ISO 12168-1:2019
(Main)Plain bearings — Hydrostatic plain journal bearings without drainage grooves under steady-state conditions — Part 1: Calculation of oil-lubricated plain journal bearings without drainage grooves
Plain bearings — Hydrostatic plain journal bearings without drainage grooves under steady-state conditions — Part 1: Calculation of oil-lubricated plain journal bearings without drainage grooves
This document specifies a calculation method of oil-lubricated plain journal bearings without drainage grooves under steady-state conditions. It applies to hydrostatic plain journal bearings under steady-state conditions. In this document, only bearings without oil drainage grooves between the recesses are taken into account.
Paliers lisses — Paliers lisses radiaux hydrostatiques sans rainure d'écoulement fonctionnant en régime stationnaire — Partie 1: Calcul pour la lubrification des paliers lisses radiaux sans rainure d'écoulement
General Information
Relations
Buy Standard
Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 12168-1
Second edition
2019-11
Plain bearings — Hydrostatic
plain journal bearings without
drainage grooves under steady-state
conditions —
Part 1:
Calculation of oil-lubricated plain
journal bearings without drainage
grooves
Paliers lisses — Paliers lisses radiaux hydrostatiques sans rainure
d'écoulement fonctionnant en régime stationnaire —
Partie 1: Calcul pour la lubrification des paliers lisses radiaux sans
rainure d'écoulement
Reference number
©
ISO 2019
© ISO 2019
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 2019 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols, terms and units . 1
5 Bases of calculation and boundary conditions . 3
6 Method of calculation . 5
6.1 General . 5
6.2 Load-carrying capacity . 5
6.3 Lubricant flow rate and pumping power . 7
6.4 Frictional power. 9
6.5 Optimization . 9
6.6 Temperatures and viscosities .11
6.7 Minimum pressure in recesses .11
Annex A (informative) Description of the approximation method for the calculation of
hydrostatic plain journal bearings .13
Annex B (informative) Examples of calculation .23
Bibliography .31
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 12168-1:2001), of which it constitutes a
minor revision.
The changes compared to the previous edition are as follows:
— adjustment to ISO/IEC Directives, Part 2:2018;
— correction of typographical errors.
A list of all parts in the ISO 12168 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 2019 – All rights reserved
Introduction
The functioning of hydrostatic bearings is characterized by the fact that the supporting pressure of the
bearing is generated by external lubrication. The special advantages of hydrostatic bearings are lack
of wear, quiet running, wide useable speed range as well as high stiffness and damping capacity. These
properties are also the reason for the special importance of hydrostatic bearing units in different fields
of application such as machine tools.
The bases of calculation described in this document apply to bearings with different numbers of
recesses and different width/diameter ratios for identical recess geometry. In this document, only
bearings without oil drainage grooves between the recesses are taken into account. As compared to
bearings with oil drainage grooves, this type needs less power with the same stiffness behaviour.
The oil is fed to each bearing recess by means of a common pump with constant pump pressure
(system p = constant) and via preceding linear restrictors (e.g. in the form of capillaries).
en
The calculation procedures listed in this document enable the user to calculate and assess a given
bearing design as well as to design a bearing as a function of some optional parameters. Furthermore,
this document contains the design of the required lubrication system including the calculation of the
restrictor data.
INTERNATIONAL STANDARD ISO 12168-1:2019(E)
Plain bearings — Hydrostatic plain journal bearings
without drainage grooves under steady-state conditions —
Part 1:
Calculation of oil-lubricated plain journal bearings without
drainage grooves
1 Scope
This document specifies a calculation method of oil-lubricated plain journal bearings without drainage
grooves under steady-state conditions.
It applies to hydrostatic plain journal bearings under steady-state conditions.
In this document, only bearings without oil drainage grooves between the recesses are taken into
account.
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 12168-2:2019, Plain bearings — Hydrostatic plain journal bearings without drainage grooves under
steady-state conditions — Part 2: Characteristic values for the calculation of oil-lubricated plain journal
bearings without drainage grooves
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
4 Symbols, terms and units
Symbols, terms and units are shown in Table 1.
Table 1 — Symbols, terms and units
Symbol Term Unit
a Inertia factor 1
A Land area m
lan
A
lan
* *
A Relative land area A =
lan lan
π ××BD
A Recess area m
p
Table 1 (continued)
Symbol Term Unit
b Width perpendicular to the direction of flow m
π×D
b Width of axial outlet b = m
ax
ax
Z
b Width of circumferential outlet ()bB= −l m
c
cax
B Bearing width m
c Stiffness coefficient N/m
.
c Specific heat capacity of the lubricant (p = constant) J/kg K
p
C Radial clearance CD=−D / 2 m
()
R
RB J
d Diameter of capillaries m
cp
D Bearing diameter (D : shaft; D : bearing; D ≈ D ≈ D ) m
J B J B
e Eccentricity (shaft displacement) m
F Load-carrying capacity (load) N
* *
F Characteristic value of load-carrying capacity [F = F/(B × D × p )] 1
en
*
Characteristic value of effective load-carrying capacity 1
F
eff
*
Characteristic value of effective load-carrying capacity for N = 0 1
F
eff,0
h Local lubricant film thickness (clearance gap height) m
h Minimum lubricant film thickness (minimum clearance gap height) m
min
h Depth of recess m
p
K Speed-dependent parameter 1
rot
l Length in the direction of flow m
l Axial land length m
ax
l Circumferential land length m
c
l Length of capillaries m
cp
−1
N Rotational frequency (speed) s
p Recess pressure, general Pa
p []() Pa
Specific bearing load pF=×BD
p Feed pressure (pump pressure) Pa
en
p Pressure in recess i Pa
i
p Pressure in recess i, when ε = 0 Pa
i,0
* *
P Power ratio (P = P /P ) 1
f p
P Frictional power W
f
P Pumping power W
p
P Total power (P = P + P ) W
tot tot p f
*
Characteristic value of total power 1
P
tot
Q Lubricant flow rate (for complete bearing) m /s
*
Q Lubricant flow rate parameter 1
R Flow resistance of capillaries Pa⋅s/m
cp
12××η l
ax
Flow resistance of one axial land R =
R Pa⋅s/m
lan,ax
lan,ax
b ×C
ax R
12××η l
c
R Flow resistance of one circumferential land R = Pa⋅s/m
lan,c
lan,c
b ×
C
R
c
2 © ISO 2019 – All rights reserved
Table 1 (continued)
Symbol Term Unit
R Flow resistance of one recess, when ε = 0, RR=05, Pa⋅s/m
()
P,0
P,0lan,ax
Re Reynolds number 1
So Sommerfeld number 1
T Temperature °C
ΔT Temperature difference K
u Flow velocity m/s
U Circumferential speed m/s
w Average velocity in restrictor m/s
Z Number of recesses 1
α Position of 1st recess related to recess centre rad
β Attitude angle of shaft °
γ Exponent in viscosity formula 1
ε Relative eccentricity (ε = e/C ) 1
R
η Dynamic viscosity Pa⋅s
R
lb×
lan,ax
ax c
κ Resistance ratio κ = = 1
R lb×
lan,c cax
R
cp
ξ Restrictor ratio ξ = 1
R
P,0
ηω×
B
π Relative frictional pressure π = 1
f
f
2
p ×
ψ
en
ρ Density kg/m
τ Shearing stress N/m
φ Angular coordinate rad
2×C
R
ψ 1
Relative bearing clearance ψ =
D
−1
ω Angular velocity ()ω =×2 π× N s
5 Bases of calculation and boundary conditions
Calculation within the meaning of this document is the mathematical determination of the operational
parameters of hydrostatic plain journal bearings as a function of operating conditions, bearing
geometry and lubrication data. This means the determination of eccentricities, load-carrying capacity,
stiffness, required feed pressure, oil flow rate, frictional and pumping power, and temperature rise.
Besides the hydrostatic pressure build-up, the influence of hydrodynamic effects is also approximated.
The Reynolds equation provides the theoretical bases for the calculation of hydrostatic bearings. In
most practical cases of application, it is, however, possible to arrive at sufficiently exact results by
approximation.
The approximation used in this document is based on two basic formulae for describing the flow via
the bearing lands, which can be derived from the Reynolds equation when special boundary conditions
...
INTERNATIONAL ISO
STANDARD 12168-1
Second edition
2019-11
Plain bearings — Hydrostatic
plain journal bearings without
drainage grooves under steady-state
conditions —
Part 1:
Calculation of oil-lubricated plain
journal bearings without drainage
grooves
Paliers lisses — Paliers lisses radiaux hydrostatiques sans rainure
d'écoulement fonctionnant en régime stationnaire —
Partie 1: Calcul pour la lubrification des paliers lisses radiaux sans
rainure d'écoulement
Reference number
©
ISO 2019
© ISO 2019
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 2019 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols, terms and units . 1
5 Bases of calculation and boundary conditions . 3
6 Method of calculation . 5
6.1 General . 5
6.2 Load-carrying capacity . 5
6.3 Lubricant flow rate and pumping power . 7
6.4 Frictional power. 9
6.5 Optimization . 9
6.6 Temperatures and viscosities .11
6.7 Minimum pressure in recesses .11
Annex A (informative) Description of the approximation method for the calculation of
hydrostatic plain journal bearings .13
Annex B (informative) Examples of calculation .23
Bibliography .31
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 12168-1:2001), of which it constitutes a
minor revision.
The changes compared to the previous edition are as follows:
— adjustment to ISO/IEC Directives, Part 2:2018;
— correction of typographical errors.
A list of all parts in the ISO 12168 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 2019 – All rights reserved
Introduction
The functioning of hydrostatic bearings is characterized by the fact that the supporting pressure of the
bearing is generated by external lubrication. The special advantages of hydrostatic bearings are lack
of wear, quiet running, wide useable speed range as well as high stiffness and damping capacity. These
properties are also the reason for the special importance of hydrostatic bearing units in different fields
of application such as machine tools.
The bases of calculation described in this document apply to bearings with different numbers of
recesses and different width/diameter ratios for identical recess geometry. In this document, only
bearings without oil drainage grooves between the recesses are taken into account. As compared to
bearings with oil drainage grooves, this type needs less power with the same stiffness behaviour.
The oil is fed to each bearing recess by means of a common pump with constant pump pressure
(system p = constant) and via preceding linear restrictors (e.g. in the form of capillaries).
en
The calculation procedures listed in this document enable the user to calculate and assess a given
bearing design as well as to design a bearing as a function of some optional parameters. Furthermore,
this document contains the design of the required lubrication system including the calculation of the
restrictor data.
INTERNATIONAL STANDARD ISO 12168-1:2019(E)
Plain bearings — Hydrostatic plain journal bearings
without drainage grooves under steady-state conditions —
Part 1:
Calculation of oil-lubricated plain journal bearings without
drainage grooves
1 Scope
This document specifies a calculation method of oil-lubricated plain journal bearings without drainage
grooves under steady-state conditions.
It applies to hydrostatic plain journal bearings under steady-state conditions.
In this document, only bearings without oil drainage grooves between the recesses are taken into
account.
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 12168-2:2019, Plain bearings — Hydrostatic plain journal bearings without drainage grooves under
steady-state conditions — Part 2: Characteristic values for the calculation of oil-lubricated plain journal
bearings without drainage grooves
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
4 Symbols, terms and units
Symbols, terms and units are shown in Table 1.
Table 1 — Symbols, terms and units
Symbol Term Unit
a Inertia factor 1
A Land area m
lan
A
lan
* *
A Relative land area A =
lan lan
π ××BD
A Recess area m
p
Table 1 (continued)
Symbol Term Unit
b Width perpendicular to the direction of flow m
π×D
b Width of axial outlet b = m
ax
ax
Z
b Width of circumferential outlet ()bB= −l m
c
cax
B Bearing width m
c Stiffness coefficient N/m
.
c Specific heat capacity of the lubricant (p = constant) J/kg K
p
C Radial clearance CD=−D / 2 m
()
R
RB J
d Diameter of capillaries m
cp
D Bearing diameter (D : shaft; D : bearing; D ≈ D ≈ D ) m
J B J B
e Eccentricity (shaft displacement) m
F Load-carrying capacity (load) N
* *
F Characteristic value of load-carrying capacity [F = F/(B × D × p )] 1
en
*
Characteristic value of effective load-carrying capacity 1
F
eff
*
Characteristic value of effective load-carrying capacity for N = 0 1
F
eff,0
h Local lubricant film thickness (clearance gap height) m
h Minimum lubricant film thickness (minimum clearance gap height) m
min
h Depth of recess m
p
K Speed-dependent parameter 1
rot
l Length in the direction of flow m
l Axial land length m
ax
l Circumferential land length m
c
l Length of capillaries m
cp
−1
N Rotational frequency (speed) s
p Recess pressure, general Pa
p []() Pa
Specific bearing load pF=×BD
p Feed pressure (pump pressure) Pa
en
p Pressure in recess i Pa
i
p Pressure in recess i, when ε = 0 Pa
i,0
* *
P Power ratio (P = P /P ) 1
f p
P Frictional power W
f
P Pumping power W
p
P Total power (P = P + P ) W
tot tot p f
*
Characteristic value of total power 1
P
tot
Q Lubricant flow rate (for complete bearing) m /s
*
Q Lubricant flow rate parameter 1
R Flow resistance of capillaries Pa⋅s/m
cp
12××η l
ax
Flow resistance of one axial land R =
R Pa⋅s/m
lan,ax
lan,ax
b ×C
ax R
12××η l
c
R Flow resistance of one circumferential land R = Pa⋅s/m
lan,c
lan,c
b ×
C
R
c
2 © ISO 2019 – All rights reserved
Table 1 (continued)
Symbol Term Unit
R Flow resistance of one recess, when ε = 0, RR=05, Pa⋅s/m
()
P,0
P,0lan,ax
Re Reynolds number 1
So Sommerfeld number 1
T Temperature °C
ΔT Temperature difference K
u Flow velocity m/s
U Circumferential speed m/s
w Average velocity in restrictor m/s
Z Number of recesses 1
α Position of 1st recess related to recess centre rad
β Attitude angle of shaft °
γ Exponent in viscosity formula 1
ε Relative eccentricity (ε = e/C ) 1
R
η Dynamic viscosity Pa⋅s
R
lb×
lan,ax
ax c
κ Resistance ratio κ = = 1
R lb×
lan,c cax
R
cp
ξ Restrictor ratio ξ = 1
R
P,0
ηω×
B
π Relative frictional pressure π = 1
f
f
2
p ×
ψ
en
ρ Density kg/m
τ Shearing stress N/m
φ Angular coordinate rad
2×C
R
ψ 1
Relative bearing clearance ψ =
D
−1
ω Angular velocity ()ω =×2 π× N s
5 Bases of calculation and boundary conditions
Calculation within the meaning of this document is the mathematical determination of the operational
parameters of hydrostatic plain journal bearings as a function of operating conditions, bearing
geometry and lubrication data. This means the determination of eccentricities, load-carrying capacity,
stiffness, required feed pressure, oil flow rate, frictional and pumping power, and temperature rise.
Besides the hydrostatic pressure build-up, the influence of hydrodynamic effects is also approximated.
The Reynolds equation provides the theoretical bases for the calculation of hydrostatic bearings. In
most practical cases of application, it is, however, possible to arrive at sufficiently exact results by
approximation.
The approximation used in this document is based on two basic formulae for describing the flow via
the bearing lands, which can be derived from the Reynolds equation when special boundary conditions
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.