Thermo Hydrodynamic Lubrication Characteristics of Power Law Fluids in Rolling/Sliding Line Contact

  • Dhaneshwar Prasad
  • S. V. Subrahmanyam
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Hydrodynamic lubrication of rollers having the same dimension and moving with different velocities is studied assuming the consistency of the non-Newtonian incompressible power law lubricants to vary with pressure and the mean film temperature. The equations of motion, continuity, and momentum energy are solved first analytically and then numerically by Runge–Kutta Fehlberg method. Some important bearing characteristics are analyzed and displayed in the form of some graphs to study their behaviors.


Line Contact Semi Analytical Solution Hydrodynamic Lubrication Film Temperature Pure Rolling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Film thickness at x = −\( \,x_{1} \)


Lubricant film thickness


Minimum film thickness

\( \overline{h} \)

h/ho etc.


Lubricant consistency


Initial consistency temperature


Consistency index of the power law lubricant


Hydrodynamic pressure


Radius of the equivalent cylinder


Lubricant temperature

\( T_{11} \)

Film temperature for y ≥ δ in region-I etc.

\( T_{m} \)

Mean film temperature

\( T_{0} \)

Ambient temperature

\( \overline{T}_{Fh + } \)

Traction force (= - (2\( \alpha \) \( T_{Fh} \)/ho)) etc.

\( U_{1},\,\,U_{2} \)

Cylinders velocities at y = - h and y = h respectively


Velocity of the lubricant in x-direction

\( u_{m} \)

The mean velocity of the lubricant


Velocity of the lubricant in y-direction


Load in y-direction

\( \overline{W} \)

Dimensionless load (= \( \alpha \)W/(Rho)½)

\( \overline{x} \)

x/(2Rho)½) etc.

\( \,x_{1} \)

Point of maximum pressure

\( x_{2} \)

Cavitation point

\( \varphi \)

\( \frac{{\rho \,c\,u_{m} }}{k}\left( {\frac{{dT_{m} }}{dx}} \right) \)

\( \alpha ,\beta \)

Pressure and temperature coefficients


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Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Dr. S.R.K. Government Arts CollegeYanamIndia
  2. 2.K. L. UniversityVaddeswaramIndia

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