Effects of slip‐velocity and viscosity variation in squeeze film lubrication of triangular plates

Introduction

Squeeze film lubrication has several practical applications in our day today life. The performance of hydraulic machines are enhanced in the presence of squeeze film lubrication. Squeeze film phenomenon is found when two relatively moving surfaces approach each other with a normal velocity. The viscous lubricant between the plates offers resistance to extrusion and builds up pressure that helps to support the load. Dowson [1] developed a generalised form of Reynolds equation which permits the variation of relevant quantities across, as well as along the lubricant film. Squeeze film characteristics of couple stress fluid between porous triangular plates is analysed in [2] . The micro additives present in the lubricant enhances the squeeze film characteristics. Vadher [3] analysed hydro magnetic squeeze film between conducting porous transversely rough triangular plates. The results shows that the magnetization parameter and the conductivity increase the load carrying capacity while, the load carrying capacity decreases due to porosity and standard deviation. Sundarammal Kesavan and Manimegalai [4] investigated the surface roughness effects on the squeeze film between two parallel porous elliptic plates. The surface roughness and the couple stress present in the lubricant results in high lubricant viscosity. Hamid Khan [7] studied the effects of squeeze flow between two large parallel plates by transforming the basic governing equations of the first grade fluid to an ordinary nonlinear differential equation using the stream functions and a transformation. Rao [9] analysed the effects of velocity-slip and viscosity variation for squeeze film lubrication of two circular plates. The load capacity and squeeze time decreases due to slip. Fathima [11] studied the combined effect of couple stress and magnetic effect on the squeeze film lubrication between porous plates of different geometry. The effect of the porous facing on couplestress squeeze film lubrication in the presence of applied magnetic field enhances pressure, load carrying capacity and squeeze film time. The results are compared to corresponding non-magnetic and Newtonian case. Umar Khan [12] applied the variation of parameters method can successfully be applied to solve the equations governing unsteady squeezing flows between parallel plates. Santhana Krishnan Narayanan and Sundarammal Kesavan [13] , analysed the magneto-hydrodynamics non-newtonian squeeze film characteristics of porous circular plates. We have analysed the effects of viscosity variation in squeeze film lubrication of circular stepped plates in [14] . In the present paper, an attempt has been made to study the effects of slip velocity and viscosity variation in squeeze film lubrication of triangular plates.

Analysis

The Navier-Stokes equation for the laminar flow between two symmetric plates as obtained by Dowson [1] is,

Where p= p(x, y) is the pressure in the film and η is the viscosity. The boundary conditions considering slip at the surfaces.

Where the suffixes 1 and 2 represent the values at z=H1 and z=H2, respectively. Here λ and δ depend on viscosity and the coefficient is sliding friction.

From equation ( 1), ( 2) and ( 4) we obtain,

Assuming slip conditions at the bearing surfaces,

Using the concept of multiple layer lubrication,

Assuming, U1= U U2=V1=V2=0

Where s V is the resultant velocity towards the film. Considering three symmetrical incompressible layers between two solid boundaries we have,

In the case of squeeze film lubrication of triangular plates we have, Where

Hence the pressure is obtained as,

The dimensionless pressure of the bearing is,

Integrating the pressure over the area of the plate the load carrying capacity of the bearing is,

The time-height relation is observed to be

Conclusion

The dimensionless pressure increases as the ratio of the viscosities increases. Also the dimensionless pressure increases when the slip parameter increases. The load carrying capacity increases as ratio of the viscosities increases. Also the load carrying capacity increases as the slip parameter increases. The load carrying capacity increases when the length of the triangle plate increases. The squeezing time decreases as ratio of the viscosities increases. Slip parameter increases as dimensionless squeeze time decreases.

Final film thickness increases as dimensionless squeeze time decreases. This indicates that when slip decreases the squeezing time also decreases.

References

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