Fatigue Analysis of Helical Spring Subjected to Multi-axial Load
381
τ =
8F D
π d 3 +
4F
π d 2 = K
8F D
π d 3
(2)
where D denotes mean coil diameter and C is the spring index. Shear stress-correction
factor k is calculated by using the following relation,
K = 1 +
0.5
C
; C =
D
d
(3)
The mean stress τ m and the amplitude stress τ a are given by [6]
τ m = K b
8F m D
π d 3 ; τ a = K b
8F a D
π d 3
(4)
K b is “Bergsträsser factor”, which is used as a correction factor due to curvature
of the spring, it can be found by using the Eq. (5).
K b =
4C + 2
4C − 3
(5)
3.2 Fatigue Life Calculation
In case of stress life approach [6], the maximum number of cycle is calculated by
using the following relation,
S f = a N
b
; N =
S f
a
1
b
(6)
Where
b = −
1
3
log
f.S ut
S e
; a =
f.S ut
S e
2
(7)
where S f is fatigue stress for N number of cycles, a and b are fatigue constant found
from Eq. (7), f is fatigue strength fraction and S e is the endurance limit for specific
material [6].
S ut =
A
d m
(8)
A is intercept coefficient equal to 2911 MPa.mm
m for wire diameter between
(5 to 10) mm, m is slope coefficient equal to 0.478 [6, p 525] for chrome-silicon
material. Then, we can find f = 0.9 [6, p 285] by approximation from fatigue