the airframe roll motion, which, in turn, causes lead–lag motion imbalance. It is found that, depending on the value of the time delay involved in the lateral cyclic control, the body couples with rotor motion in a different way. In the presence of small or no time delays, body roll couples with the rotor through the lead–lag degrees of freedom. The increase of the time delay above a certain threshold modifies this coupling: The body no longer couples with the rotor through lead–lag but directly through flap motion

An upper limb musculoskeletal model using bond graphs for rotorcraft-pilot couplings analysis

Under certain flight conditions, a rotorcraft fuselage motions and vibrations might interact with its pilot voluntary and involuntary actions leading to potentially dangerous dynamic instabilities known as rotorcraft-pilot couplings (RPCs). A better understanding of this phenomenon could be achieved by being able to reproduce the phenomenon during simulations. Design guidelines could be then obtained at an early stage of development of rotorcrafts improving flight safety for pilots and passengers. In this work, an upper limb musculoskeletal model using bond graphs is presented. It is then integrated in a larger aeroelastic rotorcraft bond graph model that allows simulating pilot-rotor-fuselage couplings under several flight conditions. Simulations are performed and compared to literature’s models and experimental data.“Complex Mechanical Systems Dynamics” project - Airbus Group Foundation - Arts et Metiers Paristec

Rotorcraft bioaeroelasticity using bond graphs

Dans certaines conditions de vol, les aéronefs à voilure tournante souffrent parfois de l’émergence d’oscillations indésirables, phénomènes potentiellement instables connus sous le nom de Couplages Pilote-Aéronef aéroélastiques (CPA). Ces phénomènes affectent de manière critique la sécurité et la performance des aéronefs. Par conséquent, il est important d’être capable de prédire l’émergence de tels phénomènes dynamiques, le plus tôt possible dans le processus de conception des hélicoptères. Une revue de la littérature révèle que ces phénomènes sont le résultat d’interactions entre les comportements biodynamique du pilote et aéroélastique des hélicoptères. Afin d’avoir une plus grande modularité et granularité dans le processus de modélisation de systèmes complexes, une approche par bond graphs est adoptée. Un modèle aéromécanique d’hélicoptère et un modèle neuro-musculo-squelettique d’un des membres supérieurs du pilote sont développés en bond graphs. Parmi les représentations proposées, trois sont originales, notamment afin de modéliser : des efforts aérodynamiques quasi-statiques, la liaison traînée-battement-pas entre pale et moyeu rotor, et les efforts musculaires à partir d’un modèle de Hill qui tient compte d’une boucle de rétroaction neuromusculaire. Des résultats encourageants sont obtenus lorsque l’on compare la transmissibilité, entre l’angle de manche de pas cyclique imposé par le pilote et des accélérations latérales de la cabine, calculée à partir du modèle biodynamique, et à partir des résultats expérimentaux tirés de la littérature. Un modèle du système bioaéroélastique homme-machine est linéarisé, au voisinage d’un vol stationnaire, et analysé en termes de stabilité. L’étude révèle, comme conjecturé dans la littérature, que le mode régressif de traînée peut être déstabilisé. De plus, il apparaît que le mode progressif de traînée peut également être déstabilisé lors d’un CPA sur l’axe latéral-roulis. Un critère d’analyse de la stabilité d’un équilibre d’un système dynamique à partir d’un modèle linéaire limite la possibilité de prendre en compte certains comportements non-linéaires et donc réduit l’espace de conception. Les premières pierres vers une méthode basée sur des fonctions de Chetaev sont posées, afin de déterminer si l’équilibre d’un système dynamique est instable, directement à partir d’un modèle mathématique non-linéaire de grande dimension, à un coût de calcul potentiellement intéressant. Afin d’illustrer la pertinence de la proposition, le cas de la résonance sol d’un hélicoptère est présentée.Under certain flight conditions, rotorcrafts might suffer from the emergence of undesirable oscillations, potentially unstable phenomena, known as aeroelastic Rotorcraft-Pilot Couplings (RPCs). These phenomena critically affect the safety and performance of rotorcraft designs. Therefore, there is an important interest in being able to predict the emergence of such dynamic phenomena, as soon as possible during the design process of helicopters. A review of the state-of-the-art reveals that these phenomena are the result of interactions between pilots’ biodynamics and helicopters’ aeroelastic behaviors. In order to provide more modularity and granularity in the modeling of complex systems, a bond graph based approach is used. A helicopter aeromechanical model and a pilot upper limb neuromusculoskeletal model are developed using bond graphs. Three original bond graph representations are proposed, to model: quasi-steady aerodynamic forces, lag-flap-pitch joint at blades’ roots, and a Hill-type muscle force model that accounts for muscle reflexive feedback. Encouraging results are found when comparing the pilot biodynamic model transmissibility cyclic lever angle to lateral cockpit accelerations computations to literature experimental results. A linear model of the coupled human-machine bioaeroelastic system around hover is analyzed in terms of stability. It reveals not only the regressing lag mode, as conjectured in literature, but also the advancing lag mode can be destabilized during a lateral-roll aeroelastic RPC. Furthermore, a criterion to assess the stability of the equilibrium of a dynamic system from a linear model limits the possibility to take into account nonlinear physical behaviors, reducing the design space. The first blocks towards a method based on Chetaev functions is proposed, to determine if an equilibrium is unstable, directly from its large nonlinear mathematical model, at a potentially interesting computational cost. The helicopter ‘ground resonance’ case illustrates the soundness of the proposal