Geometrical product specifications (GPS) -- Surface texture: Profile

This document specifies terms, definitions and parameters for the determination of surface texture by profile methods. NOTE 1   The main changes to previous ISO profile documents are described in Annex I. NOTE 2   An overview of profile and areal standards in the GPS matrix model is given in Annex J. NOTE 3   The relation of this document to the GPS matrix model is given in Annex K.

Spécification géométrique des produits (GPS) -- État de surface: Méthode du profil

Le présent document spécifie les termes, définitions et paramètres applicables à la détermination de l’état de surface au moyen de méthodes de profil. NOTE 1       Les principales modifications apportées aux précédents documents sur les profils ISO sont décrites à l'Annexe I. NOTE 2       Une vue d'ensemble des normes de profil et des normes de surface dans le modèle matriciel GPS est donnée à l'Annexe J. NOTE 3       La relation entre le présent document et le modèle de matrice GPS est donnée à l'Annexe K.

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ISO/FDIS 21920-2 - Geometrical product specifications (GPS) -- Surface texture: Profile
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FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 21920-2
ISO/TC 213
Geometrical product specifications
Secretariat: BSI
(GPS) — Surface texture: Profile —
Voting begins on:
2021-08-31
Part 2:
Voting terminates on:
Terms, definitions and surface texture
2021-10-26
parameters
Spécification géométrique des produits (GPS) — État de surface:
Méthode du profil —
Partie 2: Termes, définitions et paramètres d’état de surface
ISO/CEN PARALLEL PROCESSING
RECIPIENTS OF THIS DRAFT ARE INVITED TO
SUBMIT, WITH THEIR COMMENTS, NOTIFICATION
OF ANY RELEVANT PATENT RIGHTS OF WHICH
THEY ARE AWARE AND TO PROVIDE SUPPOR TING
DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
Reference number
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
ISO/FDIS 21920-2:2021(E)
LOGICAL, COMMERCIAL AND USER PURPOSES,
DRAFT INTERNATIONAL STANDARDS MAY ON
OCCASION HAVE TO BE CONSIDERED IN THE
LIGHT OF THEIR POTENTIAL TO BECOME STAN-
DARDS TO WHICH REFERENCE MAY BE MADE IN
NATIONAL REGULATIONS. ISO 2021
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ISO/FDIS 21920-2:2021(E)
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© ISO 2021

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ii © ISO 2021 – All rights reserved
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ISO/FDIS 21920-2:2021(E)
Contents Page

Foreword ..........................................................................................................................................................................................................................................v

Introduction ................................................................................................................................................................................................................................vi

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

3.1 General terms ........................................................................................................................................................................................... 1

3.2 Geometrical parameter terms .................................................................................................................................................13

3.3 Geometrical feature terms .........................................................................................................................................................16

4 Field parameters ...............................................................................................................................................................................................24

4.1 General ........................................................................................................................................................................................................24

4.2 Height parameters ............................................................................................................................................................................24

4.2.1 General...................................................................................................................................................................................24

4.2.2 Arithmetic mean height ..........................................................................................................................................24

4.2.3 Root mean square height .......................................................................................................................................24

4.2.4 Skewness .............................................................................................................................................................................24

4.2.5 Kurtosis .................................................................................................................................................................................24

4.2.6 Total height ........................................................................................................................................................................25

4.2.7 Maximum height per section ..............................................................................................................................25

4.3 Spatial parameters ............................................................................................................................................................................26

4.3.1 General...................................................................................................................................................................................26

4.3.2 Autocorrelation length.............................................................................................................................................26

4.3.3 Dominant spatial wavelength ............................................................................................................................26

4.4 Hybrid parameters ...........................................................................................................................................................................27

4.4.1 General...................................................................................................................................................................................27

4.4.2 Root mean square gradient .................................................................................................................................27

4.4.3 Arithmetic mean of absolute gradient .......................................................................................................27

4.4.4 Maximum absolute gradient ...............................................................................................................................27

4.4.5 Developed length ..........................................................................................................................................................27

4.4.6 Developed length ratio ............................................................................................................................................28

4.5 Material ratio functions and related parameters ...................................................................................................28

4.5.1 Material ratio functions ..........................................................................................................................................28

4.5.2 Material ratio parameters .....................................................................................................................................33

4.5.3 Parameters for stratified surfaces using the material ratio curve .....................................35

4.5.4 Parameters for stratified surfaces using the material probability curve .....................37

4.5.5 Volume parameters ....................................................................................................................................................38

5 Feature parameters ........................................................................................................................................................................................40

5.1 Parameters based on peak heights and pit depths ...............................................................................................40

5.1.1 General...................................................................................................................................................................................40

5.1.2 Maximum peak height ..............................................................................................................................................41

5.1.3 Mean peak height .........................................................................................................................................................41

5.1.4 Maximum pit depth ....................................................................................................................................................41

5.1.5 Mean pit depth ................................................................................................................................................................42

5.1.6 Maximum height ...........................................................................................................................................................42

5.2 Parameters based on profile elements ............................................................................................................................42

5.2.1 General...................................................................................................................................................................................42

5.2.2 Mean profile element spacing ...........................................................................................................................44

5.2.3 Maximum profile element spacing ................................................................................................................44

5.2.4 Standard deviation of profile element spacings ................................................................................44

5.2.5 Mean profile element height ...............................................................................................................................44

5.2.6 Maximum profile element height ...................................................................................................................44

5.2.7 Standard deviation of profile element heights .................. ..................................................................44

5.2.8 Peak count parameter ..............................................................................................................................................45

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ISO/FDIS 21920-2:2021(E)

5.3 Parameters based on feature characterization ........................................................................................................45

5.3.1 General...................................................................................................................................................................................45

5.3.2 Named feature parameters ..................................................................................................................................45

Annex A (informative) Determination of the first and second derivative ..................................................................47

Annex B (informative) Determination of the local curvature ..................................................................................................50

Annex C (normative) Determination of the material ratio curve ........................................................................................51

Annex D (normative) Determination of profile parameters for stratified surfaces ........................................52

Annex E (normative) Crossing-the-line segmentation to determine profile elements.................................60

Annex F (normative) Feature characterization ......................................................................................................................................66

Annex G (informative) Summary of profile surface texture parameters and functions ..............................70

Annex H (informative) Specification analysis workflow ...............................................................................................................73

Annex I (informative) Changes to previous ISO profile documents ..................................................................................75

Annex J (informative) Overview of profile and areal standards in the GPS matrix model ........................76

Annex K (informative) Relation to the GPS matrix model ...........................................................................................................77

Bibliography .............................................................................................................................................................................................................................78

iv © ISO 2021 – All rights reserved
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ISO/FDIS 21920-2:2021(E)
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).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

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 213, Dimensional and geometrical product

specifications and verification, in collaboration with the European Committee for Standardization (CEN)

Technical Committee CEN/TC 290, Dimensional and geometrical product specification and verification, in

accordance with the Agreement on technical cooperation between ISO and CEN (Vienna Agreement).

This first edition of ISO 21920-2 cancels and replaces ISO 4287:1997, ISO 12085:1996, ISO 13565-2:1996

and ISO 13565-3:1998, which have been technically revised.

It also incorporates the Amendment ISO 4287:1997/Amd 1:2009 and the Technical Corrigenda

ISO 4287:1997/Cor 1:1998, ISO 4287:1997/Cor 2:2005, ISO 12085:1996/Cor 1:1998 and

ISO 13565-2:1996/Cor 1:1998.
The main changes are related to ISO 4287 and are as follows:
— all field parameters are now related to the evaluation length;
— unambiguous evaluation of profile elements;

— definition of new parameters, in particular parameters based on the watershed transformation.

A list of all parts in the ISO 21920 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.
© ISO 2021 – All rights reserved v
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ISO/FDIS 21920-2:2021(E)
Introduction

This document is a geometrical product specification (GPS) standard and is to be regarded as a general

GPS standard (see ISO 14638). It influences chain link B of the chains of standards on profile surface

texture.

The ISO GPS matrix model given in ISO 14638 gives an overview of the ISO GPS system of which this

document is a part. The fundamental rules of ISO GPS given in ISO 8015 apply to this document and

the default decision rules given in ISO 14253-1 apply to the specifications made in accordance with this

document, unless otherwise indicated.

For more detailed information of the relation of this document to other standards and the GPS matrix

model, see Annex K.

This document develops the terminology, concepts and parameters for areal surface texture.

Throughout this document, parameters are written as abbreviated terms with lower-case suffixes (as

in Rq) when used in a sentence, and are written as symbols with subscripts (as in R ) when used in

formulae, to avoid misinterpretations of compound letters as an indication of multiplication between

quantities in formulae. The parameters with lower-case suffixes are used in product documentation,

drawings and data sheets.
vi © ISO 2021 – All rights reserved
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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 21920-2:2021(E)
Geometrical product specifications (GPS) — Surface
texture: Profile —
Part 2:
Terms, definitions and surface texture parameters
1 Scope

This document specifies terms, definitions and parameters for the determination of surface texture by

profile methods.

NOTE 1 The main changes to previous ISO profile documents are described in Annex I.

NOTE 2 An overview of profile and areal standards in the GPS matrix model is given in Annex J.

NOTE 3 The relation of this document to the GPS matrix model is given in Annex K.

2 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 16610-1:2015, Geometrical product specifications (GPS) — Filtration — Part 1: Overview and basic

concepts
3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 16610-1 and the following

apply.

For the purposes of this document, the terms and definitions given in [external document reference

xxx] and the following apply.

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

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1 General terms
3.1.1
skin model
non-ideal surface model

model of the physical interface of the workpiece with its environment

[SOURCE: ISO 17450-1:2011, 3.2.2]
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ISO/FDIS 21920-2:2021(E)
3.1.2
surface texture
geometrical irregularities contained in a scale-limited profile

Note 1 to entry: Surface texture does not include geometrical irregularities contributing to the form or shape of

the profile.
3.1.3
mechanical surface

boundary of the mathematical erosion, by a sphere of radius r , of the locus of the centre of an ideal

tactile sphere, also with radius r , rolled over the skin model of a workpiece

Note 1 to entry: Figure 1 is an example to show the effect of mechanical filtering and is not related to a real

measured surface.
[SOURCE: ISO 14406:2010, 3.1.1, modified — Notes to entry replaced.]
2 © ISO 2021 – All rights reserved
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ISO/FDIS 21920-2:2021(E)
Key
A skin model
ideal tactile sphere of radius r

C envelope curve of the locus of the centre of an ideal tactile sphere B rolled over the skin model

D sphere of radius r

E mechanical surface: boundary of the mathematical erosion, by the sphere D, of the envelope curve C

Figure 1 — Mechanical surface
3.1.4
profile trace

intersection of the skin model by an intersection plane perpendicular to the skin model and in a

specified direction
Note 1 to entry: See Figure 2.
Note 2 to entry: See ISO 21920-3:—, 4.3.
1) Under preparation. Stage at the time of publication: ISO/FDIS 21920-3:2021.
© ISO 2021 – All rights reserved 3
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ISO/FDIS 21920-2:2021(E)
Key
A skin model
B intersection plane
C profile trace
Figure 2 — Profile trace
3.1.5
mechanical profile

boundary of the mathematical erosion, by a circular disc of radius r, of the locus of the centre of an ideal

tactile sphere, also with radius r, rolled along a trace over the skin model of a workpiece

Note 1 to entry: Figure 3 is an example to show the effect of mechanical filtering and is not related to a real

measured profile.

Note 2 to entry: The treatment of non-measured points and spurious points is part of the extraction process (see

ISO 17450-1:2011, 8.1.3) and is not considered in this document.
4 © ISO 2021 – All rights reserved
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ISO/FDIS 21920-2:2021(E)
Key
A skin model
ideal tactile sphere of radius r

C envelope curve of the planar locus of the centre of an ideal tactile sphere rolled over the skin model

circular disc of radius r

E mechanical profile: boundary of the mathematical erosion, by the circular disc D, of the envelope curve C

Figure 3 — Mechanical profile
3.1.6
electromagnetic surface

surface obtained by the electromagnetic interaction with the skin model of a workpiece

Note 1 to entry: See Figure 4.

Note 2 to entry: The electromagnetic surface is an inherent characteristic of a skin model of a workpiece.

Note 3 to entry: Electromagnetic surfaces depend on the optical measurement principal used for extraction.

[SOURCE: ISO 14406:2010, 3.1.2, modified — Notes to entry replaced.]
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ISO/FDIS 21920-2:2021(E)
Figure 4 — Electromagnetic surface
3.1.7
electromagnetic profile

profile obtained by the electromagnetic interaction with the skin model of a workpiece

Note 1 to entry: See Figure 5.

Note 2 to entry: The electromagnetic profile is an inherent characteristic of a skin model of a workpiece.

Note 3 to entry: Electromagnetic profiles depend on the optical measurement principle used for extraction.

Note 4 to entry: In most cases, the profile trace results from the intersection of the skin model by an intersection

plane perpendicular to the skin model (3.1.1) and in a specified direction (see ISO 21920-3).

Note 5 to entry: The treatment of non-measured points and spurious points is part of the extraction process and

is not considered in this document.
Figure 5 — Electromagnetic profile
3.1.8
auxiliary surface

surface obtained by an interaction, other than mechanical or electromagnetic, with the skin model

(3.1.1) of a workpiece

Note 1 to entry: A software measurement standard is an example of an auxiliary surface. Other physical

measurement principles which differ from a mechanical or electromagnetic surface, such as scanning tunnelling

microscopy or atomic force microscopy, can also serve as an auxiliary surface. See Figure 6.

3.1.9
auxiliary profile

profile obtained by an interaction, other than mechanical or electromagnetic, with the skin model (3.1.1)

of a workpiece

Note 1 to entry: A software measurement standard is an example of an auxiliary profile. Other physical

measurement principles which differ from a mechanical or electromagnetic profile, such as scanning tunnelling

microscopy or atomic force microscopy, can also serve as an auxiliary profile. See Figure 6 and Annex H.

3.1.10
specification coordinate system
system of coordinates in which surface texture parameters are specified

Note 1 to entry: If the nominal surface is a plane (or portion of a plane), it is common in practice to use a

rectangular coordinate system in which the axes form a right-handed Cartesian set, the x -axis and the y -axis

also lying on the nominal surface, and the z -axis being in an outward direction (from the material to the

surrounding medium). This convention is adopted throughout the rest of this document.

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ISO/FDIS 21920-2:2021(E)
3.1.11
nesting index
N , N , N
is ic if

number or set of numbers indicating the relative level of nesting for a particular primary mathematical

model

Note 1 to entry: The cut-off wavelength for the Gaussian filter is an example of a nesting index.

Note 2 to entry: Using the different nesting indices, specific lateral scale components of a scale-limited profile are

extracted.

[SOURCE: ISO 16610-1:2015, 3.2.1, modified — definition and notes to entry revised.]

3.1.12
primary surface profile

surface profile trace obtained when a surface profile trace is represented as a specified primary

mathematical model with specified nesting index N

Note 1 to entry: In the ISO 21920 series, a profile S-filter is used to derive the primary surface profile from a

profile trace (e.g. mechanical profile). See Figure 6 and Annex H.

Note 2 to entry: For some applications, the profile S-filter is not used. In such cases, for example for multi-scale

analysis, the nesting index is equal to “zero”.

Note 3 to entry: In most situations, the primary surface profile can be derived with sufficient accuracy from

either the mechanical surface (the default choice), the electromagnetic surface or the auxiliary surface, using an

intersection plane perpendicular to the chosen type of surface and in a specified direction. See Figure 6.

NOTE The evaluation chain for the default case is indicated by the grey fill colour.

See 3.1.13.1 for profile S-filter.
b
See ISO 25178-2:2021, 3.1.6.1,
Under preparation. Stage at the time of publication: ISO/FDIS 25178-2:2021.
for S-filter.
See ISO 25178-2:2021, 3.1.5, for primary surface.
Figure 6 — Definition of the primary surface and primary surface profile
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ISO/FDIS 21920-2:2021(E)
3.1.13
profile filter
filtration operator applied to a profile
3.1.13.1
profile S-filter
profile filter which removes small lateral scale components from a profile
Note 1 to entry: See Figure 7.
3.1.13.2
profile L-filter
profile filter which removes large lateral scale components from a profile

Note 1 to entry: Some profile L-filters are sensitive to form and require the profile F-operation first as a prefilter

before being applied.
Note 2 to entry: See Figure 7.
3.1.13.3
profile F-operation
operation which removes form from a profile
Note 1 to entry: See Figure 7.
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ISO/FDIS 21920-2:2021(E)
Key
A small lateral scale (e.g. short wavelengths)
B large lateral scale (e.g. long wavelengths)
C scale axis
D amplitude axis
E lateral scale component extracted by the profile S-filter
F lateral scale component extracted by the profile F-operation
G lateral scale component extracted by the profile L-filter
H profile S-filter nesting index N
I profile F-operation nesting index N
J profile L-filter nesting index N
Figure 7 — Relationships between the S-filter, L-filter and F-operation
3.1.14
scale-limited profile
profile structure scale components between specified nesting indices

EXAMPLE A profile is scale-limited after applying a profile filter with a specified nesting index.

3.1.14.1
primary profile
P-profile

scale-limited profile at any position x derived from the primary surface profile by removing the form

using a profile F-operation with nesting index N

Note 1 to entry: In most cases, the primary profile can be derived with sufficient accuracy from the S-F surface

using an intersection plane perpendicular to the S-F surface and in a specified direction. See Figure 8.

Note 2 to entry: The primary profile is the basis for evaluation of the P-parameters (3.2.5). See Figures 9 and 10.

Note 3 to entry: The profile F-operation can be performed as a multi-stage operation, for example a combination

of a total least square fit and a profile L-filter.
Note 4 to entry: See Annex H for additional information.
© ISO 2021 – All rights reserved 9
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ISO/FDIS 21920-2:2021(E)

Note 1 to entry: The evaluation chain for the default case is indicated by the grey fill colour.

See ISO 25178-2:2021, 3.1.6.3, for F-operation.
See ISO 25178-2:2021, 3.1.7, for S-F surface.

Figure 8 — Primary profile derived from the primary surface profile (default) or S-F surface

...

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