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The first calculations of film thickness for an oil/refrigerant system using quantitative elastohydrodynamics are reported in this work. It is demonstrated that primary measurements of the properties of the oil/refrigerant system can be employed to accurately predict film thickness in concentrated contacts. An unusual response to lubricant inlet temperature is revealed, wherein the film thickness may increase with temperature as a result of decreasing refrigerant solubility in oil when the inlet pressure is high. There is competition between the reduction in viscosity of the oil and the reduction of refrigerant concentration with increased temperature. For high inlet pressure, the dilution effect is dominant, whereas for low inlet pressure, the temperature dependence of the viscosity of the solution dominates over the range of inlet temperatures considered. It seems that only central film thicknesses have been experimentally measured for oil/refrigerant systems leaving these calculations as the only means of assessing the minimum.

Nowadays the accurate prediction of the actual tribological parameters that characterize lubricated systems requires the development of more and more advanced tools. Concerning the numerical ones, this leads to new challenges to model and predict in a proper way the strong couplings between mass (lubricant flow) and heat (dissipation, friction) transfer that appear within and around highly confined lubricating films. This paper presents some recent advances achieved in modeling TEHL problems where shear heating and its consequences can dominate other effects.

The objectives of this study were to investigate the effects of elastohydrodynamic lubrication pressure on the rolling contact fatigue life of non-conformal contacts. In order to achieve the objectives a finite element elastohydrodynamic lubrication (EHL) model was coupled with a continuum damage mechanics model. The coupled finite element damage mechanics and EHL (DMEHL) model was then used to investigate the effects of speed and damage variable on the fatigue life of non-conformal contacts. The results demonstrate that the damage variable has a significant effect on pressure distribution within the contact and depending on the level of damage; the pressure distribution can significantly deviate from the undamaged EHL pressure. The results also demonstrated that speed has a significant effect on fatigue and failure. A parametric study was conducted to examine the effects of the damage variable on the progression of fatigue and evolution of the EHL pressure profile. The results demonstrate that the critical damage value is important to fatigue and can drastically affect the EHL pressure profiles.

In this thesis, a full-system finite element approach to elastohydrodynamic (EHD) lubrication problems is introduced. EHD lubrication is a full-film regime where the pressure generated in the conjunction is high enough to induce a significant elastic deformation of the contacting bodies. Hence, it involves a strong coupling between hydrodynamic and elastic effects. The non-linear system formed by the Reynolds’, linear elasticity and load balance equations is solved using a fully-coupled Newton-Raphson procedure. This approach provides outstanding convergence rates when compared with the semi-system one. A penalty method is used to handle the cavitation problem that arises at the outlet of the contact. Appropriate stabilized formulations are used to extend the solution to the case of highly loaded contacts. The resolution process is then extended to account for non-Newtonian behaviour of the lubricant and for thermal effects. The developed model is used to study the behaviour of EHD contacts lubricated with Ultra-Low-Viscosity Fluids. The use of such fluids as lubricants provides two main advantages: first, the frictional energy dissipation in the contact is reduced and second, in machines that work with a low viscosity operational fluid and a lubricant, the former can be used to fulfil both functions and thus the design and maintenance of such machines would become easier and their performance would be improved

A string-type vibration absorber is proposed to suppress energy from a vibrating beam. A cantilever beam is considered with a harmonic force applied at its free end. The vibration absorber is a string attached to the beam at two different points. The string is rigidly connected to the fixed end of the beam and through a spring and damper to a second point on the beam. The finite element method is used to model the system and a reduced order model is obtained through modal reduction performed on both the string and the beam. The steady state amplitude of the transverse vibration of the beam is calculated using the first two modes of the beam-string system. It is found that the maximum amplitude at a given point of the beam occurs at a forcing frequency which is a root of a sixth order polynomial. The design of the vibration absorber is done in two steps. In the first, the spring stiffness, the position of the second attachment point of the string and a preliminary damping constant are calculated using a genetic algorithm approach where the objective function is the maximum displacement on the beam. Fine tuning is done in the second optimization step, by choosing an appropriate damping constant to further improve the design. To avoid buckling, the string tension is set to a value less than the lowest buckling force of the system. Numerical simulations of the beam’s maximum amplitude with and without absorber are shown to validate the proposed design

Several researchers are actively studying Ionomeric polymer transducers (IPT) as a large strain low voltage Electro- Active Polymer (EAP) actuator. EAPs are devices that do not contain any moving parts leading to a potential large life time. Furthermore, they are light weight and flexible. An IPT is made of an ion saturated polymer usually Nafion, sandwiched between two electrodes made of a mixture of Nafion and electrically conductive particles usually RuO2 or platinum. Nafion is an acid membrane in which the cations are mobile while the anions are covalently fixed to the polymer structure. Upon the application of an electric potential on the order of 2V at the electrodes the mobile positive ions migrate towards the cathode leading to bending strains in the order of 5%. Our earlier studies demonstrate that the cations develop thin boundary layers around the electrode. Later developments in this finite element model captured the importance of adding particles in the electrode. This study presents the electromechanical coupling in ionic polymer transducers. Since all our earlier models were restricted to the electro-chemical part, here we will introduce the chemomechanical coupling. This coupling is performed based on previous studies (Akle and Leo) in which the authors experimentally showed that the mechanical strain in IPTs is proportional to a linear term and a quadratic term of the charge accumulated at the electrode. The values of the linear and quadratic terms are extracted from experimental data.

Undersea distributed networked sensor systems require a miniaturization of platforms and a means of both spatial and temporal persistence. One aspect of this system is the necessity to modulate sensor depth for optimal positioning and station-keeping. Current approaches involve pneumatic bladders or electrolysis; both require mechanical subsystems and consume significant power. These are not suitable for the miniaturization of sensor platforms. Presented in this study is a novel biologically inspired method that relies on ionic motion and osmotic pressures to displace a volume of water from the ocean into and out of the proposed buoyancy engine. At a constant device volume, the displaced water will alter buoyancy leading to either sinking or floating. The engine is composed of an enclosure sided on the ocean's end by a Nafion ionomer and by a flexible membrane separating the water from a gas enclosure. Two electrodes are placed one inside the enclosure and the other attached to the engine on the outside. The semi-permeable membrane Nafion allows water motion in and out of the enclosure while blocking anions from being transferred. The two electrodes generate local concentration changes of ions upon the application of an electrical field; these changes lead to osmotic pressures and hence the transfer of water through the semi-permeable membrane. Some aquatic organisms such as pelagic crustacean perform this buoyancy control using an exchange of ions through their tissue to modulate its density relative to the ambient sea water. In this paper, the authors provide an experimental proof of concept of this buoyancy engine. The efficiency of changing the engine's buoyancy is calculated and optimized as a function of electrode surface area. For example electrodes made of a 3mm diameter Ag/AgCl proved to transfer approximately 4mm3 of water consuming 4 Joules of electrical energy. The speed of displacement is optimized as a function of the surface area of the Nafion membran

Ionic Polymer Metal Composite (IPMC) is an Electro-Active Polymer (EAP) that is used as an electro-mechanical sensor and being investigated as an energy harvester. The IPMC transducer is proved to be inefficient as an energy harvester due to the small amount of voltage it generates when deformed. This study explores this problem by developing a fully-coupled 2D mechano-chemo-electrical finite element model that predicts the sensing behaviour in IPMC. The electrochemical element is modelled based on the Nernst-Planck and Poisson’s equations. The chemo-mechanical coupling is due to the change in the concentration of ions upon deforming the sensor. This paper is focused on developing methods to control the amount of voltage and current the IPMC sensor can generate. The developed FEM model is used to assess the effects of increasing the thickness of the transducer and of manipulating the architecture of the high surface area electrodes. The IPMC transducer is simulated and experimentally tested using two electrical boundary conditions: the open circuit voltage or the short circuit current. All numerical results are supported by experimental data. The results are shown to be in good agreement with model predictions. © (2013) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Habchi, W., Eyheramendy, D., Vergne, P., & Morales, G. (2008, September). Stabilized Finite Elements for Elastohydrodynamic Lubrication Problems. In ECT2008 Sixth International Conference on Engineering Computational Technology.

A ball is in contact with a plane, and a lubricant separates the two surfaces to decrease friction during their relative motion. To avoid wear, the lubricant film thickness should be higher than the surface roughness. The goal of this paper is to show how it is possible to solve efficiently the problem of elastohydrodynamics lubrication with Comsol Multiphysics, using a PDE on boundary to implement the Reynolds equation.

Perhaps the most thorough characterization of the elevated pressure properties of any commercial EHL lubricant is presented here for a gear oil. Compressibility, thermal conductivity, and low-shear viscosity were measured. Of particular interest is the shear dependence of viscosity, measured across four decades of stress, which shows two transitions each with a specific value of power-law exponent. An attempt to capture a suspected third transition at very high stress resulted in mechanical degradation of the liquid in the viscometer. Numerical simulations of a point contact between a steel ball and a glass disc showed good agreement over a range of slide-to-roll ratio for the measured central thickness. The agreement for the minimum thickness was excellent. A new result is that shear-thinning of a higher molecular weight component that occurs from 3 to 200 kPa had little effect on the film thickness and could therefore be neglected in a film thickness calculation.

This paper presents an extension of the reduced order finite element model to the case of circular elastohydrodynamic lubricated (EHL) contacts under isothermal Newtonian considerations. The line contact model was developed and validated in a previous work (Advances in Engineering Software, 2013; 56:51−62). The model is based on a finite element discretization of the EHL equations: Reynolds, linear elasticity and load balance with a reduced order model for the linear elasticity part. All equations are solved simultaneously in a fully-coupled framework using a damped-Newton procedure allowing fast convergence rates for the global solution. This model combines fast convergence rates, reduced memory requirements and negligible model reduction errors compared to the full model which makes it an attractive tool for EHL contact performance prediction.

So far, most of the numerical studies concerning elastohydrodynamic point contact lubrication have been realized using finite differences. This paper describes a finite element approach for the modelling of both, thick and thin film lubrication in circular contacts under isothermal elastohydrodynamic regime. Multigrid techniques are used to accelerate the convergence and reduce calculation time. The use of the finite element method (FEM) offers two advantages: first, the existence of high level ready-to-use Finite Element commercial software which reduces the time spent in implementing the method and second, the easier adaptability to different and various physical models such as lubricant rheology, starvation effects, thermal effects, non-Newtonian behaviour, etc. The numerical model is presented in detail and an example of its adaptation taking into account non-Newtonian effects is shown. Finally, a comparison is made between Newtonian and non-Newtonian solutions, exhibiting differences obtained when using both models, especially at high shear rates where the film thickness and the friction coefficients are overestimated by a Newtonian approach.

The solution of the elastohydrodynamic lubrication (EHL) problem involves the simultaneous resolution of the hydrodynamic (Reynolds equation) and elastic problems (elastic deformation of the contacting surfaces). Up to now, most of the numerical works dealing with the modeling of the isothermal EHL problem were based on a weak coupling resolution of the Reynolds and elasticity equations (semi-system approach). The latter were solved separately using iterative schemes and a finite difference discretization. Very few authors attempted to solve the problem in a fully coupled way, thus solving both equations simultaneously (full-system approach). These attempts suffered from a major drawback which is the almost full Jacobian matrix of the nonlinear system of equations. This work presents a new approach for solving the fully coupled isothermal elastohydrodynamic problem using a finite element discretization of the corresponding equations. The use of the finite element method allows the use of variable unstructured meshing and different types of elements within the same model which leads to a reduced size of the problem. The nonlinear system of equations is solved using a Newton procedure which provides faster convergence rates. Suitable stabilization techniques are used to extend the solution to the case of highly loaded contacts. The complexity is the same as for classical algorithms, but an improved convergence rate, a reduced size of the problem and a sparse Jacobian matrix are obtained. Thus, the computational effort, time and memory usage are considerably reduced.

This work presents a model for elastohydrodynamic (EHD) lubrication problems. A finite element full-system approach is employed. The hydrodynamic and elastic problems are solved simultaneously which leads to fast convergence rates. The free boundary problem at the contact’s exit is handled by a penalty method. For highly loaded contacts, the standard Galerkin solution of Reynolds equation exhibits an oscillatory behaviour. The use of artificial diffusion techniques is proposed to stabilize the solution. This approach is then extended to account for non-Newtonian lubricant behaviour and thermal effects. Artificial diffusion procedures are also introduced to stabilize the solution at high loads.

This paper presents a numerical investigation of the local behavior of highly loaded thermal elastohydrodynamic contacts. The study is a continuation to a previous work of the authors where it was found that neglecting the dependence of lubricants' thermal properties on pressure and temperature leads to an underestimation of friction coefficients under high sliding regime. In this work, the local phenomena behind these observations are investigated. The results suggest that a redistribution of heat from the center of the contact towards the environment is taking place, leading to globally lower temperatures inside the contact, which leads to higher friction coefficients

This study proposes a numerical investigation of the potential use of machinery working fluids as lubricants in contacts operating under an elastohydrodynamic regime. These fluids are usually of very low viscosity and pressure–viscosity dependence. This is why, unmixed with oil, they have been of little interest for the tribological community. Hence, their rheological properties are poorly known. In fact, these are restricted to a narrow range of conditions compared to the range of interest in EHL applications. This is why some measurements are carried out in order to determine both the viscosity and density of these uncommon lubricants. Besides, their viscosity being low, high-mean entrainment speeds are required for a sufficiently thick lubricant film to build up. This leads to an important thermal dissipation within the contact. Thermal effects are included in the analysis in order to make the estimation of film thicknesses and friction coefficients in these contacts as accurate as possible. Results are discussed in the light of the peculiar properties of machinery low-viscosity working fluids.

Lubricants which contain a polymeric thickener will often display a second Newtonian plateau in measured flow curves. Like other manifestations of shear-dependent viscosity, this shear response will lead to an inaccurate prediction when the classical film-thickness formulas are employed. A correction formula has been developed from numerical experiments for a range of parameters of the double-Newtonian modified Carreau equation. The parameters of this shear-thinning model were selected from measurements for real lubricants obtained in Couette viscometers and a capillary viscometer. In addition, a full EHL film thickness formula has been derived from the same numerical experiments. The correction formula and the full formula were successfully validated using published film thickness data and published viscosity data for an EHL reference liquid, a polymer solution. Clearly, viscometer measurements of shear-dependent viscosity which contain the inflection leading to the second Newtonian are essential for a film-thickness calculation when a high-molecular-weight component of the lubricant is present.

The aim of this paper is to study the effects of pressure and temperature dependence of a conventional lubricant's thermal properties on the behaviour of heavily loaded thermal elastohydrodynamic lubrication (TEHL) contacts. For this purpose, a typical mineral oil (Shell T9) is selected and the dependence of its transport properties on pressure and temperature is investigated. Appropriate models are then developed for these dependencies. The latter are included in a TEHL solver in order to investigate their effect on the behaviour of circular EHD contacts. The results reveal the necessity of a thermal analysis including the pressure and temperature dependence of thermal properties for a good estimation of film thicknesses and mostly traction coefficients in circular EHD contacts operating under severe conditions. Numerical results are compared with experiments, showing a very good agreement over the considered ranges. This thorough validation of a thermal EHL framework for the calculation of film thickness and friction offers a previously unavailable opportunity to investigate the effects of variations in material properties.

This paper presents a finite element model for the solution of thermal elastohydrodynamic lubrication in coated circular contacts. The model is based on a full-system finite element resolution of the elastohydrodynamic and heat transfer equations. The effects of the coating's thermal and mechanical properties on lubrication performance are investigated. Two categories of surface coatings are considered based on thermal properties: high and low thermal inertia. It is found that low thermal inertia surface coatings act as insulators leading to a localized increase in the lubricant's temperature at the center of the contact. Therefore, friction can be significantly reduced while film thickness is barely affected. The opposite effect is observed for high thermal inertia coatings. These effects increase with coating's thickness.

Reducing friction is of utmost importance to improve efficiency and lifetime of many products used in our daily lives. Thin hard coatings like diamond-like carbon (DLC) have been shown to reduce friction in full-film-lubricated contacts. In this work, it is shown that contrarily to common belief, the friction reduction stems mainly from a thermal phenomenon and not only a chemical/surface interaction one. It is shown that a few micrometer-thin DLC coating can significantly influence the thermal behavior in a lubricated mechanical system. The presented simulations, validated by experiments, show that applying a thin DLC coating to metal surfaces creates an insulating effect that due to the increased liquid lubricant film temperature at the center of the contact, locally reduces lubricant viscosity and thus friction. The results of the investigation show that the addition of thin insulating layers could lead to substantial performance increases in many applications. On a component level, the contact friction coefficient in some common machine components like gears, rolling element bearings, and cam followers can potentially be reduced by more than 40 %. This will most likely open up the way to new families of coatings with a focus on thermal properties that may be both cheaper and more suitable in certain applications than DLC coatings, Godkänd; 2014; 20140113 (andbra);Included in Nature | Research Highlights Warm carbon coat reduces friction Nature 505, 264 Published online 15 January 2014;For correction, see: Björling, M., Habchi, W., Bair, S. et al. Correction to: Friction Reduction in Elastohydrodynamic Contacts by Thin-Layer Thermal Insulation. Tribol Lett 66, 125 (2018). https://doi.org/10.1007/s11249-018-1079-x

Ionomeric polymer transducer (IPT) is an electroactive polymer that has received considerable attention due to its ability to generate large bending strain (> 5%) and moderate stress at low applied voltages (+/-2 V). Ionic polymer transducers consist of an ionomer, usually Nafion, sandwiched between two electrically conductive electrodes. A novel fabrication technique denoted as the direct assembly process (DAP) enabled controlled electrode architecture in ionic polymer transducers. A DAP built transducer consists of two high surface area electrodes made of electrically conducting particles uniformly distributed in an ionomer matrix sandwiching an ionomer membrane. The purpose of this paper is to investigate and simulate the effect of these high surface area particles on the electro-chemical response of an IPT. Theoretical investigations as well as experimental verifications are performed. The model used consists of a convection-diffusion equation describing the chemical field as well as a Poisson equation describing the electrical field. The two-dimensional model incorporates highly conductive particles randomly distributed in the electrode area. Traditionally, these kinds of electrodes were simulated with boundary conditions representing flat electrodes with a large dielectric permittivity at the polymer boundary. This model enables the design of electrodes with complicated geometrical patterns. In the experimental section, several transducers are fabricated using the DAP process on Nafion 117 membranes. The architecture of the high surface area electrodes in these samples is varied. The concentration of the high surface area RuO2 particles is varied from 30 vol% up to 60 vol% at a fixed thickness of 30 mu m, while the overall thickness of the electrode is varied from 10 mu m up to 40 mu m at a fixed concentration of 45%. The flux and charge accumulation in the materials are measured experimentally and compared to the results of the numerical simulations. Trends o