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Research Papers: Elastohydrodynamic Lubrication

Elastohydrodynamic Lubrication Modeling by a Cosserat Continuum Theory for Small Polymer Journal Bearings

[+] Author and Article Information
B. Zhu

Surface Engineering Laboratory,
School of Materials Science and Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: bzhu@dlut.edu.cn

Y. J. Cai

Surface Engineering Laboratory,
School of Materials Science and Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: yxcaicai@mail.dlut.edu.cn

Y. P. Li

Surface Engineering Laboratory,
School of Materials Science and Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: ypli@dlut.edu.cn

M. K. Lei

Surface Engineering Laboratory,
School of Materials Science and Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: surfeng@dlut.edu.cn

D. M. Guo

Key Laboratory for Precision and Non-Traditional Machining Technology of Ministry of Education,
Dalian University of Technology,
Dalian 116024, China
e-mail: guodm@dlut.edu.cn

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received February 12, 2019; final manuscript received April 24, 2019; published online May 22, 2019. Assoc. Editor: Joichi Sugimura.

J. Tribol 141(8), 081501 (May 22, 2019) (18 pages) Paper No: TRIB-19-1069; doi: 10.1115/1.4043641 History: Received February 12, 2019; Accepted April 25, 2019

Recent experiments have shown that the elastic deformation behaviors of a polymeric material are consistent with the Cosserat elasticity under nonuniform deformation at a millimeter scale. Thus, an elastohydrodynamic lubrication model in the framework of the Cosserat continuum theory is proposed to explore the lubrication performance that deviates from the classical elastohydrodynamic lubrication theory for the small polymer journal bearings with millimeter size. The elastic deformation of the bearing sleeve made of polymeric material and the pressure distribution in a lubricating film are obtained through an iterative solution of the equation of the Cosserat elasticity and the modified Reynolds’ equations with considering the boundary slippage. The effect of bearing size and Cosserat characteristic lengths for torsion and bending on the lubrication performance of the small polymer journal bearings is studied using the proposed Cosserat elastohydrodynamic lubrication model. It was found that the small changes in film thickness due to the Cosserat effect can result in large changes in film pressure. The Cosserat characteristic length of bending possesses a significant effect on the lubrication behaviors of the journal bearings, because the size effect is mainly caused by the increased apparent modulus due to the bending elastic deformation of the bearing sleeve. The boundary slip behaviors dependent on the Cosserat characteristic length are also studied using the Cosserat elastohydrodynamic model, and the numerical results show that the Cosserat characteristic length changes the optimal geometric parameters of the slip zone in terms of load carrying capacity for the small polymer journal bearings.

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Figures

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Fig. 1

(a) Schematic of the journal bearing and (b) geometry of the slip/no-slip configuration of the sleeve surface for the journal bearing

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Fig. 2

FEM models of (a) the lubricating film and (b) the bearing sleeve

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Fig. 3

The flowchart of the numerical process for the Cosserat EHD lubrication model of the journal bearing

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Fig. 4

Size effects of the journal bearing: (a) with slip/no-slip configuration and (b) without slip/no-slip configuration

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Fig. 5

Distributions of the film thickness, film pressure, and slip velocity of the journal bearing with the slip/no-slip configuration obtained by the Cosserat EHD model with different Cosserat characteristic lengths

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Fig. 6

The film pressure and thickness profiles at the central position along the θ direction obtained by the Cosserat EHD model with different Cosserat characteristic lengths: (a) film pressure and (b) film thickness

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Fig. 7

Effects of the Cosserat characteristic lengths on the behaviors of the journal bearing with the slip/no-slip configuration: (a) load support capacity, (b) power loss, and (c) load support angle

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Fig. 8

The behaviors of the journal bearing versus the eccentricity ratio obtained by the Cosserat EHD model and the conventional EHD model: (a) load support capacity, (b) power loss, and (c) load support angle

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Fig. 9

Distributions of the film pressure of the journal bearing with different initial limiting shear stresses obtained by the Cosserat EHD model with different Cosserat characteristic lengths

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Fig. 10

The film pressure profile at the central position along the θ direction obtained by the Cosserat EHD model with different initial limiting shear stresses: (a) τ0 = 0.0 kPa, (b) τ0 = 0.5 kPa, and (c) τ0 = 1.0 kPa

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Fig. 11

Distributions of the film thickness of the journal bearing with different initial limiting shear stresses obtained by the Cosserat EHD model with different Cosserat characteristic lengths

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Fig. 12

The film thickness profile at the central position along the θ direction obtained by the Cosserat EHD model with different initial limiting shear stresses: (a) τ0 = 0.0 kPa, (b) τ0 = 0.5 kPa, and (c) τ0 = 1.0 kPa

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Fig. 13

Distributions of the slip velocity of the journal bearing with different limiting shear stresses obtained by the Cosserat EHD model with different Cosserat characteristic lengths

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Fig. 14

The effects of the limiting shear stress on the behaviors of the journal bearing with the slip/no-slip configuration obtained by the Cosserat EHD model and the conventional EHD model: (a) load support capacity, (b) power loss, and (c) load support angle

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Fig. 15

Distributions of the film pressure of the journal bearing with different proportional constants obtained by the Cosserat EHD model with different Cosserat characteristic lengths

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Fig. 16

The film pressure profile at the central position along the θ direction obtained by the Cosserat EHD model with different proportional constants: (a) κ = 0.0, (b) κ = 0.004, and (c) κ = 0.014

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Fig. 17

Distributions of the film thickness of the journal bearing with different proportional constants obtained by the Cosserat EHD model with different Cosserat characteristic lengths

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Fig. 18

The film thickness profile at the central position along the θ direction obtained by the Cosserat EHD model with different proportional constants: (a) κ = 0.0, (b) κ = 0.004, and (c) κ = 0.014

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Fig. 19

Distributions of the slip velocity of the journal bearing with different proportional constants obtained by the Cosserat EHD model with different Cosserat characteristic lengths

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Fig. 20

The effects of the proportional constant on the behaviors of the journal bearing with the slip/no-slip configuration obtained by the Cosserat EHD model and the conventional EHD model: (a) load support capacity, (b) power loss, and (c) load support angle

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Fig. 21

Effect of the geometry of the slip/no-slip configuration on the behaviors of the journal bearing obtained by the Cosserat EHD model and the conventional EHD model: (a) load support capacity, (b) power loss, and (c) load support angle

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Fig. 22

Optimization results versus eccentricity ratio: (a) load support capacity and ratios of journal bearing with the slip/no-slip configuration to that of the traditional journal bearing, (b) the corresponding load support angle, and (c) the corresponding power loss

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Fig. 23

Optimized geometry of the slip/no-slip configuration versus the eccentricity ratio: (a) width of the slip/no-slip configuration and (b) length of the slip/no-slip configuration

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