Page 198 - Marks Calculation for Machine Design

P1: Shibu
January 4, 2005
Brown˙C04
Brown.cls
180
2pR
s t min = 14:25 2 STRENGTH OF MACHINES s t min
r − R 2
2
o
t max
0 s r min = 0 0 0 Axis
2Tr o
t max =
4
p r – R 4 t max
o
s t min s t min
Edge view Plan view
FIGURE 4.26 Stress element at the outside radius.
r + R 2 max
2
s t max = p o s t
2
r − R 2
o
t min
s r min s r min = –p 0 0 Axis

2TR
t = o
min
4
p r – R 4 t min
o
max max
s t s t
Edge view Plan view
FIGURE 4.27 Stress element at the radial interface.

The following quantitative calculations will provide the information needed to decide
which of the two stress elements shown in Figs. 4.26 and 4.27 have the maximum stresses.
Example 9 will look at the stresses on the element in Fig. 4.26, and Example 10 will look
at the stresses on the element in Fig. 4.27.

U.S. Customary SI/Metric
Example 9. Determine the stresses on the el- Example 9. Determine the stresses on the el-
ement in Fig. 4.26 using the dimensions of the ement in Fig. 4.26 using the dimensions of the
spur gear and shaft assembly in Example 8, the spur gear and shaft assembly in Example 8, the
interface pressure (P) found, and a torque ap- interface pressure p found, and a torque applied
plied to the gear at the outside radius equal to to the gear at the outside radius equal to
T = 6,000 ft · lb = 72,000 in · lb T = 9,000 N · m
R = 0.75 in R = 2cm = 0.02 m
r o = 4in r o = 10 cm = 0.1 m
p = 9,650 lb/in 2 p = 48,680,000 N/m 2