scholarly journals The size-dependent elastohydrodynamic lubrication contact of a coated half-plane with non-Newtonian fluid

2021 ◽  
Author(s):  
Jie Su ◽  
Hongxia Song ◽  
Liaoliang Ke ◽  
S. M. Aizikovich
Keyword(s):  
Film Thickness ◽  
Half Plane ◽  
Newtonian Fluid ◽  
Plane Stress ◽  
Coating Thickness ◽  
Fluid Pressure ◽  
Elastohydrodynamic Lubrication ◽  
Stiffness Ratio ◽  
Size Parameter ◽  
Coupled Equations

AbstractBased on the couple-stress theory, the elastohydrodynamic lubrication (EHL) contact is analyzed with a consideration of the size effect. The lubricant between the contact surface of a homogeneous coated half-plane and a rigid punch is supposed to be the non-Newtonian fluid. The density and viscosity of the lubricant are dependent on fluid pressure. Distributions of film thickness, in-plane stress, and fluid pressure are calculated by solving the nonlinear fluid-solid coupled equations with an iterative method. The effects of the punch radius, size parameter, coating thickness, slide/roll ratio, entraining velocity, resultant normal load, and stiffness ratio on lubricant film thickness, in-plane stress, and fluid pressure are investigated. The results demonstrate that fluid pressure and film thickness are obviously dependent on the size parameter, stiffness ratio, and coating thickness.

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.

Elastohydrodynamic lubrication line contact in couple-stress elasticity

2020 ◽  
pp. 108128652098079
Author(s):  
Jie Su ◽  
Hong-Xia Song ◽  
Liao-Liang Ke
Keyword(s):  
Film Thickness ◽  
Elasticity Theory ◽  
Plane Stress ◽  
Couple Stress ◽  
Normal Load ◽  
Fluid Pressure ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Classical Elasticity ◽  
Couple Stress Elasticity

By using the couple-stress elasticity theory, this article firstly analyzes the size-dependent elastohydrodynamic lubrication (EHL) line contact between a deformable half-plane and a rigid cylindrical punch. The size effect that emerged from the material microstructures is described by the characteristic material length. It is assumed that the viscosity and density of the lubricant vary with the fluid pressure. An iterative method is developed to deal with the flow rheology equation, film thickness equation, load balance equation and Reynolds equation at the same time. Then, distributions of fluid pressure, in-plane stress and film thickness are determined numerically at the lubricant contact surface. Influences of the size parameter, punch radius, resultant normal load and entraining velocity on the fluid pressure, in-plane stress and lubricant film thickness are discussed. The fluid pressure and film thickness predicted from the couple-stress elasticity theory present significant departures from the classical elasticity results. It is demonstrated that results for micro-/nano-scale EHL contact problems may be underestimated when the classical elasticity theory is employed.

Transient thermal elastohydrodynamic lubrication of point contacts subjected to normal vibration

2016 ◽  
Vol 68 (5) ◽  
pp. 536-547
Author(s):  
Jianjun Zhang ◽  
Qibo Ni ◽  
Jing Wang ◽  
Feng Guo
Keyword(s):  
Film Thickness ◽  
Newtonian Fluid ◽  
Normal Vibration ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Vibration Period ◽  
Content Type ◽  
Multi Level ◽  
Vertical Vibrations ◽  
Thermal Ehl

Purpose Vibration exists widely in all machineries working under high speed. The unpredictability of vibration and the change of the relative surface speed may result in difficulties in the elastohydrodynamic lubrication (EHL) analysis. By far, few studies on EHL relating to vibration have been published. The purpose of the present study is to investigate the effect of the vertical vibrations and the influence of temperature on the thermal EHL contacts. Design/methodology/approach The lubricant was assumed to be Newtonian fluid. The time-dependent numerical solutions were achieved instant after instant in each period of the vibration. At each instant, the pressure field was solved with a multi-level technique, the surface deformation was solved with a multi-level multi-integration method and the temperature filed was solved with a finite different scheme through a sweeping progress. The periodic error was checked at each end of the vibration period until the responses of pressure, film thickness and temperature were all periodic functions with the frequency of the roller’s vibrations. Findings The results reveal that normal vibration produces little drastic change of pressure, film thickness and temperature in EHL. Under some conditions, the vibrations of the roller can produce transient dimples within the contact conjunction. It is also showed that the lubrication in the same sliding is better than the opposite sliding. Research limitations/implications For the unpredictability of vibration, it is not easy to do the experiment to realize a real comparison with numerical results. The reach does not show any verification and consider the effect of non-Newtonian fluid. Originality/value The effect of the vertical vibrations on the thermal EHL point contact hast been studied. The effects of both the amplitude and the frequency on the predicted load-carrying capacity, minimum film thickness, center pressure and center temperature and the coefficient of friction were investigated. The role of the thermal effect was given.

Elastohydrodynamic Lubrication Line Contact Based on Surface Elasticity Theory

2020 ◽  
Vol 87 (8) ◽  
Author(s):  
Jie Su ◽  
Hong-Xia Song ◽  
Liao-Liang Ke
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Elasticity Theory ◽  
Surface Stress ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Fluid Pressure ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Residual Surface Stress

Abstract Using surface elasticity theory, this article first analyzes the surface effect on the elastohydrodynamic lubrication (EHL) line contact between an elastic half-plane and a rigid cylindrical punch. In this theory, the surface effect is characterized with two parameters: surface elastic modulus and residual surface stress. The density and viscosity of the lubricant, considered as Newtonian fluid, vary with the fluid pressure. A numerical iterative method is proposed to simultaneously deal with the flow rheology equation, Reynolds equation, load balance equation, and film thickness equation. Then, the fluid pressure and film thickness are numerically determined at the lubricant contact region. Influences of surface elastic modulus, residual surface stress, punch radius, resultant normal load, and entraining velocity on the lubricant film thickness and fluid pressure are discussed. It is found that the surface effect has remarkable influences on the micro-/nano-scale EHL contact of elastic materials.

scholarly journals Non-Newtonian Fluid Model Incorporated Into Elastohydrodynamic Lubrication of Rectangular Contacts

1984 ◽  
Vol 106 (2) ◽  
pp. 275-282 ◽  
Author(s):  
B. O. Jacobson ◽  
B. J. Hamrock
Keyword(s):  
Shear Stress ◽  
Shear Strength ◽  
Film Thickness ◽  
Numerical Solution ◽  
Newtonian Fluid ◽  
Fluid Model ◽  
Elastohydrodynamic Lubrication ◽  
Sliding Velocity ◽  
Minimum Film Thickness ◽  
Limiting Value

A procedure is outlined for the numerical solution of the complete elastohydrodynamic lubrication of rectangular contacts incorporating a non-Newtonian fluid model. The approach uses a Newtonian model as long as the shear stress is less than a limiting shear stress. If the shear stress exceeds the limiting value, the shear stress is set equal to the limiting value. The numerical solution requires the coupled solution of the pressure, film shape, and fluid rheology equations from the inlet to the outlet. Isothermal and no-side-leakage assumptions were imposed in the analysis. The influence of dimensionless speed U, load W, materials G, and sliding velocity U* and limiting-shear-strength proportionality constant γ on dimensionless minimum film thickness Hmin was investigated. Fourteen cases were investigated for an elastohydrodynamically lubricated rectangular contact incorporating a non-Newtonian fluid model. The influence of sliding velocity (U*) and limiting shear strength (γ) on minimum film thickness was observed to be small. Hence the film thickness equation obtained for a Newtonian fluid is sufficient for calculations considering non-Newtonian effects. Computer plots are also presented that indicate in detail pressure distribution, film shape, shear stress at the surfaces, and flow throughout the conjunction.

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 A Modified Equation for Thickness of the Film Fabricated by Spin Coating

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1183 ◽  
Author(s):  
Un Gi Lee ◽  
Woo-Byoung Kim ◽  
Do Hyung Han ◽  
Hyun Soo Chung
Keyword(s):  
Angular Velocity ◽  
Film Thickness ◽  
Newtonian Fluid ◽  
Coating Thickness ◽  
Spin Coating ◽  
Newtonian Fluids ◽  
Coating Film ◽  
Fluid Equation ◽  
Coating Time ◽  
New Formula

According to the equation for Newtonian fluids, the film thickness after spin coating is determined by five parameters: angular velocity, spin coating time, viscosity, density of the coating material, and initial thickness of the material before spin coating. The spin coating process is commonly controlled by adjusting only the angular velocity parameter and the coating time in the Newtonian expression. However, the measured coating thickness obtained is then compared to the theoretical thickness calculated from the Newtonian fluid equation. The measured coating thickness usually varies somewhat from the theoretical thickness; further details are described in Section 1. Thus, the Newtonian fluid equation must be modified to better represent the actual film thickness. In this paper, we derive a new formula for the spin coating film thickness, which is based on the equation for Newtonian fluids, but modified to better represent film thicknesses obtained experimentally. The statistical analysis is performed to verify our modifications.

Effect of Stiff Coatings on EHL Film Thickness in Point Contacts

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Yuchuan Liu ◽  
Q. Jane Wang ◽  
Dong Zhu
Keyword(s):  
Film Thickness ◽  
Coating Thickness ◽  
Performance Enhancement ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Thickness Variation ◽  
Grand Challenge ◽  
Maximum Increase ◽  
Wide Range ◽  
Minimum Film Thickness

Coatings are widely used for interface performance enhancement and component life improvement, as well as for corrosion prevention and surface decoration. More and more mechanical components, especially those working under severe conditions, are coated with stiff (hard) thin coatings. However, the effects of coatings on lubrication characteristics, such as film thickness and friction, have not been well understood, and designing coating for optimal tribological performance is a grand challenge. In this paper, the influences of coating material properties and coating thickness on lubricant film thickness are investigated based on a point-contact isothermal elastohydrodynamic lubrication (EHL) model developed recently by the authors. The results present the trend of minimum film thickness variation as a function of coating thickness and elastic modulus under a wide range of working conditions. Curve fitting of numerical results indicates that the maximum increase in minimum film thickness, Imax, and the corresponding optimal dimensionless coating thickness, H2max, can be expressed in the following forms: Imax=0.769M0.0238R20.0297L0.1376exp(−0.0243ln2L) and H2max=0.049M0.4557R2−0.1722L0.7611exp(−0.0504ln2M−0.0921ln2L). These formulas can be used to estimate the effect of coatings on film thickness for EHL applications.

An Efficient Numerical Model of Elastohydrodynamic Lubrication for Transversely Isotropic Materials

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Zhanjiang Wang ◽  
Yinxian Zhang
Keyword(s):  
Film Thickness ◽  
Half Space ◽  
Fluid Pressure ◽  
Elastohydrodynamic Lubrication ◽  
Transversely Isotropic ◽  
Vertical Displacement ◽  
Constant Load ◽  
Von Mises Stress ◽  
Isotropic Materials ◽  
Transversely Isotropic Materials

An elastohydrodynamic lubrication model for a rigid ball in contact with a transversely isotropic half-space is constructed. Reynolds equation, film thickness equation, and load balance equation are solved using the finite difference method, where the surface vertical displacement or deformation of transversely isotropic half-space is considered through the film thickness equation. The numerical methods are verified by comparing the displacements and stresses with those from Hertzian analytical solutions. Furthermore, the effects of elastic moduli, entertainment velocities, and lubricants on fluid pressure, film thickness, and von Mises stress are analyzed and discussed under a constant load. Finally, the modified Hamrock–Dowson equations for transversely isotropic materials to calculate central film thickness and minimum film thickness are proposed and validated.

Elastohydrodynamic Lubrication Analysis for Transversely Isotropic Coating Layer

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Li-Ming Chu ◽  
Chien-Yu Chen ◽  
Chin-Ke Tee ◽  
Qie-Da Chen ◽  
Wang-Long Li
Keyword(s):  
Film Thickness ◽  
Coating Thickness ◽  
Coating Layer ◽  
Load Condition ◽  
Elastohydrodynamic Lubrication ◽  
Transversely Isotropic ◽  
Contact Problems ◽  
Equivalent Model ◽  
Space Problem ◽  
Deformation Equation

The effects of the transversely isotropic coating layer on the elastohydrodynamic lubrication (EHL) circular contact problems are analyzed and discussed under constant load condition. The equivalent elastic modulus for an equivalent isotropic half-space problem is applied to simplify the present transversely isotropic coating. The finite element method (FEM) is utilized to solve the Reynolds equation, the load balance equation, the rheology equations, and the elastic deformation equation simultaneously. The simulation results of the present equivalent model are compared with those of an anisotropic material elasticity matrix to evaluate the applicable range of coating thickness under a fixed relative error. The pressure distribution tends to gradually escalating and concentrating toward the center with increasing longitudinal Young's modulus. The variations of pressure and film thickness become significant as the coating thickness becomes thinner. The deformations of interface are smaller than the deformations of the surface. The film thickness and pressure characteristics of the lubricant are discussed for various parameters. These characteristics are important for the design of the mechanical element with coating layer.

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