Negative pressure in the oil film of journal bearing Dr

NATIONAL
TRIBOLOGY
CONFERENCE
24-26 September 2003
THE ANNALS OF UNIVERSITY
“DUNĂREA DE JOS“ OF GALAŢI
FASCICLE VIII, TRIBOLOGY
2003 ISSN 1221-4590
215
NEGATIVE PRESSURE IN THE OIL-FILM OF JOURNAL BEARING
Tsuneo Someya
University of Tokyo, Faculty of Engineering, Tokyo, 112-0006, Japan,
t-someya@tcn-catv.ne.jp
ABSTRACT
In the present paper, negative pressure developed in the oil-film of journal
bearing is discussed. Assuming dilatational surface viscosity, negative pressure
found experimentally could be reproduced. Parameter study has shown that, when
negative pressure is developed: the load capacity increases and the friction
coefficient of bearing decreases slightly near the eccentricity 0.6, but this effect
reverses at larger eccentricity. Oil flow rate decreases under negative pressure. The
locus of center of journal in the bearing clearance is pushed outwards and
horizontally under vertical static load. This means that the stability of a turbo-rotor
can be reduced, when negative pressure is developed.
KEYWORDS: negative pressure, dilatational surface viscosity, journal bearing, oilfilm,
bubble theory
1. INTRODUCTION
Characteristics of journal bearing, such as load
capacity, frictional power loss, oil flow rate etc, are
determined by pressure distribution in the oil- film of
the bearing. Therefore, in order to get the
characteristics correctly, the pressure distribution has
to be calculated under realistic boundary condition.
In the literature, the oil film pressure has been
usually calculated under the condition that the oilfilm
can not sustain negative pressure. However,
several experimental results with negative pressure
are also reported for the oil film of journal bearing
[1, 2, 6~9]. In the present paper, distribution of
pressure including negative one should be calculated
and compared with experimental results for a journal
bearing with a circumferential oil groove as shown in
Fig.1. It should be also discussed how the
development of negative pressure influences the
characteristics of journal bearing.
Fig. 1 Journal bearing with a circumferential oil groove.

216
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THE ANNALS OF UNIVERSITY
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FASCICLE VIII, TRIBOLOGY
2003 ISSN 1221-4590
2. EXPERIMENTAL EVIDENCE OF
NEGATIVE PRESSURE
Figure 2 gives examples of measured
circumferential distribution of pressure at land center
in a bearing shown in figure 1, at shaft speed of 1500
min -1 and four bearing load W. The results show
clearly that there exists negative pressure and its
absolute value increases with bearing load. Figure 3
gives another example of negative pressure, where a
pair of parallel plates with oil-film in-between is
pulled off. Both types of pressure pickup yielded
negative pressure.
p MPa
1500 min -1 W=5.6kN
W=4.2kN
B=22.5x2mm
W=2.8kN
D=100mm
W=1.4kN
η=0.02996Pas
∆r=110µm
Fig.2 Measured pressure distribution
Fig.3 Negative pressure at reverse squeeze
t
θ
3. THEORETICAL INVESTIGATION
ON NEGATIVE PRESSURE
Using a “bubble theory” explained below,
pressure distribution in journal bearing should be
calculated and compared with experimental results. It
is assumed that the oil contains uniformly dispersed
bubbles with a constant radius R a under atmospheric
pressure p a . When this oil is introduced into bearing
gap and experiences positive or negative pressure as
it flows in the gap space in the bearing, the bubbles
will contract or expand. It is further assumed that the
bubbles remain spherical in the oil film and no
interference, no combination and breakup between
bubbles takes place. Also no evaporation and
condensation of oil and no diffusion of gas should
occur. The gas of constant mass contained in the
bubble will experience isothermal change during the
expansion and compression of bubble [10].
Figure 4 depicts the forces acting on the surface
of a bubble in oil-film. When the bubble radius
changes, surface force due to dilatational viscosity
[4, 11, 12] of the oil will oppose the radius change.
This surface dilatational viscosity is related to
Marangoni effect [5]. That is, when the surface of a
liquid enlarges, adsorption taking place in the
solution is decelerated by the resisting force, the
surface dilatational viscosity. Therefore, when the
bubble expands under negative pressure, surface
dilatational viscosity force ∆σ will resist the bubble
expansion and the bubble can withstand greater
negative pressure without rupture than when only
surface tension σ is acting and no surface dilatational
viscosity acts.
According to Scriven [11, 12], equation (1)
holds for ∆σ with surface area A and surface
dilatational viscosity κ. Taking this force into
account, equation (2) is derived for the ratio χ=R/R a
of a bubble radius R [8, 11, 12].
Considering the change of viscosity η and
density ρ due to inclusion of bubbles, a modified
Reynolds equation (3) for the gauge pressure p is
derived. As for void fraction α and density ratio
δ = ρ / ρ 1 of the oil-bubble mixture, equation (4)
and (6) can be derived [6]. For viscosity ratio
K=η/η l , an experimental formula (5) according to [6]
was used, where η l stands for viscosity of oil alone.
For the dimensionless oil-film thickness H=h/∆r,
equation (7) holds with radial clearance ∆r. In
equation (2) dimensionless numbers for surface
tension σ, oil viscosity η l and surface dilatational
viscosity κ are introduced by equations (8)~(10):
Fig.4 Forces acting on a bubble surface

NATIONAL
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FASCICLE VIII, TRIBOLOGY
2003 ISSN 1221-4590
217
1 dA
∆ σ = κ
(1)
A dt
(1 +
p
p
a
3
) χ
∧
∧
+ ( B+
C
dχ
2
) χ
dφ
∧
dχ
∧
+ D χ − (1 + B)
= 0
dφ
(2)
∂ δH
{ (
∂ϕ
K
3
∂p
) +
∂ϕ
∂ δH
(
∂ς
K
3
2
∂p
ψ
)} = 6( H
∂ς
η ω
l
∂δ
∂H
+ δ )
∂ς
∂ϕ
(3)
3
α
a
χ
α =
3
1 − α + α χ
a
a
(4)
K
= 1 + 0.5062 α + 9.044 α
2
3
− 46 .83α
+ 60 .13α
4
5
− 23 .85α
(5)
δ = 1 − α
(6)
H
= 1 − ε cos( ϕ − γ )
(7)
∧
B
=
2 σ
p R a a
(8 )
∧
C
=
4η
lω
p
a
(9 )
∧
D
=
4κω
p R a a
(10 )
Differential equations (2) for χ and (3) for p are
integrated by Runge-Kutta method and by finite
difference method, respectively, using periodic
boundary condition with period 2π. This calculation
should be called “bubble theory”. Besides, pressure
distribution was calculated using Reynolds boundary
condition, assuming p=dp/dx=0 at the boundary of
oil-film rupture. This should be called “conventional
theory”. Figures 5a, b and c depict the pressure
distribution obtained by experiment, bubble theory
and conventional theory, respectively. It can be found
that the bubble theory (b) can reproduce rather well
the experimental pressure distribution including the
negative pressure (a). With increasing load the
absolute value of negative pressure increases in
figures (a) and (b), whereas the conventional theory
(c), by assumption, can not reproduce negative
pressure.
4. INFLUENCE OF NEGATIVE
PRESSURE ON BEARING
CHARACTERISTICS
Having obtained the positive results from
bubble theory above, some parameter study should
now be made to investigate how the bearing
characteristics will be influenced by the development
of negative pressure [13~16].
Figure 6 depicts the specific bearing load p by
bubble theory and conventional theory as function of
bearing eccentricity ε. The curve for the ratio Z of
both p is also drawn. It can be seen from this figure
that the load capacity increases slightly near ε=0.6,
when negative pressure is developed in the oil-film.
At larger ε the effect reverses.

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FASCICLE VIII, TRIBOLOGY
2003 ISSN 1221-4590
Fig. 5 Pressure distribution in journal bearing (1500min -1 ).

NATIONAL
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FASCICLE VIII, TRIBOLOGY
2003 ISSN 1221-4590
219
Figure 7 shows the reduced bearing coefficient
of friction µ’= µ/ψ by both theories and their ratio Z.
The curves show that the bearing friction decreases
slightly near ε=0.6, when negative pressure is
developed. At larger ε the effect reverses.
Figure 8 depicts the journal centre orbits
calculated by both theories under vertical load. The
orbit is pushed horizontally and towards bearing
clearance circle when negative pressure is developed.
This means that the oil-film force becomes more
“unstable”, that is the equilibrium of a rotor carried
by journal bearings can become more unstable due to
the oil-film force, when negative pressure is
developed.
Figure 9 depicts the oil flow rate Q out of both
sides of the bearing. The oil flow rate decreases by
∆Q, when negative pressure is developed, because the
oil flowed out of the bearing sides is sucked again by
the negative pressure.
0
-0.2
-0.4
-0.6
-0.8
-1
ε
0 0.2 0.4 0.6 0.8 1
Conventional
theory
Fig.8 Journal orbit
Bubble theory
(MPa)
2
1.5
1
0.5
0
p
Z
Conventionaltheory
× Bubble theory
Z=Bubble theory/
Conv.theory
ε
0 0.5 1
Fig.6 Load carrying capacity
p
1
Z
0
Q
2
1.5
1
0.5
0
Conventional theory
Bubble theory
0 0.5 1 ε
Fig.9 Fig.9 Oil Oil flow flow rate rate Q
∆Q
µ’=µ/ψ
Z
150
Z
100
1
Convent. theory
50
Bubble theory
0
0
0 0.5 ε 1
Fig.7 Fig.7 Coefficient of of friction µ’
CONCLUSIONS
In this paper, existence and influences of
negative pressure are investigated for the oil-film of
journal bearing with a circumferential oil groove. The
results can be summarized as follows.
(1) Existence of negative pressure could be
verified experimentally in the oil-film.
(2) Taking into consideration the surface
dilatational viscosity, the negative pressure could be
reproduced.
(3) When negative pressure is developed in oilfilm,
the bearing load capacity increases slightly and
the frictional coefficient decreases near ε=0.6. At
larger ε these changes reverse.

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NATIONAL
TRIBOLOGY
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THE ANNALS OF UNIVERSITY
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2003 ISSN 1221-4590
(4) When negative pressure is developed, the
static journal orbit is pushed horizontally and towards
the bearing clearance circle. Rotors running in journal
bearings can become then more unstable.
(5) Oil flow is reduced by the amount of oil
sucked again by negative pressure, when it is
developed.
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