EN 16984:2016
(Main)Disc springs - Calculation
Disc springs - Calculation
This standard specifies design criteria and features of disc springs, whether as single disc springs or as stacks of disc springs. It includes the definition of relevant concepts as well as design formulae, and covers the fatigue life of such springs.
Tellerfedern - Berechnung
Die vorliegende Norm legt die Auslegungskriterien und Eigenschaften von Tellerfedern sowohl für Einzeltellerfedern als auch Tellerfedersäulen fest. Sie beinhaltet die Definition relevanter Begriffe sowie Gleichungen zur Berechnung und Angaben zur Lebensdauer dieser Federn.
Rondelles ressorts - Calculs
La présente norme spécifie les critères de conception et les propriétés des rondelles ressorts, que celles-ci se présentent sous la forme de rondelles ressorts simples ou assemblées. La présente norme comprend la définition des concepts applicables ainsi que des formules de conception, et traite de la résistance à la fatigue de tels ressorts.
Krožnikaste vzmeti - Izračun
Ta standard določa merila projektiranja in lastnosti posameznih krožnikastih vzmeti ter paketov krožnikastih vzmeti. Vključuje opredelitev ustreznih konceptov in formule projektiranja ter zajema čas obrabe teh vzmeti.
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
01-januar-2017
.URåQLNDVWHY]PHWL,]UDþXQ
Disc springs - Calculation
Tellerfedern - Berechnung
Rondelles ressorts - Calculs
Ta slovenski standard je istoveten z: EN 16984:2016
ICS:
21.160 Vzmeti Springs
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EN 16984
EUROPEAN STANDARD
NORME EUROPÉENNE
November 2016
EUROPÄISCHE NORM
ICS 21.160
English Version
Disc springs - Calculation
Rondelles ressorts - Calculs Tellerfedern - Berechnung
This European Standard was approved by CEN on 15 August 2016.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2016 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 16984:2016 E
worldwide for CEN national Members.
Contents Page
European foreword . 3
1 Scope . 4
2 Normative references . 4
3 Terms, definitions, symbols, units and abbreviated terms . 4
3.1 Terms and definitions . 4
3.2 Symbols, units and abbreviated terms . 4
4 Representation. 6
4.1 Single disc spring . 6
4.2 Disc springs stacked in parallel . 6
4.3 Disc springs stacked in series . 6
4.4 Disc spring diagram . 7
5 Design formulae for single disc springs . 7
5.1 General . 7
5.2 Test load . 7
5.3 Deflection factors . 8
5.4 Spring load . 8
5.5 Design stresses . 9
5.6 Spring rate . 10
5.7 Energy capacity of springs . 10
6 Load/deflection curve for a single disc spring . 10
7 Stacking of disc springs . 11
8 Effect of friction in load/deflection characteristic . 13
9 Design stresses . 14
10 Types of loading . 15
10.1 Static loading and moderate fatigue conditions . 15
10.2 Dynamic loading . 15
Bibliography . 16
European foreword
This document (EN 16984:2016) has been prepared by Technical Committee CEN/TC 407 “Cylindrical
helical springs made from round wire and bar - Calculation and design”, the secretariat of which is held
by AFNOR.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by May 2017, and conflicting national standards shall be
withdrawn at the latest by May 2017.
This European Standard has been prepared by the initiative of the Association of the European Spring
Federation ESF and is based on the German Standard DIN 2092 “Disc springs — Calculation”, which is
known and used in many European countries.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
According to the CEN-CENELEC Internal Regulations, the national standards organisations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
1 Scope
This standard specifies design criteria and features of disc springs, whether as single disc springs or as
stacks of disc springs. It includes the definition of relevant concepts as well as design formulae, and
covers the fatigue life of such springs.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
EN 16983:2016, Disc springs - Quality specifications - Dimensions
EN ISO 26909, Springs - Vocabulary (ISO 26909)
3 Terms, definitions, symbols, units and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in EN ISO 26909 apply.
NOTE Disc springs are annular coned elements that offer resistance to a compressive load applied axially.
They may be designed as single disc springs or as disc springs stacked in parallel or in series, either singly or in
multiples. They may be subjected to both static and fatigue loading, and may have flat bearings.
3.2 Symbols, units and abbreviated terms
For the purposes of this document, the following symbols, units and abbreviated terms apply
Table 1 — Symbols, units and abbreviated terms
Symbol Unit Description
D mm Outer diameter of spring
e
D mm Inner diameter of spring
i
D mm Diameter of centre of rotation
E MPa Modulus of elasticity (see EN 16983:2016)
F N Spring load
F , F , F . N Spring loads related to spring deflections s , s , s …
1 2 3 1 2 3
F N Design spring load when spring is in the flattened position
c
F N Spring load of springs stacked in parallel, related
ges
to spring deflection s
ges
F N Spring load of springs stacked in parallel, allowance being
ges R
made for friction
F N Test load for length L or l
t t t
K , K , K , K Constants (see 5.3)
1 2 3 4
L mm Length of springs stacked in series or in parallel, in
Symbol Unit Description
the initial position
L , L , L . mm Lengths of loaded springs stacked in series or in parallel,
1 2 3
related to spring loads F , F , F …
1 2 3
L mm Test length of springs stacked in series or in parallel
t
L mm Design length of springs stacked in series or in
c
parallel, in the flattened position
N Number of cycles to failure
R N/mm Spring rate
W N mm Energy capacity of spring
h mm Initial cone height of springs without flat bearings, h = l
0 0 0
− t
h' mm Initial cone height of springs with flat bearings, h′ = l − t′
0 0 0
i Number of disc springs or packets stacked in series
l mm Free overall height of spring in its initial position
l , l , l . mm Length of loaded spring related to spring loads F , F , F …
1 2 3 1 2 3
L mm Test length of spring
t
n Number of single disc springs stacked in parallel
P Theoretical centre of rotation of disc cross section (see
Figure 1)
s mm Deflection of single disc spring
s , s , s . mm Spring deflections related to spring loads F , F , F …
1 2 3 1 2 3
s mm Deflection of springs stacked in series or in parallel, no
ges
allowance being made for friction. Recommended
maximum value: s = 0,75 (L − L )
ges 0 c
t mm Thickness of single disc spring
′ mm Reduced thickness of single disc spring with flat bearings
t
(group 3)
w , w Coefficients of friction (see Table 3)
M R
D
Ratio of outer to inner diameter
e
δ=
D
i
µ Poisson’s ratio
σ MPa Design stress
σ , σ , σ , σ , σ MPa Design stresses at the points designated OM, I, II, III, IV
OM I II III
(see
IV
Figure 1)
σ MPa Maximum design stress in springs subject to fatigue
o
Symbol Unit Description
loading
σ MPa Minimum design stress in springs subject to fatigue
u
loading
σ MPa Fatigue stress related to the deflection of springs subject
h
to fatigue loading
σ MPa Maximum fatigue stress
O
σ MPa Minimum fatigue stress
U
σ = σ − σ MPa Permanent range of fatigue stress
H O U
V, V ′ mm Lever arms
4 Representation
4.1 Single disc spring
a) without flat bearings: b) with flat bearings:
group 1 group 3
group 2
Figure 1 — Single disc spring (sectional view), including the relevant points of loading
4.2 Disc springs stacked in parallel
The stack consists of n single disc springs stacked in parallel.
Figure 2 — Packet - Disc springs stacked in parallel
4.3 Disc springs stacked in series
The stack consists of i single disc springs stacked in series.
Figure 3 — Stack - Disc springs stacked in series
4.4 Disc spring diagram
Figure 4 — Example of disc springs stacked in series
5 Design formulae for single disc springs
5.1 General
The following formulae apply to single disc springs with or without flat bearings, where 16 < D /t < 40
e
or 1,8 < D /D < 2,5, and which are made of materials as specified in EN 16983:2016.
e i
In the case of other designs, it is recommended that the spring manufacturer should be consulted.
5.2 Test load
The test load of single disc springs or disc springs stacked in series, F , is designed for a deflection
t
s = 0,75 h . Single disc springs with flat bearings shall have the same test load for a test length L as
0 t
ones without, where the principal dimensions D , D and l are the same. Flat bearings have the effect of
e i 0
reducing the length of the lever arm. The increased load which results can be compensated by reducing
the thickness of the disc spring. The load/deflection curve of such springs deviates from those without
flat bearings, with the exception of the point at which the curves intersect, l .
t
Guideline values for the reduction in disc spring thickness as a function of dimensional series are given
in Table 2.
Table 2 — Guideline values for the reduction in disc spring thickness as a function of
dimensional series
Dimensional series A B C
t'/t 0,94 0,94 0,96
5.3 Deflection factors
D
e
(1)
δ=
D
i
δ−1
1 δ
(2)
K ×
δ+ 1 2
π
−
δδ−1 ln
δ−1
−1
lnδ
(3)
K ×
πδln
3 δ−1
K × (4)
π lnδ
CC
1 1
K=−+ + C (5)
42
where
t '
t
C = (6)
1 l tt' 3 5 l '3
× −+ × −+
4 tt 48 tt 8
C 5l
1 0
C −+11 (7)
2
32 t
t '
t
In the case of springs
...
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