Page 418 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
396
Figure 14.10 Energy storage and dissipation.

When friction is absent, the stored energy is fully recovered as the spring returns to its
original length; however, when present, the area surrounded by loading and unloading
characteristic curve represents energy loss U , as illustrated in Figure 14.10. The lost
0
energy is for overcoming friction and may generate undesirable heat, however, it can be
desirable whenever impact or vibration must be reduced. The larger the ratio of U to
0
U, the stronger the capability of shock and vibration absorption. Ring springs, Belleville
springs and multilayer leaf springs are functioned according to this principle and are
used as buffing springs widely, especially in heavy machinery.

14.2.4 Potential Failure Modes
Springs are elastic elements which can produce large deflection under applied loads.
They are expected to exert desired force or to deliver stored energy essential for the
machine operation over long periods of time. Common potential failure modes that pro-
hibit proper functioning of springs include yield, fatigue, buckling, resonance, corrosion,
creep, fretting fatigue and so on [5].
Springs are usually subjected to static or fluctuating loads during operation. Excessive
static loads may cause the induced stress to exceed the yield strength of spring material,
resulting permanent dimensional change. Fluctuating loads may cause stress variation
and eventually fatigue failure. Extreme axial load on a slender compression spring may
cause buckling. Resonance or surging may occur if cyclic operating frequencies are close
to the resonant frequency of spring.
Operating conditions may also affect failure modes. Corrosive environments may
reduce the strength and surface hardness of spring, leading to accelerated corrosion
failure. Elevated temperatures may cause thermal relaxation and creep, producing
unacceptable dimensional change or reduction of load carrying capability. As always,
it is, therefore, extremely important to identify potential failure modes and propose
proper measures to prevent failures at the design stage.

14.3 Load Carrying Capacities

14.3.1 Analysis of Helical Compression Springs
14.3.1.1 Load-Deflection Relationship
Figure 14.11 shows the load-deflection relationship at different loading conditions.
When a cylindrical helical compression spring carries no load, the free length is H .
f
At installation, an initial preload F is applied and the spring reaches installed length
i