Performance of conical bearing

1. Review Article
Influence of micropolar lubricant on
bearings performance: A review
Pankaj Khatak and HC Garg
Abstract
This article presents the applicability of the microcontinuum theories to the fluid in sliding surfaces. The classical
continuum mechanics fails to predict the accurate results when the geometric volume under consideration becomes
comparable to the material dimensions. The fluid in the presence of microstructures and in the space comparable to the
clearance of bearings showed unexpected variations in its properties as per the experimental observations. A general
class of micropolar fluid was defined by considering the microrotation vector of its particles. This review critically
analyzes the microrotation of lubricant additives and its effects on static and dynamic characteristics of the bearings.
Keywords
Micropolar lubricant, microcontinuum, journal bearings, hybrid, thermal effects
Date received: 2 October 2011; accepted: 28 February 2012
Introduction
Bearings are the devices used to support the different
moving machine elements. High speed and precision
required in the machine equipments had led to a revo-
lution in the design and development of various bearing
configurations such as slider, step, thrust, hydro-
dynamic, and hydrostatic bearings. The design of bear-
ings is based on operating conditions and the lubricant
used. The conventional bearing design is based on
Newtonian hypothesis. However, the abnormally high
values of viscosities obtained experimentally by Needs1
and Henniker2
in boundary lubrication could not be
explained on the basis of classical concepts. Solid
particle additives are used in base oil to improve lubri-
cating performance of the bearings. Also, lubricating
oil under standard operating conditions get loaded
with dirt and microscopic metal particles. Hence, the
fluid suspension properties in the bearings are influ-
enced by the microscopic events. Eringen3
termed
these fluids exhibiting the microrotational effects as
micropolar, a special case of microfluids4
to account
for the unexplained boundary layer phenomenon in a
circular pipe. Ariman5
further explained that micropo-
lar fluid points in small volume element rotate about
the centroid of volume element in addition to their rigid
motion. Allen and Kline6
on similar lines developed the
theory for microstructures in the lubricant, which was
later on confirmed by Balaram and Sastri.7
The theor-
etical results reported by the above researchers clearly
indicate that the presence of microstructures in the fluid
would alter the classical results. The microcontinuum
theories of fluids such as fluid suspensions, emulsions,
liquid crystals, and blood was reviewed by Ariman
et al.8
These micropoplar theories have been widely
applied under different conditions and principles for
various configurations of bearings. Squeeze film
action in different bearings with micropolar lubrication
was analyzed by various researchers.9–25
The time of
approach or response time for a micropolar fluid was
observed to be greater than the corresponding time
predicted by Newtonian theory. Slider bearing config-
urations (one to three dimensional) lubricated with
micropolar fluid were studied by various research-
ers.26–40
The maximum load capacity and friction
force were observed to increase with the increase in
concentration of additives and contaminants in the
lubricant. Similar results were also reported for rolling
Department of Mechanical Engineering, Guru Jambheshwar University of
Science and Technology, Hisar, India
Corresponding author:
Pankaj Khatak, Department of Mechanical Engineering, Guru
Jambheshwar University of Science and Technology, Hisar 125001, India.
Email: pankajkhatak@gmail.com
Proc IMechE Part J:
J Engineering Tribology
226(9) 775–784
! IMechE 2012
Reprints and permissions:
sagepub.co.uk/journalsPermissions.nav
DOI: 10.1177/1350650112443019
pij.sagepub.com

2. contact41
and thrust bearings42–44
under micropolar
lubrication. Journal bearings are the most studied slid-
ing bearings with different geometrical configurations
and operating conditions. The performance of jour-
nal bearings with micropolar lubricant was analyzed
by considering different parameters such as min-
imum fluid film thickness, load capacity, coefficient of
friction, side leakage flow, temperature changes, stiff-
ness, and damping coefficients. The analysis of journal
bearings for infinitely long,45–49
short,50,51
porous,52
and finite-length and finite-width53–59
configurations
showed favorable performance characteristics with
micropolar lubricant as compared to Newtonian lubri-
cant. The performance of journal bearings was also
analyzed by considering the effects of roughness, por-
osity,60,61
misalignment,62,63
dynamic loading,64,65
and
stability characteristics.66–68
Thermal and cavitational
effects were included into the study of micropolar lubri-
cated journal bearing by Wang and Zhu.69
Journal
bearing with configurations such as elliptical,70
hydro-
static,71–73
and noncircular lobed bearings74,75
with
micropolar lubrication were analyzed in detail with ref-
erence to their performance characteristics.
The introduction of micropolar parameters in the
conventional fluid flow equations had led to theoretical
results in qualitative agreement with the actual experi-
mental values of viscosity in boundary lubrication.
In this review article, an attempt has been made to
explain the performance characteristics of different
bearing configurations with micropolar lubrication
under various operating conditions. The bearing per-
formance has been measured by considering the vari-
ation in load capacity, coefficient of friction, bearing
flow, heat generation, and bearing system stability
with micropolar lubrication.
Micropolar theory for lubrication
The lubrication theories applied for the bearing analysis
by various researchers have considered only the macro-
scopic change in the properties of the lubricant.
The individual particles in the lubricant can change
their shape or rotational motion and become effective
in the region equivalent to bearing clearances. Hence,
the classical Newtonian postulate is not valid for the
fluids considering the effect of molecules. Newtonian
fluid mechanics need to be generalized when the exter-
nal length scale become comparable to the average
dimensions of the material particles in complex fluids
such as polymeric suspensions, animal blood, and
liquid crystals. Eringen3
simplified his microfluids
theory4
of 22 viscosity coefficients to 6 viscosity coeffi-
cients , , , ,

3. , and
ð Þ by ignoring the deformation
of microelements. The Navier–Stokes equations were
generalized with the introduction of a new angular
velocity vector of rotation of particles and the
corresponding viscosity coefficients. The equations for
compressible micropolar fluid proposed by Eringen3
in
vector rectangular coordinate form are
@
@t
þ r Á ðVÞ ¼ 0 ð1Þ
DV
Dt
¼ Àr þ þ 2ð Þrr Á V
À þ
2
r  r  V þ r  v þ f ð2Þ
j
Dv
Dt
¼ þ

4. þ
ð Þrr Á v À
r  r  v
þ r  V À 2v þ LB ð3Þ
It can be noted that when the micropolar viscosity
coefficients are reduced to zero i:e: ¼ ¼

5. ¼ð
¼ 0Þ, equation (2) reduces to Navier–Stokes equation
and equation (3) vanishes. The micropolar theory con-
siders only microrotation effects of microelements with
surface and body couples. Out of these six viscosity
coefficients, two and ð Þ are classical viscosity coeffi-
cients (interdependent) and four new micropolar viscos-
ity coefficients. Out of the four micropolar viscosity
coefficients , ,

6. , and
ð Þ, one independent coefficient
ð Þ is used as the coupling parameter in linear and
angular momentum equations of fluid flows. The rest
three ,

7. , and
ð Þ interdependent coefficients are used
in the angular momentum equation of micropolar fluid.
He combined one classical and two micropolar viscos-
ity coefficients into a single parameter. This parameter
was used to explain the changes in velocity profile near
the boundary layer and the reduction in surface shear,
which could not be explained by the classical Navier–
Stokes fluid theory. Ariman5
compared the velocity
profiles generated by Eringen micropolar fluid theory
and dipolar fluids on the basis of parameters defined by
Eringen3
between two concentric cylinders. Allen and
Kline6
used the triad of vectors approach for substruc-
ture particles to define their rotations and deformations
in the fluid. The effect of substructures in slider bearing
lubrication was expressed by combining radius of gyr-
ation, vortex viscosity, and geometrical parameters.
The micropolar theory of fluids proposed by Eringen3
and Allen and Kline6
was applied in the lubrication
analysis of different configuration of bearings such
as slider,26,28,29,32
thrust,9,11,16,42
step slider,19,27
and
journal bearings.14,20,22,23,52
The results showed an
appreciable variation in the performance of the above
bearings with micropolar lubricant as compared to
Newtonian lubricant. Prakash and Sinha45
explained
the concept of microcontinuum fluid flow in detail by
considering the effect of the above-defined micropolar
776 Proc IMechE Part J: J Engineering Tribology 226(9)

8. viscosity coefficients separately. They derived the
generalized Reynolds equation by combining the
continuity equation (1) with equations (2) and (3)
subjected to usual lubrication assumptions. The result-
ing equation becomes
@
@x
h3
N, l, hð Þ
@P
@x
þ
@
@y
h3
N, l, hð Þ
@P
@y
¼
U
2
@h
@x
þ
@h
@t
ð4Þ
where
N, l, hð Þ ¼
1
12
þ
l2
h2
À
Nl
2h
cot h
Nh
2l
They introduced two new parameters, namely
coupling number Nð Þ and characteristic length lð Þ to
distinguish the micropolar fluid from Newtonian one.
These two parameters were formed by combining
Newtonian viscosity coefficient ð Þ and Eringen micro-
polar viscosity coefficients and
ð Þ. Coupling number
was defined as the ratio of viscous forces of relative
rotation to Newtonian viscous forces, whereas charac-
teristic length characterizes the interaction between the
micropolar fluid and film gap. Mathematically, cou-
pling number and characteristic length were presented
by N ¼ = 2 þ ð Þ½ Š1=2
and l ¼
=4ð Þ1=2
, respectively
which were used to explain the performance character-
istics of journal bearings. The value of Nvaries from
zero to one as per the thermodynamic requirements,
whereas l varies from zero to infinity. In the limiting
case, when l approaches zero, the function becomes
1=12 and equation (4) reduces to the classical Reynolds
equation. Prakash and Sinha15
further proved that at a
particular value of N and L (characteristic length
number, L ¼ C=l), response time of the squeeze film
was almost same as the one experimentally measured
by Needs.1
It was observed that micropolar effects are
more pronounced for larger values of Nand smaller
values of L. The above two dimensionless numbers
are widely used by researchers to show the variation
of micropolar effect of the lubricant. The variation
in velocity of journal centers,17,18,66
pressure distri-
butions,33,36,41,46–48,53–55
and dynamic characteris-
tics39,40,51,56
were expressed in terms of these two
parameters. The bearing performance characteristics
were studied by considering the factors such as
misalignment,62,63
stability,67,68
elasticity of bearing
liner,59
dynamic loading,64,65
and surface rough-
ness25,60,61,70
in terms of coupling number and charac-
teristic length number. These parameters were also used
to study the performance of journal bearings with dif-
ferent configurations such as elliptical,70
multirecess
hydrostatic,71–73
and noncircular lobed bearings.74,75
It is observed from the above studies that the bearing
performance characteristics varies remarkably with the
change in micropolar effect of lubricant in terms of
coupling number and characteristic length number.
Tipei50
developed vectorial equations for micropolar
fluids by considering its viscosity and micropolar
characteristics as a function of the coordinates in the
analysis of short bearings. The variation in viscosity of
fluids was studied in terms of volume concentration and
the parameter specifying shape, size, deformation, and
distribution of additive particles in carrier oil for differ-
ent bearing configurations.34,58,59,70
Bessonov37,49
used
the concept of boundary viscosity (characteristic limit
of viscosity) in the boundary conditions of micropolar
liquid model for journal bearings and compared it with
the results suggested by Prakash and Sinha.45
The microcontinuum fluid mechanics developed by
Eringen found wide acceptability among engineering
scientists in predicting the performance of sliding
bearings.
Pressure distribution
The presence of microstructures in the lubricant has
pronounced effect on the pressure distribution and
load capacity of the bearings. Pressure generation
inside a bearing greatly depends on the oil film thick-
ness. The variation in oil film thickness can be
explained on the basis of presence of microparticles in
the oil among other factors. The effect of micropolar
lubricant on the pressure distribution and load capa-
city of thrust bearings have been studied by
works.9,11,16,42–44
Ramanaiah and Dubey11
modified
the micropolar parameter assumption of Agrawal
et al.9
in their analysis. The pressure level and load
capacity of thrust bearings were reported to increase
with the increase in micropolar parameters. The micro-
polar lubricant behavior of slider6,29,30,32,34,38,40
and
step bearings19,33,36
were studied under different oper-
ating conditions. It was reported that optimum design
of bearings increases the load capacity relatively higher
than the increased power requirements due to micropo-
lar lubricant. Ramanaiah and Dubey30
reported an
increase of 4% load capacity with micropolar fluid as
compared to classical results in slider bearing. Yousif
and Ibrahim34
considered volume concentration along
with other parameters of additive particles in the lubri-
cant for the calculation of pressure in a slider bearing.
Sinha41
observed increase in load capacity of the rolling
contact bearing due to increased viscosity of lubricant
in the presence of substructures.
Micropolar lubricant pressure distribution has been
studied widely for journal bearing under different geo-
metric and operating conditions. Prakash and Sinha45
introduced the concept of coupling number Nð Þ and
Khatak and Garg 777

9. characteristic length number Lð Þ of micropolar lubri-
cant for predicting the pressure distribution and load
capacity of journal bearings. They depicted high pres-
sures for infinitely long journal bearings to support
load in the case of small values of L and large values
of N. Similar results were reported for infinitely long,
short, and finite journal bearings by Prakash and
Sinha,46
Sinha et al.,47,48
Qiu and Lu,53
Huang
et al.,54
Khonsari and Brewe,55
and Lin.57,60
Prakash
and Sinha46
observed an increase in the peak pressure
(of the order of 20%) when Reynolds boundary condi-
tion was considered relative to half-Sommerfeld bound-
ary condition,45
as shown in Figure 1.
Qiu and Lu53
observed increase in load capacity of
about 24% when micropolar effect was considered
(Figure 2).
Lin57,60
considered cavitation phenomenon57
along
with asperity size60
for studying the pressure distribu-
tion behavior of finite journal bearing. The combined
micopolar parameters used by Shukla and Isa29
for
studying the micropolar behavior of lubricant in
slider bearing was also adopted by works20–22,52
in eval-
uating the load capacity of journal bearings. They
showed the increase in load capacity with the increase
in parameters, characterizing the concentration of addi-
tives. Tipei50
obtained higher pressures in short journal
bearing as compared to Newtonian lubricant by con-
sidering the variable coefficients of the micropolar
lubricant. The increased load capacity of journal bear-
ings was also observed while operating with micropolar
lubricant along with other factors such as mass trans-
fer,58
bearing elasticity,59
surface roughness,61
misalign-
ment,62
dynamic loading,64,65
and thermal effects.69
The micropolar pressure distribution was analyzed for
elliptical,70
multirecess hydrostatic,71
porous,24,25
non-
circular lobed,74,75
and multirecess hybrid73
journal
bearings. Nicodemus and Sharma73
showed that max-
imum fluid film pressure increases in the range 25–30%
by considering micropolar lubricant for various geo-
metric shapes of recesses in a four pocket orifice com-
pensated hybrid journal bearing.
The increased pressure generation and enhancement
in load capacity for all the bearing configurations can
be attributed to the increase in viscosity of the operat-
ing lubricant due to the presence of additives and
molecular nature of the lubricant.
Friction force and coefficient of friction
Fluid friction depends on many factors including
viscosity, film thickness, speed of sliding surfaces,
geometry of surfaces, and presence of particles in the
fluid, among others. The power loss and wear in the
operation of bearing is directly proportional to the fric-
tion generated. The friction in bearings can be
Figure 1. Pressure distribution for infinitely long journal
bearing.
Source: reprinted with permission of Elsevier from Prakash
and Sinha.46
Figure 2. Pressure distribution for finite-length journal bearing.
Source: reprinted with permission of Springer Science þ Business
Media from Qui and Lu.53
778 Proc IMechE Part J: J Engineering Tribology 226(9)

10. expressed in terms of friction force and coefficient of
friction. The variation in coefficient of friction indicates
the relative change in friction force with the load cap-
acity of the bearing. Various researchers studied the
change in friction forces and coefficient of friction for
micropolar lubricant with different bearing configur-
ations. The coefficient of friction showed the decreasing
trend with the increase in micropolar parameters of the
lubricant for slider and step bearings.6,29,33,34,36–38
Yousif and Ibrahim34
predicted an increase in friction
force with the increase in volume concentration of addi-
tives and contaminants. Khader and Vachon42
and
Yousif and Ibrahim43
reported the increase in power
loss and friction force in thrust bearing operation due
to increase of shear stress in the presence of microstruc-
tures in the lubricant. The study approach of micro-
polar lubricant phenomenon changed with the
introduction of coupling number Nð Þ and characteristic
length number Lð Þ by Prakash and Sinha.45
They
observed that coefficient of friction in infinitely long
journal bearings goes on decreasing with the decrease
in L till a particular value, as shown in Figure 3.
Prakash and Sinha,46
Sinha et al.,47,48
Qiu and Lu,53
Huang et al.,54
Khonsari and Brewe,55
and Huang and
Weng56
observed similar trends for infinitely long,
short, finite length, and finite-width journal bearings
operating with micropolar lubricant. The micropolar
effects on coefficient of friction for finite journal
bearing obtained by Khonsari and Brewe55
are shown
in Figure 4.
The coefficient of friction was reduced by 26% when
Prakash and Sinha46
considered Reynolds boundary
conditions in comparison to half Sommerfeld boundary
conditions. Huang et al.54
predicted a decrease in the
coefficient of friction in the range 8–21% for finite-
width journal bearing operating with micropolar lubri-
cant at increasing eccentricity ratios. Later on, Huang
and Weng56
reported that decreasing coefficient of
friction with micropolar lubricant in finite-width bear-
ing reduces the fluid film damping capacity. Narayanan
et al.58
observed that friction force in finite journal
bearing increases with the mass transfer and volume
concentration of additives in the micropolar lubricant.
Sinha18
showed that friction characteristic of rolling
bearings increases with the increase of coupling
number and decrease of characteristic length number
of micropolar lubricant. Zaheeruddin and Isa20
and
Isa and Zaheeruddin52
used the micropolar approach
of Shukla and Isa29
to show the variation in coefficient
of friction for infinitely long and short journal bearings.
Tipei50
reported that friction torque increases in the
range 5–30% by considering micropolar lubricant in
short bearing configuration. Lin57,60
noted that coeffi-
cient of friction decreases by considering cavitation57
and asperity60
in finite-width journal bearings with
the increasing fluid micropolarity. Das et al.62
showed
that friction parameter is lowered for micropolar fluid
than Newtonian lubricant and it further decreases with
the increase in misalignment of journal bearing, as
shown in Figure 5.
Figure 3. Coefficient of friction versus L for infinitely long
journal bearing.
Soure:reprintedwithpermissionofElsevierfromPrakashandSinha.45
Figure 4. Coefficient of friction versus L for finite journal
bearing.
Soure: reprinted with permission of NASA.55
Figure 5. Coefficient of friction versus L for misaligned journal
bearing.
Soure: reprinted with permission of Elsevier from Das et al.62
Khatak and Garg 779

11. Wang and Zhu64
and Xiaoli et al.65
concluded that
friction coefficient in a dynamically loaded journal
bearing operating with micropolar lubricant is higher
than a Newtonian fluid in contravention to the earlier
results of steadily loaded journal bearings. Nair and
Nair59
noted that frictional force in circular journal
bearing increases with the increase in volume concen-
tration of additives. Wang and Zhu69
exhibited that by
considering thermal and cavitation effects in finite jour-
nal bearing, the coefficient of friction decreases with
the increase in micropolar parameters of lubricant.
Rahmatabadi et al.74,75
observed that friction coeffi-
cient in noncircular lobed bearings decreases with the
increase in micropolar parameters. Nicodemus and
Sharma73
noticed a large reduction of coefficient of fric-
tion with the increase in micropolarity of operating
lubricant for different geometric shape recess of the
four pocket orifice compensated hybrid bearing.
It is observed from the above results that coefficient
of friction with micropolar fluids tends to be lower than
Newtonian fluids except for dynamic loading of bear-
ings. This behavior can be attributed to the particular
characteristic of micropolar lubricant by which the load
capacity increases relatively more than the correspond-
ing increase in the frictional force.
Bearing flow and end leakage
The bearing performance can be expressed in terms of
bearing flow and end leakage. These can be evaluated
on the basis of pressure distributions in the bearings.
The fluid flow rate is directly linked to the pump power
required in externally pressurized bearing.
Prakash and Sinha45
observed that flow rate reduces
for infinitely long journal bearing with the increase of
micropolar parameters in the lubricant, as can be
observed from Figure 6.
Ramanaiah and Dubey11
observed reduced flow rate
of micropolar lubricant to support a load in compari-
son to Newtonian lubricant for thrust bearing. Tipei50
reported larger side flow rate using micropolar
lubricant for short bearing configuration. Yousif and
Ibrahim,34
Nair and Nair,59
and Nair et al.70
con-
sidered mass transfer and volume concentration of
additives to show the fluid variation in infinitely long
slider bearing34
and end leakage in circular59
and
elliptical journal bearings.70
Yousif and Ibrahim43
showed decreased flow rates with micropolar lubricants
in infinitely long thrust bearing. Huang et al.54
reported
that volumetric side flow rates is same for micropolar
and Newtonian fluids operating in finite-width journal
bearing. Lin57,60
showed that side leakage flow in finite
journal bearing decreases with the micropolar lubricant
while considering cavitation and surface irregularities.
According to Wang and Zhu,64
Newtonian fluid yields
higher side leakage value than micropolar fluid in jour-
nal bearing under the same dynamic loading condi-
tions, as shown in Figure 7.
Wang and Zhu69
observed a slightly decreasing trend
for side leakage flow in the case of finite journal bearing
with increasing micropolar effects along with the ther-
mal and cavitational effects. Nicodemus and Sharma72
predicted a reduction of 6.91% in the requirement of
bearing flow for an unworn hydrostatic bearing operat-
ing with micropolar lubricant in comparison to
Newtonian lubricant. Rahmatabadi et al.74
observed
decreased side leakage flow in noncircular lobed bear-
ings with increase in coupling number of micropolar
lubricant.
Nicodemus and Sharma73
found decreased lubricant
requirement in the range 30–46% for different recess
Figure 6. Volume flow rates versus L for infinitely long
journal bearing.
Soure: reprinted with permission of Elsevier from Prakash and
Sinha.45
Figure 7. Side leakage versus crank angle for dynamic
loaded journal bearing.
Source: reprinted with permission of Elsevier from Wang and
Zhu.64
780 Proc IMechE Part J: J Engineering Tribology 226(9)

12. shapes of four pocket orifice compensated hybrid
journal bearing operating with micropolar lubricant,
as shown in Figure 8.
From the above discussion, it is observed that
lubricant requirement and the end leakage of various
bearing systems decrease with the increase in micropo-
lar effects. It could be due to increased resistance
to flow (i.e. increase in effective lubricant viscosity),
especially at increased characteristic length number of
lubricant molecules.
Heat generation and temperature
variations
Heat generated inside a bearing corresponds to loss of
mechanical energy due to shear in the lubricant film.
The temperature rise in the bearings has degrading
effects on the bearing performance. The minimum
film thickness reduces due to decrease in viscosity,
leading to bearing seizure.76
The strength of film will
fall markedly due to decrease in cohesion of lubricant
molecules and their adhesion with the metal surfaces.
Sinha et al.47
assumed the Newtonian viscosity vari-
ation along with the fluid film thickness due to the
variation of temperature in micropolar lubricant
during the working of a journal bearing. The coeffi-
cient relating the viscosity and film thickness was
determined by complete thermal calculations. They
have shown simultaneous variation of load capacity
with temperature coefficient and micropolar param-
eters (N and L). It was shown that load capacity of
journal bearing decreases with the increase in tempera-
ture coefficients, but at a particular temperature
coefficient, load capacity increases with increase in
micropolar parameters. Sinha et al.48
further assumed
the micropolar viscosity variation with temperature
along with Newtonian viscosity. They theoretically
established that working range of temperatures in
journal bearing increases by considering the additives
in the lubricant. Wang and Zhu69
plotted the tempera-
ture contours as shown in Figure 9(a) and (b)
for finite journal bearing operating with micropolar
lubricant. The temperature profiles were obtained
simultaneously by solving micropolar energy equation
for lubricant and the conduction equation for bearing
bush. The average value of viscosity used in the
temperature calculations was determined by consider-
ing viscosity as a function of temperature. Their
results indicate that temperature increases with the
increase in micropolarity of lubricant particles.
From literature, it is observed that only few
researchers have studied the combined effects of ther-
mal and micropolar aspects of the lubricants.
Furthermore, the micropolar fluid model is mainly con-
fined to isothermal analysis of simple bearing
configurations.
Figure 8. Bearing flow versus L for hybrid journal bearing.
Source: reprinted with permission of Elsevier from Nicodemus
and Sharma.73
Figure 9. Temperatures contours for finite journal bearing.
Source: reprinted with permission of Elsevier from Wang and Zhu.69
Khatak and Garg 781

13. Stability characteristics
The phenomenon of self-excited vibrations in journal
bearings caused by oil film forces are known as oil whip
or oil whirl.56
This causes a serious problem in the effi-
cient working of the high-speed machines and may
result in bearing failure for the rotation speed above
the whirl threshold.66
The stability characteristics can
be explained in terms of stiffness and damping coeffi-
cients of the bearing system. Huang and Weng56
observed that oil whirl occur easily for finite-width
journal bearing operating with micropolar lubricant
under heavy load conditions. They also showed that
dominating stiffness coefficient is larger for micropolar
lubricant while the corresponding dominating damping
coefficient has a smaller value. Das et al.63
studied the
stability of conical whirl motion of rigid rotor on
hydrodynamic journal bearing operating with micropo-
lar lubricant. They observed that conical stability
increases with the increase in coupling number of the
micropolar lubricant. Das et al.67,68
performed the sta-
bility analysis on hydrodynamic journal bearings oper-
ating with micropolar lubricant. Their results showed
that the stability of journal bearing increases with the
increase in micropolar parameters of the lubricant.
Nair et al.70
showed better stability of elliptical journal
bearing by observing that damped frequency of whirl
decreases and threshold speed increases with the
increase of concentration in the additives of micropolar
lubricant. Naduvinamani and Marali39
found increase
in dynamic stiffness film coefficient and decrease in
dynamic damping film coefficient with the increase in
coupling number of the micropolar lubricant operating
in a slider bearing. Nicodemus and Sharma72
observed
an increase of 103–112% in fluid film stiffness coeffi-
cients and 65–81% increase of fluid film damping coef-
ficients with the increase in micropolarity of the
lubricant in a hydrostatic bearing. Later on,
Nicodemus and Sharma73
dynamically analyzed four
pocket orifice compensated hybrid journal bearing of
different recess shapes operating with micropolar lubri-
cant. They observed a change of the order of 20–13% in
the fluid film stiffness coefficient and 73–75% change in
damping film coefficient for different recess shapes.
Further, they observed that triangular recess provides
the best stability for all the bearing configurations.
Thus, from literature, it is found that the increase in
stability of different configurations of bearings can be
attributed to the enhanced viscosity of the micropolar
lubricant.
Concluding remarks
The continuity assumption of classical fluid mechanics
fails in defining the material properties of fluid, when
the fluid flow is considered inside a space of scale com-
parable to the size of molecules. In these cases, the
intrinsic motion of the particles must be taken into
account. The major effect of considering the molecule
size and their rotation is the increase of effective viscos-
ity in comparison to the classical viscosity. The load
capacities showed the increasing trend while the coeffi-
cient of friction varied in reverse manner. The stability
parameters of high-speed bearing assembly were
observed to increase in comparison to Newtonian lubri-
cant. Despite the analytical prediction of performance
improvement, experimental verification of these char-
acteristics is still required. There may be some more
factors, as surface texture, elasticity, and turbulence,
which can be incorporated along with micropolar con-
cept of the lubricant. The temperature increase in jour-
nal bearings with increased micropolar effect is a matter
of concern. However, the heat generation with micro-
polar effect is not studied in detail for different bearing
configurations. Hence, urgent attention is required for
further experimental and analytical analysis of sliding
bearings considering the micropolar effect of the lubri-
cant for realistic bearing design.
Funding
This work was supported by UGC, New Delhi under FIP
scheme.
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Appendix
Notation
C clearance width
Cf coefficient of friction
f body force per unit mass
h film thickness
j microinertia constant
l characteristic length
L characteristic length number
LB body couple per unit mass
N coupling number
P hydrodynamic pressure
Q flow rate
Qleak end leakage
t time
U shaft velocity
v microrotation velocity vector
V velocity vector
x circumferential direction
y axial direction
,

16. ,
, and micropolar viscosity coefficients
crank angle
, classical viscosity coefficients
thermodynamic pressure
mass density
784 Proc IMechE Part J: J Engineering Tribology 226(9)