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“Knowledge is such a treasure which cannot be stolen”

“Invent a New India Using Knowledge”

है”ह”ह

IS 12511-1 (2004): Springs - Disc Spring, Part 1: DesignCalculation [TED 21: Spring]

IS 12511 (Part 1) :2004

W+

wmfa~vff%m

( ma-i- jqtkm )

Indian Standard

SPRINGS — DISC SPRING

PART 1 DESIGN CALCULATION

(First Revision)

ICS21.160

!

,(3 BIS 2004

IBUREAU OF INDIAN STANDARDS

IMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

,.r-

September 2004 Price Group 9

Automotive Springs and Suspension Systems Sectional Committee, TED 21

FOREWORD

This Indian Standard (Part 1) (First Revision) was adopted by the Bureau of Indian Standards, after the draflfinalized by the Automotive Springs and Suspension Systems Sectional Committee had been approved by theTransport Engineering Division Council.

This standard was originally published in 1989. This revision has been undertaken due to revision of the basestandard on which it was based upon.

The following technical changes have been incorporated:

a) Scope is elaborated.

b) In the design formulae for single discs, load/deflection curves for springs with or without ground endsprovided.

c) Effect of friction on load/deflection characteristics provided.

d) A new clause on ‘SET’ is included.

Disc springs are conical-shaped annular discs which are capable of being loaded in axial direction. They maybesubjected either to steady or to fatigue loading. Disc springs can be used either as single discs, or as springassemblies consisting of discs piled on top of one another in the same direction, or as spring columns consistingof individual discs piled on top of one another in alternating directions, or as spring columns consisting of springassemblies piled on top of one another in alternating directions. Disc springs are manufactured either with orwithout seating faces.

The fatigue strength values and its finite life fatigue strength values given in Fig. 12 to Fig. 14 in this-standardwere determined by statistical evaluation of laboratory tests conducted on test machines with uniformly sinusoidalloading. In these tests, the effect of corrosion was eliminated by adequate lubrication and by carrying out testswithout any interruptions. These fatigue strength and finite life fatigue strength diagrams are plotted with asurvival probability of 99 percent. This means that, out of a large number of disc springs of one range of platethickness, irrespective of the other dimensions, the streng$hs specified will be attained by 99 percent of thesprings without suffering a vibratory fracture. It should be mentioned in this context that the fatigue strength datagiven by the spring manufacturers may well deviate from the values given here, and from one another, due to thevarious manufacturing methods which can be used.

This part deals with design calculation of disc spring, while Part 2 covers the requiremen~. In the preparation ofthis standard, assistance has been derived from DIN 2092:1992 ‘Design of conical disc springs’, issued by theDeutsches Institut fdr Normung (DIN).

The composition of the committee responsible for the formulation of this standard is given at Annex C.

For the purpose of deciding whether a particular requirement of this standard is cpmplied with, the final value,observed or calculated, expressing the result of a test or analysis, shall be rounded off in accordance with IS 2: 1960‘Rules for rounding off numerical values (revised)’. The number of significant places retained in the rounded offvalue should be the same as that of the specified value in this standard.

IS 12511 (Part 1) :2004

Indian Standard

SPRINGS — DISC SPRING

PART 1 DESIGN CALCULATION

(First Revision)

1 SCOPE

This standard (Part 1) specifies design criteria andfeatures of conical disc springs, whether as single discsor stacks of discs. It includes the definition of relevantconcepts as well as design formula, and covers thesetting and endurance life of such springs.

2 REFERENCES

The following standard contains provisions whichthrough reference in this text, constitute provision ofthis standard. At the time of publication, the editionindicated was valid. All standards are subject torevision and parties to agreements based on thisstandard are encouraged to investigate the possibilityof applying the most recent edition of the standardindicated below:

[s No. Title

12511 (Part 2) Springs — Disc spring: Part 2Specification (jlrst revision)

3 CONCEPT

Disc springs are conical-shaped annular discs whichare capable of being loaded in axial direction. Theymay be subjected either to steady or to fatigue loading.Disc springs can be used either as single discs, or asspring assemblies consisting of discs piled on top ofone another in the same direction, or as spring columnsconsisting of individual discs piled on top of oneanother in alternating directions, or as spring columnsconsisting of spring assembles piled on top of oneanother in alternating directions. Disc springs aremanufactured either with or without seating faces.

4 SYMBOLS

Follo\ving symbols and units shall apply (see Fig,. 1

and Fig. 2):

D,

.!!)i —

D<, —.

F ——gcsR

Outside diameter, mm:

Inside diameter. mm;

Mean coil diameter, mm;

Spring load of the springs stacked inparallel, allowance being made forfriction, N;

E=

F=

Fl, Fz, FJ...=

Fc =

F=ges

LO =

Ll, L2, Lj...=

Lc

N

R

whO

h’O

i

/0

Al

n

s

.

——

.———.—

——

.

——

————

———S,, S2,S3.. . —

s ——ges

Modulus of elasticity, N/mm2;Spring force of single disc, N;Spring forces associated with springtravels s,, S2,S3...,N;Calculated spring force in the pressedflat condition, N;Spring force of the spring assemblyassociated with spring travel s~~~,N;Length of unloaded spring column or ofunloaded spring assembly, mm;Length of loaded spring column or ofunloaded spring assembly associatedwith spring forces F], F,, F~ ... .. mm;Calculated length of sp~ing column orof spring assembly in the pressed flatcondition, mm;Number of stress cycles endured up tofracture;Spring rate, N/mm;Work of elastic strain, N/mm;Operand (theoretical spring travel downto the completely flat position); hO =l.– t, mm;

Initial cone height of springs withground ends (equal to free overallheight, 10– t), mm;

Number of single discs or springassemblies piled on top of one anotherin alternating directions to form acolumn;

Overall height of unloaded single disc,mm;

Creep, mm;Number of single discs stacked on topof one another in the same direction toform an assembly;

Spring, travel of single disc, mm;

Spring travels associated with springforces F,, F,, F~..,., mm;

Spring trave-l of the spring column or ofthe spring assembly not taking frictioninto account, mm; Recommendedmaximum value : S~C$= 0.75 (L,, – Lc)

IS 12511 (Part 1) :2004

t-

D,

I

i, iv 1

[0

9 I I Di

De1

LEVER ARM

110

Di t

1A Without Seating Faces IB With Seating Faces

All dimensicmsin millimetres.

FIG. 1 SINGLEDISC SPRINGAN~CROSS SECTIONLOCATIONSOFT}iEORETICALSTRESSES

SPRING FORCE ~I

ii 1

z F,w

I 1-

1I I g F

I“,’2 Lo

EtI L

(n L1

L2Lc

!

All dlmcnswss m mdlirnetres

FIG. 2 EXAMPLEOF SPRINGCOLUMN

t = Thickness of single disc, mlm;

t’ = Reduced thickness of single disccase of disc springs with seatingmm;

Wh,,WR = Coefficients of friction;

a = Theoretical stress, N/mnlz;

in thefaces,

Theoretical stresses at location OM, 1,II,111,IV, N/mm2;

Theoretical maximum stress of disc

spring subjected to fatigue loading, N/mmz;

Theoretical minimum stress of discsprings subjected to fatigue loading,N/mm2;

Stroke stresscorrelated to the work travelof disc springs subjected to the fatigueloading, N/mm2;

Maximum stress of fatigtre limit, N/mm2;

au = Minimum stress of fatigue limit, N/mm2;

‘H= Go – Gu = fatigue stroke strength, N/mmz;

L 1K2

KB

~

= Coefficients (see 5);

K~

CJ = ~ = Diameter ratio;I

P = Poisson’s ratio, ps 0.3 for spring steel; andAF = Relaxation.

5 FORMULAE AND COEFFICIENTS FOR THE!WNGLE DISC

5.1 When calculating for the single disc spring, it mustbe taken into account that the effective lever (moment)arms will be dependent on the mode of forceintroduction during the loading of the disc spring. Asa general rule, the force is introduced via location 1

IS 12511 (Part 1) :2004

and II1asillustrated in Fig,. lA(.see also 5.2). However,the force can also be introduced via shortenedlever arms, forexample, asillustrated in Fig. lB (seealso 5.3).

5.2 Single Disc Spring with Conventional ForceIntroduction

5.2.1 If the force is introduced via location I and 111,asillustrated in Fig. 1A, the calculation shall be made asfollows.

5.2.1.1 Spring force

5.2.1.2 Theoretical streses

4Eo,. — *x:[”K2(+-fi)-K31(’)l–~’x ,

– *x~[-K2(+-fi)+K31(’)4E% =

I-P*X ,

4Et2slo– —x—

“’-l-j.? K,x D:x; x~

[(2K3-K2)HJ+K31~~4E t’ s 1

~lv = — x—l–p’ KIx D: X;X;

,.(4)

[(2K3-K20+K31...(5)

NOTES

I Positive values are tensile stresses and negative values arecompression stresses. The stress IS,Vis of secondary importanceonly.

2 For coefficients K,, K1 and K,, see 5.4.

3 The value of + = 905495 N/mmz for high grade steel

with E = 206000 N/mmz.

5.2.1.3 Spring rate

5.2.1.4 Work of elastic strain

...(6)

[H)+’l ...(7)

5.3 Single Disc Spring with Force Introduction ViaShortened Lever Arms

The force is not introduced via location I and 111illustrated in Fig. 1A, but via shortened lever arms andthe equations featured in 5.2 no longer apply. In thecase of disc springs with seating faces, for example,Group 3 disc springs conforming to IS 12511 (Part 2),the force is also introduced via shortened lever arms(see Fig. lB). On these disc springs, the disc thicknesst is reduced by the manufacturer to the thickness t‘,inorder to attain the prescribed spring force F ats z 0.75hO.It can be obtained from the following formula:

t’= et

The factor’ =‘ depends on $ ratio (see Fig. 3).

5.4 Coefficients K,, K2 and K3 (see Fig. 4 and Fig. 5along with the table under Fig. 4)

6 CHARACTERISTIC OF A SINGLE DISCSPRING

6.1 The calculated characteristic (force/travel curve)of the single disc spring is not linear (see Fig. 6). Itsshape is a function of the ratio hO/t. The actualcharacteristic deviates only slightly from the calculatedcharacteristic in lower portion of the spring travel range(see Fig. 7).

6.1.1 Fors = ho the calculated spring force is:

F=<~x*l–pz K, XD: ...(8)

[-16-12K, =1.

6

~ 5+1 2———6-1 lnti

6.1.2 For s/hO >0.75, the actual characteristic alsodeviates increasingly from the calculated characteristic,because the disc springs begin to slip relative to eachother or to the base; this steadily reduces the length ofthe lever arm (see Fig. 7).

6.1.3 When determining the characteristics by precisionmeasurement, the reference length shall be thetheoretical unloaded spring length l., or the columnlength LO,respectively.

7 COMBINATION OF SINGLE DISC SPRINGS

7.1 Frictional Force

7.1.1 The frictional force on disc springs shall be taken

3

-7

IS 12511 (Part 1): 2004

I0.98

O*97

E

0.96

0.95

O*94

0.93

0.92

0.91

r 1 I I

0.2 0-4 006 0.8 1 1.2 1.4

ho/t ~

FIG. 3 VALUE OF e FORVARIOUS hJt RATIO

into account. It will be a function of the number of thesingle disc per spring assembly and of the number ofsprings or spring assemblies in spring column. Inaddition, the surface finish and lubrication may affectthe frictional force. Due to the friction, the load valuesare likely to vary and the average variation expectedis as under:

a) Single disc assembly : + 20/0 tO So/o

b) Double disc assembly : + 40/o to 60/0c) Triple disc assembly : + 60/0 to !)”/o

d) Quadruple disc assembly : + 8’%0to 12%

7.2 Spring Assembly

7.2.1 The spring assembly consists of single discsprings stacked on top of one another in the samedirection as shown in Fig. 8.

432.5

I26

1.8

1.6

–-

7.2.1.1 In case of n single discs stacked on top of oneanother in the same direction, ignoring friction, thefollowing applies:

F,~, =nx F ...(9)

s =sges . ..(10)

LO =lO+(n–l)t ...(11)

7.3 Spring Column

The spring column consists of single disc springs orspring assemblies piled on top of one another inalternating directions.

7.3.1 Spring column consisting of single discs is shownin Fig. 9.

7.3.1.1 In case of i single disc springs piled on top ofone another in alternating directions, ignoring friction,the following applies:

4

IS 12511 (Part 1): 2004

1 2 3 4 5

DIAMETER RATIO b ~

()tizK,=! 57T~+l 2—.. —

s-l /n.Fj

6 KL Kz KB 6 K1 Kz KB

1.2 0.29 1.02 1.05 2.7 0.77 1.37 1.631.3 0.39 1.04 1.09 2.8 0.78 1.39 1.671.4 0.46 1.07 1.14 2.9 1.41 1.701.5 0.52 1.10 1.18 3.0 1.43 1.741.6 0.57 1.12 1.22 3.1 0.79 1.45 1.771.7 0.61 1.15 1.26 3.2 1.46 1.811.8 0.65 1.17 1.30 3.4 1.50 1.87

0.67 1.20 1.34 3.6 0.80 1.54 1.94;:: 0.69 1.22 1.38 1.57 2.002.1 0.71 1.24 1.42 ::! 1.60 2.072.2 0.73 1.26 1.45 4.2 0.80 1.64 2.132.3 0.74 1.29 1.49 4.4 1.67 2.192.4 0.75 1.31 1.53 4.6 0.80 1.70 2.252.5 0.76” 1.33 1.56 4.8 0.79 1.73 2.312.6 0.77 1.35 1.60 5.0 1.76 2.37

FIG. 4 COEFFICIENTK, AS A FUNCTIONOFDIAMETERRATIO6

5

IS 12511 (Part 1): 2004

2.5

2.4

2.3

2.2

2.1

2

i1.9

1.8

1.7

‘: 1.6+

1.2

1.1

11 2 3 L 5

DIAMETER RATlO b ~

()~ .~x~x ~-l , ~ .~x~x?l-l—-

2n /“.8 1“.8 3 ~ /“.8 -z-

FIG. 5 COEFFICIENTSKz ANDKS AS A FUNCTIONOFDIAMETERRATIO5

--j

6

IS 12511 (Part 1): 2004

LIMIT FOR SPRINGS CONFIRMING TO IS 12511 I

1.4

1.3

1.2

1.1

1

0.9

0.8

I 0.7

$“ 0.6u-

0.5

0.4

0.3

0.2

0.1

010 0.25 0.5 O*75

SlhO ~

1

FIG. 6 BEHAWOUR OF CALCULATEDSPRINGCHARACTERISTICFORVARIOUShoit RA~10

7

IS 12511 (Part 1): 2004

8000

6000

Loot

200(

I I I I I I

DISC SPRING B50 GR2-IS 12511

I I I I IMEASURED CHARACTERISTIC

I I I I ICALCULATED CHARACTERISTIC

zw

/

ii!co// In ~~ UJo 1-

4 w/

! sI 0

u

0 0.2 0.4 0.6 0.8 1 1.2 I.L

SPRING TRAVEL s,mm~

FIG. 7 CALCULATEDANDMEASUREDCHARACTERISTICOFA DISC SPRING

I

FIG. 8 SPRINGASSEMBLY(SINGLEDISC SELECTEDONToP OFONEANOTHER

I

IN SAMEDIRECTION)

FIG. 9 SPRINGCOLUMN(SINGLEDISC PILEDON ToP OFONE ANOTHERIN ALTERNATINGDIRECTION)

8

F,,, = F ...(12)

s =iXsges ...(13)

LO ~=ix[ ...(14)

7.3.2 Spring column consisting of spring assembliesis shown in Fig. 10.

7.3.2.1 In case of i spring assemblies piled on top ofone another in alternating directions, each assemblyconsisting of n single springs, ignoring friction, thefollowing applies:

Fge, =nx F ...(15)

s =ixsges ...(16)

LO =i[lO+(n-l)t] ...(17)

7.4 Different Arrangements of Single Disc Springs

7.4.1 Disc spring can be combined to form springcolumn in many different ways.

7.4.2 In the case of disc springs with a ratio ho/t ofmore than 1.3 approximately, it is likely that the degreeof flattening of individual disc springs in the springcolumn will vary from spring to spring.

7.4.3 In case of single disc springs stacked on top ofone another in the same direction, the spring force foran equal spring travel is directly proportional to thenumber of single disc springs in the assembly (seeFig. 11A and Fig. 1lB).

7.4.4 In the case of single disc springs piled on top ofone another in alternating directions, the spring travelfor an equal spring force is directly proportional to thenumber of single disc springs (see Fig. 11A andFig. 1lC).

7.4.5 In the case of spring assemblies piled on top ofone another in alternating directions (see Fig. 11D), thespring force will increase with the number of individualdisc springs per spring assembly and the spring travelwill ticrease with the number of individual disc springsper spring assembly, and the spring travel will increasewith the number of spring assemblies.

IS 12511 (Part 1) :2004

7.4.6 When single disc springs of different thicknessesare combined to forma spring column (see Fig. 11E),a characteristic curve with a steep slope can beobtained. The same effect can be achieved by usingsingle disc springs, all of the same thickness combinedinto spring assembly with an increasing number ofsingle disc springs per assembly and piled on top ofone another to form a spring column (see Fig, 1lF).However, in case of these last two combinations, themaximum permissible stress of the springs must betaken into account for portion 1 and 2 of the springcolumn, and the clear height hOin the disc spring mustbe altered or any exceeding of the spring travels = 0.75 hOmust be avoided by appropriate measure(spacer rings, stepped guide pins).

NOTE — The frictional force has not been taken into accountin Fig. 11A to Fig. 1IF.

8 EFFECT OF FRICTION ON LOAD/DEFLECTION CHARACTERISTICS

When designing springs, friction shall be accountedfor. The associated load component is a function ofthe number of single discs or elements making up astack of springs. In this regard, surface finish andlubrication are also of relevance.

8.1 Springs Stacked in Parallel

8.1.1 In the case of springs stacked in parallel, frictionalforces act between the conical contact surfaces of theindividual elements (factor WJ, and between thepoints of loading designated I and III and the contactsurfaces of the flat plates between which the spring iscompressed (factor WJ. Such forces have the effectof increasing the spring load when the spring is loadedand decreasing it when the load is removed. The load/deflection characteristic shall be calculated using thefollowing equation:

FWR =Fxn

l* W~(n-l)*W~ ...(18)

—

FIG. 10 SPRINGCOLUMNCONSISTINGOFSPRINGASSEMBLIES(SPRINGASSEMBLIESPILEDONToP OFONE ANOTHERINALTERNATINGDIRECTIONSTOFORMA SPRINGCOLUMN)

9

IS 12511 (Part 1) :2004

where

F =spring loaddetermined inaccordance withequation 1;

n = number of elements making up the stackof springs;

W~ = factor to account for inter-surface friction(see Table 1);

W~ = factor to account for edge friction (see Table1);

— = indicates the loaded state; and

+ = indicates the unloaded state.

Table 1 Values of Friction for VariousGroups of Springs

(Clause 8.1. 1)

SI Spring Series WM WRNo.

i) (2) (3) (4)

i) A 0.005-0.03 0.03-0.05ii) B 0,003-0.02 0.02-0,04iii) c 0.002-0.015 0.01-0.03

The equation (18) also accounts for the frictionalbehaviour of a single disc.

8.1.2 Within permissible tolerances, the actual springwill deviate from the geometrically ideal form. In thecase of springs stacked in parallel, such inevitabledeviation results in an actual load/deflection curve thatis different from the theoretical curve, particularly inthe lower range of the curve.

8.2 Springs Stacked in Series

8.2.1 In the case of multiples of springs stacked inseries, the non-uniform load distribution between thesingle discs making up each element results in relativetransverse displacement,which again results in bearingforces along the mandrel that are too high. Such forcesresult in frictional loss, particularly at the ends of thespring when it is deflecting. The satisfactory methodof dealing with the actual load/deflection curvesobtained, which deviate significantly from thetheoretical curves, has not yet been devised. At present,it is only possible to accurately account for inter-surfacefriction, as follows:

F,,,~ = Fxn

]*wm (n-l) ...(19)

and

s = is)+es ...(20)

where

F= spring load determined in accordance withequation (1);

10

n = number of single discs making up eachelement;

i = number of elements making up the stackof springs;

WM = factor to account for inter-surface friction(see Table 1);

= indicates the loaded state; and+ = indicates the unloaded state.

8.2.2 In the situation when little friction is desired,single discs should be stacked in series.

9 CALCULATION OF DISC SPRINGS SUBJEC-TED TO STEADY LOADING OR TO SELDOMALTERNATING LOADING

9.1 Steady loading or seldom alternating loadingapplies:

a)

b)

In the case of disc springs which are stressedonly statically without any load alteration, and

In the case of disc springs which are subjectedonly to occasional load alteration at widelyspaced time intervals, and to less than 104alternating load cycles during their entireplanned service life.

9.2 Critical Cross-Section Location

9.2.1 In case of disc springs subjected to steady loadingor to seldom alternating loading, the maximum stresswhich occurs shall be taken, that is the theoretical stresscrl at the top inner rim of the single disc spring (seeFig. 1). This stress shall be calculated in accordancewith equation (2) if the face is introduced in theconventional way (see 5.2).

9.3 Permissible Stresses

9.3.1 In the case of disc springs conformingtoIS12511(Part 2) subjected to steady loading or to seldomalternating loading, the theoretical stress crl at the topinner rim shall not exceed the following guidelinevalues:

a) Fors = 0.75 hO: q = 2000 to 2400 N/mm*,and

b) For.rz= hO: 0[ = 2600 to 3000 N/mmz.

9.3.1.1 At higher stresses, the disc springs are liable toset unduly.

9.3.1.2 Disc spring conforming to IS 12511 (Part 2)can be stressed steadily or under seldom alternatingload conditions up to s = 0.75 hOwithout having tofear any setting effects; this means that as a generalrule, it will not be necessary to check their theoreticalstress, if they are loaded in this way.

9.3.1.3 When materials other than that listed in

IS 12511 (Part 1) :2004

rYLU)

I II I

I

SPRING TRAVEL ~

11A

I I I

SPRING TRAVEL ~

llB

11

IS 12511 (Part 1) :2004

UJ

E0IL

0zEQm

I I

I

SPRING TRAVEL ~

Ilc

/

SPRING TRAVEL~

llD

IS 12511 (Part 1): 2004

F3

F2

1

2

3

2

1

Fa= 3F1

F2=2F1

74

SPRING TRAVEL~

llE

n I

I

3

22

3

11

/

324 hO 6h0

SPRING TRAVEL ~

llF

FIG. 11 CHANGEINCALCULATEDCHARACTERISTICSBY ARRANGINGTHESINGLEDISC SPRINGSOFTHESPRING

,’

COLUMNINDIFFERENTWAYS ANDBY SELECTINGDisc SPRINGSOFDIFFERENTTHICKNESS

13

IS 12511 (Part 1) :2004

IS 12511 (Part 2) are used, it is advisable to consultthe spring manufacturer.

9.4 Examples of calculation are given in Annex A.

10 CALCULATION OF DISC SPRING SUBJEC-TED TO VIBRATORY LOADING

10.1 Vibratory loading applies in all cases of discsprings in respect of which the loading alternatescontinuously between the prestressing spring travels,and a spring travel Sz.Under the influence of the strokestress cr~, disc springs subjected to vibratory loadingcan be subdivided into groups depending on the lengthof their service life which in turn depends on the springdesign.

a)

b)

Disc springs with a practically unlimitedservice life shall be capable of withstanding2 x 10’ or more alternating load cycles withoutfracture.

Disc springs with a limited service life shallbe able to withstand a limited number ofalternating load cycles before fracture, withinthe range of fatigue strength.

104s N<2x10G

10.2 Critical Cross-Section Location for VibratoryFracture

10.2.1 In the case of disc springs subjected to vibratoryloading, the theoretical tensile stresses at the undersideof the single disc are determining. The cross-sectionlocation 11or III (see Fig. 12) with greatest theoreticalstress is the critical one for vibratory fracture. Which

of these two cross-section locations will in fact be theone concerned will depend to a great extent on theratios DJDi and hOlt.

10.2.2 The stress a,, and air, respectively are calculatedin case of conventional force introduction (see 5.2):

a) In accordance with equation (3) for cross-section location II; and

b) In accordance with equation (4) for cross-section location 111.

IS 12511 (Part 2) lists the theoretical maximum tensilestresses at the underside of the standardized single discspring for s = 0.75 hO; therefore an approximateevaluation of the theoretical maximum stresses forthese springs at other spring travels is possible byinterpolation.

Chain-dotted lines depict the example conformingto B-1.1.

10.3 Minimum Prestressing Spring Travel forAvoiding Incipient Cracks

Disc springs subjected to vibratory loading shall beinstalled with prestressing spring travel of at leastSt= 0.15 hOto 0.20 hOin order to prevent the occurrenceof incipient cracks at the cross-section location I(see Fig. 1) as a result of internal tensile stresses fromthe setting process,

10.4 Permissible Loadings and Permissible Rangeof Spring Travel

10.4.1 Fatigue Strength Va[ues and Finite L&e FatigueStrength Values

1.4, I I I I I I I1.2 ‘ I

1

0.8

0.6 ~

0.2”1.4 1.6 2 2.4 2.8 3.2 3.6

8= De/Di~

Chain dotted lines depict the example conforming to B-1.1

FIG. 12 CRITICALCROSS-SECTIONLOCATIONFORTHEVIBRATINGFATIGUEINCASE OFGROUPDISC SPRINGCONFORMINGTO IS 12511 (Part 2) [see FIG. 1A]

14

4

1 ANDGROUP2

IS 12511 (Part 1): 2004

10.4.1.1 Figure 1lC to Figure 1lE were drawn on thebasis of statisticalevaluation of laboratory tests on testingmachines with a uniform sinusoidal loading, assuminga survival probability of 99 percent. The graphs applyto single disc springs and to spring columns with i <6single disc springs piled on top of one another inalternating directions, working at standard roomtemperature, with a surface-hardened and impeccablymachined inner or outer guide, and a minimumprestressing spring travel s,= 0.15 hOto 0.20 hO.

10.4.1.2 In order to avoid any unnecessary reductionin the length of service life, the disc springs must beprotected from mechanical damage or other potentiallyharmful outside influences.

10.4.1.3 In actual practice, it must be borne in mind thatthe mode of stressing deviates in many cases from anapproximately sinusoidal vibration. In the case of shock,such as alternating loading and as a result of naturalvibration, the length of service life maybe reduced.

10.4.1.4 The values of the graphs shall only be used inconjunction with appropriate safety factors in suchcases of loading. If necessary, the spring manufacturershould be consulted.

NOTES1 In the fatigue limit and finite life fatigue strength diagrams(Fig. 13 to Fig. 15), guideline values for the fatigue stroke

strength o,+for N> 2 x 1(Fand ibr the finite life fatigue strengthfor N= 10sand N= 5 x 10sas a function of the minimum stressau, are specified for disc springs subjected to vibratory Ioadhrg.Intermediate values for other load cycle number can beestimated.

2 There are no reliable and satisfactory fatigue strength valuesavailable today for disc springs made from material other thanthose specified with IS 12511 (Part 2) and for spring columnswith i> 6, or consisting of multiple-stacked single disc springs,and also in respect of other unfavorable influences which canalso be of thermal or chemical nature. On request, the springmanufacturers can provide guidance in such cases.

10.4.2 Determination of Permissible Work Trmel

The spring travel Sz,must not exceed the correspondingvalue of the fatigue stroke strength crHor of thespecified finite life fatigue strength in accordance withFig. 13 to Fig. 15. In each case, the maximumcalculated tensile stress at the underside of theindividual disc spring shall be determined as a fimctionof the spring travel (see 10.2 and Fig. 1). From thebehaviour of the 10.4.2.1 the stroke stress oh which iscomprised between the prestressing spring travels, andstress curve plotted against the spring travel, theassociated stroke stress cr~can be read off for each worktravel, and compared with the fatigue strength diagramor the finite life fatigue strength diagram.

10.5 Examples of calculation are given in Annex B.

LOODLLZI

800 ‘o$“

<- /

600

/

200

n

“o 200 400 600 800 1000 N/mm2 140(

MINIMUM STRESS au —

FIG. 13 FATIGUESTRENGTHANDFINITELIFEFATIGUESTRENGTHDIAGRAMFORDISC SPRINGSCONFORMINGTO IS 12511 (Part 2) (FORf <1 mm)

15

IS 12511 (Part 1) :2004

I1400

N/mm*

Do 1200

c?1000

800

600

400

(-)

H I I I 1-AFrrrrn.

*. WI I A I A I Iw “’“ ‘J‘“‘1\e.fl&%14ii

o 200 Loo 600 800 1000 N/mmz 140C

MINIMUM STRESS LJu—

FIG. 14 FATIGUESTRENGTHANDFINITELIFEFATIGUESTRENGTHDIAGRAMFORDISC SPRINGS

CONFORMINGTOIS 12511 (Part 2) (FOR 1 mm< t<6 mm)

IN

0:

03u)u-)

ii!1-U)

m-m

1-0-)

1400

I mmz ‘

1200

1000

Loo

200

00 200 400 600 800 1000 N/mm2 1400

MINIMUM STRESS OU—

FIG. 15 FATIGUESTRENGTHANDFINITELIFEFATIGUESTRENGTHDIAGRAMFORDisc SPRINGS

CONFORMINGTO IS 12511 (Part 2) (FOR6 mm < ts 14 mm)

16

-“ . .‘-l

IS 12511(Part 1): 2004

ANNEX A

(Clause 9.4)

EXAMPLES OF CALCULATION OF DISC SPRINGS SUBJECTED TO STEADYLOADING OR TO SELDOM ALTERNATING LOADING

A-1 CHECK CALCULATION OF A SINGLEDISC SPRING

A-1,1 In case of disc spring conforming to IS 12511(Part 2) subjected to steady loading or to seldomalternating loading, it is, as a general rule, not necessaryto check the spring force and the stresses at theindividual disc by calculation. Such a check calculationcan however be carried out with the aid of the equationsfeatured in 5.2.

A-1.2 The dimensions of disc spring B40GR2 —IS 12511 (Part 2) are for instance (see Table 2):

D,= 40 mm, Di = 20.4 mm, t = 1.5 mm

/0=2.65 mmandhO=l.15mm

For a spring travel S2= 0.6 mm,

h,J .15=077.——— . ,t 1.5

‘2 -0.6—- G.0.4; :=0.2t.

ti=~=~. 1.96=2Di 20.4

From Fig. 4 and Fig. 5

K1 = 0.69, K,= 1.22, K,= 1.38

A-1.3 Spring force Fl; associated with spring travelS2,is given by equation (1),

F, = 905 495X1.54

x 0.41.69x402

[(0.77 - 0.4) (0.77 - 0.2) +1] =2 010 N

A-1.4 Critical Stress at Location I (see Fig. 1)

From equation (2),

q = 905 495x1.52

x 0.40.69x402

[-(1.22 (0.77- 0.2)- 1.38] = -1530 N/mm*

A-1.5 Spring Rate (see Table 2)

For SZ= 0.6 mm

From equation (6),

R = 905 495X0.53

0.69 X402

[(0.772 -3x 0.77x 0.4 + ix 0.42 +1]= 2520 N/mm

A-1.6 Work of elastic strain, for the spring travel fromOto 0.6 mm. From equation (7),

W=; X905495X1.5s

x 0.420.69x 402

[(.77 - 0.2)2 +1] = 660 N/mm

A-1.7 Spring Force in Pressed Flat Condition

From equation (8),

FC= 905 495X1.53

x1.15 =3180N0.69x402

A-1.8 Spring Travel

The spring travels correlated to various forces can beroughly determined from equation (8) in conjunctionwith Fig. 6.

Table 2 Dimensions of Disc Spring

(Clause A-1.2)

SI Disc Spring D= D, t h. 10 F s c1No.

mm mm mm mm mm N mm N/mmz(1) (2) (3) (4) (5) (6) (7) (8) (9) (lo)

0 A 40GR2-lS 40 20.4 2.25 0.9 3.15 6500 0.68 a. = 1340ii) B 40GR2-IS 40 20.4 1.5 0.15 2.65 2620 0.86 cm = 1150iii) c 40GR2-IS 40 20.4 1 1.3 2.3 1020 0.98 am = 1070

17

IS 12511 (Part 1): 2004

From Fig. 6,

for $ = 0.77= 0.75

the calculation ofs, relating to F, = 1500 N is as under:

&_ 1500—– — =0.47 and ; * 0.36,

‘ith FC 3180 0

s, = 0.36 hO= 0.36 x 1.15 =0.414 mm.

A-2 CALCULATION OF A SPRING COLUMN

A-2. 1 Assume that the spring forceof5000 N (staticloading) is required with spring travel of 10 mm. Thediameter of guide pin must not exceed 20 mm.

Hence F] = 5000 N

s,~,, = 10 mm

Di = 20.4 mm [for a 0.4 mm clearancebetween the disc spring and the guide pin[see IS 12511 (Part 2)]

A-2.2 Solution

Starting with the guide pin, a disc spring conformingto IS 12511 (Part 2) is to be selected. Three disc springsare featured for an inside diameter Di = 20.4 mm, oneeach of Type A, B and C.

A-2.2.1 The specified conditions (see 7.3 and 7.4) canbe met either:

a) With a column of disc spring A 40GR2 —IS 12511 (Part 2) single disc springs if thesingle disc spring is not exploited to its fullestextent, or

b) With a column of spring assemblies consistingeach of two disc springs B 40GR2 —IS 12511 (Part 2).

A-2.2.2 Calculation with Respect to the ConditionIndicated in A-2.2.l(a)

A-2.2.2.1 Spring force in the pressedflat condition

From equation (8),

FC= 905 495X2.253

xO.9 =841ON0.69x402

A-2.2.2.2 Spring travel

The spring travels correlated to various forces can beroughly determined from equation (8) in conjunctionwith Fig. 6.

~ 5000— = o.sg the spring travel of the

‘ith ~=8410

single disc relating to the spring forceof5000 N,SIs 0.57 x hO= 0.57 x 0.9 = 0.51 mm

A-2.2.2.3 Required number of single discs necessaryto achieve the total travel 10 mm.

s 10i=E=— = 19.6

s, 0.51

20 discs are therefore selected.

A-2.2.2.4 Dimensions of the spring column

In this case, the spring column has the followingdimensions:

a)

b)

c)

Overall height of single disc spring:10=3.15 mm;

Length of unloaded spring columnLO=ix10=20 x3.15 =63 mm.

Length of spring column loaded withF,=5000NL,= LO–S,W= 63–20 x 0.51 = 52.8 mm.

A-2.2.3 Calculation with Respect to the ConditionIndicated in A-2.2.l(b)

If two single disc springsB40GR2—[1S12511 (Part2)] are stacked on top of one another to form a springassembly with n = 2, and a number of these springassemblies are then piled on top of one another inalternating directions to form a spring column, therequirement can also be met.

A-2.2.3. 1 Spring force for the single disc, ignoring thefriction

n 2A-2.2.3.2Spring force in the pressed~at condition

From equation (8) and A-1.7,

FC=3180N

A-2.2.3.3 Spring trmel

The spring travels correlated to various forces can beroughly determined from equation (8) in conjunctionwith Fig. 6,

4 = = 0.79‘lth ~= 3180

The spring travel of single disc of Type B and of springassembly amounts to:

SI-0.71 x hO= 0.71 x 1.15 =0.82 mm.

A-2.2.3.4 The required number of i of spring assembliesnecessary to achieve the total spring travel 10 mm.

s1ges 10i.—. — = 12.2s, 0.82

-7

18

IS 12511(Part 1): 2004

13 spring assemblies are, therefore, selected.

A-2.2.3.5 Dimensions of the spring column

In this case, spring column has the followingdimensions:

a) Overall height of single disc spring,

10= 2.65 mm,

b) Overall height of a spring assembly consistingof two disc springs,

/O+t=2.65+ 1.5=4 .15mm,

c) Length of unloaded spring column,

10=i(lO+t) 13 X4.15 =54mm; and

d) Length of spring column loaded with

F18==5000 N

L,= Lo–S,g= = 54–(13 x 0.82) =43.34 mm.

This latter spring column is, therefore, shorter and theindividual disc is exploited to greater advantage.

The calculation of stress, spring rate and work of elasticstrain is analogous to the example in A-1.

Because of the odd number of spring assemblies in thisexample,one end of the column terminated with De, whilethe other end terminated with D1. As general rule, anendeavour must be made to let both ends of the columnterminate with D, as illustrated in Fig. 9 and Fig. 10.

ANNEX B

(Clause 10.5)

EXAMPLES OF CALCULATION OF DISC SPRING SUBJECTED TO VIBRATORY LOADING

B-1 CHECK CALCULATION OF A SINGLEDISC SPRING

B-1.1 The single disc spring calculated in A-1 shallbe subjected to vibratory stressing between theprestressing force F, = 1500 N and the spring forceFz = 2010 N. A check calculation must be made toascertain whether the disc spring works within thelimits of fatigue stroke strength.

B-1.2 In accordance with A-1, the values for discspring B 40GR2 — IS 12511 (Part 2) are as follows:

F,=1500N S1= 0.414mm

F2=2010N Sz= 0.6 mm

B-1.3 Theoretical Stress

From Fig. 12, it is observed that in case of disc spring

hOwith ~ = 0.766 and 5 = 1.96,the cross-section location

0111is critical in respect of vibratory feature.

a) From equation (4) with spring travel S10.414mm, the theoretical stress at the underside ofthe disc spring (location 111)

1.52G,”= 905495 x X0.276x0.51x

0.69 X 402

[(2x 1.38-1.22)x(0.77-0.138)+1.38]=

610 N fim2

b)

where

% 0414 ()276.–’K= “ ‘t

~ = 0.138; $ = 0.77; and2t

K] = 0.69; K2 = 1.22; Kj = 1.38.

From equation (4)with spring travel s,= 0.6mm, the theoretical stress at the under~ide ofdisc spring (location 111)

cm = 905495x1.52

0.69x402X0.4X0.51X

[(2x 1.38-1.22)x (0.77 -0.2)+ 1.38]=

850 N/mm2

B-1.4Assessmentof FatigueLimit

For the given work travel of disc spring, the values areas follows:

a) Theoretical maximum stress, CO= 850 N/mm*;

b) Theoretical minimum stress, au = 610 N/mm2;and

c) Stroke stress, (J~= CO– au = 240 N/mm2.

From Fig. 14 for Ou= cru= 610 N/mmz, the value ofO.= 1010 N/mm2.

19

IS 12511(Part 1): 2004

Thefigurestroke strength amounts to aH = co – cru=400 N/mmz.

Therefore, cr~< cr~that is the disc spring operates wellwithin its fatigue range.

B-2 CHECK CALCULATION OF A SPRINGCOLUMN CONSISTING OF SINGLE DISCSPRINGS AND SUBJECTED TO VIBRATORYLOADING

B-2.1 The spring column calculated in A-2 andconsisting of 20 single disc springs A 40GR2 —IS 12511 (Part 2) shall be subjected to vibratory loadingbetween the pressing forces F,= 1500 N and the springforce Fz=5000 N. The spring column shall be verifiedin respect of fatigue strength.

B-2.1.1 Spring Force in Pressed Flat Condition

From equation (8)

FC= 905 495X2.253

0.69 X 402xO.9=841ON

B-2.1.2 Spring Travel

From Fig. 6 corresponding to

q_ 1500— –— = 0.18 for Types A spring associatedFC 8410

with the spring force 1500 N,

s, s0.155 x AO=0.155 x 0.9= 0.14 mm,

Sz= 0.5 mm (see A-2).

B-2.1.3 Theoretical Stress

From Fig. 12, it is observed that in case of disc spring

hwith Q = 0.4 and 8 = 1.96, the cross-section

locatio~ 11of the spring is critical in respect ofvibratory fracture.

a) From equation (3) with spring travel s, =0.14 mm,

2.25201, = 905 495x

0.69x402X0.062X

[-1.22 (0.4- 0.03 1)+ 1.38] = 240 N/mm2

where

s, _ 0.14—– ~ = 0.062,;t = 0.031;t.

h~ = 0.4 and K, = 0.69;K2 = 1.22;KJ = 1.38.t

b) From equation (3) with spring travel, Sz =0.5 mm,

2.252on = 905 495x

0.69x402x 0.22x

[-1.22 (0.4 -0.1 1)+ 1.38] = 937 N/mm2

where

S2—=~=o.22,:=o.11t.

B-2.1.4 Analysis of Fatigue Limit

ah= GO– ISu= 937 – 240 = 697 N/mm* when the valueof Oucorresponding to CJO= 240 N/mm* is determinedfrom Fig. 14, it is observed cr~> c~.

The spring is situated within the region of finite lifefatigue strength of 5 x 105alternating load cycles.

In the case of a spring column consisting of 20 singledisc springs, the strength shown in the diagram are notquite attained (see 10.4.1). A slightly shorter servicelife must, therefore, be anticipated.

If the disc springs are to retain fidl fatigue strengthand the maximum stress CTO= 937 N/mm2 is to bemaintained then according to Fig. 14, allowing thesafety margin, the minimum stress amounts to

ciU-500 N/mm2

By interpolation, the required prestressing spring travelbecomes

500—xO.14=0.29mm

“ >240

B-2.1.5 Necessa~ Correlated Spring Force

Fl =0.35 XFC=0.35 x 8410 =2940N.

where

FC=8410N(seeB-2.l.2)

# = 0.35 (from Fig. 6 corresponding toc

s,—=~=0.32hO .

B-2.1.6 Permissible A4i&imum Stress, PermissibleSpring Travel and Correlated Spring Force

a)

b)

If the minimum stress CU= 240 N/mm2 isretained, the permissible maximum stressallowing for a safety margin can be read offfrom Fig. 14.

00= 800 N/mm2

Permissible spring travel can be obtained byinterpolation

S2<800—xO.5 = 0.43 mm937

.-

20

c) The correlated spring force can also becalculated with the help of Fig. 6.

S2 0.43 048

<’x= “

17z=0.51 XFC=0.51 x841 O=429ON.

B-3 CHECK CALCULATION OF SPRING COLUMNCONSISTING OF SPRING ASSEMBLIES ANDSUBJECTED TO VIBRATORY LOADING

B-3. 1 The spring column calculated in A-2 andconsisting of 13 assemblies of two disc springseach, B 40GR2 — IS 12511 (Part 2) shall be subjectedto vibratory loading between the prestressing forceF1 = 1500 N and the spring force Fz =5 000 N. Thespring column shall be verified in respect of fatiguestrength.

B-3. 1.1 Spring Force for the Single Disc Ignoring theFriction

F~=-= &=750N

n

B-3. 1.2 Spring Force in the Pressed Flat Condition

From equation (8) and A-1.7

FC=3 180N.

B.3.1.3 Spring Travel

The spring travels correlated to various forces can be

roughly determined(see Fig. 6) with

fl__ 750

IS 12511(Part 1): 2004

from equation (8) in conjunction

=07A~ 3180 ““-”

Spring travel of single disc spring for Type B

s,=0.17xh0 =0.17x 1.15 =0.20 mm,

Sz= 0.78 (see A-2)

B-3. L4 Theoretical Tensile Stress

In accordance with Fig. 12, cross-section 111is thedetermining one for vibratory fracture.

From equation (4)

OU= 308 N/mm* whens, = 0.20 mm, and

crO=1060 N/mmz when S2= 0.78 mm.

The service life of the disc spring wil[ be in the regionof 105alternating load cycles approximately.

B-3.1.5 Spring Characteristic

Because the spring column, consists of springassemblies each comprising two stacked spring, thatis, 26 individual disc springs in all, the values knownin the fatigue strength diagrams can only be used ifadequate safety margins are adopted (see 10.4.1).

The spring column consisting of single disc springA 40GR2 — IS 12511 (Part 2) is superior to the springcolumn consisting of two stacked spring B 40GR2 —IS 12511 (Part 2) in respect of length of service lifewhen subjected to vibratory loading.

21

IS 12511(Part 1) :2004

ANNEX C

(Foreword)

COMMITTEE COMPOSITION

Automotive Springs and Suspension Systems Sectional Committee, TED 21

Or~anizution

Tata Motors Ltd, Jamshedpur

Akal Springs Pvt Ltd, Ludhiana

All India Springs Manufacturers Association, Mumbai

Ashok Leyland Ltd, Chennai

Association of State Road Transport Undertakings, New Delhi

Central Institute of Road Transport, Pune

Central Mechanical Engineering Research Institute, Durgaprrr

Conventry Springs & Engineering Co Pvt Ltd, Kolkata

Controllerate of Quality Assurance (CQA) (OFV) VehicleFactory, Jabalpur

Gabriel India Ltd, Mumbai

Jai Parabolic Springs Ltd, Chandigarh

Jamna Auto Industries Ltd, Yamuna Nagar

Kemen Springs Pvt Ltd, Mumbai

Mack SpringsPvt Ltd, Thane

Mahindra& MahindraLtd, Nashik

Maruti Udyog Ltd, Gurgaon

Ministry of Heavy Industry & Public Enterprises, New Delhi

Research Designs & Standards Organization, Lucknow

Stumpp, Schuele & Somappa Pvt Ltd, Bangalore

The Automotive Research Association of India, Pune

Upper India Steel Manufacturing & Engineering Co Ltd,Ludhiana

Vehicle Factory, Jabalpur

BIS Directorate General

Representative(s)

SHRIA. G. PRADHAN(Chru”rman)SrrmK. GoP.umrtrsmA (Alternare)

GENERALMANAGER

Sma A. A. MIRCHANOANI

SHRIAPPALARAJUSmrr U. JmiusmA (A/terns/e)

Stim A. S. LAKRASmu P. M. Prum? (Alternate)

Smu N. R. KACHARSSmu P. S. Mmrou (Ahernare)

Drt J. BmrDrt T. K. PAm (Alternate)

SmuA. BAFNASmu A. S. Kow (Abnafe)

GENERALMANAGER

Smti K. SUNDARARAMANSmu S. K. Btmumx (Alternate)

Smu SUNILHAROLIYA

SHRID. S. GILLSwu B. K. KHANDELWAL(Alternate)

Smu P. K. MIRCHANDANI

SHSUD. V. SHARMA

Srou Wvnwm DESHMUKH%ru KAILASHJAT (Alternate)

SHSUD. N. DAVESruu G. VUAYAN(,41~ernate)

SHRSS. K. BHARUSrua R. K. TRIPATHI(Alternate)

JonmDIRECTOR(STANDARDS)ASSISTANTDESIGNENGINESR

SHRIB. S. MOOKHERJSESmu N. C. SRSNIVA~AN(Wtermue)

Srsras. RAJu

Swo R. P. ENGIRA

SHRSM. K. MISHRASmu R. LODWAL(Afterrrate)

SHSUK. K. VASHISTHA,Dhector & Head (TED)[Representing Director General (Ex-oficio)]

Menrber-SecretarySHSUP. K. SHAM

Director (TED), BIS

22

‘.1

Bureau of Indian Standards

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Amendments are issued to standards as the need arises on the basis of comments. Standards are also reviewedperiodically; a standard along with amendments is reaffirmed when such review indicates that no changes areneeded; if the review indicates that changes are needed, it is taken up for revision. Users of Indian Standardsshould ascertain that they are in possession of the latest amendments or edition by referring to the latest issue of‘BIS Catalogue’ and ‘Standards: Monthly Additions’.

This Indian Standard has been developed from Doc : No. ”TED 21 (340).

Amendments Issued Since Publication

Amend No. Date of Issue Text Affected

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