Page 398 - Marks Calculation for Machine Design

P1: Naresh
January 4, 2005
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Brown.cls
Brown˙C09
APPLICATION TO MACHINES
380
The free, or unstretched, length (L o ) of an extension spring is the body length (L B ) plus
two times the hook distance (L hook ), given in Eq. (9.34) as
L o = L B + 2L hook (9.34)
where the body length (LB) is given by Eq. (9.35) as
L B = (N a + 1)d (9.35)
The presence of the stress-concentration factor (K) given in Eq. (9.33) prevents the hooks
from being designed as strong as the main coils of the spring.
U.S. Customary SI/Metric
Example 7. Suppose circular hooks are added Example 7. Suppose circular hooks are added
to the ends of the cylindrical helical spring to the ends of the cylindrical helical spring
designed in Example 2. Determine the stress- designed in Example 2. Determine the stress-
concentration factor (K) for the design, where concentration factor (K) for the design, where
D = 1 in (given in Example 2) D = 0.025 m (given in Example 2)
d = 0.11 in (determined in Example 2) d = 0.0027 m (determined in Example 2)
r i = (D − d)/2 = 0.445 in r i = (D − d)/2 = 0.01115 m
solution solution
Step 1. Using Eq. (9.33), determine the stress- Step 1. Using Eq. (9.33), determine the stress-
concentration factor (K) as concentration factor (K) as
d 0.11 in d 0.0027 m
K = 1 + = 1 + K = 1 + = 1 +
2r i 2(0.445 in) 2r i 2(0.01115 m)
= 1 + (0.124) = 1.12 = 1 + (0.121) = 1.12
This means the stress at the hook ends are a This means the stress at the hook ends are a
little over 12 percent greater than the stress in little over 12 percent greater than the stress in
main coils. main coils.

9.2.6 Compression Springs
As the name implies, compression springs are helical springs loaded in compression. There
are four main types of ends for compression springs: (1) plain, (2) squared, (3) plain and
ground, and (4) squared and ground. A spring with plain ends has an uninterrupted helix
angle at its ends, whereas a spring with squared ends has the helix angle flattened to zero at
its ends. For both plain and squared types, ends that are ground flush improve load transfer,
particularly with squared and ground ends.
Additional coils must be added to the design of a helical spring if the ends are not plain.
Table 9.1 gives a summary of the additional coils needed for each type. In Table 9.1, a term
appears denoted (p) for pitch. For a cylindrical helical spring with plain ends, the pitch (p)
is defined as
L o − d
p = (9.36)
N a
where the units of pitch are length per number of active coils. The pitch (p) of a helical
spring is used to determine its free length.