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Evaluation of the steady-state performance characteristics of a two-layered porous journal bearing under turbulent regimes

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Abstract

This present analysis aims to investigate the steady-state performance of two-layered porous bearing in turbulent regimes considering important design parameters, viz. load-carrying capacity, attitude angle, end flow rate and frictional parameter. Here, governing equations of flow through the porous layers have been derived with the help of Darcy’s law and the modified Reynolds equation has been derived considering the Beavers–Joseph’s criterion at the film interface on the clearance region. The effect of various design parameters (viz. Reynolds number, eccentricity ratio, slip coefficient, bearing number and bearing feeding parameter) on the bearing performance has been investigated under full-slip and no-slip conditions. Results obtained from the numerical analysis are presented in graphical form. This work also represents the three-dimensional pressure distribution in the film region of a two-layered porous journal bearing operating in turbulent regimes under various parametric conditions.

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Abbreviations

C :

Radial clearance between journal and fine porous bush (m);

D :

Diameter of the bearing (m);

L :

Length of the bearing (m);

R :

Radius of the journal (m);

\(U\) :

Journal surface velocity (m/sec);

H :

Total thickness of porous bush (m);

\({H}_{f}, {H}_{c}\) :

Thickness of the fine and coarse porous layers, respectively;

\({\lambda }_{c}\) :

Thickness ratio, \({H}_{c}/H\);

e :

Eccentricity of the bearing (m);

\(f\) :

Frictional coefficient;

\(f\left(\frac{R}{C}\right)\) :

Frictional parameter;

\(\overline{W }\) :

Total dimensionless load-carrying capacity;

\({\overline{W} }_{r}, {\overline{W} }_{t}\) :

Dimensionless components of load-carrying capacity in radial and tangential direction, respectively;

\(\overline{F}_{s}\) :

Total dimensionless frictional force;

\(\overline{F}_{s1} , \overline{F}_{s2}\) :

Dimensionless frictional force on the cavitated and non-cavitated zone, respectively;

\(h\) :

Local film thickness (m);

\(\overline{h}\) :

Dimensionless film thickness, \(\left( {\overline{h}} \right) = \frac{h}{C}\)

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

Permeability coefficient for coarse porous layer in x-, y-, and z-directions, respectively (m2);

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

Permeability coefficient for fine porous layer in x-, y-, and z-directions, respectively (m2);

\(K_{xn},\,\) \(K_{zn}\) :

Dimensionless permeability coefficient for coarse porous layer in x- and z-direction, respectively;

\(p_{c} , p_{f}\) :

Local film pressure in the porous region for coarse and fine porous layer, respectively (N/m2);

\(\overline{p}_{c}\), \(\overline{p}\) :

Dimensionless local film pressure for coarse and fine porous layer, respectively, \(\overline{p}_{c} = \frac{{p_{c} }}{{p_{s} }}\), \(\overline{p}_{f} = \frac{{p_{f} }}{{p_{s} }},\)

\(p_{s}\) :

Supply pressure (N/m2);

\(Q_{c}\) :

End flow rate (m3/sec);

\(\overline{Q}_{c}\) :

Dimensionless end flow rate;

\({\text{Re}}_{h}\) :

Local Reynolds number, \({\text{Re}}_{{\text{h}}} = {\overline{\text{h}}}.{\text{Re}}\);

\({\text{Re}}\) :

Mean Reynolds number\({\text{Re}} = 3{{\Omega\,{\rm RC}}}/{\upmu };\)

\(\alpha\) :

Slip coefficient;

\(\beta\) :

Bearing feeding parameter

\(\left( \beta \right) = 12R^{2} k_{{\overline{y}f}} /{\text{C}}^{3} {\text{H}}\);

\(\varepsilon\) :

Eccentricity ratio,

\(\varepsilon = e/C\));

\(\phi\) :

Attitude angle (degrees);

\(\xi_{n}\) :

Slip function in,

\(n = x, z\);

\(\xi_{\theta } , \xi_{{\overline{z}}}\) :

Dimensionless slip function in x- and z-direction;

\(\xi_{0\theta }\) :

Dimensionless slip function in x-direction defined by,

\(\left( {\xi_{0x} } \right) = \frac{1}{{\left( {1 + \alpha \sigma_{x} \overline{h}} \right)}}\);

\(\kappa_{sn}\) :

Turbulent shear coefficient,

\(n = x, z\);

\(\Lambda_{s}\) :

Bearing number,

\((\Lambda_{s} ) = 6\mu \Omega \left( {R/C} \right)^{2} /p_{s}\);

\(\mu\) :

Absolute viscosity of a lubricant (N/m2.sec);

\(\Omega\) :

Angular velocity of the journal surface,

\(\left( \Omega \right) = \frac{U}{R}\) (rad/s1);

\(\sigma_{nf}\) :

Dimensional permeability factor

\(\left( {C/\sqrt {k_{nf} } } \right)\),

\(n = x,z\);

\(\overline{\tau }_{c}\) :

Dimensionless Couette’s surface shear stress;

\(\theta , \overline{y}, \overline{z}\) :

Dimensionless coordinate,

\(\theta = \frac{x}{R}, \overline{y} = \frac{y}{H}, \overline{z} = \frac{z}{L/2}.\)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Engineering Science and Technology Shibpur, Howrah, West Bengal, 711103, India

    Subrata Barman & Sisir Kumar Guha

  2. Department of Mechanical Engineering, National Institute of Technology Sikkim, Ravangla, South Sikkim, 737139, India

    Shitendu Some

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Barman, S., Guha, S.K. & Some, S. Evaluation of the steady-state performance characteristics of a two-layered porous journal bearing under turbulent regimes. J Braz. Soc. Mech. Sci. Eng. 45, 597 (2023). https://doi.org/10.1007/s40430-023-04518-x

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