) Belleville spring
H
=
h
+
t
(
f
) Garter spring
(
g
) Constant force spring
(
h
) Constant force spring motor
FIGURE 18–2
Several types of springs
CHAPTER EIGHTEEN
Springs
597
without grinding. In unusual cases the ends may be ground
without squaring, or they may be left with plain ends, simply
cut to length after coiling.
You are probably familiar with many uses of helical com-
pression springs. The retractable ballpoint pen depends on the
helical compression spring, usually installed around the ink
supply barrel. Suspension systems for cars, trucks, and motor-
cycles frequently incorporate these springs. Other automotive
applications include the valve springs in engines, hood link-
age counterbalancing, and the clutch pressure-plate springs.
In manufacturing, springs are used in dies to actuate strip-
per plates; in hydraulic control valves; as pneumatic cylinder
return springs; and in the mounting of heavy equipment for
shock isolation. Many small devices such as electrical switches
and ball check valves incorporate helical compression springs.
Desk chairs have stout springs to return the chair seat to its
upright position. And don’t forget the venerable pogo stick!
The following paragraphs define the many variables
used to describe and analyze the performance of helical
compression springs.
Diameters
Figure 18–5 shows the notation used in referring to the
characteristic diameters of helical compression springs. The
outside diameter (
OD
), the inside diameter (
ID
), and the
wire diameter (
D
w
) are obvious and can be measured with
standard measuring instruments. In calculating the stress
and deflection of a spring, we use the mean diameter,
D
m
.
Notice that
➭
Spring Diameters
OD
=
D
m
+
D
w
ID
=
D
m
-
D
w
of the coil and on the elastic modulus of the spring material.
Basically, the force is related to the deformation of the strip
from its originally curved shape to the straight form.
Power springs,
sometimes called
motor
or
clock springs,
are made from flat spring steel stock, wound into a spiral
shape. A torque is exerted by the spring as it tends to un-
wrap the spiral. Figure 18–2 shows a spring motor made
from a constant-force spring.
A
torsion bar,
as its name implies, is a bar loaded in tor-
sion. When a round bar is used, the analyses for torsional
stress and deflection are similar to the analysis presented for
circular shafts in Chapters 3 and 12. Other cross-sectional
shapes can be used, and special care must be exercised at the
points of attachment.
Information about commercially available springs can
be found in Internet sites 3–5 and 13. The methods of ana-
lyzing and designing springs used in this book have been de-
veloped by applying principles from References 1–8.
18–3
HELICAL COMPRESSION
SPRINGS
In the most common form of he-
lical compression spring, round
wire is wrapped into a cylindri-
cal form with a constant pitch
between adjacent coils. This basic form is completed by a
variety of end treatments, as shown in Figure 18–3.
For medium- to large-size springs used in machinery,
