PD ISO/TR 10657:2021

Explanatory notes on ISO 76

PD ISO/TR 10657:2021 PUBLISHED DOCUMENT

National foreword

This Published Document is the UK implementation of ISO/TR 10657:2021.

The UK participation in its preparation was entrusted to Technical Committee MCE/7, Rolling bearings.

A list of organizations represented on this committee can be obtained on request to its committee manager.

Contractual and legal considerations

This publication has been prepared in good faith, however no representation, warranty, assurance or undertaking (express or implied) is or will be made, and no responsibility or liability is or will be accepted by BSI in relation to the adequacy, accuracy, completeness or reasonableness of this publication. All and any such responsibility and liability is expressly disclaimed to the full extent permitted by the law.

This publication is provided as is, and is to be used at the recipient’s own risk.

The recipient is advised to consider seeking professional guidance with respect to its use of this publication.

This publication is not intended to constitute a contract. Users are responsible for its correct application.

This publication is not to be regarded as a British Standard.

© The British Standards Institution 2021 Published by BSI Standards Limited 2021

ISBN 978 0 580 93937 2

ICS 21.100.20

Compliance with a Published Document cannot confer immunity from legal obligations.

This Published Document was published under the authority of the Standards Policy and Strategy Committee on 30 November 2021.

Amendments/corrigenda issued since publication

Date Text affected

TECHNICAL REPORT

ISO/TR 10657

Second edition

2021-11

Explanatory notes on ISO 76

Notes explicatives sur l'ISO 76

Reference number ISO/TR 10657:2021(E)

© ISO 2021

Contents Page

Foreword iv

Introduction v

1. Scope 1

2. Normative references 1

1. Terms, definitions and symbols 1

   1. Terms and definitions 1

   2. Symbols 1

1. Basic static load ratings 3

   1. General 3

      1. Basic formula for point contact 3

      2. Basic formula for line contact 5

   2. Basic static radial load rating C0r for radial ball bearings 6

      1. Radial and angular contact groove ball bearings 6

      2. Self-aligning ball bearings 8

   3. Basic static axial load rating C0a for thrust ball bearings 8

   4. Basic static radial load rating C0r for radial roller bearings 10

   5. Basic static axial load rating C0a for thrust roller bearings 10

2. Static equivalent load 11

   1. Theoretical static equivalent radial load P0r for radial bearings 11

      1. Single-row radial bearings and radial contact groove ball bearings

         (nominal contact angle α = 0°) 11

      2. Double-row radial bearings 17

   2. Theoretical static equivalent axial load P0a for thrust bearings 18

      1. Single-direction thrust bearings 18

      2. Double-direction thrust bearings 21

   3. Approximate formulae for theoretical static equivalent load 23

      1. Radial bearings 23

      2. Thrust bearings 24

   4. Practical formulae of static equivalent load 24

      1. Radial bearings 24

      2. Thrust bearings 28

   5. Static radial load factor X0 and static axial load factor Y0 29

      1. Radial bearings 29

      2. Thrust bearings 33

Annex A (normative) Values for γ, κ and E(κ) 35

Bibliography 38

© ISO 2021 – All rights reserved

iii

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 4, Rolling bearings, Subcommittee SC 8,

Load ratings and life.

This second edition cancels and replaces the first edition (ISO 10657:1991), which has been technically

revised.

The main changes compared to the previous edition are as follows:

— New subclause 0.4 and 0.5 included with explanations concerning the 2006 edition of ISO 76:2006 and ISO 76/Amd.1:2017;

• Inclusion of Clause 3 for symbols;

  
  

• Table 16 and Table 18 amended according to additional values in ISO 76:2006 (values of X0 and Y0 at contact angles 5° and 10° of angular contact ball bearings).

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.

iv © ISO 2021 – All rights reserved

Introduction

0.1 ISO/R 76:1958

ISO/R 76, Ball and Roller Bearings — Methods of Evaluating Static Load Ratings, was drawn up by Technical Committee ISO/TC 4, Ball and Roller Bearings.

ISO/R 76 was based on the studies of A. Palmgren et al[2],[3]. The basic static load ratings were defined to correspond to a total permanent deformation of rolling element and raceway at the most heavily stressed rolling element/raceway contact of 0,000 1 of the rolling element diameter. Then the standard values confined to the basic static load ratings for special inner design rolling bearings were laid down.

ISO/R 76:1958 was approved by 28 (out of a total of 38) member bodies and was then submitted to the ISO Council, which decided, in December 1958, to accept it as an ISO Recommendation.

0.2 ISO 76:1978

ISO/TC 4 decided to include the revision of ISO/R 76 in its programme of work and ISO/TC 4/SC 8 secretariat was requested to prepare a draft proposal. As a result, the secretariat submitted a draft proposal[3] in January 1976.

The draft proposal was accepted by 6 of the 8 members of ISO/TC 4/SC 8. Of the remaining two, Japan preferred further study and USA, its counter proposal, document ISO/TC 4/SC 8 N 64[4]. The draft was then submitted to the ISO Central Secretariat. After the draft had been approved by the ISO member bodies, the ISO Council decided in June 1978 to accept it as an International Standard.

ISO 76:1978 adopted the SI unit newton and was revised in total, but without essential changes of substance. However, values of X0 and Y0 for the nominal contact angles 15° and 45° for angular contact groove ball bearings were added to the table to calculate the static equivalent radial loads of radial ball bearings (see ISO 76:1978, Table 2).

0.3 ISO 76:1987

During the revision of ISO/R 76:1958, USA had in 1975 submitted a counter proposal[4] for the basic static load ratings based on a calculated contact stress.

The secretariat requested a vote on the revision of the static load ratings based on a contact stress level in January 1978 and afterward circulated the voted results in June 1978, and the item No. of revision work had become No. 157 of the programme of work of TC 4.

ISO/TC 4/SC 8, considering the proposals made in the documents TC 4/SC 8 N 75[5] and TC 4 N 865[6], as well as the comments made by TC 4 members and that several SC 8 members expressed a need for updating ISO 76, agreed to continue its study taking into account the possibility of using either permanent deformation or stress level as a basis for static load ratings, and ISO/TC 4/SC 8 requested its secretariat to prepare a new draft. The new draft was intended to be prepared with the principles and formulae of the document TC 4/SC 8 N 75, and to include levels of contact stress for various rolling element contact stated to be generally corresponding to a permanent deformation of 0,000 1 of the rolling element diameter at the centre of the most heavily stressed rolling element/raceway contact. For roller bearings a stress level of 4 000 MPa was agreed and then ISO/TC 4/SC 8 agreed, by a majority vote, that static load ratings should correspond to calculated contact stresses of

4 000 MPa for roller bearings,

4 600 MPa for self-aligning ball bearings, and

4 200 MPa for all other ball bearings to which the standard applies.

For these calculated contact stresses, a total permanent deformation occurs at the centre of the most heavily stressed rolling element/raceway contact, and its deformation is approximately 0,000 1 of the rolling element diameter.

© ISO 2021 – All rights reserved v

ISO 76 was submitted to the ISO Central Secretariat in 1985, and after it had been approved by the ISO members, the ISO Council decided in February 1987 to accept it as an International Standard.

Furthermore, ISO/TC 4/SC 8 decided that supplementary background information, regarding the derivation of formulae and factors given in ISO 76, should be published as a Technical Report. This Technical report was published as ISO/TR 10657:1991.

An Amendment to ISO 76:1987 that explains the discontinuities in load ratings between radial- and axial bearings was published as ISO 76:1987/Amd.1:1999.

0.4 ISO 76:2006

A systematic review of ISO 76:1987 was agreed in 2003, based on the prior held balloting process and documents TC 4/SC 8 N 233 and N 235.

ISO 76:2006 includes editorial adaptations and updates as well as an extension by the static safety factor S0. Furthermore, ISO 76:1987/Amd.1:1999 was integrated and became the informative Annex A “Discontinuities in the calculation of basic static load ratings”.

0.5 ISO 76:2006/Amd.1:2017

ISO 76:2006/Amd.1:2017 includes the following items:

• graphs for the factors f0, X0 and Y0 taken from draft ÖNORM M 6320 to be included in an informative annex;

• formulae for the calculation of the load rating factor f0 from ISO/TR 10657 to be introduced in the

  normative part of the standard;

  
  

• the tables for the load rating factor f0 will stay in the normative part of the standard, however a sentence will be introduced stating that the results obtained from formulae are preferred.

  
  

  
  

  vi © ISO 2021 – All rights reserved

  
  

  
  

  
  

  Explanatory notes on ISO 76

  
  

  1. Scope

     This document specifies supplementary background information regarding the derivation of formulae and factors given in ISO 76:2006.

     
     

  2. Normative references

  There are no normative references in this document.

  
  

  1. Terms, definitions and symbols

     
     

     1. Terms and definitions

        No terms and definitions are listed in this document.

        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/

1. Symbols

C0a basic static axial load rating, in newtons

C0r basic static radial load rating, in newtons

Dpw pitch diameter of ball or roller set, in millimetres

Dw nominal ball diameter, in millimetres

Dwe roller diameter applicable in the calculation of load ratings, in millimetres

E modulus of elasticity (Young’ s modulus), in megapascals

E1, E2 modulus of elasticity of body 1 (rolling element) and of body 2 (raceway), in megapascals

E(κ) complete elliptic integral of the second kind

E0 E/(1 − ν2)

Fa bearing axial load (axial component of actual bearing load), in newtons

Fr bearing radial load (radial component of actual bearing load), in newtons

F(ρ) relative curvature difference

Ja(ε) axial load integral

Jr(ε) radial load integral

K(κ) complete elliptic integral of the first kind

© ISO 2021 – All rights reserved 1