Question

A 10-mm drill rod was heat-treated and ground. The measured hardness He was found to be 300 Brinell. Estimate the endurance strength S. in MPa if the rod is used in rotating bending

Answer 1

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

$S=k_ak_bS'_e$

Here S stands for the endurance strength for rotating  bending, $S'_e$ is the endurance strength, and $k_a \text{ and } k_b$ 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 $H_e$ was found to be 300 Brinell, thus for such value we can find the ultimate tensile strength using

$S_{ut}=3.41H_e$

Replacing the hardness we get

$S_{ut}=3.41(300) MPa \\ S_{ut}=1023 MPa$

Now since the ultimate tensile strength has a value less than 1400 MPa, we can find the endurance strength using

$S'_e =0.5S_{ut}$

Replacing the tensile strength we get

$S'_e=0.5(1023) MPa \\ S'_e = 511.5 MPa$

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

$a=1.58 \text{ and } b = -0.085$

Thus the surface factor will be

$k_a=a(S_{ut})^b$

Replacing values and the ultimate tensile strength

$k_a=(1.58)1023^{-0.085}\\k_a=0.8766$

Then we can find the rotating shaft factor, for a diameter of 10 mm, we can use the equation

$k_b=1.24d^{-0.107}$

Replacing the diameter we get

$k_b=1.24(10)^{-0.107}\\k_b=0.9692$

Estimating endurance strength for rotating shaft.

We can replace now all values we have found in Marin equation.

$S=k_ak_bS'_e$

$S=(0.8766)(0.9692)(511.5) MPa$

$S=434.6 MPa$

Thus the endurance strength for the rod is 434.6 MPa