Application of Probability to Mechanical Design
101
unknown is found use the variations and calculate Eq. (2.42)
O" S -- O" s
t--t- 2
s
O- s
then the actual Pf can be found for the design.
EXAMPLE 2.19.
COMBINED FATIGUE STRESSES. A large
300-1b gear, Fig. 2.37 transmits torque in one direction through a shaft
whose bearings are preloaded with a 100-1b force so that the load in the
shaft varies from 0-200 lb. The critical area is the change in shaft diameter
which is made of SAE 4340 steel. The two shaft diameters are required.
Assume D / d = 2.
Tm = 45,000 in lb
Tr = 15,000 in lb
Mm = 150 lb (30 in) = 4500 in
Fm= 100 lb
Fr = 100 lb
Tmr 16Tm
16Tr
K Mmc
32Mm
~m=~ -= gd~;
rr=Kt7 " red3 ; axr-,B~--=KtB
~-~
4Fro.
4F
axm = ~d 2 , ~xr = gtF ~d 2
From (2.9, 2.51, 2.54)
~F = 2.35 ~ = 2.025 Ktr = 1.65 C~ = ~0.1166 (Eq. 2.69)
The stress concentration will be applied only to Eq. (2.49) a~ since the system
is considered ductile. The ar -- am curve will be drawn and allowable stress
48"
~
~
O.06d
30 :) Ib
Figure 2.37 Bull gear and shafting.
~-d
T lO01b