Plain bearings — Hydrodynamic plain tilting pad thrust bearings under steady-state conditions — Part 1: Calculation of tilting pad thrust bearings

This document specifies a calculation method for oil-lubricated hydrodynamic plain bearings with complete separation of the thrust collar and tilting pad thrust bearing surfaces by a film of lubricant. This document applies to plain thrust bearings with tilting-type sliding blocks (tilting pads), where a wedge-shaped lubrication clearance gap is automatically formed during operation. The ratio of width to length of one pad can be varied in the range B/L = 0,5 to 2. This document is not applicable to heavily loaded tilting pad thrust bearings. NOTE Equivalent calculation procedures exist that enable operating conditions to be estimated and checked against acceptable conditions. The use of them is equally admissible.

Paliers lisses — Butées hydrodynamiques à patins oscillants fonctionnant en régime stationnaire — Partie 1: Calcul des butées à patins oscillants

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Publication Date
13-Apr-2021
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6060 - International Standard published
Start Date
14-Apr-2021
Completion Date
14-Apr-2021
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INTERNATIONAL ISO
STANDARD 12130-1
Second edition
2021-04
Plain bearings — Hydrodynamic plain
tilting pad thrust bearings under
steady-state conditions —
Part 1:
Calculation of tilting pad thrust
bearings
Paliers lisses — Butées hydrodynamiques à patins oscillants
fonctionnant en régime stationnaire —
Partie 1: Calcul des butées à patins oscillants
Reference number
ISO 12130-1:2021(E)
ISO 2021
---------------------- Page: 1 ----------------------
ISO 12130-1:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 12130-1:2021(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Symbols, terms and units ............................................................................................................................................................................. 1

5 Fundamentals, assumptions and premises .............................................................................................................................. 5

6 Calculation procedure .................................................................................................................................................................................... 6

6.1 Loading operations ............................................................................................................................................................................. 6

6.1.1 General...................................................................................................................................................................................... 6

6.1.2 Wear ............................................................................................................................................................................................ 6

6.1.3 Mechanical loading ........................................................................................................................................................ 6

6.1.4 Thermal loading ............................................................................................................................................................... 6

6.1.5 Outside influences .......................................................................................................................................................... 6

6.2 Coordinate of centre of pressure ............................................................................................................................................. 7

6.3 Load-carrying capacity .................................................................................................................................................................... 7

6.4 Frictional power..................................................................................................................................................................................... 9

6.5 Lubricant flow rate .............................................................................................................................................................................. 9

6.6 Heat balance ...........................................................................................................................................................................................10

6.6.1 General...................................................................................................................................................................................10

6.6.2 Heat dissipation by convection ........................................................................................................................10

6.6.3 Heat dissipation by recirculating lubrication ......................................................................................11

6.6.4 Mixing processes in the lubrication recess ............................................................................................11

6.7 Minimum lubricant film thickness and specific bearing load .....................................................................13

6.8 Operating conditions ......................................................................................................................................................................13

6.9 Further influence factors .............................................................................................................................................................14

Annex A (informative) Examples of calculation .....................................................................................................................................15

Bibliography .............................................................................................................................................................................................................................24

© ISO 2021 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 12130-1:2021(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 123, Plain bearings, Subcommittee SC 8,

Calculation methods for plain bearings and their applications.

This second edition cancels and replaces the first edition (ISO 12130-1:2001), which has been technically

revised.
The main changes compared to the previous edition are as follows:
— addition of Introduction;
— correction of numerical values in Table A.5;
— adjustment to ISO/IEC Directives, Part 2:2018;
— correction of typographical errors.
A list of all parts in the ISO 12130 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.
iv © ISO 2021 – All rights reserved
---------------------- Page: 4 ----------------------
ISO 12130-1:2021(E)
Introduction

The aim of the ISO 12130 series is to achieve designs of plain bearings that are reliable in operation by

the application of a calculation method for oil-lubricated hydrodynamic plain bearings with complete

separation of the thrust collar and plain bearing surfaces by a film of lubricant.

The calculation method described in this document can be used for other gap shapes, e.g. parabolic

lubrication clearance gaps, as well as for other types of sliding blocks, e.g. circular sliding blocks, when

for these types the numerical solutions of Reynolds equation are present. ISO 12130-2 gives only the

characteristic values for the plane wedge-shaped gap; the values are therefore not applicable to tilting

pads with axial support.

The calculation method serves for designing and optimizing plain thrust bearings e.g. for fans, gear

units, pumps, turbines, electric machines, compressors and machine tools. It is limited to steady-state

conditions, i.e. load and angular speed of all rotating parts are constant under continuous operating

conditions.
© ISO 2021 – All rights reserved v
---------------------- Page: 5 ----------------------
INTERNATIONAL STANDARD ISO 12130-1:2021(E)
Plain bearings — Hydrodynamic plain tilting pad thrust
bearings under steady-state conditions —
Part 1:
Calculation of tilting pad thrust bearings
1 Scope

This document specifies a calculation method for oil-lubricated hydrodynamic plain bearings with

complete separation of the thrust collar and tilting pad thrust bearing surfaces by a film of lubricant.

This document applies to plain thrust bearings with tilting-type sliding blocks (tilting pads), where a

wedge-shaped lubrication clearance gap is automatically formed during operation. The ratio of width

to length of one pad can be varied in the range B/L = 0,5 to 2.
This document is not applicable to heavily loaded tilting pad thrust bearings.

NOTE Equivalent calculation procedures exist that enable operating conditions to be estimated and checked

against acceptable conditions. The use of them is equally admissible.
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 12130-2, Plain bearings — Hydrodynamic plain tilting pad thrust bearings under steady-state

conditions — Part 2: Functions for calculation of tilting pad thrust bearings

ISO 12130-3, Plain bearings — Hydrodynamic plain tilting pad thrust bearings under steady-state

conditions — Part 3: Guide values for the calculation of tilting pad thrust bearings

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, terms and units
Symbols, terms and units are shown in Table 1 and Figure 1.
Table 1 — Symbols, terms and units
Symbol Term Unit
a distance between supporting point and inlet of the clearance gap in the m
direction of motion (circumferential direction)
© ISO 2021 – All rights reserved 1
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ISO 12130-1:2021(E)
Table 1 (continued)
Symbol Term Unit
* relative distance between supporting point and inlet of the clearance gap in 1
the direction of motion (circumferential direction)
A heat-emitting surface of the bearing housing m
B width of one pad m
B axial housing width m
Cp specific heat capacity of the lubricant (p = constant) J/(kg⋅K)
C wedge depth m
wed
D mean sliding diameter m
D housing outside diameter m
D inside diameter over tilting pads m
D outside diameter over tilting pads m
f* characteristic value of friction 1
F bearing force (load) at nominal rotational frequency N
F* characteristic value of load carrying capacity 1
F bearing force (load) at standstill N
h local lubricant film thickness (clearance gap height) m
h minimum permissible lubricant film thickness during operation m
lim
h minimum permissible lubricant film thickness on transition into mixed m
lim,tr
lubrication
h minimum lubricant film thickness (minimum clearance gap height) m
min
k heat transfer coefficient related to the product B · L · Z W/(m ⋅K)
k external heat transfer coefficient (reference surface A) W/(m ⋅K)
L length of one pad in circumferential direction m
M mixing factor 1
N rotational frequency (speed) of thrust collar s
p local lubricant film pressure Pa
p Pa
specific bearing load pF=⋅/()BL⋅Z
maximum permissible specific bearing load Pa
lim
P frictional power in the bearing or power generated heat flow rate W
P heat flow rate to the environment W
th,amb
heat flow rate arising from the friction power W
th,f
P heat flow rate in the lubricant W
th,L
Q lubricant flow rate m /s
Q* characteristic value of lubricant flow rate 1
Q m /s
relative lubricant flow rate QB=⋅hU⋅⋅Z
0 min

Q lubricant flow rate at the inlet of the clearance gap (circumferential direction) m /s

characteristic value of lubricant flow rate at the inlet of the clearance gap 1

Q lubricant flow rate at the outlet of the clearance gap (circumferential direction) m /s

* **
Q characteristic value of lubricant flow rate QQ− at the outlet of the
2 13
clearance gap

Q lubricant flow rate at the sides (perpendicular to circumferential direction) m /s

characteristic value of lubricant flow rate at the sides 1
Re Reynolds' number 1
2 © ISO 2021 – All rights reserved
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ISO 12130-1:2021(E)
Table 1 (continued)
Symbol Term Unit
Re Critical Reynolds' number 1
T ambient temperature °C
amb
T bearing temperature °C
T initial bearing temperature °C
B,0
T effective lubricant film temperature °C
eff
T lubricant temperature at the inlet of the bearing °C
T lubricant temperature at the outlet of the bearing °C
T maximum permissible bearing temperature °C
lim
T lubricant temperature at the inlet of the clearance gap °C
T lubricant temperature at the outlet of the clearance gap °C
U sliding velocity relative to mean diameter of bearing ring m/s
w velocity of air surrounding the bearing housing m/s
amb
x coordinate in direction of motion (circumferential direction) m
y coordinate in direction of lubrication clearance gap (axial) m
z coordinate perpendicular to the direction of motion (radial) m
Z number of tilting-pads 1
η dynamic viscosity of the lubricant Pa⋅s
η effective dynamic viscosity of the lubricant Pa⋅s
eff
ρ 3
density of the lubricant kg/m
© ISO 2021 – All rights reserved 3
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ISO 12130-1:2021(E)
Key
1 thrust collar
2 tilting-pad
3 centre of pressure (supporting surface)
Figure 1 — Schematic view of a tilting-pad thrust bearing
4 © ISO 2021 – All rights reserved
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ISO 12130-1:2021(E)
5 Fundamentals, assumptions and premises

The calculation is always carried out with the numerical solutions of Reynolds equation for sliding

surfaces with finite width, taking into account the physically correct boundary conditions for the

generation of pressure.
∂ ∂p ∂ ∂p ∂h
   
h + h =6ηU (1)
   
∂x ∂xz∂ ∂z ∂x
   

Reference is made, e.g. to Reference [1] for the derivation of Reynolds equation and to Reference [2] for

the numerical solution.

For the solution to Formula (1), the following idealizing assumptions and premises are used, the

[3]

reliability of which has been sufficiently confirmed by experiment and in practice :

a) the lubricant corresponds to a Newtonian fluid;
b) all lubricant flows are laminar;
c) the lubricant adheres completely to the sliding surfaces;
d) the lubricant is incompressible;
e) the lubrication clearance gap is completely filled with lubricant;

f) inertia effects, gravitational and magnetic forces of the lubricant are negligible;

g) the components forming the lubrication clearance gap are rigid or their deformation is negligible;

their surfaces are completely smooth and surface roughness effects are negligible;

h) the lubricant film thickness in the radial direction (z-coordinate) is constant;

i) fluctuations in pressure within the lubricant film normal to the sliding surfaces (y-coordinate) are

negligible;
j) there is no motion normal to the sliding surfaces (y-coordinate);
k) the lubricant is isoviscous over the entire lubrication clearance gap;
l) the lubricant is fed in at the widest lubrication clearance gap;

m) the magnitude of the lubricant feed pressure is negligible as compared to the lubricant film

pressures themselves;
n) the pad shape of the sliding surfaces is replaced by rectangles.
The boundary conditions for the solution of Reynolds equation are the following:
1) the gauge pressure of the lubricant at the feeding point is p(x = 0, z) = 0;

2) the feeding of the lubricant is arranged in such a way that it does not interfere with the generation

of pressure in the lubrication clearance gap;

3) the gauge pressure of the lubricant at the lateral edges of the plain bearing is px,zB=±0,50= ;

4) the gauge pressure of the lubricant is p(x = L, z) = 0 at the end of the pressure field.

The application of the principle of similarity in hydrodynamic plain bearing theory results in

dimensionless parameters of similarity for such characteristics as load carrying capacity, friction

behaviour and lubricant flow rate.
© ISO 2021 – All rights reserved 5
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ISO 12130-1:2021(E)

The use of parameters of similarity reduces the number of necessary numerical solutions of Reynolds

equation which are compiled in ISO 12130-2. In principle, other solutions are also permitted if they

satisfy the conditions given in this document and have the corresponding numerical accuracy.

ISO 12130-3 contains guide values according to which the calculation result shall be oriented in order

to ensure the functioning of the plain bearings.

In special cases, guide values deviating from ISO 12130-3, may be agreed for specific applications.

6 Calculation procedure
6.1 Loading operations
6.1.1 General

Calculation means the mathematical determination of the correct functioning using operational

parameters (see Figure 2). The parameters shall be compared with guide values. Thereby, the operational

parameters determined under varying operation conditions shall be permissible as compared to the

guide values. For this purpose, all continuous operating conditions shall be investigated.

6.1.2 Wear

Safety against wear is ensured if complete separation of the mating bearing parts is achieved by the

lubricant. Continuous operation in the mixed lubrication range results in early loss of functioning.

Intermittent operation in the mixed lubrication regime, such as starting up and running down machines

with plain bearings, is unavoidable but can result in bearing damage if frequent. When subjected to

heavy loads, an auxiliary hydrostatic arrangement may be necessary for starting up or running down

at low speed. Running-in and adaptive wear to compensate for surface geometry deviations from ideal

geometry are permissible as long as these are limited in time and locality and occur without overloading

effects. In certain cases, a specific running-in procedure may be beneficial. This can also be influenced

by the selection of the material.
6.1.3 Mechanical loading

The limits of mechanical loading are given by the strength of the bearing material. Slight permanent

deformations are permissible as long as these do not impair correct functioning of the plain bearing.

6.1.4 Thermal loading

The limits of thermal loading result not only from the thermal stability of the bearing material but also

from the viscosity-temperature relationship and the ageing tendency of the lubricant.

6.1.5 Outside influences

Calculation of correct functioning of plain bearings presupposes that the operating conditions are

known for all cases of continuous operation. In practice however, additional disturbing influences

frequently occur which are unknown at the design stage and cannot always be computed. Therefore, the

application of an appropriate safety margin between the operational parameters and the permissible

guide values is recommended. Disturbing influences are, e.g.
— spurious forces (e.g. out-of-balance, vibrations);

— deviations from ideal geometry (e.g. machining tolerances, deviations during assembly);

— lubricants contaminated by solid, liquid and gaseous foreign materials;
— corrosion, electric erosion.
6 © ISO 2021 – All rights reserved
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ISO 12130-1:2021(E)
Information as to further influence factors is given in 6.9.

The applicability of this document, for which laminar flow in the lubrication clearance gap is a necessary

condition, shall be checked using the Reynolds' number:
ρ··Uh
min
Re=≤Re (2)
eff

For wedge-shaped gaps with h /C = 0,8 a critical Reynolds' number of Re = 600 can be assumed

min wed cr
as guide value according to Reference [4].

The plain bearing calculation comprises, starting from the known bearing dimensions and operating data:

— the relationship between load-carrying capacity and lubricant film thickness;
— the frictional power;
— the lubricant flow rate;
— the heat balance;

these all being interdependent. The solution is obtained using an iterative method, the sequence of

which is summarized in the calculation flow chart in Figure 2.

For optimization of individual parameters, parameter variation can be performed and modification of

the calculation sequence is possible.
6.2 Coordinate of centre of pressure

In the case of tilting pads, the x-coordinate of the centre of pressure a corresponds with the x-coordinate

of the axis of tilt. The x-coordinate of the centre of pressure aa= /L related to the length of the sliding

block is a function of the relative minimum lubricant film thickness h /C and the relative width of

min wed

sliding block B/L. The function af= hC/;BL/ shall be referred to ISO 12130-2:2020,

Fwmin ed
Formula (14). An approximate function is also given in ISO 12130-2.

It is essential for the calculation that the relative minimum lubricant film thickness h /C as well

min wed

as the characteristic values of load-carrying capacity, frictional power and lubricant flow rate are

specified by the selection of the supporting point a and that these values remain unchanged even

under alternating operating conditions.
6.3 Load-carrying capacity

The parameter for the load-carrying capacity is the dimensionless characteristic value of load-carrying

capacity F*:
Fh·
min
F = (3)
UL··η ··BZ
eff

The function F* = f(h /C ; B/L) shall be referred to ISO 12130-2:2020, Formula (1) on the basis of

min wed
Reference [5]. An approximate function is also given in ISO 12130-2.
© ISO 2021 – All rights reserved 7
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ISO 12130-1:2021(E)
Figure 2 — Scheme of calculation (flow chart)
8 © ISO 2021 – All rights reserved
---------------------- Page: 13 ----------------------
ISO 12130-1:2021(E)
6.4 Frictional power

The losses due to friction in a hydrodynamic plain thrust bearing are given by the characteristic value

of friction f * which is defined as Formula (4).
Ph·
f min
f = (4)
UB··η ··LZ
eff
Thus, the frictional power is calculated as Formula (5).
UB··η ··LZ
eff
Pf= · (5)
min

The function f * = f(h /C ; B/L) shall be referred to ISO 12130-2:2020, Formula (6) on the basis of

min wed
Reference [5]. An approximate function is also given in ISO 12130-2.
6.5 Lubricant flow rate

The lubricant fed to the bearing forms a solid lubricant film separating the sliding surfaces. At the same

time, the lubricant has the task of dissipating the frictional heat which develops in the bearing.

Due to the rotational motion of the thrust collar, the lubricant is carried, with increasing pressure, in

the direction of the converging clearance gap. Thereby part of the lubricant is forced out at the sides of

each pad. It is assumed that the lateral portions have approximately the same size. See Figure 3.

Key
1 tilting-pad

Figure 3 — Schematic view of the lubricant balance and heat balance of one tilting pad

In Figure 3, the relationship among Q , Q and Q is represented by Formula (6)
1 2 3
QQ=+Q (6)
12 3
where
QQ= ·Q (7)
101
QQ= ·Q (8)
303
© ISO 2021 – All rights reserved 9
---------------------- Page: 14 ----------------------
ISO 12130-1:2021(E)
QQ=−Q (9)
21 3
QB=⋅hU⋅⋅Z (10)
0 min
* *

The relative values of QQ= /Q and QQ= /Q shall be referred to ISO 12130-2:2020, Formula (9) as

1 10 3 30

a function of the geometry (B/L) and the arising relative lubricant film thickness h /C . Approximate

min wed
functions are also given in ISO 12130-2.

It is assumed that the lubricant forced out at the sides of the pads, at Q , has the temperature (T + T )/2

3 1 2
and the lubricant forced out at the ends, at Q , has the temperature T .
2 2
6.6 Heat balance
6.6.1 General
The thermal condition of the plain bearing results from the heat balance.

The heat flow P arising from the frictional power P in the bearing is dissipated via the bearing housing

th,f f

to the environment and via the lubricant emerging from the bearing. With practical applications, one of

the two kinds of heat dissipation is predominant. Additional safety is given for the design by neglecting

the other kind of heat dissipation. The following assumptions can be made:

a) With pressureless lubricated bearings (self-lubrication, natural cooling) heat dissipation to the

environment takes place mostly by convection:
P = P
f th,amb

b) With pressure-lubricated bearings (recirculating lubrication) heat dissipation takes place mostly

via the lubricant (recooling):
P = P
f th,L
Examples of calculation are shown in Annex A.
6.6.2 Heat dissipation by convection

Heat dissipation by convection [6.6.1 a)] takes place by thermal conduction and lubricant recirculation

in the bearing housing and subsequently by radiation and convection from the surface of the housing to

the environment. According to Reference [6] the complex processes during the heat dissipation can be

summarized as follows:
Pk=−··AT T (11)
th,amb A Bamb
2 2

where k = 15 W/(m ⋅K) to 20 W/(m ⋅K) or when the bearing housing is subjected to an air-flow at a

velocity of w > 1,2 m/s, K is determined by Formula (12)
amb A
kw=+712 (12)
A amb
where w is expressed in m/s and k in W/(m ⋅K).
amb A

NOTE Thereby, the factor k accounts for the thermal conduction in the bearing housing as well as for the

convection and radiation from the bearing housing to the environment. That part of the frictional heat arising in

the bearing, which is dissipated via the shaft, is neglected here due to its very small amount in most cases.

10 © ISO 2021 – All rights reserved
---------------------- Page: 15 ----------------------
ISO 12130-1:2021(E)
By equating P from Formula (5) and P from Formula (11) and with
f th,amb
kA·
k= (13)
BL··Z
the effective bearing temperature is obtained:
U ·η
eff
Tf=+· T (14)
eff amb
kh·
min
In this case, the bearing temperature is:
TT= (15)
Beff

If the heat-emitting surface A of the bearing housing is not known exactly, Formulae (16) and (17) can

be substituted as an approximation:
— for cylindrical housings
AD=+2·· π··DB (16)
HH H
— for bearings in the machine structure
AB=x··LZ· (17)
where x is defined as 15 ≤ x ≤ 20.
6.6.3 Heat dissipation by recirculating lubrication

In case of recirculating lubrication, heat dissipation takes place via the lubricant [6.6.1 b)]. The heat

flow rate in the lubricant P is defined by Formula (18).
th,L
PC=−ρ··pQ TT (18)
th,L ex en
For mineral lubricants, the volume specific heat capacity amounts to:
6 3
ρ ·,Cp=×18 10 J/·()mK
6.6.4 Mixing processes in the lubrication recess

As a tilting-pad thrust bearing consists of a certain number of separate tilting-pads, it is necessary to

consider not only the lubricant flow rate of one single tilt
...

FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 12130-1
ISO/TC 123/SC 8
Plain bearings — Hydrodynamic plain
Secretariat: JISC
tilting pad thrust bearings under
Voting begins on:
2020-11-05 steady-state conditions —
Voting terminates on:
Part 1:
2020-12-31
Calculation of tilting pad thrust
bearings
Paliers lisses — Butées hydrodynamiques à patins oscillants
fonctionnant en régime stationnaire —
Partie 1: Calcul des butées à patins oscillants
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 12130-1:2020(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 2020
---------------------- Page: 1 ----------------------
ISO/FDIS 12130-1:2020(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

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/FDIS 12130-1:2020(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Symbols, terms and units ............................................................................................................................................................................. 1

5 Fundamentals, assumptions and premises .............................................................................................................................. 5

6 Calculation procedure .................................................................................................................................................................................... 6

6.1 Loading operations ............................................................................................................................................................................. 6

6.1.1 General...................................................................................................................................................................................... 6

6.1.2 Wear ............................................................................................................................................................................................ 6

6.1.3 Mechanical loading ........................................................................................................................................................ 6

6.1.4 Thermal loading ............................................................................................................................................................... 6

6.1.5 Outside influences .......................................................................................................................................................... 6

6.2 Coordinate of centre of pressure ............................................................................................................................................. 7

6.3 Load-carrying capacity .................................................................................................................................................................... 7

6.4 Frictional power..................................................................................................................................................................................... 9

6.5 Lubricant flow rate .............................................................................................................................................................................. 9

6.6 Heat balance ...........................................................................................................................................................................................10

6.6.1 General...................................................................................................................................................................................10

6.6.2 Heat dissipation by convection ........................................................................................................................10

6.6.3 Heat dissipation by recirculating lubrication ......................................................................................11

6.6.4 Mixing processes in the lubrication recess ............................................................................................11

6.7 Minimum lubricant film thickness and specific bearing load .....................................................................13

6.8 Operating conditions ......................................................................................................................................................................13

6.9 Further influence factors .............................................................................................................................................................14

Annex A (informative) Examples of calculation .....................................................................................................................................15

Bibliography .............................................................................................................................................................................................................................24

© ISO 2020 – All rights reserved iii
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ISO/FDIS 12130-1:2020(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

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 123, Plain bearings, Subcommittee SC 8,

Calculation methods for plain bearings and their applications.

This second edition cancels and replaces the first edition (ISO 12130-1:2001), which has been technically

revised.
The main changes compared to the previous edition are as follows:
— addition of Introduction;
— correction of numerical values in Table A.5;
— adjustment to ISO/IEC Directives, Part 2:2018;
— correction of typographical errors.
A list of all parts in the ISO 12130 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.
iv © ISO 2020 – All rights reserved
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ISO/FDIS 12130-1:2020(E)
Introduction

The aim of ISO 12130 series is to achieve designs of plain bearings that are reliable in operation by

the application of a calculation method for oil-lubricated hydrodynamic plain bearings with complete

separation of the thrust collar and plain bearing surfaces by a film of lubricant.

The calculation method described in this document can be used for other gap shapes, e.g. parabolic

lubrication clearance gaps, as well as for other types of sliding blocks, e.g. circular sliding blocks, when

for these types the numerical solutions of Reynolds equation are present. ISO 12130-2 gives only the

characteristic values for the plane wedge-shaped gap; the values are therefore not applicable to tilting

pads with axial support.

The calculation method serves for designing and optimizing plain thrust bearings e.g. for fans, gear

units, pumps, turbines, electric machines, compressors and machine tools. It is limited to steady-state

conditions, i.e. load and angular speed of all rotating parts are constant under continuous operating

conditions.
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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 12130-1:2020(E)
Plain bearings — Hydrodynamic plain tilting pad thrust
bearings under steady-state conditions —
Part 1:
Calculation of tilting pad thrust bearings
1 Scope

This document specifies a calculation method for oil-lubricated hydrodynamic plain bearings with

complete separation of the thrust collar and tilting pad thrust bearing surfaces by a film of lubricant.

This document applies to plain thrust bearings with tilting-type sliding blocks (tilting pads), where a

wedge-shaped lubrication clearance gap is automatically formed during operation. The ratio of width

to length of one pad can be varied in the range B/L = 0,5 to 2.
This document is not applicable to heavily loaded tilting pad thrust bearings.

NOTE Equivalent calculation procedures exist that enable operating conditions to be estimated and checked

against acceptable conditions. The use of them is equally admissible.
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 12130-2, Plain bearings — Hydrodynamic plain tilting pad thrust bearings under steady-state

conditions — Part 2: Functions for calculation of tilting pad thrust bearings

ISO 12130-3, Plain bearings — Hydrodynamic plain tilting pad thrust bearings under steady-state

conditions — Part 3: Guide values for the calculation of tilting pad thrust bearings

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, terms and units
Symbols, terms and units are shown in Table 1 and Figure 1.
Table 1 — Symbols, terms and units
Symbol Term Unit

a distance between supporting point and inlet of the clearance gap in the direc- m

tion of motion (circumferential direction)
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ISO/FDIS 12130-1:2020(E)
Table 1 (continued)
Symbol Term Unit
* relative distance between supporting point and inlet of the clearance gap in 1
the direction of motion (circumferential direction)
A heat-emitting surface of the bearing housing m
B width of one pad m
B axial housing width m
Cp specific heat capacity of the lubricant (p = constant) J/(kg⋅K)
C wedge depth m
wed
D mean sliding diameter m
D housing outside diameter m
D inside diameter over tilting pads m
D outside diameter over tilting pads m
f* characteristic value of friction 1
F bearing force (load) at nominal rotational frequency N
F* characteristic value of load carrying capacity 1
F bearing force (load) at standstill N
h local lubricant film thickness (clearance gap height) m
h minimum permissible lubricant film thickness during operation m
lim
h minimum permissible lubricant film thickness on transition into mixed m
lim,tr
lubrication
h minimum lubricant film thickness (minimum clearance gap height) m
min
k heat transfer coefficient related to the product B × L × Z W/(m ⋅K)
k external heat transfer coefficient (reference surface A) W/(m ⋅K)
L length of one pad in circumferential direction m
M mixing factor 1
N rotational frequency (speed) of thrust collar s
p local lubricant film pressure Pa
p Pa
specific bearing load pF=×/()BL×Z
maximum permissible specific bearing load Pa
lim
P frictional power in the bearing or power generated heat flow rate W
P heat flow rate to the environment W
th,amb
heat flow rate arising from the friction power W
th,f
P heat flow rate in the lubricant W
th,L
Q lubricant flow rate m /s
Q* characteristic value of lubricant flow rate 1
Q m /s
relative lubricant flow rate QB=×hU××Z
0 min

Q lubricant flow rate at the inlet of the clearance gap (circumferential direction) m /s

characteristic value of lubricant flow rate at the inlet of the clearance gap 1

Q lubricant flow rate at the outlet of the clearance gap (circumferential direction) m /s

* **
Q characteristic value of lubricant flow rate QQ− at the outlet of the clear-
2 13
ance gap

Q lubricant flow rate at the sides (perpendicular to circumferential direction) m /s

characteristic value of lubricant flow rate at the sides 1
Re Reynolds' number 1
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ISO/FDIS 12130-1:2020(E)
Table 1 (continued)
Symbol Term Unit
Re Critical Reynolds' number 1
T ambient temperature °C
amb
T bearing temperature °C
T initial bearing temperature °C
B,0
T effective lubricant film temperature °C
eff
T lubricant temperature at the inlet of the bearing °C
T lubricant temperature at the outlet of the bearing °C
T maximum permissible bearing temperature °C
lim
T lubricant temperature at the inlet of the clearance gap °C
T lubricant temperature at the outlet of the clearance gap °C
U sliding velocity relative to mean diameter of bearing ring m/s
w velocity of air surrounding the bearing housing m/s
amb
x coordinate in direction of motion (circumferential direction) m
y coordinate in direction of lubrication clearance gap (axial) m
z coordinate perpendicular to the direction of motion (radial) m
Z number of tilting-pads 1
η dynamic viscosity of the lubricant Pa⋅s
η effective dynamic viscosity of the lubricant Pa⋅s
eff
ρ 3
density of the lubricant kg/m
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ISO/FDIS 12130-1:2020(E)
Key
1 thrust collar
2 tilting-pad
3 centre of pressure (supporting surface)
Figure 1 — Schematic view of a tilting-pad thrust bearing
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ISO/FDIS 12130-1:2020(E)
5 Fundamentals, assumptions and premises

The calculation is always carried out with the numerical solutions of Reynolds equation for sliding

surfaces with finite width, taking into account the physically correct boundary conditions for the

generation of pressure.
∂ ∂p ∂ ∂p ∂h
   
h + h =6ηU (1)
   
∂x ∂xz∂ ∂z ∂x
   

Reference is made, e.g. to Reference [1] for the derivation of Reynolds equation and to Reference [2] for

the numerical solution.

For the solution to Formula (1), the following idealizing assumptions and premises are used, the

[3]

reliability of which has been sufficiently confirmed by experiment and in practice :

a) the lubricant corresponds to a Newtonian fluid;
b) all lubricant flows are laminar;
c) the lubricant adheres completely to the sliding surfaces;
d) the lubricant is incompressible;
e) the lubrication clearance gap is completely filled with lubricant;

f) inertia effects, gravitational and magnetic forces of the lubricant are negligible;

g) the components forming the lubrication clearance gap are rigid or their deformation is negligible;

their surfaces are completely smooth and surface roughness effects are negligible;

h) the lubricant film thickness in the radial direction (z-coordinate) is constant;

i) fluctuations in pressure within the lubricant film normal to the sliding surfaces (y-coordinate) are

negligible;
j) there is no motion normal to the sliding surfaces (y-coordinate);
k) the lubricant is isoviscous over the entire lubrication clearance gap;
l) the lubricant is fed in at the widest lubrication clearance gap;

m) the magnitude of the lubricant feed pressure is negligible as compared to the lubricant film

pressures themselves;
n) the pad shape of the sliding surfaces is replaced by rectangles.
The boundary conditions for the solution of Reynolds equation are the following:
1) the gauge pressure of the lubricant at the feeding point is p(x = 0, z) = 0

2) the feeding of the lubricant is arranged in such a way that it does not interfere with the generation

of pressure in the lubrication clearance gap

3) the gauge pressure of the lubricant at the lateral edges of the plain bearing is px,zB=±0,50=

4) the gauge pressure of the lubricant is p(x = L, z) = 0 at the end of the pressure field.

The application of the principle of similarity in hydrodynamic plain bearing theory results in

dimensionless parameters of similarity for such characteristics as load carrying capacity, friction

behaviour and lubricant flow rate.
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ISO/FDIS 12130-1:2020(E)

The use of parameters of similarity reduces the number of necessary numerical solutions of Reynolds

equation which are compiled in ISO 12130-2. In principle, other solutions are also permitted if they

satisfy the conditions given in this document and have the corresponding numerical accuracy.

ISO 12130-3 contains guide values according to which the calculation result shall be oriented in order

to ensure the functioning of the plain bearings.

In special cases, guide values deviating from ISO 12130-3, may be agreed for specific applications.

6 Calculation procedure
6.1 Loading operations
6.1.1 General

Calculation means the mathematical determination of the correct functioning using operational

parameters (see Figure 2). The parameters shall be compared with guide values. Thereby, the operational

parameters determined under varying operation conditions shall be permissible as compared to the

guide values. For this purpose, all continuous operating conditions shall be investigated.

6.1.2 Wear

Safety against wear is ensured if complete separation of the mating bearing parts is achieved by the

lubricant. Continuous operation in the mixed lubrication range results in early loss of functioning.

Intermittent operation in the mixed lubrication regime, such as starting up and running down machines

with plain bearings, is unavoidable but can result in bearing damage if frequent. When subjected to

heavy loads, an auxiliary hydrostatic arrangement may be necessary for starting up or running down

at low speed. Running-in and adaptive wear to compensate for surface geometry deviations from ideal

geometry are permissible as long as these are limited in time and locality and occur without overloading

effects. In certain cases, a specific running-in procedure may be beneficial. This can also be influenced

by the selection of the material.
6.1.3 Mechanical loading

The limits of mechanical loading are given by the strength of the bearing material. Slight permanent

deformations are permissible as long as these do not impair correct functioning of the plain bearing.

6.1.4 Thermal loading

The limits of thermal loading result not only from the thermal stability of the bearing material but also

from the viscosity-temperature relationship and the ageing tendency of the lubricant.

6.1.5 Outside influences

Calculation of correct functioning of plain bearings presupposes that the operating conditions are

known for all cases of continuous operation. In practice however, additional disturbing influences

frequently occur which are unknown at the design stage and cannot always be computed. Therefore, the

application of an appropriate safety margin between the operational parameters and the permissible

guide values is recommended. Disturbing influences are, e.g.
— spurious forces (e.g. out-of-balance, vibrations);

— deviations from ideal geometry (e.g. machining tolerances, deviations during assembly);

— lubricants contaminated by solid, liquid and gaseous foreign materials;
— corrosion, electric erosion.
6 © ISO 2020 – All rights reserved
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ISO/FDIS 12130-1:2020(E)
Information as to further influence factors is given in 6.9.

The applicability of this document, for which laminar flow in the lubrication clearance gap is a necessary

condition, shall be checked using the Reynolds' number:
ρ··Uh
min
Re=≤Re (2)
eff

For wedge-shaped gaps with h /C = 0,8 a critical Reynolds' number of Re = 600 can be assumed

min wed cr
as guide value according to Reference [4].

The plain bearing calculation comprises, starting from the known bearing dimensions and operating data:

— the relationship between load-carrying capacity and lubricant film thickness;
— the frictional power;
— the lubricant flow rate;
— the heat balance;

these all being interdependent. The solution is obtained using an iterative method, the sequence of

which is summarized in the calculation flow chart in Figure 2.

For optimization of individual parameters, parameter variation can be performed; and modification of

the calculation sequence is possible.
6.2 Coordinate of centre of pressure

In the case of tilting pads, the x-coordinate of the centre of pressure a corresponds with the x-coordinate

of the axis of tilt. The x-coordinate of the centre of pressure aa= /L related to the length of the sliding

block is a function of the relative minimum lubricant film thickness h /C and the relative width of

min wed

sliding block B/L. The function af= hC/;BL/ shall be referred to ISO 12130-2 :2020,

Fwmin ed
Formula (14). An approximate function is also given there.

It is essential for the calculation that the relative minimum lubricant film thickness h /C as well

min wed

as the characteristic values of load-carrying capacity, frictional power and lubricant flow rate are

specified by the selection of the supporting point a and that these values remain unchanged even

under alternating operating conditions.
6.3 Load-carrying capacity

The parameter for the load-carrying capacity is the dimensionless characteristic value of load-carrying

capacity F*:
Fh·
min
F = (3)
UL··η ··BZ
eff

The function F* = f(h /C ; B/L) shall be referred to ISO 12130-2:2020,Formula (1) on the basis of

min wed
Reference [5]. An approximate function is also given there.
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ISO/FDIS 12130-1:2020(E)
Figure 2 — Scheme of calculation (flow chart)
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ISO/FDIS 12130-1:2020(E)
6.4 Frictional power

The losses due to friction in a hydrodynamic plain thrust bearing are given by the characteristic value

of friction f * which is defined as Formula (4).
Ph·
f min
f = (4)
UB··η ··LZ
eff
Thus, the frictional power is calculated as Formula (5).
UB··η ··LZ
eff
Pf= · (5)
min

The function f * = f(h /C ; B/L) shall be referred to ISO 12130-2:2020, Formula (6) on the basis

min wed
[5]
of. An approximate function is also given there.
6.5 Lubricant flow rate

The lubricant fed to the bearing forms a solid lubricant film separating the sliding surfaces. At the same

time, the lubricant has the task of dissipating the frictional heat which develops in the bearing.

Due to the rotational motion of the thrust collar, the lubricant is carried, with increasing pressure, in

the direction of the converging clearance gap. Thereby part of the lubricant is forced out at the sides of

each pad. It is assumed that the lateral portions have approximately the same size. See Figure 3.

Key
1 tilting-pad

Figure 3 — Schematic view of the lubricant balance and heat balance of one tilting pad

In Figure 3, the relationship among Q , Q and Q is represented by Formula (6)
1 2 3
QQ=+Q (6)
12 3
where
QQ= · Q (7)
101
QQ= · Q (8)
303
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ISO/FDIS 12130-1:2020(E)
QQ=−Q (9)
21 3
QB=× hU×× Z (10)
0 min
* *

The relative values of QQ= /Q and QQ= /Q shall be referred to ISO 12130-2:2020, Formula (9) as

1 10 3 30

a function of the geometry (B/L) and the arising relative lubricant film thickness h /C . Approximate

min wed
functions are also given there.

It is assumed that the lubricant forced out at the sides of the pads, at Q , has the temperature (T + T )/2

3 1 2
and the lubricant forced out at the ends, at Q , has the temperature T .
2 2
6.6 Heat balance
6.6.1 General
The thermal condition of the plain bearing results from the heat balance.

The heat flow P arising from the frictional power P in the bearing is dissipated via the bearing housing

th,f f

to the environment and via the lubricant emerging from the bearing. With practical applications, one of

the two kinds of heat dissipation is predominant. Additional safety is given for the design by neglecting

the other kind of heat dissipation. The following assumptions can be made:

a) With pressureless lubricated bearings (self-lubrication, natural cooling) heat dissipation to the

environment takes place mostly by convection:
P = P
f th,amb

b) With pressure-lubricated bearings (recirculating lubrication) heat dissipation takes place mostly

via the lubricant (recooling):
P = P
f th,L
Examples of calculation are shown in Annex A.
6.6.2 Heat dissipation by convection

Heat dissipation by convection [6.6.1 a)] takes place by thermal conduction and lubricant recirculation

in the bearing housing and subsequently by radiation and convection from the surface of the housing to

the environment. According to Reference [6] the complex processes during the heat dissipation can be

summarized as follows:
Pk=−·· AT T (11)
th,amb A Bamb
2 2

where k = 15 W/(m ⋅K) to 20 W/(m ⋅K) or when the bearing housing is subjected to an air-flow at a

velocity of w > 1,2 m/s, K is determined by Formula (12)
amb A
kw=+712 (12)
A amb
where w is expressed in m/s and k in W/(m ⋅K).
amb A

NOTE Thereby, the factor k accounts for the thermal conduction in the bearing housing as well as for the

convection and radiation from the bearing housing to the environment. That part of the frictional heat arising in

the bearing, which is dissipated via the shaft, is neglected here due to its very small amount in most cases.

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ISO/FDIS 12130-1:2020(E)
By equating P from Formula (5) and P from Formula (11) and with
f th,amb
kA·
k= (13)
BL··Z
the effective bearing temperature is obtained
U ·η
eff
Tf=+· T (14)
eff amb
kh·
min
In this case, the bearing temperature is
TT= (15)
Beff

If the heat-emitting surface A of the bearing housing is not known exactly, Formulae (16) and (17) can

be substituted as an approximation:
for cylindrical housings
AD=+2·· π··DB (16)
HH H
for bearings in the machine structur
...

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