Elastoplastic contact of rough surfaces: a line contact model for boundary regime of lubrication

This paper introduces an improved friction model accounting for elastoplastic behavior of interacting asperities along contiguous rough surfaces for a line contact solution. It is based on Greenwood and Tripp’s original boundary friction model and specifically tailored for a boundary regime of lubrication. The numerical solution of Reynolds’ equation is achieved by implementing Elrod’s cavitation algorithm for a one dimensional line contact. The transience in the numerical solution is retained by accounting for the squeeze film term in Reynolds’ equation under fixed loading conditions and varying sliding motion. A sliding bearing rig is used to measure friction and compare the results with the prediction made using the approach highlighted above. The numerical/experimental results show good agreement

Frictional characteristics of molecular length ultra-thin boundary adsorbed films

© 2015, Springer Science+Business Media Dordrecht. The paper presents measurements of friction of any ultra-thin film entrained into the contact of a pair of very smooth specimen subjected to entrainment in a converging micro-wedge of a special-purpose micro-tribometer. An ultra-thin film is expected to form at the boundary solids through adsorption of boundary active molecules. Fluids with linear and branched molecules are used in the investigation. It is found that the frictional characteristics of these films can be adequately described through use of Eyring thermal activation energy and a potential energy barrier to sustain conjunctional sliding motion. The combined experimental measurement and the simple activation energy approach shows that the thin molecular adsorbed films act like hydro Langmuir–Blodgett layers, the formation and frictional characteristics of which are affected by the competing mechanisms of adsorption, forced molecular re-ordering and discrete-fashion drainage through the contact by the solvation effect. This process is a complex function of the contact sliding velocity as well as a defined Eyring activation density (packing density of the molecules within the conjunction). It is shown that the contribution of solvation to friction is in the form of energy expended to eject layers of lubricant out of the contact, which unlike the case of micro-scale hydrodynamic films, is not a function of the sliding velocity

Transient mixed thermo-elastohydrodynamic lubrication in multi-speed transmissions

Noise, vibration and harshness (NVH) refinement as well as thermo‐mechanical efficiency are the key design attributes of modern compact multi‐speed transmissions. Therefore, unlike simple gear pair models, a full transmission model is required for a simultaneous study. The prominent NVH concern is transmission rattle, dominated by the intermittent unintended meshing of several lightly loaded unselected loose gear pairs arising from the system compactness. These gear pairs are subject to hydrodynamic impacts. The thermo‐mechanical efficiency is dominated by the engaged gears, with simultaneous meshing of teeth pairs subject to thermo‐elastohydrodynamic regime of lubrication, with often quite thin films, promoting asperity interactions. Therefore, a full transmission model is presented, comprising system dynamics, lubricated contacts, asperity interactions and thermal balance. Generic multi‐physics models of this type are a prerequisite for in‐depth analysis of transmission efficiency and operational refinement. Hitherto, such an approach has not been reported in literature

Analysing the effects of sliding, adhesive contact on the deformation and stresses induced within a multi-layered elastic solid

This paper presents a mathematical model of sliding, adhering contact between a rigid parabolic indenter and a multi-layered elastic solid, which is assumed to comprise of a homogeneous coating bonded through a functionally-graded transitional layer to a homogeneous substrate. The adhesive forces in this investigation are modelled using Lennard-Jones potential and an iterative algorithm is proposed that solves for the contact pressure, surface displacement and sub-surface stresses resultant within the layered solid. The effects of surface adhesion and different material properties such as varying coating/transition layer thickness and coating hardness on the solution of the contact problem are subsequently investigated in detail. The numerical approach presented in this paper demonstrates the significance of having a suitable mathematical representation for the traction distribution along the sliding, adhering contact. It is found that under weakly adhering conditions, the assumption of only Coulombic traction suffices to determine the displacements and subsurface stresses within the multi-layered solid. However, it is noted that stress concentrations within the material begin to propagate through all three layers of the elastic solid with increased surface adhesion, which could potentially induce plasticity and lead to material ploughing under sliding. The proposed model allows us to further investigate and improve our understanding of the combined effects of traction and boundary adhesion in sliding contacts, which can be used to inform the design of materials needed in such conditions

Modelling adhesive contact problems involving a layered elastic solid and cylindrical indenter using Lennard Jones potential

This paper presents an iterative algorithm that solves for the displacement and sub-surface stresses induced within a layered elastic solid adhering to a rigid cylindrical indenter under lightly loaded conditions. The solid is assumed to comprise a functionally graded coating of finite thickness bonded to a homogeneous substrate of infinite extent and is assumed to be in a state of plane strain which allows a two-dimensional analysis to be performed. The Lennard–Jones potential is used to model the adhesive force acting between the indenter and solid whilst the effects of surface adhesion are characterised using Tabor’s parameter. A selection of numerical results for the adhesive contact problem are presented which indicate that the maximum pressure and induced sub-surface stresses increase dramatically as Tabor’s parameter increases. It is also found that the shear modulus and thickness of the coating have a significant effect on material behaviour with harder coatings experiencing significantly larger tensile stresses but smaller surface displacement than softer coatings. The present investigation allows us to deduce that at smaller scales, surface adhesion can be instrumental in causing wear or potential material failure if coatings are improperly designed

On the two-dimensional solution of both adhesive and non-adhesive contact problems involving functionally graded materials

This paper presents a semi-analytical algorithm for the determination of the contact half width and surface pressure which results from both adhesive and non-adhesive contact problems involving functionally graded materials (FGM). The inhomogeneously elastic solid comprises a graded elastic coating whose shear modulus depends exponentially on the vertical coordinate and a homogeneously elastic substrate. The solid is assumed to be in a state of plane strain and thus a two-dimensional analysis is performed within this work. Using the work of Chidlow et al. (2011a) as a starting point, we derive a pair of integral equations which may be used to determine approximations to the contact pressure when either the surface deflection or the deflection gradient is known over the contact region. As these integral equations are non-singular, we use Galerkin's method to approximate the contact pressure and it is found that relatively small trial spaces allow accurate computation of the pressure. Information about the prescribed load is then used to formulate an iterative algorithm to determine the contact half width. A selection of numerical results are presented using this method and it is found that the solutions computed here compare favourably with those of other authors. A further investigation is then conducted into the solution of adhesive contact problems using the assumptions of Maugis (1992) and Johnson and Greenwood (2008) to inform the nature of the adhesive stresses outside of the contact. It is found that both JKR-like and DMT-like behaviour can be observed in contact problems involving FGMs

Formation of ultra-thin bi-molecular boundary adsorbed films

An analytical method based on statistical mechanics is proposed for the prediction of ultra-thin adsorbed films of physical fluids of molecular diversity formed on smooth surfaces. The model is representative of molecular interactions at the smooth summits of surface asperities in the nano-scale. At this physical scale the constraining effect of the solid barriers promotes discretisation of the fluid volume into molecular layers, which are usually ejected from the contact in a stepwise manner. The integrated effect of intermolecular interactions of molecular species as well as their interactions with the contiguous surfaces is responsible for this discontinuous drainage of the fluid. However, at the same time, the adsorption energy of the molecular species strives to form a molecular mono-layer upon the boundary solids. The net result of these complex interactions is an ultra-thin adsorbed film whose shear characteristics depends on a competition between the repulsive solvation pressure and the energy of molecular adsorption. It is shown that very thin low shear strength films formed in this manner depend on ideal molecular concentration and wall adsorption energy. An important implication is that boundary adherent films should be viewed as a result of surface- fluid combination for which choice of concentration and fraction content of particular species are crucial

Physio-chemical hydrodynamic mechanism underlying the formation of thin adsorbed boundary films

Formation of low shear strength surface-adhered thin films mitigates excessive friction in mixed or boundary regimes of lubrication. Tribo-films are formed as a consequence of molecular chemical reaction with the surfaces. The process is best viewed in the context of a lubricant-surface system. Therefore, it is usually surmised that the adsorption of lubricant molecular species to the contact surfaces would be underlying to the formation of ultra-thin lubricant films. The paper considers contact of smooth surfaces at close separation. This may be regarded as the contact of a pair of asperity summits, whose dimensions, however small, are far larger than the size of fluid molecules within the conjunction. In such diminishing separations the constraining effect of relatively smooth solid barriers causes oscillatory solvation of fluid molecules. This effect accounts for the conjunctional load capacity but does not contribute to mitigating friction, except when molecular adsorption is taken into account with long chain molecules which tend to inhibit solvation. The paper presents an analytical predictive model based on the Ornstein-Zernike method with Percus-Yevick approximation of a narrow interaction potential between conjunctional composition. The predictions confirm the above stated physical facts in a fundamental manner

Effect of lubricant molecular rheology on formation and shear of ultra-thin surface films

Physics of molecularly thin fluid films, formed between surface features at close range is investigated. It is found that the interplay between discrete lubricant drainage from such contacts and localised contact deflection plays an important role both on the load carrying capacity of these asperity level conjunctions as well as on friction. Small spherical molecules tend to solvate near assumed smooth surfaces of asperities at nano-scale. Their discrete drainage at steadily decreasing gaps adds to the viscous friction of any bulk lubricant film. However, at the same time the generated solvation pressures increase the load carrying capacity. Conversely, long chain molecules tend to inhibit solvation, thus show a decrease in the load carrying capacity, whilst through their wetting action reduce friction. Consequently, real lubricants should comprise molecular species which promote desired contact characteristics, as indeed is the case for most base lubricants with surmised properties of certain additives. The methodology presented underpins the rather empirical implied action of surface adhered films. This is an initial approach which must be expanded to fluids with more complex mix of species. If applicable, this could also be an alternative (potentially time saving) approach to Monte-Carlo simulations for molecular dynamics

Transient mixed thermo-elastohydrodynamic lubrication in multi-speed transmissions

Noise, vibration and harshness (NVH) refinement as well as thermo-mechanical efficiency are the key design attributes of modern compact multi-speed transmissions. Therefore, unlike simple gear pair models, a full transmission model is required for a simultaneous study. The prominent NVH concern is transmission rattle, dominated by the intermittent unintended meshing of several lightly loaded unselected loose gear pairs arising from the system compactness. These gear pairs are subject to hydrodynamic impacts. The thermo-mechanical efficiency is dominated by the engaged gears, with simultaneous meshing of teeth pairs subject to thermo-elastohydrodynamic regime of lubrication, with often quite thin films, promoting asperity interactions. Therefore, a full transmission model is presented, comprising system dynamics, lubricated contacts, asperity interactions and thermal balance. Generic multi-physics models of this type are a prerequisite for in-depth analysis of transmission efficiency and operational refinement. Hitherto, such an approach has not been reported in literature