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DesignHandbookEngineering GuideTo Spring Design1987 Edition
l0Mainstreet, Brisro,,.*::$il3: AssogffilfiS &ffi&ffiffi$ ffi
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t sectionTable of Contents
Page
I Eor to Use the Handbook
I Selccdng Spring Configurationshrsh. Pull. Twist or Energy Stofage Applications: Common Available Configurations.
3 Spring MaterialsCommon Specifications, Elastic Modulus, Magnetic Characteristics, Heat Treatment, Stress Relaxation,Corrosion, Coatings and Finishes.Spring Wire: Tensile Properties, Cost and Availability.Sprine Strip: Strength, Formability and Edge Condition.
4 Reidual Stress, Fatigue and ReliabilityLoad-Carrying Ability, Fatigue Terminology, Modified Goodman Diagram, Weibull Analysis, Load Loss.
-i Eelical Compression SpringsGeneral Definitions, Squareness, Parallelism, Hysteresis, Design Equations for Spring Rate and Stress,BucklinlChoice of Operating Stress for Static and Cyclic Applications, Dynamic Loading Impict and Resonance,Rectangular Wire, Stranded Wire, Variable Diameter, Variable Pitch and Nested Springs,Commercial Toleranc,
5 Hot-Wound SpringsDesign Considerations, End Configurations, Materials, Choice of Operating Stress, Tolerances.
7 Eelirnl Extension SpringsInitial Tension, Types of Ends and Dimensions, Design Equations, Choice of Operating Stress for Staticand Cyclic Applications, Commercial Tolerances.
t Garter SpringsJoint Design, Design Equations and Tolerances.
9 Helical Torsion SpringsMean Diameter, Length, Design Equations for Rate and Stress, End Configurations, Natural Frequency,Choiceof Operating Stress for Static and Cyclic Applications, Double Torsion and Rectangular Wire Springs, ioleranc,
l0 f,staining RingsExternal and Internal Types, Ends, Design Equations, Choice of Stress Level, Tolerances.
ll Belleville Spring WashersLoad-Deflection Characteristics, Mounting, Design Equations.Choice of Stress Level for Static andCyclic Applications, Stacking and Tolerances.
12 Flat Springs . .Design Considerations and Equations for Cantilever and Simple Beams, Choice of Stress Level andTolerances.
13 Specid Spring WashersDesign Considerations and Equations for Curved, Wave and Finger Washers, Choice of Stress Level andTolerances.
l{ Power SpringsGeneral Design Considerations and Equations, Operating Stress for Power and hestressed PowerSprings.
lS Constant Force SpringsExtension Type_, Design Equations, Mounting and Tolerances, Motor Type Design Equations for "A"and "B" Type Motors, Operating Stress and Tolerances.
f6 Spird SpringsDesign Equations for Hair Springs and Brush Springs.
17 Volute SpringsDesign Equations and Choice of Operating Stress Level.
It Wire FormsGeneral Information and How to Specify.
19 IndexandReference ln fo rmat ion . . . . . . .1Glossary of Spring Terminology, Bibliography, Trademarks, Conversion Factors, Abbreviations and Symbols,Hardness Scale Conversions, Index and Lists of Thbles and Illustrations.
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Selecting Spring Configurations
Tabb 2-1. Spring Configurations. Tv?u cor'if"IstJ&ATIoli ACTt0:ri
T\'PT. COTNCUNATION A.rTION Beam (Section 12)
Cantilever,Rectangular Section
Simple Beam
Helical Compression
Round andRecrangular\t-ire
Constant Pitch
V
_€=*:
Conrcal : :
I
i
Hourglass
(Section 5)
t
Barrel
Variable-Pitch I
hrsh or pull-wide rangeof loads, low deflectionrange.
Push-wide load and de-flection range-constant
cantilever,rate' Trapezoidal Section
-
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aea-
a-
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A
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i
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RoundorRectang",.- ffi frSwire
" (2'il[ rwist<onstantrate'
Spiral (Section 16) ,^
@w
rwistorhrsh'
Push-wide load and de-flection range. Conicalspring can be made withminimum solid height andwith constant or increasingrate. Barrel, hourglass, andvariable-pitch springs usedto minimize resonant surg-ing and vibration.
Helical Torsion (Section 9)
P l
ffi
Hairspring
Brush
Twist.
a5lotted
=a=f Finger
=fCurved
Push-high loads, low de-flections-choice of rates(constant, increasing, ordecreasing).
Push-light loads, lowdeflection-uses limitedradial space.
Ptrsh-higher defl ection sthan bellevilles.
hrsh-for axial loading ofbearings.
Push-used to absorb axial. end play.
:ili',y:,::;'@
a d )\/
Twist---exerts torque overmany turns.
Supplied in retainer.
Removed from retainer.
PrestressedPower (Section 14) Twist--+xerts torque over
many turns.
Supplied in retainer.
Removed from retainer.
rl
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Volute (Section 17)
Push-may have an inher-ently high friction damp-ing.
Constant (Section 15)ForceSpringMotorLevel Torq
Twist+xerts close-to-constant torque over manyturns.
Spring Washer (Section ll and 13)
Bellevil le
\lare
/-€-\\:r'Vxql
/raR
ryeft\1V/R\ \ - / l-:
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Spring Materials
Chemical and Physical CharacteristicsWhile certain materials have come to be regarded as
ry.i.ng materials, they are not specially design-d alloys.Spring materials are high strength alloys wtrictr ofienexhibit the greatest strength in the alloy system. Forexample: in steels, medium and high-carbon steels areregarded as spring materials. Beryllium copper is fre-quently specified when a copper base alloy is required.For titanium, cold-worked and aged Ti-l3v-llCr-3At is
Tahle 3-1 Typical Properties of Common Spring Materials.
used. The energy storage capacity of a spring is propor-tional to the square of the maximum operating stresslevel divided by the modulus. An ideal spring materialhas high strength, a high elastic limit and a low modulus.Because springs are resilient structures designed to un-dergo large deflections, spring materials must have anextensive elastic range. Other factors such as fatiguestrength, cost, availability, formability, corrosion resis-tance, magnetic permeability and electrical conductivity
sG
C!
G
G
G
G
G
G
G
G
G
G
G
CCGC
CCCC
GC
CCC-
CG(F
(l) Elastic moduli, density and electrical conductivity can vary withcold work, heat treatment and operating stress. These variations areusually minor but should be considered if one or more of theseproperties is critical.(2) Diameters for wire; thicknesses for strip.(3) Typicd surface quality ratings. (For most materials, special pro-cesses can be specified to upgrade typical values.)
a. Maximum defect depth: 0 to 0.5Vo of d or t.
b. Maximum defect depth: l.$Vo of d or t.c. Defect depth: less than 3.5Vo of d or t.
(4) Maximum service temperatures are guidelines and may vary dueto operating stress and allowable relaxation.(5) Music and hard drawn are commercial terms for patented andcold-drawn carbon steel spring wire.
INCONEL, MONEL and NI-SPAN-C are registered trademarks ofInternational Nickel Company, Inc. BARTpi is a registered trade-mark of Theis of America. Inc.
Com*on lihme
Y,o*qt*Modulrrs S {l}
MPr | {ed}r t ' l i d]
il{odnkm ofRlddly G {l}lWPr | {Dd}r d l i d
. Mtf {t}*1ffir5 {tbl,tu';
&lcr .leslCorr&rc-*iY,lty ttl% f*c$
$ias lioruelly.tvrlhblc {2}
Min. i Mrr.mm {hr.} i mm {h.}
r'rp|nl.S{r&eGQt&y,
t l
,:,.,ilil1fua,fi ..fcrycr.
, i,,'i , ({}
3Fot
Carbon Steel Wires:Music (5)Hard Drawn (5)Oil TemperedValve Spring
207207207207
(30)(30)(30)(30)
79.379.379.379.3
( l l .s)( l l .s)( l 1.5)( l1 .5 )
7.86 (0.2E4)7.85 (0.2E4)7.E6 (0.2E4)7.86 (0.284)
0.10 (0.004)0.13 (0.00s)0.s0 (0.020)1.3 (0.0s0)
6.35 (0.250)16 (0.625)16 (0.62s)6.35 (0.250)
acca
r20150r50150
250250300300
Alloy Steel Wires:Chrome VanadiumChrome Silicon
207207
(30)(30)
79.379.3
( l 1 .5)( l 1 .5)
(0.284)(0.2E4)
7.867.86
75
0.50 (0.020)0.50 (0.020)
l r (0.435)9.5 (0.375)
arbarb
220 425245 475
Stainless Steel Wires:Austenitic Type 302hecipitationHardening l7-7 PH
NiCr A2E6
193203
200
(28)(2e.s)
(2e)
69.075.E
7 r . 7
(10.)( l l )
(10.4)
(0.286)(0.2E2)
(0.290)
7.927 .E l
E.03
22
2
0.13 (0.00s)0.08 (0.002)
o.lm (0.016)
9.5 (0.375)r2.5 (0.500)
5 (0.200)
bb
b
2@ 500315 600
510 950
Copper Base Alloy Wires:Phosphor Bronze (A)Silicon Bronze (A)Silicon Bronze (B)Beryllium CopperSpring Brass, CAz6/u.
103103t17128l r 0
(15)(15)(17)(1E.5)(16)
43.438.64 . 1+8.t42.0
(6.3)(5.6)(6.4)(7.0)(6.0)
8.86 (0.320)E.s3 (0.308)E.75 (0.316)8.26 (0.298)8.53 (0.30E)
l57
t22rt7
0.10 (0.004)0.10 (0.004)0.r0 (0.004)0.0E (0.003)0.10 (0.004)
(0.500)(0.s00)(0.500)(0.500)(0.500)
12.512.5tz.512.512.5
bbbbb
9s 20095 20095 2m
205 40095 200
Nickel Base Allovs:Inconelo Alloy 600Inconel Allov X750Ni-Span-C@Monilo Allov 400Monel Alloy K500
2r42t4lE6179r79
(3 l)(3 l)(27)(26)(26)
75.E79.362.96.26.2
( l t )( l 1 .5)(e.7)(e.6)(e.6)
8.43 (0.304)8.25 (0.298)8.14 (0.2%)8.83 (0.319)E.46 (0.306)
1 . 5Ir .53.53
0.10 (0.004)0.10 (0.004)0.10 (0.004)0.05 (0.002)0.05 (0.002)
l2.s (0.500)12.5 (0.500)r2.5 (0.500)9.s (0.375)9.5 (0.375)
bbbbb
320 700595 ll009s 200
230 4502ffi 500
Carbon Steel Strip:AISI 1050
l06s1074, 1075r09s
Bartexo
2072W2W207207
(30)(30)(30)(30)(30)
79.379.379.379.379.3
( l l . s )( l 1 . 5 )( l 1 . 5 )( l r .5)( l 1 . 5 )
7.E6 (0.2E4)7.86 (0.284)7.E6 (0.2E4)7.E6 (0.2E4)7.86 (0.284)
77777
0.25 (0.010)0.0B (0.003)0.0E (0.003)0.08 (0.003)0.10 (0.004)
3 (0.125)3 (0.125)3 (0.125)3 (0.125)l (0.040)
bbbba
95 20095 2W
r20 250r20 2509s 200
Stainless Steel Strip:Austenitic Types301, 302
PrecipitationHardening l7-7 PH
193
203
(28)
(29.s)
69.0
75.8
(10)
( 1 1 )
(0.2E6)
(0.282)
7.92
7 .81
)
7
0.0E (0.003)
0.08 (0.003)
1.5 (0.063)
3 (0.125)
b
b
315 600
370 700
Copper Base Alloy Strip:Phosphor Bronze (A)Beryllium Copper
103r28
(15)(18.5)
4348
(6.3)(7.0)
E.16 (0.320)8.26 (0.298)
l52 l
0.08 (0.003)0.08 (0.003)
5 (0.18E)9.5 (0.375)
bb
9s 200205 400
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can also be important and must be considered in lightof cost, benefit. Consequently, careful selections mustte made to obtain the best compromise.
Table 3- I lists some commonly used alloys along withdau for material selection purposes. Data on mechanicalpropenies are presented in the Spring Wire and SpringStrip subsections (Pages 18 and 20 respectively). Speci-fications have been written by many national and inter-n a t i o n a l o r g a n i z a t i o n s . T h e s e s p e c i f i c a t i o n s a r ecross-referenced to Associated Spring specifications inTable 3-2r However, correlation between the specifica-tions is only approximate. Associated Spring specifica-t ions were developed exc lus ive ly for h igh qual i tymaterial for spring applications and are generally moredetailed and stringent than other specifications.
Surface quality has a major influence on fatiguestrength and is often not clearly delineated on nationalspecifications. It is important to use only those materialsuith the best surface integrity for fatigue applications,particularly those in the high cycle region.
In steel alloys, for which processing costs are a largefraction of product cost, surface quality can vary overan appreciable range. Depth of surface imperfections,such as seams, pits and die marks, can be up to3.5%of diameter for commercial spring wire grades (ASTMA-227 and A-229). Various intermediate qualities can beobtained. Highest levels are represented by music andvalve spring quality grades which are virtually free ofsurface imperfections. Decarburization, which can alsoadversely affect fatigue performance, follows a similarpattern. Surface quality of spring materials is a functionof the care exercised in their production and processesemployed. Materials produced with a high level of sur-face integrity are more costly than commercial grades.
Elastic ModulusThe modulus of elasticity in tension and shear is vital
to spring design. Table 3-1 lists recommended values forcommonly used spring alloys. For most steels and age-hardenable alloys, the modulus varies as a function ofchemical composition, cold work and degree of agrng.Usually variations ar0 small and can be compensated forby adjustment of reference parameters of the spring de-sign, (e.g. number of active coils, and coil diameter).
For most materials, moduli are temperature-dependentand vary inversely with temperature by approximatelyZVc per 55'C (100"F). Since nonambient temperature test-ing is costly, design criteria should be specified at roomtemperature after having made appropriate compensa-tion for the application temperature. Certain nickel-chromium-iron alloys are designed to have a constantmodulus over the temperature range from -5o to 65'C(-50" to 150'F) and are exceptions to the above rule.
For true isotropic materials, the elastic moduli in tension(E) and shear (G) are related through Poisson's ratio by theexpression:
EP : 6 - r
so that, for common spring materials, any one of the param-eters may be approximated using the other two.
Spring Materials
Magnetic CharacteristicsFor most applications, the question of "magnetic or
not" is adequately answered with the use of a permanentmagnet. For some applications, even very low levels ofmagnetic behavior can be detrimental. Then, it is desir-able to know the magnetic permeability of candidatematerials and reach agreement between parties on amaximum allowable value. Table 3-3 lists approximatevalues for a number of low permeability materials alongwith other frequently used alloys.
Since permeability can be altered by cold work, somevariation can be expected. In general, low permeabilitymaterials are more expensive so designers should specifylow levels only when absolutely necessary. Often, nitro-gen strpngthened manganese stainless steels are goodchoices because they have good strength at moderatecost.
Heat Treatment of SpringsHeat-treating temperatures for springs can be divided
into two ranges. Low temperature heat treatments in the175'to 510'C (347'to 950'F) range are applied to springsafter forming to reduce residual stresses and stabilizeparts dimensionally. For carbon steels, stainless steelsand some age-hardenable alloys, low temperature heattreatments are used to increase or restore the set point.Electroplated carbon steel parts are heat-treated at lowtemperatures prior to plating, and baked afterward to re-duce the susceptibility to hydrogen embritflement. Mostlow temperature stress relieving and age-hardening ofsprings are done in air and a moderate amount of oxidemay be formed on the part. No detrimental effects of thisoxide have been noted.
High temperature heat treatments are used to strength-en annealed material after spring forming. High-carbonsteels are strengthened by austenittzing in the temperat-ure range 760'to 900"C (1480" to 1652"F), quenching toform martensite and then tempering. Some nickel basealloys are strengthened by high temperature aglng treat-ments. Because substantial oxidation occurs at these el-evated temperatures, it is advisable to prevent excessiveoxidation by using an appropriate protective atmosphere.
Heat treatments suitable for many commonly used ma-terials are listed in Table 3-4. Selection of a temperaturewithin a given range can only be made after consideringthe material, size, strength level, application conditionsand desired characteristics. For additional guidance, As-sociated Spring engineers should be consulted. Unlessotherwise noted, 20 to 30 minutes exposure at tempera-ture is sufficient to obtain the bulk of the stress-relievingeffect.
Many spring-like parts involve forms which precludethe use of prehardened material. In these cases, soft orannealed material must be used and heat-treated to attainspring properties after forming. Thin high-carbon andalloy steel parts become distorted when hardened byquenching. Distortion may be reduced by fixture tem-pering; however, this process is costly and should beavoided if at all possible by using pretempered mat-erials.
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Spring Materials
Table 3-2. Related Spring Material Specifications..twoeint*d
$tri'n* CorrrnonTrldr F{ams saa ASTM AM,S Mfliarl' Ihderd
Britlih fieffirlr':f,},[H,
,lltfsrye.tI$EN 8S
Spring Wire
CG
G
G
G
C
G
G
C
C
G
C
C
C
-
CCCCCCC
CC
CCCCCcC
AS-5 Music Wire 1085J l78
1228 5tL2 s4@9 QQv/470(obsolete)
1408 or 5216520r
17223, Sheet I1 .1200
G3522,SWP-A, B, V
AS-10 Oil TemperedCarbon Steel
1066J316
L229 QQw428 2803, grade 3 17223, Sheet 2,1.1230
G3560,swo-A, B
AS.2O Cold DrawnCarbon Steel
1066J r 13
A227 49B 14085216 NS or HS
17222, Sheet I1.0500
G3521,sw-A, B, c
AS-25 Oil TemperedCarbon Steel*
1070 42,30 5 1 1 5 2803,Grades I & 2
L7223. Sheet 2 G3561,swo-v
AS-32 Oil TemperedChromeVanadium*
6150tr32
A232 &50 w-22826 QQw412 4750
17225,50CrV4
G3565,swocvry
AS-33 Oil TemperedChrome Silicon*
9254n57
A40l QQw4l2 48A 17225,67SiC15
G3566,swosc-v
AS-35 Stainless Steel 3030130302J230
A313;Type 301,Type 302
5688 QQw423(obsolete)
58A 2056 1.43001.4310t7224
G43T4,sus 302
AS.36 r7-7 PH J2T7 A'313,I}pe 531
5678 t7224,1.4568
G4314,sus 63IJl
AS44 Inconel X-750 5698. 5699
AS-45 Copper Beryllium cA-t72 Bt97 4725,Cond. A
QQW-530,Cond. A
2873,cBl0l
1766,6,2.t247.55
AS-55 Spring Brass cA-2@ BTY,n60
QQW-321,n@
2786,czrw
17660,2.0265
AS-60A. Phosphor Bronze cA-510B159,#5rc
4720 QQw40l 2873,PBlO2
17662,2.1030.39
AS-60C Phosphor Brorue cA-52r#521
AS-70 Chromium Steel s160H A'304A689
970, Part 5
Spring Strip
AS-100 1095 A682A684
5r2l5t22
s-7947AnnealedCold-Rolled
44D 1449, Part 38,csl00
17232,| . t274
G3311 ,SK4M
AS-l0 l r0741075
A682A684
5r20 42E. 14/19, Parrt38,cs. cs80
t7222,l.t2r0
G3311 ,s75CM
AS-102 1050 A682A684
5085 l$g, Paft3B,cs50
G33 l l ,s50cM
AS-103 1065 A682A684
5 1 1 5 42F 1440, Part 38,cs60. cs70
17222,l .1230
G3311,s65CM
AS-105 Bartex 1085
AS-135-AAS-135-B
Stainless Steel 3030130302
At77 55175518, 5519 s-5059 QQS-766 58A 14,y'l9, Parrt 4,
302-S-25
t7224,1.43101.4300
G43r3,sus-301-csPsus-302-csP
AS-136 t7-7 PH 55285529 SpringTemper
s-25043Cond. A
t7224,1.4568
G4313,sus-631-csP
AS-144 Inconel X-750 5542 N 7786
AS-145 Copper cA-r728194,#r72
4s30(AT)4s32(LtzHT) QQC-533
2870,cB101
r7666,2.1247.55
AS-155 Spring Brass cA-260 836,f260
4507. vzH QQB-613,Comp.2TIzH
2870,czt08
17660,2.026s
AS-1@A PhosphorBrorze
cA-5r0 8103,#510
4510SpringTemper
QQB-750,Comp. A
2870,PB1O2
17662,2.1030.39
AS-160C Phosphor Bronze cA-5218r03,#521
*Valve spring quality.
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T& 3-3. Magnetic Characteristics of Some Materials.
Spring Materials
Tempering is an effective stress-relieving treatment andresults in negligible levels of residual stress. Some springmaterials, such as beryllium copper and l7-7 PH, arestrengthened after forming by age hardening. This pro-vides a good stress relief, but may also cause distortionunless special techniques are used.
Environmental ConsiderationsFrequently, operating environment is the single most
important consideration for proper spring material se-lection. For successful application, material must becompatible with the environment and withstand effectsof temperature and corrosion without an excessive lossin spring performance. Corrosion and elevated tempera-tures decrease spring reliability. The effect of tempera-ture on spring materials is predictable and discussedbelow. Compatibility of spring materials and spring coat-ing systems with corrosive environments is discussed ingeneral terms. For specific applications, the designer isurged to rely upon previous experience or consult withAssociated Spring engineers.
Stress RelaxationPrimary concern for elevated temperature applications
of springs is stress rela:ration. Stress relaxation is theloss of load or available deflection that occurs when aspring is held or cycled under load. Temperature alsoaffects modulus, tensile and fatigue strength. For a givenspring, variables which affect stress reloration are:stress, time and temperature, with increases in any pa-rameter tending to increase the amount of rela;ration.Stress and temperature are related exponentially to re-laxation. Curves of relaxation versus these parametersare concave upward as is shown in Figures 3-1 and 3-2.Other controllable factors affecting relaxation include:
1. Alloy Type - more highly alloyed materials are gen-erally more resistant at a given temperature or can beused at higher temperatures.
2. Residual Stress - residual stresses remaining fromforming operations are detrimental to relaration resis-tance. Therefore, use of the highest practical stress-relief temperatures is beneficial. Shot peening is alsodetrimental to stress relaxation resistance.
3. Heat Setting - various procedures can be employedto expose springs to stress and heat for varying timesto prepare for subsequent exposures. Depending onthe method used, the effect is to remove a usuallylarge first-stage relaxation and/or to establish a resid-ual stress system which will lessen relaxation influ-ences. In some cases, the latter approach can be soeffective that in application, compression springs may"grow" or exhibit negative relaxation. Increase infree length does not usually exceed I to ZVo.
4. Grain Size - coarse grain size promotes relaxationresistance. This phenomenon is used only in veryhigh temperature applications.
Because so many variables are involved, it is impossibleto cite comprehensive data in a publication of this type,but Table 3-l does show approximate maximum service
iffi
-{.!rBrzsscs. BronzesCarbon SrcelsFlglol t
lnconel -{,lloys:6m5r_<x--50
Staintess Steels:Tlpe 301, spring temperTfpe 302, spring temper
631 07-7 PI{)XV-28: Nitroniso 32*
\*itronic 50*Titanium Alloys
' \ itrogen-strengthened manganese stainless steels.
ELGILOY is a registered trademark of Katy Industries, Inc. NITRONICis a registered trademark of Armco., Inc.
Tabb 34. Typical Heat Treatments for Springs AfterForming.
1114 . ,,,,,,, ,, .
Patented and Cold-Drawn Steel WireTempered Steel Wire:
CarbonAllor-
Austenitic Stainless Steel Wire
Hent,lftt C , , , : ,; r
l ' . , " . , , ; t ' :
190-230
2G4003t5-42523L510
ma-ffii:l:;i::Tl:zs-rsolsruzsoI 600-80045G950
Precipitation Hardening Stainless Wirer l l -7 PH):Condition CCondition A to TH 1050
480/l hour760/l hourcool to l5oCfollowed by565/ I hour
900/l hour1400/l hour.cool to 60"Ffollowed by1050/l hour
Vonel:.{lloy'496Allo.v K500, Spring Temper
Inconel:.{lloy'600Allol X-750:
* I TemperSpring Temper
30L315525 I 4 hours
40G510
7301 16 hours6501 4 hours
57ffio98014 hours
750-950
l350l16 hoursn00l4 hours
Copper Base, Cold Worked (Brass,Phosphor Bronze, etc.)
Beryllium Copper:hetempered (Mill Hardened)Solution Annealed,
Temper Rolled or Drawn
t75-205
20s
3r5t2-3hours
3sG400
400
6W/2:3 hours
Annealed Steels:Carbon (AISI 1050 to 1095).{, l lol ' (AISI 5150H 6150, 9254)
800$30*830{85*
1475-t525*1525-1625*
-Time depends on heating equipment and section size. Parts are auste-rutized then quenched and tempered to the desired hardness.
Prfm**rbility rr W Onrr*tdnRoom Temperesrre
INonmagnetic
> 5001.00003s
l .0 t1.00061.0035
> 3 0> 1 2> 4 01.0i lr.004
Nonmagnetic
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o'"TFlfi8AH*ffilE$ H
l
|tG
CCCGGGGGGG
CGCC
CCCCCC
CC|i
CCCCC
l 8
r2
8 r oc
.9ox
€ 8oc
l 8
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8 r oc.9oxo^ Q
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Spring Materials
Fig. 3-1. Relaxationterials.
versus Initial Stress for Spring Ma-
lnitiol stress ( 103 psi)7'5 100 125 150
g
ECorbon Chrome '
steel silicon $
Ploinspr ings -- -
Shor-peened -.- - fl
Shot-peened -- - .lond Heot set g
flE t
Exposure of 100 hours ot l49oC (300"F) f IStresses colculoted ot room femPeroture o I
.gtf
; r lg.u I
I
ilr/ I
l t
200 1000
temperatures for many commonly used materials. Itshould be remembered that, if a material is used at itsmaximum temperature, a substantial reduction must bemade in applied stress from that used at room temper-ature.
CorrosionThe effect of a corrosive environment on spring per-
formance is difficult to predict with certainty. Generalcorrosion, galvanic corrosion, stress corrosion and cor-rosion fatigue reduce life and load-carrying ability ofsprings. The two most common methods employed tocombat effects of corrosion are to specify materials thatare inert to the environment and to use protective coat-ings. Use of inert materials affords the most reliableprotection against deleterious effects of all types of cor-rosion; however, this is often costly and sometimes im-practical. Protective coatings are often the most cost-effective method to prolong spring life in corrosive en-vironments. In special situations, shot peening can beused to prevent stress corrosion and cathodic protectionsystems can be used to prevent general corrosion.
Fig. 3-2. Relaxation versus Temperature for Spring Ma-terials.
Exposure temperqture (" F)250 300 350 400
Corbon Chromesteel silicon
Ploinsprings - - -Shot-peened crrr m
Shot-peened - - -ond Heot sei
_ffg
,ff
3a
Fg .
* ' /f , t
120 r40 160 r80400 600 800Initiqlslress (MPo) Exposure temperoture (t)
3 -5. Guide for S e Ie cting Minimum Thickne s s e s forZinc and Cadmium Coatings.
Tahle
(l) Requirements for zinc coating (electrodeposited).(2) Requirements for cadmium plating (electrodeposited)'Finish Type:
A. Without supplementary chromate or phosphate treatment.B. With supplementary chromate treatment.C. With supplementary phosphate treatment.
Zixon tranerd SrnelPart PerQ8rA325 t$
Cedmirrron LuardStsclPrrrs per QQ'"I4I6 {Z}
ilfisirnur$3Th*nmm*n,till.l
.*Ilri*hBrr
S*li,$pqryTr*Sr''L $rn$,h:ftrr'..�fion:White :n$d,
,ill&turry!Thiekamrrnar,{lnJ
fiilf,$
l}pr,'
'Sl*.i
ffi,:iH$4ryl*;1ltry&C
0.025(0.0010)
ABc
%r92
r920.013
(0.00050) B 96
0.013(0.000s0)
ABc
960.008
(0.00030) B 96
0.005(0.00020)
ABc
%36
36
0.005(0.00020) B 96
ffiessog51ffifu*ffiffi$ C-1
Coatings may be classified as galvanically sacrificialor simple barrier coatings. Sacrificial coatings for highcarbon steel substrates include zinc, cadmium (and al-loys thereof) and, to a lesser degree, aluntinum. Due toits toxicity, cadmium coating should only be specifiedwhen absolutely necessary. Because sacrificial coatingsare chemically less noble than steel, the substrate is pro-tected in two ways. First, the coating acts as a barrierbetween substrate and environment. Second, galvanicaction between coating and substrate cathodically pro-tects the substrate. This characteristic allows sacrificialcoatings to continue their protective role even after thecoating is scratched, nicked or cracked. The amount ofdamage a sacrificial coating can sustain and still protectthe substrate is a function of the size of the damaged areaand the effrciency of the electrolyte involved. The saltspray life criteria for three thicknesses of sacrificial coat-ings are shown in Table 3-5. Use of conversion coat-ings, such as chromates, lengthens the time of protectionby protecting sacrificial coatings. SaIt spray (fog) is anaccelerated test and results may, or may not, correlatewith corrosive activity in the actual environment. Thetest is useful as a control to ensure the coating wasapplied properly.
Metallic coatings are normally applied by electroplat-ing. Since most high hardness steels are inherently verysusceptible to hydrogen embrittlement, plating must becarried out with great care to minimize embrittlementand subsequent delayed fracture. A baking operation af-ter plating is also essential. The designer should observethese points during design and specification:
l. Minimize sharp corners and similar stress- concen-tration points rn design
2. Keep hardness as low as possible.
3. Keep operating stress down, in accordance with low-ered hardness value.
4. Specify plating thickness, depending upon require-ments.
Specify that parts be baked after plating.
Consider use of HEPrM strips to monitor the platingoperation.
Residual stress from forming operations must be re-duced by stress relief at the highest practical temper-ature. Otherwise the combined effect of residual ten-sion and hydrogen absorbed during plating can inducecracking even before plating is completed.
Similar cautions apply if acid cleaning procedures arecontemplated.
Spring Materials
Mechanical plating provides an effective means of zincor cadmium protection with minimum hydrogen embrit-tlement. It is particularly recommended where partshave high residual stress, have been hardened aboveHRC48 and are used with high static loads. The processcan only be applied to parts that do not tangle and havea clean, fully accessible surface. Hydrogen embrittle-ment, although unlikely, is still possible if parts arecleaned by pickling. When appropriate, coatings of zinc,tin, cadmium, or an alloy of cadmium can be applied bymechanical plating processes.
Cadmium, zinc or more commonly alloys of the twocan be applied to steel spring wire during its production,and under some circumstances this alternative is highlydesirable. It is best suited to small diameter wire and,in general, for the production of springs not requiringgrinding.
Springs are almost always in contact with other metalparts. In a corrosive environment, it is important that thespring material be more noble than components in con-tact with it. Table 3-6 shows a partial list of alloys inincreasing order of nobility. When any two alloys areplaced in contact in the presence of an electrolyte, theless noble alloy (higher on the list) will be attacked. Theanack will be significantly more vigorous than that of theelectrolyte acting by itself.
Table 34. Order of Nobility.
G*lvnnic Serics $itb,,'gl$ te ,gneh gs,,se*ry8t8r.
MagnesiumZincAluminumCadmiumSteel or IronCast IronStainless Steel, series
300 (active)Hastelloy@ CNickel (active)Inconel (active)Hastelloy BBrasses, BronzesMonelNickel (passive)Inconel (passive)Stainless Steel, series
300 (passive)Titanium
Least noble (+), Anodic
Most noble (-), Cathodic
HASTELLOY is a registered trademark of Cabot Corporation.
ffi{*, Yffiffi
ffi
6 .
fFJ','r. iil;-
Spring Materials
The list of coatings which protect the base material byacting as a barrier to the environment is extensive andincreases as new finishes and techniques are developed.Table 3-7 shows protection available from some of thecommon barrier finishes. This information is not for se-lection purposes; it simply shows the range of protectionafforded. In fact, the hours of salt spray protection mayonly be valid for the specimen and test conditions em-ployed in this series of tests. The tests were conductedon springs which had undergone 4 million cycles in afatigue test prior to salt spray exposure.
While coatings frequenfly increase in effectiveness astheir thicknesses are incrbased, cautions are in order.Tendencies to crack increase as coating thickness in-creases, and the coating increases the size of the spring.For example, coatings increase the solid height and di-ametral clearances required for compression springs.Brittle coatings such as epoxy can chip under impact,leaving unprotected spots. Tough coatings such as vinylresist chipping, but bruises, tears or abrasions can ex-pose the base material and trap corrosive agents. Thisallows corrosion to continue after exposure, and in thesecircumstances coated springs occasionally exhibit short-er lives than uncoated springs.
Frequently oils, waxes or greases provide adequateprotection. Effectiveness of these coatings is often de-pendent on the nature of the surface to be protected. Ingeneral, lustrous or smooth parts will not retain oils, andwaxes, paraffrn-based oils or greases are recommended.Steels can be phosphate coated by a conversion process.Phosphate coatings have a high retention for oils,greases or paints. The combination of a phosphate andoil coating becomes a colTosion inhibitor more effectivethan either of the components. A similar effect is ob-tained by retaining or deliberately forming oxides onmetal surfaces to hold corrosion inhibitors or lubricants.Oil tempered spring wire is a notable example of thistechnique.
Spring WireTensile properties of spring wire vary with size (Figure
3-3). Common spring wires with the highest strengthare ASTM 228 and ASTM 401 materials. ASTM A313
Type 302, A232 and A230 materials have slightly lowertensile strength with surface qualities suitable for fatigueapplications. Hard-drawn (ASTM 227) and oil tempered(ASTM 229) are also supplied at lower strength levelsand are most suitable for static applications.
Most spring wires can be wrapped on their own dia-meter (bent around a pin with a diameter equal to thewire diameter). Exceptions include some copper-basedalloys and large diameter and/or high strength alloys.Because stress relieving increases yield strength of colddrawn spring wire, all sharp bends of this grade materialshould be made prior to stress relief.
Tahles 3J. SaIt Spray Resistance of Common BarrierFinishes.
I
CGGGGGG
GGGGGCC-
-
C-
CCCC
CCCCCCCCC
hotectiveMateriat
Stsnderd SaIt SprayTest Resistancc, hours Description
Paints:Japan
Lacquer
EnamelPaint
15-20
31100
5G4002s-300
Dark colored, usuallydipped, cured by baking.Usually applied by spray-ing. Air dried.Hard finish; applied byspray, brush or dip; curedby air or baking.
Oils, waxes
Phosphates withsupplementaloils, waxes,etc.
Cadmium, zinc
l-300
2440
24-100
Lubricating, rust-inhibiting, hard drying andnondrying oils.Chemical treatment convert-ing steel surface to ironphosphate crystallinesurface. Affords a bondfor oils and paints.Electroplated or mechanicallyplated.
This information is based on laboratory-controlled applications and test.The protective material selected, cleanliness of parts, method of appli-cation, subsequent operations and part usage affect performance. Thechoice of a spring finish must also consider shipping, assembly, end useand total cost.
ffiA"o#fil,&F'*ffiK$ _ -
Spring Materials
Tabk 34. Preferued Diameters for Spring Steel Wire. Spring StripMost flat springs are made from AISI grades 1050, 1065,1074 and 1095 steel strip. These compositions are listedin ASTM specifications A.682 and A684.
Tensile strength and formability characteristics areshown in Figure 3-4. The vertical inclined bands delin-eate three strength levels as functions of stock thicknessand hardness. Horizontal curves indicate minimum ben-ding radii required for the strength levels they intersect.Interpolations can be made between any two bands orlines for intermediate levels. Formability criteria are giv-en for relatively smooth bends made at reasonable ben-ding rates. Operations which apply forming forces otherthan smooth bending, or have impact characteristics,may require larger radii to prevent fracture. Four-slidepart manufacture, progressive die work and secondaryforming are examples of operations that often produceless than ideal bending.
Table 34. Ranking of Relative Costs of Common SpringWires.
Most spring wires can be purchased to tighter tolerances. Music wireand most nonferrous materials are regularly made to closer tolerances.
M*trk Sillri {ftm,ftrril Sr*cnd Third
Hrrtnct PrEfrnmr Prcfcrcns
0.100 . 1 I
0. r20. r4
0 . 1 60. r8
0.200.22
0.250.2E
0.300.35
0.400.45
0.500.55
0.600.650.70
0.800.90
1 . 0I . l
t . 2
1 . 4
1 . 8
') ',
2 .8
3 .5
4 .5
5 .5
6.57.0
9.0
r 1 . 0
13 .0
15 .0
Englicb Sirrs {la.)First $cmrd
hrcfcrrnc hefttwmcc
0.0040.0050.0060.008
0.010
0.012
0.014
0.016
0.01E
0.020
0.0220.0240.0260.028
0.030
0.0350.038
0.u20.045
0.04E0.0510.0550.0590.0630.0570.0720.0760.08r0.0850.0920.098
0. r050 . 1 r 2
0.125
0.135
0.148
0.t62
0.t770.192
0.207
0.2250.250
0.2E1
0 .3120.3430.3620.3750.4060.4370.4590.500
0.009
0 .01 l
0 .013
0.015
0.0r7
0.019
0.021
0.0310.033
0.040
0.u7
sC
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
E
C
C
C
CC
C
C
C
C
C
C
CI
t . 6
2.0
2.5
3.0
2 . 1
2.4
2.6
3 .2
3 .8
4.2
4.85 .0
6.0
0 .102
0.120
0.130
0.140
0.156
0 .170
0.200
0.218
0.262
0.306
7.5
E.5
9.510.0
12.0
14.0
16.0
Wir! Snt tffii;$:::,,.,,:::: !, , , , , , i l 1,, , , , , : , i , t
ffi,,#.2.mu|1}...'It*',...1 -Wrm-ll&wc Izrrn
Patented and Cold DrawnOil Tempered
ASTM A227ASTM A229
1.01 . 3
1 .01 .3
MusicCarbon Valve Spring
ASTM A,228ASTM A23O
2.63 . 1
1 .41 . 9
Chrome Silicon ValveStainless Steel (Type 302)
ASTM A4OIASTM A3l3 (302)
4.07.6
3 .94.7
Phosphor BronzeStainless Steel (Type 631)
(17-7 PII)
ASTMASTM A 313 (631)
8.0l l
6.78.7
Beryllium CopperInconel Alloy X-750
ASTM BI97 2744
t73 1
Table 3-10. Standard Tolerances for Spring Wire.
Dlrrmttr: rnar {ln,} tohrw: ulur,{lil;}tl&#m:Ost,d"Mnrrr:
,,il;il,,,{*n.}
0.514.71 (0.020-0.028)0.71-2.00 (0.0284.078)
0.olo (o.ooo4)0.015 (0.0006)t
0.010 (0.000+)0.015 (0.0005)
2.00-3.00 (0.0784. I tE)3.00{.00 (0.118J.240)
0.020 (0.000E)0.030 (0.0011E)
+
f
0.020 (0.0008)0.030 (0.0012)
6.0G9.00 (0.24G4.354)9.50-r6.00 (0.37s4.62s)
r 0.050 (0.00197)+ 0.070 (0.00276)
0.050 (0.002)0.070 (0.0028)
ffiAssEslf;g&ffi*ffws
N t n N r f f i---t,.
Tronsverse Bend
Also known os ocross the groin,perpendiculor to the ro l l ingdirection. Eosy or good woy.
Longitudinol Bend
Also known os with the groin,porollel to roll ing direction.
Hord or bod woy.
Spring Materials
Hardness levels above HRC 50 result in high strengthbut are not generally recommended due to notch sensi-tivity. Surface and edge smoothness become critical andplated parts become highly susceptible to static fracturedue to trapped hydrogen.
Parts which cannot be made within formability limitsof pretempered strip are made from annealed strip andhardened and tempered after forming. To maintain crit-ical dimensions, it is often necessary to fixture temperthese parts. Sharp bends are not only diffrcult to fabri-cate but are also undesirable in service because of stressconcentration. The formability limits of annealed springsteels are presented in Table 3-1 1.
In flat spring designs where the edge of the strip be-comes an edge of the part, the type of edge is important,particularly for cyclic applications. Common types ofedges available are shown in Figure 3-7. Slit edge (No.3) and deburred (No. 5) are preferred for blanked partsand static applications. No. I round edge is recom-mended for cyclic applications to reduce the stress con-centration and eliminate the edge flaws due to slitting.Configurations shown in Figure 3:7 are approximate,and it is advisable to use both the numerical designationand a description when specifying edge condition.
Commercial thickness tolerances for spring steel stripEIre presented in Table 3-12. Many flat springs and springwasher designs can tolerate this variation. Since the loadvaries as the cube of the thickness, critical designs mayrequire closer tolerances.
Fig. 3-6. Tensile Strength versus Hardness of Quenchedand Tempered Spring Steel.
l0 k9. DPH or Vickers (VHN)
350 450
1 6 0
Direction of bending with respect to rolling directionis an important consideration. Formability of strip isgreater in transverse than in longitudinal directions (Fi-gure 3-5). If a part is designed with two identical bendsat 90" to each other, it is common practice to orient thepart so that both bends are made at 45o to rolling direc-tion. Dmensionless parameter 2rlt, often referred to asbend factor, is frequently used as a measure of formabil-it1'. Materials with low values are more formable thanmaterials with high values. This measure is only a guidesince it does not allow for tooling considerations andcomplex strains associated with forming operations.
Spring steels are nonnally produced to specified hard-ness levels which are related to tensile strength (Figure3{). Composition is not shown in Figure 34 becausethe lowest carbon level (AISI 1050) can be used at highstrength levels and the highest carbon level (AISI 1095)can be tempered to the lowest strength levels. In general,higher carbon levels are used when strength is criticaland lower carbon levels when formabilitv is critical.
Fig. 34. Minimum Transverse Bending Radii for Var-ious Tempers and Thicknesses of TemperedSpring Steel.
44 46 48 50 52
Rockwel I Hordncss (HRC)
ffi
o
J
F
E 1 . 0E
o
S o.7s.cF
Fig. 3-5. orientation of Bend Axis to Rollins Directionfor Transverse and Longitudinal B-ends.
-) lndicotes Direction Of Rolling
N 1 : 2 r
24o E_
32zo *,
g6
2oo +, og
r8o E5
al€
o
. o
t40
1 2 0
28 32 36 40 444648 50 52 54
Rockwell Hordness (HRC)
Spring Materials
Other Spring MaterialsA variety of materials other than carbon steel strip is
used for flat springs (Table 3-13). When high conductiv-ity is required, copper base alloys are usually specified.Stainless steels are used in applications requiring heat orcorrosion resistance. Typical tensile strength levels'forthese alloys after heat treatment are shown in Table3-13. Bend factors and tensile elongations are for alloysin "as received" condition prior to final heat treatment.
Specifyrng HardnessHardness tests are used extensively to inspect strip
and flat springs and it is necessary to specify the correctscale. Recommended hardness scales for steels arepresented in Table 3-14. To obtain accurate readingsfree from the effect of the anvil, it is important to limitthe thickness of the material for each hardness scale asshown in Figure 3-8 for hard materials and Figure 3-9for soft materials.
Fig.3-7. Edges Available on Steel Strip.
No. I Edge
SQUAREStondordmoximum cornerrodius:0.08 mm(0.003')
ROUNDStondord
BLUNT ROUNDSpeciol
OVALSpeciol
BROKENCORNERSSpeciol
No.3 Edge
I
NOR'VIAL AS SIIT
'No.5 Edge
_lNo.3 DEBURRED
_ll:l)
_l
CC
C
C
C
C
C
C
C
C
C
C
C
C
CCCCtCCC
CC
CCccC-
C
Formability is determined by slowly bending a sample over l80o until itsends are parallel. The measured distance between the ends is Nt.For example, i f N1 = 4 and t:2, then Nr/1 = 2*Available as Barco-Form@ from Wallace Barnes Steel subsidianv ofTheis of America, Inc.
Precision rolled high-carbon steel strip is available commercially attolerances considerablv less than the values stated above.
Table 3-11. Formability of Annealed Spring Steels.
Ttulcknmr {(}mrn (in,l
Di:re�cti*nnf: Ssn6
*Iffi r0sNtll ,
AI$I T065Hrlt
*IS,*qid. :, : ::,:il,{i t:
tfrs '::il$#$.i..'t,,.,. ...[-{i tt,..' .,., I :
Ann*n|ed{*ta rd
tpr*iffitrnnx.)
*nntr$st.lmregt ,,t.!l{x"}i
Annwkd($tardflrd
lsw{stmnx.)
Annerlsd{sp l . ;'lwnst ,filflX,l*
Aaar*bd{ffiid
bnffit'.' , .m&X;},, '
A W,,.{W.,,..,.l{illffit::,, .: ,.,'1114.1g;)i
t,, .i#ffiffi '.,: ,,,r,s**:l} ,,
,,,i{ffi::..,,i,[Ufte$:,,,.ifm.i|,*
1.9 mm(0.076)-over
Il l
24
03
24
0 24
03
3)
I4
0.9-1.89 mm(0.036{.075")
I
l lI2
0I
I2
0I
I2
0I
23
02
0.374.89 mm(0.0154.035)
I
il0I
00
0I U 2
0I
II U 2
0I
12
0I
0.2-O.36 mm(0.008{.014j il
00
00
00
00
1I
00
II
0U2
Table 3-12. Tyoical High-Carbon Strip Thickness Tolerances.
Thhkns*: mrn{in,}
'#*tqgry,,Pffi;1iffi. rl;,,Srrip t#idth: rnm.{tor.}
t?.7*?6.1 t 76,3*]S4.fl(0.50*?.99) | f3 jfffl*12.00)
0. l0-0.25 (0.004-0.010) 0.005 (0.00020) 0.906 (0.00025)
0.25-0.5 I (0.010-0.020) 0.006 (0.00025) 0.009 (0.0m35)
0.5 l-0.76 (0.020-0.030) 0.009 (0.00035) 0.013 (0.00050)
0.7Gt.02 (0.030-0.erc) 0.010 (0.00040) 0.0r3 (0.000s0)
t .02- | .s2 (0.040-0. 060) 0.013 (0.00050) 0.019 (0.00075)
| .52-2.03 (0.060-0. 080) 0.025 (0.00100) 0.038 (0.001s0)
2.03-2.s4 (0.0E0-0. l 00) 0.038 (0.001s0) 0.051 (0.00200)
2.54-3.r8 (0. r00-0. 125) 0.051 (0.00200) 0.063 (0.002s0)
DPH ( I ks)500 600
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FA. J-d. Ilinimum Safe Thicknesses for Hardness Test-ing Hard Materials.
800 900.r_----t0.040
0.020
0.0r 0
035 40 45 50 55 60 65 70
Hordness N.umber
Spring Materials
Fig. 3-9. Minimum Safe Thicknesses for Hardness Test-ing Soft Materials.
60 65 70 7s 80 85Hordness Number
2; E
2 ;P 3r iF i
C o
i ;S EE ?'7 .=
E . :
(l ) Before heat treatment.
Tsblc 3-14. Recommended Hardness Scales for Hardand Soft Spring Alloys.
Thickness: mm {in.}
0.89 (0.035) and over0.64J.86 (0.025-0.034)0.35{.61 (0.01 5-0.024)0.204.36 (0.0084.014)Under 0.20 (0.008)
"tnncrlcd Stcdand Finnfcrmnr Albys
CA30Nr 5 NDPH
B457307r5TDPH
DPH ( I kg)
r00 r20 r40
in =
o
, t i lat
5E
o . E=
Tabb 3-13. Typical Properties of Spring Temper Alloy Strip.
ldfrtrr,*$lTendlc @rySrntra {rtr rd}
in t:l:t:.,fst.m|,. ,,,
,,,,, , :8fsd ,:, .';F l'{.1 ,},;,',,,., .,rif.1;tl:':.,,rr,t;,,,;,,;,;:.
h,qns., b)b
: l , : t ; i 1 , , : : ,
Steel, spring temperStainless 301Stainless 302
r70o (246)1300 (r89)1300 (189)
c50c40c40
285
534
20.7 (30)19.3 (28)19.3 (28)
0.300.310.31
Monel 400Monel K500Inconel 600
6e0 (100)rz0o (r74)1040 (151)
895c34c30
2402
552
17.9 (26)17.9 (26)2r.4 (3r)
0.320.290.29
Inconel X-750Copper-BerylliumNi- Span-C
1050 (152)1300 (189)1400 (203)
c35c40c42
2026
352
2r.4 (3r)12.8 (18.5)r8.6 (27)
0.290.33
Brass CA 260Phosphor BronzeI1J PH RH95Ol7J PH Condition C
620 (e0)6e0 (100)
1450 (210)1650 (239)
B90890c4c46
3J
61
J
2.5flat2.5
l l (16)10.3 (1s)20.3 (2e.s)20.3 (29.s)
0.330.200.340.34
Assogfrlfi8 &tr*ffiws ffi
HelicalCompression Spri ngs
ff
C
G
C
C
C
G
G
C
C
CI
C'., C
C
..: C
,,11 5
,t,, c,:;,.;;',',
-
: : : 5
li:',', C
!n,-1'""' cC
-
} CI
-I C-
l cI C-
3 cCCCC
q
*
1*<,#
k* Asso8Ftfigi%Fr*'Fs
=
-r
-t
Helical Compression Springs
Diameter increases when a spring is compressed.Although the increase in diameter is usually small,it must be considered when minimum clearances areestablished. The increase in diameter is a function ofinitial spring pitch and can be estimated from thefollowing equation where p : pitch.
O.D.4*1;6 = + d (s-t )
If the spring ends are allowed to unwind, the O.D. atsolid may be greater than calculated by this equation.Long springs buckle (see Figure 54, page 35) and mayrequire lateral support and larger diametral clearances.Spring Index
Spring index is the ratio of mean diameter to wirediameter or radial dimension of the cross section (Figure5-15, page 40). The preferred index range is 4 to lZ.Springs with high indexes tangle and may require indi-vidual packagrng, especially if the ends are noi squared.Springs with indexes lower than 4 are diffrcult to form.Free Length
Free length is overall spring length in the free or un-loaded position (Figure 5-1). If loads are not critical, freelength should be specified. When definite loads are re-quired, free length should be a reference dimension thatcan be varied to meet load requirements. Pitch is thedistance between centers of adjacent coils and is relatedto free length and number of coils.Type of Ends
Types of ends available are: plain ends, plain ends -ground, squared ends and squared ends -ground (Figure5-2).To improve squareness and reduce buckling duringoperation, a bearing surface of at least 270" is required.Sguared and ground springs are normally supplied witha bearing surface of 270 to 330". Additional grinding re-sults in thin sections. "squared ends only" are preferredon springs with small wire diameters (less than 0.5 mmor 0.020), a large index (gtreater than 12) or low springrates. Squared ends cost less to manufacture thansquared and ground ends.
--,
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-,4t
-,-,
-,-
-,-,
-.at
-
-
-
-
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I
IntroductionHelical compression springs are used to resist applied
compression forces or to store energy in the push mode.They have the most common spring configuration and arefound in many applications such as auiomotive, aero-space and consumer goods. While the most prevalentform o-f compression spring is a straight cylindri-d springmade from round wire, many other forms are produced.Conical, barrel, hourglass or cylindrical forms Ere avail-able, with or without variable spacing between coils.Such configurations are used to reduce solid height, buck-ling and surging, or to produce nonlinear load deflectioncharacteristics. Energy storage capacity is greater forround wire compression springs than for rectangular wirecompression springs and can be increased by nesting.Rectangular wire is sometimes employed to reduce solidheight or increase the space effrciency of the design. Mostdie springs are made from rectangular wire for this rea-son. The SPEC line of springs contains hundreds of com-pression spring designs using wire sizes from 0.15 to 5.26mm (0.006" 1o 0.207') diameter music or stainless steelwire. Specifying SPEC springs saves design time, reducescost for low volume applications and offers improveddelivery.
Helical Compression Spring TerminologrSpecial terminology has evolved in the spring industry
to describe features of helical compression springs. Theseterms are defined and the relationship between terms isreviewed in Figure 5-1. Communication between design-er and springmaker is improved if these common termsare used.Spring Diameter
Outside diameter, inside diameter and mean diameterare all used to describe helical compression spring di-mensions. Mean diameter is equal to the sum of O.p.and I.D. divided by two, and is employed in spring de-sign calculations for stress and deflection. The O.D. isspecified for springs that operate in a cavity, while theI.D. is specified for springs that operate over a rod, seator shaft. Minimum diametral clearance between thespring and cavity or rod is:
0.05D - when D. is greater than 13 mm (0.512')0.10D - when D. is less than 13 mm (0.512,)D. is the diameter of the rod or cavity.
Fig. 5-1. Dimensional Terminology for Helical Com-
fi
+ I f",.r ld L r
I
-TPorolleli s m ( e p )
I, l
an.h1 |A
P 2 - d :*2t l
nssgpffi,&gmp$ffi
Helical Compression Springs
Number of CoilsTotal number of coils should be specified as a refer-
ence number. For springs with squared ends, the totalnumber of coils minus two is the number of active coils.There is some activity in end coils, but during deflectionsome active material comes in contact with the end coilsand becomes inactive. Experience indicates that thisequation is a good approximation. The number of activecoils in springs with plain ends is greater than those withsquared ends and depends upon the seating method em-ployed. Some useful guidelines for estimating the num-ber of active coils are presented in Table 5-1.
Solid HeightSolid height is the length of a spring with all coils
closed. For ground springs, solid height is the numberof coils multiplied by wire diameter. For ungroundsprings, solid height is the number of coils plus one,
Fig. 5-2. Types of Endsfor Helical Compression Springs .
Squored ond Ground EndsCoiled left-hond
Ploin Ends GroundCoiled Lefi-hond
Squored or Closed EndsNot Ground, Coiled Righrhond
ffi@ffiffi@Ploin Ends
Coiled Right-hond
Table 5-1. Guidelines for Dimensional Characteristics ofCompression Springs.
,Di 'c
Ttxtqd':SS$
Ollftior,,,fhfu,,:, ,,
{tr{€t:,,$K[{l
:,Oif,;1
. , f i , . ,{G $gurd Ouly
r.s��c*d' , ' , , , ,G ,"
Solid Height(Lr)
(Nr + l)d Ntd (Nt + l )d Ntd*
Pitch(p)
L r - dN.
LrNt
L r - 3 dNa
L r - 2 dNa
Active Coils(NJ
L r - dp
L r rp
L r - 3 dp
L r - 2 dp
Total Coils(Nt)
Na N a + l N " * 2 N " + 2
Free Length(Lr)
p N t + d P N t p N a + 3 d p N 6 + 2 d
*For small index springs lower solid heights are possible.
multiplied by wire diameter (Table 5-1). If critical, solidheight should be specified as a maximum dimension.After allowances are made for plating or other coatings,it is good practice to add one-half of the wire diameterto determine maximum solid height. With larger wiresizes and fewer coils, this allowance can be decreased.Solid height is often measured by applying a force equalto 110 to l5Vo of the calculated load at solid. If solidheigtrt is not critical, this dimension should be omitted.
Direction of CoilingA helical compression spring can be either left or right-
hand coiled. If the index finger of the right hand can bebent to simulate direction of coil; so that the fingernailand coil tip are approximately at the same angular pos-ition, the spring is right-hand wound (Figure 5-3). If theindex finger of the left hand simulates the coil direction,the spring is left-hand wound. If direction of coiling isnot specified, springs may be coiled in either direction.Nested springs with small diametral clearances should becoiled in opposite directions.
Squareness and ParallelismSquareness of helical compression springs can be mea-
sured by standing a sample spring on end on a horizontalflat plate and bringing the spring against a straightedgeat right angles to the plate. The spring is rotated to pro-duce a maximum out-of-square dimension e, (Figure5-l). Normally squared and ground springs are squarewithin 3o when measured in the free position. Squarenessshould be checked at both ends. Specifying squarenessor parallelism in the free position does not assure square-ness or parallelism under load.
Parallelism (Figure 5-1) refers to the relationship ofthe ground ends, and is determined by placing a springon a flat plate and measuring the maximum differencein free length around the spring circumference ep.
HysteresisHysteresis is the loss of mechanical energy under cy-
clic loading and unloading of a spring. It results fromfrictional losses in the spring support system due to atendency of the ends to rotate as the spring is com-pressed. Hysteresis for compression springs is low and
Fig.5-3. Direction of Coiling Helical CompressionSprings.
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the contribution due to internal friction in the springmaterial itself is generally negligible.
Spring RateSpring rate for helical compression springs is defined
as the change in load per unit deflection and is expressedas shown:
Helical Compression Springs
StressWire in a helical compression spring is stressed in
torsion. Torsional stress is expressed as:
This equation is valid when the pitch angle is less thanl5o or deflection per turn is less thanD/4. For largedeflections per turn, a deflection correction factor (Re-ference 3, page 102) should be employed.
The load deflection curve for helical compressionsprings is essentially a straight line up to the elastic limit,provided that the amount of active material is constant.The initial spring rate and the rate as the spring ap-proaches solid often deviate from the average calculatedrate. When it is necessary to specify a rate, it should bespecified between two test heights which lie within 15ro 85Vo of the full deflection range (Figure 54).
When compression springs are used in parallel, thecomposite rate is the sum of the rates for individualsprings. For compression springs in series, the rate iscalculated from:
k - (s-3)
This relationship is often used to calculate the rate forsprings with variable diameters. The technique involvesdividing the spring into many small increments and cal-culating the rate for each increment. The rate for thewhole spring is computed from the rate of the incrementsaccording to the equation above.
Fig. 54. Curve for Helical
(s4)
Bending stresses Eue present but can be ignored exceptwhen the pitch angle is greater than 15o and deflectionof each coil greater thanD/4 (Reference 3, page 102).Under elastic conditions, torsional stress is not uniformaround the wire cross section due to coil curvature anda direct shear load. Murimum stress occurs at the innersurfaces of the spring and is computed using a stresscorrection factor. The most widely used stress correc-tion factor Kwr is attributed to Wahl. It is shown belowand in Figure 5-5.
t :H*-
4C - I 0.615r ( w r : 4 c - 4 -
c
I I -
. , 4 C - 1 0 . 6 1 5A w r = 4 c - 4 -
c
For 2e/o set pointor fot igue
n qK w 2 = l * t
For springs withset removed
I{*,* '
I
, P G d 4r : - : -f gD3N. (s1)
l l l l- J - - I -
k r kz k r " ' kn
(s-s)
In some circumstances after yielding occurs, resultantstresses are distributed more uniformly around the crosssection. Then, a stress correction factor Ks,2 which ac-counts only for the direct shear component is used.
K w z : 1 +0.5C
(s4)
In other circumstances, such as static loading at elevatedtemperatures, stress distribution tends to become uni-form around the cross section and can best be estimatedby using no correction factor. Use of different stresscorrection factors can lead to confirsion. In publisheddata, it is essential to know which stress correction fac-tors were used. (The stress correction factor used by adesigner must be the same as that used to develop thedata.) Methods to calculate stress for different applica-tions and the use of stress correction factors will be
Fig. 5-5. Wahl Srress Correction Factors for Round WtreHelical Compression and Extension Springs.
2 . 2
2 .0
J r . 8o
;Y ' t . 6
oI
t r . 43
o
6
C = D / d
Typical Load DeflectionCompression Springs.
Assosl$lfi8&ffi*ffiffiffiw&
Helical Compression Springs
discussed in the following paragraphs on choice of oper-ating stresses.
loadsWhen deflection is known, loads are determined by
multiplying deflection by the spring rate (Equation 5-Z).When the stress is known or assumed, loads are deter-mined from Equation 5-4. The procedure used to deter-mine loads of variable rate springs is complex. In thiscase, the load deflection curve is approximated by aseries of short chords. The spring rate is calculated foreach chord and multiplied by deflection to obtain theload. The load is then added to that calculated for thenext chord. The process is repeated until load has beencalculated for the desired value of deflection (Figures4).
Loads should be specified at a test height. Because theload deflection curve is often not linear at very low loadsor at loads near solid, loads should be specified at testheights between 15 and 85% of the full deflection range(Figure 54).
Loads are classified as static, cyclic or dynamic. Instatic loading applications, the spring is expected tooperate between specified loads only a few times. Fre-quently, springs in static applications remain loaded forlong periods of time. In typical cyclic applications,springs are required to cycle between specified loadsfrom 10,000 to more than a billion cycles. During dynam-ic loading, the rate of load application is high and causesa surge wave in the spring which will induce stresses thatexceed the value calculated from Equation 5-4.
Buckling of Compression SpringsCompression springs that have lengths greater than
four times the spring diameter can buckle. If properlyguided, either in a tube or over a rod, buckling can beminimized. However, friction between the spring andtube or rod will affect the loads, especially when theaspect ratio (I4lD) is high.
Fig. 54. Load Deflection Curve for a Variable RateSpring.
f1 t2 f3 f4
Defleaion --1.
ps = krfr + kz(fr - fr)...ks(fs - fr)
Critical buckling conditions are shown in Figure 5-7for axially loaded springs with squared and ground ends.Curve A is for springs with one end on a flat plate andthe other end free to tip (Figure 5-8). It indicates thatbuckling will occur when the spring design is above andto the right of the curve. A tendency for buckling isconsiderably less for springs compressed between paral-lel plates as shown in curve B. For applications requiringsprings with a high aspect ratio and large deflections,several springs can be used in series in a tube or overa rod, with guides between the springs to prevent bind-ing.
Choice of Operating Stress - Static ConditionsFor static applications, the yield strength or stress re-
laxation resistance of the material limits the load-carrying ability of a spring. The spring is required tooperate for a limited number of cycles, and the velocityof the end coils is low to preclude high stresses due tosurgtng or impact conditions. Maximum allowable tor-sional stress for helical compression springs used in stat-ic applications is presented in Table 5-2 as a percentageof the tensile strength for common spring materials. Forsprings that do not contain beneficial residual stressesinduced by set removal, maximum allowable torsionalstress values are from 35 to SVo of the tensile strength.To calculate the stress before set removal, it is necessaryto use the Ks,1 correction factor. If the calculated stressat solid is greater than the indicated percentage of tensilestrength, the spring will take a permanent set when de-flected to solid. Amount of set is a function of theamount that calculated stress at solid exceeds the indi-cated percent of tensile strength.
Fig. 5-7. Critical Buckling Condition Curves.
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To increase the load-carrying ability of springs in stat-ic applications, it is common practice to make the springlonger than its required free length and to compress thespring to solid. This causes the spring to set to the de-sired final length and induces favorable residual stresses.This process is called removing set or presetting and canbe conducted at either room or elevated temperatures.The loss of deflection from the free position to solid bycold set removal should be at least lVo.If the set is less,it is diffrcult to control the spring's free length. Ratiosof stress greater than 1.3 lead to distortion and do notappreciably increase the load-carrying ability. This is il-lustrated schematically in Figure 5-9.
Allowable torsion stresses in springs with set removed(Table 5-2) are significantly hiefier than for springs thathave not had set removed. It is important to note thatbecause yielding has occurred during presetting, thestress is relatively unifonn around the cross section andit is calculated using the Kwz stress correction factor. Setremoval is an added springmaking operation which in-creases the manufacturing cost but gfeatly increases theenergy storage capacity of the spring. Set removal iscommon for critical springs made from premium materi-als. In some instances, springs have the set removedduring an assembly operation.
Fig.54. End Conditions Used to Determine CriticalBuckling.
B
End Fixed Agoinst Tipping
P++ffi
- - ' /A
rA_--- V A
H
\ \ \ \ \ \ \ \ \ \ \Fixed End
Table 5-2. Maximum Allowable Torsional Stresses forHeIicaI Compression Springs in Static Appli-cations. Bending or buckling stresses not included.
Maximun Ea oI TcmileMitsrirk r $ct
Erurgrcd fi[#r]
Helical Compression Springs
If the calculated stress using the Ks,2 stress correctionfactor exceeds the percentage of tensile stength indicat-ed in Table 5-2, the spring cannot be made. In this case,it is necessary to either lower the stress by alteringspring design or selecting a higher strength material.
In some applications, maximum operating stress islimited by material stress relaxation resistance andamount of load loss that the design can tolerate. Whenload is constant, these designs are limited by materialcreep resistance. When the spring is compressed at afixed test height, stress relaxation resistance of the ma-terial is limiting. Designs limited by stress relaxation re-sistance axe more common than designs limited by creepresistance. It is suggested that creep-limited designs bereviewed by Associated Spring engineers.
Stress relaxation is defined as percentcording to the following relationship:
load loss ac- il
(sJ)
Stresses AreColculotedAt Solid.
vokelaxation = T
x too
P" is load at test height before testing.Pr is load at test height after testing.
A
End Free to Tip
ffim@ry
R
Typical stress relaxation data (Figure 5-10) indicate thatat high stresses, some spring materials such as musicwire exhibit appreciable stress relaxation after only 100hours at temperatures as low as 100"C (zn"q. Thesedata are only representative of the conditions indicated.Stress relaxation is affected by material, spring pro-cessing variables, time, temperature and stress. Associ-ated Spring engineers should be contacted for criticalapplications involving stress rela,ration resistance.
When set is removed at an elevated temperature, theprocess is called heat setting. It significantly improvesthe stress relaxation resistance of springs (Figure 3-2,page 16) at moderate temperatures and is frequently amore cost-effective method for achieving low levels ofstress relaxation than specifying a more costly springmaterial.
Fig. 5-9. Spring l-oad-Carrying Ability versus Amount of
EoEo
d
o3no
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.t1
s.Dco
tnottg
0.6
0.2
0.4Patented and colddrawn carbon steelHardened and temperedcarbon and low allovsteelAustenitic stainlesssteels\onferrous allovs
60-70
65-75
55-65
55-65
old,
1 . 0 r . l r . 2 1 . 3 1 . 4 1 . 5
Stress Before Set Removol c" t : f f i : i ,
::..,B rc.r5tl,{Ktvi}
Assog&ifi8 f&ffi#ffiffis ffi
Helical Compression Springs
Choice of Operating Stress - Cyclic ApplicationsIn cyclic applications, the load-carrying ability of a
spring is limited by material fatigue strength. Velocity ofend coils is low compared to the natural frequency. Toselect the optimum stress level, it is necessary to balancespring cost versus reliability. Reducing operating stress-es increases spring reliability as well as cost. A completeknowledge of operating environment, expected life,stress range, frequency of operation, speed of operationand permissible levels of stress relaxation are requiredin order to make the best choice between cost and reli-ability.
Because maximum stress is at the wire surface, anysurface defects such as pits or seams severely reducefatigue life. Shot peening improves fatigue life and min-imizes the harmful effect of surface defects, but it doesnot totally remove them.
Maximum allowable design stresses for fatigue appli-cations should be calculated using the Kwr correctionfactor and are shown for common spring materials inTable 5-3. These values are for a stress ratio of 0 in anambient environment with no surging. Note that shotpeening increases the fatigue strength by as mudr asZVoat lives of 10 million cycles.
Values in Table 5-3 are guidelines for designers andshould only be used in the absence of specific data. Mostsprings designed to recommended stress levels will ex-ceed the indicated lives; however, in the absence of de-tailed information on material, manufacturing methodand operating conditions, it is not possible to quantifythe reliability level.
Fatigue Life Estimation ExampleFatigue life at other stress ratios can be determined
from Table 5-3 according to the procedures outlined inSection 4. A short example illustrates the procedure:
Estimate the fatigue life of a not-shot-peened helicalcompression spring loaded sinusoidally at a rate of onecycle per second. The spring is flooded with oil and oper-ates at a maximum temperature of 40'C (104"F). The ma-terial is ASTM A228 wire and ends are squared andground. The design is given here:
d = 1.00 mm (0.039')C = 8I+ = 20.5 mm (ref) (0.807')Lr : 17.5 mm (0.689?Lz: l0 mm (0.394')L , : 8 m m ( 0 . 3 1 5 ' )N t : 8
Spring rate is determined from equation:
, G d o .t= Etr =3'2Nimm
Loads are calculated from the deflections and found tobe:
P, : (20.5 - 17.5) x 3.2: 9 .6 NP2 : (20.5 - 10.0) x 3.2: 33.6 NP, = (20 .5 - 8 ) x 3 .2 :40 N
Stresses are calculated using Equation 5-4 and are:
Sr : 232 MPaSz : 810 MPaS, : 955 MPa
Tensile strength of the wire is 2180 MPa (Figure 3-3, page19). The stress at solid is 44Vo of the tensile strength.Referring to Table 5-2, the maximum stress allowablebefore sit removal for ASTM A228 is 45% of tensilestrength. Therefore, the spring can be made and does notrequire set removal.To estimate the fatigue life, it is necessary to:
l. Plot an S-N curve on a modified Goodman diagram(Figure 5-11) using the data from Table 5-3 for not-shol-peened springs and a tensile strength of 2180MPa.
2. Plot point A on the 45" line at 67Vo of the tensilestrength.
3. Plot the stress range coordinates, point B.
4. Estimate the life by drawing a line through AB. At theintersection of this line with the vertical axis, point C,
' draw a horizontal line to intersect a S-N curve. Thepoint of, interse'Jon, D, is the estimated life of2,500,000 cycles.
Dynamic Loading - Impact-When a spring is loaded or unloaded, a surge wave is
established which transmits torsional stress from thepoint of loading along the spring length to the point ofiestraint. The surg€ wave travels at a velocity approxi--mately I / l0 of a normal torsional stress wave. Velocity ofthe torsional stress wave (V1) is given by:
i: I=Vr = 10.1./9 m/sec (or) Vr : ./9 in./sec 64)- - Y p Y p
Velocity of the surge wave V. varies with material andspring design, but is usually in the range of 50 to 500m/sec. The surge wave limits the rate at which a springcan absorb or release energy by limiting impact velocityV. Impact velocity is the spring velocity parallel to the
Tabte 5-3. Maximum Allowable Tbrsional Stesses forRound Wire Helical Compression Springs inCyclic Applications.
f*tiglrrLlfr {*yrhr}
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llld;$hot-,f,,e,nd
shd.PoGnGd
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3{1
4?393S
at*0t?,
494?4S
This information is based on the following conditions: no surging, roomtemperature and noncorrosive environment-
Stress ratio in fatigue = Pi,lil+ = gs maxlmum
s =#r*,
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Helical Compression Springs
Fig. 5-10. Spring RelaxationDataforVarious Materials. Springs were preset at room temperature and tested lM hours oindicated temperatures. The initial stress is Kwtcorrected.
Music Wire, ASTM 4228, 1.57 mm (0.062")
r l40 140
r30
r20
r30
l-roo 3o
v,
5 r 0 1 5 2 0Reloxolion, Lmd Loss (o/o)
Chrome-Sil icon Wire, ASTM A401, 1.57 ro 3.76 mm (0.062, ' to O.l4S"). Chromium Vonodium Wire, ASTM A232, 1 .57 io 3.76 mm (0.062" to 0. 140")r000
-
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Corbon Volve Spring Wire, ASTM A230, l. 57 to 3.76 mm (0.062" ro 0.148,,)
r20
i l o ?
'100 =
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l-140
I
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i-r 20
l l 0 .
i-roo I0
4=
rt
=
al=
rtl
s 1 0Reloxotion, Lood Loss ("/o)
Inconel Al loy X 750 Wire, 1.93 mm (0.075')
i lI
t ,rD
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tt v,
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60
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Stoinless Sreel 302 Wire, ASTM A313, 1.57 mm (.062")
Reloxolion, Lood Loss (o/o)
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9 0 ;
E8 0 =
70
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i ^oi-----<,-t, e/
5 r 0 r 5 2 0 2 5Reloxolion, Lood Loss (o/o)
r5
Helical ComPression SPrings
spring axis and is a function of stress and material con-
stants shown as:
ITv = 10.tt{ft m/sec (or) V = tV# in./sec (s4)
This is a surprising result because impact velocity and
stress are independent of the spring configuration. For
steels, impact velocitY reduces to:
V : * m / s e c ( o r ) v : * i n . / s e c 6 - t o t
If a spring is compressed to a given stress level and
released iistantanebusly, the maximum spRqg velocity
il;6;;rseo as tti stress divided by 35.5. Similarly, if
u tpting is loaded at a known velocity, instantaneous
stress cin be calculated. At very high loading velocities,
instantaneous stress will exceed the stress calculated
from the conventional static formula (Equation 5-4) and
*ifi fitnit design performance. Thesg equatigns for im-
pu.t u.focity are bttt' concerned with the_primary surge
*uu". Frequently, this wave will reflect from the other
end of the-spring, in.t."ring stress. Springs loaded at
high velocities are frequently subject to resonance phe-
nomena (page 39).-'Wh;; itreiatio'of the weight to be accelerated to the
weijtrt of the spring is lesslhan 1, surge-wave theory
;";;;"iy frea-icls-design performance (Figure 5-12).
Ai frigtt iveight ratios and lower velocities, an energy
t"d; is ujed to predict velocity of a weight projected
il;- th;- rprng "ia o, deflection of the spring when
i.pu.t"o uv u ."rr. velocity and deflection are re-
lated as:
For horizontal loading:
r: 3l.ovfY.- (or) r: v,ffii"'
For vertical loading:
- / w w - m w .r: 31.6v#i + u mm (or) f : v{*[ + 1- m'
w/g is the mass that is being accelerated or decelerated
"nO-V is the axial velocity of the spring'
(s-11)
(s-12)
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Fig. 5-11. Modified Goodman Diagram for Estimating Fatigue Ltfe'
Stress Cycles
:=4
o
o
ttlEt.Exo2
oA=o
tnE
Exo=
C
C(
(
(
(
Minimum Stress (103 Psi)
I
These equations assume that the spring is masslessand should only be used when the spring mass is lessthen 1 14 of the mass to be acceierated.
When the ratio of spring load to weight is less than4. the energy required to accelerate the spring itself be-comes appreciable. By assuming that all mass of thespring is concentrated at the moving end, Equations 5-10and l-l I can be corrected by substituting (W + W,/3)for W where W, is the spring weight.
Qnamic Loading - ResonanceResonance occurs in a spring when the frequency of
the cyclic loading is near natural spring frequency or amultiple of it. Resonance can increase individual coildeflection and stress levels well above amounts predict-ed by static or equilibrium analysis. Resonance can alsocause spring bounce, which results in loads considerablylower than calculated at the minimum spring deflection.To avoid resonance, natural spring frequency should be
Helical Compression Springs
For a vibration isolation system, the essential char-acteristic is that the natural frequency of the spring-mass system be as far as possible from the disturbingfrequency. Filtering of disturbing forces may be calcu-lated as:
% offorce transmitted : +, x 100 6-14)(na /n ) ' - I
where no is the frequency of the disturbing force and nthe natural frequency of the spring-mass system (Figure5-13).
If rq/n is less than l, the denominator in Equation 5-14should be changed to I - (no/n)2. Note that the fre-quency n in this equation is the frequency of the spring-mass system and not the natural spring frequency. Infact, the most commonly used equation neglecti thesplng weight and is only deflection dependenr. The gen-eral equation is:
n : 15'8 .E metric (or) n: j,p ensrirn 6-ts)7 r Y P
Special SpringsPreviously in this section, design considerations for
round wire helical compression springs of uniform diam-eter were discussed. These design techniques are mod-ified below and applied to many special spring configura-tions. Special springs are chosen to fulfill a unique setof design criteria. Springs from rectangular wire andstranded wire as well as variable diameter springs withconical, hourglass and barrel shapes, zlr€ discussed be-low. Helpful guidelines for nested springs are also re-viewed.
RectangUlar WireIn applications where space is limited and particularly
where solid height is restricted, springs designed fromrectangular or keystoned wire are often selected. Associ-ated Spring manufactures hundreds of rectangular wirespring designs. These springs are commonly referred toas die springs and are available for immediate delivery.
Fig. 5-13. Transmissibility of Spring Mounting.
at least i3 times the operating frequency.The natural frequency of a compression spring
versely proportional to the time required for awave to traverse the spring. For a compressionwithout damping and with both ends fixed:
ls ln-surge
spring
(s-r3)
" : %#,ry' ror steel n : $fi!} metric
,./qg: for steel r l4oood F
\ p r: ffiF
Englishn = gD2N"
n is in hertz.If a spring cannot be designed so the natural frequency
is more than 13 times operating frequency, or if thespring is to serve as a vibration damping device, it mustutilize one of several methods of energy absorption.Generally, these are friction devices in which the springrubs against another element such as an internal damp-er coil, arbor, housing or another portion of the spring.Variable pitch springs and springs in combination aiealso occasionally used to avoid or minimize resonantfrequency effects.
Fig. 5-12. Velocity of an Object Propelled by a Com-pression Spring.
\ \I For moss rotios of :I t Over 4 - use cose ( i )
l -4 - use cose (2)| | Under
'l - use cose (3)t l t
I
d Moss Theory (2) |\ Concenirole
\Mort t "ss Spr ing Theory ( l )
t lVo = Veloc i ty
Vm = Moximum Veloc i ty
<
1 . 4
41 . 0
sts€ o te
* 0.6
\o
9 1
5 r' E r
F
0.4
3 .0 3 .5
2 3Moss Roiio PiW,
J-- x l0O = 7o of Forcefl ! \ ' - I tronsmitted\ n / | l
Asso(;iated,r.* y!' n, T3Sprinq r'l.##*trile#$
Helical Compression Springs
Springs made from rectangular wire, with the width ofthe rectangle perpendicular to the spring axis, store moreenergy in a smaller space than equivalent round wiresprings. Even though stress distribution around the rect-angular cross section is not as uniform as the round wiresection, the energy storage capacity is higher becausemore material can be incorporated into the allocatedspace. Rectangular wire is more costly than round wire,but less costly than keystoned wire. Keystoned wire isprocessed specially so that deformation during springwinding or coiling causes the cross section to becomeapproximately rectangular. Distortion of the cross sec-tion can be estimated from the equation presented in Fig-ure 5-14. However, distortion depends upon the manu-facturing technique employed and this equation is at bestan approximation. Axial dimensional change of the wiremust always be considered when calculating solid heightsof rectangular springs.
The rate for a compression spring made from rectan-gular wire is expressed as follows:
Stranded Wire SpringsLong springs with many coils, when subjected to higb
rates of load application Ets in automatic weapons, en-counter shock wave motion and can literally be tornapart. Stranded-wire springs are often the most success-ful solution to such problems because of the frictionalresistance between the strands.
To function properly, the helix of a spring must beopposite in direction to the helix of the strands, so thatthe strands bind together when the spring is compressed.The stranded-wire spring may be wound with 2, 3 ormore strands. Springs with four or more strands aremade with a center wire core to assure necessary stabil-ity. Ends should be soldered, brazed or welded to pre-vent unraveling.
Recognizing that a stranded-wire spring can be consid-ered as single-wire springs aranged in parallel, springrate is derived on the basis given by:
, KnGda* : 8DN
where K : correction factor and n = number of strands.For a three-strand spring, K = 1.05.
Fig. 5-15. RectangularWire Compression Spring Woundon Flat or Edge.
Since the wire is loaded in torsion, the rate is the samewhether the wire is wound on flat or on edge (Figure5-15). Values for the constant K2 are shown in Figure5-16. Stress is expressed as:
k: p/r = ffi*,
s--*ftr, or #*.
(s-r7)
(s-r8)
CG
G
C
G
G
G
G
C
G
G
G
G
G
-
CC-
CCCC
CCCCCCCCC
-l I l.- till.- T r n I
| | r t _ l S p r i n g W o u n d c = 9
? l ;<1-Dhac i . i i l , ' - - - - t
t t t l* l l l IValues for Kr are shown in Figure 5-16, while values
for the stress correction factor for springs wound on theflat (Kr) and springs wound on edge (K.) are shown inFigure 5-17 and 5-18. When rectangular wire is producedby rolling round wire or if the cross section of the wiredeviates significantly from a rectangle, additional correc-tion factors are required. Whenever a round wire cannotbe used because the solid height exceeds specifications, itis possible to try a rectangular wire coiled on edge where:
, _ L- l + b / t
and d is equal the wire diameter for the equivalent roundwire spring. A typical value for a width to thick-ness ratio of 2 may be assumed in the initial design calcu-lations.
Fig. 5-14. Wire Cross Section Before and
AfterCo i l ing
t , = t ( C + ' 5 )c
Dt2-*, Spr ingWound "=9On Edge
- b
Fig.5-16. Constants for Rectangular Wire in Torsion.
I
0
tFl*-u-
It
t
il
l 0
Keyslone
l-l
l-l
BeforeCoi l ing
After CoilingRectongulor
b
I-]l l
b1
l-ll l
ISpringAxis
0.40 0.50
K' ond K,
0.60 0.70
K2 /r ,/
/ // /
ffiAssogFifig /#i, R**Fs
0. r0 0.20
I
7
=,
-
=l
=r??aaa-
a=)
alD
aaaID
IaaaE)
aaaataa
An approximation for torsional stress in each wire ofthe strand is given by Equation 5-4:
8PD--S = ; ; l (q r1
Maximum allowable stress after set removal shouldnot exceed 55 to 60% of the material tensile strength.Wire diameter (d,) for a single strand in a stranded wirespring is less than the wire diameter for a monolithicspring with the same mean diameter and rate.
lr,lumber of Strands Wire Sized, greater than 0.79 dd. greater than 0.69 dd, greater than 0.63 d
Stress in the stranded-wire spring is also less than thestress in an equivalent monolithic spring.
Fig, 5-17. Stress Correction Factors for RectangularWire Compression Springs Wound on FIat.
\\
I-c=,1
C = 8
C - l 0
C - l 2
Ir .0
' t .5 2 .0 2 .5 3 .0 3 .5 4 .0
Rotio b/t
Fig. 5-18. ,Stress Correction Factors for RectangularWire Compression Springs Wound on Edge.
2.5
Rotio b/t
Helical Compression Springs
Yariable Diameter SpringsConical, hourglass and barrel-shaped springs (Figure
5-19) are used in applications requiring a low solidheight, increased lateral stability or resistance to surgxng.Conical springs can be designed so that each coil nestswholly or partly into an adjacent coil. Solid height canbe as low as one wire diameter. Rate for conical springsusually increases with deflection (Figure 5-20) becausethe number of active coils decreases progressively as thespring approaches solid. By varying the pitch, conicalsprings can be designed to have a uniform rate. Rate forconical springs is calculated, as indicated previously, byconsidering the spring as many springs in series. Rate foreach turn or fraction of a turn is calculated using Equa-tion 5-2. Rate for a complete spring is then determined,remembering that the spring rate follows the series rela-tionship given previously in Equation 5-3.
To calculate the highest stress at a given load, themean diameter of the largest active coil at load is used.Solid height of a uniformly tapered, but not telescoping,spring with squared and ground ends made from roundwire can be estimated from:
Lr :N" . , f f i +2d (5-re)
where u : the O.D. large end minus the O.D. small enddivided by 2N".
Fig.5-19. Typical Conical, Barrel and HourglassSprings Respectively.
Fig. 5-20. Typical Load Deflection Curve for VariableDiameter Springs (Solid Line).
234 il
r.5
1 . 4:tv
; 1 . 3
.9
3 1 . 2o
I
1 . 5
: 1 . 4
gY
! 1 . 3
.9
g r . 2o
I
\
\
\
\\
\\
\ IC = 3
\
N\I
C = 4
\-14
C = 6
\\
\ C = 1 0 - -:y\
\\
C = 1 2
1 . 0 ' r .5 2.0 3.0
Assogslfig lhff*ffiffis ffi
Helical Compression Springs
Designing a variable diameter spring so that adjacentcoils rub against one another during deflection increasesresistance to resonance phenomena but may also shortenspring life due to wear.
Barrel and hourglass springs are calculated as twoconical springs in series.
Variable PitchVariable pitch springs (Figure 5-21) are used to
achieve a variable rate similar to that shown in Figure5-20 or in dynamic applications where the cyclic rate ofload application is near the natural spring frequency. Asturns of lesser pitch become inactive during deflection,the natural frequency of a spring changes. Throughoutthe cycle, the spring has a spectrum of frequency re-sponse and not a single resonant frequency. Thus, surg-ing and spring resonance Ere minimized.
Nested Compression SpringsHelical compression springs are often used in combi-
nation because of space limitations and resonance con-siderations. A nest of compression springs can storemore energy but will have lower natural frequenciesthan a single equivalent spring. Nested springs are notrecommended when the diametral space is so restrictedthat a single spring would have an index of 5 or less.The following design practices apply to nested springs:
1. To prevent internesting, the springs should be woundalternately left and right-hand.
2. Clearance between springs must be at least twice thediameter tolerance.
3. The most efficient distribution of load between indi-vidual springs varies with their indexes and the clear-ances between them. For a first approximation in de-signing a nest with two springs, one-third of the loadshould be on the inner spring and two-thirds on theouter spring.
4. Solid heights and free heights should be about thesame for all springs.
These practices result in springs with approximately thesame index.
Commercial TolerancesStandard commercial tolerances for free length, diam-
eter and load are presented in Tables 54, 5-S and 5{.Tolerance on squareness is 3o. These tolerances repre-sent a good trade-off between manufacturing costs andperformance in most applications. Certain premiumspring materials and processing methods can be used to
Fig. 5-21. Typical Variable Pitch Helical CompressionSpring.
achieve tighter tolerances. If the application requirestighter tolerances, the required tolerance levels should bediscussed with an Associated Spring engineer.
For fatigue applications, spring life is often specified.Unless otherwise stated, life is interpreted as the Sro life.This is the life at which 9Vo of the springs are expectedto survive with a 50Vo confidence level based on Weibullanalysis.
Acceptable Quality l-cvel (AQL)Quaitv levels are often expressed by an AQr, (for
example MIL-STD-l05, Sampling hocedures and Ta-bles for Inspection by Attributes). Only critical attributesshould be subject to an AQL on the drawing. Unneces-sarily tight AQL's will increase manufacturing and in-spection costs. If tolerances must be close for properfunctioning and if, for instance, nonconforming parts canbe discarded at assembly, a standard AQL will min-imize the parts cost. Springs assembled automaticallyoften require tight AQL on dimensions, while springsused in instruments and critical machines often requiretieht AQL on loads and life. A close liaison betweenAisociated Spring engineers and the designer during de-sign and prototype phases is the best way to ensureoptimum quality.
PackagingNormally, compression springs and other custom
parts are packaged in bulk. Compression springs withhigh pitch angles and large indexes are subject to tan-gling. Tangling not only makes it diffrcult to separatesprings upon arrival but can also cause distortion. Spe-ciA pictcigrne systems such as the Spring FlowrM systemwhere springs are packaged in rows (Figure 5-22) is onemethod to prevent tangling. Another method is to placesprings on adhesive-coated comrgated panels. There are
Toble 54. Free Length Tolerances of Squared andGround Helical Compression Springs.
I!*ur*lbar ofAeli?e Coi.l'*par rnrfi{in.}
ffinrmt* t:rntu/nm {h.ltn,} of fr&cril
4 * E ro t2 T{ ,5
0.02(0.5) 0.010 0 .01 l 0.012 0.013 0.015 0.0r6 0.016
0.04( l ) 0 .01 l 0.013 0.015 0.016 0.017 0.018 0.019
0.08(2) 0.013 0.015 0.017 0.019 0.020 0.022 0.023
0.2(4) 0.016 0.018 0.021 0.023 0.024 0.026 0.027
0.3(E) 0.019 0.022 0.024 0.026 0.028 0.030 0.032
0.5(12) 0.02r 0.024 0.027 0.030 0.032 0.034 0.036
0.6(16) 0.022 0.026 0.029 0.032 0.034 0.036 0.038
0.8(20) 0.023 0.027 0.031 0.034 0.036 0.038 0.040
For springs less than 12.7 mm (0.500) long, use-the-tolerances for 12-7mm (0.500). For closed ends ndt glound, multiply above values by 1.7'
CGG-
CCGCCCCCCC-
CCcCCCC
CCCCCCC5sI
' / f f i , r r - - T . ! r r l l l l
Y 700
l.bI'baaI
Daaaaaa!D
IaaIaIIttaaaataa
!r'n:nl other packaging methods used to prevent tanglingand reduce shipment bulk.
Em to SpecitvTbere are many ways to specify compression springs.
Because rhe number of variables is large, it is useful forthe designer to use the specification checklist on the nextpage to be sure that all critical aspects are specified.
Compression Spring Desrgn ExampleGiven: Squared and ground compression spring to workin a hole DH : 40 mm (1.575') and exert Pr:275 N (61.8lbfl at a height of Lt : 60 mm (2.362') and Pz : 500 Nt lll lbf) at a height of Ia : 50 mm (l .96y). Application:sadc at room temperature. Material: oil tempered wireASTI1 N29. Spring must not set when compressed tosolid height.
A. First estimate the wire diameter by solving equation(Equation A, page 33) using approximate values forunknown factors and Kq,1 = 1.
Then, calculate O.D. and D.Substitute this wire size in the load deflection equation
(Equation 5-2, page 33) and solve for N". Repeat thisprocess until a satisfactory solution is obtained.l. Rearrangng Equation 5-4 for uncorrected stress:
A _ lz.ss PDo : v Tl. Assum" ,.nril. strength of ASTM Al2}gis 1500 MPaand S: = 700 MPa uncorrected:
d -
3. For clearance, assume O.D. :0.95 Ds:
O.D. : 0.95 x 40 : 38.0 mm
Tablc 5-5. Coil Diameter Tolerances of Helical Com-pression and Extension Springs.
Helical Compression Springs
D = 38.0 - 4.2 - 33.8 mm
c = ? = # : 8 . 0Rate = k = 59- ?-T :22.5 N/mm
N " :
|rJ" =(7.93 x 104) (4.2)o= 3 .55" - 8G3*8n22i)
B. Find amount of space left between L2 and L5:1. Compare to f2.2. Find the corrected stress at solid height.
3. Compare to tensile strength of material. See Figure3-3, page 19.
L , : 5 .55 x 4 .2 :23 .3
, P, )1\I4:
kt * Lt :
zL:t + 60 :72'2 mm
fz: 72.2 - 50 : 22.2 mm
Lz - L, : 50 - 23.3 :26.7 mm
f, = 72.2 - 23.3 : 48.9 mm
15% of 48.9 : 7.3 mm
4C - l .615K w r : f f i + a : = 1 . 1 8
P, : f . x k : 48 .9 x 22 .5 :1100 N
cr _ 2.55P,D__ _ (2.55)( i l00) (33.8)(1.18)b' :
-5-K*t -
: 1510 MPa
Tensile strength of 4.2 mm diameter wire : 1400MPa. Before set is removed, ma:cimum allowable tor-sionai stress is 5Vo of TS or 700 MPa (Table 5-2,page 35). S, = 1510 is greater than 700 MPa, and thespring will set.Because (L, - L,) : 26.7 > 0.15f , :7.3, there ismore space available. Try a larger preferred wire size(Table 3{, page 20) of 4.8 mm.TS = 1400 MPa, D : 38.0 - 4.8 : 33.2 mm, C = 6.9
N " :(7.93 x l0a)(4.8y: 6.48(33.2)3 Qz.s)
- 5 06 0 -Gd48m
4 .
C.
L, : 8.4 x 4.8 : 40.3 mm
L z - L . : 5 0 - 4 0 . 3 : 9 . 7 m m
f, = 72.2 - 40.3 - 31.9 mm
(Lz - L,) : 9.7 > 0.15 f, = 4.8 mm
P, : (31.9)(22.5) = 718 N( + X 6 . e ) _ l * # : r . z z
r a w t = ( 4 x 6 . 9 ) - 4 - e t =
s , - @ : 6 7 t M p a(4.8)'
S. : 671 MPa ot ffi x loo - 48vo of rS
WircIXa.,
E(iD.)
Tolemmffr: t:mm:,(lui)
$pring lrd€n {D/d}4 6 t IB L2 l{ t6
0.38(0.01t
0.05(0.002)
0.05(0.002)
0.08(0.003)
0 .10(0.004)
0 .13(0.00s)
0 . 1 5(0.006)
0 . lE(0.007)
0.58r0.023)
0.05(0.002)
0.08(0.003)
0.10(0.004)
0 .15(0.006)
0.18(0.007)
0.20(0.008)
0.25(0.010)
0.E9r0.035)
0.05(0.m2)
0 .10(0.004)
0 .15(0.006)
0. lE(0.007)
0.23(0.00e)
0.28(0.01l)
0.33(0.013)
1 .30(0.05 r)
0.08(0.003)
0 .13(0.005)
0 .18(0.007)
0.25(0.010)
0.30(0.012)
0.38(0.0r5)
0.43(0.017)
1.93(0.076)
0 .10(0.004)
0 . lE(0.007)
0.25(0.010)
0.33(0.013)
0.41(0.016)
0.48(0.019)
0.53(0.021)
:.90r 0 . 1 1 4 )
0 . 1 5(0.006)
0.23(0.00e)
0.33(0.013)
0.46(0.01E)
0.53(0.021)
0.9(0.025)
0.74(0.029)
1.y(0 .171)
0.20(0.008)
0.30(0.012)
0.43(0.017)
0.58(0.023)
0.71(0.028)
0.84(0.033)
0.97(0.038)
6.3,((0.250)
0.28(0 .01 l )
0.38(0.01s)
0.53(0.021)
0.71(0.028)
0.90(0.035)
1.07(0.042)
1.24(0.049)
9.53(0.37t
0.41(0.016)
0 .51(0.020)
0.66(0.026)
0.94(0.037)
t . l 7(0.046)
1 .37(0.054)
1.63(0.064)
11.70r0.500)
0.53(0.021)
0.76(0.030)
r.02(0.040)
r.57(0.062)
2.03(0.0E0)
2.54(0.100)
3 . 1 8(0.12s)
Assos$tf;g& ffi*ffirys wB
Helical Compression Springs
COMPR,ESSION SPRING SPECIFICATION CHECKLIST(Fill in required doto only)
Frequency of looding
Required life cYcles'
Moteriol: Required reliobility (see Section 4)
Wo*ing Conditions: Speciol Informotion:
To work in m(in.) diometer hole
m(in. dismeter shoftSquoreness Porol lel ism
To work over FinishLood (1b0, * tl (lb0 Moximum operoting fem Peroture :c("F)
Operoting environmentx (tbO Electricol/ mognetic
Rote -N/mm ( lb f / in . ) , t -N/mm ( lb f / in . )
between -rnm(in.) qnd -mm(in.)
Moximum sol id height mm(in.)
Direction of coil (right-hond, left-hond or opfionol) -
Type of endsAlfowobfe reloxotion -o/o Hours/doys -
lmpoct looding mm/sec ( in./sec)
Design Dofo (Reference):
Wire diometer
Outside diom
lnside diometerFree length mm(in.)
Totol number of coils
CCC
Tablc 54. Load Tolerances of Helical Compression Springs.
CCcC
-
C5CCCC
C555EsssssCC55scC
First load test at not less than l5Vo of available deflectron.Final load test at not more than85% of available deflection.
Fis.5-22. Tansled Helical Compression Springs (Left)and- S pring Flow P ackaging.
Again referring to Table 5-2, page 35, it is clear that thespring can be made without presetting. Tolerances areobtaineO from Tables 54, 5-5 and 5-5. The final designbecomes:Final Design Specifications:
Material: ASTM A229Wire Diameter d: 4.8 mm (0.189) ReferenceO.D.: 38.0 -r 0.4 mm (1.500 + 0.050)Free Length I-r: 72.2 mm (2.843') ReferenceTest Height Lr: 60 mm (2.362')Test Height Lz: 50 mm (1 .96Y)Pr Load at Lr: 275 N (61.8 lbO = ll.0%Pz Load at L2: 500 N (112 lbO =7VoFinal Design Stress S,: 671 MPa (97,300 psi) or 48%TSN,: 8.4
.
X.*ugthTskrarr*::mm {in.}
r"*,l""*' *qb."r1yrd..y{,*t Tl.e.ry pry|,]:i , l.Y'H.bl,f:, .:I fien f,rom fre*,,I ,,to',.[ , mm {in.)
'l;3;7'(s.s3o)
?.54{0,ltr}
3,*r.{0,1$6}
5"S0{0"m,}
,,f,$${0,2sJ
"V,67,
t0.300)10.2
(0.400,11:,7
{ 0 }
'19*,1 ,'{s-.?50}
"28*,{r;tr}
t*.1(r
fO;il,.,(2'ffi1
'l?6 ,,.1,
{,s,; }.i,ltrEl{*$1
,,:1 ,:{6iffi}
0.13 (0.00s)0.25 (0.010)0.51 (0.020)
,: 7 .t2.22.
6.8 .5
15.5
5 .7 .
t2 .6 .5
10.l.s8.s
5 .7 . 6.
0.76 (0.030)1.0 (0.040)r.3 (0.050)
? 1 7 .22.
T4r8))
t2.15 .519.
9.512.14.5
8l012
6.7 .59.
567
s5.5
1 . 51 . 82.0
(0.060)(0.070)(0.080)
! 22.25.
1 7 .19.522.
l4l6l8
10.1 1 .12.5
89
10
6.6.57.5
5 .) . )6.
2.3 (0.0e0)2.s (0.100)5.1 (0.200) :
20.
?14.15 .5
1 lt222
8.8.5
15.5
67
t2
5 .5 .58 .5 7 .
7.6 (0.300)10.2 (0.400)12.7 (0.500)
? 172l25
t2.15 .18.5
9.5t2.14.5
7 .8.5
10.5
Helical Extension 7Spri ngs I
DaaaaaI
IIII
o"tF'!fi349*nrrs !t
Helical Extension Springs
IntroductionHelical extension springs store energy and exert a pul-
ling force. Usually, they are made from round wire andare close-wound with initial tension. Typical applicationsinclude tape cassette players, balance scales, toys, garagedoors, auiomatic waJhing machines and various types ofspring tensioning devices-
Helical extension springs are stressed in torsion in thebody. Design procedures for the body are similar to thosediscussed pleviously for compression springs (Section 5)with the following major exceptions. Most helical exten-sion springs are coiled with initial tension, equal to theminimum force required to separate adjacent coils. Heli-cal extension springs do not normally have set removed.Furthermore, untit<e compression springs, extensionsprings do not have a solid stop to prevent overloading.For these reasons, design stress levels are generally lowerfor extension than for compression springs. A specialtype of extension spring, known as a drawbar spring (fig-url 7-1), has a solid stop. It is essentially a compressionspring with special hooks.
Fig.7-1. Drawbar Spring Provides a Solid Stop.
Fie. 74. Load Deflection Curve for a Helical ExtensionSpring with Initial Tension.
tLood (P)
P1
The pulling force exerted by an extension spring bodyis tranimitted to mating parts througfi hooks or loops.When stresses in the hooks are higher than in the springbody, the hooks limit spring performance.
Alsociated Spring includes hundreds of different ex-tension spring designs with full twist loops in its SPECline of stbck iprings. These extension springs are madefrom.either music wire or stainless steel and are pre-engineered to meet a wide range of applications.
Initiat TensionInitial tension in an extension spring is rneasured ac-
cording to the procedure illustrated in Figure 7-2. T\elinear portion of the load deflection curve is extrapolatgfto zero deflection. The point of intersection on the ordi-nate is initial tension Pr. The amount of initial tensionthat can be put into a spring depends upon its index,material, method of manufacture and postcoiling stress-relief treatment. Occasionally, in critical applicationswhen stress is high, a high stress-relief'temperature isrequired to minimize unfavorable residual stresses dueto Loiling or forming the hooks. High temperature stressrelief reduces the amount of initial tension. Typical val-ues of initial tension are shown in Figure 7-3. Highstrength materials such as small diameter music wire areable io support higher levels of initial tension than lowstrength materials such as large diameter hard-drawnwire.
Types of Ends-Extension springs require a method of attachment to
other parts in an assembly. A wide variety of ends has
Fig.7-3. Torsional Stress Due to Initial Tension as aFunction of Index in Helical ExtensionSprings.
300
275
250
t| 22s
CC
C
.
CCC
.
c.
eC
caCceC
ccccC
I
C
I
cI
I
I(
I
Deflection (f) €
=3 2ooU =t v
g g t 7 s9 cj f rsoo . 9U | . =
3 s 1 2 5tn; t g
.E T rooI t
€ E 7 s
50
25
3 5 AII:
30 8.A O
t oo -t "o c
2 s E . g9 c5 P
2 0 ; Eg s.n; 6r s . E TI tp 6
l 0
l 0 1 2
lndex --+
I 4 l 6
been developed and used successfully for many years -for example, threaded inserts, swivel hooks, twisi loops,side loops, cross-center loops and extended hooks.l-oops are attachment ends that have small gaps (Figure-{). while hooks. are loops with a large gap. In fact, the'ariet-v- of ends is almost unlimited. The most commonconfigurations are those that can be formed during thespringmaking operation. Typical types include twist,cross center, side loops and extended hooks (Figure 74).Man), of these configurations are made by bending thelast coils of an extension spring to form loops. Mostspecial hooks are formed from straight sectioni of wireon the so-called "tangent ends" of an extension springbody.
Guidelines for the lengths of common loops arepresented in Figure 74. Alrhough other configuiationsand lengths are available, common loops of preferredlengths are generally the most eccnomical. If possible,a spring should be designed with one or both loops atthe prefered length. For example, if a design requiresa-total loop length equal to five times the I.D., a popularchoice is one twist loop with a length equal to the I.D.and one extended loop with length equal to four timesthe I.D. Whenever possible for extended loops, the de-signer should allow for a straight section approximatelythree wire diameters long at the end of the wire (A,Figure 74). Loops at each end can be made with a con-trolled angular relationship. Specifying an angular rela-tionship may add to the cost; therefore, whenever anapplication permits, a random angular relationshipshould be allowed. Production of special end configurir-tions may involve tool charges and generally resufts inincreased costs.
Helical Extension Springs
Stresses in loops are often higher than in the springbody. This limits spring performance, particularly in cy-clic applications. Generous bend radii in loops and re-duced end coil diameters are two methods frequentlyemployed to reduce stresses. In a full twist loop, stressreaches a maximum at point A in bending and a maxi-mum in torsion at point B (Figure 7-5). Stress at theselocations is complex, but can be estimated with reason-able accuracy by:
se : S*, - #bending t-rt
w h e r e ? - 4 C t 2 - C t - t l R rK t : + t f f i a n d c r : ?
A 8 D P / 4 C , - l \ 2 R ,Ss : A \4ffi) and Cz : ? torsion e4t
Recommended practice is to make C2geater than four.
Fig.7-5. r,ocation of Maximum Bending and TorsionStresses in Twist Loops.
P
rl\ l t l,-r;lF-
( : f - ---=r- )
Torsion Slresso t B
Fig. 74. common End configurations for Helical Extension Springs.
?ypr
TwistLoop orHook
::'--::i"T_- m - A-WJ
\UZ # @
hceCImm*ndd,,Lrn#h*Min"-t\{sx,
0 .5 -1 .7 I .D .
Cross CenterLoop orHook
t l
rmA /A-TrnF - 7r -Tr-rr-7r-
ullv/ \Jlz I .D.
SideLoop orHook
I I-uNz rz v p- 0.9-1.0 I.D.
ExtendedHook
l . l I .D . and upas required by design
SpecialEnds
A Avvvvvvv � - f f i' <
I@-Ft Q n l na i l 6 l l Yv ) L \ i Z € +' # - l - g
IE As required by design
' length is distance from last body coil to inside of end. I.D. is inside diameter of adjacent coil in spring body.
A'"oEFIf;g &wwyvW
Helical Extension Springs
Extension Spring DimensionsFree length of an extension spring is the distance be-
tween the inner surfaces of the ends (Figure 7-6). It isequal to the spring body length plus ends, where springbody length is given by Lur, = d(N + 1). The gap, whichis sometimes referred to as hook or loop opening, canbe varied by the springmaker. Certain manufacturingprocesses require a minimum gap and the designershould consult Associated Spring engineers if a gap mustbe less than one-half wire diameter. The number of ac-tive coils in a spring is approximately equal to the num-ber of coils in its body. For springs with threaded insertsor swivel hooks, the number of active coils is less thanthe total coils in the body. Hooks and loops add to thenumber of active coils. Allowances of 0.1 N" are occa-sionally made for one-half twist loops. Allowances aslarge as 0.5 N" can be made for some cross center, fulltwist and extended loops.
Desigp EquationsDesign equations for extension spring are similar to
compression springs. The rate is given by:
P - P r Gd4: mwhere Pr is initial tension. Stress is given by:
8PD--5 = --liTKw
Dynamic considerations discussed previously in Section5 are generally applicable to extension springs. Naturalfrequency when one end is fixed is given by:
5.6 x ldd EEn :5 ; ;V7 me tnc
Choice of Operating Shess - StaticRecommended maximum stresses for extension
springs used in static applications (Table 7-1) are similarto levels recommended for compression springs withoutset removal. For springs that cannot be adequatelystress-relieved due to high initial tension requirements,the ma,rimum recommended stress in the body should bereduced to that recommended for their ends. Maximumrecommended stress in the ends is lower than in thebody because the wire is often stretched, marked ordistorted during loop-making.Choice of Operating Stress - Cyclic
Maximum recommended stresses for extensionsprings used in cyclic applications are presented in Table7-2. These data are for stress-relieved springs with lowlevels of initial tension.
Tabte 7-1. Maximum Allowable Stresses ('Kn,Corrected)
for Helical Extension Springs in Static Appli-cations.
fi4rnniak
Pcrst of Twih Sftng{h
I nT n InDdf affd End
Patented, cold-drawn orhardened and temperedcarbon and low alloy steels
45-50 40 75
Austenitic stainless steeland nonferrous alloys
35 30 55
This information is based on the following conditions: set not removedand low temperanrre heat treatment applied.For springs that require high initial tension, use the same percent oftensile strength as for end.
Tobb 7-2. Maximum Allowable Stresses for ASTM A228and Tvpe 302 Stainless Steel Helical Exten-sion Sirings in Cyclic Applications.
This inforrration is based on the following conditions: not shot-peened, no surging and ambient environment with a low tempera-ture heat treatment applied. Stress ratio : 0.
1 6 : (7-3)
(74)
(7-s)
CCCCCCCCCCCC
s-
-
CCCCCC5
CCCCc55Cs
t 7 6 x l f f dforsteeln=j::+- metric
W- metn(
n: ofu.',tr Englishfc
Tooog Englishr rs tee ln :NF
Fig. 74. Typical Extension Spring Dimensions.
,.,ill ..ff,'ffd6
Scrwt-of Tadk @$
In tordffi In Ucntrry
Epdl, ffiil trffi
ld106107
363330
343028
5 14745
EA""Th!8$M I
=
--
r--
a--,
.--,
rl-
r-,-
r--
r-,<,
-
-
-
-
aaa=l
a!rrDaar}aIIIL,'FLI
ClearancesExtension springs, when deflected, do not require cen-
tral arbors or holes to prevent buckling. When a springis dynamically loaded or unloaded suddenly (as a camdrop-off), it may vibrate laterally, inducing additionalstresses. If clearance is not allowed, this lateral vibrationmay be noisy and result in premature failure from abra-sion of the ppring or adjacent parts.
TolerancesSince requesting close tolerances can increase manu-
facturing costs, only those characteristics which are crit-
Table 7-3. Commercial Free Lensth Tblerances for Heli-cal Extension Springs Wtttt Initial Tdnsion.
$pring Sree lxngttu tirsidn koolrrirnm fin-)
Helical Extension Springs
ical to spring performance should have tolerancesspecified. Commercial free length, angular relationshipof ends, and load tolerances are presented in Thbles 7-3,7-4, and 7-5 respectively. O.D. tolerances are the sameas for compression springs (Table 5-5, page 43). Thesetables should be used only as a guide since some manu-facturing operations have different process capabilitieswhich can cause variations in tolerance values. For spe-cial applications requiring closer tolerances, consult As-sociated Spring engineers.
How to SpecifyFor minimum cost, it is important to specify springs
properly. The following checklist is presented as a guide.
Table 74. Tolerances on Angular Relationship of Exten-sion Spring Ends.
Arryular Tohranm ptr Coih I Deperx
For example, tolerance for a lGcoil spring with an index of 8l 0 x + 1 . 5 = t l 5 o .If angular tolerance is greater than * 45o, or if closer tolerances thanindicated must be held, consult with Associated Spring.
Up to 12.7 (0.500)over 12.7 to 25.4 (0.500 to 1.00)Over 25.4 to 50.8 (1.00 to 2.00)Over 50.8 to 102 (2.00 to 4.00)Over 102 to 203 (4.00 to 8.00)Over 203 to 406 (8.00 to 16.0)Over 406 to 610 (16.0 to 24.0)
Tohrsscs* nrm {in.}
0.51 (0.020)0.76 (0.030)r.0 (0.040)1.5 (0.060)2.4 (0.093)4.0 (0.155)5.5 (0.2r8)
; f f i
HELICAL EXTENSION SPRINGS SPECIFICATION CHECKLIST
(Fil l in required doto only.) Suggested Design Doto:
Moteriol
Working Condit ions:
Moximum outside diometer mm(in.)In i t io l tension N(lb0
Wire diometer mm(in.)
Outside dioTotol number of coi lsFree length inside ends
Speciol Informotion:
mm( in . )
hertz
Lood N(lbf), +
of length mm(in.) Finish
Lood N(lbf), + Moximum operoting temperoture
ot length mm(in.) Operoting environment
lmpoct Looding sec ( in. /sec) Frequency of Looding
Rote N/mm(lb f / in ) Required life
Moximum extended length in service mm(in.) Required Reliobility (see Section 4)
) during instollotionDirection of coi l : r ight left
optionolTyp" of endsPosifion of ends ond toleronceGop opening ond toleronce mm(in.)
Index4 5 6 E7 9 l0 t2 t4 l6
0.75 0.9 l . l 1 . 3 1 . 5 t . 7 1 . 9 2.3 2.6 J
-Associatgd ..*,,, :':r i' :r:;,,r:,.,xff: iwffii
SPring "'"'
"M:'6'" ':': "':;";:
';;:ffi '
iJ
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IiI]
SodgI"e.qgthUirldcd
, b fIldlecth*r
*pr
Tokrrm*r: * Pstcnt of:,$hgroilld ld
{Cb*rr tohnnct* nry rt@ll dlt*ud qpcl "}
Whc Dfiril#cr: )
*JSt0..CIls)
0;56(0.f22)
*s1{0;03?}
,,,,.,f;{
t0;0*tltr"f
(0.ffiat,,3
f0,0e!)3.t
{0"r2ft:,'1,!l; . :,
{0;lft}
, ::g;l['::.,
ta;ffSt',:,1'8
{off,f,}t1. l
@8n,
4
r2864.52.51 . 50 .5
20.018.5r6.815 .01 3 . 1r0.26.2
18.517.516 .1t4.7LZ.49.95.4
17.616.715 .514 . lr2.r9.34.t
16.915.8t4.713.5l 1 . 88.94.6
16.215.013 .812.610.68.04.3
15.514.513.212.010.07.54 . 1
15.014.0t2.71 1 . 59 . 17.04.0
14.313.21 1 . 8r0.38.56.53.8
13.8t2.5tl.29.78.06 . 13 .6
r3.01 1 . 59.98.46.E5.33 .3
t2.61 1 . 09.47.96.24.83 .2
5
t2E64.5? s1 . 50.5
l7 .El6.E15.814.212.310.06.2
16.515.714.8l 3 . l1 l . 39.35.4
t5.7t4.913.8t7.310.8E.94.9
15.5t4.313.2tl.710.0E.44.6
14.813.512.31 l . l9 .68.04.4
t4.l13.01 1 . 810.59.07.74.2
13.512.5tl.410.28.77.24 . 1
l2.Etr.710.79.6E . l6.53.9
12.3rt.zr0.08.81 <
6.23 .7
12.010.69.38.06.55.03.4
I 1 . 5l 0 . l8 .77.46.r4.53 .3
6
1 2864.52.51 . 50.5
17.016.2t5.213.71 1 . 99.96.3
15.5t4.714.012.410.89.05.5
14.613 .912.91 1 . 510.28.34.9
t4.I13.4t2.31 1 . 09.87.74.7
13 .512.6I 1 . 610.59.47 .34.5
l 3 . l12.210.910.09.07.04.3
12.7tL.710.79.6E .56.74 . 1
12.01 1 . 010.09.07.96.44.0
1 1 . 510.59.4E.37.26.03.7
tt.210.08.87.66.24.93 .5
10.79.58.37 . 16.04.73.4
8
t2864.5? s
1 . 50.5
15.8r5.0t4.212.8tt.29.56.3
t4.313.713.0rt.710.28.65.6
1 3 . 112.5rr.71.0.79.57.85.0
13.012.lrt.2l0 . l8.87 . 14.8
t2.lrr.410.69.78.36.94.5
12.01 1 . 0r0.09.07.96.74.4
I 1 . 510.69.7E.77.76.54.2
r0.8l0. l9.38.37.46.24 . 1
r0.29.4E.67.E5.95.E3.9
10.09.08 . 17.26 .14.93 .6
9.5E.57.65.65.64.53 .5
r0
t2864.52.51 .50.5
14.814.2t3.4t2.310.89.26.4
13.312.E12.l10.89.68.35.7
12.01 r . 610.Er0.09.07.55 . 1
1 1 . 9rr.210.59.5E.46.94.9
1 l . l10.59.89.08.06.74.7
10.9r0.29.38.57.76.54.5
10.59.78.98 . 1t . 5
6.34.3
9.99.2E.67.E7.06.04.2
9.38.68.07.36.55.64:0
9.28.37.66.85.95.03.E
E.88.07.26.45 .54.63.7
L2
t2864.5) <1 . 50.5
14.013.212.6rr.710.58 .96.5
12.31 1 . 8rr.210.29.28.05 .8
1 l . l10.710.29.48.57.25 .3
10.8r0.29.79.0E.06.E5 . 1
10.19.69.0E.47,E6.54.9
9.E9.38.5E.07.46.34.7
9.58.98.27.67.06 . 14.5
9.0E.47.97.26.65.74.3
E.57.97.46.E5 . 15.44.2
8.27.56.96.35.64.E4.0
7.97.26.45.E< )4.53 .3
l4
T2E64.52.51 . 50 .5
13 .1t2.41 1 . 8l l . l10 .18.66.6
l 1 . 310.910.49.78.87.75.9
r0.29.89.38.78 . 17.05.4
9.79.28.88.27.66.7\ )
9 . 18.78.37 .87 . 16.35.0
8.88.37.71 J
6.76.04.8
8.48.07.57.06.55.84.6
8 . 17.67.26.76.25.54.4
7.61 ' � '
6.86.35.7< t
4.3
1 ' � '
5.86.35.8< )4.74.2
7.06.45 .95.45.04.54.0
l6
t2864.52 .51 . 50.5
12.3rr.71 1 . 010.59.78 .36.7
10.310.09.69 .18.47.45 .9
9.28.98 .58 . i7 .66.65 .5
8.68.38.07 .57.06.25 .3
8 . 17.87.57.26.76.05 . 1
1 1
7.47 . 16.86.35.85.0
7.47.26.96.56 . 15.64.8
7.26.E6.56.2> . t5.34.6
6.86.56.25 .85.45 . 14.5
6.36.05.75 .34.94.64.3
6 .15 .75.45 . 14.74.44 . 1
Helical Extension SPrings
Table 7-5. Load Tolerances for Helical Extension Springs.
C-
Gj
GCrCIE
CCCC-
C-
C3CC.
C
C
C
C
C
cC
C
C
tssociatedsnrind f&S&'ffiflq$
btDaaaaaaaaaaaaaaaaaaIIaaaaaI
aI
r-rtrrdon Spring Desi$ Example-{ spring is to be incorporated into an overload circuit
rreaker. It is to be preloaded at length Lr :25.00 mm0.84-l and must exert a load of 17.5N (3.93lbf), + IsVo,
sten the circuit breaker is closed. If overload occurs,Cre circuit breaker is tripped and the spring is extendedu a lengrh Lz : 29.00 mm (1 .142'). The load must be 30\ - ll%. to operate a lock, preventing accidental reset-nng before the malfunction is corrected. Either twist orertended loops with generous radii are satisfactory. Be-cause of surrounding components the maximum O.D. is
nrm (0.276'). Probability of overloads is small andt'reaker operation is expected only three or four timesrn a )'ear. The spring will not be extended beyond Liduring service or installation.
For static application, in an ambient environment, thematerial selected is ASTM A227.
l. Assume a clearance on O.D. of lWo:O.D. - (0 .9) (7) :6 .3 mm
l. Assume Sz : 700 MPa uncorrected; let D = O.D.: 6 . 3 m m
Calculate wire diameter d:
Helical Extension SPrings
Calculate free length I+ and deflections fr and fz;assume full twist loops:
I-r : 2(ID) + (N" + l)d : (2)(4.5) + (13.2 + 1X0.9): 21.78 mm
f, = L, - I4 : 25.00 - 21.78 = 3.22 mm
fz: Lz - Lr :29.00 - 21.78 : 7.22 mm
Calculate initial tension P1 and uncorrected stressdue to initial tension 51:
Pr : Pr - kf ' : 17.5 - (3.13)(3.22):7.42 N
d 2.55 PrDs r = - - F (0.e0)'
7.
8 .
/zffio : \ r : :
Y J
l e t d : 0 . 9 m m
Tensile strength taken from Figure 3-3, page 19, is1790 MPa.
Calculate mean diameter. D and coil index C:D = O.D. - d = 6 .3 - 0 .9 :5 .4 mm.
7 4C : D r d i ; : 6
Calculate mean stress at the extended length:
Lz = 29.00 DD, Pz = 30 N
- 2.55 PzD.,)=: -a3-n*t
t _ 4 C - 1 - 0 . 6 1 5 _ 4 ( 6 ) - I _ - 0 . 6 1 5 _ 1K w r : N c 4 6 ) - - - - : 1 . 2 5
' iv
(2.ssx30)(6.3): 0.88 mm
(2.ss)(7 .42)(s.4): 140 MPa
Referring to Figure 7-3,it can be seen that this is in thepreferred range for initial stress for an index of 6.
9. Check stresses in the hooks:Bending Stress:
A l6PD.. 4P f, 4Cr2 - C - I ,Se :fff ' - # tKr = ffi ; letCr:C
K r :4 ( . 6 ) 2 - 6 - r4(6X6 - l)
: 1.142
So : (16)(30X5.i1)9.142)
* 1^�3%, : 1340 Mpa orvA z(0'90)3 z(0'90)z
LJ 'v '
74.9%o TSTorsional stress, where Rz : 2.70 mm:
c r 8 P D 1 4 C 2 - 1 \ ^ 2 R zDB =;Ar \rc= )
t,: d
6 _ (8)(30)(s.4) t4(6) - l\ss: =1ffi (Affi ):6sr MPa or 36vo rs
Final Desig Specifications:
Free Length l-t 21.78 mm (0.854') ReferenceOutside Diameter: 6.3 + 0.10 mm (0.248 f 0.004'JWire Diameter d: 0.9 mm (0.035t ReferenceInitial Tension Load Pi: 7.45 N (1.68 lbf) ReferenceExtended Length L1: 25.00 mm (0.9&4')Extended Length Lz: 29.00 mm (1 .142')P1 Load at L1: 17.5 +2.0 N (3.93 *0.45 lbOPz Load atLz:30 +2.5 N (6.74 +0.55 lbOFinal Design Stress Sz: 708 MPa (103,000 psi) 40"76 TSN": 13.2 Coils
Refer to the load tolerances for helical extension springs(Table 7-5). Tolerance on load for P1 is -r llVo, which isless than the required + lsVo, and Pz is = 8Vo, which isless than the required + lTVo.
700
4 .
S u :(2.55X30X5.4)(1.2s)
: 708 MPa or 4Vo TS(0.eOf
6 .
Calculate rate k:
g =,Pt - P' : 39^-
Y;t :3.13 N/mmL z - L , 2 9 - 2 5
r ' L e
Calculate number of coils N":
rY Gd4 Q.g3 x 104)(0.90)4N" :dm: f f i :13 .2
AssoS&!fi$,'eP*sqres ffi
Helical TorsionSpri ngs
CCCCCCCC-
C
CC.
ff5C
C
35C
€
cI
g---- ''-'; '' "
&Lff
aa!D
!D
aaaaaaaaaaaaaaaaattDbLaaI
lntroductionHelical springs used to apply a torque or store rota-
donal energy' are commonly referred to as torsionsprings. The two most common types are single anddouble-bodied springs (Figure 9-l). Torsion springs arefound in clothes pins, window shades, counterbalancemechanisms, ratchets and various types of machine com-ponents. They are also used as couplings between con-centric shafts such as in a motor and pump assembly.Torsion springs are generally mounted around a shaft orarbor. and must be supported at three or more points.Yarious kinds of ends are available to facilitate mount-ing.
Torsion springs are stressed in bending. Rectangularuire is more efficient in bending than round wire, butdue to the premium cost of rectangular wire, round wireis preferred. If possible, a torsion spring should alwaysbe loaded in a direction that causes its body diameter todecrease. The residual forming stresses are favorable inthis direction, but unfavorable when the spring is loadedin a direction which increases body diameter. Unlessthere are unfavorable residual stresses in the end bends,springmakers normally heat-treat these springs at a lowtemperature to stabilize the end positions rather than tofulll' stress relieve them. If the direction of loading tendsto increase body diameter, the springmaker should beadvised to stress relieve the springs.
The Associated Spring SPEC line contains many tor-sion spring designs using stainless steel and music wire,either left or right-hand wound. These springs have tan-gent ends and are available for immediate delivery.\umber of Turns
The number of active turns in a helical torsion springis equal to the number of body turns, plus a contributionfrom the ends. For straight torsion ends, this contribu-tion is equal to one-third of the moment arms and isusually expressed as an equivalent number of turns:
Helical Torsion Springs
shaft or tube and spring at all times to prevent binding.The ideal shaft size is equal to, or slightly less than,90Voof the I.D. when the spring is fully deflected (minimumdiameter). Shafts significantly smaller than 907a shouldbe avoided to prevent buckling during large deflections.
LengthMost torsion springs Ere close-wound, with body
length equal to the wire diameter multiplied by the num-ber of turns plus one. When a spring is deflected in thedirection that will reduce the coil diameter, body lengthincreases according to:
L = d ( N o + 1 + 0 ) (9-4)
For applications that require minimum hysteresis,springs should be designed with space between adjacentcoils to reduce frictional losses.
Spring RateSpring rate for helical round wire torsion springs is
given by:
, M E d .t : - _ � -
e l0.8DN"(e-s)
(e-t)
Lr : length of the moment arm of the first end.Lz: length of the moment arm of the second end.
N " : N s * N . (e-2)
Nu : number of body turns.
Mean DinmeterMean diameter is equal to I.D. plus O.D. divided by
tu'o. When the direction of loading tends to reduce thebodl' diameter, the mean diameter changes with deflec-tion accordine to:
The 10.8 factor is greater than the theoretical factor of10.2 to allow for friction between adjacent spring coilsand between the spring body and the arbor. This factoris based on experience and has been found to be satis-factory. Loads for torsion springs should be specified ata fixed angular position and not at a fixed deflection fromthe free position (Figure 9-1). Presenfly, there is no stan-dard way to test loads for torsion springs. Consequently,in critical applications, it is advisable to contact Associ-ated Spring engrneers to establish a test method duringprototype work.
Fig. 9-1. Specifiing Load and Deflection Requirementsfor Torsion Springs.
Ends inFree Position
Specify:c = Angle between endsP = Lood on ends ol aL = Moment orm0 = Angulor Deflection from Frce Posiiion
C
N" : t#
D,N,D - -
N o + 0(9-3)
Ends inFree Position
*here D, is initial mean diameter and d is deflection inrevolutions. Clearance must be maintained between the
l -L
AssogFifiS&ff*nfn$ @
(e-7)
A convenient approximation for engineering calculationsis:
Helical Torsion Springs
StressStress in torsion springs is due to bending, and for
round wire is given by:n 32M,t : ff*,
(e-6t
During elastic deflection of a curved beam, the neutralaxis shifts toward the center of curvature, causing higherstress at the inner surface than the outer. Wahl (Refe-rence 3, page 102) has calculated the stress correctionfactor at the I.D. of a round wire torsion spring as:
d f" 8040d F-^,:-,-n: ,ffiV7; for steel: ffi English
and with both ends fixed:
2.5 x ld, i- 4 x t fd _- -^--:n: ffid VT ; for steel: ffi metric Q-II.
d E rfor steel : lE8od
Englishn : A",tFi.I" !- tr-I\a
To avoid or minimize resonance phenomena, the naturalfrequency must be much greater than the operating fre-quency and/or the spring should contain initial tension.
Choig of Operating Stress - StaticRecommended maximum operating stresses for static
applications are given as a percentages of tensilestrength in Table 9-1. For spring bodies or ends loadedin a direction that increases the radius of curvature,stress levels in the "stress-relieved" column are mostappropriate. These stresses should be calculated usingtfie appropriate KB stress correction factor (Equation 9-8or 9-9). When the outer surface is in tension, springswith a low index usually yield at the inner surface, whilethose with a higfr index may yield at the outer surface.For springs not stress-relieved and loaded in a directionthat decreases the radius of curvature, the stress levelsrecommended for springs with favorable residual stressare appropriate. No stress correction factor is used sincethe spring has yielded.
Fig.9-2. Com.mon Helical Torsion Spring End Config'uratrcns.
f7 4C2 - C - IABrD:
rc16 _ t)
f , 4 C - ll l B r D : 4 C _ 4
4 C + 1l ( g o p : 4 C + 4
CCC-
C
C
C
C
c.
C
C
a.
-
c3
cC
eacC
C
C
e-
f
cct
I
(e-8)
(e-e)
At low indexes, stress is significantly higtrer on the innersurface than the outer. These factors are useful to de-termine the stress range for cyclic applications and theset point for fully stress-relieved springs in static appli-cations. A stress correction factor of 1 is recommendedto determine the set point of springs that have favor-able residual stresses induced by yielding during form-ing. Yielding results in a more uniform stress distributionover the round cross section. Therefore, the actualstress correction factor approaches the recommendedvalue of l.
End ConfigurationsSome of the more common end configurations avail-
able are shown in Figure 9-2. Special configurations areavailable on request. In designing ends, it is importantto recall that bends, loaded to decrease their radius ofcurvature, have favorable residual stresses. They canoperate at higher applied stress levels than bends thatincrease the radius by loading. Frequently, spring perfor-mance is limited because the sharply bent ends havegreater stress than the body. Equation 9-6 is generallyemployed to determine maximum bending stress in theends. Torsion springs are subject to surging and reso-nance phenomena. The natural frequency n for a torsionspring with one end fixed is:
t . 2 6 x l d d r 2 x t d dn : ffi VT ; for steet : ffi meric 9-Ioi
A AO-O ftfif l/ l i l l t l
t( )) ililll\r/ I'UU
SHORT HOOK ENDS
/6\ [m(( )) ]iltl\r/ tulj
HINGE ENDS
-^./- \ \ i l l t
I t \ l r I I I( n5liltrv/ tuuSTRAIGHT OFFSET
MENDS
mTORSION
bDOU
Associatec' 4sprindl&**firys
NTORSION
,',,}t*sI\
SPECIAT
STR.AIGHT
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CLoi- of Operating Stress - Cyclic\tarimum allowed operating stresses for cyclic appli-
;arions are presented in Table 9-2 as percentages of ten-sile suength. All stresses are assumed to be calculatedrrith the appropriate Ks correction factor. This infortna-ion can be used to estimate fatigue lives at other stressranges b1' methods discussed previously (Section 4). Fre-quentll'. bending stresses are higher in the ends than inthe bodl'. In this situation, bear in mind that during for-rr.ng of sharp bends, the wire may be stretched orrrarked. resulting in stress concentrations that reducedesign stress levels below those recommended. Becauseof friction, the point of contact between torsion end andarbor is often the highest stressed area.
DouHe Torsion SpringsDouble-bodied torsion springs are designed using the
sarne methods as for single-bodied torsion springs. Therate for a double-bodied torsion spring is equal to thesum of the rates for each component. For the same wirediameter, coil diameter and wire length, double-bodiedtorsion springs have rates four times those of single-bodied types. Double-bodied torsion springs should bedesigned so they are coiled out from the center ratherthan in from the ends (Figure 9-3).
Rectangular WireRectangular wire torsion springs have higher energy
storage capacities than similar round wire springs. Thegeneral comments on round wire torsion springs applyto springs with rectangular wire. In producing springs
Tablc 9-1. Maximum Recommended Bending .Stressesfor Helical Torsion Springs in Static Applica'tions.
M.lrtrid
Fr,*mi nf : Tcrdle,Slrqfh
$trr*r'&trcv ,{,tr}{ X r C o l ,
lf,frl:f*v,otl&,,*eeied SrcrF {2}
{lio Corrac'thn Frctori
Patented andCold Drawn
EO r00
Hardened and TemperedCarbon and LowAlloy Steels
85 100
Austenitic StainlessSteels and Non-Ferrous Alloys
60 80
t l) Also for springs without residual stresses.i2) Springs that have not been stress-relieved and which have bodies and
ends loaded in a direction that decreases the radius of curvature.
Fig. 9-3. Preferred Winding for Double-Bodied TorsionSprings.
Helical Torsion Springs
from rectangular wire, the wire cross-section distortsand becomes "keystoned" (Figure 94).The wire axialdimension br can be estimated from:
(9-r2)
When axial length is critical, keystone-shaped wire canbe purchased. This wire will have a near rectangularshape after coiling. The rate equation is:
br:bF#)
k : M / 0 = 6 * K
and the stress equation is:
t :#*"These equations are for springs wound either on edge oron flat (Figure 94).Stress correction factor Ks is slie[tlylower than for round wire and can approximated by:
(e- I3)
(9-r4)
(e-r5)
(9-r6)
Kgro :
Ksoo =
4C4 C l
4C4 C + 3
Sharp corners on rectangular wire cause stress concen-trations and should be avoided, while generous cornerradii of rolled wire reduce the wire cross sections suf-ficienfly to lower the rate.
Table 9-2. Maximum Recommended Bending Stresses(Kp Corrected) for Helical Torsion Springs inCyclic Applications.
lJf"fi$kl
fucml of Tnnr*le litrugth
ASTeil A23trild TIF t&l $trtudwscel A"5Tlil A?*rO sd he3,2,
Noil Sbo{- IM l snot-n t*O.
L$oe:. 8*. ' , Sbqt-ften*d*
105106
5350
6260
5553
&62
This information is based on the following conditions: no surging,springs are in the "as-stress-relieved" condition*Not always possible.
Fig. 94. Keystoned Cross Sections of Springs Wound onEdge and Flat
Wound On Edge Wound On Flot
F' - l -l ' l--Spring
Axis
-l-br
_l_l-
br
_i_
A"TFtfi8ArynffisH
Fig. I1-2. Load Deflection Curves for BeIIeviIIe Washerswith Various h lt Ratios.
hh = 0.4
hh = o.7
h/r = L4l
h/t = 2'83
Fig. 11-3. Mounting a Belleville Washer for DeflectionPast the FIat Position.
Fig. 114.
Bellevilte SPring Washers
Fig. 11-5. Comparison of S7 and Sn for Various De-flections, h lt Ratios and Diameter Ratios (RValues) of Belleville Washers.
L rTl-T.c
#W{ffiSrz Hil t l
gherI bd*
9-': -cil t1\
4eij/ /,
z t Srr Higher. l l
+
Fig. 11-6. Compressive Stress Constants for BellevilleWashers.
- 0.6a
2 .5
6 f R - r l" t = , ' l n R l 2 )
Highest Stessed RegionsWashers.
in Belleville
== , 1 .5od
(J
U6
ao; 1 . 0o
(J
@777777V,
SpringAxis
6 l - (R - l ) ' l=;"e-l *r-1
Assogb?ifi8,r,.fuffi*,ffirys ffi
Belleville Spring Washers
Fig. 11J. Tensile Jtress Constants fo, BellevilleWashers.
Determining an optimum solution to a belleville wash-er design problem is a trial and error process which mayhave to be repeated many times. A simple approach,designed to minimize the number of repetitions, ispresented below. All of the graphs are based on bellevillewasher designs with a ratio of O.D. to I.D. of 2 (R : Z).Designs that have R approximately equal to 2 have muu(-imum energy storage capacity.
The first step is to select an appropriate h/t ratio basedon the load, outside diameter and stress constraints giv-en. For example, (referring to Figure l lJ), assume thedesired load at flat is 1125 N and outside diameter is 76mm. A washer with an h/t equal to 1.41 would have amaximum stress S. of 1500 MPa. Loads at intermediatedeflection can readily be computed with the aid of Figurell-9. Material thickness is then determined from:
t=*Vmmetric
r : l /@Engr ish\ tg.z x to?(h/t )
-
Before finalizing a design based on these graphs, it isbest to check results using the equations, making finaladjustments as required. For cyclic applications, stresslevels Srr and Sp mustbe determined in order to estimatebelleville washer life.
r0.8
3 . 0
R l n R - ( R - l ) R" = - - r . F ; t 1 n - 1 y_ 0 .5R I
I l . = - |
+ ' R - r Il t l
T z :I l r r r
teccccC
eeC
eeeeeeeaeeaeeaeaaaaaa
) ' 2.O
E . -o l . )
(J
0 .51
Fig. 11-8.
3R
o.=o!oF\
q,
U)
iII
e ' Eg EFi E.8 f r6 ;
A I L
= =o oo ora) O
(n
c r o
v, tt)
Inads and Compressive Stresses Srfor Steel Belleville Washers with Various Outside Diameters and h/t Ratios.
Lood At Flot - (lbf) When R = 2
60 80 r00 200 400 6008001000 2000 4000 60008000
10080
60
1 . 5
1 . 0
eooqoo
I.tt
IIr 0 l
81I6l
sJ4 1
I3J''r l2 1
I.5 . {
l "l '
r . lI
751 r
I).s.1 l
I37J0.
I2s1 (III
II
2
I
I
).
€-60 l-30
40 120
3 0 F 1 5
2 0 F r o
r 5 F7.s
MetricEng l l sh 100
I200
160(
120
80
60
40
30
20
o
o
2
IoE
o
o
6 '5 .
4 .
J .
2 .
6 8I
6000 r800 I 000
4 6t l
400 600
Metric Units
.- r ,4b-�1F,-' - to- \ / t 32A (h/r)
Y
,4ffi1 9 . 2 x l o ? ( h 4 )
ffiAssogb?lfi 3;"fu$.*ff F$
L o o d A t F l o t - ( H ) W h e n R = 2
.a
ItFF!pbaa!|
-
aa!)
IaatttaaattII-
atI
Ch)ic! of Sress Level - StaticFor static applications, stress at the convex inner cor-
:er S. us,uellv controls the spring set point. Carbon steel3g{l€rrlle u-ashers will start to set when stress (S") reach-Es l,l[Fr of tensile strength (Table 1l-1). Set is removed:r nilost belleville washers, and in this case stress (S.)can:each T56c of tensile strength before additional set oc-J.rrs. These calculated stresses Eue considerably higher:hen actual stresses due to yielding. If washers are to bepiarcd or operated at elevated temperatures, these valuesmust be reduced.
Cbob of Stress Level - CyclicFor cy'clic applications, it is necessary to consider
both the stress level and stress range at the concaveconrcrs Srr and Sr2. Minimum and maximum stress mustbe evaluated at both Srr and Srz using a modified Good-man diagam. The location with the more severe condi-ions u'ill control washer life. The modified Goodman
Fig. 114. Load Deflection Characteristics for BellevilleWashers.
t f ootl .{ lo o/o ur uolpolreo
Deflecion ino/o ol f ' lf OO f t
lf a *'asher is supported and loaded at its edges so that it is deflected:c1'ond the flat position, then the greatest possible deflection can be:ru-lizcd. Since the load/deflection curve beyond the horizontal position:s slmmetrical with the first part of the curve, this chart has been
Bellevitle SPring Washers
diagram (Figure 11-10) illustrates fatigue strength forvarious thicknesses of carbon and alloy steel washers atHRC 47 to 49. (Use of this diagram is discussed on page27.) Shot peening increases fatigue strength while burrs,edge cracks and surface imperfections reduce it.
Stacks of Belleville WashersTo increase deflection or loads, belleville washers can
be used in series, parallel or a combination of series andparallel (Figure 1l-11). Deflection for a series stack ofidentical belleville washers is equal to the number ofwashers multiplied by the deflection of one, while theload is equal to the load of one washer. When bellevillewashers with an h/t ratio greater than 1.3 are used ina stack, the load deflection curve will be erratic as somewashers will snap through the flat position. To avoid thisproblem, the h/t ratio for each washer in a series stackshould not exceed 1.3.
0oCL
=soooo-
o
t2.o3
oa
p l v
+ ,o
:,. E ro
o-
E l
!oo
os:oo
J
90 too4I
o.:o
o-
3B
labeled at the right and top to be read upside down for deflectionsbeyond horizontal. Dotted lines extending beyond the chart indicatecontinuation of curves beyond flat.
AssogFlf;S&H*ffirns ffi
Belleville Spring Washers
Load on a parallel stack of identical belleville washersis equal to the load of one multiplied by the number ofwashers, while deflection is equal to the deflection ofone washer.
The load deflection curve for both series and parallelstacks has a hysteresis due to friction. Hysteresis (Fi-gure 1l-I2) is greater for parallel than series stacks andcan be minimized by lubrication. The energy absorbedby this hysteresis helps to dampen vibrations. By carefulselection, stacks can be designed with increasing, ap-proximately linear or decreasing rates. Stacked bellevillewashers must be guided either over a pin or in a tube.Hardness of the guides should be at least HRC 50 tominimize wear. Clearance between washer holes and pinor tube should be about 1,.5Vo of the relevant diameter.
Fig. 11-10. Modtfted Goodman Diagram for FatigueStrength of Belleville Washers. Carbon andAlloy Steel at HRC 47-49 with Set Removed but NotShot-Peened.
Lower Tensi le Stress (103 ps i )
50 r00 I 50 200 250
Figurc | l - 10 may be read as follols:A bclleville washer 0.8mm (0.030") thick may be expected to have a life of approximately 106 cycleswhen strcssed between either
0-820 MPa (0- I 17,000 psi)or 350-990 MPa (50,000-141.000 psi)
or 700- l 170 MPa (100.000-167,000 psi)and may be expccted to harre a lifc of approximarely l0: cycles when s!rcssed bctwcen either
0-740 MPa (0-105.000 psi)or 3 15-890 MPa (45.000- 127,000 psi)
or 630- 1050 MPa (90,000- 150.000 psi)
Table 11-1. Maximum Recommended StressS, for Bel lev i l le Washers inApplications.
TolerancesTo ensure proper clearance, it is good practice to
specify outside diameter with a minus-only tolerance andinside diameter with a plus-only tolerance. Recortmen-ded tolerances are shown in Table ll-2. Load tolerancesshould be specified at a test height. For belleville wash-ers with h/t < 0.25, reqommended load tolerances zue=, l1Vo. For washers with h/t > 0.25, use + lVo. Therecommended tolerance for washers made of nonferrousmaterials generally is + lsVo. Closer diameter and loadtolerances are available.
How to SpecifyA checklist to aid the spring designer in specifying belle-
ville spring washers is shown on the next page. For wash-ers with critical load requirements, it is recommended thata test fixture be developed.
Fig. 11-11. Stacks of Belleville Washers.
Fig. 11-12. Hysteresis in Stacked Belleville Washers.
Lll, m,(h-lD*rrn*tcr, mnn{in.}
*0.ffi
o.o
o
v,o
oF
oo
A=o
aAo
oF
o
o
I
f f iRR :Combinolion of
Series ond Porollel
CCCCCCCCC3
CCCCCCCC
C
C
C
CC
C
CC5CC
z
o
LevelsStat ic
up to 5 (0.197)s-10 (0.1924.3%)tL25 (0.3,94-0.984)2s-s0 (0.98f 1.%9)5L100 (r.%9-3.937)
-0.20 (-0.00E)-0.2s (-0.0r0)-0.30 (-0.012)-0.40 (-0.016)-0.50 (-0.020)
+0.20 (+0.00E)+0.25 (+0.0r0)+0.30 (+0.012)+0.40 (+0.016)+0.50 (+0.020)
Lower Tensile Stress (MPo)
Deflection (in.)
Dcflcction (mm)
xxx Co lcu lo tcd Cuwe
--Tcst Ten in Series
- Test Five in Porollcl
Carbon or Alloy Steel
Nonferrous andAustenitic Stainless Steel
Table 11-2. Belleville Washer Diameter Tolerances.
Based on R = 2, increased tolerances are required for lower R ratios.
ffiAssoget#Affieffiffis I
B.{leritle Spring VYasber Design Exampleln a clutch. a minimum pressure of 900 N (202 lbfl is
rcquired. This pressure must be held as nearly constantas possible *'hile the clutch facing wears down 0.80 mmr0.031-r. The washer O.D. is 76 mm (2.99). Materialsclected for this application is carbon steel HRC 47-50.
l. Base the load on a value l0Vo above minimum load,or 900 + lVo :990 N. Assume O.D./I .D. = 2.From Figure 1l-9, select a load deflection curve*'hich gives approximately constant load between 50and l$Vo of deflection to flat. Choose the hlt : l.4tcurve.
2. From Figure 1l-9, the percent load at 50Vo deflectionto flat is 88%.
3. Flat load is Pr:990/0.88 : 1125 N
4. Using Figure ll{ (follow line A-B from 1125 N toh/t = 1.41, and line B-C to approximately 76 mmO.D.), estimated stress is 1500 MPa.
5. From Table 1 1- 1 , maximum static stress without set re-moved is 120% of tensile strength. From Table l9-1,page 103, tensile strength at HRC 48 will be approxi-mately 1650 MPa. Yield point without residual stresswill be 1650 x L.20 = 1980 MPa. Therefore, stress1500 MPa is less than maximum stress of 1980 MPa.
6. Stock thickne I
' /-qDF; sS rS ' :
mv 132-4hh
7. h = 1.41 t = l .4 l x 1.37 : 1 .93 mmH : h * t = 1 .93 + L .37 =3 .30 mm
Belleville Spring Washers
Referring to Figure 11-9, the load of 990 N will bereached at fr = 5Wo of maximum available deflection.fr : 0.50 x 1.93 :0.97 mm deflection, or the load of990 N will be reached at Hr : fl - fr = 3.30 - 0.97: 2.33 mm height at load. To allow for wear, thespring should be preloaded at Hz : Hr - Af (wear):2.33 - 0.80: 1.53 mm height. This preload corre-sponds to a deflection fz : H - Hz : 3.30 - 1.53 :1.77 mm. Then fzlh : 1.77 11.93 : 0.92 or 92%.
Because 92Vo of h exceeds the recommended 85Vo(the load-deflection cunre is not reliable beyond 85Vodeflection when a washer is compressed between flatsurfaces), increase the deflection range to 4Vo to85%. From Figure ll-9, the percent load at 40Vo de-flection is78.5Vo and Pr : 990 + 0.785 = l26L N. Re-peat previous procedures 4, 5, 6, 7 and 8, and findthat fz + h x 100 : SlVo of h.
Final Desrgn Specifications :Material: AISI 1074, 1075O.D.: 76 +0.00, -0.5 mm (2.99 +0.00, -0.020)
I .D. :38 +0.040,-0.00 mm (1.50 +0.016,-0.00)Thickness t: 1.40 mm (0.055') ReferenceHeight h: 1.97 mm (0.078') ReferenceLoad: 990 N (223 lbf) + lVo at h1 : 1.18 mm (0.046')Compressive S.: 1216 MPa (185,000 psi) at fz ESVo of h
8 .
9.
Tensile Stresso f h
Tensile Stresso f h
Srr: -203 MPa (-29,500 psi) at f2 85Vo
Srz: +710 MPa (103,000 psi) at fz 85%
BELLEVILLE SPR,ING WASHER SPECIFICATION CHECKLIST
(Fil l in required doto only.) Speciol Informotion:
MoteriolMoximum operoting temperoture "c("F)Operoting environment
*
To be used in o stock (type)Working Conditions:
To work in mm(in.) diometer hole Reference Doto:
To work over diometer pinThickness mm(in.)
Lood N (1b0, I -N(lb0Outside Dio
Test height mm(in.)Inside Diomefer
Reloxotion o/oFree height
Required lifem(in. )
Required reliobility (see Section 4)h/r
Assog&r#&H*ffitr$ ffi
ruffiSpecial Spri ngWashers
" @
?
CC.
CCC
C
c.
#
eecta
IntroductironSpecial spring washers exert a thrust load and absorb
rrbration. reduce end play or apply pressure. The stateof stress is primarily bending, and most of the generaldesien considerations for flat springs (Section 12) apply.Spnng u'ashers are used in seals, bearings, motors ando$er rotating mechanisms, and because of the trendtosard miniaturization and compactness, demand fortbem is increasing.
The Associated Spring SPEC product line containsrnanv precision engineered wave, curved and fingerspring washers. These washers are made to close toler-ances and are available for immediate delivery. SelectingSPEC washer designs saves design time, avoids toolingcosts and is generally more cost-effective than specifyingcustom-designed parts.
Cured WashersCurved washers exert a relatively light thrust load and
are often used to absorb axial end play. Designers mustprovide space for diametral expansion in a direction per-pendicular to the A dimension (Figure l3-1). Bearingsurfaces should be hard to prevent washer corners fromscraping or digging in. The spring rate is approximatelylinear up to 80Vo of available deflection. Beyond 80Vo therate increases and is considerably higher than calculated.
Design equations for spring waJhers are similar tothose for simple beams, discussed in Section 12, exceptfor an empirical correction factor K. The equation forload is:
Special Spring Washers
Wave WashersWave spring washers, Figure 13-3, are especially use-
ful to apply moderate thrust loads when radial space islimited. The rate is linear between 20 and 8Vo of avail-able deflection. During forming, the washer is oftenstretched at the crest and trough of the waves. Washersthat are round in the free position go out-of-round whendeflected. Generally, a ratio of D/b = 8 is a good bal-ance between flexibility and load-carrying ability. Whenthe ratio of D/b is substantially lower than 8, a belle-ville washer is preferred.
The number of waves N" can be equal to 3 or moreand is usually selected on the basis of desired springrate, since spring rate is proportional to the number ofwaves raised to the fourth power, as:
Ebt3N.oD"f t = P l f = r / o t - , (13-s)
(t 3-4)
This formula is based on the equations for a simple beamwith correction factors based on experience to improveaccuracy. Stress is given by:
3zrPDs" - 4bttN.'
o = @^ (oD)'�K
O.D. is outside diameter in the flat positionequation for stress is:
(r3-r )
and the
(13-2)
The outside diameter of the washer changes upon de-flection and at flat is given by:
(I 3-s)
Do is outside diameter in the free position. The aboveequations for load, stress and diametral change are notexact solutions, but do provide useful engineering esti-mates for design purposes.
Fig. 13-2. Empirical Stess Correction Factor K forCurved Spring Washers.
3.0
2.5 3.0
Rofio O.D./1.D. At Flor
r : T *Correction factor K is shown in Figure l3-2. These equa-tions are approximate and yield satisfactory solutionsonly for deflections up to 80Vo of h where f is less thanli 3 of O.D. Associated Spring engineers should be con-sulted when clearances are critical or more exact designsrequired.
Fig. 13-1. Typical Curved Spring Washer.
F
4.0
Yo
oe 2.5
.9
oo
e, 2.0
4.03.52.O
\
\
\\
*Long oxis of the wosher in free position
Assog&'lfi3&ffi*ffiF$ @
Special Spring Washers
Finger WashersFinger washers, Figure 134, combine the flexibility of
curved washers and the distributed loading points ofwave washers. Load, deflection and stress are approxi-mated by assuming that the fingers are cantileversprings; then samples are made and tested to prove thedesign. Finger washers are used in static applicationssuch as applying an axial load to ball bearing races toreduce vibration and noise.
Choice of Operating Stress - StaticOperating stresses recommended for special spring
washers are similar to stress levels recommended for flatsprings and are shown in Table l3-l as a percent oftensile strength. Finger washers are generally producedin the stress-relieved condition. If favorable residualstresses are required, consult Associated Spring.
Choice of Operating Stress - CyclicMaximum recommended operating stresses for cyclic
conditions are shown in Table l3-2 for curved and wavewashers. Finger washers are not recommended for cyclicapplications.
TolerancesDimensional tolerances are similar to those on flat
springs. Load tolerances depend primarily on strip thick-ness tolerances and are listed in Table l3-3. All loadtolerances should be specified at a test heigttt and onlythose dimensions critical to spring function should havetolerances. Special tolerances are available for deman-ding applications.
Fig. 134. Typical Wave Spring Washer.
How to SpecifyThe specification checklist on the next page is provid-
ed as a guide to all critical aspects of special springwashers.
Special Spring lVasher Design ExampleA wave washer is needed to go into a 80 mm (3.15')
bore and over a 60 mm (2.362') shaft, to support a loadof approximately 500 to 550 N (112 to 124 lb) with 1.8mm (0.071') deflection. The application requires a steadyload and is therefore a static application. The washer willoperate in an ambient environment. AISI 1075 is thepreferred material.
Since deflection is comparatively large for a spring ofthis type, select the most flexible design - a three waveconfiguration.
Assume a 75 mm (2.953") outside diameter and a 64mm (2.520") inside diameter to fit the given conditions.This would make the mean diameter (D) 69.5 mm(2.736") .
1. Substituting these values in the load-deflection equa-tion, solve for thickness:
, : \ = l . 3 0 m mY (207,000) ( 1 .s) (5.t (3r0t
P , = = 530N2.4 D3
Fig. 134. Typical Finger Spring Washer.
CCCcCCCCCCCCCCcCC-
C
C
C
C
C
C
C
C
3c5cCI
&D,
'-l l'-ph\-b
,* i l . -+: +.:+
h = H - t
Operating S/ressWashers in Static
Table 13-1. Maximum RecommendedLevels for Special SpringApplications.
Table 13-2. Maximum Recommended Operating StressLevels for Steel Curved and Wave Washersin Cyclic Applications.
Finger washers are not generally supplied with favorable resid-ual stresses.
This information is based on the following conditions: ambient environ-ment, free from sharp bends, burrs, and other stress concentrations.AISI 1075
Pcreent of T,mih Strerylh
H# Assos&tfi8 /fu H#,ffirp$
l. Set the maximum stress at solid at 8Vo of tensilesuenglh. Steel with a hardness of HRC 49 has a ten-sile strength of 1725 MPa (250,000 psi) (Table l3-1 andFigure 3-6, page 2l). \Vo of 1725 MPa is 1380 MPa.Solve for deflection at that stress. Using the equation:
f _ e.6 pPsD _ (9.6x69.t'�(1380x64)r r = f f i -
f, = 2.39 mm
Tablc 13-3. Load Tolerances for Special SpringWashers.
Special Spring Washers
Deflection to load of 1.8 mm is 75% of deflection tosolid, which is satisfactory. Diameter in the deflectedposition:
Do'=ff i :
Do': 75.1 mm
There is adequate clearance.
finat Dexf,gn Specifications:
Material: AISI 1075O.D.: 75 *,0.2 mm (2.953 + 0.008)I.D.: S,!, + 0.2 mm (2.520 <- 0.008)Thickness t: 1.30 mm (0.055 'r 0.002)
H: 3.69 mm (0.145') ReferenceLoad P1: 530 N + lTVo (119 lbf + l7Vo)
H,: 1.89 mm (0.074')
SPECIAL SPRING WASHER SPECIFICATION CHECKLIST
(Fil l in required doto only.)
Type of Wosher:
Curved wove
Speciol
Mqximum operoting temperoture ,"c('F)
f inger designerOperoting environmeni
recommendotionReference
Thickness
Moteriol:Working Conditions:To work in mm(in.) diometer hole Outside diometer mm(in.)To work over rm(in.) diometer pin Inside diom
I Lood N(lb0 + -N(lboi Test height mm(in.)
Required reliobility (see Section 4)
Describe one cycle
0.r-1.0 (0.0044.03e)
0.1-0.25 (0.004{.010)0.2il.30 (0.0104.012)0.H.5 (0.0124.020)0.5-1.0 (0.020{.039).1.G2.0 (0.039-0.079)
33252015t2
Assog&'ifi8/&,H*ffisu ffi
