Spring Design Table 3. Formulas for Compression Springs Machinery's Handbook, 31st Edition
318
Type of End
Open or Plain (not ground)
Open or Plain (with ends ground)
Squared or Closed (not ground)
Closed and Ground
Feature
Formula a
N FL d 3 −
N FL d 2 −
TC FL
N FL d −
Pitch ( p )
Solid Height ( SH ) Number of Active Coils ( N ) Total Coils ( TC ) Free Length ( FL )
( TC + 1) d
( TC + I) d
TC 3 d
TC 3 d
1
p FL d 2 3
p FL d 2 2
N TC
N TC p FL
N TC
N TC
= = −
= − = −
= − = −
= − = −
p FL d
1
p FL d 3 2 − +
p FL d 2 2 − +
p FL
p FL d −
( p 3 TC ) + d
( p 3 N ) + 3 d
( p 3 N ) + 2 d
p 3 TC
a The symbol notation is given on page 304 .
Table 4. Formulas for Compression and Extension Springs
Formula a, b Springs made from round wire Springs made from square wire
Feature Load, P Pounds
3
ND Gd F 8 3 4
3
Gd F 4
. P D Sd 0393 =
. 0416 P D =
Sd
=
=
. 558
ND
3
S ND GdF π =
. PD 0393
ND GdF P 2 =
D
Stress, Torsional, S Pounds per square inch
=
S
=
. 232
. 0416
d
d
3
2
3
. F Gd PND 558 4 =
. 232
8
SND
PND
Gd SND
3
2
3
2
Deflection, F Inch Number of Active Coils, N Wire Diameter, d Inch Stress due to Initial Tension, S it
π
F Gd =
=
=
Gd
4
N PD Gd F 8 3 4 = d GF SND π =
SD GdF π
. 558 N PD Gd F 4 =
GdF
=
=
2
. 232 3
SD
2
2
2
. S PD 255
. 232
SND
. 0416 PD
3
3
=
d
=
=
GF
S
S P S IT it # =
S IT
S P it =
#
a The symbol notation is given on page 304 . b Two formulas are given for each feature, and designers can use the one found to be appropriate for a given design. The end result from either of any two formulas is the same. Step 2: The 86.3 percent figure is also used to determine the deflection per coil f at 36 pounds load: 0.863 3 0.1594 = 0.1375 inch. Step 3: The number of active coils . . . AC f F 01375 125 91 = = =
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online