Effect of slip and percolation of polar additives of coupled-stress lubricant on the steady-state characteristics of double-layered porous journal bearings

Technical Paper


A theoretical study has been made into the steady-state solution of externally pressurized double-layered porous journal bearings lubricated with coupled-stress fluid with tangential velocity slip at the fine porous interface. The analysis takes into account the tangential velocity slip based on the Beavers–Joseph criterion. Moreover, the present study includes the effects of percolation of the polar additives (microstructures) into the coarse and fine layers of a porous medium. The most general modified Reynolds type equation has been derived for a porous journal bearing lubricated with coupled stress fluids. The governing equations are derived for flow in the coarse and fine layers of the porous medium incorporating the percolation of polar additives of the lubricant. The effects of slip, speed parameter, percolation factor and coupled-stress parameter on the static characteristics in terms of load capacity, attitude angle, side leakage and frictional parameter were investigated. The results are exhibited in the form of graphs.


Coupled stress Double-layered hydrostatic porous journal bearing Percolation Steady state Velocity slip 

List of symbols


Radial clearance of the bearing


Diameter of the bearing


Eccentricity of the bearing


Dimensionless total frictional force on the journal surface


Local film thickness


Dimensionless film thickness (h/C)


Thickness of the porous bush

\(H_{f} ,H_{c}\)

Thickness of the fine and coarse layers, respectively

\(k_{xf} ,k_{yf} ,k_{zf}\)

Permeability coefficient of the fine layer along the x, y, z direction, respectively

\(k_{xc} ,k_{yc} ,k_{zc}\)

Permeability coefficient of the coarse layer along the x, y, z direction, respectively

\(\bar{K}_{xf} ,\bar{K}_{zf}\)

Dimensionless permeability coefficient of the fine layer, \(k_{xf} /k_{yf} ,k_{zf} /k_{yf}\), respectively

\(\bar{K}_{xc} ,\bar{K}_{zc}\)

Dimensionless permeability coefficient of the coarse layer, \(k_{xc} /k_{yc} ,k_{zc} /k_{yc}\), respectively


Dimensionless interlayer permeability coefficient, \(k_{yc} /k_{yf}\)


Characteristic length of additives


Dimensionless characteristic length of additives, \(\bar{l} = l/C\)


Length of the bearing


Ambient pressure


Supply pressure


Dimensionless supply pressure,\(p_{s} /p_{a}\)


Local film pressure in bearing clearance


Dimensionless local film pressure in bearing clearance, \(p/p_{s}\)

\(p_{f}^{'} ,p_{c}^{'}\)

Local film pressure in the fine and coarse layers, respectively

\(\bar{p}_{s}^{'} ,\bar{p}_{c}^{'}\)

Dimensionless local film pressure in the fine and coarse layers,\(p_{f}^{'} /p_{s} , p_{c}^{'} /p_{s}\), respectively


Side leakage of lubricant


Dimensionless side leakage of lubricant \(Q\mu L/C^{3} Dp_{s}\)


Radius of journal


Dimensionless total load-carrying capacity

\(\bar{W}_{r} ,\bar{W}_{t}\)

Dimensionless components of load-carrying capacity


Cartesian coordinate axis along circumferential, radial, and axial direction, respectively

\(\theta ,\bar{y},\bar{z}\)

Dimensionless coordinates, \(\theta = \frac{x}{R} , \bar{y} = \frac{y}{H} ,\bar{z} = \frac{2z}{L}\)


Angular coordinates at which the film cavitates


Percolation factor in the n direction, \(n = x,y,z\)

\(\gamma_{nf} , \gamma_{nc}\)

Dimensionless percolation factor for the fine and coarse layers, respectively. \(n = x,y,z\)


Dimensional permeability factor, \(\sigma_{n} = C/\sqrt {k_{n} }\), n = x, z


Coefficient of classical absolute viscosity of the lubricant


Material constant with the dimension of momentum accounting for the coupled stress


Bearing feeding parameter, \(\beta = 12k_{yf} R^{2} /HC^{3}\)


Slip function in the n direction, n = x, z


Slip function defined by \(\xi_{0x} = 1/1 + \alpha \sigma_{x} \bar{h}\)

\(\chi_{nf} ,\chi_{nc}\)

Percolation function for the fine and coarse layers in the n direction n = x, z


Attitude angle


Coefficient of friction


Angular velocity of journal rotation


Eccentricity ratio \(\varepsilon_{0} = e/C\)


Slip coefficient


Coarse layer thickness ratio \(H_{C} /H\)


Bearing number \(\varLambda_{S} = 6\mu \omega R^{2} /p_{s} C^{2}\)


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of Engineering Science and TechnologyHowrahIndia

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