Page 297 - Marks Calculation for Machine Design

P1: Shashi
January 4, 2005
15:4
Brown.cls
Brown˙C07
U.S. Customary FATIGUE AND DYNAMIC DESIGN SI/Metric 279
Step 3. Using Eq. (7.5), calculate the exponent Step 3. Using Eq. (7.5), calculate the exponent
(b) as (b) as
1 0.9 S ut 1 0.9 S ut
b =− log b =− log
3 S e 3 S e
1 0.9 (90 kpsi) 1 0.9 (630 MPa)
=− log =− log
3 45.4 kpsi 3 317.5MPa
1 1
=− log (1.784) =−0.084 =− 3 log (1.786) =−0.084
3
Step 4. Using Eq. (7.3), calculate the fatigue Step 4. Using Eq. (7.3), calculate the fatigue
strength (S f ) as strength (S f ) as
b
b
S f = aN = (144.5 kpsi)(10) (5)(−0.084) S f = aN = (1,013 MPa)(10) (5)(−0.084)
= (144.5 kpsi)(0.38) = (1,013 MPa)(0.38)
= 54.9 kpsi = 384.9MPa
which is greater than the rotating-beam which is greater than the rotating-beam

endurance limit (S ) but less than the yield endurance limit (S ) but less than the yield
e
e
strength (S y ). strength (S y ).
S S
e ≤ S f ≤ S y e ≤ S f ≤ S y
45.4 ≤ 54.9 ≤ 70 317.5 ≤ 384.9 ≤ 490
Step 5. Using Eq. (7.6), calculate the expected Step 5. Using Eq. (7.6), calculate the expected
life (N) for the given amplitude stress (σ a ) of life (N) for the given amplitude stress (σ a ) of
60 kpsi as 420 MPa as
1/−0.084 1/−0.084
1/b 1/b
σ a σ a
60 kpsi 420 MPa
N = = N = =
a 144.5 kpsi a 1,013 MPa
= (0.4152) −11.9 = 35,014 cycles = (0.4146) −11.9 = 35,637 cycles
7.3 MARIN EQUATION

The endurance limit (S ) determined using the guidelines in Eq. (7.1) that were established
e
from fatigue tests on a standard test speciment must be modified for factors that will usually
be different for an actual machine element. These factors account for differences in surface
finish, size, load type, temperature, and other miscellaneous effects that may differ from
those for the test specimen.
The mathematical model commonly used to apply these factors is credited to Joseph
Marin (1962) and is given in Eq. (7.7) as
S e = k a k b k c k d k e S (7.7)
e
where S e = endurance limit for machine element under investigation
S = endurance limit obtained from guidelines in Eq. (7.1)

e
k a = surface finish factor
k b = size factor
k c = load type factor
k d = temperature factor
k e = miscellaneous effects factor