This paper presents a modelling approach for predicting the internal dynamic behaviour of ball bearings under high moment loads. This type of loading is a specific feature of helicopter main gear boxes because of special design rules and the high structural flexibility of such systems. The ball bearing model proposed here is not limited to planar systems and incorporates several different phenomena such as contact deformation, elastohydrodynamic contact, internal clearance and cage run-out. The cage-race interaction is treated as a hybrid short journal model, which ensures continuity of the contact force at the transition from the hydrodynamic to metal-to-metal regime. In the dynamic analysis of such a severely loaded bearing, the dependence of the shaft-to-inner-ring force on inner race position cannot be neglected. An equivalent viscoelastic hinge joint has been developed, it produces an additional force that represents the overall rigidity of the system. The stiffness parameters of the joint are identified using global finite element simulations. A ball bearing loaded with two different moments is chosen as an example. Relevant results concerning the internal dynamic behaviour are given. The predicted cage trajectory has been compared to experimental observations, and good agreement has been found.

-De plus en plus, les concepteurs utilisent des méthodes avancées de calcul, pour optimiser les performances des systèmes mécaniques. Ce constat est d'autant plus vrai dans le milieu aéronautique où le rapport poids puissance doit être le plus faible possible. Certains logiciels de CAO (CATIA, SO-LIDWORKS, PRO ENGINEER, etc.) off rent la possibilité d'eff ectuer des calculs de dimensionnement. Néanmoins, ce type d'outil ne permet pas, à ce jour, d'estimer facilement les pressions de contact entre deux pièces. Cet article présente les différentes méthodologies utilisables dans un environnement CAO pour le calcul des pressions de contact dans les roulements à pistes intégrées de boîte de transmission aéronautique. Ces méthodologies sont analytiques (théorie de Hertz), numériques (éléments-finis) ou hybrides. Ces différentes approches sont analysées et comparées suivant les critères de précision, de temps de calcul et de leurs aptitudes à s'intégrer dans un processus de conception industriel. A partir de cette analyse, il sera proposé une méthodologie de calcul des pressions de contact.

International audienceThis paper presents a methodology to calculate the contact pressures on the rolling elements and other significant parameters applicable to raceway bearings used in aeronautical helicopter gearboxes. The mechanism is modelled by a hybrid method where the parts are decomposed in finite elements and the bearings are described by substitution features. This hybrid method accounts for the flexibility of the parts as well as geometrical defects. In this method, the contacts between rolling element and raceways are solved analytically. The Hertz contact theory is used to calculate the contact behaviour. The geometrical defects are included in the model thus changing the value of local displacements. Our paper shows the impact of the flexibility of the different mechanical parts and its geometrical defects, on the behaviour of the bearing raceways. Three most important conclusions are brought to the fore. First the load distribution in the bearing is modified by the flexibility of the parts and the bearing raceways. Second, positioning defects in our assemblies have insignificant effect on the bearing service life. Third orientation defects increase the pressure in roller bearings and the balls orbital speed variation in ball bearings

-This work presents the dynamic modeling of ball bearing which uses multibody dynamic formalism. Such formalism allows immediate integration of the model in dynamic simulations of helicopter main gear boxes. Ball bearing is considered non-lubricated in order to predict its behavior in case of lubrication system failure. Rolling contacts are treated with the method proposed by Kalker. This approach is based on polynomial approximation of relative displacement on the contact ellipse. For low computational cost and without any spatial discretization, it gives a good estimation of tangential traction and creep. Also, a regularization of the Kalker linear creep theory is proposed. It is used here to facilitate the global convergence of the Newton iterative process. It is well suited for multibody dynamic simulations which do not need a very fine treatment of rolling contact. A numerical example of a ball bearing under thrust load is presented. Key words: Multibody dynamic / Ball bearing / Rolling contact / Kalker creep theoryRésumé -Cetteétude présente un modèle dynamique de roulementà billes utilisant le formalisme de la dynamique multicorps. Ce dernier permet l'intégration immédiate du modèle dans les simulations dynamiques de boîtes de transmission de puissance d'hélicoptères. Le roulement est considéré non lubrifié afin de prédire son comportement en cas de défaillance du système de lubrification. Le modèle mis en place pour les contacts roulants pseudo-ponctuels, issu des travaux de J.J. Kalker, se fonde sur une approximation polynomiale du déplacement relatif sur l'ellipse de contact. Ce dernier fournit, pour un temps de calcul réduit et sans discrétisation spatiale, une bonne estimation des efforts et micro-glissements au contact. Aussi, une régularisation de la théorie linéaire de Kalker est proposée. Elle est utilisée pour faciliter la convergence globale de l'algorithme de Newton. Elle estégalement bien adaptée aux simulations dynamiques multicorps qui ne nécessitent pas une modélisation très fine du contact roulant. Un roulementà billes soumisà un effort axial est présenté comme exemple numérique.

66th General Assembly of the International-Academy-for-Production-Engineering (CIRP), Guimaraes, PORTUGAL, AUG 21-27, 2016International audienceThis article presents new tools developed to improve the geometrical corrections required on roller bearings of Helicopter gearboxes suffering from heavy deflection. A complex non-linear finite element model of the whole gearbox is firstly implemented to identify the deflection of inner and outer raceways under operational loads. The computed misalignment is then used as an input to predict and check the contact pressure edge effects occurring in the contact area and iteratively optimize the roller shape. Several approaches are tested based either on Boussinesq's potential theory or on specific FEM calculations. They permit increasing the service life of the bearings while reducing the overall gearbox development lead-time. (C) 2016 CIRP

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In trying to incessantly reduce gearboxes weight, designers can negatively impact the service reliability, particularly in the aeronautic industry, where a weight reduction is often linked with stiffness decrease. Looking for weight savings, gearbox casings are classically made of magnesium or aluminium alloy. In addition, helicopter gearbox design is included the integration of several functions within the same part (like the shafts which gather one or more gears, splines and integrated bearings raceways). These particularities in the design are requiring some specific methodologies for Power Transmission bearing modelling. In this paper, a comparison between tests and simulations results of the aforementioned gearboxes is presented. The first section of the article focuses on the helicopter gearbox description and associated finite elements modelling. Then, the second section provides a comparison between the experimental observations with the results of both FEM simulation and classical analytical simulation. This comparison demonstrates the interest of using FEM simulation to analyze gearboxes behaviour.

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