THERMOHYDRODYNAMIC ANALYSIS OF PLAIN JOURNAL BEARING WITH MODIFIED VISCOSITY - TEMPERATURE EQUATION

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 11, November (2014), pp. 31-46 © IAEME
31
THERMOHYDRODYNAMIC ANALYSIS OF PLAIN
JOURNAL BEARING WITH MODIFIED VISCOSITY -
TEMPERATURE EQUATION
Kanifnath Kadam, S.S. Banwait, S.C. Laroiya
National Institute of Technical Teachers Training & Research, Sector 26, Chandigarh
ABSTRACT
The purpose of this paper is to predict the temperature distribution in fluid-film, bush housing
and journal along with pressure in fluid-film using a non-dimensional viscosity-temperature
equation. There are two main governing equations as, the Reynolds equation for the pressure
distribution and the energy equation for the temperature distribution. These governing equations are
coupled with each other through the viscosity. The viscosity decreases as temperature increases. The
hydrodynamic pressure field was obtained through the solution of the Generalized Reynolds
equation. This equation was solved numerically by using finite element method. Finite difference
method has been used for three dimensional energy equations for predicting temperature distribution
in fluid film. For finding the temperature distribution in the bush, the Fourier heat conduction
equation in the non- dimensional cylindrical coordinate has been adopted. The temperature
distribution of the journal was found out using a steady-state unidirectional heat conduction
equation.
Keywords: Journal Bearings. Reynolds Equation, Thermohydrodynamic Analysis, Viscosity-
Temperature Equation.
1. INTRODUCTION
A Journal bearing is a machine element whose function is to provide smooth relative motion
between bush and journal. In order to keep a machine workable for long periods, friction and wear of
mating parts must be kept low. The plain journal bearings are used for high speed rotating
machinery. This high speed rotating machinery fails due to failure of bearings. Due to the heavy load
and high speed, the temperature increases in the bearing. For prediction of temperature and pressure
distribution in bearing, accurate data analysis is necessary. An accurate thermo hydrodynamic
analysis is required to find the thermal response of the lubricating fluid and bush. Therefore, a need
has been felt to carry out further investigation on the thermal effects in journal bearings.
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ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 5, Issue 11, November (2014), pp. 31-46
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By considering thermal effects B. C. Majumdar [1] obtained a theoretical solution for
pressure and temperature of a finite full journal bearing. D. Dowson and J. N. Ashton [2] computed a
solution of Reynolds equation for plain journal bearing configuration. Operating characteristics were
evaluated from the computed solutions and results were presented graphically. The optimum design
objective was stated explicitly in terms of the operating characteristics and was minimized within
both design and operative constraints. J. Ferron et al. [3] solved three dimensional energy, three
dimensional heat conduction equation. They computed mixing temperature by performing a simple
energy balance of recirculating and supply oil at the inlet. H. Heshmat and O. Pinkus [4]
recommended that the mixing occurs in the thin lubricant layer attached on the surface of the journal.
This implies that no mixing occurs inside the grooves. An excellent brief review of thermo
hydrodynamic analysis was presented by M. M. Khonsari [5] for journal bearings. H. N. Chandrawat
and R. Sinhasan.
[6] simultaneously solved the generalized Reynolds equation along with the energy
and heat conduction equations. They studied the effect of viscosity variation due to rise in
temperature of the fluid film. Also they compared Gauss- Siedel iterative scheme and the linear
complementarity approach. M. M. Khonsari and J. J. Beaman [7] presented thermohydrodynamic
effects in journal bearing operating with axial groove under steady-state loading. In this analysis, the
recirculating fluid and the supply oil was considered. S. S. Banwait and H. N. Chandrawat [8]
proposed a non-uniform inlet temperature profiles and for correct simulation. They considered the
heat transfer from the outlet edge of the bush to fluid in the supply groove. L. Costa et al. [9]
presented extensive experimental results of the thermohydrodynamic behavior of a single groove
journal bearing. And developed the influence of groove location and supply pressure on some
bearing performance characteristics. M. Tanaka [10] had shown a theoretical analysis of oil film
formation and the hydrodynamic performance of a full circular journal bearing under starved
lubrication condition. Sang Myung Chun and Dae-Hong Ha [11] examined the effect on bearing
performance by the mixing between re-circulating and inlet oil. M. Tanaka and K. Hatakenaka [12]
developed a three-dimensional turbulent thermohydrodynamic lubrication model was presented on
the basis of the isothermal turbulent lubrication model by Aoki and Harada, this model was different
from both the Taniguchi model and the Mikami model. P. B. Kosasih and A. K. Tieu [13] considered
the flow field inside the supply region of different configurations and thermal mixing around the
mixing zone above the supply region for different supply conditions. Flows in the thermal mixing
zone of a journal bearing were investigated using the computational fluid dynamics. The complexity
and inertial effect of the flows inside the supply region of different configurations were considered.
M. Fillon and J. Bouyer [14] presented the thermohydrodynamic analysis of plain journal bearing
and the influence of wear defect. They analyzed the influence of a wear defect ranging from 10% to
50% of the bearing radial clearance on the characteristics of the bearing such as the temperature, the
pressure, the eccentricity ratio, the attitude angle or the minimum thickness of the lubricating film. L.
Jeddi et al. [15] outlined a new numerical analysis which was based on the coupling of the
continuity. This model allows to determine the effects of the feeding pressure and the runner velocity
on the thermohydrodynamic behavior of the lubricant in the groove of hydrodynamic journal bearing
and to emphasize the dominant phenomena in the feeding process. S. S. Banwait [16] presented a
comparative critical analysis of static performance characteristics along with the stability parameters
and temperature profiles of a misaligned non-circular of two and three lobe journal bearings
operating under thermohydrodynamic lubrication condition. U. Singh et al. [17] theoretically
performed a steady-state thermohydrodynamic analysis of an axial groove journal bearing in which
oil was supplied at constant pressure. L. Roy [18] theoretically obtained steady state
thermohydrodynamic analysis and its comparison at five different feeding locations of an axially
grooved oil journal bearing. Reynolds equation solved simultaneously along with the energy
equation and heat conduction equation in bush and shaft. B. Maneshian and S. A. Gandjalikhan
Nassab [19] presented the computational fluid dynamic techniques. They obtained the lubricant

33
velocity, pressure and temperature distributions in the circumferential and cross film directions
without considering any approximations. B. Maneshian and S. A. Gandjalikhan Nassab [20]
determined thermohydrodynamic characteristics of journal bearings with turbulent flow using
computational fluid dynamic techniques. The bearing had inﬁnite length and operates under
incompressible and steady conditions. The numerical solution of two-dimensional Navier–Stokes
equation, with the equations governing the kinetic energy of turbulence and the dissipation rate,
coupled with then energy equation in the lubricant ﬂow and the heat conduction equation in the
bearing was carried out. N. P. Mehata et al. [21] derived a generalized Reynolds equation for
carrying out the stability analysis of a two lobe hydrodynamic bearing operating with couple stress
fluids that has been solved using the finite element method. N. P. Arab Solghar et al. [22] carried out
experimental assessment of the influence of angle between the groove axis and the load line on the
thermohydrodynamic behavior of twin groove hydrodynamic journal bearings. Mukesh Sahu et al.
[23] used computational fluid dynamic technique for predicting the performance characteristics of a
plain journal bearing. Three dimensional studies have been done to predict pressure distribution
along journal surface circumferentially as well as axially. E. Sujith Prasad et al. [24] modified
average Reynolds equation that includes the Patir and Cheng’s flow factors, cross-film viscosity
integrals, average fluid-film thickness and inertia term. This was used to study the combined
influence of surface roughness, thermal and fluid-inertia on bearing performance. Abdessamed
Nessil et al. [25] presented the journal bearings lubrication aspect analysis using non-Newtonian
fluids which were described by a power law formula and thermohydrodynamic aspect. The influence
of the various values of the non- Newtonian power-law index, ݊, on the lubricant film and also
analyzed the journal bearing properties using the Reynolds equation in its generalized form.
The aim of this work is to predict the pressure and temperature distribution in plain journal
bearing. Thermohydrodynamic analysis of a plain journal bearing has been presented with an
improved viscosity-temperature equation. The equation has been modified by authors to predict the
proper relation between viscosity and temperature for forecasting the correct temperature in plain
journal bearing. The pressure and temperature distribution in the journal bearing which was almost
equal to the temperature obtained by experimental results of Ferron J. et al. [3]. The results have been
validated by comparison with experimental results of Ferron J. et al. [3]. and show good agreement.
2. GOVERNING EQUATIONS
In this present work three dimensional energy equation, heat conduction and Reynolds
equation were considered for analysis of thermohydrodynamic analysis of a plain journal bearing.
This bearing having a groove of 18° extent at the load line. The geometric details of the journal
bearing system are illustrated in Fig 1. Single axial groove has been used for supplying fluid to the
bearing under, negligible pressure. The model based on the simultaneous numerical solution of the
generalized Reynolds and three dimensional energy equations within the fluid-film and the heat
transfer within the bush body.
Fig. 1: Bearing geometry

34
2.1 Generalized Reynolds Equation
Navier derived the equations of fluid motion for a viscous fluid. Stokes also derived the
governing equations of motion for a viscous fluid, and the basic equations are known as Navier-
Stokes equations of motion. The Reynolds equation is a simplified version of Navier-Stokes
equation. A partial differential equation governing the pressure distribution in fluid film lubrication
is known as the Reynolds equation. This equation was first derived by Osborne Reynolds. The
hydrodynamic pressure and the velocity field within fluid flow were accurately described through the
solution of the complete Navier-Stokes equations. This has provided a strong foundation and basis
for the design of hydrodynamic lubricated bearings.
This paper is to deal with the finite element analysis of Reynolds’ equation. It will show how
the finite element technique is used to form an approximate solution of the basic Reynolds’ equation.
The analysis has been incorporated in a computer programme and results from it were presented. A
Reynolds equation in the following dimensionless form governs the flow of incompressible
isoviscous fluid in the clearance space of a journal bearing system. This equation in the Cartesian
coordinate system is written as,
1
2 2
0
3 3
hp p Fh F h F h h
tFα
     
     
    
    
∂ ∂ ∂ ∂∂ ∂+ = − +
∂α ∂β ∂α∂ ∂β ∂
(1)
where the non-dimensional functions of viscosity 0 1 2, andF F F are defined by,
1 1 1
1
0 1 2
00 0 0
; ; and
Fdz z z
F F dz F z dz
Fµ µ µ
 
= = = − 
 
∫ ∫ ∫
(2)
The non-dimensional functions of viscosity 0 1 2, andF F F report for the effect of variation in fluid
viscosity across the film thickness. And non dimensional minimum film thickness is given by,
1 cos sinj jh X Zα α= − − (3)
The above equation (1) was solved to satisfy the following boundary and complementarity
conditions:
i. On the bearing side boundaries,
( ), 0pβ λ= ± = (4)
ii. On the supply groove boundaries,
sp p= (5)
iii.In the positive pressure region, Positive pressures will be generated only when the fil
thickness is thin,
0, 0Q p= > (6)
iv. In the cavitated region,
0, 0, 0
p
Q p
α
∂
< = =
∂
(7)

35
Solution of Eq. (1) with above boundary and complementary conditions gives pressure at each node.
2.2 Viscosity-Temperature Equation for predicting temperature distribution in bearings
The viscosity of fluid film was extremely sensitive to the operating temperature. With
increasing temperature the viscosity of oils falls rapidly. In some cases the viscosity of oil can fall by
about 80% with a temperature increase of 25°C. From the engineering viewpoint it is important to
know the viscosity value at the operating temperature since it determines the lubricant film thickness
separating two surfaces. The fluid viscosity at a specific temperature can be either calculated from
the viscosity-temperature equation or obtained from the viscosity-temperature ASTM chart.
2.2.1 Viscosity-Temperature Equations
There were several viscosity-temperature equations available; some of them were purely
empirical whereas others were derived from theoretical models. The Vogel equation was most
accurate. In order to keep a machine workable for long periods, friction and wear of its parts must be
kept low. For effective lubrication, fluid must be viscous enough to maintain a fluid film under
operating conditions. Viscosity is the most important property of the fluid, which utilized in
hydrodynamic lubrication. The coefficient of viscosity of fluid and density changes with
temperature. If a large amount of heat is generated in the fluid film, the thickness of fluid film
changes with respect to temperature and viscosity. The viscosity of oil decreases with increasing
temperature. Hence, the change in viscosity cannot be ignored. Due to viscous shearing of fluid
layer, heat is generated; as significance, high temperatures may be anticipated. Under this condition
the fluid can experience a variation in temperature, so that it is necessary to predict the bearing
temperature and pressure.
Therefore, a need has been felt to carry out further investigations on analysis of the thermal
effects in journal bearings, so the viscosity-temperature relation given by Ferron J. et al. [3] has been
modified. The viscosity µ is a function of temperature and it was assumed to be dependent on
temperature. The viscosity of the lubricant was assumed to be variable across the film and around the
circumference. The variation of viscosity with the temperature in the non-dimensional two degree
equation was described by Ferron J. et al. [3]; this equation was expressed as,
0 1 2
0
2
f fk k T k T
µ
µ
µ
= = − + (8)
The authors modified and developed a two degree viscosity-temperature relation in to three
degree polynomial viscosity-temperature relation. This modified equation as illustrated below,
0 1 2 3
0
2 3
f f fk k T k T k T
µ
µ
µ
= = − + − (9)
J. Ferron et al. [3] used the viscosity coefficients, k0 = 3.287, k1 = 3.064, k2 = 0.777 while the
authors considered the following modified viscosity coefficients, k0 = 3.1286, k1 = 2.4817,
k2 = 1.1605 and k3=0.3266. The polynomial equation was found out for getting improved results.
Results obtained from viscosity-temperature equation which was developed by authors’ gives good
results when compared with experimental results of J. Ferron et al. [3]. This temperature distribution
in plain journal bearing shows very slight variation between temperature obtained by authors and
temperature obtained by J. Ferron et al. [3]. At different load the computed maximum bush
temperature and pressure are nearly equal for 1500, 2000, 3000 and 4000 rpm. The authors have
found during their investigation that the developed viscosity-temperature equation gives very close
values of the maximum bush temperature when compared with the experimental results of J. Ferron
et al. [3] at all above speeds. To verify the validity of the above equations and the computer code, the

36
results from the above analysis was compared with experimental values of J. Ferron et al. [3]
bearing.
2.3 Three dimensional energy equation for temperature distribution in bearing
The solution of energy equation needs the pressure field established from solution of
Reynolds equation. It is very important to carry out a three-dimensional analysis to accurately predict
the temperature distribution in bearings. Accurate prediction of various bearing characteristics, like
temperature distribution, is very important in the design of a bearing. The heat flows inside the solid
parts, such as the bearing and the shaft, and finally dissipates in the air. The total amount of heat that
flows out by convection and conduction is equal to the total amount of heat generated. Temperature
distribution in fluid-film is given by three-dimensional energy equation. Fluid temperature has been
obtained by solving the following three-dimensional energy equation which has been modified using
thin-film approximation and changing the shape of the fluid film into a rectangular field,
22 22
2
1 ( )
TT T T ff f fh u vh u w z u D Pe ez z zh z
µ
α β α
                 
      
∂∂ ∂ ∂∂ ∂ ∂+ν + − = + +
∂ ∂ ∂ ∂ ∂ ∂
∂
(10)
The non-dimensional effective inverse Peclect number ( eP ) and Dissipation number ( eD ) are
as follows,
( ) ( )22
,
c
f j
p rp j
k
P De e
C TC c
µω
ρρ ω
= =
(11)
Values of the non-dimensional velocity components in circumferential and axial direction are
as follow,
2
1
00 00 0
1 zz zp z F d z d zu h d z
FFα µ µ µ
 
 
 
  
∂
= − + ∫∫ ∫∂
(12)
1
0
2
0 0
z zp z F d zv h d z
Fβ µ µ
 
 
 
  
∂
= −∫ ∫∂
(13)
The continuity equation is partially differentiated with respect to z to determine the non-
dimensional radial component of velocity ( w) as,
2
2
0
w u v u h
h z
z z z
z
α β α
   ∂ ∂ ∂ ∂ ∂ ∂ ∂
+ + − =   
∂ ∂ ∂∂ ∂ ∂   ∂
(14)
Integrate the above equation with finite difference method considering the following
boundary conditions,
0 at 0 and at 1
h
w z w z
α
∂
= = = =
∂
(15)
The three dimensional energy equations have been solved with the following boundary
conditions,
(i) On the fluid–journal interface ( 1)z =

37
f jT T= (16)
(ii) On the fluid–bush interface ( 0)z = ,
f bT T= (17)
2.4 Thermal analysis of heat conduction equation for Bush-Housing
Heat conduction analysis was performed to determine the bush temperatures. The Fourier
heat conduction equation in the form of non-dimensional cylindrical coordinate form has been solved
for the temperature distribution in the bush and is given below,
2 2 2
2 2 2 2
1 1
0
T T T Tb b b b
r r
r rβ α
∂ ∂ ∂ ∂
+ + + =
∂ ∂ ∂∂
(18)
Using following boundary conditions, heat conduction equation was solved.
i. On the interface of fluid–bush 1( 0, )z r R= = ,
Continuity of heat flux gives,
1| | 0
f fb
b
k TTk
r zc hr R z
  
  
      
∂∂ = −
∂ ∂= =
(19)
ii. On the outer part of the bush housing 2( )r R= , The free convection and radiation
hypothesis gives,
2
2
|
|
h RT abb T Tb ar Rkr br R
   
       
∂ =− −=∂ =
(20)
iii. On the lateral faces of the bearing ( )β λ=± ,
|
|
h RT abb T Tb akb β λ
β λ
β
   
       
=±
=±
∂ =− −
∂
(21)
iv. At the outlet edge of bearing pad, free convection of heat flow from bush to fluid in the
supply groove gives,
|
( )
e
h RfbTb T Tb skbα α
α
 
 
 
  =
∂ = − −
∂
(22)
eα = Circumferential coordinate of the outlet edge of bearing.
v. At the inlet edge of the bearing ( )iα α= and at the fluid supply point on the outer surface,
2
|r R
T Tb s
=
= (23)

38
In addition, a free convection of heat between fluid and housing has been assuming,
( )
|
h RfbTb T Tb skbi
α α α
 
 
 
 
−∂ = −
∂ =
(24)
Where iα = circumferential coordinate of the inlet edge of bearing.
2.5 Heat conduction equation for Journal
For finding the temperature distribution in journal, the following assumptions were made,
i. Conduction of heat in the axial direction.
ii. Journal temperature does not vary in radial or circumferential direction at any section.
iii. Heat flows out of the journal from its axial ends.
Hence the following steady state unidirectional heat conduction equation was used for a
journal,
2
0
2
Tjk y A qj jy
 
 
 
 
 
∂
∆ + ∆ =
∂
(25)
Where q∆ = the heat input to the element( )q y∆ ; y∆ = the length of element. Above equation
reduces to the following non-dimensional form,
2
0
2
Tj qπ
β
 
 
 
 
 
∂
+ =
∂
(26)
where q is the non-dimensional heat input to journal per unit length,
2
0
1f f
j
k T
q d
hc k z
π
α
  
  
  
   
∂
=− ∫ ∂
(27)
The above equations have been solved with the following boundary condition,
At the axial ends, i.e. β λ=± ,
|
|
h RT ajj T Tj ak j β λ
β λ
β
   
   
   = ±   = ±
∂
= − −
∂
(28)
2.6 Thermal mixing of fluid in a groove
It was not possible for the experimenters to maintain the inlet fluid temperature at a constant
value. Because of low supply pressures and high fluid viscosities, the inlet fluid temperature would
rise. Thermal mixing analysis of hot recirculating and incoming cold fluid from supply groove was
used to calculate the fluid temperature at the inlet of the groove. Energy balance equation is used to
estimate the mean temperature of the fluid in a groove.
In this work, the overall energy balance equation is expressed in terms of mean temperature, Tm,
Q T Q T Q Tm re re s s= + (29)

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
ISSN 0976 – 6359(Online), Volume 5, Issue 11, November (2014), pp.
Where reT - recirculating hot fluid,
( )
1
0
Q h u d z= ∫
Q Q Qs re= −
( )
1
0
L
Q C h u d zre = ∫
( )
1
0
LT Q C h u T d zre re f= ∫
Mean temperature mT related to the assumed temperature distribution
film at the inlet of the bearing pad as below,
( )
1
0
fT T z d zm = ∫
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6359(Online), Volume 5, Issue 11, November (2014), pp. 31-46 © IAEME
39
hot fluid, For the unit length of bearing,
(30)
(31)
(32)
(33)
related to the assumed temperature distribution
let of the bearing pad as below,
(34)
Fig. 2: Solution Scheme
© IAEME
related to the assumed temperature distribution, ( )fT z across the fluid

40
3. SOLUTION PROCEDURE
The overall solution scheme for thermohydrodynamic analysis of plain journal bearing is
depicted in Fig 2. The non dimensional coefficient of viscosity has been found out. Reynolds
equation solved by finite element method for obtaining pressure distribution in the fluid-film by
iterative technique. The negative pressure nodes were set to zero and attitude angle was modified till
convergence was achieved. Pressure and temperature fields for the initial eccentricity ratio have been
recognized. The load capacity of the journal bearing was calculated by iterative method. Values of
the fluid film velocity components were calculated in circumferential, axial and radial directions.
Coefficient of contraction of fluid-film was determined. Coefficient of contraction was assumed as
unity in positive pressure zone. The mean temperature of the fluid was calculated. By using finite
difference method three dimensional energy equation was solved for temperature distribution in
fluid-film. Heat conduction equation was solved for determination of temperature distribution in
bush housing. The above procedure was repeated till convergence was achieved. One dimensional
heat conduction equation was used for temperature distribution in journal. The journal temperature
was revised after obtaining the converged temperature for fluid and bush. The energy and Fourier
conduction equations were simultaneously solved with revised journal temperature. All the above
steps were repeated until the convergence was achieved. Using modified non dimensional viscosity-
temperature relation the non dimensional viscosity was found out and modified until convergence
was achieved. After convergence achieved the temperature of fluid, bush and journal was found. For
the next value of the eccentricity ratio once the thermohydrodynamic pressure and temperature have
been established. The data used for computation of pressure and temperature in fluid, bush and
journal were depicted in Table 1.
Table 1: Bearing dimensions, operating conditions and lubricant properties
No. of nodes in one element Node 4
Outer radius bush R2 0.1 m
Radius of journal R 0.05 m
Length of bush L 0.08 m
Length to diameter ratio (Aspect ratio) L/D 0.8
Attitude angle Φ 56°
Radial clearance (c) c 0.0029
Thermal conductivity of fluid kf 0.13 W/m °C
Thermal conductivity of bush housing kb 50 W/m °C
Thermal conductivity of journal kj 50 W/m °C
Convective heat transfer coefficient of bush hab 50 W/m2
°C
Convective heat transfer coefficient of journal haj 50 W/m2
°C
Convective heat transfer coefficient of bush housing
from solid to fluid
hfb 1500 W/m2
°C
Specific heat of lubricant Cp 2000 J/kg °C
Density of lubricant ρ 860 kg/m3
Viscosity of lubricant at 40°C µ 0.0277 N-s/m2
Journal Speed N 1500, 2000, 3000 and
4000 rpm
Reference temperature of lubricant Tr 40 °C
Ambient temperature of lubricant Ta 40 °C
Supply temperature of lubricant Ts 40 °C

41
4. RESULTS AND DISCUSSION
Numerical calculations were performed by writing a computer program in C. The non-
dimensional governing equations were discretized for numerical solution. The global iterative
scheme was used for solving these equations. A mesh discretization for fluid film and bush with 68
nodes in the circumferential direction, 16 nodes in the axial direction and 16 nodes across the film
thickness and 16 nodes across the radius of bush thickness. For thermohydrodynamic analysis of
plain journal bearing the input parameters has been taken from Table 1. The present data was
assumed for aligned plain journal bearing. It was assumed that temperature of fluid equal to
temperature of bush at the fluid–bush interface. Journal temperature is also equal to temperature fluid
at the fluid–journal interface. The condition of mixing the recirculating fluid with the supply fluid
was also considered. Fig. 3 and Fig. 4 depicts the distribution of the maximum bush temperature
obtained with different eccentricity ratio for different speeds of plain journal bearing. The
experimental results of J. Ferron et al. [3] were nearly equal to theoretical results of authors as per
the modified viscosity-temperature equation. Fig. 5 and Fig. 6 predict the circumferential
temperature distribution in the mid-plane of fluid-bush interface. Theoretical predictions and
experimental results of J. Ferron et al. [3] exhibit a similar pattern, the predicted maximum
temperature value and their locations are reasonably very close to the measured values of J. Ferron et
al. [3].
Pressure variation in mid plane of plain journal bearing for various speeds and loading
conditions were shown in the Fig. 7 and Fig. 8. In the authors developed model pressure distribution
was very close to the experimental values given by J. Ferron et al. [3]. The mean journal temperature
has been computed along axial direction. Fig. 9 depicts load versus mean journal temperature at 2000
and 4000 rpm for two different loads as 4000N and 6000N respectively. The radial temperature was
negligible in the present work. Journal temperature along axial direction of the journal varies by
about one degree for 2000 rpm and very close to the 4000 rpm at 4000 N and 6000 N loads
respectively. A theoretical result predicted by authors’ modified viscosity-temperature equation gives
good agreement as compared with published experimental results of J. Ferron et al. [3].
Fig. 3: Comparison of Experimental values of Fig. 4: Comparison of Theoretical values of
Ferron J. et al. [3] with theoretical values of Ferron J. et al. [3] with theoretical values of
predicted model for Maximum bush predicted model for Maximum bush
temperature and eccentricity temperature and eccentricity
ratio at different speeds ratio at different speeds

42
Fig, 5: Temperature distribution in mid-plane Fig. 6: Temperature distribution in mid-plane
at 4000 rpm under 6000 N Load at 2000 rpm under 4000 N load
Fig. 7: Pressure variation in mid plane Fig. 8: Pressure variation in mid plane
at 4000 rpm under 6000 N Load at 2000 rpm under 4000 N Load
Fig. 9: Variation in mean journal temperature at different loads and speeds

43
5. CONCLUSIONS
On the basis of results and discussions presented in the earlier sections, the following major
conclusions are drawn:
• The developed viscosity-temperature equation for this work is more appropriate.
• The maximum pressure is noted at minimum film thickness of fluid.
• The temperature of fluid-film increases with increase in load and speed of shaft.
• Due to thermal effects the eccentricity ratio, attitude angle and side flow also changes.
• The effect of mixing of recirculating and supply temperatures of lubricant in the groove is
quite important.
• Heat transfer from the outlet edge of the bush to fluid in the supply groove must be considered
for correctly simulating the actual conditions.
• At higher speed and heavy load, developed model of viscosity-temperature predicts accurate
values for temperature in fluid, bush and journal.
• The authors have found during their investigation that the developed equation gives very close
values of the maximum fluid and bush temperature when compared with the experimental
results of J. Ferron et al. [3] at different speeds and loads respectively.
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a plain journal bearing Comparison between theory and experiments, ASME Journal of
Lubrication Technology, 105,1983, 422–428.
[4] H. Heshmat. and O. Pinkus, Mixing inlet temperature in hydrodynamic bearings, ASME
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[5] M.M. Khonsari, A review of thermal effects in hydrodynamic bearings, Part II: journal
bearing, ASLE Transaction, 30(1), 1987, 26–33.
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bearing, Tribology International, 34, 2001, 397–405.
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compared with measurements, Proceedings of the Institution of Mechanical Engineers, Part
J: Journal of Engineering Tribology, 218, 2004, 391-399.

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[13] P.B. Kosasih and A. K.Tieu, An investigation into the thermal mixing in journal bearings,
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journal bearing groove, I Mech. E, Part J: J. Engineering Tribology Proceeding, 219, 2005,
263-274.
[16] S.S. Banwait, A Comparative Performance Analysis of Non-circular Two-lobe and Three-
lobe Journal Bearings, IE (I) I Journal-M,; 86, 2006, 202-210.
[17] U. Singh, L. Roy. and M. Sahu, Steady-state thermo-hydrodynamic analysis of cylindrical
fluid film journal bearing with an axial groove, Tribology International 41, 2008, 1135–
1144.
[18] L. Roy, Thermo-hydrodynamic performance of grooved oil journal bearing, Tribology
International, 42, 2009, 1187–1198.
[19] B. Maneshian and S.A. Gandjalikhan Nassab, Thermohydrodynamic Characteristics Of
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(2),2009, 181- 194.
[20] B. Maneshian. and S. A. Gandjalikhan Nassab, Thermohydrodynamic analysis of turbulent
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Nomenclature
jA Cross-sectional area of the journal ( 2
Rπ )
c Radial clearance, (m); /c c R=
LC Coefficient of contraction , LC is unity in positive pressure region
( ) ( )
1 1
0 0
| |L
e
C u h dz u h dz
t α
= ∫ ∫
pC Specific heat of fluid, (J/kg °C)
D Diameter of Journal, (m)

45
e
D Dissipation number
e Journal Eccentricity, (m); /e cε =
0 1
2
, ,F F
F
Non dimensional Integration functions of Viscosity
h Thickness of fluid-film,(m); /h h c=
ab
h Convective heat transfer coefficient
bush, (W/ m2 0
C)
aj
h Convective heat transfer coefficient
of journal, (W/m2 0
C)
fb
h Convective heat transfer coefficient from bush to fluid in groove,
(W/m2 0
C)
0 1
2 3
,
,
k k
k k
Coefficient of Viscosity
,k k
f b
k
j
Thermal conductivity of fluid,
bush and journal, (W/m °C)
L Length of bearing, (m)
p Pressure , sp p p= (N/ m2
)
sp Supply pressure, (N/ m2
)
e
P Peclet number,
q Heat input per unit length
Q Fluid-flow, (m3
/s)
4( c R )Q Qs jω=
r Radial coordinate; /r r R=
R Radius of journal, (m)
1 2,R R
Inner and outer radius of bush, m
1 21 2/ , /R R R R R R= =
r
T Reference temperature, (°C)
a
T Ambient temperature, (°C); /a a rT T T=
b
T Bush temperature, (°C); /b b rT T T=
fT Fluid film temperature, (°C); /T T Tf f r
=
T
j Journal temperature,(°C); /j j rT T T=
T
s Supply temperature , (°C); /s s rT T T=
t Time ; / jt t ω=
, ,u v w Fluid velocity components, in
circumferential, axial and radial
directions respectively (m/s)
( ) ( ) ( )
, ,
/ / /
u v w
u v w
R R Rj j jω ω ω
= = =
, ,x y z
Cartesian Coordinate in circumferential, axial and radial direction,
/z z h=
,j jX Z Coordinates of journal centre, (m);

46
sin , cosj jX Zε φ ε φ= = −
α Circumferential cylindrical
coordinate; x R
β Axial cylindrical coordinate; y R
ε Eccentricity ratio;
λ Aspect ratio; L D
φ Attitude angle (degrees)
µ Viscosity of fluid, (N.s/m2
);
0µ Reference viscosity of fluid,(N-s/m2
)
ρ Mass density of fluid, (kg/m3
)
jω Angular speed of the journal, (rad/s)

THERMOHYDRODYNAMIC ANALYSIS OF PLAIN JOURNAL BEARING WITH MODIFIED VISCOSITY - TEMPERATURE EQUATION

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