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Dynamic Modelling of Piston Slapping Motion inCombustion EnginesM.U. Kaisan
Ahmadu Bello UniversityS. Narayan ( [email protected] )
Qassim University College of EngineeringShitu Abu bakar
Ahmadu Bello UniversityIbrahim Umar Ibrahim
Ahmadu Bello UniversityBashir Garba Ibrahim
Air Force Institute of Technology, Kaduna
Original Article
Keywords: Acoustics, Vibrations, Noise, Piston motion
Posted Date: November 4th, 2020
DOI: https://doi.org/10.21203/rs.3.rs-98295/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
Dynamic modelling of piston slapping motion in combustion engines
M.U. Kaisan1, S. Narayan2, Shitu Abu Bakar3,Ibrahim Umar Ibrahim,4 ,Bashir Garba Ibrahim5
1,3,4 Mechanical engineering department, Ahmadu Bello University, Nigeria 2 Mechanical engineering department, Qassim University, Saudi Arabia 5 Mechanical engineering department, Air force Institute of Technology, Kaduna, Nigeria
Abstract A numerical model of the piston skirt taking into account its lateral, reciprocating and rotatory motion has
been presented in order to investigate the lateral motion of piston skirt assembly and resulting vibrations induced as a
result of these motions in the engine block. Various parameters of modal analysis were obtained using mobility analysis.
The presented methodology was validated by data obtained from a diesel engine test set up. The predicted results
matched well with those of measured data, hence validating the presented scheme.
Keywords: Acoustics, Vibrations, Noise, Piston motion
Introduction
In combustion engines a lateral space is present between
skirt and cylinder liner that gives a motion freedom in
lateral direction during operation of engine [1]. The
existence of this gap puts a limit on magnitude of piston
motion [2]. The piston assembly contributes to about 30-
40% of mechanical losses and hence a major concern for
automotive engineers [3,4]. The piston thrusts liner to
other side due to changing in direction of side thrust force
due to motion of connecting rod [5,6].
A dynamic model of crank slider mechanism has been
presented by Flores et al [2]. The existence of lateral gap
this mechanism makes the system nonlinear and chaotic
in nature. The reaction force between liner and skirt also
plays an important role in dynamics of motion. As the
coefficient of restitution decreases, the motion transforms
from bouncing to a periodic one [7,8].
Mcfadden and Turnbul analyzed effects of combustion
gas pressure on primary motion of piston [9]. A two
degree of freedom system has been analyzed showing a
correlation between piston slap and resulting vibrations
[10-16]. Various parameters affecting piston motion has
been considered which includes location of center of
gravity [17], profile of skirt [18,19], effects of inertial
forces [20,21], frictional forces [22] and lubricating oil
[23]. Mounted accelerometers on block surface has been
used to simulate piston secondary motion [5].
Piston Assembly Model
The secondary motion of skirt for case of a 240 cc engine
was modeled as depicted in figure no 1. The piston was
considered as a point mass of 0.363 kg (mp) and inertia
(IP) of 7.8540X10−9 kg-m2 having two degree of freedom
in motion (Xp ,θ). The cylinder block was considered as a
lumped mass of 48.5 kg (mb) with a single degree of
freedom Xb as shown in in equation no 1.
The nominal clearance of 0.5mm allows the piston
assembly to move in the lateral direction as well as rotate
about piston pin. The clearance between skirt and liner
Xc was modeled as a mechanical stop in lateral direction.
For condition of no impact, (Xp -Xb < Xc) the motion
was governed by equation no 1. During the lateral contact
phase contact damping Ccp and stiffness Kcp were added
to model assembly as seen from equation no 2.
Figure 1. Numerical Model of piston motion
-(1)
-(2)
Piston Side Thrust force
The major factor effecting this lateral motion of skirt is
the side thrust force (Fx) imparted to skirt by connecting
rod as shown in figure no 2.
Figure 2. Force diagram of piston skirt assembly
The frictional forces act between piston skirt and cylinder
liner (Ff) as well as between rings and liner (Ffr). The
force exerted by connecting rod on piston pin was
resolved along X (FrodX) as well as Y axis (FrodY). The
side thrust force takes into consideration both inertial
forces as well as gas forces [21,22].
Fx = [Fg - mp rω2[cos(θ)+Kcos(2θ)]]λ -(3)
Where
K is crank radius-connecting rod length ratio.
λ= K cos(θ)/ √(1+[λ sin(θ)]2)
Piston Frictional Force
Various friction forces play a predominant role in the
total mechanical loss of engine [2,26]. According to
Zweiri et al [27], frictional force between rings and liner
can be obtained from the product of elastic tension and
the coefficient of frictional force. As the speed of engine
increases, the coefficient of friction decreases gradually
until minimum at mid stroke. The frictional forces
between liner and skirt (Ff) and piston rings and liner (Ffr)
may be expressed in terms of sliding velocity of piston
(V),nominal clearance (h),lubricating oil
viscosity(μ),number of piston rings (n) and shear area of
contact(As)as[27-40]꞉
Ff = μVAs1/h (4 )
Ffr = nμVAs2/h -(5)
Where As1 is shear contact area between liner and skirt
and As2 is the shear contact area between liner and rings.
Mobility Parameter Determination
The mobility may be defined as the ratio of velocity
response V(Jω) of structure to exciting force F(Jω) acting
on structure [5]:
M(Jω) = V(Jω)/F(Jω)
M(Jω) = -Jω((K-Mω2)+JCω)/Mω2(K+JCω) -(6)
In frequency range below first anti resonant frequency
value (ωa=K/m), the point mobility equation can be
approximated as [5,31, 32] :
M(Jω)= -J/mωa (7)
Above anti resonance frequency, the point mobility can
be written as :
M(Jω)= -Jωa/K (8)
Experimental Setup
Tests were done on a single cylinder HARTZ engine
having specifications as presented in Table no1.
Table 1. Engine Specifications engines
Type Diesel Engine
Make HARTZ
No of cylinders 1
Bore 69mm
Stroke 65mm
Displacement 0.243 liter
Compression 22:1
Maximum Power 3.5kW@4400RPM
Maximum Torque 10N-m @2000RPM
Table 2. Pressure Transducer Specifications
Range 0-250Bar
Sensitivity 20pC/Bar
Resonance Frequency 160kHz
The in-cylinder pressure was monitored by an AVL
transducer having specifications shown in Table 2. Block
vibrations were measured by means of a Endveco7240C
type Mono axial accelerometer having features
accelerometer are presented in Table no3.
Table 3. Accelerometer Transducer Specifications
Range 1000g
Sensitivity 3pC/g
Resonance Frequency 90kHz
Various engine testing speeds (2000RPM & 3000 RPM)
and load values (80% &100%) were chosen with an aim
to cover complete engine operational conditions. The
data recorded during each test was under steady state
conditions as seen in Table no 4.
Table 4. Testing Specifications
Case RPM Load P injection (Bar)
1 2000 80% 716
2 2000 100% 692
3 3000 80% 814
4 3000 100% 612
5 3000 - 512
Results and discussions
Figures no 3,4 depicts variations in piston side thrust
force. This force changes its direction five times in a
complete engine cycle indicating five possible instances
of lateral contact of skirt with liner.
-500 -400 -300 -200 -100 0 100 200 300-1.5
-1
-0.5
0
0.5
1x 10
4
Crank Angle
Pis
ton
Sid
e T
hru
st
Fo
rce-(
New
ton
)
Case 1
Case 2
Figure 3. Variations in Piston Side Thrust Force
(2000 RPM)
-500 -400 -300 -200 -100 0 100 200 300-1
-0.5
0
0.5
1
1.5x 10
4
Crank Angle
Pis
ton
Sid
e T
hru
st
Fo
rce
-(N
ew
ton
)
Case 3
Case 4
Case 5
Figure 4. Variations in Piston Side Thrust Force
(3000 RPM)
COMSOL 7 multi physics software was used to simulate
piston velocity for given testing conditions as shown in
figures 5,6.
-100 -90 -80 -70 -60 -50 -40 -30 -20 -10-0.4
-0.2
0
0.2
Crank Angle
Pisto
n V
elo
city
-(m
m/s)
Case 1
Case 2
Figure 5. Variations in Piston Velocity (2000 RPM)
-90 -80 -70 -60 -50 -40 -30 -20 -10 0-0.2
-0.1
0
0.1
0.2
Crank Angle
Pis
ton
Ve
locity-(m
m/s
)
Case 3
Case 4
Case 5
Figure 6. Variations in Piston Velocity (3000 RPM)
Using equation 6, the mobility was computed for the as
seen in figures 7,8.
101
102
103
104
105
106
10-25
10-20
10-15
10-10
10-5
100
Frequency-Hz
Pis
ton
Mo
bility-(
m./
N-s
)
Case 1
Case 2
1st Anti ResonantFrequency
Figure 7. Variations in Piston Mobility (2000 RPM)
101
102
103
104
105
106
10-20
10-15
10-10
10-5
Frequency-Hz
Pisto
n M
ob
ility
-(m
./N
-s)
Case 3
Case 4
Case 5
1st Anti ResonantFrequency
Figure 8. Variations in Piston Mobility (3000 RPM)
Similarly, the Mobility for cylinder block was computed
using integration of accelerometer data as shown in
Figures 9,10.
101
102
103
104
105
106
10-10
10-8
10-6
10-4
10-2
Frequency-Hz
Lin
er
Mo
bil
ity
-(m
./N
-s)
Case 1
Case 2
1st Resonantfrequency
Figure 9. Variations in Piston Mobility (2000 RPM)
101
102
103
104
105
106
10-9
10-8
10-7
10-6
10-5
10-4
10-3
Frequency-Hz
Lin
er M
ob
ility
-(m
./N
-s)
Case 3
Case 4
Case 5
1ST ResonantFrequency
Figure 10. Variations in Piston Mobility (3000 RPM)
Using the concept of anti-resonant frequency(ωa) as
discussed in previous section, various dynamic
parameters of liner-piston were computed for given test
conditions as seen in Table no 5.
Table 5. Dynamic Features of system
Test case Piston parameter Liner parameter
1 ωa 100Hz ωa 39Hz
Cp 109330(kg/s) Cb 42884(kg/s)
Kp 174(kg/s2) Kb 175(kg/s2)
mp 174(kg) mb 175(kg)
2 ωa 100Hz ωa 39Hz
Cp 109330(kg/s) Cb 109330(kg/s)
Kp 174(kg/s2) Kb 174(kg/s2)
mp 174(kg) mb 174(kg)
3 ωa 158Hz ωa 63Hz
Cp 172750 (kg/s) Cb 69669 (kg/s)
Kp 174(kg/s2) Kb 175(kg/s2)
mp 174(kg) mb 176(kg)
4 ωa 158Hz ωa 63Hz
Cp 109330(kg/s) Cb 109330(kg/s)
Kp 174(kg/s2) Kb 174(kg/s2)
mp 174(kg) mb 174(kg)
5 ωa 158Hz ωa 63Hz
Cp 172750 (kg/s) Cb 69669 (kg/s)
Kp 174(kg/s2) Kb 175(kg/s2)
mp 174(kg) mb 176(kg)
During motion simulation the bottom dead center
positions (BDC) was taken as reference point. The initial
location of piston is set at 0 mm as bottom boundary of
liner and the upper boundary of the cylinder liner is set at
0.5 mm which is clearance between the skirt and liner.
As seen from figure 11, the tilting angle of piston changes
its direction at both dead centers. In order to visualize the
pistons secondary motion during the reciprocating
motion, the piston secondary motion is represented in a
graphical form and the piston lateral motion and rotating
motion are normalized to the piston stroke position based
on the reciprocating motion of piston as shown in figure
12.
-500 -400 -300 -200 -100 0 100 200 300
0.1
0.12
0.14
0.16
Str
oke length
-m
m
crank angle
-500 -400 -300 -200 -100 0 100 200 30010
20
30
40
Ro
tati
on
al
an
gle
Figure 11. Variations in Rotation Motion of skirt (Case
1)
It is evident from the plot that piston remains lower
boundary cylinder liner for a longer time as compared
with upper boundary of cylinder wall. Also, piston is
predicted to slide for a crank angle of 100º before TDC
along the cylinder liner(Figure 12).
-500 -400 -300 -200 -100 0 100 200 3000.08
0.1
0.12
0.14
0.16
Str
ok
e l
en
gth
-m
m
crank angle
-500 -400 -300 -200 -100 0 100 200 300-0.02
0
0.02
0.04
0.06
Late
ral
Dsip
lacem
en
t-m
m
Piston Sliding Duration
Figure12. Piston secondary Motion (Case 1)
-500 -400 -300 -200 -100 0 100 200 3002
3
4
5
6
7
8
9
10x 10
-3
crank angle
Vib
rati
on
Am
pli
tud
e -m
Figure13.Vibration Response of engine block
(Case 1)
Figure no 13 shows the measured vibratory response of
cylinder block in the vibration amplitudes as captured by
accelerometer. The vibration of the cylinder decays after
first impact of the piston on upper boundary of liner. The
vibration is induced once again when the piston impacts
lower cylinder liner. The induced vibrations had an
amplitude of order 7X10-3m. As the engine operating
speed increases, the piston side thrust force which is a
function of the engine rotating speed increases. An
increase in side thrust force acting on the piston, results
in piston bouncing off the cylinder liner more frequently
at higher speeds as seen from figure no 14,15.
-50 -40 -30 -20 -10 0 10 20 30 40 50
3
3.5
4
4.5
5
5.5
6
6.5
7x 10
-3
crank angle
Vib
ra
tio
n A
mp
litu
de
-m
Case 1
Case 2
Figure 14. Effects of variations in engine speed on
engine block Vibrations(2000RPM)
-15 -10 -5 0 5 10 15
3
3.5
4
4.5
5
5.5
6
6.5
7x 10
-3
crank angle
Vib
ra
tio
n A
mp
litu
de
-m
Case 3
Case 4
Case 5
Figure 15. Effects of variations in engine speed
on Block Vibrations(3000RPM)
The induced vibrations of block also increase with engine
speed. The sliding duration also falls with an increase in
velocity as shown in figure 16,17. This is due to higher
impact force and acceleration generated during the piston
slap and the reaction impact force from liner acting on
skirt increases. At lower engine speeds, the vibration
response of the cylinder block induced by first slap of
piston has a longer duration to decay before second slap
occurs. However, with speed increase the vibration
response of block has a shorter duration of decay and
response from second slap is combined with first one.
-500 -400 -300 -200 -100 0 100 200 300-5
0
5
10
15
20x 10
-3
crank angle
La
tera
l A
mp
litu
de
-m
m
Case 1
Case 2
Figure 16. Effects of variations in engine speed
on secondary motion of skirt (2000RPM)
-500 -400 -300 -200 -100 0 100 200 300-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
crank angle
Late
ral
Am
pli
tud
e -m
m
Case 5
Case 4
Case 3
Figure 17. Effects of variations in engine speed
on secondary motion of skirt (3000RPM)
Conclusions
The presented work presents a modal analysis-based
model of piston slapping motion. Dynamic parameters
were used to simulate this motion. Effects of varying
engine operational parameters like load and speed were
investigated. Sliding motion of skirt along cylinder liner
was found to increase with an increase in load, speed,
coefficient of friction and stiffness of piston rings.
Declarations
Availability of data and materials-Not applicable
Competing interests-Not applicable
Funding-Not applicable
Authors' contributions-All authors have equal
contributions
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Declarations
Figures
Figure 1
Numerical Model of piston motion
Figure 1
Numerical Model of piston motion
Figure 2
Force diagram of piston skirt assembly
Figure 2
Force diagram of piston skirt assembly
Figure 3
Variations in Piston Side Thrust Force (2000 RPM)
Figure 3
Variations in Piston Side Thrust Force (2000 RPM)
Figure 4
Variations in Piston Side Thrust Force (3000 RPM)
Figure 4
Variations in Piston Side Thrust Force (3000 RPM)
Figure 5
Variations in Piston Velocity (2000 RPM)
Figure 5
Variations in Piston Velocity (2000 RPM)
Figure 6
Variations in Piston Velocity (3000 RPM)
Figure 6
Variations in Piston Velocity (3000 RPM)
Figure 7
Variations in Piston Mobility (2000 RPM)
Figure 7
Variations in Piston Mobility (2000 RPM)
Figure 8
Variations in Piston Mobility (3000 RPM)
Figure 8
Variations in Piston Mobility (3000 RPM)
Figure 9
Variations in Piston Mobility (2000 RPM)
Figure 9
Variations in Piston Mobility (2000 RPM)
Figure 10
Variations in Piston Mobility (3000 RPM)
Figure 10
Variations in Piston Mobility (3000 RPM)
Figure 11
Variations in Rotation Motion of skirt (Case 1)
Figure 11
Variations in Rotation Motion of skirt (Case 1)
Figure 12
Piston secondary Motion (Case 1)
Figure 12
Piston secondary Motion (Case 1)
Figure 13
Vibration Response of engine block (Case 1)
Figure 13
Vibration Response of engine block (Case 1)
Figure 14
Effects of variations in engine speed on engine block Vibrations(2000RPM)
Figure 14
Effects of variations in engine speed on engine block Vibrations(2000RPM)
Figure 15
Effects of variations in engine speed on Block Vibrations(3000RPM)
Figure 15
Effects of variations in engine speed on Block Vibrations(3000RPM)
Figure 16
Effects of variations in engine speed on secondary motion of skirt (2000RPM)
Figure 16
Effects of variations in engine speed on secondary motion of skirt (2000RPM)
Figure 17
Effects of variations in engine speed on secondary motion of skirt (3000RPM)
Figure 17
Effects of variations in engine speed on secondary motion of skirt (3000RPM)