Question

$\text{A natural feed journal bearing of diameter 50 mm and length 50 mm operating at 20 revolution/sec. carries a load of 2.0 kN. The lubricant used has a viscocity of 20 mPa.s. The radial clearance is}50\mu m\text{. The Sommerfeld number for the bearings is}$

• A. $0.250$
• B. $0.062$
• C. $0.125$
• D. $0.785$

Answer 1

The correct option is C $0.125$

Sommerfeld number,
$S={\left(\frac{r}{c}\right)}^2\times \frac{\mu N}{p}$
where, $r$ is radius ofjournal
$\mu$ is viscosity of lubricant
$N$ is number of revolution per second
$p$ is bearing pressure on projected area
$C$ isradial clearance
Therefore,
$p=\frac{W}{d\times l}=\frac{2000}{50\times 50}=0.8N/m{m}^2$
$S=\left(\frac{25}{50\times {10}^{-3}}\right)\times \frac{20\times 20\times {10}^{-3}}{0.8\times {10}^6}=0.125$