ISO 6834:2022

Plain bearings — Thermo-hydrodynamic lubrication design charts for circular cylindrical bearings under steady-state conditions

This document specifies a calculation procedure for the maximum bearing temperature and effective dynamic viscosity in the lubricant film of oil-lubricated and statically loaded hydrodynamic plain journal bearings with a circular cylindrical shape, angular span Ω of 360° and width ratio B* of 0,5 to 1,5 under fluid lubrication regime. The bearing characteristics are obtained by design charts from four dimensionless numbers which are calculated from bearing dimensions, operating conditions and viscosity characteristics of the lubricant.

Paliers lisses — Diagrammes de conception de la lubrification thermo-hydrodynamique des paliers cylindriques circulaires dans des conditions de régime permanent

General Information

• Status: Published
• Publication Date: 27-Oct-2022
• ICS: 21.100.10 - Plain bearings
• Technical Committee: ISO/TC 123/SC 8 - Calculation methods for plain bearings and their applications
• Drafting Committee: ISO/TC 123/SC 8 - Calculation methods for plain bearings and their applications
• Current Stage: 6060 - International Standard published
• Start Date: 28-Oct-2022
• Due Date: 12-Apr-2024
• Completion Date: 28-Oct-2022

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 6834
First edition
2022-10
Plain bearings — Thermo-
hydrodynamic lubrication design
charts for circular cylindrical bearings
under steady-state conditions
Paliers lisses — Diagrammes de conception de la lubrification
thermo-hydrodynamique des paliers cylindriques circulaires dans des
conditions de régime permanent
Reference number
ISO 6834:2022(E)
© ISO 2022

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ISO 6834:2022(E)
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© ISO 2022
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
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Published in Switzerland
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ISO 6834:2022(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols, units and abbreviated terms . 1
5 Basis of calculation, assumptions, and preconditions . 5
5.1 Assumptions and preconditions . 5
5.2 ISOADI THL model . 6
5.2.1 General . 6
5.2.2 Generalized Reynolds equation . 6
5.2.3 Energy equation for lubricant film temperature distribution . 7
5.2.4 Formula for lubricant film thickness . 7
5.2.5 Formula for axial contraction ratio of lubricant streamlet . 8
5.2.6 Temperature-viscosity relationship . 8
5.2.7 Zero net heat flow method for journal surface temperature. 8
5.2.8 Formula for mixing temperature . 8
5.2.9 Balance of bearing load and lubricant film reaction force . 9
5.3 Boundary conditions . 9
5.3.1 Pressure distribution of lubricant film . 9
5.3.2 Temperature distribution of lubricant film . 9
5.4 Basis of calculation . 9
6 Design charts .10
6.1 General . 10
6.2 Input of design charts . 12
6.3 Axes of design charts .13
6.4 Read of design charts. 13
6.5 Conversion of modified dimensionless values from design charts to dimensional
ones . 13
7 Calculation procedure.14
Annex A (informative) Calculation examples .16
Bibliography .24
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ISO 6834:2022(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO’s adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 123, Plain bearings, Subcommittee SC 8,
Calculation methods for plain bearings and their applications.
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.
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ISO 6834:2022(E)
Introduction
The calculation procedure specified in ISO 7902-1:2020 is useful to calculate the performance of
hydrodynamic plain journal bearings with a circular cylindrical shape. This procedure, however,
does not specify the maximum bearing temperature, which is one of the most important bearing
characteristics. The reason for this is that ISO 7902-1:2020 is based on the Reynolds equation which
assumes a constant lubricant film temperature. Therefore, the calculation procedure requires some
numerical iteration before the effective dynamic viscosity in the lubricant film is converged.
This document provides a calculation procedure for the maximum bearing temperature and the
effective dynamic viscosity in the lubricant film of oil-lubricated and statically loaded hydrodynamic
plain journal bearings with a circular cylindrical shape, without any complicated numerical analysis and
iterative calculation. The basic formulae contain the energy equation and the formula of temperature-
viscosity of the lubricant to obtain the maximum bearing temperature. Since the results already satisfy
the energy balance, no iterative calculation is required.
For the reason given above, the effective dynamic viscosity in the lubricant film obtained by the
procedure in this document can also be a good input data for ISO 7902-1:2020. Annex A shows an
example of how the calculated results serve to provide input data for ISO 7902-1:2020.
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INTERNATIONAL STANDARD ISO 6834:2022(E)
Plain bearings — Thermo-hydrodynamic lubrication
design charts for circular cylindrical bearings under
steady-state conditions
1 Scope
This document specifies a calculation procedure for the maximum bearing temperature and effective
dynamic viscosity in the lubricant film of oil-lubricated and statically loaded hydrodynamic plain
journal bearings with a circular cylindrical shape, angular span Ω of 360° and width ratio B* of 0,5
to 1,5 under fluid lubrication regime. The bearing characteristics are obtained by design charts from
four dimensionless numbers which are calculated from bearing dimensions, operating conditions and
viscosity characteristics of the lubricant.
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 4378-1, Plain bearings — Terms, definitions, classification and symbols — Part 1: Design, bearing
materials and their properties
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 4378-1 and the following
apply.
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/
3.1
streamlet
axially separated stream of lubricant flow at bearing clearance where the gap increases in the rotational
direction
4 Symbols, units and abbreviated terms
Symbols and units are defined in Figure 1 and Table 1. Abbreviated terms are defined in Table 2.
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ISO 6834:2022(E)
Figure 1 — Illustration of symbols
Table 1 — Symbols and their designations
Symbol Designation Unit
B Bearing width m
* *
B Width ratio (B = B/D) 1
C Bearing radial clearance (C = R − R ) m
R R J
c Specific heat of the lubricant J/(kg·K)
p
D Inside diameter of journal bearing m
D Journal diameter m
J
E Function of relative dynamic viscosity of the lubricant 1
0
E Function of relative dynamic viscosity of the lubricant 1
1
e Eccentricity between journal and bearing axis m
e Eccentricity in the horizontal direction between journal and bearing axis m
h
e Eccentricity in the vertical direction between journal and bearing axis m
v
*
Relative heat energy of lubricant at the exit of the gap 1
e
3
F Bearing load N
F Function of relative dynamic viscosity of the lubricant 1
0
F Function of relative dynamic viscosity of the lubricant 1
1
F Function of relative dynamic viscosity of the lubricant 1
2
h Local lubricant film thickness m
* *
h Relative local lubricant film thickness (h = h/C ) 1
R
-1
N Rotational frequency of the rotor s
O Centerline of circular cylindrical bearing 1
B
O Centerline of journal 1
J
NOTE 1 S number is frequently referred to as Sommerfeld number. See References [4] to [6].
[1]
NOTE 2 In ISO 4378-5, β is defined as the attitude angle or the temperature viscosity coefficient. In ISO 7902-1:2020, β is
defined as the attitude angle. However, in this document, the attitude angle and the temperature viscosity coefficient are
represented by φ and β, respectively, to avoid confusion due to duplication.
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ISO 6834:2022(E)
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Designation Unit
2
Pe Peclet number (Pe = Ccρω/ λ ) 1
R p
p Local lubricant film pressure Pa
* * 2
p Relative local lubricant film pressure [p = pψ /(η ω)] 1
0
Lubricant side flow rate leaking out of one of the bearing side ends due to
3
Q m /s
sf
hydrodynamic pressure
Lubricant side flow rate parameter leaking out of one of the bearing side ends
*
1
Q
*
sf
due to hydrodynamic pressure [QQ= / RBC ω ]
()
sf sf R
3
Q Lubricant flow rate at the entrance into the gap (φ = φ ) m /s
1 1
3
Q Lubricant flow rate at the exit of the gap (φ = φ ) m /s
3 3
* *
1
Q Lubricant flow rate parameter at the exit of the gap [QQ= / RBC ω ]
()
3 33 R
R Journal bearing inside radius (R = D/2) m
R Journal radius (R = D /2) m
J J J
2
S S number formed with η and ω [S = BDη ω/(Fψ )] 1
0 0 0 0
T Lubricant temperature °C
T Average temperature of lubricant film °C
a
Relative difference between average temperature of lubricant film and lubri-
ΔT 1
a,r 2
cant supplying temperature [ΔT = ψ ρc (T − T )/(η ω)]
a,r p a 0 0
T Bearing temperature °C
B
T Maximum bearing temperature °C
B,max
Relative difference between bearing temperature and lubricant supplying
ΔT 1
B,r 2
temperature [ΔT = ψ ρc (T − T )/(η ω)]
B,r p B 0 0
Relative difference between maximum bearing temperature and lubricant
ΔT 1
B,max,r 2
supplying temperature [ΔT = ψ ρc (T − T )/(η ω)]
B,max,r p B,max 0 0
Logarithmic modified relative difference between maximum bearing
 temperature and lubricant supplying temperature [
1
ΔT
Bm,,ax r
**−0,,154 1758

ΔΔTT= log BP e β ]
()
Bm,,ax rB10 ,,maxr
T Effective lubricant film temperature °C
eff
T Assumed initial lubricant temperature at bearing exit °C
ex,0
T Calculated lubricant temperature at bearing exit °C
ex,1
T Journal surface temperature °C
J
Relative difference between journal surface temperature and lubricant sup-
ΔT 1
J,r 2
plying temperature [ΔT = ψ ρc (T − T )/(η ω)]
J,r p J 0 0
Relative difference between lubricant temperature and lubricant supplying
ΔT 1
r 2
temperature [ΔT = ψ ρc (T − T )/(η ω)]
r p 0 0
T Lubricant supplying temperature °C
0
T Lubricant temperature at the entrance into the gap (φ = φ ) °C
1 1
Relative difference between lubricant temperature at the entrance into the
ΔT 1
1,r 2
gap and lubricant supplying temperature [ΔT = ψ ρc (T − T )/(η ω)]
1,r p 1 0 0
T Lubricant temperature at the exit of the gap (φ = φ ) °C
3 3
U Circumferential speed of the journal (U = R ω) m/s
J J J
u Velocity component in the circumferential direction m/s
* *
u Relative velocity component in the circumferential direction (u = u/U ) 1
J
NOTE 1 S number is frequently referred to as Sommerfeld number. See References [4] to [6].
[1]
NOTE 2 In ISO 4378-5, β is defined as the attitude angle or the temperature viscosity coefficient. In ISO 7902-1:2020, β is
defined as the attitude angle. However, in this document, the attitude angle and the temperature viscosity coefficient are
represented by φ and β, respectively, to avoid confusion due to duplication.
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ISO 6834:2022(E)
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Designation Unit
v Velocity component in the cross-film direction m/s
* *
v Relative velocity component in the cross-film direction [v = v/(C ω)] 1
R
w Velocity component in the axial direction m/s
* *
w Relative velocity component in the axial direction [w = w/(Bω)] 1
y Coordinate across the lubricating film m
* *
y Relative coordinate across the lubricating film ( y = y/h) 1
z Coordinate in the axial direction m
* *
z Relative coordinate in the axial direction (z = z/B) 1
α Contraction ratio of the lubricant streamlet 1
β Temperature viscosity coefficient of the lubricant [β = ln(η /η )/60] 1/°C
40 100
* * 2
β Relative temperature viscosity coefficient of the lubricant [β = η ωβ/(ρc ψ )] 1
0 p
The first logarithmic relative coordinate variable in design chart for
difference between maximum bearing temperature and lubricant supplying
γ
1
ΔT
B,max
*15, 4
temperature [ γ =log SB ]
()
ΔT 10 0
Bm, ax
The first logarithmic relative coordinate variable in design chart for effective
γ
1
η *19, 0
effr,
relative dynamic viscosity in lubricant film [ γ = log SB ]
()
η 10 0
effr,
ε Relative eccentricity (ε = e/C ) 1
R
ε Relative eccentricity in the horizontal direction (ε = e /C ) 1
h h h R
ε Vertical eccentricity in the vertical direction (ε = e /C ) 1
v v v R
η Dynamic viscosity of the lubricant Pa·s
Average dynamic viscosity in lubricant film corresponding to difference ΔT
a
η between average temperature of lubricant film and lubricant supplying tem- Pa·s
a
perature
Relative average dynamic viscosity in lubricant film corresponding to relative
η difference ΔT between average temperature of lubricant film and lubricant 1
a,r a,r
supplying temperature (η = η /η )
a,r a 0
η Effective dynamic viscosity in lubricant film Pa·s
eff
η Effective relative dynamic viscosity in lubricant film (η = η /η ) 1
eff,r eff,r eff 0
η Relative dynamic viscosity of the lubricant (η = η/η ) 1
rel rel 0
η Dynamic viscosity at the lubricant supplying temperature Pa·s
0
η Dynamic viscosity of the lubricant at 40 °C Pa·s
40
η Dynamic viscosity of the lubricant at 100 °C Pa·s
100
Logarithmic modified effective relative dynamic viscosity in lubricant film [

1
η  **−00,,11 10 23, 5
effr,
ηη= log BP e β ]
()
effr,,10 effr
The second logarithmic relative coordinate variable in design chart for
difference between maximum bearing temperature and lubricant supplying
κ
1
ΔT
Bm, ax
*4
temperature [κβ =log Pe ]
()
ΔT 10
Bm, ax
The second logarithmic relative coordinate variable in design chart for
effective relative dynamic viscosity of lubricant film [
κ
1
η
effr,
*19, 5
κβ= log Pe ]
()
η 10
effr,
λ Thermal conductivity of the lubricant W/(m·K)
NOTE 1 S number is frequently referred to as Sommerfeld number. See References [4] to [6].
[1]
NOTE 2 In ISO 4378-5, β is defined as the attitude angle or the temperature viscosity coefficient. In ISO 7902-1:2020, β is
defined as the attitude angle. However, in this document, the attitude angle and the temperature viscosity coefficient are
represented by φ and β, respectively, to avoid confusion due to duplication.
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ISO 6834:2022(E)
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Designation Unit
π Circular constant (π = 3,141 592 …) 1
3
ρ Density of the lubricant kg/m
φ Angular coordinate in the circumferential direction rad
φ Angular coordinate at the entrance into the gap (φ = 0) rad
1 1
φ Angular coordinate at the end of the hydrodynamic pressure build-up rad
2
φ Angular coordinate at the end of the gap (φ = 2π) rad
3 3
Attitude angle (angular position of the shaft eccentricity related to the direc-
φ
°
tion of load)
ψ Relative bearing clearance (ψ = C /R) 1
R
Ω Angular span of bearing segment (Ω = 360°) °
Ω Angular span of lubricant pocket (Ω = 0°) °
G G
ω Angular speed of the rotor (ω = 2πN) rad/s
NOTE 1 S number is frequently referred to as Sommerfeld number. See References [4] to [6].
[1]
NOTE 2 In ISO 4378-5, β is defined as the attitude angle or the temperature viscosity coefficient. In ISO 7902-1:2020, β is
defined as the attitude angle. However, in this document, the attitude angle and the temperature viscosity coefficient are
represented by φ and β, respectively, to avoid confusion due to duplication.
Table 2 — Abbreviated terms and their designations
Abbreviated term Designation
isothermal condition at the journal surface (lubricant film-journal interface) and
ISOADI
adiabatic condition at the bearing surface (lubricant film-bearing interface)
THL thermo-hydrodynamic lubrication
5 Basis of calculation, assumptions, and preconditions
5.1 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 is incompressible.
d) Inertia effects, gravitational and magnetic force of the lubricant are negligible.
e) The components forming the lubrication clearance gap are rigid or their deformation is negligible;
their surfaces are ideal circular cylinders.
f) The lubricant adheres completely to the sliding surfaces.
g) The lubrication clearance gap in the convergent clearance is fully filled with the lubricant. The
lubrication film in the divergent clearance ruptures and divides into multiple streamlets from
* *
φ = φ where p = ∂p /∂φ = 0. The streamlet shrinks its width as the lubrication clearance gap
2
increases along the circumferential direction (φ-coordinate). The circumferential centerline of
each streamlet coincides with each of the circumferential computational grid lines. The density and
the thermal properties such as specific heat and thermal conductivity of the lubricant are uniform
in the streamlets. There exist stationary air cavities between the streamlets.
h) The lubricant film thickness in the axial direction (z-coordinate) is constant.
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ISO 6834:2022(E)
i) The radii of curvature of the surfaces in relative motion are large in comparison with the lubricant
film thicknesses.
j) There is no motion normal to the bearing surfaces (y-coordinate).
k) Fluctuations in pressure within the lubricant film normal to the bearing surfaces (y-coordinate)
are negligible.
l) The viscous force due to the cross-film gradient of the circumferential and the axial velocity
components (φ- and z-coordinate) is significantly larger than the other viscous forces.
m) The temperature and viscosity of the lubricant film are two-dimensionally distributed within the
lubrication clearance gap (φy-plane). They vary little in the axial direction (z-coordinate) and can
be represented by the distribution in the midplane of the bearing width.
n) The heat flow due to heat conduction within the lubrication clearance gap is significantly larger in
the cross-film direction (y-coordinate) than in the other directions (φ- and z-coordinate).
o) The viscous energy of the lubricant film dissipated by the cross-film gradient of the circumferential
velocity component (φ-coordinate) is significantly larger than those due to the other velocity
gradients.
p) The surface temperature of the rotating journal is uniform in the circumferential and the axial
directions (φ- and z-coordinate).
q) The stationary bearing surface is adiabatic and does not allow heat flux to pass through.
r) The viscosity of the lubricant changes exponentially with the temperature.
s) Lubricant at a constant temperature is fed from the single pocket located at the apex of bearing.
The angular span of the lubricant pocket Ω is negligibly small (Ω = 0°). The magnitude of the
G G
lubricant feed pressure is negligible in comparison with the lubricant film pressure. The lubricant
feeding rate is the same as the lubricant leakage rate from the bearing side ends. The fed lubricant
and the recirculating lubricant are fully mixed and form a uniform mixing temperature. It flows
into the lubrication clearance gap.
5.2 ISOADI THL model
5.2.1 General
ISOADI THL model, which is classified as one of simplified THL models in References [5] and [6], is
adopted to prepare the design charts to read the maximum bearing temperature and the effective
viscosity in lubricant film for the THL bearing design in the dimensionless form. The model assumes
an isothermal journal surface (T constant) and an adiabatic bearing surface. The model uses four
J
*
dimensionless bearing design variables (S number S , width ratio B , Peclet number Pe and relative
0
*
temperature viscosity coefficient of the lubricant β ) as input data. The model solves the generalized
[7]
Reynolds equation and the energy equation simultaneously, coupled with some related formulae
such as lubricant film thickness, lubricant viscosity, etc. The maximum bearing temperature and the
effective dynamic viscosity in the lubricant film are calculated for a wide range of bearing specifications
and operating conditions in the dimensionless form.
5.2.2 Generalized Reynolds equation
The generalized Reynolds equation for a journal bearing with finite width is defined as Formula (1) in
the dimensionless form:
* *
   
FF
∂ ∂p 1 ∂ ∂p ∂   
*3 *3 * 1
hF + hF = h 1− (1)
   
2 2   
**2 *
∂ϕϕ∂ ϕ F
∂
   
4Bz∂ ∂z   0 
   
6
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ISO 6834:2022(E)
where
FE= ()ϕ,,1
00
FE= ϕ,,1
()
11
2
*2
1
F
y
* 1
F =−dy ,
2
∫
0
η F
rel 0
as
* *
*
y y
1 y
* ** *
Eyϕ,,= dy Eyϕ, = dy
() ()
01
∫ ∫
0 0
η η
rel rel
Formula (1) is numerically solved, taking into account the boundary conditions for the generation of
pressure. See Reference [7] for the derivation of the generalized Reynolds equation.
5.2.3 Energy equation for lubricant film temperature distribution
The energy equation for the lubricant film temperature distribution along the midplane of the bearing
width is defined as Formula (2) in the dimensionless form:
2
* *
    η  
∂ΔΔT 11∂h ∂ T ∂ ∂ΔT ∂u
* ** * rel
r r r
u +−vy u = + (2)
     
*   **  *2 *  *2  * 
∂ϕϕ∂
h ∂yy∂ Peh ∂y h ∂y
 
   
* *
where u and v are defined as shown by Formulae (3) and (4):
*
*
Eyϕ,
()
 F  ∂p
0
**2 **
1
uh= Eyϕϕ,,− Ey + (3)
() ()
 1 0 
F ∂ϕ F
 0  0
*
** **
y  
∂uy ∂hu∂
** *
vh=− − dy (4)
 
∫
 
* *
0
∂ϕϕ∂
h ∂y
 
Formula (2) is numerically solved, taking into account the simplified boundary conditions for the
lubricant film temperature distribution. See Reference [4] for the derivation of the energy equation.
5.2.4 Formula for lubricant film thickness
The relative local lubricant film thickness of a circular cylindrical bearing is given in Formula (5):
*
h =+1 εϕcoss+ε inϕ (5)
vh
where
εε= cosφ ,
v
εε= sinφ .
h
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ISO 6834:2022(E)
5.2.5 Formula for axial contraction ratio of lubricant streamlet
The axial contraction ratio α of the lubricant streamlet is calculated based on the law of conservation
of mass and the assumption of uniform width in the cross-film direction (y-coordinate) as shown by
Formula (6):
 
F ϕ
()
* 12
h ϕ 1−
() 
2
 
F ϕ
()
02
 
α = (6)
 
F ϕ
()
* 1
h ϕ 1−
() 
 
F ϕ
()
0
 
In the case of α > 1, α is corrected to 1.
5.2.6 Temperature-viscosity relationship
The relative dynamic viscosity of the lubricant is given as Formula (7) following the exponential model:
*
−β ΔT
r
η = e (7)
rel
5.2.7 Zero net heat flow method for journal surface temperature
A uniform journal surface temperature ∆T is determined by applying the zero net heat flow method in
J,r
which the total heat flow exchanged between the journal and the surrounding lubricant film is equal to
zero as Formula (8) in the dimensionless form:
2π  
∂ΔT
* r
αϕh d =0 (8)
 
∫  
*
0
*
∂y
 
y =1
5.2.8 Formula for mixing temperature
The uniform mixing temperature, which corresponds to the lubricant temperature at the entrance into
the gap, is given as Formula (9) in the dimensi
...