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Because of deflections under load, contacts on tooth flanks can occur outside the theoretical plane of action between nonconjugated profiles especially when tooth modifications are not appropriate. The main objective of the present paper is to introduce an original model of the dynamic behavior of spur gears when submitted to these particular meshing conditions. The pinion and the gear of a pair are modeled as two rigid cylinders linked by stiffnesses and dampers whose amplitudes and orientations vary in order to simulate the evolutions of the meshing conditions. For the sake of simplicity, only three torsional degrees-of-freedom on the pinion, the gear and the motor are considered. The results show that the contacts between non-conjugated flanks lead to a particular dynamic behavior characterized by i) an actual contact ratio larger than the theoretical one, ii) the possibility of impacts at engagement whose amplitudes depend on transmitted loads and speeds.

This paper deals with face gear design. The goal is to propose a simple formula for predicting the width of the wheel as a function of the main design parameters. A specific software was used to achieve this goal. This numerical tool is able to simulate the geometry and the quasistatic loaded behavior of a face gear. The statistical method used for analyzing the influence of data is described: The design of experiments leads to a simple regression model taking into account the influential parameters and their couplings. In the last part of this paper, the results of the formulas are compared to those of the software and an optimal design is proposed based on the regression model.

This paper introduces a new modeling method suitable for the simulation of shell fracture under impact. This method relies on an entirely meshless approach based on the smoothed particle hydrodynamics (SPH) method. The paper also presents the SPH shell formulation being used as well as the different test cases used for its validation. A plasticity model of the global type throughout the thickness is also proposed and validated. Finally, in order to illustrate the capabilities of the method, fracture simulations using a simplified fracture criterion are presented.

A semi-analytical method for the tridimensional thermal-elastic-plastic contact between two hemispherical asperities is proposed. This first part of the paper describes the algorithm used to deal with the normal contact, which can be either load-driven (ld) or displacement-driven (dd). Both formulations use the Conjugate Gradient (CG) method and the Discrete Convolution and Fast Fourier Transform (DC-FFT) technique. A validation of the code is made in the case of the displacement-driven formulation for an elastic-plastic body in contact with a rigid punch, simulating a nano-indentation test. For both formulations (ld and dd) a very good convergence rate is found. Another new feature is the treatment of the contact between two elastic-plastic bodies. The model is first validated through comparison with the Finite Element Method (FEM). The contact pressure distribution, the hydrostatic pressure and the equivalent plastic strain state below the contacting surfaces are also found to be strongly modified in comparison to the case of an elastic-plastic body in contact with a purely elastic body. An application to the tugging between two spherical asperities in simple sliding (dd formulation) is made in part II of the paper.© 2006 ASME

For high-precision mechanisms such as machine tools or gas-turbine engines, which operate at extreme conditions, it is particularly important to accurately predict the behavior of the included bearing. This prediction includes, among other things, its load distribution, stiffness, and power dissipation. Although shaft speeds tend to increase, rings and shaft walls are becoming thinner due to size and weight constraints. Thus, bearing behavior is no longer independent of the housing and ring stiffness. This paper focuses on the problem of elastic ring deformation and certain behaviors of high-speed intershaft cylindrical roller bearings such as heat dissipation, contact pressure, and risk of bearing failure due to scuffing. The paper presents an analytical method to account for the structural deformation of the rings based on Roark's formulas. The elastic deformation of thin cylindrical rings has been introduced in the set of displacement and load equations that describes the bearing equilibrium. A correla...

The first part of this two-part paper presents an analytical model to predict the performances of double-row tapered roller bearings (DRTRB). The model has been structured in two major parts: (1)- A conventional quasi-static analysis to determine the internal load distribution, the bearing stiffness and the fatigue life and (2)- A quasi-dynamic analysis which integrates the differential equations for each bearing element in order to determine the amount of skidding, the friction forces and moments and consequently the heat dissipation. The proposed model allows one to take into account a general external loading (shaft tilting moments, radial and axial loads), the initial axial compression introduced while mounting, the operating speed and the lubricant properties. Some numerical results are presented in the second part of this two-part paper. Presented at the 56th Annual Meeting in Orlando, Florida May 20–24, 2001

Aircraft performances at landing or takeoff depend strongly on runway surface conditions. There is a need to provide aircraft pilots with reliable information in view of determining landing performance. Currently, these information are based on a description of the type and the depth of contaminants on the runway surface. This paper presents a new method to improve the correlation between friction coefficients and braking coefficients measured respectively by ground vehicles and aircrafts. A three steps approach is proposed, using a friction model developed by ESDU, to weight the measured coefficients by factors taking into account the characteristics of the devices and of the contaminants. The friction ESDU model is used on contaminated surfaces. The methodology is applied to data collected from extensive friction tests conducted between 1996 and 2003 (Joint Winter Runaway Friction Measurement Program). Characteristics of ground friction measuring devices and aircrafts are provided as inputs for ESDU model. It was found that the correlation between weighted ground friction and braking coefficients is improved significantly compared with the correlation between unweighted coefficients. Advantages of the newly proposed method are discussed in terms of using ground friction coefficients as a promising alternative to determine Runway condition code for aircraft pilots.

LGEP 2011 ID = 876; International audience; In order to find better solution for the development of Electric Vehicles (EVs), many research are performed by companies, universities and research laboratories. The main goal of these works is to provide some solutions to reduce the cost, increase the compactness, improve the autonomy and the reliability as well as the vehicle energetic efficiency and last but not least, reduce the global carbon emissions impact of the vehicle. This paper deals with an on-board battery charger for EVs or PHEVs where power electronics are reduced thanks to the use of same power converters in traction and charger mode. RST controllers in discrete time are design to control the PWM rectifier for the single-phase case.

Fatigue strength is of prior concern for automotive chassis parts design. In a reliability framework, its assessment still requires long and expensive test campaigns. In particular, high-cycle endurance tests usually involve several specimens undergoing million-cycle procedures. In order to reduce the specimen number (e.g. expensive prototypes) and to shorten testing procedures (i.e. time-to-result delay), Accelerated Life Tests (AFT) are developed under the constraint of the needed high-reliability assessment. These methods do not involve high frequency load cycling, but are mainly based on stress magnification and fatigue damage equivalence. In this paper, at first a review of the fatigue test procedures currently used in the automotive industry (e.g. StrairCase, Locati and StairCase-Locati) is addressed. Thus, numerical simulations are used in order to assess the efficiency of these test procedures and compare their performances.

National audience; This paper presents a steering assistance system that prevents unintended lane departures. The assistance intervenes only when the driver is inattentive and the vehicle is about to leave the lane. Road curvatures represent a challenge for the control law concerning the lane keeping performance as well as the lane overshoot in the case of activation in curves. To address these issues, the control law has been designed by using invariant sets theory and bilinear matrix inequalities optimization methods. Field tests have shown the theoretical expectations to be fulfilled and have demonstrated the high robustness properties of the implemented control law.

The paper proposes a comprehensive model to predict the skew movement of a roller in tapered roller bearings. Numerical solutions are given on a LM48548/LM48510 bearing. The effect of the shaft speed, ring misalignment, and lubricant temperature on the roller skew angle is presented and compared to the experimental data available in the literature. The results indicate that the skew angle depends first on the misalignment angle between the cup and the cone. The roller skew is also greatly influenced by the traction at the roller-flange contact, the skew angle increasing with the traction at this contact, and by the geometry of the roller end.

Nowadays, the wheels of worm gears with a low module can be made of plastic, thus classical modeling can no longer be used satisfactorily. The present paper describes an original method for studying the quasi-static loaded behavior of a worm gear, with a steel worm and a nylon wheel. A generalized Kelvin model is proposed and the computation of load sharing is described by using an equation of displacement compatibility. The history of previous deformation and the effect of the nylon’s structural damping are also taken into account. Experimental measurements of the Loaded Transmission Error are performed with the help of optical encoders rigidly connected to the worm and gear shafts, giving access to their instantaneous angular positions. The numerical simulations fit quite well with the experimental results.Copyright © 2007 by ASME

An analysis of an arched ball bearing that considers centrifugal forces and gyroscopic effects is performed. Based on operating conditions of a 5 DOF inner ring and Coulomb friction model, the conventional bearing theory is extended from 2 to 3 and 4 contacts. The commonly used control criterion of a ball bearing by the inner or outer raceway is debatable and is known to fit experimental data with difficulty, and when more than two contact points are involved it becomes obsolete. The paper presents a mathematical model to describe the ball internal kinematics under the effect of the operating conditions. This analysis makes it clear that the total power loss varies strongly with the one or two added sources of friction. The maximum PV factor is also affected by the full sliding of the lightly loaded contacts induced by the arched design.

When investigating the electrical characteristics of granular assemblies under dynamical solicitations (powder, steel bead assemblies, etc.), it is difficult to distinguish between effects that are purely electrical and those that are strongly dependent on mechanical effects. Although numerous experimental works have permitted better understanding of the static electrical behaviour of such media, it is difficult to determine the effects control the multi-physical behaviour of the medium, especially under dynamical solicitations. In the present paper, numerical investigations of the electrical characteristics of granular material are proposed. Moreover, it presents the formulation of a new model, embedded in the general scheme of discrete element methods, that couples electrical and mechanical effects and takes into account the oxidation phenomenon. Numerical simulations on the basis of experimental works are performed to validate the model, and the results of dynamical simulations are discussed. Copyright © 2007 John Wiley & Sons, Ltd.

An analysis of double arched ball bearing, which considers centrifugal forces and gyroscopic effects, is performed. Based on operating conditions of a five DOF inner ring and Coulomb friction model, the conventional bearing theory is extended from two to three or four-contact points. The commonly used control criterion of ball bearing by the inner or outer raceway is debatable and is known to fit with difficulty with experimental data. In addition, when more than two-contact points are involved, it becomes obsolete. The paper presents a mathematical model to describe the complex ball bearing internal kinematics under the effect of the external working conditions. Lubricant thickness is taken into account in geometrical equations and the nonlinear system of this quasistatic model is solved by a Newton-Raphson method. The model is first validated through comparisons with published data for conventional or single arched ball bearings. Results are also compared to those provided by the commercial software RBL4. The analysis of a double arched ball bearing is finally performed and the complex motion of the ball highlighted.

In a previous paper (Changenet, and Velex, 2007, “A Model for the Prediction of Churning Losses in Geared Transmissions—Preliminary Results,” ASME J. Mech. Des., 129(1), pp. 128–133), a series of empirical formulas were presented enabling accurate predictions of churning losses for one gear, which is typical of automotive transmission geometry. However, this formulation does not take into account the influence of flanges and deflectors. In order to extend the proposed methodology, a test rig has been set up in which several movable walls can be inserted, thus making it possible to modify the radial and axial clearances, i.e., the distances between the tested gear and the walls. Based on a qualitative evaluation of the various fluid flow regimes possible in gearboxes, the influence of the global volume of the oil sump on churning losses is analyzed. By considering a number of flange and deflector arrangements, the following conclusions are drawn: (a) Radial clearances have a weaker influence than axial clearances and (b) power losses can be minimized by properly chosen axial clearances.

International audience; The paper presents a numerical analysis of the rolling contact between an elastic ellipsoid and an elastic-plastic flat. Numerical simulations have been performed with the help of a contact solver called Plast-Kid®, with an algorithm based on an integral formulation or semi-analytical method. The application of both the conjugate gradient method and the discrete convolution and fast Fourier transform technique allows keeping the computing time reasonable when performing transient 3D simulations while solving the contact problem and calculating the subsurface stress and strain states. The effects of the ellipticity ratio k—ranging from 1 to 16—and of the normal load—from 4.2 GPa to 8 GPa—are investigated. The reference simulation corresponds to the rolling of a ceramic ball on a steel plate made of an AISI 52100 bearing steel under a load of 5.7 GPa. The results that are presented are, first, the permanent deformation of the surface and, second, the contact pressure distribution, the von Mises stress field, the hydrostatic pressure, and the equivalent plastic strain state within the elastic-plastic body. A comparison with an experimental surface deformation profile is also given to validate the theoretical background and the numerical procedure.

The design of spiral bevel gears in aeronautical gear boxes requires very precise and realistic numerical simulations. One important criteria is the loaded transmission error (LTE) that gear designers attempt to reduce at the nominal torque. This paper presents a numerical tool that simulates the loaded meshing of spiral bevel gears and experimental tests carried out on a real helicopter gear box. Tooth profile is defined by the Gleason cutting process and tooth bending effects and contact deformations are both taken into account. The bending effect computation uses a three-dimensional finite element model, while the contact deformations are obtained by using Boussinesq’s theory. Experimental measurements of the LTE were performed using magnetic and optical encoders rigidly connected with the pinion and gear shafts, giving access to the records of the instantaneous angular positions. The numerical simulations fit quite well the experimental results.

The extended finite element method (X-FEM) was used with success in the past few years for linear elastic fracture mechanics (LEFM). In the case of elastic–plastic fracture mechanics (EPFM), this method cannot be used without adequate asymptotic solutions to enrich the shape function basis. In this paper, we propose to use the well-known Hutchinson–Rice–Rosengren (HRR) fields to represent the singularities in EPFM. The analysis we are presenting is done in the context of confined plasticity, and shall be used to predict fatigue crack growth without remeshing. A Fourier analysis of the HRR fields is done in order to extract a proper elastic–plastic enrichment basis. Several strategies of enrichment, based on the Fourier analysis results, are compared and a six-enrichment-functions basis is proposed. This new tip enrichment basis is coupled with a Newton like iteration scheme and a radial return method for plastic flow. Numerical comparisons with and without unloading of fracture parameters are made with classical finite element results and show good agreements.

In order to characterize the timing, mode and size of a possible lower head failure (LHF) of the reactor pressure vessel (RPV) in the event of a core meltdown accident, several large-scale LHF experiments were performed under the USNRC/SNL LHF program. The experiments examined lower head failure at high pressures (10 MPa in most cases) and with small throughwall temperature differentials. Another USNRC/SNL LHF program, called the OLHF program, has been undertaken in the framework of an OECD project. This was an extension of the first program and dealt with low and moderate pressures (2–5 MPa) but with large through wall temperature differentials. These experiments should lead to a better understanding of the mechanical behavior of the reactor vessel lower head, which is of importance both in severe accident assessment and the definition of accident mitigation strategies. A well-characterized failure of the lower head is of prime importance for the evaluation of the quantity of core material that can escape into the containment, since this defines the initial conditions for all external-vessel events. The large quantity of escaping corium may lead to direct heating of the containment. This is an important severe accident issue because of its potential to cause early containment failure. The experiments also provide data for model development and validation. For our part, as one of the program partners, numerical modeling was performed to simulate these experiments. This paper presents a detailed description of three of our numerical models used for the simulation. The first model is a simplified semi-analytical approach based on the theory of a spherical shell subjected to internal pressure. The two other methods deal with 2D finite element (2D-FE) modeling: one combines the Norton–Bailey creep law with a damage model proposed by Lemaitre–Chaboche while the other uses only a creep failure criterion but takes into account thermo-metallurgical phase transformations. One of the objectives of the simulation is the development of a simplified and valid analytical code that can be implemented in integral severe accident computer codes. The numerical results are consistent with the experimental measurements. The effect on the numerical results of the multiphase transformation of the shell material and of the two failure criteria used, one involving necking (Considere's criterion) and the other involving creep damage (Lemaitre–Chaboche) is discussed.

This paper presents a methodology to evaluate the impact of the MC-CDMA physical layer algorithms on the downlink capacity in a multi-cellular environment. It presents a Monte Carlo simulation approach for capacity estimation at the system level and introduces a novel indicator for qualitative capacity evaluation at the link level. An illustration of this methodology shows very good agreement between the link level qualitative and system level quantitative capacity evaluations. The novel capacity indicator is therefore an efficient and accurate tool at the link level for optimizing the MC-CDMA physical layer algorithms and identifying the most appropriate physical layer configurations. On the other hand, the system level quantitative capacity evaluation allows to quantify more precisely the impact of the physical layer algorithms on the system capacity for a given environment.

This paper is devoted to the presentation of the Extended Finite Element Method (X-FEM) compared to usual Finite Element Method for simulation of 3D fatigue crack propagation under complex loading. This type of situation is very typical of crack propagation in tribological environment. The X-FEM method will be presented in a first part, and two techniques allowing the discretization of cracks will be explained. The interaction integral concept, which allows to compute with a very good accuracy the stress intensity factors KI, KII, KIII, in complex situation will be presented. Once these tools are available, the method can be used very efficiently to simulate crack propagation without remeshing. This property is essential because it guarantees exact energy conservation when the crack is updated. The precise knowledge of individual stress intensity factors KI ,KII and KIII allows deciding the direction of the crack growth (using any crack propagation law). This tool can hence be used to identify the propagation laws in complex cases using comparison between experimental and numerical studies. One example of stress intensity factor computation using a 3D real crack measured by tomography will be shown. 3D crack propagation simulation will be presented. Very recent results will be given for small scale yielding and crack closure situations, which permit to explain, for instance, slowed down crack propagation due to overload.

International audience; This paper presents a general study of the stability of variable-mesh dynamic calculations using an energy approach. This study, whose scope is limited to the calculation of dynamic crack propagation with remeshing, enables us to establish the conditions which are necessary to ensure stability and allow control of energy transfers during the evolution of the mesh. The problem of the implicit calculation of the crack length is also presented. The results obtained on an sample problem are analyzed to illustrate the effectiveness of the proposed methods.

The model developed to predict the performance of double-row tapered roller bearings (DRTRB) and described in the first part of the paper is now exemplified. For a given example results on the internal load distribution, bearing fatigue life and hear generation are presented and discussed for various operating conditions including the mounting preload. It is revealed that some sliding occurs at the contact between the rollers and the cone that contributes significantly to the total power dissipated within the bearing. It is also shown that an optimum axial compression (or mounting preload) may be found in terms of fatigue life and heat dissipated. As the main conclusion the initial compression between bearing rows was found to play a major role upon the bearing behavior and therefore should be considered carefully for each application. Presented at the 56th Annual Meeting in Orlando, Florida May 20–24, 2001

After a short background history on solid third bodies, this paper proposes a tribological approach for understanding how a contact takes place when first bodies are in relative movement and are separated by a solid third body. This approach, based on rheology and third body flows, enables friction and wear in contacts “lubricated” by a solid third body to be identified and progressively modelled. Flows and rheology are the two notions used for analysing and structuring dynamic phenomena created by contacts and their interaction with the environment, in the physico-chemical and mechanical sense, i.e. with the ambient atmosphere and the mechanism concerned with the contact, respectively. Due to in-situ instrumentation difficulties, flows are evaluated in relation to those visualised in real time through one transparent first body. Rheology is also evaluated relatively, but by distinguishing the cohesion and ductility of the elements making up the third body that moves in the contact, over a given observation scale. As an illustration, this presentation relies on the behaviour of a contact containing a third body formed in-situ from a coating of MoS 1.6 .

The paper considers the behavior of third bodies in dry contacts. A description of the mechanism operating in contacts is given and the influence of external parameters outlined. Both physicochemical and mechanical conditions greatly influence third body behavior. Depending on third-body composition, the external influence can be more or less dramatic. Due to difficulties with experimentation, numerical modeling is suggested as a complementary tool. Two approaches for such modeling are described, the continuum and the discrete approach. At present these models are at an early development stage (two-dimensional simulations), and great efforts should be made for their further development. While an experimental apparatus can study phenomena at only one scale; namely the nanometer with AFM, or the micron to millimeter with fretting machines, modeling is able to range from the microscopic properties (particle interactions like coefficient of restitution) to the macroscopic properties by integration or averaging (load capacity, friction coefficient).

This paper presents an experimental investigation of the mean axial velocity and temperature excess of three-dimensional vertical and then horizontal wall jet, with opposite buoyancy forces. The initial Archimed number is used to establish an empirical model to estimate the maximum quantities of the jet, with reference to the inlet conditions. These measurements also enabled us to deduce the penetration law of the vertical jet and the separation distance law of the horizontal flow according to the inlet conditions.

Numerical simulation of creep rupture of a reactor pressure vessel in a severe hypothetical accident needs to perfectly take account of interactions between creep phenomena and damage. This paper presents a numerical method for solving constitutive equations of a material behaviour model coupling elastoviscoplasticity and creep damage through the effective stress concept. The numerical technique rests upon a semi-implicit time integration of the constitutive equations. The method is validated on both simple ID cases the results of which can be compared to other numerical or analytical solutions and in the case of an axisymmetric reference problem (RUPTHER 4 test) under thermal and mechanical loading. The efficiency of different tangent stiffness matrices is analysed.