<p>Detta examensarbete har utförts på Fläktwoods AB i Växjö, som producerar stora axialfläktar för olika industriapplikationer. Syftet är att öka kunskapen om fettsmorda axiella kullager genom FE analyser.</p><p>Projektet har genomförts i fem delsteg för att avgöra påverkan av en eller några få parametrar i taget. De studerade parametrarna är: elementstorlek, kontaktstyvhet, last, lagergeometri (dvs. oskulation), ickelinjär geometri och ickelinjära materialegenskaper (dvs. plasticitet).</p><p>Slutsatsen är att elementstorleken bör väljas fint nog för att ge ett jämnt resultat men grovt nog för att beräkningstiden skal vara rimlig. Kontaktstyvheten har inte stor, men tydlig, inverkan på kontakttrycket och penetrationen. Förändringar av oskulationen leder till förändringar i kontaktellipsens form medan olika laster inte påverkar formen på ellipsen, utan snarare storleken. När det handlar om plasticitet är sträckgränsen den viktigaste faktorn att beakta.</p> / <p>This thesis project was carried out at Fläktwoods AB in Växjö who produces large axial fans for different industry applications. The purpose is to increase the knowledge of grease lubricated axial ball bearings through FE analyses.</p><p>The project was executed into five sub steps to determine the influence of one or few parameters at a time. The studied parameters are: mesh density, contact stiffness, load, bearing geometry (i.e. osculation), geometrical nonlinearity and material nonlinearity (i.e. plasticity).</p><p>It is concluded that the mesh density should be selected fine enough to give a smooth result but course enough to give a reasonable calculation time. The contact stiffness has not a major, but a clear, impact on the contact pressure and penetration. Changes of the osculation lead to changes of the contact ellipse shape and applying different load level does not affect the shape of the ellipse but rather the size. When dealing with plasticity the yield strength is the most important factor to take in consideration.</p>

Dans un système de machines rotatives comme un moteur à turbine, les paliers d'éléments roulants à grande vitesse jouent un rôle important dans le support de l'arbre ou du rotor rotatif, et ont besoin d'une lubrification pour assurer leur fonction. Sauf qu'une petite quantité d'huile est nécessaire pour former le film lubrifiant élastohydrodynamique dans la zone de contact, la plus grande partie du lubrifiant reste en suspension dans l'air, formant un mélange huile/air. Ce phénomène entraîne des pertes hydrauliques parasitaires excessives lorsque les éléments roulants se translatent et tournent dans l'environnement fluide, ce qui peut constituer une partie relativement importante de la perte de puissance totale du roulement, appelée traînée d'enroulement et pertes de barattage. Pour une vitesse de rotation jusqu'à 3× 106 Ndm, la contribution de la traînée/dérive au total peut atteindre 50%. Cependant, jusqu'à présent, il existe peu d'approches utilisées directement pour l'estimation des pertes par traînage, qui ne pouvait fournir qu'une approximation plutôt grossière. Dans cette thèse, la méthode CFD est utilisée pour analyser d'abord l'écoulement autour d'un cylindre circulaire de longueur finie avec deux extrémités libres dans un espace ouvert. Ensuite, le modèle est remplacé par plusieurs cylindres circulaires en ligne pris en sandwich par deux parois plates, ce qui représente une approche simplifiée. Le fluide est ici considéré comme incompressible, représentant un fluide monophasé équivalent pour l'écoulement diphasique huile/air à l'intérieur de la cavité de palier avec des propriétés de fluide spécifiées. Les résultats indiquent que l'écoulement autour de l'élément de rouleau de longueur finie est perturbé par ses deux extrémités libres, les anneaux environnants, la cage et d'autres éléments roulants. Il est proposé une relation entre le coefficient de traînée et le nombre de Reynolds approprié pour un cylindre circulaire dans les roulements à rouleaux (1<L/D<6), ainsi qu'une formulation pour la prévision des pertes de barattage. L'écoulement diphasique huile/air à l'intérieur de la cavité de palier avec lubrification sous la course est également étudié dans ce travail. Le volume couplé de niveau de fluide (CLS-VOF) est utilisé pour démontrer la distribution du lubrifiant le long de la circonférence du palier. L'effet de divers facteurs est étudié, par ex. la vitesse d'injection d'huile, le diamètre de la buse, les propriétés de l'huile et l'angle d'injection de l'huile. La vitesse de rotation de tous les composants du palier est étudiée en particulier pour quantifier leur influence sur la fraction du volume d'huile à l'intérieur de la cavité du palier. Les résultats démontrent que non seulement la vitesse de rotation relative de l'anneau interne, mais la vitesse de la cage elle-même pourrait changer la distribution d'huile. / In a rotating machinery system like turbine engine, high speed rolling element bearings play an important role in supporting the rotating shaft or rotor, and need lubrication to insure their function. Except a small quantity of oil is needed to form the elastohydrodynamic lubricant film in the contact zone, most of lubricant remains in suspension in air, forming an oil/air mixture. This phenomenon leads to excessive parasitic hydraulic losses when rolling elements translate and rotate into the fluid environment, which may constitute a relatively large portion of the bearing's total power loss, named windage drag and churning losses. For high speed applications, i.e. for rotational speed up to 3× 10^6 Ndm, the contribution of drag/windage loss to the total one may reach up to 50%. However, so far there are few approaches used directly for drag and churning losses estimation, which could only provide a rather gross approximation. In this thesis, the Computational Fluid Dynamics (CFD) method is employed to analyze first the flow around one finite-length circular cylinder with two free ends in an open space. Then the model is changed to several in-line circular cylinders sandwiched by two flat walls, which represents a simplified approach. The fluid here is regarded as incompressible, representing an equivalent one-phase fluid for the oil/air two-phase flow inside the bearing cavity with specified fluid properties. The results indicate that the flow around the finite length roller element is perturbed by its two free ends, the surrounding rings, the cage and other rolling elements. A relationship between the drag coefficient and the Reynolds number suitable for circular cylinder in roller bearings (1<L/D<6) is proposed, as well as a formulation for churning losses prediction. The oil/air two phase flow inside the bearing cavity with under-race lubrication is also studied in this work. The coupled level-set volume of fluid (CLS-VOF) method is employed to demonstrate the lubricant distribution along the bearing circumference. The effect of various factors is studied, e.g. the oil injection velocity, the nozzle diameter, the oil properties, and the oil injecting angle. Rotational speed of all the bearing components are studied particularly to quantify their influence to the oil volume fraction inside the bearing cavity. The results demonstrate that not only the inner-ring relative rotational speed, but the cage speed itself could change the oil distribution. The results can be used for the precise lubrication design to optimate the oil distribution inside the bearing.

Detta examensarbete har utförts på Fläktwoods AB i Växjö, som producerar stora axialfläktar för olika industriapplikationer. Syftet är att öka kunskapen om fettsmorda axiella kullager genom FE analyser. Projektet har genomförts i fem delsteg för att avgöra påverkan av en eller några få parametrar i taget. De studerade parametrarna är: elementstorlek, kontaktstyvhet, last, lagergeometri (dvs. oskulation), ickelinjär geometri och ickelinjära materialegenskaper (dvs. plasticitet). Slutsatsen är att elementstorleken bör väljas fint nog för att ge ett jämnt resultat men grovt nog för att beräkningstiden skal vara rimlig. Kontaktstyvheten har inte stor, men tydlig, inverkan på kontakttrycket och penetrationen. Förändringar av oskulationen leder till förändringar i kontaktellipsens form medan olika laster inte påverkar formen på ellipsen, utan snarare storleken. När det handlar om plasticitet är sträckgränsen den viktigaste faktorn att beakta. / This thesis project was carried out at Fläktwoods AB in Växjö who produces large axial fans for different industry applications. The purpose is to increase the knowledge of grease lubricated axial ball bearings through FE analyses. The project was executed into five sub steps to determine the influence of one or few parameters at a time. The studied parameters are: mesh density, contact stiffness, load, bearing geometry (i.e. osculation), geometrical nonlinearity and material nonlinearity (i.e. plasticity). It is concluded that the mesh density should be selected fine enough to give a smooth result but course enough to give a reasonable calculation time. The contact stiffness has not a major, but a clear, impact on the contact pressure and penetration. Changes of the osculation lead to changes of the contact ellipse shape and applying different load level does not affect the shape of the ellipse but rather the size. When dealing with plasticity the yield strength is the most important factor to take in consideration.

La quête de minimisation du ratio poids-puissance, omniprésente dans l'industrie aéronautique, conduit à une plus grande souplesse structurelle des boîtes de transmission de puissance d'hélicoptères.Cette souplesse structurelle, associée aux sollicitations sévères mises en jeu, entraîne des déformations non négligeables des arbres et carters, et nuit naturellement à la tenue en service des roulements.S'il n’est pas maîtrisé, le désalignement des portées de roulements accroît fortement les efforts vus par la cage et peut conduire à sa rupture en fatigue.Le travail proposé s'intéresse à la modélisation du comportement dynamique des roulements de réducteurs aéronautiques et vise plus particulièrement à anticiper ce mode de ruine.Le modèle développé permet d'estimer les sollicitations de la cage en fonctionnement.Ces informations, précieuses aux ingénieurs, permettront de mieux maîtriser, et donc d'optimiser le processus de dimensionnement des roulements. / The quest for minimizing the power to weight ratio, omnipresent in the aircraft industry, has led to greater structural flexibility of helicopter gearboxes.This increasing flexibility combined with the severe loads which it involves, causes significant strains on shafts and housings, and may be detrimental to rolling bearing service life expectancy.An unchecked misalignment of bearing seats greatly increases cage stresses and it may cause its premature fatigue failure.The present work focuses on modeling the dynamic behavior of rolling bearings of aeronautical gearboxes and it specifically anticipates this failure mode.The model developed is able to estimate cage stresses in operation. This information is valuable to engineers, it allows a better control and thus an optimization of the rolling bearings design process.

<p dir="ltr">Rolling element bearings (REBs) are common components in rotating equipment. They are used to carry loads and allow for rotation and misalignments with minimal friction. There exists a wide variety of ball and roller bearings that are suited for a wide variety of applications. All varieties of REBs operate with the same fundamental principles: force transferred from the shaft is applied to the inner race of a bearing, distributed among the rolling elements, and passed on through the outer race to the bearing housing. Load distribution among the rolling elements and the dynamic performance of the bearing is dependent on the bearing’s specifications and operating conditions. Bearing-housing and inner race-shaft fit classifications also control the bearing radial internal clearance (RIC), which eventually affects the bearing performance and load transferred to the housing.</p><p dir="ltr">This thesis experimentally and analytically investigates the load distribution and dynamic performance of rolling elements and investigates roller slip, tilt, and skew in a spherical roller bearing (SRB) under various combinations of loads and speeds. In order to have better insight into the effect of flexible housing and shaft on load distribution and dynamics of REBs, it was experimentally investigated the variation of inner race-shaft and outer race-housing interfaces on load and pressure maps at the bearing-housing interface for four different varieties of rolling element bearing: deep groove ball bearings, angular contact ball bearings, cylindrical roller bearings, and spherical roller bearings. Moreover, an integrated rotor-bearing housing system model developed to examine the behaviors of the rotor, bearing, and housing operating under various conditions.</p><p dir="ltr">In order to gain a deeper understanding of the dynamic behavior of REBs, a full six degree of freedom SRB dynamic model was developed in MSC ADAMS software. C++ based ADAMS/Solver subroutines, called dynamic bearing model (DBM), were developed and incorporated in ADAMS to compute reaction forces and moments in a rolling element bearing. DBM is based on the discrete element method (DEM), which assumes each of the bearing elements (i.e., rolling elements, cage, inner race, and outer race) to be a rigid body with six degrees-of freedom (DOF) in a three-dimensional space. A novel test rig (spherical roller bearing test rig, SRBTR) was also designed and developed to investigate load distribution and roller slip, tilt, and skew in an SRB. The test rig utilized a double-row SRB and was designed to allow for direct visual access to each row using a high-speed camera. The dynamic behavior of the rollers was corroborated with the developed analytical model. The experimental and analytical results indicate that the roller tilt angle increases with axial load, remains constant with speed, and decreases with increasing radial load when the roller is located in the load zone. Furthermore, roller skew in the load zone increases with axial load and shaft speed; however, it decreases with the radial load. The results indicate that when the radial-to-axial load ratio is greater than 4, roller tilt and skew are minimized. Due to roller intermittent slip and roller cage pocket collision in the unload zone, tilt and skew become unpredictable. The magnitude of the tilt and skew in the unload zone is directly related to the roller-race and roller-cage pocket clearances, respectively. Another test rig (pressure mapping test rig, PMTR) was designed to solely investigate how bearing-housing and inner race-shaft interfaces affect the load distribution in REBs. Thin film pressure sensors were utilized and placed around the perimeter of the test bearings inside of a housing to experimentally evaluate the pressure distribution between REBs and a housing under different loads and bearing-shaft and bearing-housing interfaces. Pressure map results were used to evaluate the effect of radial internal clearance on the load distribution of different bearing types. Pressure map results confirmed that the amplitude of load variation reduces with the bearing internal clearance. The thin film sensor system was also used to investigate the circumferential load distribution on the housing.</p><p dir="ltr">Previous ADAMS bearing models have assumed the bearing outer race to be fixed to the ground and the bearing inner race to be attached to a rigid shaft. In order to develop a more realistic and versatile bearing simulation tool, ADAMS bearing models were combined with flexible housings and rotor. To achieve an integrated rotor-bearing housing system model, the ADAMS bearing model was coupled through a set of interface points using component-mode-synthesis (CMS) for the rotor and housing model. The bearing outer races were discretized into multiple nodes to compute the force and deformation at the bearing housing conformal contact as well as to minimize the computational requirements associated with the conformal contact problems. The integrated model was then utilized to investigate the effects of rotor flexibility in the bearing rotor system and the effect of bearing clearance and housing clearance on bearing dynamics. It was demonstrated that the flexibility of the rotor has a significant effect on bearing element motion and dynamics. The results also indicated that depending on the bearing type, the shaft deflection can induce a moment within the bearing that is not readily identifiable from elementary theory. The results showed that the flexible housing undergoes deformations that create ovality in the bearing housing, thus affecting bearing dynamics. The model was also used to investigate bearing performance in a miniature wind turbine main shaft, utilizing a combination of SRB and cylindrical roller bearing (CRB) ADAMS models. Results suggest that the axial-to-radial load ratio should be less than the tangent of the SRB contact angle to avoid premature failure due to rollers sliding in the SRB as well as detrimental parallel misalignment in the CRB.</p>