ISO 4378-5:2009
(Main)Plain bearings — Terms, definitions, classification and symbols — Part 5: Application of symbols
Plain bearings — Terms, definitions, classification and symbols — Part 5: Application of symbols
ISO 4378-5:2009 specifies practical applications of the general symbols defined in ISO 4378-4, with regard to the calculations, design and testing of plain bearings.
Gleitlager - Begriffe, Definitionen und Einteilung - Teil 5: Formelzeichen
Paliers lisses — Termes, définitions, classification et symboles — Partie 5: Application des symboles
L'ISO 4378-5:2009 précise l'utilisation pratique des symboles généraux définis dans l'ISO 4378‑4 pour le calcul, la conception et l'essai des paliers lisses.
Drsni ležaji - Izrazi, definicije, klasifikacija in simboli - 5. del: Način uporabe simbolov
Ta del standarda ISO 4378 določa praktično uporabo splošnih simbolov iz standarda ISO 4378-4
v zvezi z izračuni, konstrukcijo in preskušanjem drsnih ležajev. Standard ISO 4378-4 ločuje med osnovnimi in dodatnimi znaki. Dodatni znaki so nadpisani ali podpisani. Simboli, potrebni za izračun, konstrukcijo, proizvodnjo in preskušanje drsnih ležajev, so le osnovni znaki ali kombinacije osnovnih in dodatnih znakov.
V tem delu standarda ISO 4378 so navedeni simboli, potrebni za izračune, konstrukcijo in preskušanje drsnih ležajev. Opredeljeni so bili v skladu s priporočili iz standarda ISO 4378-4. Koti in smer rotacije so opredeljeni pozitivno kot vrtenje v levo (v nasprotni smeri urnega kazalca); enako velja za vrtilno frekvenco ter obodno in kotno hitrost.
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INTERNATIONAL ISO
STANDARD 4378-5
First edition
2009-09-01
Plain bearings — Terms, definitions,
classification and symbols —
Part 5:
Application of symbols
Paliers lisses — Termes, définitions, classification et symboles —
Partie 5: Application des symboles
Reference number
ISO 4378-5:2009(E)
©
ISO 2009
---------------------- Page: 1 ----------------------
ISO 4378-5:2009(E)
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ii © ISO 2009 – All rights reserved
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ISO 4378-5:2009(E)
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Symbols and terms .1
3.1 Symbols of the Roman alphabet.1
3.2 Symbols of the Greek alphabet.18
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ISO 4378-5:2009(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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
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.
ISO 4378-5 was prepared by Technical Committee ISO/TC 123, Plain bearings, Subcommittee SC 6, Terms
and common items.
This first edition cancels and replaces ISO 4378-4:1997 as well as ISO 7904-2:1995, which have been
technically revised.
ISO 4378 consists of the following parts, under the general title Plain bearings — Terms, definitions,
classification and symbols:
⎯ Part 1: Design, bearing materials and their properties
⎯ Part 2: Friction and wear
⎯ Part 3: Lubrication
⎯ Part 4: Basic symbols
⎯ Part 5: Application of symbols
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ISO 4378-5:2009(E)
Introduction
As there is a large number of multiple designations in the domain of plain bearings, there is a considerable
risk of error in the interpretation of standards and technical literature. This uncertainty leads to the continuous
addition of supplementary designations, which only serves to increase the misunderstanding.
This part of ISO 4378 specifies pratical applications of the general symbols used in the field of plain bearings.
© ISO 2009 – All rights reserved v
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INTERNATIONAL STANDARD ISO 4378-5:2009(E)
Plain bearings — Terms, definitions, classification and
symbols —
Part 5:
Application of symbols
1 Scope
This part of ISO 4378 specifies practical applications of the general symbols defined in ISO 4378-4, with
regard to the calculations, design and testing of plain bearings.
ISO 4378-4 distinguishes between basic characters and additional signs. Additional signs are subscripts and
superscripts. The symbols necessary for plain bearing calculations, design, manufacture and testing are just
basic characters or combinations of basic characters and additional signs.
This part of ISO 4378 lists symbols which have been found necessary for the calculations, design and testing
of plain bearings. They have been defined in accordance with the recommendations given in ISO 4378-4.
Angles and directions of rotation are defined positively as rotating in a left-hand (anticlockwise) direction; the
same applies to rotational frequencies, and circumferential and angular velocities.
2 Normative references
The following referenced documents are indispensable for the application 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 4378-4, Plain bearings — Terms, definitions, classification and symbols — Part 4: Basic symbols
3 Symbols and terms
The following listings are not necessarily complete. They may be enlarged, if necessary.
NOTE Some letters of the Roman and Greek alphabet have not yet been used. Therefore, these letters are not listed
below.
3.1 Symbols of the Roman alphabet
A heat-emitting surface area (bearing housing), elongation at fracture
A* heat-emitting surface area parameter [thrust bearing, A* = A/(B × L × Z )]
ax
A area of segment or pad
B
A area of groove cross-section
G
A heat-emitting surface area (bearing housing) inside of the machine (flange bearing)
i
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ISO 4378-5:2009(E)
A land area
lan
* *
A relative land area ( A = A /(π × D × B) for hydrostatic journal bearings)
lan lan
lan
A heat-emitting surface area (bearing housing) outside of the machine (flange bearing)
o
A area of lubricant pocket
P
A area of cross-section
S
A specific area of tube
T
A area of tube cross-section flowed through
T,i
a distance, acceleration, thermal diffusivity, inertia factor
a distance between leading edge and pivot position of pad (tilting-pad bearing)
F
*
a relative distance between leading edge and pivot position of pad (tilting-pad bearing)
F
a minimum distance between two circular thrust pads
min
a distance between temperature measuring point and bearing sliding surface
T
B width parallel to the sliding surface, normal to the direction of motion; bearing width, nominal
bearing width, pad width, nominal pad width
B* relative width, relative bearing width, relative pad width, width ratio (B* = B/D)
B width of thrust bearing or thrust pad [B = (D − D )/2]
ax ax o i
B effective bearing width (without grooves, chamfers, etc.), effective pad width
eff
B outer width of bearing housing in axial direction
H
B total bearing width
tot
b width parallel to the sliding surface, normal to the direction of motion or flow
b width of circumferential discharge (hydrostatic bearing, b = B − b )
c c lan
b width of lubricant groove, width of lubricant supply groove, width of bleed groove
G
b land width parallel to the sliding surface, normal to the direction of flow
lan
b width of lubricant pocket, width of lubricant supply pocket
P
*
b relative width of lubricant pocket, relative width of lubricant supply pocket
P
C bearing clearance, nominal bearing clearance, chamfer, concentration
C axial bearing clearance (thrust bearing)
ax
C mean value of C [C = (C + C )/2]
ax,m ax ax,m ax,min ax,max
C maximum value of C
ax,max ax
C minimum value of C
ax,min ax
C bearing clearance, bearing diametral clearance (difference between bearing bore and journal
D
diameter of a journal bearing, C = D − D )
D J
C mean value of C [C = (C + C )/2]
D,m D D,m D,min D,max
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ISO 4378-5:2009(E)
C effective bearing diametral clearance
D,eff
C maximum value of C
D,max D
C minimum value of C
D,min D
C circumference of groove cross-section
G
C bearing radial clearance (difference between bearing bore and journal radius of a journal bearing,
R
C = R − R )
R J
∆C elastic change of C
R,el R
C effective bearing radial clearance
R,eff
C mean value of C [C = (C + C )/2]
R,m R R,m R,min R,max
C maximum value of C
R,max R
C minimum value of C
R,min R
∆C thermal change of C
R,th R
∆C total change of C (∆C = ∆C + ∆C )
R,tot R R,tot R,el R,th
c specific heat capacity, lubricant specific heat capacity, stiffness
c axial bearing stiffness
ax
c axial stiffness of the bearing when load is directed into the machine (flange bearing)
ax,i
c axial stiffness of the bearing when load is directed out of the machine (flange bearing)
ax,o
c vertical stiffness of the bearing loaded downwards
dw
c stiffness of pad pivot support in direction of load (tilting-pad bearing)
F
c horizontal bearing stiffness
h
c lubricant film stiffness coefficient of journal bearing (i, k = 1, 2)
ik
*
c non-dimensional lubricant film stiffness coefficient of journal bearing
ik
3
ψ
*
cc=×i,1k=,2
() ( )
ik ik
2××B ηω×
c inner lubricant film stiffness coefficient of journal bearing (i, k = 1, 2)
ik,i
c outer lubricant film stiffness coefficient of journal bearing (i, k = 1, 2)
ik,o
c flexural stiffness of the Jeffcott Rotor
JR
c specific heat capacity of the lubricant (at constant pressure)
p
c specific heat capacity of the coolant (at constant pressure)
p,cl
c flexural stiffness of shaft
sh
c stiffness of isotropic bearing or bearing shell support
sup
c stiffness coefficient of anisotropic bearing or bearing shell support (i, k = 1, 2)
sup,ik
c vertical stiffness of the bearing loaded upwards
up
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ISO 4378-5:2009(E)
c vertical bearing stiffness
v
c angular stiffness of pad pivot support (tilting-pad bearing)
ϑ
D bearing diameter (inside diameter of journal bearing), nominal bearing diameter
D twice the lobe or pad bore radius of a multi-lobed or tilting-pad journal bearing
B
D mean value of D [D = (D + D )/2]
B,m B B,m B,min B,max
D maximum value of D
B,max B
D minimum value of D
B,min B
D outside diameter of bearing shell or pad of a fixed-pad or tilting-pad journal bearing
B,o
D (outside) diameter of lubricating ring fixed to the shaft
fi
D inside diameter of bearing housing
H,i
D outside diameter of bearing housing
H,o
D inside diameter of thrust bearing sliding surface
i
D journal diameter (diameter of the shaft section located inside of a journal bearing)
J
D mean value of D [D = (D + D )/2]
J,m J J,m J,min J,max
D maximum value of D
J,max J
D minimum value of D
J,min J
D (outside) diameter of loose lubricating ring
lo
D mean diameter of thrust bearing sliding surface [D = (D + D )/2]
m m i o
D maximum value of D
max
D minimum value of D
min
D outside diameter of thrust bearing sliding surface
o
D inside diameter of tube
T,i
D outside diameter of tube
T,o
d diameter, distance, depth, damping
d diameter of circular thrust pad
B
d diameter of capillary
cp
d damping of eigenfrequency, system damping
e
d damping of pad pivot support in direction of load (tilting-pad bearing)
F
d diameter of groove
G
d mean diameter of groove
G,m
d lubricant film damping coefficient of journal bearing (i, k = 1, 2)
ik
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ISO 4378-5:2009(E)
*
d non-dimensional lubricant film damping coefficient of journal bearing
ik
3
⎡⎤
ψ
*
dd=×ω×i,1k=,2
⎢⎥()
ik ik
2××B ηω×
⎢⎥
⎣⎦
d lubrication hole diameter
L
d inside diameter of orifice
orf,i
d outside diameter of orifice
orf,o
d diameter of lubricating pocket
P
d damping of isotropic bearing or bearing shell support
sup
d damping coefficient of anisotropic bearing or bearing shell support (i, k = 1, 2)
sup,ik
d angular damping of pad pivot support (tilting-pad bearing)
ϑ
E Young's modulus (modulus of elasticity)
E Young's modulus of bearing material
B
E Young's modulus of journal material
J
E resultant Young's modulus
res
E Young's modulus of shaft material
sh
e eccentricity (distance between journal and bearing axis)
e eccentricity of bearing sliding surfaces (segments or pads) of a multi-lobed or tilting-pad journal
B
bearing
e eccentricity of bearing sliding surfaces (segments) of a multi-lobed journal bearing in the
B,h
horizontal direction
e eccentricity of bearing sliding surfaces (segments) of a multi-lobed journal bearing in the vertical
B,v
direction
e eccentricity of centre of gravity (distance between centre of gravity and shaft axis)
CG
e component of eccentricity normal to direction of load
x
e component of eccentricity in direction of load
y
F bearing force, bearing load, nominal bearing load, load-carrying capacity
F* bearing force parameter
∆F additional dynamic force
2
∆ψF ×
∆F* additional dynamic force parameter (∆F* = for journal bearings)
BD××η×ω
F axial bearing force, axial bearing load, thrust bearing load (nominal load)
ax
F maximum admissible thrust bearing load
ax,lim
F maximum admissible thrust bearing load directed into the machine (flange bearing)
ax,lim,i
F maximum admissible thrust bearing load directed out of the machine (flange bearing)
ax,lim,o
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ISO 4378-5:2009(E)
F segment or pad load
B
F damping force
d
F dynamic bearing force, dynamic bearing load
dyn
F resonance amplitude of dynamic bearing force
dyn,rsn
F component of F in the x-direction
dyn,x dyn
F component of F in the y-direction
dyn,y dyn
F bearing force considering elasticity
e
* *
F bearing force parameter considering elasticity ( F = K × F*)
e e
el
F bearing force considering elasticity at transition to mixed friction
e,tr
*
F bearing force parameter considering elasticity at transition to mixed friction
e,tr
F effective load-carrying capacity
eff
* *
F effective load-carrying capacity parameter [FF=×/()b l×Z×p for hydrostatic journal
eff eff hs c ax en
bearings]
*
F effective load-carrying capacity parameter at N = 0
eff,0
F exciting force
exc
F friction force (F = f × F )
f f
f
*
*
F friction force parameter ( F =× So for journal bearings)
f f
ψ
F friction force of thrust bearing (F = f × F )
f,ax f,ax ax ax
F friction force of thrust bearing segment or pad
f,B
Fh×
* * f,B ax,min
F friction force parameter of thrust bearing segment or pad ( F = )
f,B f,B
2
BR××η×ω
ax m
F friction force in the area of the lubricant groove
f,G
*
F friction force parameter in the area of the lubricant groove
f,G
F friction force in the loaded area of the lubricant film
f,ld
*
F friction force parameter in the loaded area of the lubricant film
f,ld
F friction force in the area of the lubricant pocket
f,P
*
F friction force parameter in the area of the lubricant pocket
f,P
F friction force of journal bearing (F = f × F )
f,r f,r r r
F friction force in the unloaded area of the lubricant film
f,uld
*
F friction force parameter in the unloaded area of the lubricant film
f,uld
F maximum admissible bearing load
lim
F maximum admissible bearing load in vertical direction downwards
lim,dw
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ISO 4378-5:2009(E)
F maximum admissible bearing load in the horizontal direction
lim,h
F maximum admissible bearing load in the vertical direction upwards
lim,up
F normal force (normal to the sliding surface)
n
F radial bearing force, radial bearing load, journal bearing load (nominal load)
r
F maximum admissible journal bearing load
r,lim
F resulting force, resulting load
res
F bearing force component due to rotation
rot
F static bearing force, static bearing load
sc
F spring force
sp
F bearing force component due to squeezing
sq
F bearing force at start (N ≈ 0)
str
F bearing force at stop (N ≈ 0)
stp
F bearing force at transition to mixed friction
tr
*
F bearing force parameter at transition to mixed friction
tr
F unbalance force
u
F bearing force at N = 0
0
f friction factor (coefficient of friction), deflection, function, frequency
f* friction parameter
f coefficient of friction of thrust bearing
ax
f downward deflection of segment or pad
B
f bearing eigenfrequency
e
f hydrodynamic coefficient of friction
hd
f hydrodynamic coefficient of friction in the area of mixed friction
hd,m
f journal deflection
J
f minimum coefficient of friction, coefficient of friction at minimum of Stribeck curve
min
f coefficient of friction of journal bearing
r
f solid coefficient of friction
s
f solid coefficient of friction in the area of mixed friction
s,m
* *
f friction parameter of taper land thrust bearing ( f = f* × h /h )
tl tl wed ax,min
f coefficient of friction at transition to mixed friction
tr
G shear modulus
g acceleration due to gravity
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ISO 4378-5:2009(E)
H height, bearing height, nominal bearing height, hardness
H height of bearing housing
H
h height, depth, thickness, lubricant film thickness, local lubricant film thickness, gap
h* relative lubricant film thickness, relative local lubricant film thickness (h* = h/C for journal
R
bearings)
h lubricant film thickness at the entrance gap
en
h lubricant film thickness at the exit gap
ex
h depth of lubricant groove, depth of lubricant supply groove
G
h minimum admissible lubricant film thickness during operation
lim
* *
h minimum admissible relative lubricant film thickness during operation ( h = h /C for journal
lim lim
r,lim R
bearings)
h minimum admissible lubricant film thickness at transition to mixed friction (minimum value of
lim,tr
minimum lubricant film thickness still permitting full separation of bearing and shaft sliding
surfaces by a lubricant film)
*
h minimum admissible relative lubricant film thickness at transition to mixed friction
lim,tr
*
( h = h /C for journal bearings)
lim,tr
lim,tr R
h minimum lubricant film thickness, minimum gap
min
* *
h minimum relative lubricant film thickness, minimum relative gap ( h = h /C for journal
min min
r,min R
*
bearings, h = h /h for thrust bearings)
min ax, min wed
h minimum lubricant film thickness at transition to mixed friction
min,tr
* *
h minimum relative lubricant film thickness at transition to mixed friction ( h = h /C for
min,tr min,tr min,tr R
journal bearings)
h reference value of h
min,0 min
h depth of lubricant pocket, depth of lubricant supply pocket
P
h minimum admissible lubricant film thickness of journal bearing during operation
r,lim
h minimum lubricant film thickness of journal bearing
r,min
h waviness of sliding surface
wav
h effective waviness of sliding surface
wav,eff
h maximum admissible effective waviness of sliding surface
wav,eff,lim
h maximum admissible waviness of sliding surface
wav,lim
h wedge depth (thrust bearing)
wed
* *
h relative wedge depth (thrust bearing, h = h /l )
wed wed wed wed
h wedge depth in radial direction (thrust bearing)
wed,r
h local gap at ε = 0 (journal bearing)
0
* *
h relative local gap at ε = 0 ( h = h /C )
0 0 0 R
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ISO 4378-5:2009(E)
h maximum gap at ε = 0
0,max
* *
h maximum relative gap at ε = 0, gap ratio ( h = h /C )
0,max 0,max
0,max R
I geometrical moment of inertia
i −1
J mass moment of inertia
J bearing mass moment of inertia with reference to the X-axis
X
J bearing mass moment of inertia with reference to the Y-axis
Y
J bearing mass moment of inertia with reference to the Z-axis
Z
j −1
K coefficient, constant, factor, parameter, auxiliary variable
2
K dissipation parameter [K = η × ω/(ρ × c × T × ψ ) for journal bearings]
d d p
K elasticity influence parameter
el
K fill factor
fil
K correction factor considering the heat transition resistance of bearing insulation
I
K profile factor [relative difference between lobe or pad bore radius and journal radius,
P
K = 1/(1 − m)]
P
K effective profile factor
P,eff
∆K elastic change of K
P,el P
K profile factor at temperature T
P,T
∆K thermal change of K
P,th P
∆K total change of K (∆K = ∆K + ∆K )
P,tot P P,tot P,el P,th
K rotational speed influence parameter
rot
ηω×
0
K heating parameter ( K = for journal bearings)
T T
2
ρψ××cT×
p0
K wear coefficient
w
1
K heat conduction parameter ( K = for journal bearings)
λ λ
Re××Pr ψ
k heat transition coefficient
k heat transition coefficient referring to A*
A*
k* heat transition parameter [k* = 2 × ψ × k × A/(λ × D) for journal bearings]
A
k heat transition coefficient referring to A
A
k heat transition coefficient referring to bearing sliding surface (heat transition coefficient at the
B
interface between lubricant film and bearing sliding surface)
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ISO 4378-5:2009(E)
k heat transition coefficient of tube
T
L length parallel to the sliding surface, in direction of motion; nominal length, pad length, nominal
pad length
L length of bearing housing at right angles to the axis
H
L length of tube
T
l length in the direction of flow, exponent of Falz's formula for the dependency of η on
− l
⎡⎤
⎛⎞
η T
⎢⎥
T =
⎜⎟
⎢⎥
η T
00⎝⎠
⎣⎦
l length of capillary
cp
l length of lubricant groove (circumferential direction), length of lubricant supply groove, length of
G
drainage groove, length of bleed groove
l length of axial discharge [l = π × D/Z − (l + l ) for hydrostatic journal bearings]
ax ax ax lan G
l land length in the direction of flow (thrust bearing)
lan
l length of lubricant pocket, length of lubricant supply pocket
P
l wedge length (thrust bearing)
wed
M moment, mixing factor
M moment of bearing load
F
M friction moment (M = R × F for journal bearings, M = R × F for thrust bearings)
f f f,r f m f,ax
m mass, preload of bearing or pad sliding surface
m bearing mass
B
m mass of the Jeffcott Rotor
JR
N rotational speed (rotational frequency) of the rotor (revolutions per time unit)
N rotational speed (rotational frequency) of the bearing
B
N critical speed (critical rotational frequency) of the rigidly supported rotor
cr
N rotational speed (rotational frequency) of the bearing force
F
N rotational speed (rotational frequency) at minimum of Stribeck curve
f,min
N rotational speed (rotational frequency) at the stability speed limit of the rotor supported by plain
lim
bearings
N maximum rotational speed (maximum rotational frequency)
max
N minimum rotational speed (minimum rotational frequency)
min
N resonance speed (resonance rotational frequency) of the rotor supported by plain bearings
rsn
N rotational speed (rotational frequency) at transition to mixed friction, transition rotational speed,
tr
transition rotational frequency
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ISO 4378-5:2009(E)
N reference value of N
0
Nu Nusselt number
n number
O point of origin, centre, centreline, order of magnitude
O centreline of plain bearing
B
O centreline of sliding surface No. i
i
O centreline of journal
J
P power, heat flow
P* power ratio (P* = P /P )
f Pu
P heat flow discharged from the bearing to the ambient air via convection
cv,B
P heat flow discharged from the shaft to the ambient air via convection
cv,sh
P frictional power
f
P frictional power of thrust bearing (P = F × U )
f,ax f,ax f,ax m
P frictional power in the lubricant pocket(s)
f,P
P frictional power of journal bearing (P = F × U )
f,r f,r f,r J
P pumping power
Pu
P parasitic power loss
pa
P parasitic power loss of thrust bearing
pa,ax
P parasitic power loss of journal bearing
pa,r
P heat flow (quantity of heat transferred by heat or mass transfer per time unit)
th
P heat flow to the ambient air
th,amb
P heat flow via the cooling system
th,cl
P heat flow due to frictional power
th,f
P heat flow via the Iubricant
th,L
P heat flow supplied to the bearing via the lubricant
th,L,en
P heat flow discharged from the bearing via the lubricant
th,L,ex
P heat flow discharged from the bearing via the lubricant side flow rate
th,sf
P total power
tot
P
*
* tot
P total power parameter ( P = for journal bearings)
tot tot
F××ω C
rR
P heat flow discharged from the bearing via heat conduction in the shaft
λ,sh
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ISO 4378-5:2009(E)
η × c
p
Pr Prandtl number (Pr = )
λ
p Iubricant film pressure, local Iubricant film pressure (pressure built up in the lubricant film of a
plain bearing by hydrodynamic or hydrostatic effects)
p specific bearing load (bearing load per unit of projected bearing area)
p ambient pressure (pressure in the immediate vicinity of bearing shell or pad)
amb
p ambient pressure at D (thrust bearing)
amb,i i
p ambient pressure at D (thrust bearing)
amb,o o
p specific load of thrust bearing [ p = F /(B × L × Z )]
ax ax ax ax
p profile of bearing or pad sliding surface
B
p dynamic specific bearing force, dynamic specific bearing load ( p = F /(B × D) for journal
dyn dyn
dyn
bearings, p = F /(B × L × Z ) for thrust bearings)
dyn
dyn ax
p Iubricant supply pressure (pressure by which the lubricant is supplied to the bearing)
en
2
p ×ψ
* *
en
p lubricant supply pressure parameter ( p = for journal bearings)
en en
η ×ω
p maximum admissible Iubricant film pressure
lim
p maximum admissible specific bearing Ioad (limiting value of specific bearing load; exceeding this
lim
value may lead to bearing failure)
p maximum admissible specific bearing Ioad at transition to mixed friction
lim,tr
p maximum lubricant film pressure
max
* *
p maximum lubricant film pressure parameter ( p = p / p )
max max
max
p Iubricant pressure in the lubricant pocket
P
p Iubricant pressure in the lubricant pocket No. i
P,i
p Iubricant pressure in the lubricant pocket No. i at ε = 0 (journal bearing)
P,i,0
p specific load of journal bearing [ p = F /(B × D)]
r r
r
p static specific bearing force, static specific bearing load [ p = F /(B × D) for journal bearings,
sc sc
sc
p = F /(B × L × Z ) for thrust bearings]
sc
sc ax
p specific bearing load at start (N ≈ 0)
str
p specific bearing load at stop (N ≈ 0)
stp
p specific bearing load at transition to mixed friction [ p = F /(B × D) for journal bearings]
tr tr
tr
Q lubricant flow rate (volume of lubricant passing through the bearing per time unit, Q = Q + Q )
3 p
Q* lubricant flow rate parameter, relative lubricant flow rate (Q* = Q/Q )
0
Q lubricant flow rate of thrust bearing
ax
Q lubricant flow rate supplied to the thrust bearing
ax,en
12 © ISO 2009 – All rights reserved
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ISO 4378-5:2009(E)
Q lubricant flow rate at leading edge of segment or pad
le
Q lubricant side flow rate of segment or pad
sf
Q lubricant flow rate at trailing edge of segment or pad
te
Q coolant flow rate
cl
Q lubricant flow rate per lubricant pocket
P
Q lubricant flow rate at pump
Pu
Q maximum admissible lubricant flow rate at pump
Pu,lim
Q lubricant flow rate due to supply pressure
p
* * *
Q lubricant flow rate parameter due to supply pressure [ Q = Q /( p × Q )]
p p en
p 0
Q lubricant side flow rate of lubricant pocket
P,sf
Q lubricant flow rate of journal bearing
r
Q lubricant flow rate supplied to the journal bearing
r,en
3
3
Q reference value of Q (Q = R × ω × ψ for hydrodynamic journal bearings, QC=×p /η for
0 0 0R en
2
hydrostatic journal bearings, Q = B × h × U × Z or Qh=×ω×R for thrust
0 ax ax,min m ax 0ax,min m
bearings)
Q lubricant flow rate at the entrance into
...
SLOVENSKI STANDARD
SIST ISO 4378-5:2015
01-marec-2015
1DGRPHãþD
SIST ISO 7904-2:2002
'UVQLOHåDML,]UD]LGHILQLFLMHNODVLILNDFLMDLQVLPEROLGHO 1DþLQXSRUDEH
VLPERORY
Plain bearings - Terms, definitions, classification and symbols - Part 5: Application of
symbols
Gleitlager - Begriffe, Definitionen und Einteilung - Teil 5: Formelzeichen
Paliers lisses - Termes, définitions, classification et symboles - Partie 5: Application des
symboles
Ta slovenski standard je istoveten z: ISO 4378-5:2009
ICS:
01.040.21 Mehanski sistemi in deli za Mechanical systems and
splošno rabo (Slovarji) components for general use
(Vocabularies)
21.100.10 Drsni ležaji Plain bearings
SIST ISO 4378-5:2015 en,fr
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 4378-5:2015
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SIST ISO 4378-5:2015
INTERNATIONAL ISO
STANDARD 4378-5
First edition
2009-09-01
Plain bearings — Terms, definitions,
classification and symbols —
Part 5:
Application of symbols
Paliers lisses — Termes, définitions, classification et symboles —
Partie 5: Application des symboles
Reference number
ISO 4378-5:2009(E)
©
ISO 2009
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SIST ISO 4378-5:2015
ISO 4378-5:2009(E)
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Published in Switzerland
ii © ISO 2009 – All rights reserved
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SIST ISO 4378-5:2015
ISO 4378-5:2009(E)
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Symbols and terms .1
3.1 Symbols of the Roman alphabet.1
3.2 Symbols of the Greek alphabet.18
© ISO 2009 – All rights reserved iii
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SIST ISO 4378-5:2015
ISO 4378-5:2009(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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
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.
ISO 4378-5 was prepared by Technical Committee ISO/TC 123, Plain bearings, Subcommittee SC 6, Terms
and common items.
This first edition cancels and replaces ISO 4378-4:1997 as well as ISO 7904-2:1995, which have been
technically revised.
ISO 4378 consists of the following parts, under the general title Plain bearings — Terms, definitions,
classification and symbols:
⎯ Part 1: Design, bearing materials and their properties
⎯ Part 2: Friction and wear
⎯ Part 3: Lubrication
⎯ Part 4: Basic symbols
⎯ Part 5: Application of symbols
iv © ISO 2009 – All rights reserved
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ISO 4378-5:2009(E)
Introduction
As there is a large number of multiple designations in the domain of plain bearings, there is a considerable
risk of error in the interpretation of standards and technical literature. This uncertainty leads to the continuous
addition of supplementary designations, which only serves to increase the misunderstanding.
This part of ISO 4378 specifies pratical applications of the general symbols used in the field of plain bearings.
© ISO 2009 – All rights reserved v
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SIST ISO 4378-5:2015
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SIST ISO 4378-5:2015
INTERNATIONAL STANDARD ISO 4378-5:2009(E)
Plain bearings — Terms, definitions, classification and
symbols —
Part 5:
Application of symbols
1 Scope
This part of ISO 4378 specifies practical applications of the general symbols defined in ISO 4378-4, with
regard to the calculations, design and testing of plain bearings.
ISO 4378-4 distinguishes between basic characters and additional signs. Additional signs are subscripts and
superscripts. The symbols necessary for plain bearing calculations, design, manufacture and testing are just
basic characters or combinations of basic characters and additional signs.
This part of ISO 4378 lists symbols which have been found necessary for the calculations, design and testing
of plain bearings. They have been defined in accordance with the recommendations given in ISO 4378-4.
Angles and directions of rotation are defined positively as rotating in a left-hand (anticlockwise) direction; the
same applies to rotational frequencies, and circumferential and angular velocities.
2 Normative references
The following referenced documents are indispensable for the application 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 4378-4, Plain bearings — Terms, definitions, classification and symbols — Part 4: Basic symbols
3 Symbols and terms
The following listings are not necessarily complete. They may be enlarged, if necessary.
NOTE Some letters of the Roman and Greek alphabet have not yet been used. Therefore, these letters are not listed
below.
3.1 Symbols of the Roman alphabet
A heat-emitting surface area (bearing housing), elongation at fracture
A* heat-emitting surface area parameter [thrust bearing, A* = A/(B × L × Z )]
ax
A area of segment or pad
B
A area of groove cross-section
G
A heat-emitting surface area (bearing housing) inside of the machine (flange bearing)
i
© ISO 2009 – All rights reserved 1
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A land area
lan
* *
A relative land area ( A = A /(π × D × B) for hydrostatic journal bearings)
lan lan
lan
A heat-emitting surface area (bearing housing) outside of the machine (flange bearing)
o
A area of lubricant pocket
P
A area of cross-section
S
A specific area of tube
T
A area of tube cross-section flowed through
T,i
a distance, acceleration, thermal diffusivity, inertia factor
a distance between leading edge and pivot position of pad (tilting-pad bearing)
F
*
a relative distance between leading edge and pivot position of pad (tilting-pad bearing)
F
a minimum distance between two circular thrust pads
min
a distance between temperature measuring point and bearing sliding surface
T
B width parallel to the sliding surface, normal to the direction of motion; bearing width, nominal
bearing width, pad width, nominal pad width
B* relative width, relative bearing width, relative pad width, width ratio (B* = B/D)
B width of thrust bearing or thrust pad [B = (D − D )/2]
ax ax o i
B effective bearing width (without grooves, chamfers, etc.), effective pad width
eff
B outer width of bearing housing in axial direction
H
B total bearing width
tot
b width parallel to the sliding surface, normal to the direction of motion or flow
b width of circumferential discharge (hydrostatic bearing, b = B − b )
c c lan
b width of lubricant groove, width of lubricant supply groove, width of bleed groove
G
b land width parallel to the sliding surface, normal to the direction of flow
lan
b width of lubricant pocket, width of lubricant supply pocket
P
*
b relative width of lubricant pocket, relative width of lubricant supply pocket
P
C bearing clearance, nominal bearing clearance, chamfer, concentration
C axial bearing clearance (thrust bearing)
ax
C mean value of C [C = (C + C )/2]
ax,m ax ax,m ax,min ax,max
C maximum value of C
ax,max ax
C minimum value of C
ax,min ax
C bearing clearance, bearing diametral clearance (difference between bearing bore and journal
D
diameter of a journal bearing, C = D − D )
D J
C mean value of C [C = (C + C )/2]
D,m D D,m D,min D,max
2 © ISO 2009 – All rights reserved
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C effective bearing diametral clearance
D,eff
C maximum value of C
D,max D
C minimum value of C
D,min D
C circumference of groove cross-section
G
C bearing radial clearance (difference between bearing bore and journal radius of a journal bearing,
R
C = R − R )
R J
∆C elastic change of C
R,el R
C effective bearing radial clearance
R,eff
C mean value of C [C = (C + C )/2]
R,m R R,m R,min R,max
C maximum value of C
R,max R
C minimum value of C
R,min R
∆C thermal change of C
R,th R
∆C total change of C (∆C = ∆C + ∆C )
R,tot R R,tot R,el R,th
c specific heat capacity, lubricant specific heat capacity, stiffness
c axial bearing stiffness
ax
c axial stiffness of the bearing when load is directed into the machine (flange bearing)
ax,i
c axial stiffness of the bearing when load is directed out of the machine (flange bearing)
ax,o
c vertical stiffness of the bearing loaded downwards
dw
c stiffness of pad pivot support in direction of load (tilting-pad bearing)
F
c horizontal bearing stiffness
h
c lubricant film stiffness coefficient of journal bearing (i, k = 1, 2)
ik
*
c non-dimensional lubricant film stiffness coefficient of journal bearing
ik
3
ψ
*
cc=×i,1k=,2
() ( )
ik ik
2××B ηω×
c inner lubricant film stiffness coefficient of journal bearing (i, k = 1, 2)
ik,i
c outer lubricant film stiffness coefficient of journal bearing (i, k = 1, 2)
ik,o
c flexural stiffness of the Jeffcott Rotor
JR
c specific heat capacity of the lubricant (at constant pressure)
p
c specific heat capacity of the coolant (at constant pressure)
p,cl
c flexural stiffness of shaft
sh
c stiffness of isotropic bearing or bearing shell support
sup
c stiffness coefficient of anisotropic bearing or bearing shell support (i, k = 1, 2)
sup,ik
c vertical stiffness of the bearing loaded upwards
up
© ISO 2009 – All rights reserved 3
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c vertical bearing stiffness
v
c angular stiffness of pad pivot support (tilting-pad bearing)
ϑ
D bearing diameter (inside diameter of journal bearing), nominal bearing diameter
D twice the lobe or pad bore radius of a multi-lobed or tilting-pad journal bearing
B
D mean value of D [D = (D + D )/2]
B,m B B,m B,min B,max
D maximum value of D
B,max B
D minimum value of D
B,min B
D outside diameter of bearing shell or pad of a fixed-pad or tilting-pad journal bearing
B,o
D (outside) diameter of lubricating ring fixed to the shaft
fi
D inside diameter of bearing housing
H,i
D outside diameter of bearing housing
H,o
D inside diameter of thrust bearing sliding surface
i
D journal diameter (diameter of the shaft section located inside of a journal bearing)
J
D mean value of D [D = (D + D )/2]
J,m J J,m J,min J,max
D maximum value of D
J,max J
D minimum value of D
J,min J
D (outside) diameter of loose lubricating ring
lo
D mean diameter of thrust bearing sliding surface [D = (D + D )/2]
m m i o
D maximum value of D
max
D minimum value of D
min
D outside diameter of thrust bearing sliding surface
o
D inside diameter of tube
T,i
D outside diameter of tube
T,o
d diameter, distance, depth, damping
d diameter of circular thrust pad
B
d diameter of capillary
cp
d damping of eigenfrequency, system damping
e
d damping of pad pivot support in direction of load (tilting-pad bearing)
F
d diameter of groove
G
d mean diameter of groove
G,m
d lubricant film damping coefficient of journal bearing (i, k = 1, 2)
ik
4 © ISO 2009 – All rights reserved
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ISO 4378-5:2009(E)
*
d non-dimensional lubricant film damping coefficient of journal bearing
ik
3
⎡⎤
ψ
*
dd=×ω×i,1k=,2
⎢⎥()
ik ik
2××B ηω×
⎢⎥
⎣⎦
d lubrication hole diameter
L
d inside diameter of orifice
orf,i
d outside diameter of orifice
orf,o
d diameter of lubricating pocket
P
d damping of isotropic bearing or bearing shell support
sup
d damping coefficient of anisotropic bearing or bearing shell support (i, k = 1, 2)
sup,ik
d angular damping of pad pivot support (tilting-pad bearing)
ϑ
E Young's modulus (modulus of elasticity)
E Young's modulus of bearing material
B
E Young's modulus of journal material
J
E resultant Young's modulus
res
E Young's modulus of shaft material
sh
e eccentricity (distance between journal and bearing axis)
e eccentricity of bearing sliding surfaces (segments or pads) of a multi-lobed or tilting-pad journal
B
bearing
e eccentricity of bearing sliding surfaces (segments) of a multi-lobed journal bearing in the
B,h
horizontal direction
e eccentricity of bearing sliding surfaces (segments) of a multi-lobed journal bearing in the vertical
B,v
direction
e eccentricity of centre of gravity (distance between centre of gravity and shaft axis)
CG
e component of eccentricity normal to direction of load
x
e component of eccentricity in direction of load
y
F bearing force, bearing load, nominal bearing load, load-carrying capacity
F* bearing force parameter
∆F additional dynamic force
2
∆ψF ×
∆F* additional dynamic force parameter (∆F* = for journal bearings)
BD××η×ω
F axial bearing force, axial bearing load, thrust bearing load (nominal load)
ax
F maximum admissible thrust bearing load
ax,lim
F maximum admissible thrust bearing load directed into the machine (flange bearing)
ax,lim,i
F maximum admissible thrust bearing load directed out of the machine (flange bearing)
ax,lim,o
© ISO 2009 – All rights reserved 5
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SIST ISO 4378-5:2015
ISO 4378-5:2009(E)
F segment or pad load
B
F damping force
d
F dynamic bearing force, dynamic bearing load
dyn
F resonance amplitude of dynamic bearing force
dyn,rsn
F component of F in the x-direction
dyn,x dyn
F component of F in the y-direction
dyn,y dyn
F bearing force considering elasticity
e
* *
F bearing force parameter considering elasticity ( F = K × F*)
e e
el
F bearing force considering elasticity at transition to mixed friction
e,tr
*
F bearing force parameter considering elasticity at transition to mixed friction
e,tr
F effective load-carrying capacity
eff
* *
F effective load-carrying capacity parameter [FF=×/()b l×Z×p for hydrostatic journal
eff eff hs c ax en
bearings]
*
F effective load-carrying capacity parameter at N = 0
eff,0
F exciting force
exc
F friction force (F = f × F )
f f
f
*
*
F friction force parameter ( F =× So for journal bearings)
f f
ψ
F friction force of thrust bearing (F = f × F )
f,ax f,ax ax ax
F friction force of thrust bearing segment or pad
f,B
Fh×
* * f,B ax,min
F friction force parameter of thrust bearing segment or pad ( F = )
f,B f,B
2
BR××η×ω
ax m
F friction force in the area of the lubricant groove
f,G
*
F friction force parameter in the area of the lubricant groove
f,G
F friction force in the loaded area of the lubricant film
f,ld
*
F friction force parameter in the loaded area of the lubricant film
f,ld
F friction force in the area of the lubricant pocket
f,P
*
F friction force parameter in the area of the lubricant pocket
f,P
F friction force of journal bearing (F = f × F )
f,r f,r r r
F friction force in the unloaded area of the lubricant film
f,uld
*
F friction force parameter in the unloaded area of the lubricant film
f,uld
F maximum admissible bearing load
lim
F maximum admissible bearing load in vertical direction downwards
lim,dw
6 © ISO 2009 – All rights reserved
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ISO 4378-5:2009(E)
F maximum admissible bearing load in the horizontal direction
lim,h
F maximum admissible bearing load in the vertical direction upwards
lim,up
F normal force (normal to the sliding surface)
n
F radial bearing force, radial bearing load, journal bearing load (nominal load)
r
F maximum admissible journal bearing load
r,lim
F resulting force, resulting load
res
F bearing force component due to rotation
rot
F static bearing force, static bearing load
sc
F spring force
sp
F bearing force component due to squeezing
sq
F bearing force at start (N ≈ 0)
str
F bearing force at stop (N ≈ 0)
stp
F bearing force at transition to mixed friction
tr
*
F bearing force parameter at transition to mixed friction
tr
F unbalance force
u
F bearing force at N = 0
0
f friction factor (coefficient of friction), deflection, function, frequency
f* friction parameter
f coefficient of friction of thrust bearing
ax
f downward deflection of segment or pad
B
f bearing eigenfrequency
e
f hydrodynamic coefficient of friction
hd
f hydrodynamic coefficient of friction in the area of mixed friction
hd,m
f journal deflection
J
f minimum coefficient of friction, coefficient of friction at minimum of Stribeck curve
min
f coefficient of friction of journal bearing
r
f solid coefficient of friction
s
f solid coefficient of friction in the area of mixed friction
s,m
* *
f friction parameter of taper land thrust bearing ( f = f* × h /h )
tl tl wed ax,min
f coefficient of friction at transition to mixed friction
tr
G shear modulus
g acceleration due to gravity
© ISO 2009 – All rights reserved 7
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SIST ISO 4378-5:2015
ISO 4378-5:2009(E)
H height, bearing height, nominal bearing height, hardness
H height of bearing housing
H
h height, depth, thickness, lubricant film thickness, local lubricant film thickness, gap
h* relative lubricant film thickness, relative local lubricant film thickness (h* = h/C for journal
R
bearings)
h lubricant film thickness at the entrance gap
en
h lubricant film thickness at the exit gap
ex
h depth of lubricant groove, depth of lubricant supply groove
G
h minimum admissible lubricant film thickness during operation
lim
* *
h minimum admissible relative lubricant film thickness during operation ( h = h /C for journal
lim lim
r,lim R
bearings)
h minimum admissible lubricant film thickness at transition to mixed friction (minimum value of
lim,tr
minimum lubricant film thickness still permitting full separation of bearing and shaft sliding
surfaces by a lubricant film)
*
h minimum admissible relative lubricant film thickness at transition to mixed friction
lim,tr
*
( h = h /C for journal bearings)
lim,tr
lim,tr R
h minimum lubricant film thickness, minimum gap
min
* *
h minimum relative lubricant film thickness, minimum relative gap ( h = h /C for journal
min min
r,min R
*
bearings, h = h /h for thrust bearings)
min ax, min wed
h minimum lubricant film thickness at transition to mixed friction
min,tr
* *
h minimum relative lubricant film thickness at transition to mixed friction ( h = h /C for
min,tr min,tr min,tr R
journal bearings)
h reference value of h
min,0 min
h depth of lubricant pocket, depth of lubricant supply pocket
P
h minimum admissible lubricant film thickness of journal bearing during operation
r,lim
h minimum lubricant film thickness of journal bearing
r,min
h waviness of sliding surface
wav
h effective waviness of sliding surface
wav,eff
h maximum admissible effective waviness of sliding surface
wav,eff,lim
h maximum admissible waviness of sliding surface
wav,lim
h wedge depth (thrust bearing)
wed
* *
h relative wedge depth (thrust bearing, h = h /l )
wed wed wed wed
h wedge depth in radial direction (thrust bearing)
wed,r
h local gap at ε = 0 (journal bearing)
0
* *
h relative local gap at ε = 0 ( h = h /C )
0 0 0 R
8 © ISO 2009 – All rights reserved
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h maximum gap at ε = 0
0,max
* *
h maximum relative gap at ε = 0, gap ratio ( h = h /C )
0,max 0,max
0,max R
I geometrical moment of inertia
i −1
J mass moment of inertia
J bearing mass moment of inertia with reference to the X-axis
X
J bearing mass moment of inertia with reference to the Y-axis
Y
J bearing mass moment of inertia with reference to the Z-axis
Z
j −1
K coefficient, constant, factor, parameter, auxiliary variable
2
K dissipation parameter [K = η × ω/(ρ × c × T × ψ ) for journal bearings]
d d p
K elasticity influence parameter
el
K fill factor
fil
K correction factor considering the heat transition resistance of bearing insulation
I
K profile factor [relative difference between lobe or pad bore radius and journal radius,
P
K = 1/(1 − m)]
P
K effective profile factor
P,eff
∆K elastic change of K
P,el P
K profile factor at temperature T
P,T
∆K thermal change of K
P,th P
∆K total change of K (∆K = ∆K + ∆K )
P,tot P P,tot P,el P,th
K rotational speed influence parameter
rot
ηω×
0
K heating parameter ( K = for journal bearings)
T T
2
ρψ××cT×
p0
K wear coefficient
w
1
K heat conduction parameter ( K = for journal bearings)
λ λ
Re××Pr ψ
k heat transition coefficient
k heat transition coefficient referring to A*
A*
k* heat transition parameter [k* = 2 × ψ × k × A/(λ × D) for journal bearings]
A
k heat transition coefficient referring to A
A
k heat transition coefficient referring to bearing sliding surface (heat transition coefficient at the
B
interface between lubricant film and bearing sliding surface)
© ISO 2009 – All rights reserved 9
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k heat transition coefficient of tube
T
L length parallel to the sliding surface, in direction of motion; nominal length, pad length, nominal
pad length
L length of bearing housing at right angles to the axis
H
L length of tube
T
l length in the direction of flow, exponent of Falz's formula for the dependency of η on
− l
⎡⎤
⎛⎞
η T
⎢⎥
T =
⎜⎟
⎢⎥
η T
00⎝⎠
⎣⎦
l length of capillary
cp
l length of lubricant groove (circumferential direction), length of lubricant supply groove, length of
G
drainage groove, length of bleed groove
l length of axial discharge [l = π × D/Z − (l + l ) for hydrostatic journal bearings]
ax ax ax lan G
l land length in the direction of flow (thrust bearing)
lan
l length of lubricant pocket, length of lubricant supply pocket
P
l wedge length (thrust bearing)
wed
M moment, mixing factor
M moment of bearing load
F
M friction moment (M = R × F for journal bearings, M = R × F for thrust bearings)
f f f,r f m f,ax
m mass, preload of bearing or pad sliding surface
m bearing mass
B
m mass of the Jeffcott Rotor
JR
N rotational speed (rotational frequency) of the rotor (revolutions per time unit)
N rotational speed (rotational frequency) of the bearing
B
N critical speed (critical rotational frequency) of the rigidly supported rotor
cr
N rotational speed (rotational frequency) of the bearing force
F
N rotational speed (rotational frequency) at minimum of Stribeck curve
f,min
N rotational speed (rotational frequency) at the stability speed limit of the rotor supported by plain
lim
bearings
N maximum rotational speed (maximum rotational frequency)
max
N minimum rotational speed (minimum rotational frequency)
min
N resonance speed (resonance rotational frequency) of the rotor supported by plain bearings
rsn
N rotational speed (rotational frequency) at transition to mixed friction, transition rotational speed,
tr
transition rotational frequency
10 © ISO 2009 – All rights reserved
---------------------- Page: 18 ----------------------
SIST ISO 4378-5:2015
ISO 4378-5:2009(E)
N reference value of N
0
Nu Nusselt number
n number
O point of origin, centre, centreline, order of magnitude
O centreline of plain bearing
B
O centreline of sliding surface No. i
i
O centreline of journal
J
P power, heat flow
P* power ratio (P* = P /P )
f Pu
P heat flow discharged from the bearing to the ambient air via convection
cv,B
P heat flow discharged from the shaft to the ambient air via convection
cv,sh
P frictional power
f
P frictional power of thrust bearing (P = F × U )
f,ax f,ax f,ax m
P frictional power in the lubricant pocket(s)
f,P
P frictional power of journal bearing (P = F × U )
f,r f,r f,r J
P pumping power
Pu
P parasitic power loss
pa
P parasitic power loss of thrust bearing
pa,ax
P parasitic power loss of journal bearing
pa,r
P heat flow (quantity of heat transferred by heat or mass transfer per time unit)
th
P heat flow to the ambient air
th,amb
P heat flow via the cooling system
th,cl
P heat flow due to frictional power
th,f
P heat flow via the Iubricant
th,L
P heat flow supplied to the bearing via the lubricant
th,L,en
P heat flow discharged from the bearing via the lubricant
th,L,ex
P heat flow discharged from the bearing via the lubricant side flow rate
th,sf
P total power
tot
P
*
* tot
P total power parameter ( P = for journal bearings)
tot tot
F××ω C
rR
P heat flow discharged from the bearing via heat conduction in the shaft
λ,sh
© ISO 2009 – All rights reserved 11
---------------------- Page: 19 ----------------------
SIST ISO 4378-5:2015
ISO 4378-5:2009(E)
η × c
p
Pr Prandtl number (Pr = )
λ
p Iubricant film pressure, local Iubricant film pressure (pressure built up in the lubricant film of a
plain bearing by hydrodynamic or hydrostatic effects)
p specific bearing load (bearing load per unit of projected bearing area)
p ambient pressure (pressure in the immediate vicinity of bearing shell or pad)
amb
p ambient pressure at D (thrust bearing)
amb,i i
p ambient pressure at D (thrust bearing)
amb,o o
p specific load of thrust bearing [ p = F /(B × L × Z )]
ax ax ax ax
p profile of bearing or pad sliding surface
B
p dynamic specific bearing force, dynamic specific bearing load ( p = F /(B × D) for journal
dyn dyn
dyn
bearings, p = F /(B × L × Z ) for thrust bearings)
dyn
dyn ax
p Iubricant supply pressure (pressure by which the lubricant is supplied to the bearing)
en
2
p ×ψ
* *
en
p lubricant supply pressure parameter ( p = for journal bearings)
en en
η ×ω
p maximum admissible Iubricant film pressure
lim
p maximum admissible specific bearing Ioad (limiting value of specific bearing load; exceeding this
lim
value may lead to bearing failure)
p maximum admissible specific bearing Ioad at transition to mixed friction
lim,tr
p maximum lubricant film pressure
max
* *
p maximum lubricant film pressure parameter ( p = p / p )
max max
max
p Iubricant pressure in the lubricant pocket
P
p Iubricant pressure in the lubricant pocket No. i
P,i
p Iubricant pressure in the lubricant pocket No. i at ε = 0 (journal bearing)
P,i,0
p specific load of journal bearing [ p = F /(B × D)]
r r
r
p static specific bearing force, static specific bearing load [ p = F /(B × D) for journal bearings,
sc sc
sc
p = F /(B × L × Z ) for thrust bearings]
sc
sc ax
p specific bearing load at start (N ≈ 0)
str
p
...
NORME ISO
INTERNATIONALE 4378-5
Première édition
2009-09-01
Paliers lisses — Termes, définitions,
classification et symboles —
Partie 5:
Application des symboles
Plain bearings — Terms, definitions, classification and symbols —
Part 5: Application of symbols
Numéro de référence
ISO 4378-5:2009(F)
©
ISO 2009
---------------------- Page: 1 ----------------------
ISO 4378-5:2009(F)
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Publié en Suisse
ii © ISO 2009 – Tous droits réservés
---------------------- Page: 2 ----------------------
ISO 4378-5:2009(F)
Sommaire Page
Avant-propos .iv
Introduction.v
1 Domaine d'application .1
2 Références normatives.1
3 Symboles et termes.1
3.1 Symboles (alphabet romain) .1
3.2 Symboles (alphabet grec).18
© ISO 2009 – Tous droits réservés iii
---------------------- Page: 3 ----------------------
ISO 4378-5:2009(F)
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes nationaux de
normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est en général confiée
aux comités techniques de l'ISO. Chaque comité membre intéressé par une étude a le droit de faire partie du
comité technique créé à cet effet. Les organisations internationales, gouvernementales et non
gouvernementales, en liaison avec l'ISO participent également aux travaux. L'ISO collabore étroitement avec
la Commission électrotechnique internationale (CEI) en ce qui concerne la normalisation électrotechnique.
Les Normes internationales sont rédigées conformément aux règles données dans les Directives ISO/CEI,
Partie 2.
La tâche principale des comités techniques est d'élaborer les Normes internationales. Les projets de Normes
internationales adoptés par les comités techniques sont soumis aux comités membres pour vote. Leur
publication comme Normes internationales requiert l'approbation de 75 % au moins des comités membres
votants.
L'attention est appelée sur le fait que certains des éléments du présent document peuvent faire l'objet de
droits de propriété intellectuelle ou de droits analogues. L'ISO ne saurait être tenue pour responsable de ne
pas avoir identifié de tels droits de propriété et averti de leur existence.
L'ISO 4378-5 a été élaborée par le comité technique ISO/TC 123, Paliers lisses, sous-comité SC 6, Termes et
sujets communs.
Cette première édition annule et remplace l'ISO 4378-4:1997 et l'ISO 7904-2:1995, qui ont fait l'objet d'une
révision technique.
L'ISO 4378 comprend les parties suivantes, présentées sous le titre général Paliers lisses — Termes,
définitions, classification et symboles:
⎯ Partie 1: Conception, matériaux pour paliers et leurs propriétés
⎯ Partie 2: Frottement et usure
⎯ Partie 3: Lubrification
⎯ Partie 4: Symboles de base
⎯ Partie 5: Application des symboles
iv © ISO 2009 – Tous droits réservés
---------------------- Page: 4 ----------------------
ISO 4378-5:2009(F)
Introduction
Un grand nombre de désignations multiples sont présentes dans le domaine des paliers lisses, ce qui
entraîne un risque considérable d'erreurs lors de l'interprétation des normes et de la littérature technique. Du
fait de cette incertitude, des désignations nouvelles sont constamment ajoutées, ce qui augmente encore la
confusion.
La présente partie de l'ISO 4378 précise l'utilisation pratique des symboles utilisés dans le domaine des
paliers lisses.
© ISO 2009 – Tous droits réservés v
---------------------- Page: 5 ----------------------
NORME INTERNATIONALE ISO 4378-5:2009(F)
Paliers lisses — Termes, définitions, classification et
symboles —
Partie 5:
Application des symboles
1 Domaine d'application
La présente partie de l'ISO 4378 précise l'utilisation pratique des symboles généraux définis dans
l'ISO 4378-4 pour le calcul, la conception et l'essai des paliers lisses.
L'ISO 4378-4 distingue les caractères de base des signes complémentaires. Les signes complémentaires
sont les indices et les exposants. Les symboles requis pour les calculs, la conception, la fabrication et les
essais des paliers lisses peuvent être simplement des caractères de base ou bien des combinaisons de
caractères de base et de signes complémentaires.
La présente partie de l'ISO 4378 énumère les symboles jugés nécessaires pour les calculs, la conception et
les essais des paliers lisses. Ils ont été définis conformément aux recommandations données dans
l'ISO 4378-4.
Les angles et directions de rotation sont définis comme positifs en rotation à gauche (sens inverse des
aiguilles d'une montre); idem pour les fréquences de rotation et les vitesses périphériques et angulaires.
2 Références normatives
Les documents de référence suivants sont indispensables pour l'application du présent document. Pour les
références datées, seule l'édition citée s'applique. Pour les références non datées, la dernière édition du
document de référence s'applique (y compris les éventuels amendements).
ISO 4378-4, Paliers lisses — Termes, définitions, classification et symboles — Partie 4: Symboles de base
3 Symboles et termes
Les listes suivantes ne sont pas exhaustives. Elles peuvent être complétées si nécessaire.
NOTE Certaines lettres des alphabets romain et grec n'ont pas été utilisées jusqu'à présent. Elles ne sont donc pas
répertoriées ci-dessous.
3.1 Symboles (alphabet romain)
A aire de la surface émettant de la chaleur (logement du palier), allongement à la rupture
A* paramètre de l'aire de la surface émettant de la chaleur [butée, A* = A/(B × L × Z )]
ax
A aire du segment ou du patin
B
A aire de la section transversale de la rainure
G
© ISO 2009 – Tous droits réservés 1
---------------------- Page: 6 ----------------------
ISO 4378-5:2009(F)
A aire de la surface émettant de la chaleur (logement du palier) à l'intérieur de la machine (palier à
i
collerette)
A aire de la face portante
lan
* *
A aire relative de la face portante [ A = A /(π × D × B) pour les paliers radiaux hydrostatiques]
lan lan
lan
A aire de la surface émettant de la chaleur (logement du palier) à l'extérieur de la machine (palier à
o
collerette)
A aire de la poche de lubrifiant
P
A aire de la section transversale
S
A aire spécifique du tube
T
A aire de la section transversale du tube inondée
T,i
a distance, accélération, diffusivité thermique, facteur d'inertie
a distance entre le bord d'attaque et le point de pivot du patin (palier à patins oscillants)
F
*
a distance relative entre le bord d'attaque et le point de pivot du patin (palier à patins oscillants)
F
a distance minimale entre deux patins de butée circulaires
min
a distance entre le point de mesure de la température et la surface de glissement du palier
T
B largeur parallèle à la surface de glissement, perpendiculaire à la direction du mouvement; largeur
de palier, largeur nominale de palier, largeur de patin, largeur de patin nominale
B* largeur relative, largeur du palier relative, largeur du patin relative, rapport de largeur (B* = B/D)
B largeur de la butée ou du segment axial [B = (D − D )/2]
ax ax o i
B largeur du palier effective (sans rainures, chanfrein, etc.), largeur du patin effective
eff
B largeur extérieure du logement du palier dans la direction axiale
H
B largeur du palier totale
tot
b largeur parallèle à la surface de glissement, perpendiculaire à la direction du mouvement ou flux
b largeur de décharge périphérique (palier hydrostatique, b = B − b )
c c lan
b largeur de rainure de lubrification, largeur de rainure d'alimentation en lubrifiant, largeur de
G
rainure de purge
b largeur de la face portante parallèle à la surface de glissement, perpendiculaire à la direction du
lan
flux
b largeur de la poche de lubrifiant, largeur de la poche d'alimentation en lubrifiant
P
*
b largeur relative de la poche de lubrifiant, largeur relative de la poche d'alimentation en lubrifiant
P
C jeu du palier, jeu nominal du palier, chanfrein, concentration
C jeu axial du palier (butée)
ax
C valeur moyenne de C [C = (C + C )/2]
ax,m ax ax,m ax,min ax,max
C valeur maximale de C
ax,max ax
2 © ISO 2009 – Tous droits réservés
---------------------- Page: 7 ----------------------
ISO 4378-5:2009(F)
C valeur minimale de C
ax,min ax
C jeu du palier, jeu du diamètre du palier (différence entre l'alésage et le diamètre du tourillon d'un
D
palier radial, C = D − D )
D J
C valeur moyenne de C [C = (C + C )/2]
D,m D D,m D,min D,max
C jeu diamétral effectif du palier
D,eff
C valeur maximale de C
D,max D
C valeur minimale de C
D,min D
C périmètre de la section transversale de la rainure
G
C jeu radial du palier (différence entre l'alésage et le rayon de tourillon d'un palier radial,
R
C = R − R )
R J
∆C changement élastique de C
R,el R
C jeu radial effectif de palier
R,eff
C valeur moyenne de C [C = (C + C )/2]
R,m R R,m R,min R,max
C valeur maximale de C
R,max R
C valeur minimale de C
R,min R
∆C changement thermique de C
R,th R
∆C changement total de C (∆C = ∆C + ∆C )
R,tot R R,tot R,el R,th
c capacité thermique massique, capacité thermique massique de lubrifiant, rigidité
c rigidité axiale du palier
ax
c rigidité axiale du palier lorsque la charge est dirigée dans la machine (paliers à collerette)
ax,i
c rigidité axiale du palier lorsque la charge est dirigée hors de la machine (paliers à collerette)
ax,o
c rigidité verticale du palier chargé vers le bas
dw
c rigidité du support de pivot du patin dans la direction de la charge (palier à patins oscillants)
F
c rigidité horizontale du palier
h
c coefficient de rigidité du film de lubrifiant d'un palier radial (i, k = 1, 2)
ik
*
c coefficient de rigidité du film de lubrifiant non dimensionnel d'un palier radial
ik
3
ψ
*
cc=×i,1k=,2
()
ik ik
2××B ηω×
c coefficient de rigidité du film de lubrifiant intérieur d'un palier radial (i, k = 1, 2)
ik,i
c coefficient de rigidité du film de lubrifiant extérieur d'un palier radial (i, k = 1, 2)
ik,o
c rigidité à la flexion du rotor de Jeffcott
JR
c capacité de chaleur massique du lubrifiant (à pression constante)
p
c capacité de chaleur massique du refroidisseur (à pression constante)
p,cl
© ISO 2009 – Tous droits réservés 3
---------------------- Page: 8 ----------------------
ISO 4378-5:2009(F)
c rigidité à la flexion de l'arbre
sh
c rigidité du support de coquille du coussinet ou palier isotrope
sup
c coefficient de rigidité du support de coquille du coussinet ou palier anisotrope (i, k = 1, 2)
sup,ik
c rigidité verticale du palier chargé vers le haut
up
c rigidité verticale du palier
v
c rigidité angulaire du support de pivot du patin (palier à patins oscillants)
ϑ
D diamètre du palier (diamètre intérieur de palier radial), diamètre nominal du palier
D double du rayon du lobe ou du patin d'un palier radial à lobes multiples ou patins oscillants
B
D valeur moyenne de D [D = (D + D )/2]
B,m B B,m B,min B,max
D valeur maximale de D
B,max B
D valeur minimale de D
B,min B
D diamètre extérieur de la coquille du coussinet ou du patin d'un palier radial à patins fixes ou
B,o
oscillants
D diamètre (extérieur) de la bague de lubrification fixé à l'arbre
fi
D diamètre intérieur du logement du palier
H,i
D diamètre extérieur du logement du palier
H,o
D diamètre intérieur de la surface de glissement d'une butée
i
D diamètre du tourillon (diamètre de la partie d'arbre située à l'intérieur d'un palier radial)
J
D valeur moyenne de D [D = (D + D )/2]
J,m J J,m J,min J,max
D valeur maximale de D
J,max J
D valeur minimale de D
J,min J
D diamètre (extérieur) de la bague de lubrification libre
lo
D diamètre moyen de la surface de glissement de la butée [D = (D + D )/2]
m m i o
D valeur maximale de D
max
D valeur minimale de D
min
D diamètre extérieur de la surface de glissement de la butée
o
D diamètre intérieur du tube
T,i
D diamètre extérieur du tube
T,o
d diamètre, distance, profondeur, amortissement
d diamètre du segment axial circulaire
B
d diamètre de capillaire
cp
d amortissement de la fréquence propre, amortissement du système
e
4 © ISO 2009 – Tous droits réservés
---------------------- Page: 9 ----------------------
ISO 4378-5:2009(F)
d amortissement du support de pivot du patin dans la direction de la charge (palier à patins
F
oscillants)
d diamètre de la rainure
G
d diamètre moyen de la rainure
G,m
d coefficient d'amortissement du film de lubrifiant du palier radial (i, k = 1, 2)
ik
*
d coefficient d'amortissement du film de lubrifiant non dimensionnel du palier radial
ik
3
ψ
*
dd=×ω×i,1k=,2
()
ik ik
2××B ηω×
d diamètre du trou de lubrification
L
d diamètre intérieur du trou
orf,i
d diamètre extérieur du trou
orf,o
d diamètre de la poche de lubrification
P
d amortissement du support de la coquille du coussinet ou du palier isotrope
sup
d coefficient d'amortissement du support de la coquille du coussinet ou du palier anisotrope
sup,ik
(i, k = 1, 2)
d amortissement angulaire du support de pivot du patin (palier à patins oscillants)
ϑ
E module de Young (module d'élasticité)
E module de Young du matériau du palier
B
E module de Young du matériau du tourillon
J
E module de Young résultant
res
E module de Young du matériau de l'arbre
sh
e excentricité (distance entre les axes du tourillon et du palier)
e excentricité des surfaces de glissement (segments ou patins) d'un palier radial à lobes multiples
B
ou patins oscillants
e excentricité des surfaces de glissement (segments) d'un palier radial à lobes multiples dans la
B,h
direction horizontale
e excentricité des surfaces de glissement (segments) d'un palier radial à lobes multiples dans la
B,v
direction verticale
e excentricité de centre de gravité (distance entre le centre de gravité et l'axe de l'arbre)
CG
e composante de l'excentricité perpendiculaire à la direction de la charge
x
e composante de l'excentricité dans la direction de la charge
y
F force d'appui, charge, charge nominale, capacité de charge
F* paramètre de la force d'appui
∆F force dynamique supplémentaire
© ISO 2009 – Tous droits réservés 5
---------------------- Page: 10 ----------------------
ISO 4378-5:2009(F)
2
∆ψF ×
∆F* paramètre de la force dynamique supplémentaire (∆F* = pour les paliers radiaux)
BD××η×ω
F force d'appui axiale, charge axiale, charge de la butée (charge nominale)
ax
F charge de la butée admissible maximale
ax,lim
F charge de la butée admissible maximale lorsque la charge est dirigée dans la machine (palier à
ax,lim,i
collerette)
F charge de la butée admissible maximale lorsque la charge est dirigée hors de la machine (palier
ax,lim,o
à collerette)
F charge de segment ou patin
B
F force d'amortissement
d
F force d'appui dynamique, charge dynamique
dyn
F amplitude de résonance de la force d'appui dynamique
dyn,rsn
F composante de F dans la direction x
dyn,x dyn
F composante de F dans la direction y
dyn,y dyn
F force d'appui tenant compte de l'élasticité
e
* *
F paramètre de force d'appui tenant compte de l'élasticité ( F = K × F*)
e e el
F force d'appui tenant compte de l'élasticité à la transition au frottement mixte
e,tr
*
F paramètre de force d'appui tenant compte de l'élasticité à la transition au frottement mixte
e,tr
F capacité effective du support de la charge
eff
* *
F paramètre de capacité effective du support de la charge [FF=×/()b l×Z×p pour les
eff eff hs c ax en
paliers radiaux hydrostatiques]
*
F paramètre de capacité effective du support de la charge à N = 0
eff,0
F force excitatrice
exc
F force de frottement (F = f × F )
f f
f
* *
F paramètre de la force de frottement ( F =× So pour les paliers radiaux)
f f
ψ
F force de frottement de la butée (F = f × F )
f,ax f,ax ax ax
F force de frottement du segment ou du patin de la butée
f,B
Fh×
f,B ax,min
* *
F paramètre de la force du frottement du segment ou du patin de la butée ( F = )
f,B f,B
2
BR××η×ω
ax m
F force de frottement dans la zone de la rainure de lubrification
f,G
*
F paramètre de la force de frottement dans la zone de la rainure de lubrification
f,G
F force de frottement dans la zone chargée du film de lubrifiant
f,ld
*
F paramètre de force de frottement dans la zone chargée du film de lubrifiant
f,ld
F force de frottement dans la zone de la poche de lubrifiant
f,P
*
F paramètre de la force de frottement dans la zone de la poche de lubrifiant
f,P
6 © ISO 2009 – Tous droits réservés
---------------------- Page: 11 ----------------------
ISO 4378-5:2009(F)
F force de frottement du palier radial (F = f × F )
f,r f,r r r
F force de frottement dans la zone non chargée du film lubrifiant
f,uld
*
F paramètre de la force de frottement dans la zone non chargée du film de lubrifiant
f,uld
F charge admissible maximale
lim
F charge admissible maximale dans la direction verticale vers le bas
lim,dw
F charge admissible maximale dans la direction horizontale
lim,h
F charge admissible maximale dans la direction verticale vers le haut
lim,up
F force normale (perpendiculaire à la surface de glissement)
n
F force d'appui radial, charge radiale, charge de palier radial (charge nominale)
r
F charge de palier radial admissible maximale
r,lim
F force résultante, charge résultante
res
F composante de la force d'appui due à la rotation
rot
F force d'appui statique, charge statique
sc
F force de ressort
sp
F composante de la force d'appui due au pincement
sq
F force d'appui au démarrage (N ≈ 0)
str
F force d'appui à l'arrêt (N ≈ 0)
stp
F force d'appui à la transition au frottement mixte
tr
*
F paramètre de force d'appui à la transition au frottement mixte
tr
F force de déséquilibre
u
F force d'appui à N = 0
0
f facteur de frottement (coefficient de frottement), flèche, fonction, fréquence
f* paramètre de frottement
f coefficient de frottement de la butée
ax
f flèche vers le bas du segment ou du patin
B
f fréquence propre du palier
e
f coefficient de frottement hydrodynamique
hd
f coefficient de friction hydrodynamique dans la zone de frottement mixte
hd,m
f flèche du tourillon
J
f coefficient de frottement minimal, coefficient de frottement au minimum de la courbe de Stribeck
min
f coefficient de frottement du palier radial
r
f coefficient de frottement d'un solide
s
© ISO 2009 – Tous droits réservés 7
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ISO 4378-5:2009(F)
f coefficient de frottement d'un solide dans la zone de frottement mixte
s,m
* *
f paramètre de frottement de la butée conique ( f = f* × h /h )
tl tl
wed ax,min
f coefficient de frottement à la transition au frottement mixte
tr
G module de cisaillement
g accélération due à la pesanteur
H hauteur, hauteur du palier, hauteur du palier nominale, dureté
H hauteur du logement du palier
H
h hauteur, profondeur, épaisseur, épaisseur du film de lubrifiant, épaisseur locale du film de
lubrifiant, intervalle
h* épaisseur relative du film de lubrifiant, épaisseur locale relative du film de lubrifiant (h* = h/C
R
pour les paliers radiaux)
h épaisseur du film de lubrifiant à l'entrée
en
h épaisseur du film de lubrifiant à la sortie
ex
h profondeur de rainure de lubrification, profondeur de rainure d'approvisionnement en lubrifiant
G
h épaisseur du film de lubrifiant admissible minimale au cours du fonctionnement
lim
*
h épaisseur relative du film de lubrifiant admissible minimale au cours du fonctionnement
lim
*
( h = h /C pour les paliers radiaux)
lim
r,lim R
h épaisseur du film de lubrifiant admissible minimale à la transition au frottement mixte (valeur de
lim,tr
l'épaisseur du film de lubrifiant minimale permettant encore une séparation complète des
surfaces de glissement du palier et de l'arbre par un film de lubrifiant)
*
h épaisseur relative du film de lubrifiant admissible minimale à la transition au frottement mixte
lim,tr
*
( h = h /C pour les paliers radiaux)
lim,tr lim,tr R
h épaisseur du film de lubrifiant minimale, intervalle minimal
min
* *
h épaisseur relative du film de lubrifiant minimale, intervalle relatif minimal ( h = h /C pour
min min
r,min R
*
les paliers radiaux, h = h /h pour les butées)
min
ax, min wed
h épaisseur du film de lubrifiant minimale à la transition au frottement mixte
min,tr
*
h épaisseur relative du film de lubrifiant minimale à la transition au frottement mixte
min,tr
*
( h = h /C pour les paliers radiaux)
min,tr
min,tr R
h valeur de référence de h
min,0 min
h profondeur de la poche de lubrifiant, profondeur de la poche d'alimentation en lubrifiant
P
h épaisseur du film de lubrifiant admissible minimale pour un palier radial en fonctionnement
r,lim
h épaisseur du film de lubrifiant minimale pour un palier radial
r,min
h ondulation de la surface de glissement
wav
h ondulation effective de la surface de glissement
wav,eff
h ondulation effective admissible maximale de la surface de glissement
wav,eff,lim
8 © ISO 2009 – Tous droits réservés
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ISO 4378-5:2009(F)
h ondulation admissible maximale de la surface de glissement
wav,lim
h profondeur de la clavette (butée)
wed
* *
h profondeur relative de la clavette (butée, h = h /l )
wed wed
wed wed
h profondeur de la clavette dans la direction radiale (butée)
wed,r
h intervalle local à ε = 0 (palier radial)
0
* *
h intervalle local relatif à ε = 0 ( h = h /C )
0 0
0 R
h intervalle maximal à ε = 0
0,max
* *
h intervalle relatif maximal à ε = 0, rapport d'intervalle ( h = h /C )
0,max 0,max
0,max R
I moment d'inertie géométrique
i −1
J moment d'inertie massique
J moment d'inertie massique de palier par rapport à l'axe X
X
J moment d'inertie massique de palier par rapport à l'axe Y
Y
J moment d'inertie massique de palier par rapport à l'axe Z
Z
j −1
K coefficient, constante, facteur, paramètre, variable auxiliaire
2
K paramètre de dissipation (K = η × ω/(ρ × c × T × ψ ) pour les paliers radiaux)
d d p
K paramètre d'influence d'élasticité
el
K facteur de remplissage
fil
K facteur de correction tenant compte de la résistance de transition thermique de l'isolation du
I
palier
K facteur du profil [différence relative entre le rayon du lobe ou du patin et le rayon du tourillon,
P
K = 1/(1 − m)]
P
K facteur du profil effectif
P,eff
∆K changement élastique de K
P,el P
K facteur du profil à la température T
P,T
∆K changement thermique de K
P,th P
∆K changement total de K (∆K = ∆K + ∆K )
P,tot P P,tot P,el P,th
K paramètre de l'influence de la vitesse de rotation
rot
ηω×
0
K paramètre thermique ( pour les paliers radiaux)
K =
T T
2
ρψ××cT×
p0
K coefficient d'usure
w
1
K paramètre de conduction thermique ( K = pour les paliers radiaux)
λ
λ
Re××Pr ψ
© ISO 2009 – Tous droits réservés 9
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ISO 4378-5:2009(F)
k coefficient de transfert thermique
k coefficient de transfert thermique par rapport à A*
A*
k* paramètre de transfert thermique [k* = 2 × ψ × k × A/(λ × D) pour les paliers radiaux]
A
k coefficient de transfert thermique par rapport à A
A
k coefficient de transfert thermique par rapport à la surface de glissement du palier (transfert
B
thermique à l'interface entre le film de lubrifiant et la surface de glissement du palier)
k coefficient de transfert thermique du tube
T
L longueur parallèle à la surface de glissement, dans la direction du mouvement, longueur
nominale, longueur nominale de patin
L longueur de logement du palier à angles droits de l'axe
H
L longueur du tube
T
l longueur en direction du flux, exposant de la formule de Falz pour l'expression de η dans
− l
⎡⎤
⎛⎞
η T
⎢⎥
T =
⎜⎟
⎢⎥
η T
00⎝⎠
⎣⎦
l longueur de capillaire
cp
l longueur de la rainure de lubrification (direction périphérique), longueur de la rainure
G
d'approvisionnement en lubrifiant, longueur de la rainure de drainage, longueur de la rainure de
purge
l longueur de décharge axiale [l = π × D/Z − (l + l ) pour les paliers radiaux hydrostatiques]
ax ax ax lan G
l longueur de la surface d'appui dans le sens du flux (butée)
lan
l longueur de la poche de lubrifiant, longueur de la poche d'alimentation en lubrifiant
P
l longueur de la clavette (butée)
wed
M moment, facteur de mélange
Μ moment de charge
F
M moment de frottement (M = R × F pour les paliers radiaux, M = R × F pour les butées)
f f f,r f m f,ax
m masse, précharge de la surface de glissement du palier ou du patin
m masse de palier
B
m masse de rotor Jeffcott
JR
N vitesse de rotation (fréquence de rotation) du rotor (tours par unité de temps)
N vitesse de rotation (fréquence de rotation) du palier
B
N vitesse critique (fréquence de rotation critique) du rotor à support rigide
cr
N vitesse de rotation (fréquence de rotation) de la force d'appui
F
N vitesse de rotation (fréquence de rotation) au minimum de la courbe de Stribeck
f,min
10 © ISO 2009 – Tous droits réservés
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ISO 4378-5:2009(F)
N vitesse de rotation (fréquence de rotation) à la vitesse limite de stabilité du rotor supporté par des
lim
paliers lisses
N vitesse de rotation maximale (fréquence de rotation maximale)
max
N vitesse de rotation minimale (fréquence de rotation minimale)
min
N vitesse de résonance (fréquence de rotation de résonance) du rotor supporté par des paliers
rsn
lisses
N vitesse de rotation (fréquence de rotation) de transition au frottement mixte, vitesse de rotation
tr
de transition, fréquence de rotation de transition
N valeur de référence de N
0
Nu nombre de Nusselt
n nombre
O point de l'origine, centre, axe, ordre de grandeur
O axe du palier lisse
B
O axe de la surface de glissement No. i
i
O axe du tourillon
J
P puissance, flux thermique
P* rapport de puissance (P* = P /P )
f Pu
P flux thermique déchargé du palier dans l'air ambiant par convection
cv,B
P flux thermique déchargé de l'arbre dans l'air ambiant par convection
cv,sh
P puissance de frottement
f
P puissance de frottement de la butée (P = F × U )
f,ax f,ax f,ax m
P puissance de frottement dans la (les) poche(s) de lubrifiant
f,P
P puissance de frottement du palier radial (P = F × U )
f,r f,r f,r J
P puissance de pompage
Pu
P perte de puissance parasite
pa
P perte de puissance parasite de la butée
pa,ax
P perte de puissance parasite du palier radial
pa,r
P flux thermique (quantité de chaleur transférée par transfert thermique ou massique par unité de
th
temps)
P flux thermique vers l'air ambiant
th,amb
P flux thermique via le système de refroidissement
th,cl
P flux thermique dû à la puissance de frottement
th,f
P flux thermique via le lubrifiant
th,L
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ISO 4378-5:2009(F)
P flux thermique apporté au palier via le lubrifiant
th,L,en
P flux thermique quittant le palier via le lubrifiant
th,L,ex
P flux thermique quittant le palier via le débit latéral du lubrifiant
th,sf
P puissance totale
tot
P
* * tot
P paramètre de la puissance totale ( P = pour les paliers radiaux)
tot tot
F××ω C
rR
P flux thermique quittant le palier via conduction thermique dans l'arbre
λ,sh
η × c
p
Pr nombre de Prandtl (Pr = )
λ
p pression du film de lubrifiant, pression du film de lubrifiant locale (pression accumulée dans le
film de lubrifiant d'un palier lisse par effets hydrodynamique ou hydrostatique)
p charge spécifique (charge par uni
...
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