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Multiscale hydrodynamics in thrust bearing involving surface roughness

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Abstract

When the surface roughness is comparable to the surface separation in a hydrodynamic thrust bearing, the effect of the surface roughness should be considered. In the condition of low bearing clearances such as on the scales of 1 nm and 10 nm, normally not only the surface roughness but also the physically adsorbed layer on the bearing surface should be simultaneously considered in evaluating the bearing performance. The present paper presents the numerical calculation results of the surface roughness influences on the hydrodynamic pressure and carried load of the inclined fixed pad thrust bearing with low bearing clearances when the effect of the adsorbed layer is incorporated. It is shown that the influence of the surface roughness is strongly dependent on the adsorbed layer and it is significantly increased with the increase in the interaction strength between the fluid and the bearing surface when the bearing clearance is low. For a weak fluid-bearing surface interaction, the results are close to those obtained from the classical hydrodynamic theory indicating the increase in the hydrodynamic pressure and carried load of the bearing with the increase in the surface roughness, while for the medium or strong fluid-bearing surface interactions, this surface roughness effect is much stronger. The results reveal the new mechanism in the studied model of the bearing regarding the coupled effects of the surface roughness and the physically adsorbed layer on the bearing surface.

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Abbreviations

\(a_{0},a_{1},a_{2} \) :

Constant for formulating \(C_{y} \), Eq. (10)

\(C_{q} \) :

Ratio of the average density of the adsorbed layer to the fluid bulk density, \(\rho _{{bf},K}^{{eff}}/\rho _{K}\)

\(C_{y} \) :

Ratio of the effective viscosity of the adsorbed layer to the fluid bulk viscosity, \(\eta _{{bf},K}^{{eff}} /\eta _{K}\)

D :

Fluid molecule diameter

h :

Thickness of the intermediate continuum fluid film

\(h_{bf} \) :

Adsorbed layer thickness

\(h_{cr,{bf}}\) :

Critical thickness for characterizing the rheological properties of the adsorbed layer

\(h_{o} \) :

Continuum fluid film thicknesses on the bearing exit

\(h_{t} \) :

Surface separation

\(h_{t,o} \) :

Surface separation on the bearing exit

\(H_{bf}\) :

\(h_{{bf}} /h_{cr,{bf}}\)

\(H_{t,o}\) :

\(h_{t,o} /h_{bf}\)

i, j :

Order numbers of the fluid molecules across the adsorbed layer thickness, respectively

l :

Width of the bearing

\(m_{0}, m_{1}, m_{2}, m_{3} \) :

Constant for formulating \(C_{q} \), Eq. (9)

n :

Equivalent number of the fluid molecules across the adsorbed layer thickness

N :

Maximum order number of the discretized points

p :

Hydrodynamic pressure

P :

Dimensionless hydrodynamic pressure, \(ph_{t,o} /(u\eta _{a} )\)

\(q_{0} \) :

Ratio of the neighboring fluid molecule separations across the adsorbed layer thickness, \(\Delta _{j+i} /\Delta _{j}\)

\(q_{m} \) :

Mass flow rate per unit contact length through the bearing

\(Q_{m} \) :

Dimensionless mass flow rate per unit contact length through the bearing, \(q_{m} /(u\rho _{a} h_{t,o} )\)

\(Q_{m,\max }, \quad Q_{m,\min } \) :

Upper and lower limits of the range where the real value of \(Q_{m} \) exists, respectively

\(R_{z} \) :

Maximum height of the surface roughness

u :

Sliding speed of the bearing

w :

Load per unit contact length carried by the bearing

W :

Dimensionless load, \(w/(u\eta _{a} )\)

x :

Coordinate in the flow direction

X :

Dimensionless coordinate, x/l

\(\theta \) :

Bearing tilting angle

\(\delta _{x} \) :

Distance between the neighboring discretized points in the lubricated area, l/N

\(\rho \) :

Fluid bulk density

\(\rho _{bf}^{eff}\) :

Average density of the adsorbed layer

\(\rho _{a} \) :

Fluid bulk density at atmospheric pressure

\(\eta \) :

Fluid bulk viscosity

\(\eta _{{bf}}^{{eff}} \) :

Effective viscosity of the adsorbed layer

\(\eta _{a} \) :

Fluid bulk viscosity at atmospheric pressure

\(\lambda _{bf} \) :

Ratio of the thickness of the adsorbed layer to the thickness of the intermediate continuum fluid film, \(h_{bf} /h\)

\(\Delta _{j} \) :

Separation between the \((j+1)\textrm{th}\) and \(j{\textrm{th}}\) fluid molecules across the adsorbed layer thickness

\(\Delta x\) :

Separation between the neighboring fluid molecules in the x coordinate direction in the adsorbed layer

\(\Delta _{n-2} \) :

Separation between the neighboring fluid molecules across the adsorbed layer thickness just on the boundary between the adsorbed layer and the continuum fluid

J, K :

On the Jth and Kth discretized points in the lubricated area, respectively

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  1. College of Mechanical Engineering, Changzhou University, Changzhou, Jiangsu Province, China

    Chen Huang & Yongbin Zhang

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Huang, C., Zhang, Y. Multiscale hydrodynamics in thrust bearing involving surface roughness. Continuum Mech. Thermodyn. 36, 445–458 (2024). https://doi.org/10.1007/s00161-023-01275-z

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