Model for Elastohydrodynamic Lubrication of Multilayered Materials

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Zhanjiang Wang ◽  
Chenjiao Yu ◽  
Qian Wang
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Functionally Graded ◽  
Material System ◽  
Multilayer Material ◽  
Influence Coefficients ◽  
Surface Displacements ◽  
Graded Material ◽  
Multilayered Materials ◽  
Novel Model

A novel model is constructed for solving elastohydrodynamic lubrication (EHL) of multilayered materials. Because the film thickness equation needs the term of the deformation caused by pressure, the key problem for the EHL of elastic multilayered materials is to develop a method for calculating their surface deformations, or displacements, caused by pressure. The elastic displacements and stresses can be calculated by employing the discrete-convolution and fast Fourier transform (DC-FFT) method with influence coefficients. For the contact of layered materials, the frequency response functions (FRFs), relating pressure to surface displacements and stress components, derived from the Papkovich–Neuber potentials are applied. The influence coefficients can be obtained by employing FRFs. The EHL of functionally graded material (FGM) can also be well solved using a multilayer material system. The effects of material layers and property gradient on EHL film thickness and pressure are further investigated.

Elastohydrodynamic Lubrication Line Contact of a Functionally Graded Material Coated Half-Plane

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
Jie Su ◽  
Liao-Liang Ke
Keyword(s):  
Film Thickness ◽  
Half Plane ◽  
Functionally Graded Material ◽  
Normal Load ◽  
Fluid Pressure ◽  
Elastohydrodynamic Lubrication ◽  
Functionally Graded ◽  
Fluid Viscosity ◽  
Line Contact ◽  
Graded Material

Abstract The elastohydrodynamic lubrication line contact problem between a functionally graded material (FGM) coated half-plane and a rigid cylindrical punch is investigated. The inhomogeneous elastic properties of the FGM coating are expressed by the exponential model. The lubricant between two solids is supposed to be the Newtonian fluid. The fluid viscosity and density are considered to be dependent on the fluid pressure. To determine the unknown film thickness and fluid pressure at the lubricant contact region, a numerical iterative method is employed to simultaneously solve the flow rheology equation, Reynolds equation, load balance equation, and film thickness equation. Influences of the stiffness ratio of the FGM coating, the resultant normal load, the punch radius, and the entraining velocity on the lubricant film thickness and fluid pressure are analyzed.

An Elastohydrodynamic Lubrication Model for Coated Surfaces in Point Contacts

2007 ◽  
Vol 129 (3) ◽  
pp. 509-516 ◽  
Author(s):  
Yuchuan Liu ◽  
W. Wayne Chen ◽  
Dong Zhu ◽  
Shuangbiao Liu ◽  
Q. Jane Wang
Keyword(s):  
Fourier Transform ◽  
Film Thickness ◽  
Fast Fourier Transform ◽  
Elastic Deformation ◽  
Elastohydrodynamic Lubrication ◽  
Contact Radius ◽  
Point Contacts ◽  
Compliant Coating ◽  
Influence Coefficients ◽  
Coated Surfaces

An elastohydrodynamic lubrication (EHL) model for coated surfaces in point contacts has been developed by combining the elastic deformation formulation for the coated surfaces with an EHL model. Inverse fast Fourier transform (IFFT) is employed first to obtain the influence coefficients (ICs) from the frequency response function (FRF). The subsequent calculation of elastic deformation is performed using the efficient algorithm of discrete convolution and fast Fourier transform (DC-FFT). The coating EHL model is verified by the comparison to available numerical results. The effects of coating on lubrication under various loads, speeds, rheological models, and pressure-viscosity behaviors are numerically investigated. Similar to the observations from dry contact, stiffer coatings in EHL tend to reduce the nominal contact radius but increase the maximum contact pressure, and vice versa for more compliant coatings. However, as coating thickness increases, the influence of coatings on film thickness, including the central and the minimum film thicknesses, does not follow a monotonic variation, and therefore, cannot be predicted by any simple film thickness equation. The reason for that is the pressure viscosity effect which tends to counterbalance the effect of coating. The average friction coefficient in lubricant film increases in stiff coating cases but decreases for compliant coating cases. Furthermore, two possible approaches to improving the minimum film thickness thus reducing friction and wear in mixed lubrication are indicated: a thin stiff coating for conventional EHL and a thick compliant coating for soft EHL.

Elastohydrodynamic Lubrication of Inhomogeneous Materials Using the Equivalent Inclusion Method

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Zhanjiang Wang ◽  
Dong Zhu ◽  
Qian Wang
Keyword(s):  
Film Thickness ◽  
Surface Deformation ◽  
Fluid Pressure ◽  
Surface Displacement ◽  
Elastohydrodynamic Lubrication ◽  
Functionally Graded ◽  
Inhomogeneous Materials ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion

Solid materials forming the boundaries of a lubrication interface may be elastoplastic, heat treated, coated with multilayers, or functionally graded. They may also be composites reinforced by particles or have impurities and defects. Presented in this paper is a model for elastohydrodynamic lubrication interfaces formed with these realistic materials. This model considers the surface deformation and subsurface stresses influenced by material inhomogeneities, where the inhomogeneities are replaced by inclusions with properly determined eigenstrains by means of the equivalent inclusion method. The surface displacement or deformation caused by inhomogeneities is introduced to the film thickness equation. The stresses are the sum of those caused by the fluid pressure and the eigenstrains. The lubrication of a material with a single inhomogeneity, multiple inhomogeneities, and functionally graded coatings are analyzed to reveal the influence of inhomogeneities on film thickness, pressure distribution, and subsurface stresses.

Analytical modelling of thermal residual stresses in exponential functionally graded material system

2010 ◽  
Vol 31 (1) ◽  
pp. 560-563 ◽  
Author(s):  
Ali Bouchafa ◽  
Abdelnour Benzair ◽  
Abdelouahed Tounsi ◽  
Kada Draiche ◽  
Ismail Mechab ◽  
...  
Keyword(s):  
Residual Stresses ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Analytical Modelling ◽  
Material System ◽  
Thermal Residual Stresses ◽  
Graded Material

A Numerical Model to Predict Dynamic Performance of Layered Gears at Starved Lubrication

2019 ◽  
Author(s):  
Qingbing Dong ◽  
Jing Wei ◽  
Yan Li ◽  
Lixin Xu
Keyword(s):  
Reynolds Equation ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Material System ◽  
Stress Concentrations ◽  
Damage Resistance ◽  
Influence Coefficients ◽  
Load Carrying ◽  
Potential Energy Method

Abstract Gears of modern industry are required to have a good fatigue performance to transmit power and motion through the contact interfaces. Composite layered surfaces can effectively improve the damage resistance of gears and decrease the friction coefficients. However, improper surface modification may induce intensive stress concentrations at the joint interfaces of the strengthening layers and cause unexpected damages to the flanks. Furthermore, the amount of lubricant at the inlet may probably be insufficient to establish fully flooded condition, which may result in starvation and accelerate damages to the gear sets. In this study, a starved elastohydrodynamic lubrication (EHL) model in three-dimensional (3D) line contact for layered gears is developed. The potential energy method is employed to determine the load distribution along the action line. The loading force is assumed to be balanced by the lubrication pressure, which is derived by discretizing the dimensional Reynolds equation into a solvable matrix with the consideration of the enforced boundary conditions due to the inlet oil supply. The transient evolution of lubrication is investigated to evaluate the load-carrying capability of the lubricant film at various starvation conditions. The influence coefficients related to the displacements and stresses of the layered material system are determined with the assistance of the fast Fourier transform (FFT) algorithm, and the effects of the layer properties and the fabrication methods are evaluated. Such analysis may provide insightful information for the optimization of material systems with fabricated layers and engineering design of gears.

Elastohydrodynamic lubrication analysis of a functionally graded layered bearing surface, with particular reference to ‘cushion form bearings’ for artificial knee joints

2003 ◽  
Vol 217 (3) ◽  
pp. 191-198 ◽  
Author(s):  
S S Virdee ◽  
F C Wang ◽  
H Xu ◽  
Z M Jin
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Pressure Distribution ◽  
Single Layer ◽  
Elastohydrodynamic Lubrication ◽  
Functionally Graded ◽  
Operating Conditions ◽  
Knee Joints ◽  
Bearing Surface ◽  
Elasticity Equation

Elastohydrodynamic lubrication of a functionally graded layered (FGL) bearing surface, whose elastic modulus increases with depth from the bearing surface, was investigated in this study. The finite difference method was employed to solve the Reynolds equation, simultaneously with the elasticity equation of the bearing surface, under circular point contacts. The finite element method was adopted to solve the elasticity equation for the FGL bearing surface. The displacement coefficients thus obtained were used to calculate the elastic deformation of the bearing surface, required for the elastohydrodynamic lubrication analysis. Good agreement of the predicted film thickness and pressure distribution was obtained, between the present method and a previous study for a single layered bearing surface with a uniform elastic modulus. The general numerical methodology was then applied to an FGL bearing surface with both linear and exponential variations in elastic modulus, with particular reference to the ‘cushion form bearing’ for artificial knee joints. The predicted film thickness and pressure distribution were shown to be quite close to those obtained for a single layer under typical operating conditions representative of artificial knee joints, provided that the elastic modulus of the single layer was chosen to be the average elastic modulus of the graded layer.

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