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.

scholarly journals Analysis of Line Contact Elastohydrodynamic Lubrication with the Particles under Rough Contact Surface

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Keying Chen ◽  
Liangcai Zeng ◽  
Juan Chen ◽  
Xianzhong Ding
Keyword(s):  
Film Thickness ◽  
Rough Surface ◽  
Thickness Distribution ◽  
Traction Force ◽  
Elastohydrodynamic Lubrication ◽  
Equation System ◽  
Line Contact ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix

A numerical solution for line contact elastohydrodynamic lubrication (EHL) occurring on the rough surface of heterogeneous materials with a group of particles is presented in this study. The film thickness disturbance caused by particles and roughness is considered into the solution system, and the film pressure between the contact gap generated by the particles and the surface roughness is obtained through a unified Reynold equation system. The inclusions buried in the matrix are made equivalent to areas with the same material as that of the matrix through Eshelby’s equivalent inclusion method and the roughness is characterized by related functions. The results present the effects of different rough topographies combined with the related parameters of the particles on the EHL performance, and the minimum film thickness distribution under different loads, running speeds, and initial viscosities are also investigated. The results show that the roughness morphology and the particles can affect the behavior of the EHL, the traction force on a square rough surface is smaller, and the soft particles have more advantages for improving the EHL performance.

A Three-Dimensional Model of Line-Contact Elastohydrodynamic Lubrication for Heterogeneous Materials with Inclusions

2016 ◽  
Vol 08 (02) ◽  
pp. 1650014 ◽  
Author(s):  
Kun Zhou ◽  
Qingbing Dong
Keyword(s):  
Film Thickness ◽  
Half Space ◽  
Surface Deformation ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Lubricant Film ◽  
Line Contact ◽  
Lubricant Film Thickness ◽  
Equivalent Inclusion Method ◽  
Surface Contact

This paper develops a three-dimensional (3D) model for a heterogeneous half-space with inclusions distributed periodically beneath its surface subject to elastohydrodynamic lubrication (EHL) line-contact applied by a cylindrical loading body. The model takes into account the interactions between the loading body, the fluid lubricant and the heterogeneous half-space. In the absence of subsurface inclusions, the surface contact pressure distribution, the half-space surface deformation and the lubricant film thickness profile are obtained through solving a unified Reynolds equation system. The inclusions are homogenized according to Eshelby’s equivalent inclusion method (EIM) with unknown eigenstrains to be determined. The disturbed half-space surface deformations induced by the subsurface inclusions or eigenstrains are iteratively introduced into the lubricant film thickness until the surface deformation finally converges. Both time-independent smooth surface contact and time-dependent rough surface contact are considered for the lubricated contact problem.

Multiple Inhomogeneous Inclusions and Cracks in a Half Space Under Elastohydrodynamic Lubrication Contact

2015 ◽  
Vol 07 (01) ◽  
pp. 1550003 ◽  
Author(s):  
Qingbing Dong ◽  
Kun Zhou
Keyword(s):  
Half Space ◽  
Analytic Solution ◽  
Fluid Pressure ◽  
Elastohydrodynamic Lubrication ◽  
Governing Equations ◽  
Equivalent Inclusion Method ◽  
Surface Displacements ◽  
Equivalent Inclusion ◽  
Lubricated Contact ◽  
Modified Conjugate Gradient Method

A semi-analytic solution is presented for multiple inhomogeneous inclusions and cracks in a half-space under elastohydrodynamic lubrication contact. In formulating the governing equations, each inhomogeneous inclusion embedded under the contacting surfaces is modeled as a homogeneous inclusion with initial eigenstrains plus unknown equivalent eigenstrains by employing Eshelby's equivalent inclusion method, while each crack of mixed modes I and II is treated as a distribution of climb and glide dislocations with unknown densities according to the dislocation distribution technique. Such a treatment converts the problem into a homogeneous lubricated contact with disturbed deformation due to the inclusions and cracks. The unknowns in the governing equations are integrated by a numerical algorithm and determined iteratively by utilizing a modified conjugate gradient method. The iterative process is performed until the convergence of the half-space surface displacements, which involve the displacements due to the inhomogeneous inclusions and cracks as well as the fluid pressure. Samples are presented to demonstrate the generality of the solution.

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.

Elastic Fields in Double Inhomogeneity by the Equivalent Inclusion Method

2000 ◽  
Vol 68 (1) ◽  
pp. 3-10 ◽  
Author(s):  
H. M. Shodja ◽  
A. S. Sarvestani
Keyword(s):  
Elastic Constants ◽  
Present Method ◽  
Present Theory ◽  
Actual Distribution ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Ellipsoidal Inhomogeneity ◽  
Equivalent Inclusion ◽  
Comparison Results ◽  
Special Cases

Consider a double-inhomogeneity system whose microstructural configuration is composed of an ellipsoidal inhomogeneity of arbitrary elastic constants, size, and orientation encapsulated in another ellipsoidal inhomogeneity, which in turn is surrounded by an infinite medium. Each of these three constituents in general possesses elastic constants different from one another. The double-inhomogeneity system under consideration is subjected to far-field strain (stress). Using the equivalent inclusion method (EIM), the double inhomogeneity is replaced by an equivalent double-inclusion (EDI) problem with proper polynomial eigenstrains. The double inclusion is subsequently broken down to single-inclusion problems by means of superposition. The present theory is the first to obtain the actual distribution rather than the averages of the field quantities over the double inhomogeneity using Eshelby’s EIM. The present method is precise and is valid for thin as well as thick layers of coatings, and accommodates eccentric heterogeneity of arbitrary size and orientation. To establish the accuracy and robustness of the present method and for the sake of comparison, results on some of the previously reported problems, which are special cases encompassed by the present theory, will be re-examined. The formulations are easily extended to treat multi-inhomogeneity cases, where an inhomogeneity is surrounded by many layers of coatings. Employing an averaging scheme to the present theory, the average consistency conditions reported by Hori and Nemat-Nasser for the evaluation of average strains and stresses are recovered.

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