ISO/TR 20051:2020

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 2020
© ISO 2020
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ii © ISO 2020 – All rights reserved

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
Foreword
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This document was prepared by Technical Committee ISO/TC 4, Rolling bearings, Subcommittee SC 8,
Load ratings and life.
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iv © ISO 2020 – All rights reserved

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.
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
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
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
tact radial spherical plain bearings, function versus θ and τ, in newtons per square
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 )
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)
2 © ISO 2020 – All rights reserved

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
...