Question 21.16: A full journal bearing, 200 mm in diameter and 200 mm long, ......
A full journal bearing, 200 mm in diameter and 200 mm long, is to support a radial load of 45 kN at an operating speed of 960 rpm. If it is to be operated at a Sommerfeld number of 0.08 when the radial clearance is 0.2 mm, determine the viscosity of the oil to be used. Estimate also the power loss in the bearing if the resulting coefficient of friction value is 0.00315. Sommerfeld number is determined with speed in rps.
(i) Sommerfeld number
N^*=\frac{960}{60}=16 \mathrm{~rps}
p=\frac{W}{L D}=\frac{45000}{200 \times 200}=1.125 \mathrm{~MPa}
Sommerfeld number is given as
S=\left(\frac{\mu N^*}{p}\right)\left(\frac{r}{C_r}\right)^2=\left(\frac{\mu \times 16}{1.125}\right)\left(\frac{100}{0.2}\right)^2=0.08
Solving, we get
\mu=2.25 \times 10^{-8} \mathrm{~N} \cdot \mathrm{s} / \mathrm{mm}^2=0.0225 \mathrm{Ns} / \mathrm{m}^2
(ii) Power loss in the bearing
H_f=f W \times V=f W\left(\frac{\pi D N}{60,000}\right)=0.00315 \times 45000\left(\frac{\pi \times 200 \times 960}{60,000}\right)=1425 \mathrm{~W}