ISO/TR 20051:2020

Spherical plain bearings — Derivation of the load rating factors

This document gives supplementary background information regarding the derivation of factors given in ISO 20015.

Rotules lisses — Explication sur le calcul des charges de base

General Information

• Status: Published
• Publication Date: 11-May-2020
• ICS: 21.100.10 - Plain bearings
• Technical Committee: ISO/TC 4/SC 8 - Load ratings and life
• Drafting Committee: ISO/TC 4/SC 8 - Load ratings and life
• Current Stage: 6060 - International Standard published
• Start Date: 12-May-2020
• Completion Date: 12-May-2020

Standards Content (Sample)

TECHNICAL ISO/TR
REPORT 20051
First edition
2020-05
Spherical plain bearings — Derivation
of the load rating factors
Rotules lisses — Explication sur le calcul des charges de base
Reference number
ISO/TR 20051:2020(E)
©
ISO 2020

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ISO/TR 20051:2020(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2020
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
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Published in Switzerland
ii © ISO 2020 – All rights reserved

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ISO/TR 20051:2020(E)

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 1
5 General . 3
6 Radial spherical plain bearings . 3
6.1 Bearing load distribution on the sliding contact area . 3
6.2 Bearing load rating . 5
6.3 Bearing load rating calculation for engineering . 6
7 Angular contact thrust spherical plain bearings . 6
7.1 Bearing load distribution on the sliding contact area . 6
7.2 Bearing load rating . 8
7.3 Bearing load rating calculation for engineering . 8
8 Angular contact radial spherical plain bearings . 9
8.1 Bearing load distribution on the sliding contact area . 9
8.2 Bearing load rating .10
8.2.1 General.10
8.2.2 Radial load rating .10
8.2.3 Axial load rating . .10
8.3 Bearing load rating calculation for engineering .11
8.3.1 General.11
8.3.2 Radial load rating .11
8.3.3 Axial load rating . .11
Annex A (informative) Values of factors for spherical plain bearings with steel/steel
contacting surfaces .12
Bibliography .13
© ISO 2020 – All rights reserved iii

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ISO/TR 20051:2020(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
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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
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iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 4, Rolling bearings, Subcommittee SC 8,
Load ratings and life.
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 2020 – All rights reserved

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ISO/TR 20051:2020(E)

Introduction
Different calculating methods for static and dynamic load ratings of spherical plain bearings have been
used in different countries, thus making it difficult to compare different solutions. A unified method for
the calculation of static and dynamic load ratings has been standardized in ISO 20015.
ISO 20015 leaves the load rating factors to the manufacturers to determine because they are dependent
on design and material. Bearing manufacturers don't have unified methods to determine these factors
themselves. This document gives the supplementary background information regarding the derivation
of factors in ISO 20015.
© ISO 2020 – All rights reserved v

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TECHNICAL REPORT ISO/TR 20051:2020(E)
Spherical plain bearings — Derivation of the load rating
factors
1 Scope
This document gives supplementary background information regarding the derivation of factors given
in ISO 20015.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
No terms and definitions are listed in this document.
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/
4 Symbols
2
A contact area on bearing sliding surface, in square millimetres (mm )
B inner ring width, in millimetres (mm)
C outer ring width, in millimetres (mm)
effective width of distribution of contact load, in millimetres (mm)
C
effective width of distribution of contact load function versus θ , in millimetres (mm)
C ()θ
C dynamic axial load rating, in newtons (N)
a
C dynamic radial load rating, in newtons (N)
r
C static axial load rating, in newtons (N)
0a
C static radial load rating, in newtons (N)
0r
D outside diameter, in millimetres (mm)
D smallest diameter of sliding contact surface of the outer ring, in millimetres (mm)
S1
D largest diameter of sliding contact surface of the outer ring, in millimetres (mm)
S2
d bore diameter, in millimetres (mm)
d sphere diameter, in millimetres (mm)
k
F axial load, in newtons (N)
a
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ISO/TR 20051:2020(E)

F radial load, in newtons (N)
r
f factor for the calculation of dynamic axial load ratings of the sliding contact area, which
a
depends on design and material, in newtons per square millimetre (MPa)
f (τ) factor for the calculation of axial load ratings of the sliding contact area for angular con-
a
tact radial spherical plain bearings and angular contact thrust spherical plain bearings,
function versus τ, in newtons per square millimetre (MPa)
f (θτ, ) factor for the calculation of radial load ratings of the sliding contact area for angular con-
ar
0
tact radial spherical plain bearings, function versus θ and τ, in newtons per square
0
millimetre (MPa)
f factor for the calculation of static axial load ratings of the sliding contact area, which
0a
depends on design and material, in newtons per square millimetre (MPa)
f factor for the calculation of dynamic radial load ratings of the sliding contact area, which
r
depends on design and material, in newtons per square millimetre (MPa)
f (ε) factor for the calculation of radial load ratings of the sliding contact area for radial spherical
r
plain bearing, function versus ε, in newtons per square millimetre (MPa)
f factor for the calculation of static radial load ratings of the sliding contact area, which
0r
depends on design and material, in newtons per square millimetre (MPa)
g (β ) axial contact stress distribution dimensionless function versus β
a
g (θζ, ) contact stress distribution dimensionless function versus θ and ζ for angular contact
ar
radial spherical plain bearing
radial contact stress distribution dimensionless function versus θ
g (θ )
r
surface integral of radial contact stress distribution dimensionless function versus θ
I(θ )
0
0
surface integral of axial contact stress distribution dimensionless function versus τ
J(τ)
factor affecting the accuracy for manufacturing (k ≤ 1)
k
p(θ ) contact stress function versus θ, in newtons per square millimetre (MPa)
contact stress function versus β, in newtons per square millimetre (MPa)
p(β)
p(θβ, ) contact stress function versus θ and β, in newtons per square millimetre (MPa)
p(θϕ, ) contact stress function versus θ and φ, in newtons per square millimetre (MPa)
axial contact stress function versus θ, in newtons per square millimetre (MPa)
p (θ )
a
axial contact stress function versus β, in newtons per square millimetre (MPa)
p (β)
a
p (θ , β) axial contact stress function versus θ and β, in newtons per square millimetre (MPa)
a
p (θ ) radial contact stress function versus θ, in newtons per square millimetre (MPa)
r
radial contact stress function versus β, in newtons per square millimetre (MPa)
p (β)
r
p (θ , β) radial contact stress function versus θ and β, in newtons per square millimetre (MPa)
r
p (θζ, ) radial contact stress function versus θ and ζ, in newtons per square millimetre (MPa)
r
p allowable contact stress of bearing material, in newtons per square millimetre (MPa)
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ISO/TR 20051:2020(E)

r variable of integration of radius of contact area
S width of contact area in spherical surface direction, in millimetres (mm)
s variable of integration of width of contact area in spherical surface direction
T bearing width, in millimetres (mm)
z coordinate variable along z axis
α variable angle in arising contact area, in radians (rad) (see Figure 3)
β variable angle in arising contact area, in radians (rad) (see Figure 3)
ε dimensionles
...