Page 97 - Analysis and Design of Machine Elements

F ΔF F Detachable Joints and Fastening Methods 75
F Q F
Q
t
Q p Q p
F
t
k b k m
Qʹ p
θ b θ m
O b O m
λ λ Δλ
Δλ
λ b λ m

Figure 3.13 Preloaded tension bolt subjected to combined preload and variable axial load.

Figure 3.13. The alternating stress experienced by the bolt is then
Q Q p
= and = (3.22)
max 1 min 1 2
d 2 4 d 1
4 1
Therefore, the minimum value of stress keeps constant and the amplitude of stress is
calculated by
max − min k b 2F
= = ⋅ 2 (3.23)
2 k + k d
b m 1
From the endurance limit diagram and methods introduced in Chapter 2, the fatigue
safety factor can be obtained by duplicating Eq. (2.30) as

2 −1 +(K − ) min

S = ≥ S (2.30)
ca
(K + )(2 + min )
a

If the design is not satisfactory, additional bolts and/or a different sized bolt may be
called for.
3.5.4 Measures to Improve Fatigue Strength of Bolted Joints
The fatigue strength of a multiply bolted joint depends on the strength of each indi-
vidual bolt in the group. Many factors affect bolt fatigue strength, including the stress
amplitude, the distribution of load among thread teeth, stress concentration, mechanical
properties and processing methods. The following will analyse typical factors affecting
fatigue strength and propose measures for improvement.

1. Reduce cyclic stress amplitudes on the bolt
When the minimum stress keeps constant, stress amplitude greatly affects fatigue
strength [12]. For a preloaded bolt, when the external operating load varies between
0 and F, the total load acting on the bolt varies from Q to Q, as illustrated in
p
Figure 3.13. The load variation in the bolt will reduce if the stiffness of the bolt is
reduced or the stiffness of the clamped members is increased, as can be noticed
from Eq. (3.18).