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Mechanical Design of Machine Elements Complete after watching watching Module 44: Randomly Varying Stresses and Miner's Rule Example 2
Worksheet 9: Miner’s Rule
The varying, fluctuating stresses shown to the below are found at the critical location location of a component. The material is steel, steel, the fully adjusted a djusted endurance limit is 22 ksi, the ultimate strength is 105 ksi. The fatigue strength fraction is f = 0.84. 1) What is the accumulative damage of this part? 2) What is the life of the part in hours h ours if this 6 second stress stress pattern continues to repeat for the remainder of the part’s life?
ksi 80 60 40 20
t (sec)
0 -20 -40 -60 -80
n
sigma min sigma max sigma a sigma m
Cycle 1
2
-20
20
-
-
Cycle 2
3
-60
60
-
-
Cycle 3
2
-20
40
30
10
Note that cycle 1 and cycle 2 are fully reversible
Mechanical Design of Machine Elements Complete after watching Module 44: Randomly Varying Stresses and Miner's Rule Example 2
Worksheet 9: Miner’s Rule
The varying, fluctuating stresses shown to the below are found at the critical location of a component. The material is steel, the fully adjusted endurance limit is 22 ksi, the ultimate strength is 105 ksi. The fatigue strength fraction is f = 0.84. 1) What is the accumulative damage of this part? 2) What is the life of the part in hours if this 6 second stress pattern continues to repeat for the remainder of the part’s life? n
sigma min sigma max sigma a sigma m
Cycle 1
3
-60
60
-
-
Cycle 2
2
-20
20
-
-
Cycle 3
2
-20
40
30
10
As cycle 1 is below the endurance limit, the number of cycles is infinite. As cycle 2 is fully reversible, a = b =
( fS ut )2
=
S e 1 3
[(0.84)(105)]2 22
353.6
=
æ fS ut ö 0.2010 = è S e ø÷
log ç
æ ö N = ç rev ÷ è a ø
1
b
æ 60 ö =ç è 353.6 ø÷
1
0.201
=
6798
Cycle 3 is fluctuating, and to calculate the number of cycles, a sigma equivalent is necessary a
rev _ eq =
1
æ ö N = ç rev ÷ è a ø
= m
S ut 1
b
30 10 1 105
æ 33.2 ö =ç è 353.6 ø÷
1
=
33.2
0.201
=
129920
Mechanical Design of Machine Elements Complete after watching Module 44: Randomly Varying Stresses and Miner's Rule Example 2
Worksheet 9: Miner’s Rule
The varying, fluctuating stresses shown to the below are found at the critical location of a component. The material is steel, the fully adjusted endurance limit is 22 ksi, the ultimate strength is 105 ksi. The fatigue strength fraction is f = 0.84. 1) What is the accumulative damage of this part? 2) What is the life of the part in hours if this 6 second stress pattern continues to repeat for the remainder of the part’s life?
