SIST ISO 7902-1:2015
Hydrodynamic plain journal bearings under steady-state conditions - Circular cylindrical bearings - Part 1: Calculation procedure
Hydrodynamic plain journal bearings under steady-state conditions - Circular cylindrical bearings - Part 1: Calculation procedure
ISO 7902-1:2013 specifies a calculation procedure for oil-lubricated hydrodynamic plain bearings, with complete separation of the shaft and bearing sliding surfaces by a film of lubricant, used for designing plain bearings that are reliable in operation. It deals with circular cylindrical bearings having angular spans, Ω, of 360°, 180°, 150°, 120° and 90°, the arc segment being loaded centrally.
Paliers lisses hydrodynamiques radiaux fonctionnant en régime stabilisé - Paliers circulaires cylindriques - Partie 1: Méthode de calcul
Hidrodinamični radialni drsni ležaji za neprekinjeno obratovanje - Valjasti ležaji - 1. del: Postopek dimenzioniranja
Ta del standarda ISO 7902 določa postopek dimenzioniranja hidrodinamičnih radialnih drsnih ležajev z oljnim mazanjem s popolno ločitvijo grede in drsečih površin ležaja s plastjo maziva, ki se uporabljajo za načrtovanje radialnih ležajev z zanesljivim delovanjem.
Zajema valjaste ležaje s kotnim razponom, Ω, 360°, 180°, 150°, 120° in 90° ter sredinsko umeščenim obločnim delom. Geometrija razdalj je stalna z izjemo zanemarljivih deformacij, ki so posledica pritiska in temperature plasti maziva.
Postopek izračuna služi izmeri in optimizaciji drsnih ležajev v turbinah, generatorjih, električnih motorjih, menjalnikih, valjarnah, črpalkah in drugih strojih. Omejen je na neprekinjeno delovanje, t. j. pri neprekinjenih delovnih pogojih, s konstantno magnitudo, smerjo obremenitve in konstantnimi kotnimi hitrostmi vseh vrtljivih delov. Uporabiti ga je mogoče tudi, če je drsni ležaj izpostavljen stalni sili s katero koli hitrostjo vrtenja. Dinamične obremenitve, npr. tiste, pri katerih se magnituda in smer s časom spreminjata ter so lahko posledica učinkov vibracij in nestabilnosti hitro delujočih motorjev, niso zajete.
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INTERNATIONAL ISO
STANDARD 7902-1
Second edition
2013-11-01
Hydrodynamic plain journal bearings
under steady-state conditions —
Circular cylindrical bearings —
Part 1:
Calculation procedure
Paliers lisses hydrodynamiques radiaux fonctionnant en régime
stabilisé — Paliers circulaires cylindriques —
Partie 1: Méthode de calcul
Reference number
©
ISO 2013
© ISO 2013
All rights reserved. Unless otherwise specified, 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
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2013 – All rights reserved
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Basis of calculation, assumptions, and preconditions . 1
4 Calculation procedure . 3
5 Symbols and units . 5
6 Definition of symbols . 6
6.1 Load-carrying capacity . 6
6.2 Frictional power loss . 9
6.3 Lubricant flow rate .10
6.4 Heat balance .11
6.5 Minimum lubricant film thickness and specific bearing load .13
6.6 Operational conditions.14
6.7 Further influencing factors .15
Annex A (normative) Calculation examples .17
Bibliography .32
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. 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. 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.
The committee responsible for this document is ISO/TC 123, Plain bearings, Subcommittee SC 4, Methods
of calculation of plain bearings.
This second edition cancels and replaces the first edition (ISO 7902-1:1998), which has been
technically revised.
ISO 7902 consists of the following parts, under the general title Hydrodynamic plain journal bearings
under steady-state conditions — Circular cylindrical bearings:
— Part 1: Calculation procedure
— Part 2: Functions used in the calculation procedure
— Part 3: Permissible operational parameters
iv © ISO 2013 – All rights reserved
INTERNATIONAL STANDARD ISO 7902-1:2013(E)
Hydrodynamic plain journal bearings under steady-state
conditions — Circular cylindrical bearings —
Part 1:
Calculation procedure
1 Scope
This part of ISO 7902 specifies a calculation procedure for oil-lubricated hydrodynamic plain bearings,
with complete separation of the shaft and bearing sliding surfaces by a film of lubricant, used for
designing plain bearings that are reliable in operation.
It deals with circular cylindrical bearings having angular spans, Ω, of 360°, 180°, 150°, 120°, and 90°,
the arc segment being loaded centrally. Their clearance geometry is constant except for negligible
deformations resulting from lubricant film pressure and temperature.
The calculation procedure serves to dimension and optimize plain bearings in turbines, generators,
electric motors, gear units, rolling mills, pumps, and other machines. It is limited to steady-state
operation, i.e. under continuously driven operating conditions, with the magnitude and direction
of loading as well as the angular speeds of all rotating parts constant. It can also be applied if a full
plain bearing is subjected to a constant force rotating at any speed. Dynamic loadings, i.e. those whose
magnitude and direction vary with time, such as can result from vibration effects and instabilities of
rapid-running rotors, are not taken into account.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. 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 7902-2:1998, Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical
bearings — Part 2: Functions used in the calculation procedure
ISO 7902-3, Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical
bearings — Part 3: Permissible operational parameters
3 Basis of calculation, assumptions, and preconditions
3.1 The basis of calculation is the numerical solution to Reynolds’ differential equation for a finite bearing
length, taking into account the physically correct boundary conditions for the generation of pressure:
∂ ∂p ∂ ∂p ∂h
h + h =+6η uu (1)
()
JB
∂x ∂xx∂ ∂z ∂x
The symbols are given in Clause 5.
See References [1] to [3] and References [11] to [14] for the derivation of Reynolds’ differential equation
and References [4] to [6], [12], and [13] for its numerical solution.
3.2 The following idealizing assumptions and preconditions are made, the permissibility of which has
been sufficiently confirmed both experimentally 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 lubricant clearance gap in the loaded area is completely filled with lubricant. Filling up of the
unloaded area depends on the way the lubricant is supplied to the bearing.
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 ideal circular cylinders.
h) The radii of curvature of the surfaces in relative motion are large in comparison with the lubricant
film thicknesses.
i) The lubricant film thickness in the axial direction (z-coordinate) is constant.
j) Fluctuations in pressure within the lubricant film normal to the bearing surfaces (y-coordinate)
are negligible.
k) There is no motion normal to the bearing surfaces ( y-coordinate).
l) The lubricant is isoviscous over the entire lubrication clearance gap.
m) The lubricant is fed in at the start of the bearing liner or where the lubrication clearance gap is
widest; the magnitude of the lubricant feed pressure is negligible in comparison with the lubricant
film pressures.
3.3 The boundary conditions for the generation of lubricant film pressure fulfil the following
continuity conditions:
— at the leading edge of the pressure profile: pzϕ , =0 ;
()
— at the bearing rim: pzϕ, =±B 20= ;
()
— at the trailing edge of the pressure profile: pzϕ ,z =0 ;
()
— ∂∂pzϕϕ ,z =0 .
()
For some types and sizes of bearing, the boundary conditions may be specified.
In partial bearings, if Formula (2) is satisfied:
π
ϕπ−−β < (2)
()
then the trailing edge of the pressure profile lies at the outlet end of the bearing:
pzϕϕ= , =0 (3)
()
3.4 The numerical integration of the Reynolds’ differential equation is carried out (possibly by
applying transformation of pressure as suggested in References [3], [11], and [12]) by a transformation
to a differential formula which is applied to a grid system of supporting points, and which results in a
system of linear formulae. The number of supporting points is significant to the accuracy of the numerical
2 © ISO 2013 – All rights reserved
integration; the use of a non-equidistant grid as given in References [6] and [13] is advantageous. After
substituting the boundary conditions at the trailing edge of the pressure profile, integration yields the
pressure distribution in the circumferential and axial directions.
The application of the similarity principle to hydrodynamic plain bearing theory results in dimensionless
magnitudes of similarity for parameters of interest, such as load-carrying capacity, frictional behaviour,
lubricant flow rate, and relative bearing length. The application of magnitudes of similarity reduces the
number of numerical solutions required of Reynolds’ differential equation specified in ISO 7902-2. Other
solutions may also be applied, provided they fulfil the conditions laid down in ISO 7902-2 and are of a
similar numerical accuracy.
3.5 ISO 7902-3 includes permissible operational parameters towards which the result of the calculation
shall be oriented in order to ensure correct functioning of the plain bearings.
In special cases, operational parameters deviating from ISO 7902-3 may be agreed upon for specific
applications.
4 Calculation procedure
4.1 Calculation is understood to mean determination of correct operation by computation using actual
operating parameters (see Figure 1), which can be compared with operational parameters. The operating
parameters determined under varying operating conditions shall therefore lie within the range of
permissibility as compared with the operational parameters. To this end, all operating conditions during
continuous operation shall be investigated.
4.2 Freedom from wear is guaranteed only if complete separation of the mating bearing parts is
achieved by the lubricant. Continuous operation in the mixed friction range results in failure. Short-time
operation in the mixed friction range, for example starting up and running down machines with plain
bearings, is unavoidable and does not generally result in bearing damage. When a bearing is subjected to
heavy load, an auxiliary hydrostatic arrangement may be necessary for starting up and running down at a
slow speed. Running-in and adaptive wear to compensate for deviations of the surface geometry from the
ideal are permissible as long as they are limited in area and time and occur without overloading effects.
In certain cases, a specific running-in procedure may be beneficial, depending on the choice of materials.
4.3 The limits of mechanical loading are a function of the strength of the bearing material. Slight permanent
deformations are permissible as long as they do not impair correct functioning of the plain bearing.
4.4 The limits of thermal loading result not only from the thermal stability of the bearing material but
also from the viscosity-temperature relationship and by degradation of the lubricant.
4.5 A correct calculation for plain bearings presupposes that the operating conditions are known for
...
SLOVENSKI STANDARD
01-marec-2015
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SIST ISO 7902-1:2002
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Hydrodynamic plain journal bearings under steady-state conditions - Circular cylindrical
bearings - Part 1: Calculation procedure
Paliers lisses hydrodynamiques radiaux fonctionnant en régime stabilisé - Paliers
circulaires cylindriques - Partie 1: Méthode de calcul
Ta slovenski standard je istoveten z: ISO 7902-1:2013
ICS:
21.100.10 Drsni ležaji Plain bearings
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL ISO
STANDARD 7902-1
Second edition
2013-11-01
Hydrodynamic plain journal bearings
under steady-state conditions —
Circular cylindrical bearings —
Part 1:
Calculation procedure
Paliers lisses hydrodynamiques radiaux fonctionnant en régime
stabilisé — Paliers circulaires cylindriques —
Partie 1: Méthode de calcul
Reference number
©
ISO 2013
© ISO 2013
All rights reserved. Unless otherwise specified, 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
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2013 – All rights reserved
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Basis of calculation, assumptions, and preconditions . 1
4 Calculation procedure . 3
5 Symbols and units . 5
6 Definition of symbols . 6
6.1 Load-carrying capacity . 6
6.2 Frictional power loss . 9
6.3 Lubricant flow rate .10
6.4 Heat balance .11
6.5 Minimum lubricant film thickness and specific bearing load .13
6.6 Operational conditions.14
6.7 Further influencing factors .15
Annex A (normative) Calculation examples .17
Bibliography .32
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. 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. 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.
The committee responsible for this document is ISO/TC 123, Plain bearings, Subcommittee SC 4, Methods
of calculation of plain bearings.
This second edition cancels and replaces the first edition (ISO 7902-1:1998), which has been
technically revised.
ISO 7902 consists of the following parts, under the general title Hydrodynamic plain journal bearings
under steady-state conditions — Circular cylindrical bearings:
— Part 1: Calculation procedure
— Part 2: Functions used in the calculation procedure
— Part 3: Permissible operational parameters
iv © ISO 2013 – All rights reserved
INTERNATIONAL STANDARD ISO 7902-1:2013(E)
Hydrodynamic plain journal bearings under steady-state
conditions — Circular cylindrical bearings —
Part 1:
Calculation procedure
1 Scope
This part of ISO 7902 specifies a calculation procedure for oil-lubricated hydrodynamic plain bearings,
with complete separation of the shaft and bearing sliding surfaces by a film of lubricant, used for
designing plain bearings that are reliable in operation.
It deals with circular cylindrical bearings having angular spans, Ω, of 360°, 180°, 150°, 120°, and 90°,
the arc segment being loaded centrally. Their clearance geometry is constant except for negligible
deformations resulting from lubricant film pressure and temperature.
The calculation procedure serves to dimension and optimize plain bearings in turbines, generators,
electric motors, gear units, rolling mills, pumps, and other machines. It is limited to steady-state
operation, i.e. under continuously driven operating conditions, with the magnitude and direction
of loading as well as the angular speeds of all rotating parts constant. It can also be applied if a full
plain bearing is subjected to a constant force rotating at any speed. Dynamic loadings, i.e. those whose
magnitude and direction vary with time, such as can result from vibration effects and instabilities of
rapid-running rotors, are not taken into account.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. 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 7902-2:1998, Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical
bearings — Part 2: Functions used in the calculation procedure
ISO 7902-3, Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical
bearings — Part 3: Permissible operational parameters
3 Basis of calculation, assumptions, and preconditions
3.1 The basis of calculation is the numerical solution to Reynolds’ differential equation for a finite bearing
length, taking into account the physically correct boundary conditions for the generation of pressure:
∂ ∂p ∂ ∂p ∂h
h + h =+6η uu (1)
()
JB
∂x ∂xx∂ ∂z ∂x
The symbols are given in Clause 5.
See References [1] to [3] and References [11] to [14] for the derivation of Reynolds’ differential equation
and References [4] to [6], [12], and [13] for its numerical solution.
3.2 The following idealizing assumptions and preconditions are made, the permissibility of which has
been sufficiently confirmed both experimentally 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 lubricant clearance gap in the loaded area is completely filled with lubricant. Filling up of the
unloaded area depends on the way the lubricant is supplied to the bearing.
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 ideal circular cylinders.
h) The radii of curvature of the surfaces in relative motion are large in comparison with the lubricant
film thicknesses.
i) The lubricant film thickness in the axial direction (z-coordinate) is constant.
j) Fluctuations in pressure within the lubricant film normal to the bearing surfaces (y-coordinate)
are negligible.
k) There is no motion normal to the bearing surfaces ( y-coordinate).
l) The lubricant is isoviscous over the entire lubrication clearance gap.
m) The lubricant is fed in at the start of the bearing liner or where the lubrication clearance gap is
widest; the magnitude of the lubricant feed pressure is negligible in comparison with the lubricant
film pressures.
3.3 The boundary conditions for the generation of lubricant film pressure fulfil the following
continuity conditions:
— at the leading edge of the pressure profile: pzϕ , =0 ;
()
— at the bearing rim: pzϕ, =±B 20= ;
()
— at the trailing edge of the pressure profile: pzϕ ,z =0 ;
()
— ∂∂pzϕϕ ,z =0 .
()
For some types and sizes of bearing, the boundary conditions may be specified.
In partial bearings, if Formula (2) is satisfied:
π
ϕπ−−β < (2)
()
then the trailing edge of the pressure profile lies at the outlet end of the bearing:
pzϕϕ= , =0 (3)
()
3.4 The numerical integration of the Reynolds’ differential equation is carried out (possibly by
applying transformation of pressure as suggested in References [3], [11], and [12]) by a transformation
to a differential formula which is applied to a grid system of supporting points, and which results in a
system of linear formulae. The number of supporting points is significant to the accuracy of the numerical
2 © ISO 2013 – All rights reserved
integration; the use of a non-equidistant grid as given in References [6] and [13] is advantageous. After
substituting the boundary conditions at the trailing edge of the pressure profile, integration yields the
pressure distribution in the circumferential and axial directions.
The application of the similarity principle to hydrodynamic plain bearing theory results in dimensionless
magnitudes of similarity for parameters of interest, such as load-carrying capacity, frictional behaviour,
lubricant flow rate, and relative bearing length. The application of magnitudes of similarity reduces the
number of numerical solutions required of Reynolds’ differential equation specified in ISO 7902-2. Other
solutions may also be applied, provided they fulfil the conditions laid down in ISO 7902-2 and are of a
similar numerical accuracy.
3.5 ISO 7902-3 includes permissible operational parameters towards which the result of the calculation
shall be oriented in order to ensure correct functioning of the plain bearings.
In special cases, operational parameters deviating from ISO 7902-3 may be agreed upon for specific
applications.
4 Calculation procedure
4.1 Calculation is understood to mean determination of correct operation by computation using actual
operating parameters (see Figure 1), which can be compared with operational parameters. The operating
parameters determined under varying operating conditions shall therefore lie within the range of
permissibility as compared with the operational parameters. To this end, all operating conditions during
continuous operation shall be investigated.
4.2 Freedom from wear is guaranteed only if complete separation of the mating bearing parts is
achieved by the lubricant. Continuous operation in the mixed friction range results in failure. Short-time
operation in the mixed friction range, for example starting up and running down machines with plain
bearings, is unavoidable and does
...
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