ISO/DIS 16249

ISO/DIS 16249: Springs — Symbols

ISO/DIS 16249:2026(en)

ISO/TC 227

Secretariat: JISC

Date: 2026-01-14

Springs — Symbols

Ressorts — Symboles

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Contents

Foreword iv

Introduction v

1 Scope 1

2 Normative references 1

3 Terms and definitions 1

4 Composition of spring symbols 2

4.1 General 2

4.2 Basic characters 2

4.3 Subscripts 2

5 Creation of new spring symbols 3

5.1 General 3

5.2 Latin letters and Greek letters for basic characters 3

5.3 Upper case letters and lower case letters for basic characters 3

5.4 Latin letters and Greek letters for subscripts 3

5.5 Upper case letters and lower case letters for subscripts 4

5.6 Roman numerals for subscripts 4

6 Basic character and subscript components of spring symbols 4

6.1 Basic character components 4

6.2 Subscript components 6

7 Application symbols for helical compression springs 7

8 Application symbols for helical extension springs 9

9 Application symbols for helical torsion springs 12

10 Application symbols for flat springs 16

11 Application symbols for leaf springs 17

12 Application symbols for disc springs 19

Annex A (informative) List of interim symbols 22

Annex B (informative) Index of application symbols 24

Bibliography 28

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).

ISO draws attention to the possibility that the implementation of this document may involve the use of (a) patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a) patent(s) which may be required to implement this document. However, implementers are cautioned that this may not represent the latest information, which may be obtained from the patent database available at www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.

Any trade name used in this document is information given for the convenience of users and does not constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISO's adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.

This document was prepared by Technical Committee ISO/TC 227, Springs.

This second edition cancels and replaces the first edition (ISO 16249:2013), which has been technically revised.

The main changes are as follows:

— the symbols used in ISO 22705-1 have been incorporated in the table 1, 2 and the clause of 7;

— the symbols used in ISO 22705-2 have been incorporated in the table 1, 2 and the clause of 8;

— the symbols used in ISO 22705-3 have been incorporated in the table 1, 2 and the clause of 9;

— the symbols used in ISO 18137 have been incorporated in the table 1, 2 and the clause of 11;

— the symbols used in ISO 19690 have been incorporated in the table 1, 2 and the clause of 12;

A list of all parts in the ISO 16249 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A complete listing of these bodies can be found at www.iso.org/members.html.

Introduction

The standardized symbols representation of various spring types is intended to ensure clarity, uniformity, and consistency, thereby supporting effective communication between designers, manufacturers, and other involved parties.

The symbols are utilized in technical drawings, order forms, product descriptions, and software used in the design and manufacturing processes across various industries where spring components are specified or used, as well as in the preparation and revision of spring standards.

In this International Standard, existing spring symbols that have been used globally and customarily among several nations or regions are adopted without major alteration.

Existing spring symbols that have been used locally or in a limited nation/region have been redesigned in a logical way according to a particular rule for creating new spring symbols.

Springs — Symbols

1.0 Scope

This document establishes general principles for the creation of symbols of physical quantities, coefficients, and parameters for metal springs. It specifies the presentation of basic characters, subscripts, and application symbols for use in the field of helical compression springs, helical extension springs, helical torsion springs, flat springs, leaf springs and disc springs. This document is applicable to technical product documentation, especially for describing and ordering.

2.0 Normative references

The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 26909, Springs — Vocabulary

3.0 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 26909 and the following apply.

ISO and IEC maintain terminology databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https://www.iso.org/obp

— IEC Electropedia: available at https://www.electropedia.org/

3.1

basic character

main part of spring symbols representing physical quantities, coefficients, and parameters of springs

3.2

subscript

second part of spring symbols that follows basic characters in order to modify the physical quantities, coefficients, and parameters with respect to properties, feature, numbering, etc.

3.3

application symbol

combination of basic character and subscript

EXAMPLE Application symbol

4.0 Composition of spring symbols

4.1 General

Simple spring symbols consist of basic characters alone. Subscripts may be added to these basic characters to create more complex symbols.

Quantities and units used are specified in accordance with ISO 80000-1 and ISO 80000-4.

For the purpose of international applicability, all basic characters and subscripts should be derived from English words, and designations used in technical literature up to the time of publication of this International Standard are adopted as far as possible. Wide conformity of the symbols for springs has been attempted.

The characters that are permitted to be used for spring symbols are Latin letters (upper case or lower case), Greek letters (upper case or lower case), Arabic numerals and Roman numerals (upper case).

NOTE 1 As there is a risk of confusion with the Arabic numeral 0, the following Latin letters have not been specified: O (upper case letter), o (lower case letter).

NOTE 2 As there is a risk of confusion with Latin letters, the following Greek letters have not been specified: Α, Β, Ε, Ζ, Η, Ι, Κ, κ, Μ, Ν, Ο, ο, Ρ, Τ, Υ and Χ.

4.1.1 Basic characters

Basic characters consist of one upper case letter or lower case letter written in Latin or Greek alphabet.

The letter should be derived from the corresponding spring term or designation in English.

Variables shall be in italic typeface.

EXAMPLES D for coil diameter, τ for torsional/shear stress

4.1.2 Subscripts

Subscripts consist of one or more letters, digits, or letter/digit combinations of Latin letters, Greek letters, Arabic numerals or Roman numerals.

Subscripts should be as short as possible. A single letter/digit is preferable; however, when the symbol of a single letter/digit overlaps with an existing symbol or if it is difficult to describe the meaning with a single letter/digit, more than one letter/digit is acceptable.

The letters should be derived from the corresponding spring terms or designation in English.

EXAMPLE 1 D_e (e: one letter)

EXAMPLE 2 l_ST (ST: two letters)

EXAMPLE 3 d_max (max: three letters)

EXAMPLE 4 d_wire (wire: four letters taken from “wire”)

Subscripts that represent physical quantities shall be printed in italic typeface. Others shall be printed in roman typeface. Subscripts of Arabic numerals and Roman numerals should be printed in roman typeface.

EXAMPLE 5 L_B (B: coiling body: roman type)

EXAMPLE 6 σ _I (I: position I: roman type)

Up to two sets of subscripts are permitted in one spring symbol. In this case, they shall be separated by means of a comma (,) but without a space between them.

EXAMPLE 7 r_w,1 (w,1: effective working radius of leg 1)

5.0 Creation of new spring symbols

5.1 General

New spring symbols created in the future should follow the rules described below. The composition of the symbols should conform to Clause 4.

5.1.1 Latin letters and Greek letters for basic characters

Latin letters for basic characters are used when describing coefficients or quantities measured by devices or instruments, e.g. length, diameter, and load (including mean value).

Greek letters for basic characters are used when describing the quantities calculated, e.g. stress, deflection, and amount of loss.

5.1.2 Upper case letters and lower case letters for basic characters

Upper case letters for basic characters are used when describing quantities of the whole spring shape or function.

EXAMPLES 1 L for spring length, D for diameter of coil, F for spring load

Exceptionally, lower case may be used if it is customarily used in more than one countries.

EXAMPLES 2 l for length of beam, l for length of span

Lower case letters for basic characters are used when describing quantities of spring materials or partial dimensions.

EXAMPLES 3 d for diameter of wire, l for straight length at coil end

5.1.3 Latin letters and Greek letters for subscripts

Basic Latin letters and Greek letters shall be used for subscripts.

When subscripts are abbreviated terms, they shall be in Latin typeface only.

5.1.4 Upper case letters and lower case letters for subscripts

In the case of subscripts consisting of a single character, upper case letters should be used basically.

When a subscript consists of a single character and the upper case letter of this character is already used for an existing symbol, the lower case letter may be used.

When an upper case letter is used as a basic character, the corresponding subscript should be the upper case letter.

When a lower case letter is used as a basic character, the corresponding subscript should be the lower case letter.

In the case of subscripts consisting of more than one characters, lower case letters should be used basically.

5.1.5 Roman numerals for subscripts

Roman numerals shall be used for subscripts in upper case to describe direction or specific stress component.

EXAMPLE σ _I for the calculated or measured stress

6.0 Basic character and subscript components of spring symbols

6.1 Basic character components

Basic characters are shown in Table 1.

Table 1 — List of basic characters

No.	Symbol	Parameter	Compression	Extension	Torsion	Flat	Leaf	Disc
1.1	b	width or breadth	—	—	—	X	X	X
1.2	c	offset of leg	—	—	X	—	—	—
1.3	C	camber height	—	—	—	—	X	—
1.3	C	coefficients	—	—	—	—	—	X
1.4	D	spring diameter	X	X	X	—	—	X
1.5	d	wire diameter	X	X	X	—	—	—
		pin diameter	—	—	X	—	—	—
		eye diameter	—	—	—	—	X	—
		spring diameter	—	—	—	—	—	X
1.6	E	modulus of elasticity	X	X	X	X	X	X
1.7	e	perpendicularity	X	—	—	—	—	—
1.7	e	parallelism	X	—	—	—	—	—
1.8	F See Annex A	spring load or force	X	X	X	X	X	X
1.9	f	frequency	X	X	X	X	X	X
1.10	G	shear modulus	X	X	X	X	X	X
1.11	H	spring height	—	—	—	—	X	X
1.12	h	height	—	—	—	—	—	X
1.13	i	number of discs	—	—	—	—	—	X
1.14	k	coefficients	—	—	—	—	—	X
1.15	L	spring length	X	X	X	—	—	X
1.16	l	leg length	—	—	X	—	—	—
		beam length	—	—	—	X	—	—
		span length	—	—	—	—	X	—
1.17	M	moment or spring torque	—	—	X	X	—	—
1.18	m	hook opening	—	X	—	—	—	—
1.19	N	number of cycles	X	X	X	X	X	X
1.20	n See Annex A	number of coils	X	X	X	—	—	—
		number of leaves	—	—	—	—	X	—
		number of discs	—	—	—	—	—	X
1.21	p	pitch	X	X	X	—	—	—
1.22	R See Annex A	spring rate	X	X	X	X	X	X
1.23	r	radius	—	X	X	X	—	X
1.24	s See Annex A	spring deflection	X	X	—	X	X	X
1.25	T	temperature	X	X	X	X	X	X
1.26	t	thickness of spring	—	—	—	X	X	X
1.27	u	distance between the coils	X	X	X	—	—	—
1.28	V	length of lever arms	—	—	—	—	—	X
1.29	W	energy capacity	—	—	—	—	—	X
1.30	α	torsional angle of the spring	—	—	X	—	—	—
1.30	α	ratio of diameter	—	—	—	—	—	X
1.31	Δ	amount of change	X	X	X	X	X	X
1.32	δ	flank bending	—	—	—	—	X	—
1.33	ε	angle between fixed loading pin and moved loading pin	—	—	X	—	—	—
1.34	φ	bending angle on leg	—	—	X	—	—	—
1.35	γ	relative angle between two legs	—	—	X	—	—	—
1.36	ν	Poisson’s ratio	—	—	—	—	—	X
1.37	σ See Annex A	bending stress	—	—	X	X	X	X
1.38	τ See Annex A	torsional/shear stress	X	X	—	—	—	—

6.1.1 Subscript components

Subscripts are shown in Table 2.

Table 2 — List of subscripts

No.	Symbol	Parameter	Compression	Extension	Torsion	Flat	Leaf	Disc
2.1	A	spring end	—	—	—	—	X	—
		Inner of eye	—	—	—	—	X	—
		eye A	—	—	—	—	X	—
2.2	B	coiling body	—	X	X	—	—	—
2.2	B	eye B	—	—	—	—	X	—
2.3	c	solid or flattened position	X	—	—	—	—	X
2.4	d	mandrel or inner guide	X	—	X	—	—	—
2.4	d	design	—	—	—	—	X	—
2.5	E	assembled	—	—	—	—	X	—
2.6	e	external or outside	X	X	X	—	—	—
2.6	e	natural	X	X	X	X	X	X
2.7	f	flat bearings	—	—	—	—	—	X
2.8	G	combining	—	—	—	—	—	X
2.9	H	hook	—	X	—	—	—	—
2.9	H	alternative	—	—	—	—	—	X
2.10	h	deflection between two positions	X	X	X	—	—	—
2.11	i	inside or inner	X	X	X	—	X	—
2.11	i	initial	—	X	—	—	—	—
2.12	max	maximum	X	X	X	X	X	X
2.13	min	minimum	X	X	X	X	X	X
2.14	n	maximum test point	X	X	X	—	—	—
2.15	R	required	X	X	X	X	X	X
2.15	R	loading pin	—	—	X	—	—	—
2.16	r	scar	—	—	—	—	—	X
2.17	ST	straight	—	—	—	—	X	—
2.18	s	clean cut	—	—	—	—	—	X
2.19	t	total	X	X	—	—	—	—
2.19	t	test	—	—	—	—	X	X
2.20	w	effective working	—	—	X	—	—	—
2.21	wire	actual wire	X	X	X	—	—	—
2.22	0	free condition or unloaded	X	X	X	X	X	X
2.23	Arabic numerals	position or condition	X	X	X	X	X	X
2.24	Roman numerals	position or condition	X	X	X	X	X	X

7.0 Application symbols for helical compression springs

Application symbols for helical compression springs are shown in Table 3, and some sample symbols are shown in Figure 1 and 2.

Table 3 — List of application symbols for helical compression springs

No.	Symbol	Unit	Parameter
3.1	D	mm	mean diameter of spring (see Figure 1)
3.2	D_d	mm	mandrel diameter (inner guide)
3.3	D_e See Annex A	mm	outside (external) diameter of spring (see Figure 1)
3.4	D_i See Annex A	mm	inside diameter of spring (see Figure 1)
3.5	d	mm	diameter of wire
3.6	d_wire	mm	actual wire diameter
3.7	E	N/mm², MPa	modulus of elasticity
3.8	e₁	mm	perpendicularity (see Figure 2)
3.9	e₂	mm	parallelism (see Figure 2)
3.10	F See Annex A	N	spring load or force
3.11	F_c	N	spring load at solid length, L_c (see Figure 1)
3.12	F_n	N	spring load for the minimum test length, L_n (see Figure 1)
3.13	F₁, F₂, … See Annex A	N	specified spring loads for the specified spring lengths, L₁, L₂, … (see Figure 1)
3.14	f	Hz, s⁻¹	load cycle frequency
3.15	f_e	Hz, s⁻¹	natural frequency
3.16	G	N/mm², MPa	shear modulus
3.17	L_c	mm	solid length (see Figure 1)
3.18	L_n	mm	minimum acceptable test length for F_n (see Figure 1)
3.19	L₀ See Annex A	mm	free length (see Figure 1)
3.20	L₁, L₂, …	mm	specified spring lengths for the specified spring loads, F₁, F₂, … (see Figure 1)
3.21	N	—	number of repetition times to spring failure
3.22	N_R	—	required number of repetition times for testing
3.23	n See Annex A	—	active coils
3.24	n_t See Annex A	—	total number of coils
3.25	p	mm	spring pitch (see Figure 1)
3.26	R See Annex A	N/mm	spring rate
3.27	s See Annex A	mm	deflection of spring
3.28	s_c	mm	deflection of spring for the solid length, L_c (see Figure 1)
3.29	s_h	mm	deflection of spring (stroke) between two loads (see Figure 1)
3.30	s_n	mm	maximum test spring deflection for the spring load, F_n (see Figure 1)
3.31	s₁, s₂, … See Annex A	mm	specified spring deflections for the specified spring loads, F₁, F₂, … (see Figure 1)
3.32	T	°C	working temperature
3.33	u	mm	distance between the coils (see Figure 1)
3.34	ΔD_e	mm	enlargement of outside diameter of spring when loaded
3.35	τ See Annex A	N/mm², MPa	torsional/shear stress
3.36	τ_c	N/mm², MPa	torsional/shear stress for the solid length, L_c (see Figure 1)
3.37	τ_n	N/mm², MPa	maximum torsional/shear stress for the spring load, F_n (see Figure 1)
3.38	τ₁, τ₂, … See Annex A	N/mm², MPa	torsional/shear stresses for the specified spring loads, F₁, F₂, … (see Figure 1)

Key

D, D_e, D_i	diameters of spring
F_c, F_n, F₁, F₂	spring loads
L_c, L_n, L₀, L₁, L₂	spring lengths
p	spring pitch
s_c, s_h, s_n, s₁, s₂	deflections of spring
u	distance between the coils
τ_c, τ_n, τ₁, τ₂	torsional/shear stresses

Figure 1 — Symbols for helical compression spring

Key

e₁ perpendicularity

e₂ parallelism

Figure 2 — Symbols of perpendicularity and parallelism

8.0 Application symbols for helical extension springs

Application symbols for helical extension springs are shown in Table 4, and some sample symbols are shown in Figure 3 and 4.

Table 4 — List of application symbols for helical extension springs

No.	Symbol	Unit	Parameter
4.1	D	mm	mean diameter of spring (see Figure 3)
4.2	D_e See Annex A	mm	outside (external) diameter of spring (see Figure 3)
4.3	D_i See Annex A	mm	inside diameter of spring (see Figure 3)
4.4	d	mm	diameter of wire
4.5	d_wire	mm	actual wire diameter
4.6	E	N/mm², MPa	modulus of elasticity
4.7	F See Annex A	N	spring load or force
4.8	F_i See Annex A	N	initial tension force (preload) (see Figure 3)
4.9	F_n	N	maximum permissible spring force for the maximum permissible spring length L_n (see Figure 3)
4.10	F₁, F₂, … See Annex A	N	specified spring loads for the specified spring lengths, L₁, L₂, … (see Figure 3)
4.11	f	Hz, s⁻¹	load cycle frequency
4.12	G	N/mm², MPa	shear modulus
4.13	L_B	mm	body length when unloaded but subject to initial tension force (see Figure 3)
4.14	L_H	mm	spring hook length (see Figure 3)
4.15	L_n	mm	maximum acceptable spring length measured spring hooks inner radii for F_n (see Figure 3)
4.16	L₀ See Annex A	mm	free length (see Figure 3)
4.17	L₁, L₂, …	mm	specified spring lengths for the spring loads, F₁, F₂, … (see Figure 3)
4.18	m	mm	hook opening (see Figure 3)
4.19	N	—	number of repetition times to spring failure
4.20	N_R	—	required number of repetition times for testing
4.21	n See Annex A	—	number of active coils
4.22	n_t See Annex A	–	total number of coils
4.23	p	mm	spring pitch (see Figure 4)
4.24	R See Annex A	N/mm	spring rate
4.25	r	mm	bending radius (see Figure 3)
4.26	s See Annex A	mm	deflection of spring
4.27	s_h	mm	deflection of spring (stroke) between two loads (see Figure 3)
4.28	s_n	mm	maximum test spring deflection for the spring load, F_n (see Figure 3)
4.29	s₁, s₂, … See Annex A	mm	specified spring deflections for the specified spring loads, F₁, F₂, … (see Figure 3)
4.30	T	°C	working temperature
4.31	u	mm	distance between the coils (see Figure 4)
4.32	τ See Annex A	N/mm², MPa	torsional/shear stress
4.33	τ_i See Annex A	N/mm², MPa	initial torsional/shear stress (see Figure 3)
4.34	τ_n	N/mm², MPa	maximum torsional/shear stress for the spring load, F_n (see Figure 3)
4.35	τ₁, τ₂, … See Annex A	N/mm², MPa	torsional/shear stresses for the specified spring loads, F₁, F₂, … (see Figure 3)

Key

D, D_e, D_i	diameters of spring
F_i, F_n, F₁, F₂	spring loads
L_n, L₀, L₁, L₂	spring lengths measured between hook inner radii
L_B	body length when unloaded but subject to initial tension force
L_H	spring hook length
m	hook opening
r	bending radius
s_h, s_n, s₁, s₂	deflections of spring
τ_i, τ_n, τ₁, τ₂	torsional/shear stresses

Figure 3 — Symbols for helical extension spring

Key

p spring pitch

u distance between the coils

Figure 4 — Symbols for helical extension spring with distance between the coils (without load)

9.0 Application symbols for helical torsion springs

Application symbols for helical torsion springs are shown in Table 5, and some sample symbols are shown in Figure 5, 6, 7, 8, and 9.

Table 5 — List of application symbols for helical torsion springs

No.	Symbol	Unit	Parameter
5.1	c	mm	offset of leg (see Figure 7)
5.2	D	mm	mean diameter of spring
5.3	D_d	mm	mandrel diameter (inner guide) (see Figure 9)
5.4	D_e See Annex A	mm	outside (external) diameter of spring (see Figure 5)
5.5	D_i See Annex A	mm	inside diameter of spring (see Figure 5 and 6)
5.6	d	mm	diameter of wire (see Figure 5 and 6)
5.7	d_R	mm	diameter of loading pins (see Figure 8)
5.8	d_wire	mm	actual wire diameter
5.9	E	N/mm², MPa	modulus of elasticity
5.10	F See Annex A	N	spring load or force
5.11	F_n	N	spring load for the maximum test torsional angle and related leg length
5.12	F₁, F₂, … See Annex A	N	specified spring loads for the specified moments, M₁, M₂, …
5.13	f	Hz, s⁻¹	load cycle frequency
5.14	G	N/mm², MPa	shear modulus
5.15	L_B	mm	body length in axis direction (excluding legs) when unloaded (see Figure 5)
5.16	l	mm	length of leg (without considering working effect)
5.17	l_w	mm	effective working length of leg
5.18	l_w,1, l_w,2, ...	mm	effective working length of legs (see Figure 8)
5.19	l₁, l₂, ...	mm	length of leg segments (without considering working effect) (see Figure 5 and 6)
5.20	M	N · mm	spring torque or moment
5.21	M_n	N · mm	spring torque for the maximum test torsional angle and related leg length (see Figure 8)
5.22	M₁, M₂, …	N · mm	spring torques for the specified spring loads, F₁, F₂, … (see Figure 8)
5.23	N	—	number of repetition times to spring failure
5.24	N_R	—	required number of repetition times for testing
5.25	n See Annex A	—	number of coils
5.26	p	mm	spring pitch (see Figure 5)
5.27	R_M See Annex A	N · mm/rad, N · mm/degree	angular spring rate (increase of spring torque per unit angular deflection)
5.28	r	mm	bending radius
5.29	r_w	mm	effective working radius of leg
5.30	r_w,1, r_w,2, ...	mm	effective working radius of legs (see Figures 8)
5.31	r₁, r₂, ...	mm	inner bend radius on legs (see Figure 6)
5.32	T	°C	working temperature
5.33	u	mm	distance between the coils (see Figure 5)
5.34	α	rad, degree	torsional angle of the spring
5.35	α_h	rad, degree	angular deflection of torsional angle (stroke) between two positions (see Figure 8)
5.36	α_n	rad, degree	maximum permissible test torsional angle (see Figure 8)
5.37	α₁, α₂, …	rad, degree	torsional angles for the specified spring torques, M₁, M₂, … (see Figure 8)
5.38	ΔD	mm	change in mean diameter of spring when loaded
5.39	ε	rad, degree	angle between fixed loading pin and moved loading pin
5.40	ε_n	rad, degree	maximum permissible torsion angle for the spring test corresponding to α_n (see Figure 9)
5.41	ε₀	rad, degree	relative end fixture angle for unloaded spring (see Figure 9)
5.42	ε₁, ε₂, …	rad, degree	relative end fixture angle corresponding to α₁, α₂, ... (see Figure 9)
5.43	φ	rad, degree	bending angle on leg
5.44	φ₁, φ₂, …	rad, degree	angle of bend on legs (see Figure 6)
5.45	γ	rad, degree	relative angle between two legs
5.46	γ₀	rad, degree	position angle between two legs when unloaded (see Figure 6)
5.47	σ See Annex A	N/mm², MPa	bending stress
5.48	σ_n	N/mm², MPa	bending stress for the specified spring torque, M_n
5.49	σ₁, σ₂, … See Annex A	N/mm², MPa	bending stresses for the specified spring torques, M₁, M₂, …

Key

D_e, D_i	diameters of spring
d	diameter of wire
L_B	body length in axis direction (excluding legs) when unloaded
l₁, l₂	length of leg segments (without considering working effect)
p	spring pitch
u	distance between the coils

Figure 5 — Symbols for unloaded torsion spring

Key

D_i	inside diameter of spring
d	diameter of wire
l₁, l₂, l₃	length of leg segments (without considering working effect)
r₁	inner bend radius on legs
φ₁	angle of bend on legs
γ₀	position angle between two legs when unloaded

Figure 6 — Torsion spring with tangential ends

Key

c offset of leg

Figure 7 — Symbols for helical torsion spring offset of leg

Key

d_R	diameter of loading pins
l_w,1, l_w,2	effective working length of legs
M_n, M₁, M₂	spring torque or moment
r_w,1, r_w,2	effective working radius of legs
α_h	deflection of torsional angle (stroke) between two positions
α_n, α₁, α₂	torsional angles (working angles)

Figure 8 — Torsion spring when loaded

Key

D_d	mandrel diameter (inner guide)
ε_n	maximum permissible torsion angle for the spring test
ε₀	relative end fixture angle for unloaded spring
ε₁, ε₂, …	relative end fixture angle corresponding to α₁, α₂, …

Figure 9 — Relative end fixture angle for unloaded spring and corresponding to α₁, α₂, …

10.0 Application symbols for flat springs

Application symbols for flat springs are shown in Table 6, and some sample symbols are shown in Figure 10.

Table 6 — List of application symbols for flat springs

No.	Symbol	Unit	Parameter
6.1	b	mm	width or breadth of beam
6.2	E	N/mm², MPa	modulus of elasticity
6.3	F See Annex A	N	spring load or force (see Figure 10)
6.4	G	N/mm², MPa	shear modulus
6.5	l	mm	length of beam (see Figure 10)
6.6	M	N · mm	bending moment or spring torque
6.7	N	—	number of repetition times to spring failure
6.8	N_R	—	required number of repetition times for testing
6.9	R See Annex A	N/mm	spring rate
6.10	r	mm	bending radius
6.11	s See Annex A	mm	deflection of beam (see Figure 10)
6.12	T	°C	working temperature
6.13	t	mm	thickness of beam (see Figure 10)
6.14	σ See Annex A	N/mm², MPa	bending stress

Key

F spring load or force

l length of beam

s deflection of beam

t thickness of beam

Figure 10 — Symbols for flat spring

11.0 Application symbols for leaf springs

Application symbols for leaf springs are shown in Table 7, and some sample symbols are shown in Figure 11 and 12.

Table 7 — List of application symbols for leaf springs

No.	Symbol	Unit	Parameter
7.1	b	mm	width or breadth of leaf (see Figure 12)
7.2	b_A	mm	width of the spring eye or sliding end (see Figure 11)
7.3	b_E	mm	width of the assembly in the range of U-clamping (see Figure 11)
7.4	C	mm	camber height (see Figure 11)
7.5	C_d	mm	camber height under design (nominal) load
7.6	C₀	mm	camber height when free or at zero load
7.7	d_A	mm	eye inner diameter (see Figure 11)
7.8	d_i	mm	eye bush inner diameter (see Figure 11)
7.9	E	N/mm², MPa	modulus of elasticity
7.10	F See Annex A	N	total spring load (see Figure 11)
7.11	F_A	N	spring load at eye A (see Figure 11)
7.12	F_B	N	spring load at eye B (see Figure 11)
7.13	F_d	N	design load
7.14	f	Hz, s⁻¹	load cycle frequency
7.15	f_e	Hz, s⁻¹	natural frequency
7.16	G	N/mm², MPa	shear modulus
7.17	H	mm	spring height (see Figure 11)
7.18	H_d	mm	design height
7.19	H₀	mm	spring height when unloaded
7.20	l	mm	length of span between eye A and eye B when loaded or unloaded (see Figure 11)
7.21	l_A	mm	length of span between eye A and centre when loaded or unloaded (see Figure 11)
7.22	l_B	mm	length of span between eye B and centre when loaded or unloaded (see Figure 11)
7.23	l_ST	mm	length of straight span between eye A and eye B (see Figure 11)
7.24	l_ST,A	mm	length of straight span between eye A and centre (see Figure 11)
7.25	l_ST,B	mm	length of straight span between eye B and centre (see Figure 11)
7.26	N	—	number of repetition times to spring failure
7.27	N_R	—	required number of repetition times for testing
7.28	n	—	total number of leaves
7.29	R See Annex A	N/mm	spring rate
7.30	s See Annex A	mm	deflection
7.31	s_d	mm	design deflection
7.32	T	°C	working temperature
7.33	t	mm	thickness of single sheet of leaf (see Figure 11)
7.34	δ	mm	flank bending (see Figure 12)
7.35	σ See Annex A	N/mm², MPa	bending stress

Key

A	position A
B	position B
b_A	width of the spring eye or sliding end
b_E	width of the assembly in the range of U-clamping
C	camber height
d_A	eye inner diameter
d_i	eye bush inner diameter
F	total spring load
F_A, F_B	spring loads at eye A or eye B
H	spring height
l	length of span between eye A and eye B when loaded or unloaded
l_A, l_B	lengths of span between eye A and centre, eye B and centre when loaded or unloaded
l_ST	length of straight span between eye A and eye B
l_ST,A, l_ST,B	length of straight span between eye A and centre, eye B and centre
t	thickness of single sheet of leaf

Figure 11 — Symbols for leaf spring

Key

b width or breadth of leaf

δ flank bending

Figure 12 — Flank bending of a leaf spring

12.0 Application symbols for disc springs

Application symbols for disc springs are shown in Table 8, and some sample symbols are shown in Figure 13 and 14.

Table 8 — List of application symbols for disc springs

No.	Symbol	Unit	Parameter
8.1	b_r	mm	width of scar (see Figure 14)
8.2	C₁, C₂, C₃, C₄	—	coefficients
8.3	D	mm	external diameter of spring (see Figure 13 a) and b))
8.4	D₀	mm	diameter of centre of rotation (see Figure 13 a) and b))
8.5	d	mm	internal diameter of spring (see Figure 13 a) and b))
8.6	E	N/mm², MPa	modulus of elasticity
8.7	F See Annex A	N	spring load (see Figure 13 a) and b))
8.8	F_G	N	spring load at the time of combining springs
8.9	F_c	N	design spring load when spring is in the flattened position
8.10	F_t	N	spring test load at H_t
8.11	G	N/mm², MPa	shear modulus
8.12	H_t	mm	height of spring when measuring spring load, H_t = H₀ – 0,75 h₀
8.13	H₀	mm	free height of spring (see Figure 13 a) and b))
8.14	h_s	mm	clean cut (see Figure 14)
8.15	h₀	mm	initial cone height of springs without flat bearings, h₀ = H₀ – t (see Figure 13 a))
8.16	h_0,f	mm	initial cone height of springs with flat bearings, h_0,f = H₀ – t_f (see Figure 13 b))
8.17	i	—	number of springs combined in series
8.18	k₁, k₂	—	coefficients
8.19	L₀	mm	free height at the time of combining springs
8.20	N	—	number of cycles for fatigue life
8.21	n	—	number of springs piled in parallel
8.22	R See Annex A	N/mm	spring rate
8.23	r	mm	radius at edge (see Figure 13 a))
8.24	s See Annex A	mm	deflection of spring
8.25	s_G	mm	deflection of stack
8.26	s₁	mm	deflection of spring preloaded
8.27	T	°C	working temperature
8.28	t	mm	thickness of spring (see Figure 13 a))
8.29	t_f	mm	reduced thickness of single disc spring with flat bearings (see Figure 13 b))
8.30	V	mm	length of lever arms (see Figure 13 a))
8.31	V_f	mm	length of lever arms with flat bearings (see Figure 13 b))
8.32	W	N·mm	energy capacity of springs
8.33	α	—	ratio of external diameter to internal diameter
8.34	ΔF	N	spring load loss
8.35	Δh₀	mm	initial cone height loss of spring
8.36	ν	—	Poisson’s ratio of material
8.37	σ_H	N/mm²	alternative stress
8.38	σ_OM	N/mm², MPa	stress at position OM
8.39	σ _I	N/mm², MPa	stress at position I
8.40	σ _II	N/mm², MPa	stress at position II
8.41	σ _III	N/mm², MPa	stress at position III
8.42	σ _IV	N/mm², MPa	stress at position IV

a) Without flat bearings

b) With flat bearings

Key

D external diameter of spring

D₀ diameter of centre of rotation

d internal diameter of spring

F spring load

H₀ free height of spring

h₀ initial cone height of springs without flat bearings, h₀ = H₀ – t

h_0,f initial cone height of springs with flat bearings, h_0,f = H₀ – t_f

OM point at upper surface of the spring perpendicular to the centre line at point P

P theoretical centre of rotation of disc cross section

r radius at edge

t thickness of spring

t_f reduced thickness of single disc spring with flat bearings

V length of lever arms

V_f length of lever arms with flat bearings

I position I

II position II

III position III

IV position IV

Figure 13 — Symbols for disc spring

Key

1 scar

2 clean cut part

3 tear off

b_r width of scar

h_s clean cut

Figure 14 — Scar and clean cut on a punching surface of a disc spring

(informative)

List of interim symbols

The interim symbols in Table A.1 are used customarily in the relevant region. In order to take global relevance into consideration in ISO, it is permitted to use the interim symbols if all the following conditions are met:

a) condition 1: the interim symbol is in wide use in area(s), but is not being used in a single country;

b) condition 2: in case the immediate implementation of this International Standard can cause any major possible confusion among stakeholders in the region;

To avoid any confusion, where issues arise over nomenclature in international standards, they should be resolved by the manufacturer and customer.

Table A.1 — List of interim symbols

Common symbol	No.	Parameter	Interim symbol			Remark
Common symbol	No.	Parameter	Europe	Asia	North, Central, and South America	Remark
D_e	3.3, 4.2, 5.4	outside (external) diameter of spring	—	—	OD
D_i	3.4, 4.3, 5.5	inside diameter of spring	—	—	ID
F	1.8, 3.10, 4.7, 5.10, 6.3, 7.10, 8.7	spring load or force	—	—	P
F_i	4.8	initial tension force (preload)	F₀	—	P_i	“F₀” and ”P_i” are for extension spring only
F₁, F₂, …	3.13, 4.10, 5.12	specified spring loads for the specified spring lengths L₁, L₂, …	—	—	P₁, P₂, …
L₀	3.19, 4.16, 8.19	free length	—	—	L_f
n	1.20, 3.23, 4.21, 5.25	active coils	—	—	N_a
n_t	3.24, 4.22	total number of coils	—	—	N_t
R	1.22, 3.26, 4.24, 6.9, 7.29, 8.22	spring rate	—	k or F ’	k
R_M	5.27	angular spring rate	—	k_T	k
s	1.24, 3.27, 4.26, 6.11, 7.30, 8.24	deflection of spring	—	—	f
s₁, s₂, …	3.31, 4.29	specified spring deflections for the specified spring loads, F₁, F₂, …	—	—	f₁, f₂, …
σ	1.37, 5.47, 6.14, 7.35	bending stress	—	—	S
σ₁, σ₂, …	5.49	bending stresses for the specified spring torques, M₁, M₂, …	—	—	S₁, S₂, …
τ	1.38, 3.35, 4.32	torsional/shear stress	—	—	S
τ_i	4.33	initial torsional/shear stress	τ₀	—	—	“τ₀” is for extension spring only
τ₁, τ₂, …	3.38, 4.35	torsional/shear stresses for the specified spring loads, F₁, F₂, …	—	—	S₁, S₂, …

(informative)

Index of application symbols

Table B.1 shows the index of application symbols.

Table B.1 — Index of application symbols

Symbol	Helical compres- sion spring no.	Helical exten- sion spring no.	Helical torsion spring no.	Flat spring no.	Leaf spring no.	Disc spring no.
b	—	—	—	6.1	7.1	—
b_A	—	—	—	—	7.2	—
b_E	—	—	—	—	7.3	—
b_r	—	—	—	—	—	8.1
C	—	—	—	—	7.4	—
C_d	—	—	—	—	7.5	—
C₀	—	—	—	—	7.6	—
C₁, C₂, C₃, C₄	—	—	—	—	—	8.2
c	—	—	5.1	—	—	—
D	3.1	4.1	5.2	—	—	8.3
D_d	3.2	—	5.3	—	—	—
D_e	3.3	4.2	5.4	—	—	—
D_i	3.4	4.3	5.5	—	—	—
D₀	—	—	—	—	—	8.4
d	3.5	4.4	5.6	—	—	8.5
d_A	—	—	—	—	7.7	—
d_R	—	—	5.7	—	—	—
d_i	—	—	—	—	7.8	—
d_wire	3.6	4.5	5.8	—	—	—
E	3.7	4.6	5.9	6.2	7.9	8.6
e₁	3.8	—	—	—	—	—
e₂	3.9	—	—	—	—	—
F	3.10	4.7	5.10	6.3	7.10	8.7
F_A	—	—	—	—	7.11	—
F_B	—	—	—	—	7.12	—
F_G	—	—	—	—	—	8.8
F_c	3.11	—	—	—	—	8.9
F_d	—	—	—	—	7.13	—
F_i	—	4.8	—	—	—	—
F_n	3.12	4.9	5.11	—	—	—
F_t	—	—	—	—	—	8.10
F₁, F₂, …	3.13	4.10	5.12	—	—	—
f	3.14	4.11	5.13	—	7.14	—
f_e	3.15	—	—	—	7.15	—
G	3.16	4.12	5.14	6.4	7.16	8.11
H	—	—	—	—	7.17	—
H_d	—	—	—	—	7.18	—
H_t	—	—	—	—	—	8.12
H₀	—	—	—	—	7.19	8.13
h_s	—	—	—	—	—	8.14
h₀	—	—	—	—	—	8.15
h_0,f	—	—	—	—	—	8.16
i	—	—	—	—	—	8.17
k₁, k₂	—	—	—	—	—	8.18
L_B	—	4.13	5.15	—	—	—
L_c	3.17	—	—	—	—	—
L_H	—	4.14	—	—	—	—
L_n	3.18	4.15	—	—	—	—
L₀	3.19	4.16	—	—	—	8.19
L₁, L₂, …	3.20	4.17	—	—	—	—
l	—	—	5.16	6.5	7.20	—
l_A	—	—	—	—	7.21	—
l_B	—	—	—	—	7.22	—
l_ST	—	—	—	—	7.23	—
l_ST,A	—	—	—	—	7.24	—
l_ST,B	—	—	—	—	7.25	—
l_w	—	—	5.17	—	—	—
l_w,1, l_w,2, ...	—	—	5.18	—	—	—
l₁, l₂, …	—	—	5.19	—	—	—
M	—	—	5.20	6.6	—	—
M_n	—	—	5.21	—	—	—
M₁, M₂, …	—	—	5.22	—	—	—
m	—	4.18	—	—	—	—
N	3.21	4.19	5.23	6.7	7.26	8.20
N_R	3.22	4.20	5.24	6.8	7.27	—
n	3.23	4.21	5.25	—	7.28	8.21
n_t	3.24	4.22	—	—	—	—
p	3.25	4.23	5.26	—	—	—
R	3.26	4.24	—	6.9	7.29	8.22
R_M	—	—	5.27	—	—	—
r	—	4.25	5.28	6.10	—	8.23
r_w	—	—	5.29	—	—	—
r_w,1, r_w,2, ...	—	—	5.30	—	—	—
r₁, r₂, ...	—	—	5.31	—	—	—
s	3.27	4.26	—	6.11	7.30	8.24
s_G	—	—	—	—	—	8.25
s_c	3.28	—	—	—	—	—
s_d	—	—	—	—	7.31	—
s_h	3.29	4.27	—	—	—	—
s_n	3.30	4.28	—	—	—	—
s₁	—	—	—	—	—	8.26
s₁, s₂, …	3.31	4.29	—	—	—	—
T	3.32	4.30	5.32	6.12	7.32	8.27
t	—	—	—	6.13	7.33	8.28
t_f	—	—	—	—	—	8.29
u	3.33	4.31	5.33	—	—	—
V	—	—	—	—	—	8.30
V_f	—	—	—	—	—	8.31
W	—	—	—	—	—	8.32
α	—	—	5.34	—	—	8.33
α_h	—	—	5.35	—	—	—
α_n	—	—	5.36	—	—	—
α₁, α₂, …	—	—	5.37	—	—	—
ΔD	—	—	5.38	—	—	—
ΔD_e	3.34	—	—	—	—	—
ΔF	—	—	—	—	—	8.34
Δh₀	—	—	—	—	—	8.35
δ	—	—	—	—	7.34	—
ε	—	—	5.39	—	—	—
ε_n	—	—	5.40	—	—	—
ε₀	—	—	5.41	—	—	—
ε₁, ε₂, …	—	—	5.42	—	—	—
φ	—	—	5.43	—	—	—
φ₁, φ₂, …	—	—	5.44	—	—	—
γ	—	—	5.45	—	—	—
γ₀	—	—	5.46	—	—	—
ν	—	—	—	—	—	8.36
σ	—	—	5.47	6.14	7.35	—
σ_H	—	—	—	—	—	8.37
σ_OM	—	—	—	—	—	8.38
σ_n	—	—	5.48	—	—	—
σ _I	—	—	—	—	—	8.39
σ _II	—	—	—	—	—	8.40
σ _III	—	—	—	—	—	8.41
σ _IV	—	—	—	—	—	8.42
σ₁, σ₂, …	—	—	5.49	—	—	—
τ	3.35	4.32	—	—	—	—
τ_c	3.36	—	—	—	—	—
τ_i	—	4.33	—	—	—	—
τ_n	3.37	4.34	—	—	—	—
τ₁, τ₂, …	3.38	4.35	—	—	—	—

Bibliography

[1] ISO 80000‑1, Quantities and units — Part 1: General

[2] ISO 80000‑4, Quantities and units — Part 4: Mechanics

[3] ISO 22705‑1, Springs — Measurement and test parameters — Part 1: Cold formed cylindrical helical compression springs

[4] ISO 22705‑2, Springs — Measurement and test parameters — Part 2: Cold formed cylindrical helical extension springs

[5] ISO 22705‑3, Springs — Measurement and test parameters — Part 3: Cold formed cylindrical helical torsion springs

[6] ISO 18137, Leaf springs — Technical specifications

[7] ISO 19690‑1, Disc springs — Part 1: Calculation

[8] ISO 19690‑2, Disc springs — Part 2: Technical specifications

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