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A hydrodynamic journal bearing is subject to 2000 N load at a rotational speed of 2000 rpm. Both bearing bore diameter and length are 40 mm. If radial clearance is 20 μm and bearing is lubricated with an oil having viscosity 0.03 Pa.s, the Sommerfeld number of the bearing is _______

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Concept:

The Sommerfeld number is given by:

\(S = {\left( {\frac{r}{c}} \right)^2}\frac{{μ {n_s}}}{P}\)

Where,

c = radial clearance (mm)

r = radius of journal (mm)

μ = viscosity of the lubricant (Ns/mm2) or (MPa-s)

ns = journal speed (rev/s)

P = unit bearing pressure (N/mm2)

Calculation

Given:

r = 20 mm, L = d = 40 mm, W = 2000 N, N = 2000 rpm, μ = 0.03 Pa-s

\(P = \frac{W}{{Ld}}\)

\(S = {\left( {\frac{r}{c}} \right)^2}\frac{{μ {n_s}}}{P}\)

\(\begin{array}{l} \Rightarrow S =( \frac{{{20 \times {{10}^{ - 3}}}}}{{20 \times {{10}^{ - 6}}}} )^2 \times \frac{{0.03 \times \frac{{2000}}{{60}}}}{{\left( {\frac{{2000}}{{40 \times 40 \times {{10}^{ - 6}}}}} \right)}} = 0.8 \end{array}\)

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