Page 303 - Marks Calculation for Machine Design

P1: Shashi
January 4, 2005
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Brown.cls
Brown˙C07
U.S. Customary FATIGUE AND DYNAMIC DESIGN SI/Metric 285
Step 5. Using Eq. (6.23), along with the given Step 5. Using Eq. (6.23), along with the given
values for the geometric stress concentration values for the geometric stress concentration
factor (K t ) and notch sensitivity (q), calculate factor (K t ) and notch sensitivity (q), calculate
the reduced stress concentration factor (K f ) as the reduced stress concentration factor (K f ) as
K f = 1 + q(K t − 1) = 1 + (0.8)(2.15 − 1) K f = 1 + q(K t − 1) = 1 + (0.8)(2.15 − 1)
= 1 + 0.92 = 1.92 = 1 + 0.92 = 1.92
Step 6. Using the reduced stress concentration Step 6. Using the reduced stress concentration
factor (K f ) found in step 5, calculate the mis- factor (K f ) found in step 5, calculate the mis-
cellaneous effects factor (k e ) using Eq. (7.16) cellaneous effects factor (k e ) using Eq. (7.16)
as as
1 1 1 1
k e = = = 0.52 k e = = = 0.52
K f 1.92 K f 1.92
Step 7. Using the given ultimate tensile stress Step 7. Using the given ultimate tensile stress
(S ut ) and Eq. (7.1), calculate the test specimen (S ut ) and Eq. (7.1), calculate the test specimen
endurance limit (S ) as endurance limit (S ) as

e e

S = 0.504 S ut = (0.504)(120 kpsi) S = 0.504 S ut = (0.504)(840 MPa)
e
e
= 60.5 kpsi = 423.4MPa
Step 8. Using the test specimen endurance Step 8. Using the test specimen endurance

limit (S ) found in step 7 and the modifying limit (S ) found in step 7 and the modifying

e e
factors found in steps 1 through 6, calculate the factors found in steps 1 through 6, calculate the
endurance limit (S e ) for the machine element endurance limit (S e ) for the machine element
using the Marin equation in Eq. (7.7) as using the Marin equation in Eq. (7.7) as
S e = k a k b k c k d k e S S e = k a k b k c k d k e S
e e
= (0.76)(0.87)(1)(1)(0.52)(60.5 kpsi) = (0.76)(0.87)(1)(1)(0.52)(423.4MPa)
= (0.344)(60.5 kpsi) = 20.8 kpsi = (0.344)(423.4MPa) = 145.6MPa
Notice that the biggest reduction, almost 50 percent, in the endurance limit (S e ) for the
machine element came from the stress concentration caused by the transverse hole in the
shaft. Accounting for all five factors reduced the endurance limit (S e ) to one-third the test

specimen endurance limit (S ) found from the R. R. Moore rotating-beam machine. This
e
translates into a minimum factor-of-safety (n = 3) to have a safe design under repeated
reversed loading. Again, this is why the first law of machine design is “When in doubt,
make it stout!”
Consider now the possibility that the dynamic loading is fluctuating rather than being
completely reversed as has been the assumption so far.
7.4 FLUCTUATING LOADING

The second type of dynamic loading to be presented is called fluctuating loading, where
the load on the machine element varies about some mean stress (σ m ), which can be
positive or negative, by an amount called the alternating stress (σ a ). Note that if the