Page 431 - Analysis and Design of Machine Elements

14.4.3 Design Criteria Springs 409
To ensure proper function of spring, spring design must satisfy both strength and
load-deflection requirements. The design criteria involve two basic equations, the
strength equation Eq. (14.12) and the deflection equation Eq. (14.21). The static
strength calculation determines mean diameter D and spring wire diameter d, while
the rigidity calculation decides the number of active coils n.Whenaspring is subjected
to fluctuating loads, Eqs. (14.16)–(14.18) are used against fatigue failure.
Besides, for a long and slender cylindrical helical compression spring, a proper slen-
derness ratio should be selected by Figure 14.13 to prevent buckling. Springs works in
an application requiring rapid reciprocating motion are recommended to have a funda-
mental natural frequency at least 15 times the operating frequency to avoid resonances
[5]. Otherwise the spring needs to be redesigned by increasing the spring rate k or reduc-
ing mass m.

14.4.4 Design Procedures and Guidelines
Spring design, like the design of other elements, is inherently an iterative process where
design criteria need to be satisfied and desired load-deflection response to be obtained.
The design procedure and guidelines are provided next, and design cases are presented
in the next section.
1) Select spring materials and heat treatments according to operating conditions and
decide the allowable stresses [ ]and [ ].
b
2) Select spring index C and compute Wahl factor K .
w
The recommended range of spring index C is between 4 and 12, and preferably
around 5–8. Springs with an index C less than 4 are difficult to form; while those
with C exceeding 12 tend to cause tangling [5].
Assume a trial mean diameter D according to the installation space, and from
Eq. (14.22)
F Gd Gd 4
k = = =
3
8C n 8D n
3
3
We know that spring rate k is proportional to the reverse of C . With the increase
of spring index C,springrate k decreases dramatically. Spring index C will affect
the stresses and deflection in springs. And a large C value helps eliminate the spring
buckling tendency [2]. Spring rate k is in proportion to the reverse of n,thatis, with
the increase of n,springrate k will decrease. Also, for a constant deflection ,with
the increase of spring rate k, the load F also increases.
3) Compute the wire diameter d
To satisfy the stress requirement, the wire diameter d canbedeterminedby
Eq. (14.13) and selected from a series of standard diameters.
4) Compute the number of active coils n and total number of coils n
total
The number of active coils is the number of turns over which the wire twists under
load, and therefore contributes to spring deflection. For preloaded extension springs,
it is calculated by
Gd
n = max ≥ 3
8(F max − F )C 3
0