Question

A 10-mm steel drill rod was heat-treated and ground. The measured hardness was found to be 290 Brinell. Estimate the endurance strength, Se, in MPa if the rod is used in rotating bending.

Answer 1

Answer:

the endurance strength  $S_e$ = 421.24  MPa

Explanation:

From the given information; The objective is to estimate the endurance strength, Se, in MPa .

To do that; let's for see the expression that shows the relationship between the ultimate tensile strength and Brinell hardness number .

It is expressed as:

$200 \leq H_B \leq 450$

$S_{ut} = 3.41 H_B$

where;

$H_B$ = Brinell hardness number

$S_{ut}$ =  Ultimate tensile strength

From ;

$S_{ut} = 3.41 H_B$; replace 290 for $H_B$ ; we have

$S_{ut} = 3.41 (290)$

$S_{ut} =$ 988.9 MPa

We can see that the derived value for the ultimate tensile strength when the Brinell harness number = 290 is less than 1400 MPa ( i.e it is 988.9 MPa)

So; we can say

$S_{ut} < 1400$

The Endurance limit can be represented by the formula:

$S_e ' = 0.5 S_{ut}$

$S_e ' = 0.5 (988.9)$

$S_e '$ = 494.45 MPa

Using Table 6.2 for parameter for Marin Surface modification factor. The value for a and b are derived; which are :

a = 1.58

b =  -0.085

The value of the surface factor can be calculate by using the equation

$k_a = aS^b_{ut}$

$K_a = 1.58 (988.9)^{-0.085$

$K_a = 0.8792$

The formula that is used to determine the value of  $k_b$ for the rotating shaft of size factor d = 10 mm is as follows:

$k_b = 1.24d^{-0.107}$

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

$k_b = 0.969$

Finally; the the endurance strength, Se, in MPa if the rod is used in rotating bending is determined by using the expression;

$S_e =k_ak_b S' _e$

$S_e$= 0.8792×0.969×494.45

$S_e$ = 421.24  MPa

Thus; the endurance strength  $S_e$ = 421.24  MPa