ISO 31657-1:2025
(Main)Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part 1: Calculation of multi-lobed and tilting pad journal bearings
Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part 1: Calculation of multi-lobed and tilting pad journal bearings
This document specifies the general principles, assumptions and preconditions for the calculation of multi-lobed and tilting-pad journal bearings by means of an easy-to-use calculation procedure based on numerous simplifying assumptions. The calculation method applies to the design and optimisation of plain bearings, for example in turbines, compressors, generators, electric motors, gears and pumps. It is restricted to steady-state operation, i.e. in continuous operating states the load according to size and direction and the angular velocity of the rotor are constant.
Paliers lisses — Paliers lisses hydrodynamiques radiaux fonctionnant en régime stabilisé — Partie 1: Calcul pour les paliers radiaux multilobés et à patins oscillants
General Information
Standards Content (Sample)
International
Standard
ISO 31657-1
First edition
Plain bearings — Hydrodynamic
2025-10
plain journal bearings under
steady-state conditions —
Part 1:
Calculation of multi-lobed and
tilting pad journal bearings
Paliers lisses — Paliers lisses hydrodynamiques radiaux
fonctionnant en régime stabilisé —
Partie 1: Calcul pour les paliers radiaux multilobés et à patins
oscillants
Reference number
© ISO 2025
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
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and units. 1
5 General principles, assumptions and preconditions . 7
6 Calculation method .12
6.1 General . 12
6.2 Load-carrying capacity .14
6.3 Frictional power .14
6.4 Lubricant flow rate .14
6.5 Heat balance . . 15
6.6 Maximum lubricant film temperature .17
6.7 Maximum lubricant film pressure .18
6.8 Operating states .18
6.9 Further influencing parameters .18
6.10 Stiffness and damping coefficients .19
Annex A (informative) Calculation examples .24
Bibliography .38
iii
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
ISO technical committees. Each member body interested in a subject for which a technical committee
has been established has the right to be represented on that committee. International organizations,
governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely
with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
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 first edition of ISO 31657-1 cancels and replaces ISO/TS 31657-1:2020, which has been technically
revised.
The main changes are as follows:
— Clause 7 has been deleted;
— correction of typographical errors.
A list of all parts in the ISO 31657 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
Introduction
The aim of this document is the operationally-safe design of plain journal bearings for medium or high
journal circumferential velocities, U , up to approximately 90 m/s by applying a calculation method for oil-
J
lubricated hydrodynamic plain bearings with complete separation of journal and bearing sliding surfaces by
a lubricating film.
For low circumferential velocities up to approximately 30 m/s, circular cylindrical bearings are normally
applied. For these bearings, a similar calculation method is given in ISO 7902-1, ISO 7902-2 and ISO 7902-3.
Based on practical experience, the calculation procedure is usable for application cases where specific
bearing load times circumferential speed, pU⋅ , does not exceed approximately 200 MPa·m/s.
J
This document discusses multi-lobed journal bearings with two, three and four equal, symmetrical sliding
surfaces, which are separated by laterally-closed lubrication pockets, and symmetrically-loaded tilting-pad
journal bearings with four and five pads. Here, the curvature radii, R , of the sliding surfaces are usually
B
chosen larger than half the bearing diameter, D, so that an increased bearing clearance results at the pad ends.
The calculation method described here can also be used for other gap forms, for example asymmetrical
multi-lobed journal bearings like offset-halves bearings, pressure-dam bearings or other tilting-pad journal
bearing designs, if the numerical solutions of the basic formulae are available for these designs.
For a reliable evaluation of the results of this calculation method, it is indispensable to consider the
physical implications of these assumptions as well as practical experiences for instance from temperature
measurements carried out on real machinery under typical operating conditions. Applied in this sense, this
document presents a simple way to predict the approximate performance of plain journal bearings for those
unable to access more complex and accurate calculation techniques.
Unsteady operating states are not recorded. The stiffness and damping coefficients of the plain journal
bearings required for the linear vibration and stability investigations are indicated in ISO 31657-2 and
ISO 31657-3.
NOTE Equivalent calculation procedures exist that enable operating conditions to be estimated and checked
against acceptable conditions. Another calculation procedure is equally admissible.
v
International Standard ISO 31657-1:2025(en)
Plain bearings — Hydrodynamic plain journal bearings under
steady-state conditions —
Part 1:
Calculation of multi-lobed and tilting pad journal bearings
1 Scope
This document specifies the general principles, assumptions and preconditions for the calculation of multi-
lobed and tilting-pad journal bearings by means of an easy-to-use calculation procedure based on numerous
simplifying assumptions.
The calculation method applies to the design and optimisation of plain bearings, for example in turbines,
compressors, generators, electric motors, gears and pumps. It is restricted to steady-state operation, i.e. in
continuous operating states the load according to size and direction and the angular velocity of the rotor are
constant.
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 31657-2, Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part 2:
Characteristic values for calculation of multi-lobed journal bearings
ISO 31657-3, Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part 3:
Characteristic values for calculation of tilting pad journal bearings
ISO 31657-4, Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part 4:
Permissible operational parameters for calculation of multi-lobed and tilting pad journal bearings
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 Symbols and units
Table 1 contains the symbols used in the ISO 31657 series.
Table 1 — Symbols and units
Symbol Description Unit
B Bearing width m
B
*
*
Relative bearing width, width ratio as given by: B =
B
D
b Width of lubricant pocket m
P
b
* P
*
b Relative width of lubricant pocket, as given by: b =
P P
B
Bearing radial clearance, as given by: CR=−R
C
m
RJ
R
C
Effective radial bearing clearance m
R,eff
c Stiffness coefficient of lubricant film (i,k = 1,2) N/m
ik
Non-dimensional stiffness coefficient of lubricant film, as given by:
*
ψ
c
* eff
ik
c = ⋅=ci(),,k 12
ik ik
2⋅⋅B ηω⋅
eff
c
Specific heat capacity (p = constant) J/(kg K)
p
D Nominal bearing diameter (inside diameter of journal bearing) m
D Maximum value of D m
max
D Minimum value of D m
min
D
Journal diameter (diameter of the shaft section located inside of a journal bearing) m
J
D Maximum value of D
m
Jm, ax J
D Minimum value of D
m
Jm, in J
d Damping coefficient of lubricant film (i,k = 1,2) N s/m
ik
Non-dimensional damping coefficient of lubricant film, as given by:
*
ψ 1
d
* eff
ik
d = ⋅⋅ω di(),,k =12
ik ik
2⋅⋅B ηω⋅
eff
e Eccentricity (distance between journal and bearing axis) m
Eccentricity of the bearing sliding surfaces (pads) of a multi-lobed or tilting-pad journal bear-
e m
B
ing
F Bearing force, bearing load, nominal bearing load, load-carrying capacity N
F Friction force, as given by: Ff=⋅F N
f f
f
*
*
Friction force parameter, as given by: F =⋅So 1
F
f
f
ψ
eff
F
Bearing force at transition to mixed friction N
tr
f Coefficient of friction 1
f
Journal deflection m
J
h(φ) Local lubricant film thickness m
h()ϕ
*
*
Relative local lubricant film thickness, as given by: h ()ϕ = 1
h ()ϕ
C
R
h Minimum admissible lubricant film thickness at transition to mixed friction m
lim,tr
Minimum admissible relati
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.