Question

A natural feed journal bearing of diameter 50 mm and length 50 mm operating at 20 revolution/second carries a load of 2.0 kN. The lubricant used has a viscosity of 20 mPa s. The radial clearance is 50 μm. The Sommerfield number for the bearing is
1. 0.062
2. 0.125
3. 0.250
4. 0.785

Answer 1

Correct Answer - Option 2 : 0.125

Given that :

Radial clearance, λ = 50 μm

Load, F = 2 kN, N = 20 rps 

diameter, d = 50 mm

viscosity, μ = 20 mPa-s

length, L = 50 mm                 

 

\(P = \frac{F}{A} = \frac{F}{{L \times d}} \\= \frac{{2000}}{{50 \times 50}} = 0.8\;\frac{N}{{m{m^2}}}\)

sommerfield number

\(Z = \frac{{\mu N}}{P}{\left( {\frac{r}{\lambda}} \right)^2}\)

\(= \frac{{\left( {20 \times {{10}^{ - 3}}} \right) \times 20}}{{\left( {0.8 \times {{10}^6}} \right)}} \times {\left( {\frac{{25\times10^{-3}}}{{50\times10^{-6}}}} \right)^2}\)

= 0.125