Analysis of thermoelastohydrodynamic performance of journal misaligned engine main bearings
CHINESE JOURNAL OF MECHANICAL ENGINEERING
Analysis of Thermoelastohydrodynamic Performance of Journal Misaligned Engine Main Bearings
BI Fengrong 0 1
SHAO Kang 0 1
LIU Changwen 0 1
WANG Xia 0 1
ZHANG Jian 0 1
0 State Key Laboratory of Engines, Tianjin University , Tianjin 300072 , China
1 WANG Xia, born in 1984, is currently a PhD candidate at State Key Laboratory of Engines, Tianjin University, China. She is currently studying the digital signal processing of engine's noise and vibration
To understand the engine main bearings' working condition is important in order to improve the performance of engine. However, thermal effects and thermal effect deformations of engine main bearings are rarely considered simultaneously in most studies. A typical finite element model is selected and the effect of thermoelastohydrodynamic(TEHD) reaction on engine main bearings is investigated. The calculated method of main bearing's thermal hydrodynamic reaction and journal misalignment effect is finite difference method, and its deformation reaction is calculated by using finite element method. The oil film pressure is solved numerically with Reynolds boundary conditions when various bearing characteristics are calculated. The whole model considers a temperature-pressure-viscosity relationship for the lubricant, surface roughness effect, and also an angular misalignment between the journal and the bearing. Numerical simulations of operation of a typical I6 diesel engine main bearing is conducted and importance of several contributing factors in mixed lubrication is discussed. The performance characteristics of journal misaligned main bearings under elastohydrodynamic(EHD) and TEHD loads of an I6 diesel engine are received, and then the journal center orbit movement, minimum oil film thickness and maximum oil film pressure of main bearings are estimated over a wide range of engine operation. The model is verified through the comparison with other present models. The TEHD performance of engine main bearings with various effects under the influences of journal misalignment is revealed, this is helpful to understand EHD and TEHD effect of misaligned engine main bearings.
main bearings; journal misaligned; oil film pressure; Reynolds equation; finite difference methods; thermoelastohydrodynamic(TEHD)
Nowadays there are more requirements for internal
combustion engines with high performance and reliability
to improve the journal bearings performance. With the
trends in automotive industry, such as higher peak cylinder
pressure, lower fuel consumption, engine downsizing and
lower level of emission, all these tasks have been becoming
a great challenge in the development of engine main
In recent years, computer simulations have gained an
increasing role in more complex simulation of technical
problems even for bigger calculation domains with the
increase of computer power. It is utmost necessary for
research on the lubricant of main bearing for internal
combustion engine. Traditional static linear finite element
modeling techniques are not able to capture the
nonlinearities and complex interactions among components
specific to internal combustion engines[
investigations have focused on the analysis of dynamically
loaded journal bearing with the purpose of emphasizing its
operating properties and performance characteristics[
VORST, et al[
], used the finite-length impedance bearing
theory to model the steady-state behavior of flexible
rotor-dynamic systems bearings. OSMAN, et al[
presented a numerical study of the performance of a
dynamically loaded finite journal plastic bearing lubricated
with a non-Newtonian of the bearing. The Reynolds
equation was solved numerically, considering three values
of the flow-behavior index and a wide range of journal
speeds, materials and clearance ratios. MA, et al[
investigated the behavior of dynamically loaded journal
bearings lubricated with non-Newtonian couple stress
fluids. And the film pressure was solved numerically with
Reynolds boundary conditions and the various bearing
characteristics were calculated. MONTAZERSADGH, et
], studied first dynamic load analysis of the crankshaft
investigated. Finite element analysis was performed to
obtain the variation of stress magnitude at critical locations
while a dynamic simulation was conducted on a crankshaft.
] used a finite element method based on rectangular
isoparametric element for evaluating the stiffness and
damping coefficients of hydrodynamic bearings which was
verified by calculated the pressure distribution of a short
bearings and dynamic coefficients. AGOSTINO, et al[
identified the journal stability threshold by using an
original approximate analytical approach for the non-steady
fluid film force and the stiffness and damping coefficients
description in the case of low loaded porous journal
bearings. ZARBANE, et al[
], presented a numerical study
of the behavior of fluid film subjected to a periodic squeeze
action which showed the effects of the frequency and the
average film thickness on the film load-carrying ant the
rupture. There were some other studies[
] of oil film
dynamic characteristics for journal bearings analysis. All
above these researches are based on journal aligned
hydrodynamic bearings. In the past two years, more and
] are considering the
thermoelastohydrodynamic(TEHD) bearing performance as
thermal effects the bearing performances.
Taking into account the couple stress effects due to the
lubricants, a modified Reynolds equation for dynamic loads
of the film pressure is derived by utilizing the finite
difference method which is capable to predict the
hydrodynamic characteristics of a thin lubricant film
subjected to a periodic squeezing between conforming
surfaces. In this paper, a dimensionless cycle simulation
model of diesel engine has been developed that can be used
to estimate the thermoelastohydrodyanmic misaligned
bearing performance in a 6-cylinder 4-stroke engine with
firing order 1-5-3-6-2-4. The pressure data obtained from
the cycle simulation of diesel engine are introduced into the
tribology model, which is a hydrodynamic lubricant
analysis between crankshaft and engine block. And then
journal center orbit, minimum oil film thickness and
maximum oil film pressure in the main bearings are derived
and presented for different engine operations when
considering thermoelastohydrodynamica and different
working conditions listed in this paper are length to radius
ratio(λ) changes, journal misalignment, and surface
Research on the behavior of engine main bearing under
static loads is not sufficient for the design optimization. It
is required to study the estimation of the dynamic load of
journal bearing while the engine runs at different speeds.
The model in this paper is a dynamically loaded journal
bearing lubricated with an incompressible couple stress
fluid. As for the analysis presented in this paper, the
following assumptions were adopted:
(2) Laminar flow;
(3) Newtonian lubricant with non-compression fluid;
(4) Flex bearing surfaces;
(5) Reynolds boundary condition;
2.1 Modified Reynolds equation
Fig. 1 shows a journal rotates with angular velocity ωj.
The radius of journal is Rj and the bearing housing radius is
Rb. The journal rotates with a constant angular velocity is
ωj while the bearing is stationary. The radial clearance C is
defined as the distance between the journal surface and the
bearing housing surface when both are concentric:
C = Rb - Rj.
Both the journal and the bearing have the same length L
in the z direction. The journal center and the bearings
housing center are not always concentric due to the applied
loads impacted the journal and its rotation. The distance
between journal center and bearing center is e. The
eccentricity ratio is ε:
where ∆h=hrough+hdef, hrough is surface roughness effect and
hdef is journal-bearing deformation effect.
The maximum oil film thickness is hmax, while the
minimum oil film thickness is hmin:
ìïïhmax = C + e = C (1+ ) + Dh,
ïïî hmin = C - e = C (1- ) + Dh.
The oil film pressure distribution in journal bearings is
described by the Reynolds equation, which is derived from
the Navier-Strokes equations for incompressible flow and
= e , Î [
h = C + e cos( - ),
And oil film thickness h at any angle θ for main bearing is
where θ and φ are illustrated in Fig. 1.
In this paper, the effect of surface roughness and
journal-bearing’s deformation ∆h was considered, then the
oil film thickness changes as
h = C + e cos( - ) + Dh,
the continuity equation under simplifying assumptions[
For a Newtonian lubricant with non-compression fluid, the
Reynolds equation under dynamic loads is written as
6 ( j +b )
¶ h+12 ¶ h
where p(z, θ, t) is the oil film pressure, ρ is the lubricant
density, Rj is the crankshaft main journal radius, h(z, θ, t) is
the oil film thickness, μ is the oil viscosity of film, and ωj,
ωb is the journal angular velocity and bearing angular
Oil film temperature plays an important part in the
dynamic performance of engine main bearing. The
lubricant dynamic viscosity μ and density ρ are all affected
with the temperature change:
= 0 exp(- (T -T0 )),
= 0 exp(1- T (T -T0 )),
where μ0 is lubricant dynamic viscosity at temperature T0,
ρ0 is lubricant density at temperature T0, β is
viscosity-temperature coefficient, αT is coefficient of
In order to apply the finite difference method in the
Reynolds equation, it is convenient to suppose the
relationships of parameters and dimensionless parameters.
With this purpose, the following assumptions of the
dimensionless parameters are proposed:
h = h = 1+ cos( - )+ Dh , z = z , p =
C C L
t = t, = L , q = 2 d
R * dt
, R = Rj » Rb ,
where ω* is the effective angular velocity, * = - 2 d
q is the dynamic parameter.
Substituting the dimensionless parameters in Eq. (7), the
Reynolds equation in Eq. (5) is converted to
¶¶ èçaeççh3 ¶¶p ø÷ö÷÷ + 12 ¶¶z èçaeççh 3 ¶¶pz ø÷ö÷÷ = 6 ¶¶h +12 ¶¶ht =
- sin + q cos .
The dimensionless Reynolds equation represents the pure
squeeze film behavior of journal bearing. Eq. (8) is solved
by the finite difference method. In order to solve the
differential Eq. (8), it is considered that atmospheric
pressure prevails at the edges of the main bearing and the
boundary conditions of the oil film pressure are
p |z =1= 0, ¶z |z =0 = 0, p ( , z ) = p ( , z + 2).
The sustentation hydrodynamic force can be calculated
integrating the pressure while the hydrodynamic pressure is
known. And the dimensionless loading-carrying capacity of
pressure over the bearing area is calculated as
Fy = ò dz ò
Fx = ò dz ò
p sin d ,
p cos d ,
where Fy , Fx is the total dimensionless force of main
bearing that along axis y and axis x.
The total dimensionless oil film force F and the
attitude angle, defined as the angle between the vertical
axis and the line that connects the centers of the journal and
the bearing housing, angle ψ is calculated by
Fy2 + Fx2 ,
= arctanaeççç Fx ÷÷ö÷÷.
çè Fy ÷ø
2.3 Journal misalignment
Journal misalignment is one of the most important faults
of journal bearings. Journal misalignment can be a
particular working bearing condition, due to the
deformations of the bearing system. Fig. 2 shows a journal
The force applied to the journal changes its position
relative to the bearing housing, modifying the eccentricity
ratio and the hydrodynamic force until equilibrium is
reached. An equilibrium eccentricity ratio can then be
defined as the value of ε that generates a hydrodynamic
total force in the oil film with the same modulus of the
external applied force[
2.2 Energy equations
The thermal changes behavior of oil film is determined
from the energy equation when heat conduction in the
circumferential and axial are all neglected.
c ççççèae¶¶Tt + u ¶T + v ¶T + w ¶¶Tz ø÷÷÷÷ö =
k ¶¶2yT2 + êêêéçèçççae¶¶uy ø÷÷÷÷ö2 +çççèçae¶¶wyø÷÷÷÷ö2 úúúù .
Main bearing temperature can be obtained by solving the
transient heat equation which can be reduced for the simple
c ¶¶Tt = k èaeçççç¶¶2xT2 + ¶¶2zT2 ÷÷÷÷øö.
misalignment bearing. The main difference between
misaligned bearing and aligned bearing is oil film thickness
between journal and bearing. The dimensionless oil film
thickness of this misaligned bearing can be calculated[
h = tan ççz
÷÷cos( - -0 ) C +
1+ 0 cos( -0 )+ r + d ,
where ε0 is eccentricity of aligned bearing and ε’ is the
misaligned journal bearing. α is the angle between the
journal rear center-line projection and eccentricity vector. Λ
is the angle of journal misalignment, which means the
included angle between journal center line and bearing
center line, the bearing center line means Z axis. The
included angle between journal center line and axis X and
axis Y is defined as Λx and Λy. And the changes of these
angles are Ax and Ay. Φ0 is the angle between the journal
vertical center-line and X axis. δr is main bearing’s surface
roughness. d is main bearing’s deformation.
2.4 Numerical solution method
The theoretical aspects of the algorithm were already
presented. The next section will explain numerical solution
methods of the simulation. The centered finite difference
method is used in the governing the Reynolds equation,
which was used in the oil film pressure. All these programs
will be executed in MATLAB.
The centered finite difference method that is used in the
governing equations was integrated by iterative techniques.
Derivatives in Reynolds equation were expressed by suing
second order, centered finite differences[
ï (i, j) »
ïïï¶p (i, j) »
ïï¶ 2 (i, j) »
ïîï ¶z2 (i, j) »
p(i +1, j)- p(i -1, j),
p(i, j +1)- p(i, j -1),
p(i +1, j)- 2 p(i, j)+ p(i -1, j),
p(i, j +1)- 2 p(i, j)+ p(i, j -1)
p(i, j) =
Based on the central difference method for derivatives,
Eq. (8) changes as
A • p(i+1, j) + B • p(i-1, j) +C • p(i, j+1) + D • p(i, j-1) - E
An equally spaced computational grid is covered in this
paper. The numbers of internals in the axial and in the
radial direction size is 400×40 which gives a rapid rate of
convergence and suitable computer working time. And a
linear equation system which is in the same number of
unknown pressure was determined when boundary
condition was determined. The iterative procedure is
terminated when the difference tolerance is
(k+1) - pi(,kj)
å å pi, j
å å pi, j
Fig. 3 shows the general solution flowchart of main
journal bearing that is used in this study. It gives a general
overview of the algorithm and summarizes all steps.
In order to test the validity of present analysis, a
4-cylinder 4-stroke engine was firstly present, and the test
data of structural parameters, etc. of crankshaft and bearing
given in SUN, et al[
], were used. Figs. 4 and 5 show the
comparison of the maximum film pressure of #1 connecting
rod bearing and #4 main bearing in an engine cycle under
dynamic loads with rotational speed 2600 r/min. In Figs. 4
and 5, the maximum oil film pressure of #1 big end bearing
and #4 main bearing are calculated in good agreement with
SUN, et al[
]. The difference in the maximum oil film
pressure can be attributed to different gas pressures and
different main parts properties.
These two comparisons validate the application of the
proposed theory and model for the rest part of the presented
results. It also confirms that the method used in this paper
is agreeable with the fact and it can be used in other
realistic engine bearings analysis. And the accuracy of the
present lubrication analysis based on Reynolds equation is
General solution flowchart of engine main journal bearing
Results and Discussions
3.1 Gas forces and main bearing load
Forces in a diesel engine may be divided into inertia
forces and pressure forces. Inertia forces are divided into
two objects: rotating inertia forces and reciprocating inertia
forces. There are two main forces that engine block is
affected in its work, one is gas force in cylinder, the other is
inertia force and moment that is made by moving parts,
such as piston slap force and main bearing force. Gas
forces in cylinders affects piston head, cylinder head and on
side wall of the cylinder. The gas forces are transmitted to
the crankshaft through the piston and connecting rod. In
this study, cylinder pressure curves for 7.0 L diesel engine
studied under full load at 2300 r/min over the cycle
simulation corresponding to Fig. 6. As shown in Fig. 6, the
highest pressure is 17.97 MPa and the fire order is
Gas pressure at 2300 r/min
The effect of load on pressure in a cylinder could be
estimated with the cycle simulation. The pressure in the
cylinder was introduced into the lubrication model of the
engine main bearings[
]. There are two different loads
acting on the main bearings. One is the inertia of rotating
components that applies forces to the crankshaft and this
force increases with the engine speed up. The other load is
source force applied to the crankshaft due to the gas
combustion in the cylinder bore. Fig. 7 shows loads on the
#2 main bearing over the engine cycle. There the Y and Z
are the hydrodynamic forces in horizontal and vertical
Fig. 8 shows the comparison of journal center orbits in
different λ of #2 main journal bearing. As shown, for
different λ, the orbits of journal center are similar in shape.
With the increase of λ, the journal center orbit gradually
shrinks to the center of the journal which indicates that λ
benefits to the increase of the oil film thickness in the
dynamically loaded bearings. The minimum oil film
thickness hmin and the maximum oil film pressure pmax in
different λ are showed in Fig. 9 and Fig. 10 respectively.
The results show that lubricant is affected by λ under
compression and expansion stokes. Fig. 9 presents the
comparison of the minimum oil film thickness of #2 main
bearing by considering elasohydrodynamic effect and
TEHD effect. The minimum oil film thickness increases in
these three different models when considering thermo
effect. And also the minimum oil film thickness increases
with the increase of λ. As indicated in Fig. 10, under the
dynamic loads the maximum oil film pressure is decreased
while λ is enhanced. The thermo affects the maximum oil
film pressure and makes it decreases. All these trends are
similar with FATU’s, et al[
3.2 Length to radius effect
Considering mathematical model, the governing
parameters are eccentricity ratio(ε), length to radius ratio(λ).
In order to accomplish this simulation, the configuration
parameters of the main bearings are modeled as λ=0.75,
λ=1.00, λ=1.25, and main journal bearing variables used in
this paper are listed in Table 1.
3.3 Surface roughness effect
Bearing surfaces, even after the most careful polishing,
will still be rough at a microscopic scale[
]. Based on
], the RMS surface roughness of main journal
bearing is considered as 0.15 μm. And the typical surface
topography digitized from the ground main journal surface
is shown in Fig. 11. As shown in Fig. 11, the numerical
surface roughness is random generated by using MATLAB.
The number of surface nodes is 400×40, which was
corresponded to the dimension of the oil film’s distribution.
The roughness size is included in the ∆h, which was defined
in Eqs. (3b) and (4).
Fig. 12 shows the comparison of journal center orbits by
considering smooth surface and rough surface of #2 main
journal bearing under EHD and TEHD working conditions.
As shown in this figure, the shape of journal center orbit
expands with rough surface effect. And when considering
the thermal effect, the shape of journal center orbit shrinks.
Fig. 13 and Fig. 14 shows the comparisons of minimum oil
film thickness and maximum oil film pressure respectively.
When consider surface roughness effect, the minimum oil
film thickness decreases and maximum oil film pressure
increases in both EHD and TEHD working conditions. And
also, when considering the thermal effect, the minimum oil
film thickness is larger than that without thermal effect.
And the maximum oil film pressure is smaller than that
without thermal effect.
3.4 Journal misalignment effect
Misalignment is one of the most important faults of main
journal bearing. With the deformation of the journal and
bearing, misalignment of main bearing is inevitable. Figs.
1517 show the effect of journal misaligned angle with and
without considering thermal effect. In these figures, Ax
means the included angle changes between journal center
line with the positive of x axis and Ay means the angle
changes between journal center line with y axis positive.
And the original journal center line coaxial with bearing
center line. Ax=0.0°, Ay=0.0° means a center line aligned
bearing. Fig. 15 gives journal center orbit changes with a
variety of the misaligned angle. It is shown that with the
increase of misaligned angle, the shape of journal center
orbit expands. When consider thermal effect, the orbit
outline is smaller than the non-thermal effect journal. Fig.
16 shows the minimum oil film thickness of main bearing
#2 in different misaligned angle. With the increase of
misalign angle, the minimum oil film thickness increase
while the minimum position change a lot. When the journal
misaligned angle Ax=0.0°, Ay=0.0°, the curve of journal
center orbit, minimum oil film thickness and maximum oil
film pressure are all the same with Figs. 1214, while
considering surface roughness. Fig. 17 shows the maximum
oil film pressure in a working cycling. The trends of
maximum oil film pressure are almost in the same way.
And the maximum oil film pressure increased with the
increase of the misaligned angle. The lower pressure can be
got when thermal effect is considered. The different
between them are almost 2 MPa.
Fig. 15. Comparison of journal center orbit of #2
main bearing in different journal misaligned angle
(1) For dynamically loaded of journal bearing lubricated
with nonlinear fluid, the influence of λ, surface roughness
and misaligned angle are significant apparently. With the
increase of λ, the minimum oil film thickness increases, the
maximum oil film pressure decreases. With the increase of
surface roughness, the minimum oil film thickness and
maximum oil film are all decreased. With the increase of
misaligned angle, the minimum oil film thickness and
maximum oil film are all increased.
(2) TEHD effect should be considered in bearing
performance calculation because it can decrease the
minimum oil film thickness and maximum oil film pressure
than that calculated with elastohydrodynamic effect.
(3) Pressure in the cylinder over the engine cycle is
introduced into the hydrodynamic lubrication analysis of
engine main bearing. The journal center orbits that occurs a
variety of phenomenon, the bearing is driven by a
dynamically load. And all full hydrodynamic model of the
main bearing should be considered by the realistic orbit
(4) Bearing performance calculated by using the finite
difference method is a simple convenient, time saving, and
high precision method in the calculate engine main
bearings. And the model can also be used in analysis of
other compressors and reciprocating engines with transient
load which is supported by bearings.
ZHANG Jian, born in 1983, is currently a PhD candidate at State
Key Laboratory of Engines, Tianjin University, China. He is
currently studying the engine vibration signal processing.
 BELOIU D M. Modeling and analysis of powertrain NVH[G] . SAE Technical Paper , 2012 - 01 -0888.
 PANDA S , MISHRA D. A multi-objective optimum design of dynamically loaded journal bearing for a prescribed π extent film[G] . SAE Technical Paper , 2009 - 01 -1679.
 VAN DE VORST E L B , FEY R H B, DE KRAKER A , et al. Steady-state behaviour of flexible rotordynamic systems with oil journal bearings [J]. Nonlinear Dynamics , 1996 , 11 ( 3 ): 295 - 313 .
 OSMAN T A , NADA G S , SAFAR Z S. Different magnetic models in the design of hydrodynamic journal bearings lubricated with non-Newtonian ferrofluid [J]. Tribology Letters , 2003 , 14 ( 3 ): 211 - 223 .
 MA Y Y, WANG W H , CHENG X H. A study of dynamically loaded journal bearings lubricated with non-Newtonian couple stress fluids [J]. Tribology Letters , 2004 , 17 ( 1 ): 69 - 74 .
 MONTAZERSADGH F H , FATEMI A. Dynamic load and stress analysis of a crankshaft[G] . SAE Technical Paper , 2007 - 01 -0258.
 TANG B. Computing the main journal bearings dynamic coefficients in a six-cylinder in-line diesel engine[G] . SAE Technical Paper , 2007 - 01 - 1968 .
 D 'AGOSTINO V , RUGGIERO A , SENATORE A. Unsteady oil film forces in porous bearings: analysis of permeability effect on the rotor linear stability[J] . Meccanica , 2008 , 44 ( 2 ): 207 - 214 .
 ZARBANE K , ZEGHLOUL T , HAJJAM M. A numerical study of lubricant film behaviour subject to periodic loading[J] . Tribology International , 2011 , 44 ( 12 ): 1659 - 1667 .
 EBRAT O , MOURELAOS Z P , VLAHOPOULOS N , et al. Oil film dynamic characteristics for journal bearing elastohydrodynamic analysis based on a finite difference formulation[G] . SAE Technical Paper , 2003 - 01 -1669.
 CHENG M , MENG G , JING J P. Non-linear dynamics of a rotor-bearing-seal system[J] . Archive of Applied Mechanics , 2006 , 76 ( 3 ): 215 - 227 .
 SHEEN Y T , LIU Y H. A quantified index for bearing vibration analysis based on the resonance modes of mechanical system[J] . Journal of Intelligent Manufacturing , 2009 , 23 ( 2 ): 189 - 203 .
 EI-MARHOMY A A. Dynamics and stability of elastic shaft-bearing systems with nonlinear bearing parameters [J]. Heat and Mass Transfer , 1999 , 35 ( 4 ): 334 - 344 .
 KURKA P R G , IZUKA J H, PAULINO K L G. Dynamic loads of reciprocating compressors with flexible bearings[J] . Mechanism and Machine Theory , 2012 , 52 : 130 - 143 .
 CRUZ R F D , GALLI L A F. Comparison of hydrodynamic and elastohydrodynamic simulation applied to journal bearings[G] . SAE Technical Paper , 2010 - 36 -0360.
 SUN J , ZHAO X Y , WANG H . Lubrication Analysis of crankshaft bearing considering crankshaft deformation[G] . SAE Technical Paper , 2011 - 01 -0613.
 ZHANG Z S , DAI X D, XIE Y B. Thermoelastohydrodynamic behavior of misaligned plain journal bearings[J] . Proceedings of the Institution of Mechanical Engineers , Part C : Institution of Mechanical Engineers Science, 2013 , 227 ( 11 ): 2582 - 2599 .
 ZHAO X Y , SUN J , WANG C M , et al. Study on thermoelastohydrodynamic performance of bearing with surface roughness considering shaft deformation under load in shaft-bearing system[J] . Industrial Lubrication and Tribology , 2013 , 65 ( 2 ): 119 - 128 .
 PINKUS O , STTERNLICHT B . Theory of hydrodynamic lubrication[M]. McGraw Hill Inc ., 1961 .
 SALLES B , BITTENCOURT M L , C R UZ R , et al. Radial surface bearing optimization for internal combustion engines[G] . SAE Technical Paper , 2009 - 36 -0191.
 SUN J , GUI C L. Hydrodynamic lubrication analysis of journal bearing considering misalignment caused by shaft deformation[J] . Tribology International , 2004 , 37 ( 10 ): 841 - 848 .
 DURAK E , KURBANOĞLU C , BIYIKLIOĞLU A , et al. Measurement of friction force and effects of oil fortifier in engine journal bearings under dynamic loading conditions [J]. Tribology International , 2003 , 36 ( 8 ): 599 - 607 .
 SUN J , GUI C L. Effect of lubrication status of bearing on crankshaft strength[J] . Journal of Tribology-Transactions of the ASME , 2007 , 129 ( 4 ): 887 - 894 .
 OZASA T , NIIZEKI M , SAKURAI S , et al. Lubrication analysis of a con-rod bearing using a cycle simulation of gasoline engines with a/f variation[G] . SAE Technical Paper , 2011 - 01 -2118.
 FATU A , HAJJAM M , BONNEAU D . A new model of thermoelastohydrodynamic lubrication in dynamically loaded journal bearings[J] . Journal of Tribology-Transactions of the ASME , 2006 , 128 ( 1 ): 85 - 95 .
 JAGADEESHA K M , NAGARAJU T , SHARMA S C , et al. 3D surface roughness effects on transient non-newtonian response of dynamically loaded journal bearings [J]. Tribology Transactions , 2012 , 55 ( 1 ): 32 - 42 .
 LEOPOLD J. Surface quality control using biocomputational algorithms [J]. Journal of Intelligent Manufacturing , 1998 , 9 : 377 - 382 .
 DENKENA B , HENNING H . Multicriteria dimensioning of hardfinishing operations regarding cross-process interdependencies[J] . Journal of Intelligent Manufacturing , 2010 , 23 ( 6 ): 2333 - 2342 .
Biographical notes BI Fengrong, born in 1965, is currently a professor at Tianjin University, China. He received his PhD degree from Tianjin University, China, in 2003 . His research interests include engine noise and vibration control, automobile dynamics, etc .
Tel : + 86 - 13802167153 ; E-mail: SHAO Kang, born in 1981, is currently a PhD candidate at State Key Laboratory of Engines, Tianjin University, China. He received his master degree from Tianjin University, China, in 2009 . His research interests include engine crankshaft dynamic .
Tel : + 86 - 15822457519 ; E-mail: kangshao1981@tju .edu.cn