Machinery's Handbook, 31st Edition
Spring Design
345
Table 19. Formulas for Flat Springs Table 19. (Continued) Formulas for Flat Springs
P
P
P
P y L
L
L
L
y
y
y
Feature
b 4
Plan
Plan
b
b
b
b
2 3 6
S bt PL 6 b 2 =
L Ety 6 2
S bt PL 6 b 2 =
S bt PL =
S bt PL b 2 =
Stress , S b Bending psi
2
b
3
L Ety 2
L Ety 2
. L Ety 087 2 =
=
=
=
2
Ey S L 3 2 b 2
. 087
S L 6 b
Ey S L b
S L
2
2
2
t
t
t
t
. 522 b Ey
=
=
= =
=
Ey
Thickness, t Inches
Eby PL 6
3
Eby PL 4 3
PL
PL
3
3
3
3
3 =
3 =
=
4
Eby
Eby
Based on standard beam formulas where the deflection is small. y is deflection, see page 304 for other notation. Note: Where two formulas are given for one feature, the designer should use the one found to be appropriate for the given design. The result from either of any two formulas is the same. Belleville washers or disc springs: These washer type springs can sustain relatively large loads with small deflections, and the loads and deflections can be increased by stacking the springs. Information on springs of this type is given in the section DISC SPRINGS starting on page 350 . Volute springs: These springs are often used on army tanks and heavy field artillery, and seldom find additional uses because of their high cost, long production time, difficulties in manufacture, and unavailability of a wide range of materials and sizes. Small volute springs are often replaced with standard compression springs. Torsion bars: Although the more simple types are often used on motor cars, the more complicated types with specially forged ends are finding fewer applications. Moduli of Elasticity of Spring Materials.— The modulus of elasticity in tension, denoted by the letter E , and the modulus of elasticity in torsion, denoted by the letter G , are used in formulas relating to spring design. Values of these moduli for various ferrous and nonfer- rous spring materials are given in Table 20. General Heat Treating Information for Springs.— The following is general information on the heat treatment of springs, and is applicable to pre-tempered or hard-drawn spring materials only. Compression springs are baked after coiling (before setting) to relieve residual stresses and thus permit larger deflections before taking a permanent set. Extension springs also are baked, but heat removes some of the initial tension. Allow ance should be made for this loss. Baking at 500 degrees F for 30 minutes removes approx imately 50 percent of the initial tension. The shrinkage in diameter however, will slightly increase the load and rate. Outside diameters shrink when springs of music wire, pretempered MB, and other car bon or alloy steels are baked. Baking also slightly increases the free length and these changes produce a little stronger load and increase the rate. Outside diameters expand when springs of stainless steel (18-8) are baked. The free length is also reduced slightly and these changes result in a little lighter load and a de- crease in the spring rate. Inconel, Monel, and nickel alloys do not change much when baked.
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