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.

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.

Surface Effects on Large Deflection of Nanobeams Subjected to a Follower Load

2020 ◽  
Vol 12 (06) ◽  
pp. 2050067
Author(s):  
Yun Xing ◽  
Yi Han ◽  
Hua Liu ◽  
Jialing Yang
Keyword(s):  
Large Deformation ◽  
Surface Stress ◽  
Large Deflection ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Surface Residual Stress ◽  
Residual Surface Stress ◽  
Deformation Problem ◽  
Cross Sectional Dimension

As a basic element of the micro/nanodevices, nanobeams have remarkable physical properties and have attracted considerable attention in the previous studies. However, previous publications did not study the large deformation problem of nanobeams under follower loading when the surface effect becomes significant and especially for the influence of surface effect on mechanical behaviors of the nanobeams under follower loading remains unclear. In this paper, we investigated the large deformation behavior of nanobeams subjected to follower loads in consideration of the surface effects. The mechanical model of large deflection of extensible cantilever nanobeams under follower loading is presented in combination with the surface elasticity and residual surface stress, and then a MATLAB program of shooting method with a technique for determining the initial value was developed to solve the problems. The results indicate that the surface effects have an important influence on the large deflection of nanobeams under follower loading: when the surface residual stress is positive, the maximums of displacement in horizontal and vertical directions and the rotation angle of the free end become lager, but the corresponding follower force related to those maximums becomes smaller. When the residual surface stress is negative, the results are the opposite. In addition, the influence of the cross-sectional dimension of the nanobeams under follower loading on surface effects was discussed. This work is beneficial to understand the mechanism of large deformation of nanobeams with surface effects subjected to follower loads, and can also provide inspirations to design advanced nanomaterials and nanoscaled devices.

Elastic Energy of Surfaces and Residually Stressed Solids: An Energy Approach for the Mechanics of Nanostructures

2015 ◽  
Vol 82 (1) ◽  
Author(s):  
Xiang Gao ◽  
Daining Fang
Keyword(s):  
Surface Energy ◽  
Elastic Energy ◽  
Surface Stress ◽  
Strain Energy ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Small Deformation ◽  
Energy Approach ◽  
Residual Surface Stress ◽  
The Impact

The surface energy plays a significant role in solids and structures at the small scales, and an explicit expression for surface energy is prerequisite for studying the nanostructures via energy methods. In this study, a general formula for surface energy at finite deformation is constructed, which has simple forms and clearly physical meanings. Next, the strain energy formulas both for isotropic and anisotropic surfaces under small deformation are derived. It is demonstrated that the surface elastic energy is also dependent on the nonlinear Green strain due to the impact of residual surface stress. Then, the strain energy formula for residually stressed elastic solids is given. These results are instrumental to the energy approach for nanomechanics. Finally, the proposed results are applied to investigate the elastic stability and natural frequency of nanowires. A deep analysis of these two examples reveals two length scales characterizing the significance of surface energy. One is the critical length of nanostructures for self-buckling; the other reflects the competition between residual surface stress and surface elasticity, indicating that the surface effect does not always strengthen the stiffness of nanostructures. These results are conducive to shed light on the importance of the residual surface stress and the initial stress in the bulk solids.

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.

Mixed lubrication of soft contacts: An engineering look

2016 ◽  
Vol 231 (2) ◽  
pp. 263-273 ◽  
Author(s):  
M Masjedi ◽  
MM Khonsari
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Load Ratio ◽  
Soft Materials ◽  
Line Contact ◽  
Soft Contact ◽  
Lubrication Regime ◽  
Low Elastic Modulus ◽  
Stribeck Curves

Mixed elastohydrodynamic lubrication of materials with low elastic modulus (soft materials) is investigated. Expressions for prediction of film thickness and the asperity load ratio in soft line-contact elastohydrodynamic lubrication are presented. The traction behavior of soft contact in mixed elastohydrodynamic lubrication regime is also studied in terms of the Stribeck curves.

Elastohydrodynamic Lubrication of Elliptical Contacts for Materials of Low Elastic Modulus I—Fully Flooded Conjunction

1978 ◽  
Vol 100 (2) ◽  
pp. 236-245 ◽  
Author(s):  
Bernard J. Hamrock ◽  
Duncan Dowson
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Pressure Distribution ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Low Elastic Modulus ◽  
Minimum Film Thickness ◽  
Contour Plots ◽  
Order Of Magnitude ◽  
Ellipticity Parameter

Our earlier studies of elastohydrodynamic lubrication of conjunctions of elliptical form are applied to the particular and interesting situation exhibited by materials of low elastic modulus. By modifying the procedures we outlined in an earlier publication, the influence of the ellipticity parameter k and the dimensionless speed U, load W, and material G parameters on minimum film thickness for these materials has been investigated. The ellipticity parameter was varied from 1 (a ball-on-plate configuration) to 12 (a configuration approaching a line contact). The dimensionless speed and load parameters were varied by 1 order of magnitude. Seventeen different cases were used to generate the following minimum- and central-film-thickness relations: H˜min=7.43(1−0.85e−0.31k)U0.65W−0.21H˜c=7.32(1−0.72e−0.28k)U0.64W−0.22 Contour plots are presented that illustrate in detail the pressure distribution and film thickness in the conjunction.

scholarly journals On the Stress Transfer of Nanoscale Interlayer with Surface Effects

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Quan Yuan ◽  
Mengjun Wu
Keyword(s):  
Surface Effect ◽  
Surface Elasticity ◽  
Stress Transfer ◽  
Interfacial Stress ◽  
Interlayer Thickness ◽  
Shear Lag ◽  
Multilayered Structures ◽  
Residual Surface Stress ◽  
Shear Lag Model ◽  
Lag Model

An improved shear-lag model is proposed to investigate the mechanism through which the surface effect influences the stress transfer of multilayered structures. The surface effect of the interlayer is characterized in terms of interfacial stress and surface elasticity by using Gurtin–Murdoch elasticity theory. Our calculation result shows that the surface effect influences the efficiency of stress transfer. The surface effect is enhanced with decreasing interlayer thickness and elastic modulus. Nonuniform and large residual surface stress distribution amplifies the influence of the surface effect on stress concentration.

Size effect on thermal elastohydrodynamic lubrication of industrial chain bush-pin hinge pair

2019 ◽  
Vol 71 (9) ◽  
pp. 1080-1085 ◽  
Author(s):  
Mingyu Zhang ◽  
Jing Wang ◽  
Yi Liu ◽  
Longjie Dai ◽  
Zhaohua Shang
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Temperature Rise ◽  
Elastohydrodynamic Lubrication ◽  
Curvature Radius ◽  
Line Contact ◽  
Content Type ◽  
Oil Film ◽  
Industrial Chain ◽  
Infinite Line

Purpose The purpose of this paper is to use elastohydrodynamic lubrication (EHL) theory to study the variation of the equivalent curvature radius “R” on the change of oil film thickness, pressure, temperature rise and friction coefficient in the contact zone between bush-pin in industrial chain drive. Design/methodology/approach In this paper, the contact between bush and pin is simplified as infinitely long line contact. The lubrication state is studied by numerical simulation using steady-state line contact thermal EHL. The two constitutive equations, namely, Newton fluid and Ree–Eyring fluid are used in the calculations. Findings It is found that with the increase of equivalent curvature radius, the thickness of oil film decreases and the temperature rise increases. Under the same condition, the friction coefficient of Newton fluid is higher than that of Ree–Eyring fluid. When the load increases, the oil film thickness decreases, the temperature rise increases and the friction coefficient decreases; and the film thickness increases with the increase of the entraining speed under the condition “R < 1,000 mm”. Research limitations/implications The infinite line contact assumption is only an approximation. For example, the distances between the two inner plates are 5.72 mm, by considering the two parts assembled into the inner plates, the total length of the bush is less than 6 mm. The diameter of the pin and the bore diameter of the bush are 3.28 and 3.33 mm. However, the infinite line contact is also helpful in understanding the general variation of oil film characteristics and provides a reference for the future study of finite line contact of chain problems. Originality/value The change of the equivalent radius R on the variation of the oil film in the contact of the bush and the pin in industrial chain drive was investigated. The size effect influences the lubrication characteristic greatly in the bush-pin pair.

Surface Effects on the Buckling of Piezoelectric Nanobeams

2012 ◽  
Vol 486 ◽  
pp. 519-523 ◽  
Author(s):  
Kai Fa Wang ◽  
Bao Lin Wang
Keyword(s):  
Shear Deformation ◽  
Electric Potential ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Residual Surface Stress ◽  
Buckling Behavior ◽  
Stress Surface ◽  
Piezoelectric Nanobeam

In this paper, we analyze the influence of surface effects including residual surface stress, surface piezoelectric and surface elasticity on the buckling behavior of piezoelectric nanobeams by using the Timoshenko beam theory and surface piezoelectricity model. The critical electric potential for buckling of piezoelectric nanobeams with different boundary condition is obtained analytically. From the results, it is found that the surface piezoelectric reduces the critical electric potential. However, a positive residual surface stress increases the critical electric potential. In addition, the shear deformation reduces the critical electric potential, and the influence of shear deformation become more significant for a stubby piezoelectric nanobeam.

Size-dependent resonance frequencies of cantilevered and bridged nanosensors

2018 ◽  
Vol 32 (07) ◽  
pp. 1850095 ◽  
Author(s):  
W. Shi ◽  
J. Zou ◽  
K. Y. Lee ◽  
X. F. Li
Keyword(s):  
Surface Effect ◽  
Surface Elasticity ◽  
Integral Equation Method ◽  
Mode Shapes ◽  
Concentrated Mass ◽  
Approximation Accuracy ◽  
Mass System ◽  
Residual Surface Stress ◽  
Resonance Frequencies ◽  
Mechanical Sensors

This paper studies transverse vibration of nanoscale cantilevered and bridged sensors carrying a nanoparticle. The nanoscale sensors are modelled as Euler–Bernoulli beams with surface effect and nanoparticle as a concentrated mass. Frequency equations of cantilevered and bridged beam-mass system are derived and exact resonance frequencies are calculated. An alternative Fredholm integral equation method is used to obtain an approximate explicit expression for the fundamental frequency for both cases. A comparison between the approximate and analytical results is made and the approximation accuracy is satisfactory. The influences of the residual surface stress, surface elasticity, and attached mass on the resonance frequencies and mode shapes are discussed. These results are useful to illustrate the surface phenomena and are helpful to design micro-/nano-mechanical sensors.

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