891

Theoretical evaluation of the e
ects of crank o
set on

the reduction of engine friction

Myung-Rae Cho1, Dae-Yoon Oh1, Tae-Seon Moon2* and Dong-Chul Han2

1Gasoline Engine Test Team, Hyundai Motor Company, Kyunggi-Do, South Korea
2School of Aerospace and Mechanical Engineering, Seoul National University, Seoul, South Korea

Abstract: This study discusses the e
ects of crankshaft o
sets to the piston thrust side on engine
friction. An analytical model to interpret some key friction parts of an engine, such as crankshaft
bearings, pistons and piston rings, is considered, and the e
ects of a crankshaft o
set on the moving
parts is calculated using numerical analysis. Analytical results show that the crankshaft o
set has
some in
uence mainly on the side force upon the piston and e
ects variation in the piston sliding
speed. The crankshaft o
set can reduce signicantly friction loss of the piston skirt, whereas friction
loss in other parts is negligible. The optimum o
set to minimize skirt friction loss depends on the
operating conditions. Upon calculation and measurement it is determined that reduction in friction
loss occurs mainly at low engine speed and low engine load. When the speed and load increase,
benet is conned to the lowest o
sets, and at higher o
sets the friction increases. Analytical and
experimental results indicate that crank o
set is e
ective in reducing engine friction and improving
fuel economy in the low and medium engine speed region.

Keywords: crankshaft, o
set, friction, side force, piston skirt, fuel economy

NOTATION eb radial velocity of the piston top

t
E Young’s modulus
a distance from the top of the skirt to the F total normal force in the skirt
pin F connecting rod bearing force
bx,y
A bearing surface area F asperity contact normal force
c
A real contact area F connecting rod force
c con
b F total friction force
distance from the top of the skirt to the f
F asperity contact friction force
centre of gravity fc
F hydrodynamic friction force
b
p
ring width fh
F combustion gas force
B bearing width gas
F hydrodynamic normal force in the skirt
C clearance between the skirt and the h
F hydrodynamic force of the ring
cylinder oil
F inertia force due to the pin mass in the
C distance between the centre of gravity pinx
g x direction
and the wrist pin
F inertia force due to the pin mass in the
C crank o
set piny
o y direction
C distance between the wrist pin and the
p F inertia force due to the piston mass in
geometrical centre of the piston pisx
the x direction
C radial clearance of the engine bearing
R F inertia force due to the piston mass in
e eccentric length of the piston bottom pisy
b the y direction
e eccentric length of the piston top
t F total ring force
eb radial velocity of the piston bottom pr
b F f reaction force of the bearing
r,
h nominal lm thickness
The MS was received on 21 January 2003 and was accepted after revision h minimum oil lm thickness
m
for publication on 30 May 2003. H dimensionless oil lm thickness =h /s
* Corresponding author: School of Aerospace and Mechanical I piston moment of inertia
Engineering, Seoul National University, San 56-1, Shillim-Dong, pis
Kwanak-Gu, Seoul, 1510750, South Korea. l connecting rod length
Email: moon_sun@amed.snu.ac.kr L piston skirt length
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892 MYUNG-RAE CHO, DAE-YOON OH, TAE-SEON MOON AND DONG-CHUL HAN

m equivalent mass of the crank journal high-eciency and low fuel consumption engine. Many
j
and pin researchers are interested not only in improving engine
m wrist pin mass performance but also in reducing emissions as a result of
pin
m piston skirt mass better fuel consumption eciency using gasoline direct
pis
M total moment about the wrist pin injection (GDI ), variable valve timing ( VVT ), variable
M asperity contact moment valve lift ( VVL) and other technologies. Reducing friction
c
M total friction moment loss, which causes about 5 per cent of total power loss in
f
M friction moment due to asperity contact the engine, is another area receiving much attention with
fc
M friction moment due to hydrodynamics a view to improving fuel consumption [1–3]. Reducing
fh
M hydrodynamic moment friction loss would improve considerably mechanical
h
M inertia moment of the piston skirt eciency. It is reported that a 10 per cent reduction in
pis
M rotating mass of the crankshaft engine friction would improve fuel economy by 1–1.5 per
r
p hydrodynamic pressure cent at full load [4].
p back pressure in the ring groove All friction losses in the engine are generated in the
b
p ring tension valvetrain, the piston assembly, the crankshaft and other
TE
P asperity contact pressure moving parts. Among these, the friction loss in the piston
c
r crank radius assembly is up to 40–65 per cent [5], of which the loss in
c
R nominal radius of the piston skirt the piston skirt is about 40–50 per cent. Recently, a crank
t time o
set technology was proposed to reduce friction loss in
U sliding speed the piston assembly [6 ]. Only a few studies, however, have
W external force in the bearing focused on the crank o
set, and the friction reduction has
= F2 +F 2 not been thoroughly studied and established thus far.
bx by
Ÿ piston skirt acceleration Shinichi et al. [7] reported that, when a crank o
set is
applied, fuel economy is improved by 3 per cent at low
a piston skirt bearing angle engine speed and low engine load, and there is an optimum
b connecting rod angle point to maximize the o
set e
ect. Nakayama et al. [6 ]
b asperity radius of curvature
r conrm the o
set e
ect by a
oating liner and explain that
e eccentricity in the bearing this e
ect is due to the piston side force and sliding speed.
e eccentricity of the piston bottom
b They conclude, however, that it is very hard to apply this
e eccentricity of the piston top
t technique to mass production of engines.
eb radial velocity of the piston bottom
b This study sets up a useful model to analyse lubrication
eb radial velocity of the piston top
t and the friction characteristics of the engine bearing, the
g oil viscosity piston ring and the piston to examine the e
ect of crank
h crank angle o
set on reduction in friction. The results of this study will
m asperity density be helpful in developing a crank o
set engine.
m boundary friction coecient
f
s composite r.m.s. roughness = s2 +s2
1 2
t hydrodynamic component of the shear
stress 2 THEORETICAL MODEL
w attitude angle of the bearing
w ,w ,w shear stress factor 2.1 Equations of motion
f fp fs
w shear
ow factor
s Figure 1 shows a schematic diagram of the crank o
set
w ,w pressure
ow factor
x y engine. In such an engine the crankshaft centre is dis-
Q, h̃ bearing angular coordinate
v rotational speed placed to the piston thrust side from the cylinder bore.
The amount of o
set chosen is within a range ensuring
that the rotation of the crankshaft is not disturbed by
the cylinder block. With application of the o
set, it is
1 INTRODUCTION
necessary to adjust the connecting rod length and the
crank radius to t the combustion chamber volume and
In recent years, as the regulations concerned with emis- compression ratio.
sions, such as CO regulation in Europe and US Federal The piston sliding speed and the acceleration with an
2
regulations in North America, have become more severe o
set are dened as follows
and market demand for low fuel consumption vehicles has
increased, the ecient consumption of fuel has become Yb =r sin h +r vM cos h (l2
M2)Õ 1/2 (1)
c c
one of the most important factors for the automotive
Ÿ =r v2 cos h +(r vM cos h )2(l2
M2)Õ3/2
industry. Among e
orts to improve the fuel economy in c c
vehicles, much research has been carried out to develop a +{(r v cos h )2
r v2M sin h }(l2
M2)Õ0.5 (2)
c c
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 THEORETICAL EVALUATION OF THE EFFECTS OF CRANK OFFSET 893

Fig. 1 Schematic diagram of piston–crankshaft assembly with

crank o
set

where
M =r sin h +C
C (3)
c p o
The change in piston acceleration with the o
set a
ects
the piston inertial force and the load on the piston pin
and the crankpin. These changes in load and speed a
ect
the dynamics and lubrication characteristics of the
engine moving parts. Figure 2 shows analytical models
for obtaining the equation of motion for each moving
part of the engine.
In addition to the primary axial motion of the piston,
there is also a secondary lateral and rotational motion
within the bore. The lateral motion proceeds transversely
in the bore and the rotational motion is around the wrist
pin axis.
The governing equation for the dynamic motion of
the piston from Fig. 2a can be obtained as follows [8–10]
Fig. 2 Dynamic modelling of engine moving parts

C A B A B
D
a b a b
m 1
+m 1
m +m
pin L pis L pin L pis L
lm and asperity contact pressure by the surface

A B
I b b I roughness.
pis +m (a
b) 1
m (a
b)
pis
L pis L pis L L As shown in Fig. 2b, the journal movement in the
engine bearing can be expressed as non-linear equilib-

GH
ë rium equations for the radial and circumferential
× t
ë directions as follows [11].
b
m C [ë
ewb 2]=F +W cos w
C D
F
(F +F +F +F ) tan w j R r
(5)
= f gas pisy piny (4)
M +M +F C
F C m C [eẅ +2ewb ]=Ff
W sin w (6)
f gas p pisy g j R
In equation (4), reaction forces, F, F , M and M can In equations ( 5) and (6), the reaction forces of the oil
f f
be calculated using hydrodynamic pressure by the oil lm, F and Ff , can be derived by integrating the oil lm
r
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894 MYUNG-RAE CHO, DAE-YOON OH, TAE-SEON MOON AND DONG-CHUL HAN

pressure. Here, W is the load working upon the con- The reaction forces in equations (4) to (7) can be
necting rod and the main bearing. The load on the calculated from the oil lm pressure and the contact
connecting rod can be obtained from the combustion pressure as follows:
pressure and the inertial force of the reciprocating mass
piston skirt
of the connecting rod. To calculate the load on the main
bearing, however, some statically indeterminate method F =F +F , M =M +M (11)
h c h c
is needed in which the crankshaft is supported by several
bearings, but such calculation is very dicult. To sim-
plify the model, a statically determinate method is used
F =R
h PP p cos(h̃
a ) dh̃ dy (12)

to calculate the load applied to each main bearing [12]. A

PP
In the piston ring pack, the pressure of the oil lm
M =R p(a
y) cos (h̃
a ) dh̃ dy (13)
and the asperity contact pressure are in balance with the h
ring tension and the ring back pressure. Thus, the load A

PP
equilibrium equation of the piston ring becomes [13, 14]
F =R P cos(h̃
a ) dh̃ dy (14)

A B
dh c c
F h , =F +F
2ðRb ( p +p )=0 (7)
pr m dt oil c p TE b A
With such an equilibrium equation for each moving
part, the reaction force by the oil lm and the surface
M =R
c PP P (a
y) cos(h̃
a ) dh̃ dy
c
(15)

roughness can be calculated using hydrodynamic and A

boundary lubrication theory, as explained below. engine bearing

2.2 Lubrication and friction analysis

F=
r PP p cos Q dQ dz (16)

A
The governing equation for lubrication analysis used in
this study is an average Reynolds equation as follows
[15, 16 ]
Ff =
PP p sin Q dQ dz (17)

A B A B
d w h3 dp d w h3 dp
x + y piston ring
dx g dx dy g dy

P
bp
dh¯ dh¯ F =2ðR p dx (18)
A B
dw
t +6s s +12 t oil
=6|U| (8) 0
dy dy dt

P
bp
In order to apply this equation to each engine part, it is F =2ðR P dx (19)
c c
assumed that the engine bearing works in the fully 0
hydrodynamic lubrication area and the piston ring and Lastly, the total friction force in each moving system is
skirt work in the mixed lubrication area. Therefore, the dened as the sum of viscous friction and boundary fric-

ow factor for surface roughness in equation (8) is tion, the shearing force and the friction force and the
ignored in engine bearing analysis. Because the ring friction moment. Only viscous friction is considered for
width of the piston ring pack compared with the ring the engine bearing
h¯ qP
length of the circumference is very short, only the press-
mU
ure gradient along the ring circumference is considered t =
¯ [w +w ]+w h (20)
as one-dimensional analysis. Oil starvation of the ring h h f fs fp 2 qy

PP PP
pack is not considered in this study.
In equation (8), to calculate oil lm pressure, use is F= t dA+m P dA (21)
f h f c c
made of the conventional Reynolds boundary condition.

PP PP
Oil lm pressure is calculated using a nite di
erence
method and then iterative calculation. M= t ã dA +m P ã dA (22)
f h f c c
However, to calculate the contact pressure with sur-
face roughness, use is made of Greenwood and Tripp’s Table 1 shows specications and input variables of the
[17] asperity contact theory as follows test engine used for numerical analysis.

8 ã2
S
s
P (H )= ð ( mb s)2E F (H ) (9)
c 15 r b 2.5 2.3 Numerical analysis

P
1 2 Oil lm thickness and the friction of each moving part
F (H )= (s
H )n eÕse/2 ds (10)
n ã2ð are calculated as follows:
H
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 THEORETICAL EVALUATION OF THE EFFECTS OF CRANK OFFSET 895

1. Assume the initial position of the journal centre, the

piston ring and the skirt.
2. Calculate the oil lm thickness and then decide its

ow factors.
3. Solve equation (8) using direct integration or the
alternative directing implicit (ADI ) iterative method,
and obtain the pressure distribution of the oil lm.
The contact pressure is calculated using equation (9).
4. Calculate the oil lm reaction force and the asperity
contact load by integrating the oil lm pressure and
contact pressure [equations (11) to (22)].
5. Calculate the new journal centre and the new position
of the piston ring and the skirt using the fourth-order
Runge–Kutta method [equations (4) to ( 6)] or the
Newton–Raphson method [equation ( 7)]. Repeat the
above steps until the position or the oil lm thickness
converges during an entire engine cycle.

3 RESULTS AND DISCUSSION

Figure 3 shows the variation in the side force working

upon the piston as a result of the crank o
set under full
engine load. Because of the applied crank o
set, the side
force working in the piston thrust direction decreases to
an extent that increases with increase in o
set magni-
tude. Because of the crank o
set, however, the side force
to the antithrust side increases. The mean side force vari-
ation, depending on the o
set magnitude at each engine
speed, is shown in Fig. 4. At each engine speed it is
proved that there is an o
set magnitude that minimizes
the mean side forces. When the engine speed increases,
the o
set magnitude at which the mean side force is
minimal tends to decrease, and the o
set has a good
e
ect on reduction in the mean side force at low engine
speed. Considering that the secondary motion of the
piston skirt is a
ected by the side force working upon
the piston, it is expected that the mean side force
reduction by o
set would be e
ective in reducing friction
in the piston skirt. Fig. 3 Calculated results of side force variation at full
Table 2 shows analytical results of the maximum and engine load
mean load working upon each engine bearing. It shows
that, even though the side force is reduced by the o
set, shows the variation in the piston sliding speed by apply-
the load carried to the engine bearing does not change ing o
set. In the range from
90 to 90° the sliding speed
considerably. The load carried to the engine bearing is decreases, and therefore the viscous friction generated at
determined from the vertical load by the combustion gas the piston ring and the piston skirt decreases. In other
pressure and the side force carried on the piston pin. ranges, the sliding speed increases and consequently the
Because the side force working upon the pin is approxi- viscous friction increases as well. Therefore, it is expected
mately 10 per cent of the vertical force by the combustion that the e
ect of sliding speed variation is counterbal-
pressure, the side force variation does not a
ect the load anced and has little impact on the friction loss of the
carried on the engine bearing very much. Because of the piston ring. This suggestion can be veried by analytical
negligible variation in the bearing load, there is little examination of the friction loss in the piston ring pack
variation in the minimum oil lm thickness and conse- shown in Fig. 7.
quently in the friction torque created on the engine bear- Figure 8 shows analytical results of the friction loss in
ing as well. This phenomenon is shown in Fig. 5. the piston skirt with the crank o
set. The friction loss
In addition to the side force variation, there is a piston tends to decrease until the o
set reaches a certain point
sliding speed variation because of the o
set. Figure 6 and then increases again. The secondary motion of the
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896 MYUNG-RAE CHO, DAE-YOON OH, TAE-SEON MOON AND DONG-CHUL HAN

Fig. 4 E
ect of crank o
set on the mean side force at full Fig. 5 E
ect of crank o
set on the mean friction torque in
engine load engine bearings at full engine load

Table 1 Specication of test engine and input

parameters

Engine type L4/1.5L

Bore ×stroke (mm) 75.5×83.5
Valve type Direct, HLA
Working oil 7.5W30
Oil supply temperature (°C ) 90
Piston mass (kg) 0.305
Total ring tension (N ) 50
Ring width (mm) 1.5/1.5/3.0
Crank journal and pin diameter (mm) 50/45
Crank journal and pin width (mm) 18/16
Con-rod mass (kg) 0.450
Composite surface roughness (ím) 0.1
Product mb ó 0.05
r
Ratio s/b 0.001
r
Boundary friction coecient 0.05

Table 2 Calculated results of maximum and mean bearing

force at 2000 r/min and full load Fig. 6 E
ect of crank o
set on the piston sliding speed at
2000 r/min
Maximum and mean load (kN )
O
set
(mm) Con-rod Main 1 Main 2 Main 3

0 18.0/2.85 9.12/1.34 9.59/2.56 8.99/2.53

5 17.9/2.84 9.08/1.33 9.56/2.55 8.94/2.52
9 17.8/2.83 9.05/1.33 9.54/2.55 8.91/2.52
12 17.8/2.83 9.04/1.33 9.53/2.55 8.90/2.52
15 17.8/2.83 9.03/1.33 9.52/2.55 8.89/2.52
20 17.7/2.84 9.03/1.33 9.52/2.56 8.88/2.53
25 17.8/2.84 9.04/1.34 9.54/2.57 8.89/2.53

piston generally determines the friction loss in the piston

skirt, and the side force working upon the piston mainly
a
ects this motion. Therefore, because of the side force
reduction due to the o
set, the friction loss in the piston
skirt decreases as well. At low engine speed the friction
loss reaches a minimum around an o
set of 15–20 mm.
However, the o
set magnitude at which the friction loss
is minimized gradually decreases with increase in engine
speed. This trend is similar to the mean side force Fig. 7 E
ect of crank o
set on the mean power loss of the
variation shown in Fig. 4. piston ring pack at full engine load
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 THEORETICAL EVALUATION OF THE EFFECTS OF CRANK OFFSET 897

Fig. 8 E
ect of crank o
set on the mean power loss of the

piston skirt

Figure 9 shows the rate of friction reduction in the

piston skirt with the magnitude of the o
set at each
engine speed. It can be seen that the optimum magnitude
of o
set to maximize the reduction depends upon the
operating condition. The friction reduction e
ect is great
at low speed and part load. It decreases, however, when
the engine speed and the load increase. Under part load Fig. 9 Rate of reduction in skirt friction with crank o
set,
expressed as a percentage of the maximum modulus of
the reduction in skirt friction is maximized at an o
set
the rate
of 15–20 mm, but under full load it is maximized
at 12–15 mm. When the engine speed increases, the
reduction in friction is greater at a smaller o
set.
Figure 10 shows comparative results of the expected trend between the experimental and the calculated
pure mechanical friction loss, and measured motoring results is caused by consideration of pumping and
friction loss, including the pumping loss, with and auxiliary system loss. The calculations did not include
without crank o
set. The expected mechanical friction the e
ect of pumping and auxiliary system loss. From
loss includes the friction loss of the valvetrain and the expected result in Fig. 10, the o
set engine shows
auxiliary system. The di
erence in magnitude and lower engine friction than the conventional engine
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898 MYUNG-RAE CHO, DAE-YOON OH, TAE-SEON MOON AND DONG-CHUL HAN

REFERENCES

1 Kovach, J. T., Tsakris, E. A. and Wang, L. T. Engine fric-

tion reduction or improved fuel economy. SAE paper
820085, 1985.
2 Pohlmann, J. D. and Kuck, H. A. The in
uence of design
parameters on engine friction. In Proceedings of
Conference on Combustion Engines—Reduction of Friction
and Wear, 1985, C73/85, pp. 67–73.
3 Hoshi, M. Reducing friction losses in automobile engines.
Tribology Int., 1984, 17(4), 185–189.
4 Parker, D. A., Adams, D. R. and Barrett, D. J. S. The
reduction of friction in the internal combustion engine. AE
Technical Symposium, 1982, paper 29.
5 Rao, V. D. N., Kabat, D. M., Yeager, D. and Lizotte, B.
Engine studies of solid lm lubrication coated pistons. SAE
paper 970009, 1997.
Fig. 10 Calculated full load and measured motoring engine 6 Nakayama, K., Tamaki, S., Miki, H. and Takiguchi, M.
friction with and without crank o
set The e
ect of crankshaft o
set on piston friction force in a
gasoline engine. SAE paper 2000-02-0922, 2000.
7 Shinichi, S., Eiichi, K. and Tatehito, U. Improvement of
until the engine speed reaches 3000 r/min. Measuring thermal eciency by o
setting the crankshaft center to the
the motoring friction loss gives similar results, but the cylinder bore center. JSAE paper 9638770, 1996.
8 Zhu, D., Cheng, H. S., Arai, T. and Hamai, K. A numerical
friction due to the o
set tends to increase above
analysis for piston skirts in mixed lubrication. Part I: basic
4000 r/min. In consideration of the above results, if
modeling. Trans. ASME, J. Tribology, 1992, 114, 553–562.
crank o
set technology is applied in the engine, an 9 Zhu, D., Hu, Y. Z., Cheng, H. S., Arai, T. and Hamai, K.
improvement in fuel eciency can be expected at A numerical analysis for piston skirts in mixed lubric-
low and medium engine speed owing to the friction ation. Part II: deformation considerations. Trans. ASME,
reduction, but an adverse e
ect at higher engine speed. J. Tribology, 1993, 115, 125–133.
10 Liu, K., Xie, Y. B. and Gui, C. L. A comprehensive study
of the friction and dynamic motion of the piston assembly.
4 CONCLUSION Proc. Instn Mech. Engrs, Part J: J. Engng Tribology, 1998,
212, 221–226.
This study discusses the friction reduction e
ect of a 11 Cho, M. R., Han, D. C. and Choi, J. K. Oil lm thickness
in engine connecting-rod bearing with consideration of
crank o
set towards the thrust side of the engine. An
thermal e
ects: comparison between theory and experi-
analytical model is presented for each moving part in
ment. Trans. ASME, J. Tribology, 1999, 121, 901–907.
the engine to explore the friction reduction e
ect. As a 12 Cho, M. R., Oh, D. Y., Ryu, S. H. and Han, D. C. Load
result of the analysis and experiment, the following characteristics of engine main bearing: comparison between
conclusions may be drawn: theory and experiment. Kor. Soc. Mech. Engrs, Int. J., 2002,
1. The crank o
set mainly a
ects the side force working 16(8), 1095–1101.
13 Rohde, S. M. A mixed friction model for dynamically
upon the piston and the sliding speed of the piston.
loaded contacts with application to piston ring lubrication.
2. The crank o
set reduces the piston skirt friction
In Proceedings of 7th Leeds–Lyon Symposium on
mainly because of a reduced side force of the piston Tribology, 1980, pp. 262–278 ( Elsevier Science/ Harcourt,
skirt. Burlington, MA).
3. Friction reduction as a result of the o
set appears 14 Wakuri, Y., Hamatake, T., Soejima, M. and Kitahara, T.
greater at low engine speed and low engine load. Study on the mixed lubrication of piston rings in internal
When the speed and load increase, benet is conned combustion engine. Jap. Soc. Mech. Engrs, Part C, 1995,
to the lowest o
sets, and at higher o
sets the friction 61(538), 1123–1128.
increases. The magnitude of the o
set at which the 15 Patir, N. and Cheng, H. S. An average
ow model for deter-
friction loss is minimized tends to decrease when the mining e
ects of three dimensional roughness on partial
engine speed increases. hydrodynamic lubrication. Trans. ASME, J. Lubrication
Technol., 1978, 100(1), 12–17.
4. Crank o
set applied to an engine would contribute
16 Patir, N. and Cheng, H. S. Application of average
ow
to improvement in fuel consumption at low speed
model to lubrication between rough sliding surface. Trans.
and load. ASME, J. Lubrication Technol., 1979, 121(2), 220–230.
5. To maximize the o
set e
ect, the magnitude of the 17 Greenwood, J. A. and Tripp, J. H. The contact of two
o
set should be selected properly, and a way to com- nominally
at rough surfaces. Proc. Instn Mech. Engrs,
pensate for the friction increase at high engine speed 1970–1, 185, 625–633.
should be developed.
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