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ESE Mechanical 2013 Official Paper - 2

Option 4 : Length and diameter of the bearing, bearing load, speed of rotation and viscosity of the lubricant.

__Concept:__

Several dimensionless numbers are used to understand the performance of bearing. Some of them are –

- Bearing Characteristic Number = \( \frac{{Z{N_s}}}{P}\)
- Bearing Modulus: The value of Bearing characteristic number when the co-efficient of friction is minimum.
- Sommerfield number: It is used to co-relate the working condition of a different machine which are operating under the same bearing. It is given by

\( {\rm{S}} = \left( {\frac{{{\rm{Z}}{{\rm{N}}_{\rm{s}}}}}{{\rm{P}}}} \right){\left( {\frac{{\rm{r}}}{{\rm{C}}}} \right)^2}\)

where Z = Absolute viscosity of the lubricant, Ns = Revolution per sec, P = Bearing pressure, r = Radius of the shaft, c = Radial clearance of bearing and shaft, and ho = film thickness.

- Eccentricity ratio/Attitude: It is the ratio of eccentricity to radial clearance.

\({\rm{e}} = \frac{{{\rm{eccentricity}}}}{{{\rm{radial\;clearance}}}} = \frac{{\left( {R - r} \right) - {h_o}}}{{\left( {R - r} \right)}} = 1 - \frac{{{h_o}}}{c}\)

__Explanation:__

From the above formula, it is evident that

Bearing characteristic number depends on

**Z (Viscosity)****N (Speed of rotation)****P (Bearing pressure)**

**Bearing Pressure is dependent on Bearing load and Bearing effective area (length and diameter of the bearing)**