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Multiscale Analysis of Hydrodynamic Journal Bearing Considering the Effect of the Physically Adsorbed Boundary Layer

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Abstract

In itself, there is a very thin boundary layer physically adsorbed to the bearing surface. When the bearing clearance is far larger than the thickness of this layer, the boundary layer effect in the bearing is negligible, and conventional hydrodynamic lubrication theory just addresses on this topic. However, with the worsening of the operating condition, the bearing clearance can be largely reduced and comparable to the thickness of the adsorbed boundary layer. For this case, the effect of the adsorbed boundary layer must be considered. The present paper presents the multiscale analysis for the performance of the hydrodynamic journal bearing in a wide range of bearing clearance considering the effect of the physically adsorbed boundary layer. The calculation results indicate for how low bearing clearances the adsorbed boundary layer effect should be incorporated. When the minimum bearing clearance is on the same scale with the thickness of the adsorbed boundary layer, the hydrodynamic pressure in the bearing is locally largely increased by the effect of the adsorbed boundary layer, and the load-carrying capacity of the bearing is correspondingly largely increased. This is particularly significant for a strong fluid-bearing surface interaction. The study shows the great contribution of the physically adsorbed boundary layer to the performance of the hydrodynamic journal bearing in the condition of low surface clearances, and indicates the necessity of the multiscale analysis for this bearing.

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Abbreviations

a 0, a 1, a 2 :

constants

c :

bearing clearance, R-r

C q :

ρ effbf /ρ

C y :

η effbf /η

D :

fluid molecule diameter

e :

eccentricity of the bearing

h :

continuum fluid film thickness

h bf :

thicknesses of the adsorbed boundary layer

h cr,bf :

critical thickness

H bf :

hbf/hcr,bf

K :

hbf/c

m 0, m 1, m 2, m 3 :

constants

N :

numbers of the discretized points

p :

hydrodynamic pressure

P :

dimensionless hydrodynamic pressure

P conv :

hydrodynamic pressure calculated from the conventional hydrodynamic theory

q 0 :

Δj+1/Δj

q m :

mass flow rate per unit contact length through the bearing

Q m :

dimensionless mass flow rate per unit contact length through the bearing

r :

radius of the shaft

R :

radius of the sleeve

u :

shaft circumferential speed

w :

load per unit contact length carried by the bearing

W :

dimensionless load per unit contact length carried by the bearing

x, y :

coordinates

β :

angel, Equation (20)

γ :

exponent

ε :

eccentricity ratio, e/c

ε 0 :

parameter, Equation (28)

λ bf :

hbf/h

ϕ :

angular coordinate

ϕ 0 :

angular coordinate of the location where the maximum pressure occurs in the bearing

ϕ e :

angular coordinate of the exit of the bearing

Δϕ :

envelope angles of the two neighboring discretized points

Δx :

separation between the neighboring fluid molecules in the circumferential direction in the adsorbed layer

Δj :

separation between the (j+1)th and jth fluid molecules across the layer thickness

Δn−2 :

separation between the neighboring fluid molecules across the layer thickness just on the adsorbed layer-fluid interface

θ 0,conv :

sommerfeld transformation angle, π-β

ρ :

fluid bulk density

ρ effbf : effective density of the adsorbed layer η :

fluid bulk viscosity

η eff bf :

effective viscosity of the adsorbed boundary layer

η linc, j−1 :

local viscosity between the jth and (j−1)th fluid molecules across the adsorbed layer thickness

conv :

calculated from the conventional hydrodynamic theory

i :

on the ith discretized point

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Authors and Affiliations

  1. College of Mechanical Engineering, Changzhou University, Changzhou, 213164, China

    Kaicheng Gu, Shaojin Shao & Yongbin Zhang

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  1. Kaicheng Gu
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  2. Shaojin Shao
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  3. Yongbin Zhang
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Correspondence to Yongbin Zhang.

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Gu, K., Shao, S. & Zhang, Y. Multiscale Analysis of Hydrodynamic Journal Bearing Considering the Effect of the Physically Adsorbed Boundary Layer. Int.J Automot. Technol. 24, 335–345 (2023). https://doi.org/10.1007/s12239-023-0028-3

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  • DOI: https://doi.org/10.1007/s12239-023-0028-3

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