Page 549 - Shigley's Mechanical Engineering Design

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Mechanical Springs 523
For steels, this turns out to be

D
L 0 < 2.63 (10–13)
α
For squared and ground ends α = 0.5 and L 0 < 5.26D.

10–6 Spring Materials

Springs are manufactured either by hot- or cold-working processes, depending upon
the size of the material, the spring index, and the properties desired. In general, pre-
hardened wire should not be used if D/d < 4 or if d > 1 4 in. Winding of the spring
induces residual stresses through bending, but these are normal to the direction of the
torsional working stresses in a coil spring. Quite frequently in spring manufacture,
they are relieved, after winding, by a mild thermal treatment.
A great variety of spring materials are available to the designer, including plain
carbon steels, alloy steels, and corrosion-resisting steels, as well as nonferrous materi-
als such as phosphor bronze, spring brass, beryllium copper, and various nickel alloys.
Descriptions of the most commonly used steels will be found in Table 10–3. The UNS
steels listed in Appendix A should be used in designing hot-worked, heavy-coil springs,
as well as flat springs, leaf springs, and torsion bars.
Spring materials may be compared by an examination of their tensile strengths;
these vary so much with wire size that they cannot be specified until the wire size is
known. The material and its processing also, of course, have an effect on tensile
strength. It turns out that the graph of tensile strength versus wire diameter is almost
a straight line for some materials when plotted on log-log paper. Writing the equation
of this line as

A
S ut = (10–14)
d m
furnishes a good means of estimating minimum tensile strengths when the intercept A
and the slope m of the line are known. Values of these constants have been worked out
from recent data and are given for strengths in units of kpsi and MPa in Table 10–4.
m
In Eq. (10–14) when d is measured in millimeters, then A is in MPa · mm and when
m
d is measured in inches, then A is in kpsi · in .
Although the torsional yield strength is needed to design the spring and to analyze
the performance, spring materials customarily are tested only for tensile strength—
perhaps because it is such an easy and economical test to make. A very rough estimate
of the torsional yield strength can be obtained by assuming that the tensile yield strength
is between 60 and 90 percent of the tensile strength. Then the distortion-energy theory
can be employed to obtain the torsional yield strength (S ys = 0.577S y ). This approach
results in the range

0.35S ut ≤ S sy ≤ 0.52S ut (10–15)
for steels.
For wires listed in Table 10–5, the maximum allowable shear stress in a spring
can be seen in column 3. Music wire and hard-drawn steel spring wire have a low end
of range S sy = 0.45S ut . Valve spring wire, Cr-Va, Cr-Si, and other (not shown) hard-
ened and tempered carbon and low-alloy steel wires as a group have S sy ≥ 0.50S ut .
Many nonferrous materials (not shown) as a group have S sy ≥ 0.35S ut . In view of this,