ISO 7902-1:2026

International
Standard
ISO 7902-1
Fourth edition
Hydrodynamic plain journal
2026-05
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 2026
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Published in Switzerland
ii
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and units. 2
5 Basis of calculation, assumptions, and preconditions . 5
5.1 Reynolds equation .5
5.2 Assumptions and preconditions .5
5.3 Boundary conditions .5
5.4 Basis of calculation .6
5.5 Permissible operational parameters .6
6 Calculation procedure. 6
6.1 General .6
6.2 Freedom from wear .6
6.3 The limits of mechanical loading .7
6.4 The limits of thermal loading .7
6.5 Influencing factors .7
6.6 Reynolds number .7
6.7 Calculation factors .7
7 Definition of symbols . 9
7.1 Load-carrying capacity .9
7.2 Frictional power loss .9
7.3 Lubricant flow rate .9
7.3.1 General .9
7.3.2 Lubricant feed elements .10
7.3.3 Lubrication grooves .10
7.3.4 Lubrication pockets .10
7.3.5 Lubricant flow rate .11
7.4 Heat balance . .11
7.4.1 General .11
7.4.2 Heat dissipation by convection . 12
7.4.3 Heat dissipation via the lubricant . 12
7.5 Minimum lubricant film thickness and specific bearing load . 13
7.6 Operational conditions . 13
7.7 Further influencing factors .14
Annex A (informative) Calculation examples . 17
Bibliography .32

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
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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 document 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).
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This document was prepared by Technical Committee ISO/TC 123, Plain bearings, Subcommittee SC 8,
Calculation methods for plain bearings and their applications.
This fourth edition cancels and replaces the third edition (ISO 7902-1:2020), of which it constitutes a minor
revision.
The changes are as follows:
— the bibliography has been updated and cross references have been renumbered.
A list of all parts in the ISO 7902 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
International Standard ISO 7902-1:2026(en)
Hydrodynamic plain journal bearings under steady-state
conditions — Circular cylindrical bearings —
Part 1:
Calculation procedure
1 Scope
This document 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 provide dimensions 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 those that can result from vibration effects and instabilities of rapid-running rotors, are not
taken into account.
NOTE Equivalent calculation procedures exist that enable operating conditions to be estimated and checked
against acceptable conditions. The use of them is equally admissible.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 7902-2, 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 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
Symbols and units are defined in Figure 1 and Table 1.
Figure 1 — Illustration of symbols
Table 1 — Symbols and their designations
Symbol Designation Unit
A Area of heat-emitting surface (bearing housing) m
B Nominal bearing width m
B Length of the axial housing m
H
b Width of lubrication groove m
G
b Width of lubrication pocket m
P
C Nominal bearing clearance m
C Effective bearing radial clearance m
R,eff
c Specific heat capacity of the lubricant J/(kg·K)
p
D Nominal bearing diameter (inside diameter) m
D Length of the outside diameter of the housing m
H
D Nominal shaft diameter m
J
D Maximum value of D m
J,max J
D Minimum value of D m
J,min J
D Maximum value of D m
max
D Minimum value of D m
min
d Lubrication hole diameter m
L
e Eccentricity between the axis of the shaft and the bearing axis m
F Bearing force (nominal load) N

TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Designation Unit
F Friction force in the loaded area of the lubricant film N
f
Frictional force in both the loaded and the unloaded area of the lubricant film N
′
F
f
f Coefficient of friction in the loaded area of the lubricant film ( f = F /F) 1
f
f′ Coefficient of friction in both the loaded and unloaded area of the lubricant film 1
H Length of the total height of the pedestal bearing m
h Local lubricant film thickness m
h Effective lubricant film thickness m
eff
h Depth of lubrication groove m
G
h Minimum permissible lubricant film thickness m
lim
h Minimum lubricant film thickness m
min
h Depth of lubrication pocket m
P
k Heat transfer coefficient W/(m ·K)
A
−1
N Rotational frequency of the bearing s
B
−1
N Rotational frequency of the shaft s
J
P Frictional power W
f
P ′ Frictional power in both the loaded and the unloaded area of the lubricant film W
f
P Heat flow rate W
th
P Heat flow rate to the ambient W
th,amb
P Heat flow rate due to frictional power W
th,f
P Heat flow rate in the lubricant W
th,L
p Local lubricant film pressure Pa
p Specific bearing load Pa
p Lubricant feed pressure Pa
en
p Maximum permissible lubricant film pressure Pa
lim
Maximum permissible specific bearing load Pa
p
lim
Q Lubricant flow rate m /s
Q Lubricant flow rate due to hydrodynamic pressure m /s
* Lubricant flow rate parameter due to hydrodynamic pressure 1
Q
Q Lubricant flow rate due to feed pressure m /s
p
Lubricant flow rate parameter due to feed pressure 1
*
Q
p
q Coefficient related to lubricant flow rate due to feed pressure 1
L
q Coefficient related to lubricant flow rate from pocket 1
P
Rz Average peak-to-valley height of bearing sliding surface m
B
Rz Average peak-to-valley height of shaft mating surface m
J
Re Reynolds number 1
So Sommerfeld number 1
So Transition Sommerfeld number 1
u
T Ambient temperature °C
amb
T Bearing temperature °C
B
T Assumed initial bearing temperature °C
B,0
T Calculated bearing temperature resulting from iteration procedure °C
B,1
T Effective lubricant temperature °C
eff
T Lubricant temperature at bearing entrance °C
en
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Designation Unit
T Lubricant temperature at bearing exit °C
ex
T Assumed initial lubricant temperature at bearing exit °C
ex,0
T Calculated lubricant temperature at bearing exit °C
ex,1
T Shaft temperature °C
J
T Maximum permissible bearing temperature °C
lim
Mean lubricant temperature °C
T
L
U Linear velocity (peripheral speed) of bearing m/s
B
U Linear velocity (peripheral speed) of shaft m/s
J
V Air ventilating velocity m/s
a
x Coordinate parallel to the sliding surface in the circumferential direction m
y Coordinate perpendicular to the sliding surface m
z Coordinate parallel to the sliding surface in the axial direction m
−1
α Linear heat expansion coefficient of the bearing K
l,B
−1
α Linear heat expansion coefficient of the shaft K
l,J
Attitude angle (angular position of the shaft eccentricity related to the direction of °
β
load)
ε Relative eccentricity [ε = 2e/(D – D )] 1
J
ε Transition eccentricity 1
u
η Dynamic viscosity of the lubricant Pa·s
η Effective dynamic viscosity of the lubricant Pa·s
eff
v Kinematic viscosity of the lubricant m /s
ξ Coefficient of resistance to rotation in the loaded area of the lubricant film 1
Coefficient of resistance to rotation in both the loaded and the unloaded area of the 1


lubricant film
Coefficient of resistance to rotation in the area of circumferential groove 1
ξ
G
Coefficient of resistance to rotation in the area of the pocket 1
ξ
P
ρ Density of lubricant kg/m
φ Angular coordinate in the circumferential direction rad
φ Angular coordinate of pressure leading edge rad
φ Angular coordinate of pressure trailing edge rad
ψ
Relative bearing clearance 1
ψ Mean relative bearing clearance 1
Effective relative bearing clearance 1
ψ
eff
Maximum relative bearing clearance 1
ψ
max
Minimum relative bearing clearance 1
ψ
min
−1
ω Angular velocity of bearing s
B
−1
ω Angular velocity of rotating force s
F
−1
ω Hydrodynamic angular velocity s
h
−1
ω Angular velocity of shaft s
J
Ω Angular span of bearing segment °
Ω Angular span of lubrication groove °
G
Ω Angular span of lubrication pocket °
P
5 Basis of calculation, assumptions, and preconditions
5.1 Reynolds equation
The basis of calculation is the numerical solution to Reynolds equation for a finite bearing length, taking
into account the physically correct boundary conditions for the generation of pressure. Reynolds equation is
defined as Formula (1).
  p   p h
h  h 6 UU (1)

   
JB
x xz z x
   
See References [2] to [4] and References [9] to [12] for the derivation of Reynolds equation and References [5]
to [7], [10] and [11] for its numerical solution.
5.2 Assumptions and preconditions
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.
5.3 Boundary conditions
The boundary conditions for the generation of lubricant film pressure fulfil the following continuity
conditions:
— at the leading edge of the pressure profile:pz , 0 ;

— at the bearing rim:pz,/B 20 ;

— at the trailing edge of the pressure profile:pz ,z 0 ;

 2 
— pz/, z 0 .

 2 
For some types and sizes of bearing, the boundary conditions may be specified.
In partial bearings, if Formula (2) is satisfied:

  (2)

Then the trailing edge of the pressure profile lies at the outlet end of the bearing is:
pz , 0

5.4 Basis of calculation
The numerical integration of the Reynolds equation is carried out (possibly by applying transformation of
pressure as suggested in References [4], [9] and [10]) 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 integration; the use of a non-equidistant
grid as given in References [7] and [11] 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 equation specified in ISO 7902-2. Other solutions may
also be applied, provided they are in accordance with the conditions laid down in ISO 7902-2 and are of a
similar numerical accuracy.
5.5 Permissible operational parameters
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.
6 Calculation procedure
6.1 General
Calculation is understood to mean determination of correct operation by computation using actual operating
parameters (see Figure 2), 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.
6.2 Freedom from wear
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.
6.3 The limits of mechanical loading
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.
6.4 The limits of 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 by degradation of the lubricant.
6.5 Influencing factors
A correct calculation for plain bearings presupposes that the operating conditions are known for all cases
of continuous operation. In practice, however, additional influences frequently occur, which are unknown at
the design stage and cannot always be predicted. The application of an appropriate safety margin between
the actual operating parameters and permissible operational parameters is recommended. Influences
include, for example:
— spurious forces (e.g. out-of-balance, vibrations);
— deviations from the ideal geometry (e.g. machining tolerances, deviations during assembly);
— lubricants contaminated by, for example, dirt, water, air;
— corrosion, electrical erosion.
Data on other influencing factors are given in 7.7.
6.6 Reynolds number
The Reynolds number shall be used to verify that ISO 7902-2, for which laminar flow in the lubrication
clearance gap is a necessary condition, can be applied:
C C
Re,,ff Reff
U DN
J J
D
Re 41,3 (3)
 v C
Re, ff
In the case of plain bearings with Re>41,3 DC/ (e.g. as a result of high peripheral speed), higher loss
R,eff
coefficients and bearing temperatures shall be expected. Calculations for bearings with turbulent flow
cannot be carried out in accordance with this document.
6.7 Calculation factors
The plain bearing calculation takes into account the following factors (starting with the known bearing
dimensions and operational data):
— the relationship between load-carrying capacity and lubricant film thickness;
— the frictional power rate;
— the lubricant flow rate;
— the heat balance.
All these factors are mutually dependent.

The solution is obtained using an iterative method; the sequence is outlined in the flow chart in Figure 2.
For optimization of individual parameters, parameter variation can be applied; modification of the
calculation sequence is possible.
Figure 2 — Outline of calculation

7 Definition of symbols
7.1 Load-carrying capacity
A characteristic parameter for the load-carrying capacity is the dimensionless Sommerfeld number, So:
F
 B 
eff
SoSo ,, (4)
 
DB D
 
effh
Values of So as a function of the relative eccentricity, ε, the relative bearing length, B/D, and the angular span
of bearing segment, Ω, are given in ISO 7902-2. The variables ω , η , and ψ take into account the thermal
h eff
eff
effects and the angular velocities of shaft, bearing, and bearing force (see 7.4 and 7.7).
The relative eccentricity, ε, together with the attitude angle, β (see ISO 7902-2), describes the magnitude
and position of the minimum thickness of lubricant film. For a full bearing (Ω = 360°), the oil should be
introduced at the greatest lubricant clearance gap or, with respect to the direction of rotation, shortly before
it. For this reason, it is useful to know the attitude angle, β.
7.2 Frictional power loss
Friction in a hydrodynamic plain bearing due to viscous shear stress is given by the coefficient of friction
f = F /F and the derived non-dimensional characteristics of frictional power loss ξ and f /ψ :
f
eff
F
feff
  (5)
DB
effh
f 
 (6)
 So
eff
They are applied if the frictional power loss is encountered only in the loaded area of the lubricant film.
It is still necessary to calculate frictional power loss in both the loaded and unloaded areas. Then the values,
f f
fF,,, and , are substituted by fF,,, and , respectively in Formulae (5) and (6). This means
f f
 
eff eff
that the whole of the clearance gap is filled with lubricant.

The values of f /ψ and f / for various values of ε, B/D, and Ω are given in ISO 7902-2. It also gives the
eff eff
approximation formulae, based on Reference [13], which are used to determine frictional power loss values
in the bearings, taking account of the influence of lubrication pockets and grooves.
The frictional power in a bearing or the amount of heat generated is given by Formulae (7) and (8).
D
PP fF  (7)
fthf, h
D
 
Pf F  (8)
fh
7.3 Lubricant flow rate
7.3.1 General
The lubricant fed to the bearing forms a film of lubricant separating the sliding surfaces. The pressure build-
up in this film forces lubricant out of the ends of the bearing. This is the proportion Q of the lubricant flow
rate, resulting from the build-up of hydrodynamic pressure.

3 *
QD  Q (9)
3 effh 3
**
where QQ ,/BD, is given in ISO 7902-2.

There is also a flow of lubricant in the peripheral direction through the narrowest clearance gap into the
diverging, pressure-free gap. For increased loading and with a small lubrication gap clearance, however, this
proportion of the lubricant flow is negligible.
The lubricant feed pressure, p , forces additional lubricant out of the ends of the plain bearing. This is the
en
amount Q of the lubricant flow rate resulting from feed pressure as defined by Formula (10).
p
Dp
effen *
Q  Q (10)
p p

eff
**
where QQ ,/BD, is given in ISO 7902-2.

pp
7.3.2 Lubricant feed elements
Lubricant feed elements are lubrication holes, lubrication grooves, and lubrication pockets. The lubricant
feed pressure, p , should be markedly less than the specific bearing load, p , to avoid additional hydrostatic
en
loads. Usually, p lies between 0,05 MPa and 0,2 MPa. The depth of the lubrication grooves and lubrication
en
pockets is considerably greater than the bearing clearance.
7.3.3 Lubrication grooves
Lubrication grooves are elements designed to distribute lubricant in the circumferential direction. The
recesses machined into the sliding surface run circumferentially and are kept narrow in the axial direction.
If lubrication grooves are located in the vicinity of pressure rise, the pressure distribution is split into two
independent pressure “hills” and the load-carrying capacity is markedly reduced (see Figure 3). In this case,
the calculation shall be carried out for half the load applied to each half bearing. However, because of the
build-up of hydrodynamic pressure, Q , only half of the lubricant flow rate shall be taken into account when
balancing heat losses (see 7.4), since the return into the lubrication groove plays no part in dissipating heat.
It is more advantageous, for a full bearing, to arrange the lubrication groove in the unloaded part. The entire
lubricant flow amount, Q , goes into the heat balance.
p
7.3.4 Lubrication pockets
Lubrication pockets are elements for distributing the lubricant over the length of the bearing. The recesses
machined into the sliding surface are oriented in the axial direction and should be as short as possible in
the circumferential direction. Relative pocket lengths should be such as b /B < 0,7. Although larger values
p
increase the lubricant flow rate, the oil emerging over the narrow, restricting webs at the ends plays no
part in dissipating heat. This is even more true if the end webs are penetrated axially. For full bearings
(Ω = 360°), a lubrication pocket opposite to the direction of load as well as two lubrication pockets normal
to the direction of loading are machined in. Since the lubricant flow rate, even in the unloaded part of the
bearing, provides for the dissipation of frictional heat arising from shearing, the lubrication pockets shall
be fully taken into account in the heat balance. For shell segments (Ω < 360°), the lubricant flow rate due to
feed pressure through lubrication pockets at the inlet or outlet of the shell segment makes practically no
contribution to heat dissipation, since the lubrication pockets are scarcely restricted at the segment ends
and the greater proportion of this lubricant flow emerges directly.

Key
1 lubrication hole
2 lubrication groove
Figure 3 — Lubricant film pressure in bearings with lubrication groove
7.3.5 Lubricant flow rate
If the lubricant fills the loaded area of the bearing and there is no lubricant in the unloaded part, then the
heat dissipation counts as lubricant flow rate in the loaded part only.
The influence of the type and the arrangement of the lubricant feed elements on the lubricant flow rate are
dealt with in ISO 7902-2.
The overall lubricant flow rate is given by
— for lubricant filling only in the loaded area of the bearing:
QQ= (11)
— for lubricant filling in the whole circular lubrication clearance gap including unloaded part, i.e. 2π:
QQ Q (12)
3p
7.4 Heat balance
7.4.1 General
The thermal condition of the plain bearing can be obtained from the heat balance. The heat flow, P ,
th,f
arising from frictional power in the bearing, P , is dissipated via the bearing housing to the environment
f
and the lubricant emerging from the bearing. In practice, one or other of the two types of heat dissipation
dominates. By neglecting the other, an additional safety margin is obtained during the design stage. The
following assumptions can be made:
a) pressureless-lubricated bearings (e.g. ring lubrication) dissipate heat mainly through convection to the
environment: P = P ;
th,f th,amb
b) pressure-lubricated bearings dissipate heat mainly via the lubricant: P = P .
th,f th,L
Calculation examples are introduced in Annex A.

7.4.2 Heat dissipation by convection
Heat dissipation by convection takes place by thermal conduction in the bearing housing and radiation and
convection from the surface of the housing to the environment. The complex processes during the heat
transfer can be summed up by:
PkAT T (13)

th,ambA Bamb
where
k  15 to 20 Wm/ K


A
or, by ventilating the bearing housing with air at a velocity of V > 1,2 m/s
a
kV712
Aa
See References [4] and [12].
Should the area of the heat-emitting surface, A, of the bearing housing not be known exactly, the following
can be used as an approximation
— for cylindrical housings:

AD2 DD B

HH H
— for pedestal bearings:
 H 
AH B
 
H
 
— for bearings in the machine structure:
AD 15 to 20 B

7.4.3 Heat dissipation via the lubricant
In the case of force-feed lubrication, heat dissipation is via the lubricant:
Pc QT T (14)

th,Lep xen
For mineral lubricants, the volume-specific heat is given by:
c 18,/10 Jm K

p
From the heat balance, it follows that PP= for pressureless-lubricated bearings and PP= for
th,,fthamb th,,fthL
pressure-lubricated bearings.
This gives bearing temperature, T (see Reference [13]), and lubricant outlet temperature, T
B ex
(see Reference [13]). The effective film lubricant temperature with reference to the lubricant viscosity is
a) in the case of pure convection: T = T , and
eff B
b) in the case of heat dissipation via the lubricant: T =T = 0,5 (T + T ).
eff en ex
L
At high peripheral speed, it is possible to select, instead of these mean values, a temperature which lies
nearer to the lubricant outlet temperature.
The values calculated for T and T shall be checked for their permissibility by comparison with the
B ex
permissible operational parameters, T , given in ISO 7902-3.
lim
In the sequence of calculations, at first only the operational data T or T are known, but not the effective
amb en
temperature, T , which is required at the start of the calculation. The solution is obtained by first starting
eff
the calculation using an estimated temperature rise, i.e.
a) T − T = 20 K
B,0 amb
b) T − T = 20 K
ex,0 en
and the corresponding operating temperatures, T . From the heat balance, corrected temperatures, T or
eff B,1
T , are obtained, which, by averaging with the temperatures previously assumed (T or T ), are
ex,1 B,0 ex,0
iteratively improved until the difference between the values with index 0 and 1 becomes negligibly small,
for example 2 K. The condition then attained corresponds to the steady condition. During the iterative steps,
the influencing factors given in 7.7 shall be taken into account. As a rule, the iteration converges rapidly. It
can also be replaced by graphical interpolation in which, for calculating P and P or P , several
th,f th,amb th,L
temperature differences are assumed. If the heat flows Pf T or Pf T are plotted, then
 
th,ambB th,Lex
the steady condition is given by the intersection of the two curves (see Figure A.1).
7.5 Minimum lubricant film thickness and specific bearing load
The clearance gap, h, in a circular cylindrical journal bearing with the shaft offset is a function given by:
hD05, 1 cos

eff
starting with  , in the widest clearance gap (see Figure 1).
The minimum lubricant film thickness
hD05, 1 (15)

mineff
shall be compared with the permissible operational parameter, h , specified in ISO 7902-3.
lim
The specific bearing load:
F
p= (16)
DB
shall be compared with the permissible operational parameter, p , specified in ISO 7902-3.
lim
In partial bearings, if the follow formula is satisfied:

 

then
hD05, 1 cos

min 2
7.6 Operational conditions
Should the plain bearing be operated under several, varying sets of operating conditions over lengthy
periods, then they shall be checked for the most unfavourable p , h , and T . First, a decision shall be
min B
reached as to whether or not the bearing can be lubricated without pressure and whether or not the heat

dissipation by convection suffices. The most unfavourable thermal case shall be investigated, which, as a
rule, corresponds to an operating condition at high rotary frequency together with heavy loading. If, for
pure convection, excessive bearing temperatures occur, which even by increasing the dimensions of the
bearing or of the surface area of the housing to their greatest possible extent cannot be lowered to
permissible values, then force-feed lubrication and oil cooling are necessary.
If an operating condition under high thermal loading (low dynamic lubricant viscosity) is followed directly
by one with high specific bearing load and low rotary frequency, this new operating condition should be
investigated while keeping the thermal condition from the preceding operating point.
The transition to mixed friction is due to contact of the roughness peaks of the shaft and bearing under the
criteria for h specified in ISO 7902-3, whereby deformation is also to be taken into account. A transition
lim
eccentricity:
h
lim
 1
u
D

eff
and a transition Sommerfeld number:
F
 B 
eff
So  f  ,,
 
u u
DB D
 
effh
(see ISO 7902-2) can be assigned to this value. Thus, the individual transition conditions (load, viscosity,
and rotary speed) can be determined. The transition condition can be described by just three coexistent
parameters. In order to be able to determine one of them, the two others shall be substituted in the manner
appropriate to this condition. For rapid run-down of the machine, the thermal state corresponds mostly
to the previous continuously driven operating condition of high thermal loading. If cooling is shut off
immediately when the machine is switched off, this can result in an accumulation of heat in the bearing, so
that a yet more unfavourable value shall be selected for h . If the machine runs down slowly, lowering of the
eff
temperature of the lubricant or bearing is to be expected.
7.7 Further influencing factors
The calculation procedure applies to steady-state operation, in particular for loading that is constant in
magnitude and direction and in which it is possible for the shaft and the bearing to rotate with uniform
speed. The effective angular velocity is given by:
 (17)
hJ B
The calculation procedure, however, also applies for the case of a constant load which rotates at an angular
velocity ω . In this case, the angular velocity is given by:
F
2
hJ BF
For an out-of-balance force rotating with the shaft (ω = ω ), then:
F J
 
hJ B
The absolute value of ω shall be used to calculate the Sommerfeld number. It shall be borne in mind that in
h
the case where ω < 0, the shaft eccentricity is at the angle −β (see Figure 4).
h
NOTE All rotary motions and angular directions are positive with respect to the direction of shaft rotation.
The dynamic viscosity is strongly dependent on temperature. It is thus necessary to know the temperature
dependence of the lubricant and its specification (see ISO 3448). The effective dynamic viscosity, η , is
eff
determined by means of the effective lubricant film temperature, T , that is η results from averaging
eff eff
temperatures T and T and not from averaging the dynamic viscosities η(T ) and η(T ).
en ex en ex
The dynamic viscosity is also pressure-dependent, but to a lesser degree. For bearings in steady-state
conditions and under the usual specific bearing loads, p , the pressure dependence can, however, be
neglected. This neglecting of pressure dependency represents an additional design factor of safety.
For non-Newtonian lubricants (intrinsically viscous oils, multi-range oils), reversible and irreversible
fluctuations in viscosity occur as a function of the shear loading within the lubricant clearance gap and of
[8]
the service life. These effects are investigated only for a few lubricants and are not taken into account in
all parts of ISO 7902.
The operation bearing clearance results from the fit and the thermal expansion behaviour of bearing and
shaft. In the installed condition (20 °C), the relative bearing clearance is given by:
DD
maxJ,min
  (18)
max
D
DD
minJ,max
  (19)
min
D
 05,  (20)

maxmin
The deciding factor in the calculation is the effective relative bearing clearance, ψ , at the effective lubricant
eff
film temperature, T , which can be regarded (subject to the assumptions in 5.5) as the mean temperature of
eff
bearing and shaft. Insofar as the coefficients of linear expansion of the shaft, α , and of the bearing, α , do
l,J l,B
not differ, the clearance when cold (20 °C) is equal to the clearance when hot (T ). Should shaft and bearing
eff
(bearing line
...