dynamic modelling of piston slapping motion in combustion

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

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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

mailto:3.5kW@4400

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


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


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


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)


Cp 109330(kg/s) Cb 109330(kg/s)

Kp 174(kg/s2) Kb 174(kg/s2)

mp 174(kg) mb 174(kg)


Cp 172750 (kg/s) Cb 69669 (kg/s)

Kp 174(kg/s2) Kb 175(kg/s2)

mp 174(kg) mb 176(kg)


Cp 109330(kg/s) Cb 109330(kg/s)

Kp 174(kg/s2) Kb 174(kg/s2)

mp 174(kg) mb 174(kg)


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


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


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


Figure 4


Figure 4


Figure 5

Variations in Piston Velocity (2000 RPM)

Figure 5


Figure 6


Figure 6


Figure 7

Variations in Piston Mobility (2000 RPM)

Figure 7


Figure 8


Figure 8


Figure 9


Figure 9


Figure 10


Figure 10


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


Figure 17


Figure 17


dynamic modelling of piston slapping motion in combustion

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