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Research Papers: Elastohydrodynamic Lubrication

Model for Elastohydrodynamic Lubrication of Multilayered Materials

[+] Author and Article Information
Zhanjiang Wang

State Key Laboratory of
Mechanical Transmission,
Chongqing University,
Chongqing 400030, China
e-mail: wangzhanjiang001@gmail.com

Chenjiao Yu

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

Qian Wang

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208;
State Key Laboratory of
Mechanical Transmission,
Chongqing University,
Chongqing 400030, China

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received April 27, 2014; final manuscript received August 17, 2014; published online October 3, 2014. Assoc. Editor: Mircea Teodorescu.

J. Tribol 137(1), 011501 (Oct 03, 2014) (14 pages) Paper No: TRIB-14-1097; doi: 10.1115/1.4028408 History: Received April 27, 2014; Revised August 17, 2014

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.

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Figures

Grahic Jump Location
Fig. 1

Model of multilayered materials in an EHL contact, where the layers of different elastic constants and thicknesses are perfectly joined together. The Cartesian coordinates are used and the origin of the z axis in each layer is located at its top surface or at the interface.

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Fig. 2

Central film thickness and minimum film thickness obtained from the present method (case 2: E1 = E2 = Es) and Hamrock–Dowson equations [43]

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Fig. 3

Dimensionless fluid pressure and film thickness for the cases of stiffer layers (case 1: E1 = 2E2 = 4Es), homogeneous materials (case 2: E1 = E2 = Es) and compliant layers (case 3: E1 = 0.5E2 = 0.25Es) at entraining velocity U = 1 m/s: (a) along the x axis and (b) along the y axis

Grahic Jump Location
Fig. 4

Contour plots of dimensionless film thickness for different cases: (a) case 1: E1 = 2E2 = 4Es, (b) case 2: E1 = E2 = Es, and (c) case 3: E1 = 0.5E2 = 0.25Es

Grahic Jump Location
Fig. 5

Dimensionless fluid pressure and film thickness for the cases with stiffer layers (case 1: E1 = 2E2 = 4Es), homogeneous materials (case 2: E1 = E2 = Es) and compliant layers (case 3: E1 = 0.5E2 = 0.25Es) at entraining velocity U = 10 m/s: (a) along the x axis and (b) along the y axis

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Fig. 6

Central film thickness and minimum film thickness affected by the entraining velocity

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Fig. 7

Dimensionless fluid pressure and film thickness for the cases with layers with larger Poisson's ratio (case 4: ν1 = ν2 = 0.45, νs = 0.3), homogeneous materials (case 2: ν1 = ν2 = νs = 0.3) and smaller Poisson's ratio (case 5: ν1 = ν2 = 0.2, νs = 0.3) at entraining velocity U = 1 m/s: (a) along the x axis and (b) along the y axis

Grahic Jump Location
Fig. 8

Contour plots of subsurface von Mises stress in the x–z plane for the cases of various layers: (a) case 1: E1 = 2E2 = 4Es, (b) case 2: E1 = E2 = Es, (c) case 3: E1 = 0.5E2 = 0.25Es, (d) case 4: ν1 = ν2 = 0.45, νs = 0.3, and (e) case 5: ν1 = ν2 = 0.2, νs = 0.3

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Fig. 9

Dimensionless fluid pressure and film thickness for the cases of various substrates from 0.1E to infinity at entraining velocity U = 1 m/s: (a) E1 = 2E2 = 4E, (b) E1 = E2 = E, and (c) E1 = 0.5E2 = 0.25E

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Fig. 10

Central film thickness and minimum film thickness affected by the substrate stiffness, Es

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Fig. 11

Dimensionless fluid pressure and film thickness along the x axis and subsurface von Mises stress in the x–z plane at different entraining velocities U = 1 m/s and U = 10 m/s (various layers but with the rigid substrate): (a) E1 = 2E2 = 4E, (b) E1 = E2 = E, and (c) E1 = 0.5E2 = 0.25E

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Fig. 12

Dimensionless surface stress σxx/ph along the x axis at different entraining velocities (various layers but with the rigid substrate): (a) U = 1 m/s and (b) U = 10 m/s

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Fig. 13

Dimensionless fluid pressure and film thickness along the x axis for different lubricants at entraining velocity U = 1 m/s: (a) for the material with decreasing modulus Ej = [4–0.6 × (j − 1)] × E (j = 1,…,5); (b) for the material with alternative modulus Ej = 4E (j = 1,3,5) and Ej = E (j = 2,4)

Grahic Jump Location
Fig. 14

Dimensionless fluid pressure and film thickness along the x axis and subsurface von Mises stress in the x–z plane at entraining velocities U = 1 m/s: (a) for the surface system with decreasing modulus Ej = [4–0.6 × (j − 1)] × E (j = 1,…,5) and (b) for the surface system with alternative modulus Ej = 4E (j = 1,3,5) and Ej = E (j = 2,4)

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Fig. 15

Dimensionless fluid pressure and film thickness for two typical functionally gradient coatings (Young's modulus increases or decreases along the z direction) for lubricant 1 and under different velocities: (a) along the x axis and (b) along the y axis

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Fig. 16

Dimensionless fluid pressure and film thickness affected by coating thickness for lubricant 1 and at entraining velocity U = 1 m/s: (a) E0 = 4Es and (b) E0 = 0.25Es

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Fig. 17

Central film thickness and minimum film thickness affected by coating thickness for lubricant 1 and at entraining velocity U = 1 m/s: (a) central film thickness and (b) minimum film thickness

Grahic Jump Location
Fig. 18

Central film thickness and minimum film thickness affected by coating thickness for lubricant 1 and at entraining velocity U = 10 m/s: (a) central film thickness and (b) minimum film thickness

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Fig. 19

Central film thickness and minimum film thickness affected by coating thickness for lubricant 2 and at entraining velocity U = 1 m/s: (a) central film thickness and (b) minimum film thickness

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