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

The aim of this document 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[1]. This document applies to plain thrust bearings with incorporated wedge and supporting surfaces having any ratio of wedge surface length lwed to length of one pad L. It deals with the value lwed/L = 0,75 as this value represents the optimum ratio[2]. The ratio of width to length of one pad can be varied in the range B/L = 0,5 to 2. The calculation method described in this document can be used for other incorporated gap shapes, e.g. plain thrust bearings with integrated baffle, when for these types the numerical solutions of Reynolds equation are known. The calculation method serves for designing and optimizing plain thrust bearings e.g. for fans, gear units, pumps, turbines, electrical 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. Dynamic operating conditions are not included.

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

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Publication Date
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6060 - International Standard published
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13-Jul-2020
Completion Date
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INTERNATIONAL ISO
STANDARD 12131-1
Second edition
2020-07
Plain bearings — Hydrodynamic plain
thrust pad bearings under steady-
state conditions —
Part 1:
Calculation of thrust pad bearings
Paliers lisses — Butées hydrodynamiques à patins géométrie fixe
fonctionnant en régime stationnaire —
Partie 1: Calcul des butées à segments
Reference number
ISO 12131-1:2020(E)
ISO 2020
---------------------- Page: 1 ----------------------
ISO 12131-1:2020(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 12131-1:2020(E)
Contents Page

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

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

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

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

4 Symbols and units ............................................................................................................................................................................................... 2

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 Load carrying capacity ..................................................................................................................................................................... 8

6.3 Frictional power..................................................................................................................................................................................... 9

6.4 Lubricant flow rate .............................................................................................................................................................................. 9

6.5 Heat balance ...........................................................................................................................................................................................10

6.5.1 General...................................................................................................................................................................................10

6.5.2 Heat dissipation by convection ........................................................................................................................10

6.5.3 Heat dissipation by recirculating lubrication ......................................................................................12

6.6 Minimum lubricant film thickness and specific bearing load .....................................................................14

6.7 Operating conditions ......................................................................................................................................................................14

6.8 Further influence factors .............................................................................................................................................................15

Annex A (informative) Examples of calculation .....................................................................................................................................16

Bibliography .............................................................................................................................................................................................................................25

© ISO 2020 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 12131-1:2020(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 12131-1:2001), which has been technically

revised.

The main changes compared to the previous edition are the correction of typographical errors.

A list of all parts in the ISO 12131 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
---------------------- Page: 4 ----------------------
INTERNATIONAL STANDARD ISO 12131-1:2020(E)
Plain bearings — Hydrodynamic plain thrust pad bearings
under steady-state conditions —
Part 1:
Calculation of thrust pad bearings
1 Scope

The aim of this document 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

[1]

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

This document applies to plain thrust bearings with incorporated wedge and supporting surfaces

having any ratio of wedge surface length l to length of one pad L. It deals with the value l /L = 0,75

wed wed
[2]

as this value represents the optimum ratio . The ratio of width to length of one pad can be varied in

the range B/L = 0,5 to 2.

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

plain thrust bearings with integrated baffle, when for these types the numerical solutions of Reynolds

equation are known.

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

units, pumps, turbines, electrical 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. Dynamic operating conditions are not included.
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 3448, Industrial liquid lubricants — ISO viscosity classification

ISO 12131-2:2016, Plain bearings — Hydrodynamic plain thrust pad bearings under steady-state

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

ISO 12131-3, Plain bearings — Hydrodynamic plain thrust pad bearings under steady-state conditions —

Part 3: Guide values for the calculation of thrust pad 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/
© ISO 2020 – All rights reserved 1
---------------------- Page: 5 ----------------------
ISO 12131-1:2020(E)
4 Symbols and units
See Table 1 and Figure 1.
Table 1 — Symbols and units
Symbol Designation Unit
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 (diameter of thrust bearing ring) m
D Housing outside diameter m
D Inside diameter of thrust bearing ring m
D Outside diameter of thrust bearing ring m
f* Characteristic value of friction 1
f * Characteristic value of friction for thrust pad bearing 1
F Bearing force (nominal load) N
F* Characteristic value of load carrying capacity 1
F * Characteristic value of load carrying capacity for thrust pad bearing 1
F Bearing force (load) under stationary conditions 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 in the 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 Wedge length m
wed
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 Specific bearing load p = F/(B × L × Z)
P Frictional power in the bearing or heat flow rate generated by it W
Maximum permissible specific bearing load Pa
lim
P Heat flow rate to the environment W
th, amb
P Heat flow rate arising from the frictional 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 Relative lubricant flow rate Q = B × h × U × Z m /s
0 0 min

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

Q* 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 Q* − Q* at the outlet of the clear- 1

2 1 3
ance gap
2 © ISO 2020 – All rights reserved
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ISO 12131-1:2020(E)
Table 1 (continued)
Symbol Designation Unit

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

Q* Characteristic value of lubricant flow rate at the sides 1
Re Reynolds number 1
Critical Reynolds' number 1
T Ambient temperature °C
amb
T Bearing temperature °C
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 pads 1
η Dynamic viscosity of the lubricant Pa⋅s
η Effective dynamic viscosity of the lubricant Pa⋅s
eff
ρ Density of the lubricant kg/m
© ISO 2020 – All rights reserved 3
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ISO 12131-1:2020(E)
Key
1 wedge surface
2 supporting surface
3 thrust collar
4 lubrication groove
5 thrust bearing ring

Figure 1 — Schematic view of a thrust pad bearing (bearing with incorporated wedge

and supporting surfaces)
4 © ISO 2020 – All rights reserved
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ISO 12131-1:2020(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 =×6 η××U (1)
   
∂x ∂xz∂ ∂z ∂x
   

See reference [1] for the derivation of Reynolds equation and reference [2] for the numerical solution.

For the solution of 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 and 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; the magnitude of the lubricant feed

pressure is negligible as compared to the lubricant film pressures themselves;
m) 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 p (x, z = 0,5 b) = 0;

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.

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

equation which are compiled in ISO 12131-2. In principle, other solutions are also permitted provided

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

© ISO 2020 – All rights reserved 5
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ISO 12131-1:2020(E)

ISO 12131-3, contains guide values according to which the calculation result is to be oriented in order to

ensure the functioning of the plain bearings.

In special cases, guide values deviating from ISO 12131-3, 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) which can 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 given if complete separation of the mating bearing parts is achieved by the

lubricant. Continuous operation in the mixed lubrication range results in premature 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 load, an auxiliary hydrostatic arrangement may be necessary for starting up or running down

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

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

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

influenced by the selection of the material. Attention is drawn to the fact that in the case of this bearing

design, wear can lead to a rapid decrease in the load carrying capacity.
6.1.3 Mechanical loading

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

deformation is permissible as long as it does 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 (out-of-balance, vibrations, etc.);

— deviations from the ideal geometry (machining tolerances, deviations during assembly, etc.);

— lubricants contaminated by solid, liquid and gaseous foreign matters;
— corrosion, electric erosion, etc.
Information as to further influence factors is given in 6.8.
6 © ISO 2020 – All rights reserved
---------------------- Page: 10 ----------------------
ISO 12131-1:2020(E)

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

condition, is to be checked by the Reynolds' number:
ρ××Uh
min
Re= ≤Re (2)
eff
Figure 2 — Scheme of calculation (flow chart)

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 [4].
© ISO 2020 – All rights reserved 7
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ISO 12131-1:2020(E)

Starting from the known bearing dimensions and operating data the plain bearing calculation

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

These shall be 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; modification of the

calculation sequence is possible.
6.2 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

Firstly, the minimum lubricant film thickness h as well as the effective viscosity η are still unknown

min eff

in Formula (3). In order to avoid a double iteration via the minimum lubricant film thickness h and

min

the effective bearing temperature T , the characteristic value of load carrying capacity F according to

eff

[5] is modified as follows to be the characteristic value of load carrying capacity for the calculation of

thrust pad bearings:
 
wed
FF=× (4)
 
 
min

F is a function of fh /;CB/L explained in ISO 12131-2 on the basis of the findings in

B minwed
reference [6]. Approximate functions are also given there.
8 © ISO 2020 – All rights reserved
---------------------- Page: 12 ----------------------
ISO 12131-1:2020(E)
6.3 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 follows:
min
fP=× (5)
UB××η ××LZ
eff

The characteristic value of friction f defined by Formula (5) is also modified as follows to be the

characteristic value of friction for thrust pad bearings f according to reference [5]:

wed
ff=× (6)
min
Thus the frictional power is calculated by using Formula (7)
UB××η ××LZ
eff
Pf=× (7)
wed

The characteristic value of friction for thrust pad bearings f defined by Formula (6) can be taken

from ISO 12131-2 as a function of the film thickness ratio h /C and of the ratio B/L and with this,

min wed
the frictional power loss P can be calculated.
6.4 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 to dissipate the frictional heat developing in the bearing. See Figure 3.

Key
1 wedge surface
2 supporting surface
Figure 3 — Schematic view of the lubricant balance and heat balance of one pad

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 approximately have the same size.

© ISO 2020 – All rights reserved 9
---------------------- Page: 13 ----------------------
ISO 12131-1:2020(E)
In Figure 3 the relationship of Q , Q and Q are defined by Formula (8).
1 2 3
Q = Q + Q (8)
1 2 3
with
Q = Q × Q (9)
1 1 0
Q = Q × Q (10)
3 3 0
Q = Q – Q (11)
2 1 3
Q = B × h × U × Z (12)
0 min
* *

The relative values of Q = Q /Q and Q = Q /Q can be taken from ISO 12131-2 as a function of

1 1 0 3 3 0

the geometry (B/L and l /L = 0,75) and the arising relative lubricant film thickness h /C .

wed min wed
Approximate functions are also given there.

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

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

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

th, f f

housing to the environment and via the lubricant emerging from the bearing. In practical applications,

one of the two kinds of heat dissipation is predominant. Additional safety is given to 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 mostly takes place by convection:
P = P
f th, amb

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

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

Heat dissipation by convection [6.5.1 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

10 © ISO 2020 – All rights reserved
---------------------- Page: 14 ----------------------
ISO 12131-1:2020(E)

to the environment. According to [7] the complex processes during the heat dissipation can be

summarized as follows:
P = k × A × (T − T) (13)
th, amb A B amb
with
2 2
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, the factor k is

amb A
defined by Formula (14).
kw=+712 (14)
Aamb
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.

The effective bearing temperature is obtained by equating P from Formula (7) and P from

f th, amb
Formula (13) and substituting Formula (15).
kA×
k= (15)
BL××Z
Thus, the effective bearing temperature is obtained as Formula (16).
U ×η
eff
Tf=× +T (16)
effB amb
kC×
wed
In this case, the bearing temperature is
T = T (17)
B eff

If the heat-emitting surface A of the bearing housing is not known exactly, Formula (18) or Formula (19)

can be substituted as an approximation:
for cylindrical housings
AD=×2 ×+π××DB (18)
HH H
for bearings in the machine structure
A = (15 to 20) × B × L × Z (19)
© ISO 2020 – All rights reserved 11
---------------------- Page: 15 ----------------------
ISO 12131-1:2020(E)
6.5.3 Heat dissipation by recirculating lubrication

In case of recirculating lubrication, heat dissipation takes place via the lubricant [6.5.1 b)]. The heat

flow rate in the lubricant P is defined by Formula (20).
th, L
P = ρ × Cp × Q × (T − T) (20)
th, L ex en
For mineral lubricants, the volume specific heat capacity amounts to
6 3
ρ × Cp = 1,8 × 10 J/(m ·K)
Mixing processes in the lubrication recess.

Since a thrust pad bearing consists of a certain number of separate pads it is necessary to consider not

only the lubricant flow rate of one single pad but also the lubricant flow rate of the complete bearing

and thus the mutual influence of the lubricant flow rate. The lubricant forced out at the end of the pads

Q (according to Figure 3) is mixed with newly fed lubricant in the following oil recess, i.e. the lubricant

temperature T at the inlet of the lubrication clearance gap is higher by ΔT than that of the newly fed

1 1
lubricant with temperature T (see Figure 4).
When determining the temperature difference by using Formula (21),
ΔT = T − T (21)
1 1 en

an empirical factor shall be introduced because a purely theoretical consideration of this mixing

problem has not yet led to satisfying results.

A mixing factor M can be introduced by using Formula (22) in order to achieve conformity with the

experience gathered up to now (see [5]):
Q Q
2 2
ΔΔT = ×=T ×ΔT (22)
12 2
* *
MQ×+ 1−MQ×
() MQ×+ 1−MQ×
for Q ≥ Q and Q* ≥ Q* respectively.
3 3
12 © ISO 2020 – All rights reserved
---------------------- Page: 16 ----------------------
ISO 12131-1:2020(E)
Key
X length of lubrication clearance gap
Y temperature

Figure 4 — Graphical representation of the temperature distribution in the lubricant film

To explain the mixing factor we s
...

FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 12131-1
ISO/TC 123/SC 8
Plain bearings — Hydrodynamic plain
Secretariat: JISC
thrust pad bearings under steady-
Voting begins on:
2020-03-24 state conditions —
Voting terminates on:
Part 1:
2020-05-19
Calculation of thrust pad bearings
Paliers lisses — Butées hydrodynamiques à patins géométrie fixe
fonctionnant en régime stationnaire —
Partie 1: Calcul des butées à segments
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 12131-1:2020(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 12131-1:2020(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
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/FDIS 12131-1:2020(E)
Contents Page

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

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

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

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

4 Symbols and units ............................................................................................................................................................................................... 2

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 Load carrying capacity ..................................................................................................................................................................... 8

6.3 Frictional power..................................................................................................................................................................................... 9

6.4 Lubricant flow rate .............................................................................................................................................................................. 9

6.5 Heat balance ...........................................................................................................................................................................................10

6.5.1 General...................................................................................................................................................................................10

6.5.2 Heat dissipation by convection ........................................................................................................................10

6.5.3 Heat dissipation by recirculating lubrication ......................................................................................12

6.6 Minimum lubricant film thickness and specific bearing load .....................................................................14

6.7 Operating conditions ......................................................................................................................................................................14

6.8 Further influence factors .............................................................................................................................................................15

Annex A (informative) Examples of calculation .....................................................................................................................................16

Bibliography .............................................................................................................................................................................................................................25

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ISO/FDIS 12131-1:2020(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 12131-1:2001), which has been technically

revised.

The main changes compared to the previous edition are the correction of typographical errors.

A list of all parts in the ISO 12131 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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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 12131-1:2020(E)
Plain bearings — Hydrodynamic plain thrust pad bearings
under steady-state conditions —
Part 1:
Calculation of thrust pad bearings
1 Scope

The aim of this document 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

[1]

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

This document applies to plain thrust bearings with incorporated wedge and supporting surfaces

having any ratio of wedge surface length l to length of one pad L. It deals with the value l /L = 0,75

wed wed
[2]

as this value represents the optimum ratio . The ratio of width to length of one pad can be varied in

the range B/L = 0,5 to 2.

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

plain thrust bearings with integrated baffle, when for these types the numerical solutions of Reynolds

equation are known.

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

units, pumps, turbines, electrical 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. Dynamic operating conditions are not included.
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 3448, Industrial liquid lubricants — ISO viscosity classification

ISO 12131-2:2016, Plain bearings — Hydrodynamic plain thrust pad bearings under steady-state

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

ISO 12131-3, Plain bearings — Hydrodynamic plain thrust pad bearings under steady-state conditions —

Part 3: Guide values for the calculation of thrust pad 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/
© ISO 2020 – All rights reserved 1
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ISO/FDIS 12131-1:2020(E)
4 Symbols and units
See Table 1 and Figure 1.
Table 1 — Symbols and units
Symbol Designation Unit
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 (diameter of thrust bearing ring) m
D Housing outside diameter m
D Inside diameter of thrust bearing ring m
D Outside diameter of thrust bearing ring m
f* Characteristic value of friction 1
f * Characteristic value of friction for thrust pad bearing 1
F Bearing force (nominal load) N
F* Characteristic value of load carrying capacity 1
F * Characteristic value of load carrying capacity for thrust pad bearing 1
F Bearing force (load) under stationary conditions 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 in the 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 Wedge length m
wed
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 Specific bearing load p = F/(B × L × Z)
P Frictional power in the bearing or heat flow rate generated by it W
Maximum permissible specific bearing load Pa
lim
P Heat flow rate to the environment W
th, amb
P Heat flow rate arising from the frictional 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 Relative lubricant flow rate Q = B × h × U × Z m /s
0 0 min

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

Q* 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 Q* − Q* at the outlet of the clear- 1

2 1 3
ance gap
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ISO/FDIS 12131-1:2020(E)
Table 1 (continued)
Symbol Designation Unit

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

Q* Characteristic value of lubricant flow rate at the sides 1
Re Reynolds number 1
Critical Reynolds' number 1
T Ambient temperature °C
amb
T Bearing temperature °C
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 pads 1
η Dynamic viscosity of the lubricant Pa⋅s
η Effective dynamic viscosity of the lubricant Pa⋅s
eff
ρ Density of the lubricant kg/m
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ISO/FDIS 12131-1:2020(E)
Key
1 wedge surface
2 thrust collar
3 supporting surface
4 lubrication groove
5 thrust bearing ring

Figure 1 — Schematic view of a thrust pad bearing (bearing with incorporated wedge

and supporting surfaces)
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ISO/FDIS 12131-1:2020(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 =×6 η××U (1)
   
∂x ∂xz∂ ∂z ∂x
   

See [1] for the derivation of Reynolds equation and [2] for the numerical solution.

For the solution of 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 and 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 even.

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; the magnitude of the lubricant feed

pressure is negligible as compared to the lubricant film pressures themselves.
m) 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 p (x, z = 0,5 B) = 0.

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.

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

equation which are compiled in ISO 12131-2. In principle, other solutions are also permitted provided

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

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ISO/FDIS 12131-1:2020(E)

ISO 12131-3, contains guide values according to which the calculation result is to be oriented in order to

ensure the functioning of the plain bearings.

In special cases, guide values deviating from ISO 12131-3, 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) which can 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 given if complete separation of the mating bearing parts is achieved by the

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

Short-time operation in the mixed lubrication range such as starting up and running down machines

with plain bearings, is unavoidable and can result in bearing damage after frequent occurrence.

When subjected to heavy load, an auxiliary hydrostatic arrangement may be necessary for starting up

or running down at a low speed. Running-in and adaptive wear to compensate for surface geometry

deviations from the ideal geometry are permissible as long as these are limited in time and locality and

occur without overload effects. In certain cases, a specific running-in procedure may be beneficial. This

can also be influenced by the selection of the material. Attention is drawn to the fact that in the case of

this bearing design, wear can lead to a rapid decrease in the load carrying capacity.

6.1.3 Mechanical loading

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

deformation is permissible as long as it does 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 (out-of-balance, vibrations, etc.);

— deviations from the ideal geometry (machining tolerances, deviations during assembly, etc.);

— lubricants contaminated by solid, liquid and gaseous foreign matters;
— corrosion, electric erosion, etc.
Information as to further influence factors is given in 6.8.
6 © ISO 2020 – All rights reserved
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ISO/FDIS 12131-1:2020(E)

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

condition, is to be checked by the Reynolds' number:
ρ××Uh
min
Re= ≤Re (2)
eff
Figure 2 — Scheme of calculation (flow chart)

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 [4].
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ISO/FDIS 12131-1:2020(E)

Starting from the known bearing dimensions and operating data the plain bearing calculation

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

These shall be 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; modification of the

calculation sequence is possible.
6.2 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

Firstly, the minimum lubricant film thickness h as well as the effective viscosity η are still unknown

min eff

in Formula (3). In order to avoid a double iteration via the minimum lubricant film thickness h and

min

the effective bearing temperature T , the characteristic value of load carrying capacity F according to

eff

[5] is modified as follows to be the characteristic value of load carrying capacity for the calculation of

thrust pad bearings:
 
wed
FF=× (4)
 
 
min

The function Ff= hC/;BL/ is explained in ISO 12131-2 on the basis of the findings in [6].

Bmin wed
Approximate functions are also given there.
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ISO/FDIS 12131-1:2020(E)
6.3 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 follows:
min
fP=× (5)
UB××η ××LZ
eff

The characteristic value of friction f defined by Formula (5) is also modified as follows to be the

characteristic value of friction for thrust pad bearings f according to [5]:
wed
ff=× (6)
min
Thus the frictional power is calculated by using Formula (7)
UB××η ××LZ
eff
Pf=× (7)
wed

The characteristic value of friction for thrust pad bearings f defined by Formula (6) can be taken

from ISO 12131-2 as a function of the film thickness ratio h /C and of the ratio B/L and with this,

min wed
the frictional power loss P can be calculated.
6.4 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 to dissipate the frictional heat developing in the bearing. See Figure 3.

Key
1 wedge surface
2 supporting surface
Figure 3 — Schematic view of the lubricant balance and heat balance of one pad

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 approximately have the same size.

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ISO/FDIS 12131-1:2020(E)
In Figure 3 the relationship of Q , Q and Q are defined by Formula (8).
1 2 3
Q = Q + Q (8)
1 2 3
with
Q = Q × Q (9)
1 1 0
Q = Q × Q (10)
3 3 0
Q = Q – Q (11)
2 1 3
Q = B × h × U × Z (12)
0 min
* *

The relative values of Q = Q /Q and Q = Q /Q can be taken from ISO 12131-2 as a function of

1 1 0 3 3 0

the geometry (B/L and l /L = 0,75) and the arising relative lubricant film thickness h /C .

wed min wed
Approximate functions are also given there.

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

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

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

th, f f

housing to the environment and via the lubricant emerging from the bearing. In practical applications,

one of the two kinds of heat dissipation is predominant. Additional safety is given to 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 mostly takes place by convection:
P = P
f th, amb

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

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

Heat dissipation by convection [6.5.1 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

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ISO/FDIS 12131-1:2020(E)

to the environment. According to [7] the complex processes during the heat dissipation can be

summarized as follows:
P = k × A × (T − T) (13)
th, amb A B amb
with
2 2
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, the factor k is

amb A
defined by Formula (14).
kw=+712 (14)
Aamb
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.

The effective bearing temperature is obtained by equating P from Formula (7) and P from

f th, amb
Formula (13) and substituting Formula (15).
kA×
k= (15)
BL××Z
Thus, the effective bearing temperature is obtained as Formula (16).
U ×η
eff
Tf=× +T (16)
effB amb
kC×
wed
In this case, the bearing temperature is
T = T (17)
B eff

If the heat-emitting surface A of the bearing housing is not known exactly, Formula (18) or Formula (19)

can be substituted as an approximation:
for cylindrical housings
AD=×2 ×+π××DB (18)
HH H
for bearings in the machine structure
A = (15 to 20) × B × L × Z (19)
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ISO/FDIS 12131-1:2020(E)
6.5.3 Heat dissipation by recirculating lubrication

In case of recirculating lubrication, heat dissipation takes place via the lubricant [6.5.1 b)]. The heat

flow rate in the lubricant P is defined by Formula (20).
th, L
P = ρ × Cp × Q × (T − T) (20)
th, L ex en
For mineral lubricants, the volume specific heat capacity amounts to
6 3
ρ × Cp = 1,8 × 10 J/(m ·K)
Mixing processes in the lubrication recess.

Since a thrust pad bearing consists of a certain number of separate pads it is necessary to consider not

only the lubricant flow rate of one single pad but also the lubricant flow rate of the complete bearing

and thus the mutual influence of the lubricant flow rate. The lubricant forced out at the end of the pads

Q (according to Figure 3) is mixed with newly fed lubricant in the following oil recess, i.e. the lubricant

temperature T at the inlet of the lubrication clearance gap is higher by ΔT than that of the newly fed

1 1
lubricant with temperature T (see Figure 4).
When determining the temperature difference by using Formula (21),
ΔT = T − T (21)
1 1 en

an empirical factor shall be introduced because a purely theoretical consideration of

...

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