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

This document specifies parameters for the determination of surface texture by areal methods.

Spécification géométrique des produits (GPS) -- État de surface: Surfacique

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Publication Date
19-Dec-2021
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5060 - Close of voting Proof returned by Secretariat
Start Date
27-Oct-2021
Completion Date
26-Oct-2021
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ISO/FDIS 25178-2 - Geometrical product specifications (GPS) -- Surface texture: Areal
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FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 25178-2
ISO/TC 213
Geometrical product specifications
Secretariat: BSI
(GPS) — Surface texture: Areal —
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:
Surfacique —
Partie 2: Termes, définitions et paramètres d'états 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 25178-2:2021(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 25178-2:2021(E)
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ii © ISO 2021 – All rights reserved
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ISO/FDIS 25178-2:2021(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 .................................................................................................................................................... 5

3.3 Geometrical feature terms .........................................................................................................................................................11

4 Field parameters ...............................................................................................................................................................................................15

4.1 General ........................................................................................................................................................................................................15

4.2 Height parameters ............................................................................................................................................................................15

4.2.1 General...................................................................................................................................................................................15

4.2.2 Root mean square height .......................................................................................................................................15

4.2.3 Skewness .............................................................................................................................................................................15

4.2.4 Kurtosis .................................................................................................................................................................................15

4.2.5 Maximum peak height ..............................................................................................................................................16

4.2.6 Maximum pit depth ....................................................................................................................................................16

4.2.7 Maximum height ...........................................................................................................................................................16

4.2.8 Arithmetic mean height ..........................................................................................................................................16

4.3 Spatial parameters ............................................................................................................................................................................16

4.3.1 General...................................................................................................................................................................................16

4.3.2 Autocorrelation length.............................................................................................................................................16

4.3.3 Texture aspect ratio ....................................................................................................................................................17

4.3.4 Texture direction ..........................................................................................................................................................18

4.3.5 Dominant spatial wavelength ............................................................................................................................18

4.4 Hybrid parameters ...........................................................................................................................................................................18

4.4.1 General...................................................................................................................................................................................18

4.4.2 Root mean square gradient .................................................................................................................................18

4.4.3 Developed interfacial area ratio ......................................................................................................................18

4.5 Material ratio functions and related parameters ...................................................................................................19

4.5.1 Areal material ratio.....................................................................................................................................................19

4.5.2 Inverse areal material ratio .................................................................................................................................19

4.5.3 Material ratio height difference .......................................................................................................................20

4.5.4 Areal parameter for stratified surfaces .....................................................................................................21

4.5.5 Areal material probability parameters ......................................................................................................23

4.5.6 Void volume .......................................................................................................................................................................24

4.5.7 Material volume .............................................................................................................................................................25

4.6 Gradient distribution ......................................................................................................................................................................26

4.7 Multiscale geometric (fractal) methods .........................................................................................................................28

4.7.1 Morphological volume-scale function ........................................................................................................28

4.7.2 Relative area .....................................................................................................................................................................28

4.7.3 Relative length ................................................................................................................................................................28

4.7.4 Scale of observation ...................................................................................................................................................28

4.7.5 Volume-scale fractal complexity......................................................................................................................29

4.7.6 Area-scale fractal complexity .............................................................................................................................29

4.7.7 Length-scale fractal complexity .......................................................................................................................29

4.7.8 Crossover scale ...............................................................................................................................................................29

5 Feature parameters ........................................................................................................................................................................................30

5.1 General ........................................................................................................................................................................................................30

5.2 Type of texture feature ..................................................................................................................................................................31

5.3 Segmentation .........................................................................................................................................................................................31

5.4 Determining significant features ..........................................................................................................................................31

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ISO/FDIS 25178-2:2021(E)

5.5 Section of feature attributes .....................................................................................................................................................33

5.6 Attribute statistics .............................................................................................................................................................................34

5.7 Feature characterization convention ................................................................................................................................34

5.8 Named feature parameters........................................................................................................................................................34

5.8.1 General...................................................................................................................................................................................34

5.8.2 Density of peaks ............................................................................................................................................................34

5.8.3 Density of pits ..................................................................................................................................................................35

5.8.4 Arithmetic mean peak curvature ....................................................................................................................35

5.8.5 Arithmetic mean pit curvature .........................................................................................................................35

5.8.6 Five-point peak height .............................................................................................................................................35

5.8.7 Five-point pit depth ....................................................................................................................................................36

5.8.8 Ten-point height ............................................................................................................................................................36

5.9 Additional feature parameters ...............................................................................................................................................36

5.9.1 General...................................................................................................................................................................................36

5.9.2 Shape parameters ........................................................................................................................................................37

Annex A (informative) Multiscale geometric (fractal) methods ...........................................................................................39

Annex B (informative) Determination of areal parameters for stratified functional surfaces ............46

Annex C (informative) Basis for areal surface texture standards — Timetable of events .........................49

Annex D (informative) Implementation details .....................................................................................................................................50

Annex E (informative) Changes made to the 2012 edition of this document ..........................................................54

Annex F (informative) Summary of areal surface texture parameters ..........................................................................56

Annex G (informative) Specification analysis workflow ...............................................................................................................58

Annex H (informative) Relation with the GPS matrix ......................................................................................................................59

Annex I (informative) Overview of profile and areal standards in the GPS matrix model ........................60

Bibliography .............................................................................................................................................................................................................................61

iv © ISO 2021 – All rights reserved
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ISO/FDIS 25178-2:2021(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 second edition cancels and replaces the first edition (ISO 25178-2:2012), which has been technically

revised. The main changes to the previous edition are described in Annex E. A short history of the work

done on areal surface texture can be found in Annex C.
A list of all parts in the ISO 25178 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 25178-2:2021(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 the chain link B of the chains of standards on areal 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 H. An overview of standards on profiles and areal surface texture is given in Annex I.

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

Throughout this document, parameters are written as abbreviations with lower case suffixes (as in

Sq or Vmp) when used in a sentence and are written as symbols with subscripts (as in S or V ) when

q mp

used in equations, to avoid misinterpretations of compound letters as an indication of multiplication

between quantities in equations. The parameters in lower case are used in product documentation,

drawings and data sheets.

Parameters are calculated from coordinates defined in the specification coordinate system, or from

derived quantities (e.g. gradient, curvature).

Parameters are defined for the continuous case, but in verification they are calculated on discrete

surfaces such as the primary extracted surface.

A short history of the work done on areal surface texture can be found in Annex C.

vi © ISO 2021 – All rights reserved
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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 25178-2:2021(E)
Geometrical product specifications (GPS) — Surface
texture: Areal —
Part 2:
Terms, definitions and surface texture parameters
1 Scope

This document specifies parameters for the determination of surface texture by areal methods.

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

ISO 17450-1:2011, Geometrical product specifications (GPS) — General concepts — Part 1: Model for

geometrical specification and verification
3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 16610-1:2015 and

ISO 17450-1:2011 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

model of the physical interface of the workpiece with its environment

[SOURCE: ISO 17450-1:2011, 3.2.2]
3.1.2
surface texture
geometrical irregularities contained in a scale-limited surface (3.1.9)

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

shape of the surface.
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ISO/FDIS 25178-2:2021(E)
3.1.3
mechanical surface

boundary of the 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 (3.1.1) of a workpiece
[SOURCE: ISO 14406:2010, 3.1.1, modified — Notes to entry removed.]
3.1.3.1
electromagnetic surface

surface obtained by the electromagnetic interaction with the skin model (3.1.1) of a workpiece

[SOURCE: ISO 14406:2010, 3.1.2, modified — Notes to entry removed.]
3.1.3.2
auxiliary surface

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

(3.1.1) of a workpiece

Note 1 to entry: A mathematical surface (softgauge) is an example of an auxiliary surface.

Note 2 to entry: Other physical measurement principles, such as tunnelling microscopy or atomic force

microscopy, can also serve as an auxiliary surface. See Figure 1 and Annex G.
3.1.4
specification coordinate system
system of coordinates in which surface texture parameters are specified

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

3.1.5
primary surface

surface portion obtained when a surface portion is represented as a specified primary mathematical

model with specified nesting index (3.1.6.4)

Note 1 to entry: In this document, an S-filter is used to derive the primary surface. See Figure 1.

[SOURCE: ISO 16610-1:2015, 3.3, modified — Note 1 to entry added.]
Figure 1 — Definition of primary surface
2 © ISO 2021 – All rights reserved
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ISO/FDIS 25178-2:2021(E)
3.1.5.1
primary extracted surface
finite set of data points sampled from the primary surface (3.1.5)
[SOURCE: ISO 14406:2010, 3.7, modified — Notes to entry removed.]
3.1.6
surface filter
filtration operator applied to a surface
3.1.6.1
S-filter

surface filter (3.1.6) which removes small-scale lateral components from the surface, resulting in the

primary surface (3.1.5)
3.1.6.2
L-filter

surface filter (3.1.6) which removes large-scale lateral components from the primary surface (3.1.5) or

S-F surface (3.1.7)

Note 1 to entry: When the L-filter is not tolerant to form, it needs to be applied on an S-F surface; when it is

tolerant to form, it can be applied either on the primary surface or on an S-F surface.

3.1.6.3
F-operation
operation which removes form from the primary surface (3.1.5)

Note 1 to entry: Some F-operations (such as association) have a very different action to that of filtration. Though

their action can limit the larger lateral scales of a surface, this action is very fuzzy. It is represented in Figure 2

using the same convention as for a filter.

Note 2 to entry: Some L-filters are not tolerant to form and require an F-operation first as a prefilter before being

applied.

Note 3 to entry: An F-operation can be a filtration operation such as a robust Gaussian filter.

3.1.6.4
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

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

3.1.7
S-F surface

surface derived from the primary surface (3.1.5) by removing the form using an F-operation (3.1.6.3)

Note 1 to entry: Figure 2 illustrates the relationship between the S-F surface and the S-filter and F-operation.

Note 2 to entry: If filtered with N nesting index to remove the shortest wavelengths from the surface, the surface

is equivalent to a “primary surface”. In this case, N is the areal equivalent of the λs cut-off. See 4 in Figure 2 and

Annex G.

Note 3 to entry: If filtered with N nesting index to separate longer from shorter wavelengths, the surface is

equivalent to a “waviness surface”. In this case, N is the areal equivalent of the λc cut-off. See 5 in Figure 2 and

Annex G.

Note 4 to entry: The concepts of “roughness” or “waviness” are less important in areal surface texture than in

profile surface texture. Some surfaces can exhibit roughness in one direction and waviness in the perpendicular

direction. That is why the concepts of S-L surface and S-F surface are preferred in this document.

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ISO/FDIS 25178-2:2021(E)
3.1.8
S-L surface

surface derived from the S-F surface (3.1.7) by removing the large-scale components using an L-filter

(3.1.6.2)

Note 1 to entry: Figure 2 illustrates the relationship between the S-L surface and the S-filter and L-filter.

Note 2 to entry: If the S-filter nesting index N is chosen to remove the shortest wavelengths from the surface

and the L-filter nesting index N is chosen in order to separate longer from shorter wavelengths, the surface is

equivalent to a “roughness surface”. See 6 in Figure 2 and Annex G.

Note 3 to entry: A series of S-L surfaces can be generated with narrow bandwidth using an S-filter and an L-filter

of close nesting indices (or equal), in order to achieve a multiscale exploration of the surface. See Figure 3.

Key
1 S-filter
2 L-filter
3 F-operation
4 S-F surface (see 3.1.7, Note 2 to entry)
5 S-F surface (see 3.1.7, Note 3 to entry)
6 S-L surface (see 3.1.8, Note 2 to entry)
Small scale.
Large scale.

Figure 2 — Relationships between the S-filter, L-filter, F-operation and S-F and S-L surfaces

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ISO/FDIS 25178-2:2021(E)
Key
S S-filter
L L-filter
Small scale.
Large scale.
Figure 3 — Example of bandpass filters used to generate a bank of S-L surfaces
3.1.9
scale-limited surface
S-F surface (3.1.7) or S-L surface (3.1.8)
3.1.10
reference surface

surface associated to the scale-limited surface (3.1.9) according to a criterion

Note 1 to entry: This reference surface is used as the origin of heights for surface texture parameters.

EXAMPLE Plane, cylinder and sphere.
3.1.11
evaluation area

portion of the scale-limited surface (3.1.9) for specifying the area under evaluation

Note 1 to entry: See ISO 25178-3 for more information.

Note 2 to entry: Throughout this document, the symbol A is used for the numerical value of the evaluation area

and the symbol A for the domain (of integration or definition).
3.2 Geometrical parameter terms
3.2.1
field parameter
parameter defined from all the points on a scale-limited surface (3.1.9)
Note 1 to entry: Field parameters are defined in Clause 4.
3.2.2
feature parameter

parameter defined from a subset of predefined topographic features from the scale-limited surface

(3.1.9)
Note 1 to entry: Feature parameters are defined in Clause 5.
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ISO/FDIS 25178-2:2021(E)
3.2.3
V-parameter
material volume or void volume field parameter (3.2.1)
3.2.4
S-parameter

field parameter (3.2.1) or feature parameter (3.2.2) that is not a V-parameter (3.2.3)

3.2.5
height
ordinate value
z(x,y)

signed normal distance from the reference surface (3.1.10) to the scale-limited surface (3.1.9)

Note 1 to entry: Throughout this document, the term “height” is either used for a distance or for an a

...

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