Question

Determine the sommerfeld number of a bearing whose clearance ratio is 600 & the bearing load is 750 lbf the length and the radius of given bearing is 1.75 inch & 0.75inch respectively the viscosity of oil inside the bearing is u=6 reyn the bearing is rotating at a speed of 1800 rpm

Answer 1

Given that,

Clearance ratio = 600 μm

Bearing load = 750 lbf = 3336.17 N

Length = 1.75 inch = 0.04445 m

Radius = 0.75 inch = 0.01905 m

Viscosity of oil = 6 dyne

Speed = 1800 rpm = 30 rps

We need to calculate the sommerfeld number of the bearing

Using formula of sommerfeld number

$s=(\dfrac{r}{c})^2\times\dfrac{\mu n_{s}}{P}$

$s=(\dfrac{r}{c})^2\times\dfrac{\mu n_{s}A}{F}$

Where,

r = radius

c = radial clearance

μ = dynamic viscosity

n = speed in r.p.s

A = area

F = load

Put the value in to the formula

$s=(\dfrac{0.01905}{600\times10^{-6}})^2\times\dfrac{6\times30\times0.04445\times2\times0.01905}{3336.17}$

$s=0.09$

Hence, The sommerfeld number of the bearing is 0.09.