Question 21.15: A full journal bearing operating under a steady load has the......

(i) Sommerfeld number

S=\left(\frac{\mu N^*}{p}\right)\left(\frac{r}{C_r}\right)^2=\left(\frac{80 \times 10^{-9} \times 17}{0.778}\right)\left(\frac{30}{0.05}\right)^2=0.629

N^*=\frac{1020}{60}=17 \mathrm{~rps}

p=\frac{W}{L D}=\frac{2800}{60 \times 60}=0.778 \mathrm{~MPa}

From the table, corresponding to S = 0.629 = 0.63 (This table is given in the paper)

\frac{r}{C_r} f= coefficient of friction variable = CFV = 12.8

f=\frac{12.8 \times 0.05}{30}=0.02133

(ii) Power loss in friction

H_f=f W \times V=f W\left(\frac{\pi D N}{60,000}\right)=0.02133 \times 2800\left(\frac{\pi \times 60 \times 1020}{60,000}\right)=191.41 \mathrm{~W}

(iii) Temperature rise, from the table

\text { Flow variable }=\mathrm{FV}=\frac{Q}{r C_r N^* L}=3.59

\text { Temperature rise variable }=\frac{\rho C_p \Delta T}{p}=\frac{860 \times 1760 \Delta T}{p} \text { and } p \text { must be in } \mathrm{N} / \mathrm{m}^2

From Eq. (21.62)

\frac{\rho C_p \Delta T}{p}=\frac{f\left(\frac{r}{C_r}\right)}{\left(\frac{Q}{r C_r N^* L}\right)}(4 \pi) (21.62)

\frac{\rho C_p \Delta T}{p}=\frac{f\left(\frac{r}{C_r}\right)}{\left(\frac{Q}{r C_r N^* L}\right)}(4 \pi)=\frac{\mathrm{CFV}}{\mathrm{FV}} \times 4 \pi=\frac{12.8}{3.59} \times 4 \pi=44.81

\Delta T=\frac{44.81 \times p}{\rho C_p}=\frac{44.81 \times 0.778 \times 10^6}{860 \times 1760}=23.03^{\circ} \mathrm{C}

(iv) Minimum film thickness

\frac{h_0}{C_r}=0.8

Minimum oil film thickness is

h_0=0.8 \times 0.05=0.04 \mathrm{~mm}

Location is \phi=74.02^{\circ}