Answer:
the endurance strength
= 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](https://tex.z-dn.net/?f=200%20%5Cleq%20H_B%20%5Cleq%20450)
![S_{ut} = 3.41 H_B](https://tex.z-dn.net/?f=S_%7But%7D%20%3D%203.41%20H_B)
where;
= Brinell hardness number
= Ultimate tensile strength
From ;
; replace 290 for
; we have
![S_{ut} = 3.41 (290)](https://tex.z-dn.net/?f=S_%7But%7D%20%3D%203.41%20%28290%29)
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](https://tex.z-dn.net/?f=S_%7But%7D%20%3C%201400)
The Endurance limit can be represented by the formula:
![S_e ' = 0.5 S_{ut}](https://tex.z-dn.net/?f=S_e%20%27%20%3D%200.5%20S_%7But%7D)
![S_e ' = 0.5 (988.9)](https://tex.z-dn.net/?f=S_e%20%27%20%3D%200.5%20%28988.9%29)
= 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}](https://tex.z-dn.net/?f=k_a%20%3D%20aS%5Eb_%7But%7D)
![K_a = 1.58 (988.9)^{-0.085](https://tex.z-dn.net/?f=K_a%20%3D%201.58%20%28988.9%29%5E%7B-0.085)
![K_a = 0.8792](https://tex.z-dn.net/?f=K_a%20%3D%200.8792)
The formula that is used to determine the value of
for the rotating shaft of size factor d = 10 mm is as follows:
![k_b = 1.24d^{-0.107}](https://tex.z-dn.net/?f=k_b%20%3D%201.24d%5E%7B-0.107%7D)
![k_b = 1.24(10)^{-0.107}](https://tex.z-dn.net/?f=k_b%20%3D%201.24%2810%29%5E%7B-0.107%7D)
![k_b = 0.969](https://tex.z-dn.net/?f=k_b%20%3D%200.969)
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](https://tex.z-dn.net/?f=S_e%20%3Dk_ak_b%20S%27%20_e)
= 0.8792×0.969×494.45
= 421.24 MPa
Thus; the endurance strength
= 421.24 MPa