Answer:
The endurance strength for the rod is 434.6 MPa
Explanation:
Since the rod is used in rotating bending, we need to use Marin equation given by
[tex]S=k_ak_bS'_e[/tex]
Here S stands for the endurance strength for rotating bending, [tex]S'_e[/tex] is the endurance strength, and [tex]k_a \text{ and } k_b[/tex] are the parameters for Marin surface modification factor.
Endurance strength.
We can start finding the endurance strength, from the directions we know that the hardness [tex]H_e[/tex] was found to be 300 Brinell, thus for such value we can find the ultimate tensile strength using
[tex]S_{ut}=3.41H_e[/tex]
Replacing the hardness we get
[tex]S_{ut}=3.41(300) MPa \\ S_{ut}=1023 MPa[/tex]
Now since the ultimate tensile strength has a value less than 1400 MPa, we can find the endurance strength using
[tex]S'_e =0.5S_{ut}[/tex]
Replacing the tensile strength we get
[tex]S'_e=0.5(1023) MPa \\ S'_e = 511.5 MPa[/tex]
Parameters for Marin surface modification factor.
From the directions we know that the drill rod has a ground surface finish, so then from tables we get
[tex]a=1.58 \text{ and } b = -0.085[/tex]
Thus the surface factor will be
[tex]k_a=a(S_{ut})^b[/tex]
Replacing values and the ultimate tensile strength
[tex]k_a=(1.58)1023^{-0.085}\\k_a=0.8766[/tex]
Then we can find the rotating shaft factor, for a diameter of 10 mm, we can use the equation
[tex]k_b=1.24d^{-0.107}[/tex]
Replacing the diameter we get
[tex]k_b=1.24(10)^{-0.107}\\k_b=0.9692[/tex]
Estimating endurance strength for rotating shaft.
We can replace now all values we have found in Marin equation.
[tex]S=k_ak_bS'_e[/tex]
[tex]S=(0.8766)(0.9692)(511.5) MPa[/tex]
[tex]S=434.6 MPa[/tex]
Thus the endurance strength for the rod is 434.6 MPa
