Page 302 - Marks Calculation for Machine Design

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January 4, 2005
Brown.cls
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and the coefficients (a) and (b), both dimensionless, are given in Eq. (7.18) as
1 STRENGTH OF MACHINES 1
1
a = and b =− log (7.18)
K f 3 K f
where the reduced stress concentration factor (K f ) is found from Eq. (6.23).
Consider the following example that brings together all the modifying factors in the
Marin equation for a particular machine element.
U.S. Customary SI/Metric
Example 2. Determine the endurance limit Example 2. Determine the endurance limit
(S e ) using the Marin equation for a 1.0-in di- (S e ) using the Marin equation for a 25-mm di-
ameter machined shaft with a transverse hole ameter machined shaft with a transverse hole
under reversed bending at room temperature, under reversed bending at room temperature,
where where
S ut = 120 kpsi S ut = 840 MPa
S y = 80 kpsi S y = 560 MPa
K t = 2.15 (0.125-in transverse hole) K t = 2.15 (3.2-mm transverse hole)
q = 0.8 (notch sensitivity) q = 0.8 (notch sensitivity)
solution solution
Step 1. Using Eq. (7.8) and values for the Step 1. Using Eq. (7.8) and values for the
coefficient (a) and exponent (b) from Table 7.1, coefficient (a) and exponent (b) from Table 7.1,
calculate the surface finish factor (k a ) as calculate the surface finish factor (k a ) as
k a = aS ut b k a = aS ut b
= (2.70 kpsi)(120 kpsi) −0.265 = (4.51 MPa)(840 MPa) −0.265
= (2.70)(0.2812) = (4.51)(0.1679)
= 0.76 = 0.76
Step 2. Using Eq. (7.10) calculate the size Step 2. Using Eq. (7.10) calculate the size
factor (k b ) as factor (k b ) as
−0.1133 −0.1133 −0.1133 −0.1133
d 1 d 25

k b = = k b = =
0.3 0.3 7.62 7.62
= (3.33) −0.1133 = 0.87 = (3.28) −0.1133 = 0.87
Step 3. As the shaft is bending, the load type Step 3. As the shaft is bending, the load type
factor (k c ) from Eq. (7.14) is factor (k c ) from Eq. (7.14) is
k c = 1 k c = 1
Step 4. As the shaft is operating at room Step 4. As the shaft is operating at room
temperature, the temperature factor (k d ) from temperature, the temperature factor (k d ) from
Eq. (7.15) and Table 7.2 is Eq. (7.15) and Table 7.2 is
k d = 1 k d = 1