Question

Figure P14.28 shows two bearings supporting a 1000-rpm shaft and gear. The bearing on the left carries a 5-kN radial load and 1-KN thrust load. The loading is borderline between "light" and "moderate" impact. The required life is 5000 hours with only 2% probability of failure. Select a 200 series radial-contact ball bearing for the left bearing. Shaft Bearing Gear FIGURE P14.28

Answer 1

Given data 1

N= 1000 rpm

F, = 5 kN

F =1 kN

$\textup{From Table 14.3, for light-moderate impact}\left ( K_{a} \right )=1.5$

$L_{h}=5000\textup{ h}$

$\textup{reability}=1-0.02=0.98$

$\textup{From Table 14.3, with 98 percent reliability }\left ( K_{r} \right )=0.33$

Solution →

$\textup{Life in million revolutions are}$

$L=L_{h}*N*60$

$L=5000*1000*60=3*10^{8}\textup{ rev}$

$\textup{The life corresponding to rated capacity}\left ( L_{R} \right )=90*10^{6}$

$\frac{F_{a}}{F_{r}}=\frac{1}{5}=0.2< 0.35$

$\textup{For a radial bearing, Eq. (14.3) gives}$

$F_{e}=F_{r}=5\textup{ kN}$

$\textup{For a radial bearing, from Eq. (14.5b), the required value of rated capacity for the application}$$C_{req}=F_{e}K_{a}*\left ( \frac{L}{K_{r}L_{R}} \right )^{0.3}$

$C_{req}=5*1.5*\left ( \frac{3*10^{8}}{0.33*90*10^{6}} \right )^{0.3}$

$C_{req}=15.00\textup{ kN}$

$\textup{From Table 14.2, a 200 radial bearing with a rated capacity of 16 kN would be sufficient for left bearing with bore 65 mm}$