# SIST EN ISO 13565-3:2002

(Main)## Geometrical Product Specifications (GPS) - Surface texture: Profile method; surfaces having stratified functional properties - Part 3: Height characterization using the material probability curve (ISO 13565-3:1998)

## Geometrical Product Specifications (GPS) - Surface texture: Profile method; surfaces having stratified functional properties - Part 3: Height characterization using the material probability curve (ISO 13565-3:1998)

## Geometrische Produktspezifikation (GPS) - Oberflächenbeschaffenheit: Tastschnittverfahren; Oberflächen mit plateauartigen funktionsrelevanten Eigenschaften - Teil 3: Beschreibung der Höhe von Oberflächen mit der Wahrscheinlichkeitsdichtekurve (ISO 13565-3:1998)

Dieser Teil von ISO 13565 legt den Auswertevorgang für die Ermittlung von Parametern aus der linearen Regression der Wahrscheinlichkeitsdichtekurve fest, die die Gaußsche Darstellung der Materialanteilkurve ist. Die Parameter sind für die Beschreibung des tribologischen Verhaltens, beispielsweise von geschmierten Gleitflächen und zur Regelung des Herstellungsprozesses vorgesehen.

## Spécification géométrique des produits (GPS) - Etat de surface: Méthode du profil; surfaces ayant des propriétés fonctionnelles différentes suivant les niveaux - Partie 3: Caractérisation des hauteurs par la courbe de probabilité de matiere (ISO 13565-3:1998)

La présente partie de l'ISO 13565 établit le procédé d'évaluation permettant de déterminer les paramètres issus des régions linéaires de la courbe de probabilité de matière, qui constitue la représentation gaussienne de la courbe du taux de longueur portante. Ces paramètres sont destinés à faciliter l'évaluation du comportement tribologique, par exemple de surfaces de glissement lubrifiées, et à maîtriser le procédé de fabrication.

## Specifikacija geometrijskih veličin izdelka - Tekstura površine: profilna metoda - Površine s slojevitimi funkcionalnimi lastnostmi - 3. del: Določevanje višine na osnovi krivulje verjetnosti (ISO 13565-3:1998)

### General Information

### Relations

### Standards Content (Sample)

SLOVENSKI STANDARD

SIST EN ISO 13565-3:2002

01-januar-2002

6SHFLILNDFLMDJHRPHWULMVNLKYHOLþLQL]GHOND7HNVWXUDSRYUãLQHSURILOQDPHWRGD

3RYUãLQHVVORMHYLWLPLIXQNFLRQDOQLPLODVWQRVWPLGHO'RORþHYDQMHYLãLQHQD

RVQRYLNULYXOMHYHUMHWQRVWL,62

Geometrical Product Specifications (GPS) - Surface texture: Profile method; surfaces

having stratified functional properties - Part 3: Height characterization using the material

probability curve (ISO 13565-3:1998)

Geometrische Produktspezifikation (GPS) - Oberflächenbeschaffenheit:

Tastschnittverfahren; Oberflächen mit plateauartigen funktionsrelevanten Eigenschaften

- Teil 3: Beschreibung der Höhe von Oberflächen mit der Wahrscheinlichkeitsdichtekurve

(ISO 13565-3:1998)

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

surfaces ayant des propriétés fonctionnelles différentes suivant les niveaux - Partie 3:

Caractérisation des hauteurs par la courbe de probabilité de matiere (ISO 13565-3:1998)

Ta slovenski standard je istoveten z: EN ISO 13565-3:2000

ICS:

17.040.20 Lastnosti površin Properties of surfaces

SIST EN ISO 13565-3:2002 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 13565-3:2002

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SIST EN ISO 13565-3:2002

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SIST EN ISO 13565-3:2002

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SIST EN ISO 13565-3:2002

INTERNATIONAL ISO

STANDARD 13565-3

First edition

1998-11-15

Geometrical Product Specifications (GPS) —

Surface texture: Profile method; Surfaces

having stratified functional properties —

Part 3:

Height characterization using the material

probability curve

Spécification géométrique des produits (GPS) — État de surface: Méthode

du profil; surfaces ayant des propriétés fonctionnelles différentes suivant

les niveaux —

Partie 3: Cartactérisation des hauteurs par la courbe de probabilité

de matière

A

Reference number

ISO 13565-3:1998(E)

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SIST EN ISO 13565-3:2002

ISO 13565-3:1998(E)

Contents Page

1 Scope .1

2 Normative references .1

3 Definitions .1

4 Procedure .2

5 Measurement process requirements .3

6 Drawing indications.3

Annex A (normative) Procedures for determining the limits of the linear regions .4

Annex B (informative) Background information .9

Annex C (informative) Determination of UPL and LVL via second derivatives.13

Annex D (informative) Normalization of the bounded material probability curve .16

Annex E (informative) Relation to the GPS matrix model .18

Annex F (informative) Bibliography.20

© ISO 1998

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic

or mechanical, including photocopying and microfilm, without permission in writing from the publisher.

International Organization for Standardization

Case postale 56 • CH-1211 Genève 20 • Switzerland

Internet iso@iso.ch

Printed in Switzerland

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SIST EN ISO 13565-3:2002

© ISO

ISO 13565-3:1998(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.

Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.

Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.

International Standard ISO 13565-3 was prepared by Technical Committee ISO/TC 213, Dimensional and

geometrical product specifications and verification.

ISO 13565 consists of the following parts under the general title Geometrical product specifications (GPS) —

Surface texture: Profile method; Surfaces having stratified functional properties:

Part 1: Filtering and general measurement conditions

Part 2: Height characterization using the linear material ratio curve

Part 3: Height characterization using the material probability curve

Annex A forms an integral part of this part of ISO 13565. Annexes B to F are for information only.

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SIST EN ISO 13565-3:2002

©

ISO

ISO 13565-3:1998(E)

Introduction

This part of ISO 13565 is a geometrical product specification (GPS) standard and is to be regarded as a general

GPS standard (see ISO/TR 14638). It influences the chain link 2 of the chains of standards on roughness profile

and primary profile.

For more detailed information on the relation of this standard to the GPS matrix model see annex E.

This part of ISO 13565 provides a numerical characterization of surfaces consisting of two vertical random

components, namely, a relatively coarse "valley" texture and a finer "plateau" texture. This type of surface is used

for lubricated, sliding contact, for example in cylinder liners and fuel injectors. The calculations necessary to

determine the parameters Rpq, Rvq, and Rmq (Ppq, Pvq, and Pmq) used to characterize these two components

separately involves the generation of the material probability curve, the determination of its linear regions, and the

linear regressions through these regions.

The parameters are undefined for surfaces not consisting of two such components.

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SIST EN ISO 13565-3:2002

INTERNATIONAL STANDARD © ISO ISO 13565-3:1998(E)

Geometrical Product Specifications (GPS) — Surface texture:

Profile method; Surfaces having stratified functional properties —

Part 3:

Height characterization using the material probability curve

1 Scope

This part of ISO 13565 establishes the evaluation process for determining parameters from the linear regions of the

material probability curve, which is the Gaussian representation of the material ratio curve. The parameters are

intended to aid in assessing tribological behaviour, for example of lubricated, sliding surfaces, and to control the

manufacturing process.

2 Normative references

The following standards contain provisions which, through reference in this text, constitute provisions of this part of

ISO 13565. At the time of publication, the editions indicated were valid. All Standards are subject to revision, and

parties to agreements based on this part of ISO 13565 are encouraged to investigate the possibility of applying the

most recent editions of the standards indicated below. Members of IEC and ISO maintain registers of currently valid

International Standards.

ISO 1302:1992, Technical drawings — Methods of indicating surface texture.

ISO 3274:1996, Geometrical Product Specifications (GPS) — Surface texture: Profile method — Nominal

characteristics of contact (stylus) instruments.

ISO 4287:1997, Geometrical Product Specifications (GPS) — Surface texture: Profile method — Terms, definitions

and surface texture parameters.

ISO 13565-1:1996, Geometrical Product Specifications (GPS) — Surface texture: Profile method; Surfaces having

stratified functional properties — Part 1: Filtering and general measurement conditions.

ISO 13565-2:1996, Geometrical Product Specifications (GPS) — Surface Texture: Profile method; Surfaces having

stratified functional properties — Part 2: Height characterization using the linear material ratio curve.

3 Definitions

For the purposes of this part of ISO 13565, the definitions given in ISO 3274, ISO 4287, ISO 13565-2 and the

following apply.

3.1

material probability curve

a representation of the material ratio curve in which the profile material length ratio is expressed as Gaussian

probability in standard deviation values, plotted linearly on the horizontal axis

NOTE — This scale is expressed linearly in standard deviations according to the Gaussian distribution. In this scale the

material ratio curve of a Gaussian distribution becomes a straight line. For stratified surfaces composed of two Gaussian

distributions, the material probability curve will exhibit two linear regions (see 1 and 2 in figure 1).

1

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SIST EN ISO 13565-3:2002

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ISO 13565-3:1998(E)

Key

1 Plateau region

2 Valley region

3 Debris or outlying peaks in the data (profile)

4 Deep scratches or outlying valleys in the data (profile)

5 Unstable region (curvature) introduced at the plateau to valley transition point based on the combination of two distributions

Figure 1 — Material probability curve

3.2

Rpq (Ppq) parameter

slope of a linear regression performed through the plateau region

See figure 2.

NOTE — Rpq (Ppq) can thus be interpreted as the Rq (Pq)-value (in micrometres) of the random process that generated the

plateau component of the profile.

3.3

Rvq (Pvq) parameter

slope of a linear regression performed through the valley region

See figure 2.

NOTE — Rvq (Pvq) can thus be interpreted as the Rq (Pq)-value (in micrometres) of the random process that generated the

valley component of the profile.

3.4

( )

Rmq Pmq parameter

relative material ratio at the plateau to valley intersection

See figure 2.

4 Procedure

The roughness profile used for determining the parameters Rpq, Rvq and Rmq shall be calculated in accordance with

ISO 13565-1. This roughness profile is different from that in ISO 4287. The profile for determining the parameters

Ppq, Pvq and Pmq shall be the primary profile.

Three non-linear effects can be present in the material probability curve as shown in figure 1 for measured surface

data from a two-process surface. These effects shall be eliminated by limiting the fitted portions of the material

probability curve, using only the statistically sound, Gaussian portions of the material probability curve excluding a

number of influences.

2

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SIST EN ISO 13565-3:2002

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ISO 13565-3:1998(E)

In figure 1 the non-linear effects originate from:

debris or outlying peaks in the data (profile) (labelled 3);

deep scratches or outlying valleys in the data (profile) (labelled 4); and

unstable region (curvature) introduced at the plateau to valley transition point based on the combination of two

distributions (labelled 5).

These exclusions are intended keep the parameters more stable for repeated measurements of a given surface.

Figure 2 shows a profile with its corresponding material probability curve and its plateau and valley regions and the

parts of the surface that defines the two regions. The profile has a peak that is outlying and the figure shows how it

does not influence the parameters. Figure 2 also shows how the bottom parts of the deepest groves, which will vary

significantly depending on where the measurements are made on a surface, are disregarded when determining the

parameters.

Figure 2 — Roughness profile with its corresponding material probability curve and the regions used

in the definitions of the parameters Rpq, Rvq, and Rmq

5 Measurement process requirements

The following criteria are designed to ensure that the profile represents a proper two-process surface and that the

measuring process is adequate for calculating a stable material probability curve resulting in reliable parameter

values. These criteria shall be met in order for the parameters Rpq, Rvq, and Rmq (Ppq, Pvq, and Pmq) to be defined:

The instrument shall be capable of measuring a value of Rq from an optical flat that is less than 30 % of the

nominal value of Rpq (Ppq).

The vertical resolution of the material probability curve shall be such that at least 40 classes fall within the linear

plateau and linear valley regions respectively.

The digital data density of the material probability curve shall be such that at least 100 profile ordinates fall

within the linear plateau and linear valley regions respectively.

The ratio Rvq: Rpq (Pvq: Ppq) shall be at least 5.

The conic section regressions result in a hyperbolic solution (see annex A).

If the profile does not satisfy the above criteria, a suitable warning message shall give the reason for the failure.

6 Drawing indications

The parameters specified in this part of ISO 13565 shall be indicated on drawings in accordance with ISO 1302.

3

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ISO 13565-3:1998(E)

Annex A

(normative)

Procedures for determining the limits of the linear regions

Clauses A.1 through A.3 specify the procedures for determining the upper plateau limit, UPL, and the lower valley

limit, LVL. Clauses A.4 through A.6 specify the procedures for determining the lower plateau limit, LPL, and the

upper valley limit, UVL . Clause A.7 specifies the procedure for determining the calculation of parameters.

A.1 Initial conic fit

A conic section is initially fitted through the material probability curve since it is a very good approximation of the

expected form of the material probability curve of surfaces consisting of two vertical random components. This initial

conic fit provides a framework for subsequent operations on the material probability curve.

Fit a conic section

2 2

z = Ax + Bxz + Cz + Dx + E

where

z is the profile height;

x is the material probability expressed in standard deviations;

through the entire curve (see figure A.1).

Figure A.1 — Conic section based on the entire material probability curve

A.2 Estimation of plateau to valley transition

Determine the asymptotes of the conic section (lines designated "a" in figure A.1). Bisect the asymptotes with a line

(line designated "b" in figure A.1). The intersection of this line with the conic section serves as an initial estimate of

the plateau to valley transition (see A in figure A.2).

NOTE — Graphically the bisector line may appear to be at a improper angle (see figure A.1). This is because of the different

scaling of the two axis on figure A.1. See also clause A.4 and annex D for the normalized material probability curve, where the

bisector line appears consistent.

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A.3 Determination of UPL and LVL

The second derivative is computed at each point of the material probability curve starting at the transition point "c"

and working upward through the plateau region and downward through the valley region.

The second derivative at each point is computed using a "window" of 0,05 standard deviations (– 0,025 × s around

the point at which the derivative is to be recorded). See B in figure A.2.

NOTE — The number of points within the window will vary as it is passed through the curve.

For the valley region and the plateau region individually:

find 25 % of the number of points to one side of the point "c"; call this value i;

working out from point "c", the standard deviation, s , is computed for the second derivative values using

i

i

points on one side;

the value of the second derivative at the next point (D ) is divided by the standard deviation, s :

i + 1 i

D

i+1

T =

s

i

if T < 6, increment i by 1, recompute s and T;

i

if T > 6, data point i is the limit of that region (UPL for the plateau region and LVL for the valley region,

respectively). See also C in figure A.2.

Figure A.2 — Bisection of the asymptotes is the initial transition point between the two regions

of the material probability curve and the corresponding second derivatives

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ISO 13565-3:1998(E)

A.4 Normalization of the bounded region

The Z-axis of the material probability curve is normalized such that the bounded region (region between UPL and

LVL) is "square" (see annex D). This insures consistent bisection of the conic section asymptotes (see figure A.3).

A.5 Second conic section fit

The conic section is now regressed through the region within UPL and LVL. The asymptotes are constructed (see

figure A.3).

NOTE — For k , see annex D.

s

Figure A.3 — Conic section determined within the upper plateau limit, UPL, and the lower valley limit,

LVL — Normalized material probability curve

A.6 Determination of LPL and UVL

To determine the lower plateau limit, LPL , and the upper valley limit, UVL , the asymptotes are bisected three times

(b: first time; P2 and V2: second time; P3 and V3: third time). The intersection of thes

**...**

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