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Due to their properties, ceramic materials can improve both reliability and efficiency of rolling bearings. Most of the studies have investigated the power losses and temperatures of ball bearings with balls made of silicon nitride (Si3N4) versus steel ones. This study thus focuses on tapered rollers. Thanks to experimental and numerical means, the thermal behavior of tapered roller bearings is investigated for both steel and silicon nitride rollers. Various operating conditions (rotational speed, oil flow rate and oil temperature) are tested to allow the comparison of the behavior of both bearing set-ups (full-steel and hybrid). A thermal model is developed according to the thermal network method and is validated thanks to experimental results. It is then used to analyze behaviors observed during experiments, related to thermal exchanges and power losses. The effect of changing the mechanical and thermal properties of the roller material is investigated.

Accurate modelling of friction coefficient is of primary importance in efficiency, vibration and failure analyses of enclosed gear drives. After showing the influence of surface/lubricant interactions on friction, the authors used a semi-empirical model which can take all these aspects into account. Lubricant is modelled as an Eyring–Reynolds fluid and rough surfaces are described with two parameters via a stochastic approach. A specific two-disc machine is used to perform series of friction measurements on smooth and rough discs. Smooth discs allow to operate under full film lubrication and to measure a reference shear stress of lubricant, whereas rough discs reproduce gear tooth roughness and generate a representative value of friction on asperities. The purpose of this present paper is to describe calculations of this physical-based friction coefficient model and to present the experimental process. On the basis of new results, the impact of a surface finishing process is assessed as well as the consequence of calculating friction coefficient based on oil injection instead of local bulk temperature.

During their lifetime, gears may undergo starved lubrication operating conditions. Starvation has an impact on friction between gears and leads to modified gearbox efficiency. In this article, lubr...

In the present study, some measurements have been conducted on a dedicated test rig to investigate rolling element bearing thermal behaviour. This test rig makes possible the determination of the tested rolling element bearing power losses through the resistive torque measurement. Some thermocouples are located on fixed parts of the system (housing, rolling element bearing outer ring) and others on rotating parts (rolling element bearing inner ring and shaft) via a telemetry system. A deep groove ball bearing, whose pitch diameter is equal to 85 mm, has been tested under oil jet lubrication for different operating conditions. Measurements of the penetration ratio, defined as the proportion of oil actually entering the rolling element bearing versus the oil injected, have also been conducted. An extended thermal network of the test rig has been established to enable a closer understanding of the rolling element bearing inner thermal behaviour. Based upon the first principle of thermodynamics for transient conditions, the studied system is divided into lumped elements at uniform temperature connected by thermal resistances which account for conduction, radiation and convection. Convection within the rolling element bearing depends on the amount of oil in the oil–air mixture known as the volume fraction. At specific test conditions, the developed model found good agreements with experiences for a given oil volume fraction of 15%. This value of volume fraction leads to an adapted formula for volume fraction in the case of jet lubrication which includes the measured penetration ratio.

Planetary gears are used in several applications given that they provide high reduction ratio in a compact size. Two kinds of lubrication are used in these applications: injection or splash lubrication. In case of splash lubrication, the authors already highlighted the importance of the centrifugal effects leading to the formation of an oil ring inside the reducer, therefore giving a method to compute churning power losses. In this paper, another flow regime is underlined when centrifugal forces are not sufficient to turn the oil sump into a ring. In addition to this observation, an in-depth analysis is given regarding the dependence of the churning power losses with operating conditions and oil characteristics.

In the present study, no-load losses of different splash lubricated spiral bevel gears were measured. The authors used a specific test rig, and a set of gears, to investigate churning losses at higher tangential speeds: up to 60 m/s. An uncommon behavior of the drag torque was highlighted: the torque increased with the rotational speed until a local maximum was reached; then the torque decreased and a local minimum was noticed; at higher rotational speed the torque increased. The torque decrease seems to be linked with a windage phenomenon, which becomes non-negligible at such speeds. In this work, efforts were made to characterize this reduction of gear immersion depth in order to be able to predict no-load losses. It was found that the evolution of oil immersion was linked to a Froude number. Finally a new analytical model of no-load losses was developed for churning losses combined with windage effects. This formulation takes into account several parameters such as rotational speed, gear immersion depth, oil properties, and gear geometrical parameters.

In high-speed rolling element bearings, the drag forces can be prominent and it is demonstrated in this investigation that the classical models may not be appropriate for correctly estimating this ...

In this paper, an experimental investigation on a FZG test rig is presented. The proposed approach aims to at highlight the influence of micropitting on power losses and temperatures in this geared system. Micropitting has been gradually developed on the gear pair by applying increasing load levels. The influence of this defect on power losses and temperatures has been evaluated with specific characterization tests performed alongside micropitting growth. The modification of the gear surface roughness was monitored during these tests. This study shows power loss and oil temperature increase due to micropitting development. Furthermore, it is possible to correlate power loss and temperature variations to surface feature measurements.

Oil sump lubrication is commonly used in gearboxes. When considering consistent speeds, oil immersion is usually set to low level in order to reduce associated power losses. This configuration is already used in some parts of helicopter mechanical transmissions, and it is under consideration as a lubrication solution for future electric powertrain where gearbox input speeds may be very high. The gear drag power losses are generally evaluated from either a churning power loss model for classic oil sump lubrication or a windage power loss model for oil jet lubrication. One may thus wonder how to estimate drag losses when considering a gear that only a small part is immersed. In this study, the authors investigate the transition between churning and windage phenomena for a spur gear. A series of torque measurements on a single spur gear rotating in an oil bath at numerous oil immersion levels have been carried out. Based on these results, a criterion to indicate which power loss model to use is proposed.

This study aims to implement multi-objective optimization of a gear unit in order to minimize the power loss and the vibrational excitation generated by the meshing, via a multi-scale approach that extends from gear contact to the complete transmission. All these indicators are closely linked to the macro and micro-geometry definition of the gear pair. The optimization is carried out using a genetic algorithm, namely the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). The design variables chosen for the problem are the pressure angle and the helix angle, as macro-geometry characteristics of the gear, and/or the length and the amount of tooth profile modifications, as micro-geometry characteristics of the gear. Constraints are imposed in order to not exceed a maximum bending stress at the tooth root of the gear and to not fall below a minimum total contact ratio. From the results obtained, it is found that the multi-objective optimization with both micro and macro-geometry parameters simultaneously gives different results than those obtained with macro-geometry first and then micro-geometry parameters. In order to study the importance, or not, to take into account the complete gear unit, a comparison is made between the local power loss generated by gear tooth friction and the total power loss in the single stage gear unit in terms of design variables values.

Literature agrees that thermal effects have a great influence on friction. However, the heat flows and the thermal behaviour of test rigs used to characterize friction coefficient are largely dependent on their architecture. As a consequence, some discrepancies can be noted between the frictional responses measured by different test benches. Therefore, a thermal model of a twin-disc machine has been developed using the thermal network methodology. This model allows thermal analyses of the traction tests performed with this twin-disc machine. The results reveal that the disc bulk temperature has a significant impact on friction coefficient. Some scuffing experiments are also studied thanks to this numerical model, and a thermal interpretation of classical scuffing criteria is proposed.

International audience; Gear unit condition monitoring is a key factor for mechanical system reliability management. When they are subjected to failure, gears and bearings may generate excessive vibration, debris and heat. Vibratory, acoustic or debris analyses are proven approaches to perform condition monitoring. An alternative to those methods is to use temperature as a condition indicator to detect gearbox failure.The review focuses on condition monitoring studies which use this thermal approach. According to the failure type and the measurement method, it exists a distinction whether it is contact (e.g. thermocouple) or non-contact temperature sensor (e.g. thermography). Capabilities and limitations of this approach are discussed. It is shown that the use of temperature for condition monitoring has a clear potential as an alternative to vibratory or acoustic health monitoring.

Rolling element bearing is an essential component in mechanical transmission because it reduces friction between two rotating parts. Two main approaches to evaluate power losses are proposed in literature: (i) global engineering models using few input data; (ii) local models which are more accurate but need much more information on rolling element bearing geometry. Based on thermal network approach, an intermediate model is developed in this study. This new model allows obtaining lumped information (temperature of rings) with a minimum of input data (external geometry only) and by using global power loss models. This intermediate model is developed for angular contact ball bearing under oil jet lubrication for high speed application. Thermal network results are compared with experimental findings.

A thermomechanical model of the FZG test rig is presented. The numerical model is based on the thermal network method and takes into account power losses due to tooth friction, rolling element bearings (REBs), oil churning, and shaft seals. Some measurements underline that REB rings run at different temperatures. To investigate this difference, several REB models are proposed and compared to measurements. Their influence on the global thermal behavior of the gear unit is discussed and analyzed.

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International audience; This paper investigates the windage power losses generated by helical gears rotating in pure air based on experimental results and a computational fluid dynamic code. It is found that the simulated flow patterns are totally different from those calculated for spur gears and that both tooth face width and helix angle are influential. The windage losses derived from Dawson’s and Townsend’s formulae are critically assessed using computational fluid dynamic results thus highlighting the limits of a unique formulation for accurate windage loss prediction. Finally, an analytical approach is suggested which gives good results providing that the flow rates at the boundaries of the inter-tooth domains can be estimated.

In order to use electric motors which run up to 40,000 rpm in future automotive applications, this study aims to experimentally investigate if splash lubrication technique is worth considering for high-speed gears, i.e., for tangential gear speed up to 60 m/s. To this end, a specific test rig has been used to operate a single spur or helical gear in various operating conditions (lubricant, oil sump volume, temperature, etc.). Churning loss is measured and, as the fraction of air in the lubricant (namely, oil aeration) can be influential on this source of dissipation, a specific sensor is also employed for online monitoring of oil sump aeration. By inserting some moveable walls in the gearbox, it is demonstrated that churning losses and oil aeration can be significantly reduced by mounting these flanges at an appropriate distance to the gear lateral faces. Based on dimensional analysis, an engineering criterion is proposed to properly choose the clearance between the tested gear and the flanges.

In high-speed rolling element bearings the drag force generated by the motion of the balls in an air–oil mixture is frequently taken into account using the results for a sphere in an infinite medium. This approach is surprising because important interaction between the flows around the balls may occur. The drag coefficient value should be then adjusted to the configuration that is observed in a rolling element bearing (REB). In this article, a computational fluid dynamics code is applied to simulate three configurations: one single sphere, two spheres in tandem, and a set of spheres that are aligned along the air flow. It can be seen that both the flow pattern around one sphere and its drag coefficient are modified when placing another sphere in its vicinity. Furthermore, in REB configuration the drag coefficient value is far from the one observed when the obstacle is isolated and mainly depends on the space between the obstacles.

International audience; In this paper a computational fluid dynamics (CFD) code is applied to three-dimensional simulations of windage power loss generated by spur gears rotating in air. Emphasis is placed on the simplification which can be made in the numerical approach in order to gain cost and time needed for reaching a converged solution when using both fine mesh and important angular velocity. It appears that the similarity of the flows which are observed in the vicinity of both gear and disk sides is helpful. It is finally possible to compute the flow pattern near the teeth without simulating the contribution of the sides when appropriate boundary conditions are applied at the inlet of a truncated computational domain. The predictions of windage power losses using this original method are satisfying.

International audience; In rolling contact fatigue (RCF), failure mechanisms are known to be very sensitive to material microstructure. Yet, among the different numerical models developed to predict the RCF life, few models use a microstructure representation. A granular cohesive finite element model has been developed to simulate progressive damage of a structure subject to RCF and to investigate failure initiation mechanisms. This paper focuses on the implementation of crystal elasticity in the model. The numerical analysis of a representative volume element (RVE) validates the use of cubic elasticity to represent crystal behavior. The influence of the RVE size and the influence of boundary conditions applied on the RVE are evaluated in the finite element approximation framework. As regards the implementation of cubic elasticity in the RCF model, the generation of stress singularities at triple junctions is first highlighted. Then the average value of the intergranular shear stress is proved to be mesh size independent and therefore can be used as damage criterion. Finally, the influence of crystal elasticity on micro-cracks distribution is presented.

International audience; A thermal model of a back-to-back gear test rig relying on a network approach is presented in which the predictions of temperatures and power losses are coupled. The numerical findings are in good agreement with the measurements for transient regimes on a FZG test rig and it is demonstrated that the proposed simulation is reliable. A number of results are presented which illustrate the influence of the pinion and gear immersion depths. It is found that, in certain conditions, the classic isothermal method for estimating integral temperatures is highly questionable because the actual bulk temperature can substantially deviate from that of the oil sump. The practical consequences in terms of scuffing capacity are emphasised.

An investigation of heat transfer between a flow and a horizontal non-circular slender cylinder is presented in this article. Both experimental and numerical approaches are considered here. When using identical cylinders and free-stream velocities, a comparison between experimental data and numerical estimation emphasizes the shear stress transport k–ω turbulent model associated with fine mesh near wall to be appropriate for estimating an average value of heat transfer coefficient in the present configuration. From a numerical parametric investigation, which is based on the latter approach, two formulations of heat transfer are to be considered as thickness does not have a real influence in heat transfer for low Reynolds numbers, whereas for higher values, both thickness and width participate in heat transfer.

A new method is proposed to control the evaporator superheat with an electronic expansion valve. The conventional proportional-integral-derivative (PID) control with invariable parameters cannot show good performance because of the variation of refrigeration unit parameters under disturbances. To solve this problem, this paper presents a method for the use of predictive functional controllers (PFCs) on superheat of an evaporator. This method is based on a physical model of the appliance studied to allow calculation of parameters needed for the use of PFCs. The control system created is incorporated into an industrial programmable logic controller and used for experiments on a refrigerating machine containing a shell and tubes evaporator with R410A as refrigerant fluid. The comparison between the two types of controller, i.e. PID and PFC, indicates that superheat may be more efficiently controlled by using the latter type of controller: the setting value is only slightly exceeded, there are only small oscillations of measured superheat, and the energy efficiency of the refrigeration unit may be improved.

Colloque avec actes et comité de lecture. Internationale.; International audience; Un modèle thermo mécanique d'un banc FZG est développé. Le modèle numérique se base sur la méthode des réseaux thermiques et prend en compte les pertes de puissance dues aux dentures, aux roulements et au brassage du bain d'huile. Des mesures soulignent que les bagues des roulements présentent un gradient de température significatif. Pour expliquer ce gradient, deux modèles de roulement sont proposés et comparés aux mesures. Leur influence sur le comportement thermique global de la transmission mécanique est discutée et analysée.

Colloque avec actes et comité de lecture. Internationale.; International audience; Les mécanismes d'initiation de fissures en fatigue de contact sont fortement liés à la microstructrure du matériau. Cependant, la plupart des modèles utilisés pour prédire la durée de vie en fatigue de contact se situent à l'échelle macroscopique. Un modèle basé sur une représentation de type Voronoi des grains (échelle mésoscopique) est développé afin d'analyser les mécanismes d'initiation. Le concept d'endommagement est appliqué aux joints de grain modélisés par la méthode des zones cohésives (CZM). La représentativité du modèle a été améliorée par la modélisation de l'anisotropie cristalline. Enfin, une nouvelle méthode d'application de l'endommagement aux joints de grain a permis de rendre les résultats plus cohérents en termes d'estimation de la durée de vie.

Colloque avec actes et comité de lecture. Internationale.; International audience; Le principal composant du pont est un couple conique, spiro-conique ou hypoïde, qui joue un rôle majeur en termes de pertes. Le frottement au niveau du contact est étudié, en s'intéressant d'une part aux paramètres de la denture, et d'autre part au comportement thermique général du pont qui peut influer sur les caractéristiques du film lubrifiant.

Colloque avec actes et comité de lecture. Internationale.; International audience; Dans cette étude, une méthode originale pour analyser la répartition des pertes de puissance dans un réducteur épicycloïdal est présentée. Elle est basée sur le couplage fort entre le rendement d'une transmission et son comportement thermique. Ce modèle est utilisé pour analyser les résultats expérimentaux obtenus à l'aide d'un banc d'essai. Dans le cas du réducteur épicycloïdal testé, les résultats montrent que les pertes de puissance indépendantes de la charge produites par la transmission sont majoritairement dues aux pertes hydrodynamiques générées dans les roulements des satellites et que les effets de ventilation sont négligeables.

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A series of formulas are presented which enable accurate predictions of churning losses for one pinion characteristic of automotive transmission geometry. The results are based on dimensional analysis and have been experimentally validated over a wide range of speeds, gear geometries, lubricants, and immersion depths. The case of a pinion-gear pair in mesh has been considered, and it has been proved that, depending on the sense of rotation, the superposition of the individual losses of the pinion and of the gear leads to erroneous figures. A new formula devoted to a pinion and gear rotating anticlockwise has been derived and validated by comparison with experimental evidence.

Power losses in high-speed gears come from the friction between the teeth (sliding and rolling), the lubrication process (dip or jet lubrication), the pumping of a gas-lubricant mixture during the meshing and the losses associated with windage effects. The objective of this paper is to present a number of preliminary experimental and theoretical findings on the prediction of windage losses. Experiments were conducted on a test bench whose principle consists in driving a gear to a given speed and then measuring its deceleration once it has been disconnected from the motor. The transmission between the motor and the rotor is ensured by a friction wheel which also plays the role of speed multiplier. A pneumatic jack either imposes a sufficient contact pressure between the driving wheel and the rotor (transmission of rotation), or is used for separating the parts when the maximum speed is reached. A disk and 4 different gears were tested in the absence of a lubricant at speeds ranging from 0 to 12 000 rpm. Two different theoretical approaches have been developed: i) a dimensional analysis based upon the dimensionless groups of terms which account for the flow characteristics (Reynolds number), the gear geometry (tooth number, pitch diameter, face width) and the speed, ii) a quasi-analytical model considering in detail the fluid flow on the gear faces and inside the teeth. It is found that both approaches give good results in comparison with the experimental evidence and two analytical formulae aimed at predicting windage losses in high-speed gears are proposed.© 2003 ASME

International audience; Churning losses are a complex phenomenon which generates significant power losses when considering splash lubrication of gear units. However, only few works deal with bevel gears dipped lubrication losses. The objective of this study is to provide a wide variety of experimental tests on churning losses, especially getting interested in geometry of spiral bevel gears influence. A specific test rig was used in order to study a single spiral bevel gear partially immersed in an oil bath. Experiments have been conducted for several operating conditions in terms of speeds, lubricants, temperatures and gear geometries to study their impact on splash lubrication power losses. These experimental results are compared with the predictions from various literature sources. As the results did not agree well with the predictions for all operating conditions, an extended equation derived from previous works is introduced to estimate churning losses of bevel gears.

International audience; This study aims to experimentally investigate churning power losses generated by a planetary gear set which is splash lubricated. To this end, a specific test rig has been used to operate a planetary gear train under unloaded conditions in various configurations within a range of the planet-carrier rotational speed. Churning loss is isolated from the measured drag torque and the effects of several parameters (rotational speed, temperature, oil sump level, planet number…) on this source of dissipation are quantified. Beyond the influence of speed or oil level, it is concluded that the number of planets is of primary importance on churning power losses. Moreover, a first assumption is made concerning the oil sump behavior regarding the experiments: an oil ring is created explaining the evolution of the churning losses measured. In addition, this study compares the churning phenomenon occurring in cylindrical gear trains with the one observed during the experiments. It is shown that the approach used for conventional gear trains cannot be used for epicyclic ones: in planetary gear sets the centrifugal effects are predominant whereas the gravity forces have a larger influence on the free surface flows which occur in cylindrical gear sets.

A thermo-mechanical model of a splash lubricated one-stage gear unit is presented. This system corresponds to a first step towards the design of a hybrid vehicle gearbox which can operate up to 40,000 rpm on its primary shaft. The numerical model is based on the thermal network method and takes into account power losses due to tooth friction, rolling elements bearings and oil churning. Some calculations underline that oil churning causes a high amount of power loss. A simple method to reduce this source of power losses is presented, and its influence on the gear unit efficiency and its thermal capacity is quantified.

International audience; When considering high-speed gear transmission, the power loss due to the fluid drag torque generated by the gear rotation in air/oil mist may dominate the other losses. This windage power loss (WPL) must be therefore studied in order to mitigate its impact. Numerous investigations have been made in the past essentially to propose WPL model. However the influence of helix angle is not clearly understood since most of the previous studies considered spur gears. Experiments have still shown that WPL value is modified when helix angle value becomes not null. More investigations are therefore needed to reach appropriate model. The purpose of this paper is to build a numerical model using CFD method which is capable to estimate WPL generated by helical gears whose characteristics differ from their helix angle values. The helix angle influence is highlighted since both the volumetric flow rate which is expelled by the rotating gear and WPL are affected by a modification of this parameter.

This paper presents an original method to investigate the power losses distribution into a planetary gear unit. A thermal model, which allows the estimation of power losses linked to the temperature distribution, is established. This model is used to analyse some experimental results obtained on a specific test rig. For the planetary gear set studied here, it is demonstrated that load-independent power losses are mainly due to hydrodynamic power losses generated in planets bearings and that gears windage effects are negligible.

International audience; In this paper, a test rig for measuring no-load power losses in planetary gears is presented. The influence of rotational speed, oil temperature and oil flow rate on power loss distribution in the gear unit are experimentally analysed. A number of experimental and numerical results concerning planet-carrier drag losses with and without oil injection are presented and commented upon.

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