Page 423 - Analysis and Design of Machine Elements

Springs
is sufficient. For important springs working under variable stresses with millions of 401
cycles during lifetime, it is necessary to calculate fatigue strength.
When the load varies from preload F to operating load F , according to Eq. (14.12)
i
o
the maximum stress is
8K D
w
= F (14.14)
max 3 o
d
And the minimum stress is
8K D
w
= F (14.15)
min 3 i
d
For the variation of stress with the feature of constant mean stress, that is, = Const.
m
or constant minimum stress, that is, min = Const., the fatigue strength and static
strength can be calculated by referring discussions in Chapter 2.
When = Const., from Eq. (2.29), we have the fatigue strength safety factor as
m
−1 +(K − ) m

S = ≥ [S] (14.16)
ca
K ( + )
a
m

While for min = Const, from Eq. (2.30), the fatigue strength safety factor is
2 −1 +(K − ) min

S = ≥ [S] (14.17)
ca
(K + )(2 + min )
a

The static strength safety factor for both cases is
s
S = ≥ [S] (14.18)
ca
+
m a
The meaning of variables from Eqs. (14.16)–(14.18) can be referred to in Chapter 2.
The allowable safety factor is usually selected within the range of 1.2–2.5.
14.3.1.4 Rigidity Analysis
1) Deflection
Assume an initially unloaded spring carries an external axial force F and generates a
linear deflection .Thework w done by force F is expressed as
1
w = F (14.19)
2
The primary load on the wire of helical compression spring is torsion. Under the
influence of induced torque T, the wire will twist, generating a twist angle of .The
strain energy is
1
U = T (14.20)
2
The angle of twist ,fromthe Mechanics of Materials [13], is
TL
=
GJ