382
T. A. Musalli et al.
strength fraction curvature for the corresponding value of S ut
S e = K a .K b .K c .K d .K e .K f .S
e
(9)
where K a , K b , K c , K d , K e , K f and S
e are surface factor, size factor, load factor,
Temperature factor, reliability factor, miscellaneous factor, rotary-beam test specimen endurance limit, respectively. The values of K d , K e , K f = 1; K a = 0.84
K b = 1.4 [6, p 282] K c = 0.59 [1, p 290] and S
e is the rotary-beam test specimen
endurance limit which equal to S
e = 700 MPa for S ut > 1400 MPa. Using the
modified Goodman criterion to find the fatigue load S f [6]
τ a
S f
+
τ m
S u
= 1; S f =
τ a
1 −
τ m
S u
(10)
where
τ m = K b
8F m D
π d 3 ; τ a = K b
8F a D
π d 3
(11)
F m =
F max + F min
2
; F a =
F max − F min
2
(12)
4 Numerical Simulation
The spring geometry was modeled using Solid Work platform as per the nomenclature
given in Table 1. The ANSYS commercial program was employed in helical spring
fatigue analysis to predict the number of cycles [8]. The two compounds of forces
viz. amplitude force F a and the midrange force F m have been applied. Instead of
using fatigue rates to describe the relationship between stresses, a non-proportional
loading procedure was employed that required the use of two loading environments
for the calculation [9] and stress-life and strain-life approaches were considered for
the fatigue life evaluation. The FE mesh with 68,000 elements was generated using
quadratic tetrahedral [2]. The mesh quality of the average elements is 84.1% (Fig. 4).
4.1 Stress-Life Approach
Unlike the stress-life approach, the strain-life approach considers the effect of plasticity and elasticity. The equation relating total strain amplitude ε n to the stress
amplitude σ a is given as [10],
T. A. Musalli et al.
strength fraction curvature for the corresponding value of S ut
S e = K a .K b .K c .K d .K e .K f .S
e
(9)
where K a , K b , K c , K d , K e , K f and S
e are surface factor, size factor, load factor,
Temperature factor, reliability factor, miscellaneous factor, rotary-beam test specimen endurance limit, respectively. The values of K d , K e , K f = 1; K a = 0.84
K b = 1.4 [6, p 282] K c = 0.59 [1, p 290] and S
e is the rotary-beam test specimen
endurance limit which equal to S
e = 700 MPa for S ut > 1400 MPa. Using the
modified Goodman criterion to find the fatigue load S f [6]
τ a
S f
+
τ m
S u
= 1; S f =
τ a
1 −
τ m
S u
(10)
where
τ m = K b
8F m D
π d 3 ; τ a = K b
8F a D
π d 3
(11)
F m =
F max + F min
2
; F a =
F max − F min
2
(12)
4 Numerical Simulation
The spring geometry was modeled using Solid Work platform as per the nomenclature
given in Table 1. The ANSYS commercial program was employed in helical spring
fatigue analysis to predict the number of cycles [8]. The two compounds of forces
viz. amplitude force F a and the midrange force F m have been applied. Instead of
using fatigue rates to describe the relationship between stresses, a non-proportional
loading procedure was employed that required the use of two loading environments
for the calculation [9] and stress-life and strain-life approaches were considered for
the fatigue life evaluation. The FE mesh with 68,000 elements was generated using
quadratic tetrahedral [2]. The mesh quality of the average elements is 84.1% (Fig. 4).
4.1 Stress-Life Approach
Unlike the stress-life approach, the strain-life approach considers the effect of plasticity and elasticity. The equation relating total strain amplitude ε n to the stress
amplitude σ a is given as [10],