REDUCTION OF PISTON SLAP EXCITATION BY OPTIMIZING PISTON PROFILES

Takayuki KOIZUMI, Nobutaka TSUJIUCHI, Masahiro OKAMURA, and Hisashi TSUKIJIMA

Department of Engineering. Doshisha University, Kyoto, Japan

Isamu KUBOMOTO, Eiichi ISHIDA Kubota Corporation

Sakai, Osaka, Japan

ABSTRACT

This paper presents an analytical model for the prediction of piston secondary motion and the vibration due to piston slap. For the modeling of piston slap phenomenon, cylinder liner is modeled as a several spring-mass system that are connected by modal characteristics, and lubricant film between the piston and the cylinder is modeled as reaction force vectors which excite resonant mode of them. By comparing experimental results and analytical ones, the validity of the proposed model has been confirmed. The optimization of the piston skirt profile is also carried out with the analytical model, and it is confirmed that the round shape of the lower part of piston skirt is effective for the reduction of piston slap excitation.

1.INTRODUCTION

Small air-cooled gasoline engines are used around us as small farm machineries, pumps, generators and so on. However, in some case, noises radiated from them exceed the acceptable noise level and they causes serious problems for the operators. Therefore, in recent years, low noise and low vibration has been required more strongly for present engines.

This paper presents an analytical model for the prediction of the vibration of the cylinder wall caused by piston slap phenomenon and the optimization of the piston skirt profile for the reduction of the vibration. For the analytical model, the characteristics of lubrication film are one of the key factors to simulate the piston secondary motion [1-3]. On the other hand, the dynamic characteristics of cylinder walls are also of great importance [4-5]. Nevertheless, no method that takes both of them into account is found. In this study, we propose an analytical model for the coupled system of piston and cylinder wall via lubricant to simulate the behavior of piston inside a cylinder wall and the vibration response.

2.MMEASUREMENT OF THE PISTON BEHAVIOR

The piston behavior in the cylinder is measured for the comprehension of piston slap phenomenon. The experimental setup is shown in Fig.1. The measurement on the test engine for generators is carried out in the condition of rated engine speed 3600[rpm], and rated load 3.6[kW].

2.1.Experimental Setup

In order to measure the behavior of piston, four eddy current gap sensors that measure the clearance between piston skirt and cylinder are embedded in the each edge of piston skirt. The locations of the sensors are shown in Fig.2. The signals from the sensors are lead out of engine via connecting rod and a linkage system. The linkage system is shown in Fig.3.

In order to estimate the crank angle, an inductive pickup is attached on the spark plug, and the cylinder pressure is measured by means of a pressure sensor, that is installed in the spark plug.

POWERO N

O FF

SYSTEMRES ET

ONO-SOKKI 4 CHANNEL INTELLIGENT FFT ANALYZER CF6400

1 C HT R IGSIG OUT

OVER-12dB

2 C H

OVER-12dB

3 C H

OVER-12dB

4 C H

OVER-12dB

CURSOR & DISPLAY MEMORY

COMMAND

MEASUREMENT

INPUT

FFT ANALYZER

TEAC RD-1 35T DAT RECORDER

Inductive Pickup

Pressure Transducer

Load 3.6[Kw]

IGNITION SIGNALCYLINDER PRESSURE

GASOLINE ENGINE with GENERATOR

CHARGE AMPLIFIER

GAP SENSORAMPLIFIER

FFT ANALYZER

POWERO N

O FF

SYSTEMRESET

ONO-SOKKI 4 CH ANNEL IN TE LLIGENT FFT ANALYZER CF6400

1 C HT R IGSIG OUT

OVER-12dB

2 C H

OVER-12dB

3 C H

OVER-12dB

4 C H

OVER-12dB

CURSOR & DISPLAY MEMORY

COMMAND

MEASUREMENT

INPUT

FFT ANALYZER

DAT RECORDER

GAIN1 0

60

2 0

70

30

8040

9 0

50

00

7 6 5

ZERO1 0

60

2 0

70

30

8040

90

50

00

76

5

LINEAR1 0

60

2 0

70

30

804

0

9 0

50

00

7 6 5

V

55MS-M RCLEARANCETEMPERATURE Fig.1. Set-up for tne Measurement of Piston Behavior

5[mm]

8[mm]

5[mm]

8[mm]GAP SENSORS

Fig.2. Locations of the Gap Sensors in the Piston Skirt

107

Fig.3. Linkage system for Leading the Signals

3.ANALYTICAL MODEL FOR PISTON SECONDARY MOTION

For the prediction of piston slap phenomenon, an analytical model that consists of lubrication film and modal characteristics of the cylinder liner is built. The model is based on a two-dimentional lumped mass model, and constant crank rotation is assumed. The program is coded in FORTRAN, and the Newmark Beta Method is employed for obtaining the time history response.

3.1.Governing Equation

The coordinate system for the reciprocating machinery is shown in Fig.4, where α is crank angle, px and py is the

lateral and vertical displacement of pistion pin, pθ is the

tilt of piston, and β is the tilt of connecting rod.

The vertical displacement py can be represented as a

function of crank angle α and tilt of connecting rod β as follows;

)()coscos( rllry p +−+= βα (1)

And the vertical acceleration of piston pin is derived as follows;

ββββαω cossincos 222

2&&& llr

dt

yd p −−−= (2)

In operating conditions, combustion force gF , frictions

between piston ring and cylinder liner rlF , frictions between piston and cylinder plF , the connecting rod

reaction force lF and the friction torque between piston pin and connecting rod pT act on piston as shown in Fig.5.

From the balance of the forces, following equations are derived.

βθ

θ

sinsin

)( 2

2

2

2

lcouplepg

pyp

ppinrp

FFFWdtd

Gmdtxd

mmm

+++=

−++

∑ (3)

Thrust Side Antithrust Side

py

α

θ

0

y

x

opx oBx

pθ

l

r

rl +

β

Fig.4. Coordinate System of Reciprocating Machinery

w

w pinr mm +

pm

rgm rlFrlF

plF

plF

pTlF

coupleFyGxG

opx

β

gF Antithrust SideThrust Side

sixsiy

rix

Fig.5. Forces act on Piston

gmmmmFFFF

dtd

Gmdtyd

mmmm

rgpinrp

rlpllpg

pxp

prgpinrp

)( coscos

)( 2

2

2

2

+++−

∑−∑−+−=

++++

βθ

θ

(4)

oprgxpp

rirlsiplopgsi

py

pxp

ppinp

gxmgGmT

xFxFxFWy

dtxd

Gdtyd

Gmdtd

II

−−+

−−−−=

−++

∑∑∑

)( 2

2

2

2

2

2θ

(5)

where pm is the mass of the piston, rm is the mass of

the small-end of the connecting rod, pinm is the mass of

the piston pin, rgm is the mass of the piston ring, pI is the

moment of inertia, pinr is the radius of piston pin,

yx GG , are the offset of center of gravity from the center of

the piston pin and opx is the horizontal offset of the piston

pin from the center of piston. six and siy are the location of the i -th collision point of the piston, that are defined on the piston skirt and the cylinder liner. By solving these equations and carrying out time history integration, the piston behavior can be calculated.

108

3.2.Lubrication Film Reaction Forces act between Piston Skirt and Cylinder Liner

In general, there is lubricant between piston and cylinder liner. A coordinate system seen from the top of the engine for the calculation of lubrication film reaction forces is shown in Fig.6

Assume that the piston with radius R and length L moves toward the cylinder liner, and there is film of lubricant of viscosity µ and thickness oilh between the piston and the cylinder. The pressure distribution p on the piston surface along the cylinder axis y is described by the following Reynolds equation.

th

yhU

yph

y ∂∂

+∂∂

=

∂∂

∂∂ 126

3

µ (6)

The oil film thickness h can be represented by a function of angle θ as follows;

)cos1( θε−= Ch (7)

where C is the clearance between the piston skirt and the cylinder liner when piston is at the center of the cylinder liner, and ε is the eccentricity ratio of the center of the piston.

∫∫∫∫

−−⋅−=

⋅⋅=

θεθεθµ

θθ

ddd

)cos1(cosd)(6

ddcos

3

2

2 tyyLy

CR

yRpw

i

ii (8)

where L is the length of the piston skirt and iR is the radius of piston at the i -th collision point.

Applying Sommerfeld transformation defined in equation(9) and integrating equation(8) from maxθ− to

maxθ with respect to θ derives lubrication film reaction force iw at the i -th collision point.

ϕεεθεcos1

1cos12

+−=− (9)

( )[ ]

( ) ( )

−−−⋅

−+++⋅−

=

32

14Sin)1(2dd

16

3322

21-25.222

ababL

AAAAtC

Rw ii εεε

εµ

(10)

221

212

11)1(ε

εεAAAA

−−+

= (11)

2121 1, AA

ChC

A oil −=−

=ε

(12)

where a and b are upper and lower limit of integration with respect to y . They are defined as follows;

y xθ

z

Piston

h

dy

w

maxθ

hoilhLubrication Film

w− p p

LinerCylinder

Fig.6. Schematic of the Skirt Surface and Liner Surface with Coordinate System

[ ]lφ

W

Fig.7. Lubrication Film Reaction Force Vector

==∆

−=

−+−=∆

+=∆

−=

+=∆

==

),2

(,2

)1,,22

,12

,,3,2(2

,2

)12

,1(2

,0

NNiLbyLa

NNNiyybyya

Niyba

ii LL

(13)

where N is the number of the collision points, iy is the location of the i -th collision point, and y∆ is the distance between collision points.

However, as it is reported that there is space between piston and lubricant [6], it is assumed that no forces acts between the piston and the cylinder under the condition the distance between piston and cylinder liner is more than oilh .

3.3.Lubrication Force Vectors

Piston collides with cylinder liner via lubricant. In this paper, the lubricant is modeled as a forces acting on collision points on the piston skirt and the cylinder liner. After calculated, the forces are aligned to vectors and it is assumed they vibrate the each natural vibration mode of the piston skirt and cylinder liner as shown in Fig.7. 24 collision points are defined on each side of the cylinder liner. The same numbers of collision points are also defined on piston skirt, and collision always happens between the corresponding points.

109

3.4.Model of Cylinder Liner

For the prediction of the vibration induced by piston slap, the modal characteristics of the cylinder liner are of great importance. The coupled vibration is represented by the linear combination of natural vibration modes as follows;

∑=

=++=N

iiiNN uuu

111 ΦΦΦx L (14)

where ),,1( Nii L=Φ is the i -th mode shape vector and iu is the response of i -th mode.

The dynamics equation that is normalized by mass for cylinder liner is derived as following;

( )

′=

+

+

llrlrl ff WuuuO

O

&

O

O

&&

O

O2241 πζπ

(15)

where rf is the natural frequency of the r -th mode and rζ is the loss factor of the r -th mode.

By carrying out the time history integration, the response of the i -th mode iu after a small time step is derived. By composing them by means of equation (14), the response of the cylinder liner in physical coordinate system lx is derived. And by calculating in the same way, the response of piston skirt can be derived. The modal parameters of piston skirt and cylinder liner are obtained by hammer test.

3.5.Calculation Procedure

The calculation procedure is shown in Fig.8.

1.The environments between the piston skirt and the cylinder liner changes due to the crank rotation and cylinder pressure.

2.As the change of the environment, lubrication film reaction forces are calculated on each collision point and they are aligned to vectors.

3.The lubrication force vectors are transformed into the modal coordinate systems of the piston skirt and the cylinder liner.

4.The responses of the natural vibration modes are calculated by means of Newmark Beta Method.

5.The results are transformed to the physical coordinate system

6.The results are fed back to the next calculation.

The calculation is carried out from 0[deg] to 720[deg], and the final state of the calculation is given as the initial condition of the next calculation. The calculation is terminated when the result converged. The engine speed is set to 3636[rpm], which is estimated from the signals measured by inductive pickup. The viscosity of the oil is calculated by assuming the temperature inside engine as 80 degree centigrade.

4.VARIDATION OF THE PROPOSED MODEL

In order to verify the validity of the analytical model, the comparisons of the results are carried out. The calculated

The Change of the Condition

Translation into Modal Domain

M1W

5W

1st Mode

5th Mode

Time Historical IntegrationM

1W

5W

1st Mode

5th Mode

Translation into Physical Domain

The Change of the State of the System

Lubrication Film Reacting Force Occurs

The State of Modes After Small Time Step

Calculation of Lubrication Film Reaction Force

The State of Cylinder Linebefore Small Timer Step

The State of Modes before Small Time Step

The State of Cylinder Linerafter Small Timer Step

Calculation of Piston Movement

sx

Lubricant

Piston

Cylinder Liner

[ ]lφ

W [ ]lφ

W

Thrust Side Antithrust Side

Fig.8. Algorithm for Calculation

clearances between piston skirt and cylinder liner are compared with experimental results. The clearance at the thrust side is shown in Fig.9. Piston collides with the thrust side of cylinder liner three times in 720 degrees, and the strongest one occuers around 380[deg]. In Fig.10, there are jumps of signal around 180[deg] and 540[deg]. This is because the lower gap sensors get out from cylinder liner around BDC. However, as the strongest collision happens around TDC, they are negligible.

By comparing the number and the timing of the collision, simulation result corresponds with the experimental one in the whole area. The analytical model simulates the collision of the piston with cylinder liner quite well especially around TDC, where piston slap occurs.

The comparison of piston behavior is also carried out. The behavior of piston near TDC is shown in Fig.10. As shown in the figure, the timing of the collision, tilt of the piston and speed has sufficient agreement. From these results, the validity of the model is confirmed and it is verified that the model is efficient for the prediction of piston secondary motion.

The comparison of the vibration response on thrust side of cylinder liner is shown in Fig.11. As shown in the figure, the timing of the collision, the muximum level of the vibration response and the number of the collision correspond to each other very well. The spectra of them are also shown in Fig.12. From the result, the spectra match quite well in whole frequency range. From this result, the model of cylinder liner is also validated.

110

0

50

100

150

200

0 180 360 540 720Crank Angle[deg]

Cle

aran

ce[m

icro

n]

SIMULATIONEXPERIMENT

(Upper Thrust Side)

0

50

100

150

200

0 180 360 540 720Crank Angle[deg]

Cle

aran

ce[m

icro

n]

SIMULATIONEXPERIMENT

(Lower Thrust Side)

Fig.9. Comparison between Experimental Result and Analytical Result

350[deg]

450[deg]EXPERIMENTSIMURATION

Fig.10. Comparison between Experimental Result and

Analytical Result (In the vicinity of collision)

5.OPTIMIZATION OF PISTON SKIRT PROFILE

For the reduction of the piston slap excitation, the shape of the skirt is one of the key factors [7-8]. The optimization of the piston skirt shape is carried out by means of the proposed model.

5.1.Evaluation of piston slap intensity

In order to evaluate the intensity of piston slap quantitatively, RMS value of the acceleration on thrust side of cylinder liner a is used as a criterion as follows;

αdaaRMS ∫=540

360

2 (16)

where the range of crank angle α is from 360[deg] to 540[deg], which is the expansion process, because piston slap occurs shortly after TDC.

-40

-20

0

20

40

0 180 360 540 720Crank Angle[deg]

Acce

lera

tion[

G]

SIMULATIONEXPERIMENT

Fig.11. Comparison between Experimental Result and

Analytical Result (Acceleration on Thrust Side of Cylinder liner)

020406080

100120140

0 1600 3200 4800 6400Frequency[Hz]

Acce

lera

tion[

G(d

B)]

SIMULATIONEXPERIMENT

Fig.12. Comparison between Experimental Result and

Analytical Result (Vibration Spectra)

1α0 l

)0(3 dxdy=α

m][µy

]mm[x

2α

4α

)(xfy =

max5 y=α

Fig.13 Definition of design variables for the optimization of

the piston skirt shape

5.2.Definition of the design variables

In this study, the shapes of the piston skirt are described in fourth order polynomial format as follows;

44

33

2210)( xCxCxCxCCxfy ++++== (17)

Each coefficient ,, 21 CC … 5,C is calculated by using 5 design variables which are proposed to define the shape of the piston skirt as shown in Fig.13. In the figure, 1α is

the radius of the piston at the top, 2α is the radius of the

piston at the bottom limit, 3α is the gradient at the top, and

54 ,αα are x and y position where radius is maximum. The origin of the coordinate system is located at the point where is 39[mm] from the center of the top of piston skirt.

111

In general, narrow clearance reduces piston slap. In order to confirm it, the analysis of several width of clearance is carried out. Fig.14 shows the result with the proposed model, and it shows the corresponding result. From this result, the variables 4α and 5α that give maximum radius are assumed to be constant. The initial design variables are 1α = 394.22 [ µ m], 2α = 431. [ µ m], 3α = 7 [ - ], 4α = 7.13 [mm], and 5α = 447.76[ µ m], respectively.

In order to avoid generating physically impossible designs, the following constraints are applied. The radiuses of pistons are allowed to range from –50[ µ m] to +10[ µ m] from the initial shape. Shapes that include inflection points are deleted in order to keep them barreled. By using these constraints, the 3-dimensional design space is defined.

200300400500600700

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03Clearance Variation [mm]

Eval

uatio

n a RMS

Fig.14 Effect of Clearance on Piston Slap Intensity

200300400500600700

0.20 0.21 0.22 0.23 0.24 0.25Mass of Piston [kg]

Eval

uatio

n a RMS

Fig.15 Effect of Mass of Piston

200300400500600700

100 120 140 160 180 200Moment of Inertia [kg mm2]

Eval

uatio

n aRMS

Fig.16 Effect of Moment of Inertia

200300400500600700

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3Lateral Distance from Piston Center of Gravity

to Center of Piston [mm]

Eval

uato

n a

RM

S

Fig.17 Effect of Lateral Position of Piston Center of Gravity

5.3.Results

An uniform grid is defined in the 3-dimensional design space. For geometrical reasons, the upper and lower bounds of 3 variables that define the design space are 344.22 ≤≤ 1α 404.22[ µ m], 381.57 ≤≤ 2α 441.57[ µ m], 1 ≤≤ 3α 60 [ - ], respectively. The increment of 1α and 2α are 5[ µ m], and increment of 3α is 1[ - ]. Skirt designs are created by the combination of 3 variables. After applying the aforesaid constraints to these skirt designs, 750 skirt designs remained. Intensities of piston slap were evaluated for the skirt designs. Physical specifications such as mass, moment of inertia and offset of center of gravity vary along with the skirt designs. However, it is reported that the influence on piston slap excitation is very small. It is confirmed with the proposed model as shown in Fig.15,16,17 and 18. In these figures, filled circle indicate the initial value.

The comparison of the designs between original shape and the optimized shape are shown in Fig.19 and Table.1. As shown in Fig.19, the optimal skirt design is much rounder than the initial design. As the reason, it is considered that a rounder skirt makes the collision smoothly because the piston contact the cylinder from lower side and have strong impact at the upper skirt end.

Fig.20 shows the comparison of vibration response on the thrust side of the cylinder liner between the initial and the optimal designs. As shown in the figure, the peak value of the optimal design decreased compared with the one of the initial design The RMS value of the acceleration decresed 8 percent as shown in Table.1.

200300400500600700

-15.0 -13.0 -11.0 -9.0 -7.0 -5.0Axial Distance from Piston Center of Gravity

to Center of Piston [mm]

Eval

uato

n aRMS

Fig.18 Effect of Axial Position of Piston Center of Gravity

-40

-30

-20

-10

0

10

20

39.38 39.40 39.42 39.44 39.46Radius of Piston [mm]

Dis

tanc

e fro

m P

isto

n Pi

n [m

m

Initial DesignOptimum Design

Fig.19 Comparison between the Initial and Optimal

Designs 112

Variables α1 α2 α3 α4 α5 aRMSInitial Design 394.22 431.57 24 447.76 7.13 417.91

Optimal Design 389.22 396.57 24 447.76 7.13 384.53 Table.1 Design Variables for the Initial and Optimal

Designs

-40

-20

0

20

40

270 360 450 540Crank Angle[deg]

Acce

lera

tion[

G]

Inital DesignOptimal Design

Fig.20 The comparison of the vibration response between

the results of the initial design and the optimal design

CONCLUSIONS

1. An analytical model that consists of lubrication film and cylinder liner is built. And by comparing these results, the analytical results coincide with experimental result. From these results, the validity of the proposed model for the prediction of piston behavior is confirmed.

2. By using the analytical model, the optimization of the piston skirt shape is carried out. As the result, the reduction of the vibration due to piston slap has accomplished and it is confirmed that round shape of the lower edge of the skirt is effective for the reduction of piston slap excitation.

ACKNOWLEDGEMENT

This work was supported by a grant to RCAST at Doshisha University from the Ministry of Education, Culture, Sports, Science, and Technology, Japan.

REFERENCES

(1) A Numerical Approach for Piston Secondary motion Analysis and its Application to the Piston Related Noise, Teruo Nakada (ISUZU Advanced Engineering Center, Ltd.), SAE Technical Paper Series, 972043, pp.1361-1370, 1997

(2) A Numerical Model of Piston Secondary Motion and Piston Slap in Partially Flooded Elastohydrodynamics Skirt lubrication Victor W. Young (MIT) etc, Yoshiki Sekiya (Nissan Motor Co.) etc, SAE Technical Paper Series, 940696, pp.81-95, 1994

(3) An Automotive Piston lubrication Model Dennis F. Li, etc (General Motors Research Laboratories), SAE Technical Paper Series, Vol26,2, pp.151-160

(4) Piston Slap Induced Noise and Vibration of Internal Combustion Engines(1st Report, Theoretical Analysis and Simulation), Kazuhide Ohta (Mitsubishi Heavy Industries, Ltd.) etc. , SAE Technical Paper Series, 870990, pp.3.133-3.138, 1987

(5) A Technique for the Analysis of Cylinder Liner Vibrations and Cavitation, Gerald W. Green(John

Deere Engine Engineering), SAE Technical Paper Series, 930582, pp.79-87, 1993

(6) Analysis Oil Film Bahavior between Piston and Cylinder Liner by using Scanning-LIF, Motoichi Murakami etc, Proceeding of the 10th joint symposium of internal combusion, pp.181-186, 1992

(7) Reduction Disagreeable Idle Sound in Two-stroke Engines, Tohru Goto etc, Proceeding of the 10th joint symposium of internal combusion, pp.163-168, 1992

(8) Piston Slap Analysis for FRM Liner Cylinder Block, Kazuhide Tak etc, Honde R&D Technical Review, Vol10, pp.98-105, 1998

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