Analysis of collocated feedback controllers for four-bar planar mechanisms with joint clearances

International audienceThis article presents an analysis of two-dimensional four-bar mechanisms with joint clearance, when one joint is actuated by collocated open-loop or state feedback controllers (proportional-derivative, state feedback linearization, passivity-based control). The study is led with numerical simulations obtained with a projected Moreau-Jean's event-capturing algorithm. The contact/impact model uses kinematic coefficients of restitution, and Coulomb's friction. The focus is put on how much the performance deteriorates when clearances are added in the joints. It is shown that collocated feedback controllers behave in a very robust way

Analysis of four-bar planar mechanisms with joint clearances

International audienceThis work deals with four-bar planar mechanisms with clearances at the joints, which induce unilateral constraints, impacts and friction, rendering the dynamics nonsmooth. The objective is to determine sets of parameters (clearance value, restitution coefficients, friction coefficients) such that the system's trajectories stay in a neighborhood of the trajectories of mechanism with no clearance. The analysis is based on numerical simulations obtained with the projected Moreau-Jean time-stepping scheme

Simulation and experimental response of four-bar mechanism with tolerance stack

An Equivalent Contact Stiffness (ECS) approach is proposed in this article to estimate the precise contact parameters for a revolute joint. Estimated contact parameters are used as input variables for the MBD simulation of a four-bar mechanism with tolerance stack. Simulations were carried out using Impact Force Method (IFM) and Restitution Method (RM) in MSC ADAMS. An experimental setup of the four-bar mechanism is developed with a unique feature to measure the angular velocity of the follower with respect to the crank position. The effect of tolerance stack on the angular velocity of the follower is investigated experimentally to validate the MBD simulation. The angular velocity of coupler and rocker is increased by 15.69% and 27% respectively due to tolerance stack. MBD analysis using the ECS approach provides accurate and reliable results in absence of experimental contact data. This work shall facilitate the designers to simulate the actual behaviour of the mechanism prior to prototype

Analysis of four-bar planar mechanisms with joint clearances

International audienceThis work deals with four-bar planar mechanisms with clearances at the joints, which induce unilateral constraints, impacts and friction, rendering the dynamics nonsmooth. The objective is to determine sets of parameters (clearance value, restitution coefficients, friction coefficients) such that the system's trajectories stay in a neighborhood of the trajectories of mechanism with no clearance. The analysis is based on numerical simulations obtained with the projected Moreau-Jean time-stepping scheme

3D Revolute Joint with Clearance in Multibody Systems

International audienceThe aim of this paper is to understand the influence of radial and axial clearance in the revolute joints on the overall performance of a circuit breaker. A circuit breaker mechanism is made of seven links, seven revolute joints with clearance in both radial and axial direction, four unilateral contacts with friction, and it has forty-two degrees of freedom. The Moreau-Jean nonsmooth contact dynamics (NSCD) numerical method is used to perform the simulations. The numerical results are validated by careful comparisons with experimental data

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

"Available online 19 December 2017"A comprehensive survey of the literature of the most relevant analytical, numerical, and experimental approaches for the kinematic and dynamic analyses of multibody mechanical systems with clearance joints is presented in this review. Both dry and lubricated clearance joints are addressed here, and an effort is made to include a large number of research works in this particular field, which have been published since the 1960′s. First, the most frequently utilized methods for modeling planar and spatial multibody mechanical systems with clearance joints are analyzed, and compared. Other important phenomena commonly associated with clearance joint models, such as wear, non-smooth behavior, optimization and control, chaos, and uncertainty and links’ flexibility, are then discussed. The main assumptions procedures and conclusions for the different methodologies are also examined and compared. Finally, future developments and new applications of clearance joint modeling and analysis are highlighted.This research was supported in part by the China 111 Project (B16003) and the National Natural Science Foundation of China under Grants 11290151, 11472042 and 11221202. The work was also supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersio

Numerical modelling of mechanism. Effect of clearance, deformation and multiple impacts in joints

La simulation de la dynamique des systèmes multicorps avec contact frottant joue un rôle important dans un grand nombre d'applications industrielles.Elle est même devenue une partie importante du développement de nouveaux produits, de la vérification et même de l'optimisation de leur conception pour améliorer les anciens produits.Les travaux présentés dans cette thèse font partie d'une collaboration entre l'équipe BiPoP, équipe de recherche de l'INRIA Grenoble, et Schneider Electric.Le but principal de ces travaux est de comprendre l'influence du jeu dans les articulations, ainsi que l'influence du dimensionnement industriel et les tolérances géométriques sur lecomportement global des liaisons mécaniques. Plus spécifiquement nous avons étudié le mini-disjoncteur C-60 (domaine dans lequel la sécurité humaine doit être garantie), pour répondre à cette demande de robustesse, tout en respectant les tolérances sur les pièces constituant le disjoncteur C-60.Le jeu radial dans les articulations pivot est une source de variabilité dans les conditions initiales du système, mais également dans la dégradation de ses performances.La dégradation du système se présente toujours sous forme de vibrations, de bruit, de forces de réactions très grandes dans les articulations, de mauvaise précision et exactitude de la sortie.Le but est d'étudier l'influence des conditions initiales et le déplacement hors-plan, ainsi que l'effet de polarisation en trois dimensions.Un objectif supplémentaire est de développer un banc d'essai virtuel efficace pour reproduire les mesures obtenues sur un vrai banc d'essai en laboratoire, en utilisant la plateforme logicielle SICONOS qui utilise la méthode NSCD (Non Smooth Contact Dynamic) introduite par J.J. Moreau et M. Jean.Le schéma NSCD a prouvé son efficacité numérique: il est capable de traiter des problèmes de complémentarité, le contact ainsi que les impacts et les lois de frottement multivaluées.Le but est de comprendre quelle est la meilleure description géométrique pour simuler de très petits jeux.L'étude complète est divisée en deux parties. La progression part du cas planaire pour arriver au cas spatial, et la complexité suit le même chemin.Dans le cas planaire, on analyse un mécanisme à quatre barres avec du jeu quand une des articulations est commandée en boucle ouverte, ou par retour d'état linéaire ou non-linéaire(PD, linéarisation par retour d'état, ou commande passive).L'accent est mis sur la quantification de la dégradation des performances quand du jeu est ajouté dans les articulations. On montre alors que les commandes par retour d'état se comportent de façon robuste.Dans le cas spatial, le mécanisme C-60 est analysé précisément pour explorer les possibilités de relaxer les tolérances industrielles sur les pièces sans compromettre ni les performances ni la sécurité. L'influence de l'entrée, du modèle et des incertitudes numériques sur le modèle C-60 est étudiée.L'influence induite par le jeu et le coefficient de frottement dans les articulations sur la performance du produit est étudiée.Pour valider le modèle de simulation, des expériences sont effectuées sur des prototypes d'essai et les résultats sont comparés avec les simulations numériques.Nous avons trouvé une bonne correlation entre les résultats numériques et expérimentaux.L'analyse statistique~(analyse du pire cas, et par des simulations basées sur la méthode de Monte-Carlo) a été réalisée pour trouver la dispersion des conditions fonctionnelles.En plus des variations dimensionnelles, la tolérence aux variations géométriques comme la forme, l'orientation et la position, est analysée.Ce travail de recherche devrait aider les concepteurs à simuler le comportement du système mécanique avec une articulation de révolution imparfaite,depuis l'étape de conception préliminaire jusqu'à la fin de la conception pour avoir une amélioration significative de la planification et du budget.Dynamic simulation of multibody systems with unilateral contact and friction plays an important role in a wide range of industrial applications. It has become an integral part of new product development, verification/optimization of the design and to enhance the old products.This work is a part of collaboration between the BiPoP research team of INRIA Grenoble and the Schneider Electric company.The main goal of this thesis is to understand the influence of clearances in the revolute joints on the overall behaviour of the linkage mechanisms and specifically on the C-60 miniature circuit breaker where human safety must be guaranteed.In other words, the objective is to address the robustness of the C-60 breaker with respect to the production tolerances, which areexpressed in the form of dimensional and geometrical variations on the parts. These variations are the source of clearance in the joints of the mechanism.The radial clearance in the revolute joints is a source of variability in the initial conditions of the system and also the degradation of the system's performance. The degradation of the system isalways in the form of vibration, noise, very high reaction forces at the joints.The aim is to study the influence of initial conditions and the out-of-plane motion, so the polarization effect in three dimensional case.Another objective is to develop the time efficient virtual test bench to reproduce the measurements of real test bench in the laboratory using the open-source simulation software SICONOS which is based on the NonSmooth Contact Dynamic method (NSCD) introduced by J.J. Moreau and M. Jean.The NSCD scheme is proven to be a quite efficient numerical method, capable of handling complementarity conditions, as well as impacts and set-valued friction laws.The goal is to understand what is the most appropriate geometricdescription which allows to simulate very small clearances.The complete study is divided in two main sections.The progress through these partsgoes from the planar to the spatial case, the complexity follows the same advance.In the planar case, a four-bar mechanism with joint clearance, when one joint is actuated by collocated open-loop or state feedback controllers (PD, statefeedback linearization, passivity-based) is analysed. The focus is put on how much the performancedeteriorates when clearances are added in the joints. It is shown that collocated feedback controllersbehave in a robust way.In the spatial case, the C-60 mechanism is analysed precisely to explore the possibilities to relax the manufacturing tolerances on the parts withoutany compromise on either performance or the human safelyThe influence of the input, model and numerical uncertainties on the C-60 model is studied. The joint-wise influences of the clearance and coefficient of friction on theproduct performance are studied.To validate the simulation model, experiments are carried-out on the prototype samples and the results are compared with the simulations.We found quite good correlation between the virtual and experimental results.A statistical analysis~(worst-case and Monte Carlo simulation) has been carried out to find out the dispersion of the functional conditions.In addition to dimensional variations, the geometrical variations such as form, orientation and position tolerances are also analyzed.This research work shall help the designers to simulate the real time behaviour of the mechanical systems with the imperfect revolutejoint from the pre-design stage till the end of the design, to have good improvement on schedule and budget

Multibody systems with 3D revolute joints with clearances: an industrial case study with an experimental validation

International audienceThis article is devoted to the analysis of the influence of the joint clearances in a mechanism of a circuit breaker, which is a forty-two degrees of freedom mechanism made of seven links, seven revolute joints, and four unilateral contacts with friction. Spatial (3D) revolute joints are modelled with both radial and axial clearances taking into account contact with flanges. Unilateral contact, Coulomb's friction and Newton impact laws are modeled within the framework of nonsmooth mechanics without resorting to some regularizations or compliance/damping at contact. The nonsmooth contact dynamics method based on an event-capturing time–stepping scheme with a second order cone complementarity solver is used to perform the numerical integration. Futhermore, the stabilization of the constraints at the position level is made thanks to the stabilized combined projected Moreau–Jean scheme. The nonsmooth modeling approach together with an event–capturing time–stepping scheme allows us to simulate, in an efficient and robust way, the contact and impacts phenomena that occur in joints with clearances. In particular, comparing with the event–detecting time–stepping schemes, the event–capturing scheme enables to perform the time–integration with large number of events (impacts, sliding/sticking transitions, changes in the direction of sliding) and possibly with finite time accumulations with a reasonable time–step length. Comparing with compliant contact models, we avoid stiff problems related with high stiffnesses at contact which generate some issues in contact stabilization and spurious oscillations during persistent contact periods. In the studied mechanisms of the circuit breakers, the numerical methods deals more than seventy contact points without any problems. Furthermore , the number of contact parameters is small : one coefficient of restitution and one coefficient of friction. Though they are sometimes difficult to measure accurately, the sensitivity of the simulation result with respect to contact parameters is low in the mechanism of the circuit breaker. It is demonstrated that this method, thanks to its robustness and efficiency allows to perform a sensitivity analysis using a Monte Carlo method. The numerical results are also validated by careful comparisons with experimental data which show a very good correlation

Influence of imperfect joints and geometrical tolerances on a circuit breaker dynamics

International audienceThe aim of this paper is to understand the influence of clearances in the kinematic joints, dimensional and geometrical tolerances associated with the parts, on the performance of a circuit breaker mechanism in the trip operation. Operating mechanism and trip unit are the essential components of a miniature circuit breaker. The operating and trip mechanisms are made of ten parts with revolute and cylindrical joints with clearance, and ve unilateral contacts with friction. This mechanism is based on quick-make and quick-break principle. The Moreau-Jean nonsmooth contact dynamics (NSCD) numerical method is used to perform the simulations. The numerical results are validated by careful comparisons with experimental data