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Determination of friction coefficient for water-lubricated journal bearing considering rough surface EHL contacts

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Abstract

This work aims to study the tribological performance of the water-lubricated journal bearings by developing an EHL model considering non-Gaussian roughness and cavitation. An elastohydrodynamic lubrication (EHL) model is established by solving the Reynolds equation, elastic deformation and film thickness equations in a coupling manner by using the finite difference method with a successive over-relaxation scheme. The non-Gaussian flow factors and cavitation factors are incorporated in the Reynolds equation to tackle the roughness and non-Gaussian roughness effects. The result shows that the coefficient of friction increases with an increase in skewness. A significantly increase in the minimum film thickness is observed for a surface having high negative skewness. The friction coefficient decreases with an increase in the L/D ratio.

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Abbreviations

WLJB :

Water-lubricated journal bearing

SOR :

Successive over relaxation

CoF :

Friction coefficient

EHL:

Elastohydrodynamic lubrication

S sk :

Skewness

S ku :

Kurtosis

N r :

Speed of the shaft, RPM

C :

Radial clearance, µm

ε :

Eccentricity ratio, e/C

D :

Bearing diameter, mm

T :

Bushing thickness, mm

W t :

Tangential load, N

W r :

Radial load, N

W :

Total load, N

\(\overline{h}\) :

Dimensionless film thickness, \({h \mathord{\left/ {\vphantom {h C}} \right. \kern-0pt} C}\)

\(h\) :

Water film thickness, µm

\(\theta\) :

Circumferential angle in radian

\(\varphi\) :

Attitude angle (radian)

\(\overline{z}\) :

Dimensionless z-coordinate, \({z \mathord{\left/ {\vphantom {z {\left( {{L \mathord{\left/ {\vphantom {L 2}} \right. \kern-0pt} 2}} \right)}}} \right. \kern-0pt} {\left( {{L \mathord{\left/ {\vphantom {L 2}} \right. \kern-0pt} 2}} \right)}}\)

S q :

Composite root mean square (RMS) roughness, µm

R :

Bearing radius, mm

L :

Length of the shaft, mm

U :

Surface speed of the shaft, m/s

p hyd :

Hydrodynamic pressure

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Authors and Affiliations

  1. School of Mechanical Engineering, Lovely Professional University, Phagwara, Punjab, 144411, India

    Deepak K. Prajapati & Chander Prakash

  2. Department of Mechanical Engineering, SRM Institute of Science & Technology, Kattankulathur, Chennai, Tamil Nadu, 603203, India

    Jitendra Kumar Katiyar

Authors
  1. Deepak K. Prajapati
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  2. Jitendra Kumar Katiyar
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  3. Chander Prakash
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Correspondence to Deepak K. Prajapati.

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Appendix A

Appendix A

1.1 Brief description of topography parameters

1.1.1 Root mean square (RMS) roughness (S q )

For a discrete residual surface, z (xi, yi), the statistical expression for determining RMS roughness is given in Eq. A1.

$$ S_{q} = \sqrt {\frac{1}{MN}\mathop \sum \limits_{i = 1}^{M} \mathop \sum \limits_{j = 1}^{N} z^{2} \left( {x_{i} ,y_{i} } \right)} $$
(A1)

1.1.2 Skewness (S sk )

The skewness measures the asymmetry of surface deviation from the mean plane. Positive skewness represents a greater number of roughness peaks than valleys from the mean plane of a rough surface. At the same time, negative skewness represents a higher number of valleys than roughness peaks. For a discrete residual surface, z (xi, yi), the statistical expression for determining skewness (Ssk), is given in Eq. A2.

$$ S_{sk} = \frac{1}{{MNS_{q}^{3} }}\mathop \sum \limits_{i = 1}^{M} \mathop \sum \limits_{j = 1}^{N} z^{3} \left( {x_{i} ,y_{i} } \right) $$
(A2)

where M and N are total number of sampling points within the measured area

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Prajapati, D.K., Katiyar, J.K. & Prakash, C. Determination of friction coefficient for water-lubricated journal bearing considering rough surface EHL contacts. Int J Interact Des Manuf (2023). https://doi.org/10.1007/s12008-023-01466-7

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  • DOI: https://doi.org/10.1007/s12008-023-01466-7

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