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
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Abstract

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.

Keywords

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

List of symbols

\(C\)

Radial clearance of the bearing

\(D\)

Diameter of the bearing

\(e\)

Eccentricity of the bearing

\(\bar{F}_{\text{s}}\)

Dimensionless total frictional force on the journal surface

\(h\)

Local film thickness

\(\bar{h}\)

Dimensionless film thickness (h/C)

\(H\)

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

\(\bar{K}_{yc}\)

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

\(l\)

Characteristic length of additives

\(\bar{l}\)

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

\(L\)

Length of the bearing

\(p_{a}\)

Ambient pressure

\(p_{s}\)

Supply pressure

\(\bar{p}_{s}\)

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

\(p\)

Local film pressure in bearing clearance

\(\bar{p}\)

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

\(Q\)

Side leakage of lubricant

\(\bar{Q}_{c}\)

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

\(R\)

Radius of journal

\(\bar{W}\)

Dimensionless total load-carrying capacity

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

Dimensionless components of load-carrying capacity

\(x,y,z\)

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

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

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

\(\theta_{c}\)

Angular coordinates at which the film cavitates

\(\gamma_{n}\)

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

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

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

\(\sigma_{n}\)

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

\(\mu\)

Coefficient of classical absolute viscosity of the lubricant

\(\eta\)

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

\(\beta\)

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

\(\xi_{n}\)

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

\(\xi_{0x}\)

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

\(\phi_{0}\)

Attitude angle

\(\mu_{f}\)

Coefficient of friction

\(\omega\)

Angular velocity of journal rotation

\(\varepsilon_{0}\)

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

\(\alpha\)

Slip coefficient

\(\lambda_{c}\)

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

\(\varLambda_{S}\)

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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