Machine Design Databook Episode 2 part 7 pdf

The general expression for size factor

Wire diameter

SELECTION OF MATERIALS AND

STRESSES FOR SPRINGS

For materials for springs7

The torsional yield strength

The maximum allowable torsional stress for static

applications according to Joerres8;9;11

The maximum allowable torsional stress according to

Shigley and Mischke9

The shear endurance limit according to Zimmerli10

The torsional modulus of rupture

esz ¼ 0:86 þ

0:07

d USCS ð20-45cÞ

for steel, where d in in

esz ¼ 0:986 þ

0:0043

d USCS ð20-45dÞ

for monel metal, where d in in

esz ¼ 0:86 þ

1:8

d SI ð20-45eÞ

for steel, where d in mm

esz ¼ 0:986 þ

0:1

d SI ð20-45fÞ

for monel metal, where d in mm

ksz ¼ 4:66h0:35 where h in m SI ð20-46aÞ

ksz ¼ 1:27h0:35 where h in in USCS ð20-46bÞ

ksz ¼ 0:415h0:35 where h in mm SI ð20-46cÞ

d ¼ 3

ffiffiffiffiffiffiffiffiffiffiffiffiffi

8kFD

d esz s

ð20-47Þ

Refer to Tables 20-8 and 20-10 and Figs. 20-7b and

20-7c.

0:35sut sy 0:52sut for steels ð20-47aÞ

sy ¼ a ¼

0:45sut cold-drawn carbon steel

0:50sut hardened and tempered

carbon and low-alloy steel

0:35sut austenitic stainless steel

and nonferrous alloys

8

>>>>><

>>>>>:

ð20-47bÞ

where sy ¼ torsional yield strength, MPa (psi)

sy ¼ a ¼ 0:56sut ð20-47cÞ

sf ¼ 310 MPa ð45 kpsiÞ ð20-47dÞ

for unpeened springs

sf ¼ 465 MPa ð67:5 kpsiÞ ð20-47eÞ

for peened springs

su ¼ 0:67sut ð20-47fÞ

Particular Formula

20.14 CHAPTER TWENTY

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SPRINGS

The weight of the active coil of a helical spring

For free-length tolerances, coil diameter tolerances,

and load tolerances of helical compression springs

DESIGN OF HELICAL COMPRESSION SPRINGS

Design stress

The size factor

The design stress

W ¼
2

d2

Di

4 ð20-47gÞ

where ¼ weight of coil of helical spring per unit

volume

Refer to Tables 20-11 to 20-13.

ksz ¼ d0:35

0:355 where d in m SI ð20-48aÞ

ksz ¼ d0:25

0:84 where d in in USCS ð20-48bÞ

ksz ¼ d0:25

1:89 where d in mm SI ð20-48cÞ

ds ¼ e

naksz

¼ 0:335e

nad0:25 SI ð20-49aÞ

where e in MPa and d in m

ds ¼ e

naksz

¼ 0:84e

nad0:25 USCS ð20-49bÞ

where e in psi and d in in

TABLE 20-8

Spring design stress,
d , MPa (kpsi)

Severe service Average service Light

Wire diameter, mm MPa kpsi MPa kpsi MPa kpsi

2.15 413.8 60 517.3 75 641.4 93

2.15–4.70 379.0 55 476.6 69 585.4 85

4.70–8.10 331.0 48 413.8 60 510.0 74

8.10–13.45 289.3 42 358.4 52 448.2 65

13.45–24.65 248.1 36 310.4 45 385.9 56

24.65–38.10 220.6 32 275.6 40 344.7 50

TABLE 20-9

Factors for helical springs with wires of rectangular cross section

Ratio b=h ¼ m 1 1.2 1.5 2.0 2.5 3 5 10 1

Factor k 0.416 0.438 0.462 0.492 0.516 0.534 0.582 0.624 0.666

Factor k2 0.180 0.212 0.250 0.292 0.317 0.335 0.371 0.398 0.424

Particular Formula

SPRINGS 20.15

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SPRINGS

TABLE 20-10

Chemical composition and mechanical properties of spring materials

Tensile properties Torsional properties of wire

Analysis Ultimate strength Elastic limit Modulus of elasticity, E Ultimate strength Elastic limit Modulus in torsion, G

Material Element % Mpa kpsi GPa kpsi GPa Mpsi Rockwell hardness MPa kpsi GPa kpsi GPa Mpsi Chief uses

Flat Cold-rolled Spring Steel

Watch spring steel C 1.10–1.19 2274–2412 330–350 2.14–2.28 310–330 220 32 C55–55 Not used Not used Not used Main springs for watches

Mn 0.15–0.25 and similar uses

Clock spring steel Clock and motor springs,

AS 100 C 0.90–1.05 1240–2343 180–340 1.03–2.14 150–310 207 30 C40–52 Not used Not used Not used miscellaneous flat springs

SAE 1095 Mn 0.20–0.50 for high stress

Flat spring steel

AS 101 C 0.65–0.80 1103–2206 160–320 0.86–1.93 125–280 207 30 Annealed, B70–85 Not used Not used Not used Miscellaneous flat springs

SAE 1074 Mn 0.50–0.90 tempered C38–50

Carbon Steel Wires

High–carbon wire C 0.85–0.95 1382–1725 200–250 1.10–1.45 160–210 207 30 C44–48 1103 160–200 0.76 110–150 79 11.5 High-grade helical springs

AS 8 Mn 0.25–0.60 1377 1.03 or wire forms

Oil-tempered wire

(ASTM A229–41) C 0.60–0.70 1068–2059 155–300 0.83–1.73 120–250 794 115–200 0.55 80–130 General spring use

AS10 Mn 0.60–0.90 200 29 C42–46 1377 0.90 79 11. 5

Music wire (ASTM

A228–47) C 0.70–1.00 1725–3790 250–500 1.03–2.41 1 50–350 1034 150–300 0.62 90–180 79 11.5 Miscellaneous small

AS 5 Mn 0.30–0.60 207 30 2069 1.24 82 12.0 springs of various types—

depending high quality

on size

Hard-drawn spring

wire

(ASTM A227–47) C 0.60–0.70

1034–2068

150–300 0.69–1.38 100–200 828 120–220 0.51 75–130 Same uses as music wire

AS 20 Mn 0.90–1.20 200 29 1515 0.90 79 11.5 but lower-quality wire

Hot-rolled Special Steel

Hot-rolled bars

SAE 1095, C 0.90–1.05 1206–1377 175–200 0.73–0.97 105–140 760 110–140 0.51 75 Hot-rolled heavy coil or

ASTM A14–42 Mn 0.25–0.50 196 28.5 C40–46 965 0.76 110 72 10.5 flat springs

Alloy and Stainless Spring Materials

Chrome-vanadium C 0.45–0.55 1377 200–250 1.24 180–230 965 0.69 100–130

alloy steel Mn 0.50–0.80 207 30 C42–48 140–175 79 11.5 Cold–rolled or drawn:

(SAE 6150) Cr 0.80–1.10 1725 1.58 1206 0.90 special applications

AS 32 V 0.15–0.18

Silico-manganese C 0.55–0.65

alloy steel Mn 0.60–0.90 Used as a lower–cost

(SAE 9260) Si 1.80–2.20 About the same as chrome vanadium About the same as chrome vanadium material in place of

Type 18–8 stainless C 17–20 1103 160–330 0.41 60–260 chrome vanadium

(Type 302, Ni 7–10 193 28 C35–45 828 120–240 0.31 45–140

SAE 30915) C 0.08–0.15 2275 1.79 69 10 Best corrosion resistance,

Mn 2 max 1653 0.97 fair temperature

Si 0.30–0.75 resistance

20.16

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SPRINGS

Cutlery-type

stainless Cr 12–14 1171 170–250 0.90 130–200 828 120–180 0.55 80–120 76 Resists corrosion when

(Type 420) C 0.25–0.40 1725 1.38 193 28 C42–47 1240 0.83 11 polished; good

temperature resistance

Nonferrous Spring Materials

Spring brass For electrical

AS 55 Cu 64–74 691 100–130 0.27 308 45–90 0.21 30–60 conductivity at low

AS 155 Zn balance 897 0.41 107 15 B90 622 0.41 38 5.5 stresses; for corrosion

resistance

Nickel silver Cu 56 897 130–150 0.55 80–110 588 85–100 0.41 60–70 Used for its color;

Zn 25 1034 0.76 110 16 B95–100 691 0.48 38 5.5 corrosion resistance

Ni 18

Phosphor bronze Cu 91–93 691 100–150 0.41 60–110

AS 60 Sn 7–9 554 0.35 Used for corrosion

AS 160 or 103 15 B90–100 80–105 50–85 43 6.25 resistance and electrical

Cu 94–96 102 0.76 725 0.59 conductivity

Sn 4–6

Nonferrous Spring Materials

Silicon bronze (made Si 2–3

under various trade Sn or Small Used as substitute for

names) Mn amounts Properties similar to those of phosphor bronze Properties similar to those of phosphor bronze phosphor bronze

AS 46 Cu balance

AS 146

Monel Ni 64 691 100–140 0.55 80–120 519 75–110 0.31 45–70 Resists corrosion;

AS 40 Cu 26 964 0.83 179 26 C23–28 760 0.48 65 9.5 moderate stresses to

AS 140 Mn 2.5 204.58C

Fe 2.25

Inconel Ni 80 965 140–175 0.76 110–135 651 95–120 0.38 55–80 Resists corrosion; high

AS 40 Cr 14 1206 0.93 213 31 C30–40 828 0.55 76 11 stresses to 3438C

AS140 Fe Balance

K–Monel Ni 66 1103 160–180 0.79 115–145 725 105–125 0.45 65–85 Resists corrosion; high

AS 40 Cr 29 1241 1.00 179 26 C33–40 862 0.58 65 9.5 stresses to 2328C

AS 140 Al 2.75

Fe 0.90

Z–nickel Ni 98 1241 0.90 828 0.41

Cu 180–230 130–170 207 30 C36–46 120–150 60–90 76 11 Resists corrosion; high

Mn Small 1583 1.17 1034 0.68 stresses to 2888C

Fe amounts

Si

Beryllium-coppcr Cu 98 1103 160–200 0.69 100–150 110 16–18.5 691 100–130 0.45 65–95 41 6–7 Corrosion resistance like

AS 45 Be 2 1377 1.03 127 Subject to C35–42 897 0.66 48 copper; high physical

AS 145 heat Subject to properties for electrical

treatment heat work; low hysteresis

treatment

Note: The property values given in this table do not specify the minimum properties.

Source: Handbook of Mechanical Spring Design, courtesy Associated Spring, Barnes Group Inc., Bristol, Connecticut.

20.17

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SPRINGS