IS 12511-1: Springs - Disc Spring, Part 1: Design Calculation

2004·2 MB·English

by  Bureau of Indian Standards

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

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Indian Standard
SPRINGS — DISC SPRING
PART 1 DESIGN CALCULATION
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(First Revision)
ICS21.160

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,
(3 BIS2004
I
BUREAU OF INDIAN STANDARDS
I
MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG
NEW DELHI 110002

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 drafl
finalized by the Automotive Springs and Suspension Systems Sectional Committee had been approved by the
Transport Engineering Division Council.
This standard was originally published in 1989. This revision has been undertaken due to revision of the base
standard onwhich itwas based upon.
The following technical changes have been incorporated:
a) Scope iselaborated.
b) Inthe design formulae for single discs, load/deflection curves for springs with or without ground ends
provided.
c) Effect of friction onload/deflection characteristics provided.
d) A new clause on ‘SET’ isincluded.
Disc springs are conical-shaped annular discswhich arecapable ofbeing loaded inaxial direction. They maybe
subjected either to steady or to fatigue loading. Disc springs can be used either as single discs, or as spring
assemblies consisting ofdiscspiled ontop ofone another inthe samedirection, orasspring columns consisting
ofindividual discspiled ontop ofoneanother inalternating directions, orasspring columns consisting ofspring
assemblies piled on top of one another in alternating directions. Disc springs are manufactured either with or
without seating faces.
The fatigue strength values and itsfinite life fatigue strength values given inFig. 12to Fig. 14inthis-standard
weredetermined bystatisticalevaluation oflaboratorytestsconducted ontestmachineswithuniformly sinusoidal
loading. In these tests, the effect of corrosion was eliminated by adequate lubrication and by carrying out tests
without any interruptions. These fatigue strength and finite life fatigue strength diagrams are plotted with a
survival probability of 99percent. This means that, out of alarge number of disc springs of one range of plate
thickness, irrespective of the ot h er dimensions, the streng$hsspecified will be attained by 99 percent of the
springs without suffering avibratory fracture. Itshouldbementioned inthiscontext thatthefatigue strength data
given bythe spring manufacturers may welldeviate fromthevaluesgiven here, and from oneanother, due tothe
various manufacturing methods which canbeused.
This part deals with design calculation ofdiscspring, while Part2covers therequiremen~. Inthe preparation of
this standard, assistance has been derived from DIN2092:1992 ‘Design ofconical disc springs’, issued by the
Deutsches Institut fdr Normung (DIN).
The composition ofthe committee responsible forthe formulation ofthis standard isgiven atAnnex C.
For the purpose of deciding whether aparticular requirement ofthis standard is cpmplied with, the final value,
observed orcalculated, expressingtheresultofatestoranalysis,shallberoundedoffinaccordancewithIS2: 1960
‘Rules forrounding off numerical values (revised)’. Thenumber ofsignificant places retained intherounded off
value should bethe same asthat ofthe specified value inthis standard.
IS 12511 (Part 1) :2004
Indian Standard
SPRINGS — DISC SPRING
PART 1 DESIGN CALCULATION
(First Revision)
1SCOPE E= Modulus ofelasticity, N/mm2;
F= Spring force of single disc, N;
This standard (Part 1) specifies design criteria and
Fl, Fz,FJ...= Spring forces associated with spring
features of conical disc springs, whether as single discs
travels s,, S2,S3...,N;
orstacks ofdiscs. It includes the definition of relevant
Fc = Calculated spring force in the pressed
concepts as well as design formula, and covers the
flat condition, N;
setting and endurance life of such springs.
F= Spring force of the spring assembly
ges
2REFERENCES associated with spring travel s~~~N,;
LO = Length ofunloaded spring column orof
The following standard contains provisions which
unloaded spring assembly, mm;
through reference in this text, constitute provision of
Ll, L2,Lj...= Length of loaded spring column or of
this standard. At the time of publication, the edition
unloaded spring assembly associated
indicated was valid. All standards are subject to
with spring forces F], F,, F~.....mm;
revision and parties to agreements based on this
.
standard are encouraged to investigate the possibility Lc Calculated length of sp~ing column or
of spring assembly in the pressed flat
of applying the most recent edition of the standard
condition, mm;
indicated below:
N ——Number of stress cycles endured up to
[s No. Title
fracture;
12511 (Part 2) Springs — Disc spring: Part 2 R .—Spring rate, N/mm;
Specification (jlrst revision) w ——Work of elastic strain, N/mm;
hO .—Operand (theoretical spring travel down
3 CONCEPT
to the completely flat position); hO=

Disc springs are conical-shaped a nnular discs which l.– t, mm;

are capable of being loaded in axial direction. They h’O ——Initial cone height of springs with
may be subjected either to steady orto fatigue loading.
ground ends (equal to free overall
Disc springs can be used either as single discs, or as
height, 10– t), mm;
spring assemblies consisting of discs piled on top of i . Number of single discs or spring
one another inthe same direction, oras spring columns
assemblies piled on top of one another
consisting of individual discs piled on top of one
in alternating directions to form a
another inalternating directions, or as spring columns
column;
consisting of spring assembles piled on top of one /0 ——Overall height of unloaded single disc,
another in alternating directions. Disc springs are
mm;
manufactured either with or without seating faces. Al ——Creep, mm;
4 SYMBOLS n ——Number of single discs stacked on top
of one another inthe same direction to
Follo\ving symbols and units shall apply (see Fig,. 1
form an assembly;
and Fig. 2): s ——Spring, travel of single disc, mm;
—
D, Outside diameter, mm: S,, S2,S3... —Spring travels associated with spring
.!!)i —Inside diameter. mm; forces F,, F,, F~..,., mm;
D<, —.Mean coil diameter, mm; s ——Spring trave-lof the spring column or of
ges
F ——Spring load of the springs stacked in the spring assembly not taking friction
gcsR
parallel, allowance being made for into account, mm; Recommended
friction, N; maximum value :S~C$= 0.75 (L,,– Lc)
IS 12511 (Part 1) :2004
D,
De
t- 1
LEVER ARM
I
i, iv 1 1
[0 10
t
Di
9 I I Di
1A Without Seating Faces IB With Seating Faces
Alldimensicmsinmillimetres.
FIG. 1 SINGLEDISCSPRINGAN~CROSSSECTIONLOCATIONSOFT}iEORETICALSTRESSES
SPRING FORCE ~
I
1
ii
z F,
I I w
g F
I 1-
1
2 Lo
I“,’
E
t
L
I
(n L1
L2
Lc
!
Alldlmcnswss mmdlirnetres

FIG.2 EXAMPLEOFSPRINGCOLUMN
t = Thickness of single disc, mlm; au = Minimum stressoffatigue limit,N/mm2;
t’ = Reduced thickness of single disc in the = Go – Gu = fatigue stroke strength, N/mmz;
‘H
case of disc springs with seating faces,
L 1
mm; K2
Wh,,WR = Coefficients of friction; KB = Coefficients (see 5);
a = Theoretical stress, N/mnlz; K~ ~
Theoretical stresses at location OM,1,II,
CJ = ~ = Diameter ratio;
111,IV, N/mm2;
I
Theoretical maximum stress of disc P = Poisson’s ratio, ps 0.3forspring steel; and
spring subjected to fatigue loading, N/ AF = Relaxation.
mmz;
Theoretical minimum stress of disc 5 FORMULAE AND COEFFICIENTS FOR THE
springs subjected to fatigue loading, !WNGLE DISC
N/mm2;
5.1 When calculating for the single disc spring, itmust
Stroke stresscorrelated tothe work travel
betaken into account that the effective lever (moment)
of disc springs subjected to the fatigue
arms will be dependent on the mode of force
loading, N/mm2; introduction during the loading of the disc spring. As
Maximum stress of fatigtre limit, N/mm2; a general rule, the force is introduced via location 1
IS 12511 (Part 1) :2004
and II1asillustrated inFig,.lA(.see also 5.2). However, [H)+’l
the force can also be introduced via shortened ...(7)
lever arms, forexample, asillustrated in Fig. lB (see
also 5.3).
5.3 Single DiscSpring with Force Introduction Via
5.2 Single Disc Spring with Conventional Force Shortened Lever Arms
Introduction
The force is not introduced via location I and 111
5.2.1 Iftheforce isintroduced vialocation Iand111,as illustrated inFig. 1A,butviashortened leverarms and
illustrated inFig. 1A,the calculation shallbemade as the equations featured in 5.2 no longer apply. In the
follows. case of disc springs with seating faces, for example,
Group 3discsprings conforming toIS 12511(Part 2),
5.2.1.1 Spring force
the force isalso introduced via shortened lever arms
(seeFig. lB). Onthese discsprings, thediscthickness
tisreduced bythemanufacturer tothe thickness t‘,in
order toattaintheprescribed spring force Fats z 0.75
hO.Itcan beobtained from the following formula:
5.2.1.2 Theoretical streses
t’= et
4E *x:[”K2((’+)-fi)-K31
o,. —
The factor’ =‘ depends on $ ratio (see Fig. 3).
l–~’x ,
5.4 Coefficients K,, K2and K3(see Fig. 4 and Fig. 5
*x~[-K2(+(’-)fi)+K31
4E
along with the table under Fig. 4)
% =
I-P*X ,
–
6 CHARACTERISTIC OF A SINGLE DISC
4Et2sl SPRING
o– —x—
“’-l-j.? K,x D:x; x~ 6.1 The calculated characteristic (force/travel curve)
[(K23-K2)HJ~+~Kof th3e sin1gle disc spring isnot linear (see Fig. 6). Its
,.(4) shape is a function of the ratio hO/t. The actual
characteristic deviatesonlyslightly fromthecalculated
characteristic inlowerportion ofthespringtravel range
4E t’ s 1
~lv = — x— (see Fig. 7).
l–p’ KIx D: X;X;
[(K23-K20+K316.1.1 Fors =hothe calculated spring force is:
...(5)

F=<~x* ...(8)
NOTES l–pz6-K2, X1D:
I Positive values aretensile stresses andnegativevaluesare
[-1
compressionstresses.ThestressIS,Visofsecondaryimportance
only. 6
K, =1.
2 Forcoefficients K,, K1andK,,see5.4. ~ 5+1 2
———
3 Thevalue of + =905495 N/mmzforhighgradesteel 6-1 lnti
withE=206000 N/mmz. 6.1.2 For s/hO>0.75, the actual characteristic also
deviatesincreasinglyfromthecalculated characteristic,
5.2.1.3 Spring rate
because the disc springs begin to slip relative to each
other ortothe base;this steadily reduces the length of
the lever arm (see Fig. 7).
6.1.3Whendeterminingthecharacteristicsbyprecision
measurement, the reference length shall be the
...(6)
theoretical unloaded spring length l., or the column
length LO,respectively.
5.2.1.4 Work of elastic strain
7COMBINATION OF SINGLE DISC SPRINGS
7.1 Frictional Force
7.1.1 Thefrictional forceondiscsprings shallbetaken

3
-7
IS 12511 (Part 1): 2004
0.98
I
4
3
O*97 r 1 I I
2.5
I
E
26
0.96
1.8
0.95
1.6
O*94
–-
0.93
0.92
0.91
0.2 0-4 006 0.8 1 1.2 1.4
ho/t ~

FIG. 3 VALUEOFe FORVARIOUShJt RATIO
intoaccount. Itwill beafunction ofthe number ofthe 7.2.1.1 Incaseof nsingle discs stacked ontop of one
single disc per spring assembly and of the number of another in the same direction, ignoring friction, the
springs or spring assemblies in spring column. In following applies:
addition, the surface finish and lubrication may affect
F,~,=nx F ...(9)
the frictional force. Duetothefriction, theloadvalues
are likely to vary and the average variation expected sges =s ...(10)
isasunder:
LO =lO+(n–l)t ...(11)
a) Single disc assembly : +20/0tOSo/o 7.3 Spring Column
b) Double disc assembly : + 60/0
40/o to
The spring column consists of single disc springs or
c) Triple disc assembly : + 60/0to !)”/o spring assemblies piled on top of one another in
d) Quadruple disc assembly : + 8’%0to 12% alternating directions.
7.3.1Springcolumnconsisting ofsinglediscsisshown
7.2 Spring Assembly
inFig. 9.
7.2.1 The spring assembly consists of single disc
7.3.1.1 In case of isingle disc springs piled on top of
springs stacked on top of one another in the same
oneanother inalternating directions, ignoring friction,
direction as shown in Fig. 8.
the following applies:

4
IS 12511 (Part 1): 2004
1 2 3 4 5
DIAMETER RATIO b ~

(ti)z
K,=! 5
7T—~+.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 1.63
1.3 0.39 1.04 1.09 2.8 1.39 1.67
0.78
1.4 0.46 1.07 1.14 2.9 1.41 1.70
1.5 0.52 1.10 1.18 3.0 1.43 1.74
1.6 0.57 1.12 1.22 3.1 0.79 1.45 1.77
1.7 0.61 1.15 1.26 3.2 1.46 1.81
1.8 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 2.00
2.1 0.71 1.24 1.42 ::! 1.60 2.07
2.2 0.73 1.26 1.45 4.2 0.80 1.64 2.13
2.3 0.74 1.29 1.49 4.4 1.67 2.19
2.4 0.75 1.31 1.53 4.6 0.80 1.70 2.25
2.5 0.76” 1.33 1.56 4.8 0.79 1.73 2.31
2.6 0.77 1.35 1.60 5.0 1.76 2.37
FIG. 4 COEFFICIENTK, ASAFUNCTIONOFDIAMETERRATIO6

5