effect of engine position (full paper)

8/8/2019 Effect of Engine Position (Full Paper)

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Abstract ² In this paper, a programming of

dynamic system calculation is developed to

determine the body tilt angle in relation to

minimize the shaking forces on the diesel engine¶s

crankshaft. In this study, 1-cylinder diesel engine is

taken as an example. Position, velocity, andacceleration of pins of the engine mechanism

determined by using vector analysis. Masses and

mass moments of inertia of the linkage are used to

generate the forces and moments. Cartesian

coordinate principle is used to form linear

equations. These equations are solved by using

gauss elimination method to obtain the shaking

forces on the crankshaft. Calculation result is

validated by comparing it to the polygon method

and Newton principles. Based on the graphs, the

optimum tilt angle of the engine¶s body had been

obtained at 072.87! F for minimum horizontal

shaking force 07.2! x

R Newton.

Keyword: dynamic system, vector analysis, gauss elimination,

shaking forces, tilt angle.

I. I NTRODUCTION

Recently, researches of diesel engines become more

attractive because of its fuel has similar characteristic with

the environment-friendly fuel resources, such as biodiesel.

In the fact that, biodiesel can be used to replace the

conventional diesel fuel and it is made from the renewable

resources.

Biodiesel is a kind of environment-friendly resources of fuel, clean, grown locally. P alm Oil Methyl Esters (POME)

is one of those. Researchs on this area had been carried out

by researchers such as Agarwal [1], Ramadhas [2], and

Murugesan [3].

This work was supported in part by ANPCYT.* F.N. Balia, PhD student at Mechanical and Manufacturing Engineering

Faculty, UTHM. (corresponding author: e-mail: f n [email protected]).** S. Mahzan, Lecturer at Mech and Manufacturing Eng Faculty, UTHM.***M.I. Ghazali, Professor at Mech and Manufacturing Eng Faculty,

UTHM.***Abas AB Wahab, Professor at Mech and Manufacturing Eng Faculty,

UTHM.

Researches on the vibration analysis on the diesel engines

had been carried out by researchers as follows: Geng, et al

[4], carried out their research on the piston-slap-induced

vibration of 6-cylinder diesel engine. Garlucci, at al [5],

carried out the research on the relation between injection

parameter variation and block vibration of the diesel engine

(FIAT, 2000 cc). Brusa, et al [6], investigated concer ned

with the effect of non-constant moment of inertia of torsional vibration on the crankshaft of 4-cylinder

Lycoming O-360-A3A propeller engine. Guzzomi, et al [7],

conducted the study concer ned with the effect of the piston

friction on the torsional natural frequency of crankshaft of a

single cylinder reciprocating engine.

This research is a preliminary work on the diesel engines

area and its development to the biodiesel engine purpose.

This paper emphasize on the programming of a dynamic

system on the diesel engines. Determining the body tilt

angle in relation to minimize the shaking forces on the

diesel engine¶s crankshaft is very important to reduce the

shaking forces on the body. For illustration, 1-cylinder

diesel engine taken as an example.

II. PROBLEM FORMULATION

In analyzing the shaking forces due to the combustion

process in the chamber on the engine¶s crankshaft can be

describe as follows:

2.1 Kinematic Formulation

The calculation steps of an engine has to be started at the

kinematic formulation, to calculate the position, velocity,

and acceleration of pins and center of mass. Vector analysis

principles are used to calculate those parameters. The

mechanism of engine shown below.

F

Y

X

2

3

4

1

Figure 1, Mechanism of Engine

EFFECT OF BODY TILT ANGLE TO THE SHAK ING FOR CES

ON THE DIESEL ENGINE¶S CRANKSHAFT

*Fuadi Noor Balia,

**Shahruddin bin Mahzan,

***Mohd Imran bin Ghazali, and

***Abas AB Wahab

Proceedings of MUCEET2009

Malaysian Technical Universities Conference on Engineering and Technology

June 20-22, 2009, MS Garden,Kuantan, Pahang, Malaysia

MUCEET2009



2

Figure 1, shows a system of the engine mechanism, in

which the body tilt angle is included as a parameter that

can effect to minimize the shaking forces on the engine¶s

crankshaft. Link 1 is cylinder block and jour nal bearing,

link 2 is crankshaft, link 3 is connecting rod, and link 4 is

piston that can move freely on the cylinder (body) axis

direction.

Figure 2, shows the vector model of engine mechanism

for calculating the position, velocity, and acceleration of

pins and center of mass of the linkages. In this modeling,

vector r2 represent the crankshaft, vector r3 represent the

connecting rod, and vector r4 represent the motion line of

piston. 2U is angle of r2 to x, 2U( is angle of r2 to r4, 3U

is angle of r3 to x, J is angle of r3 to r4, F is angle of r4

to x.

r2

r3

r4

X

Y

F2

3

2

Figure 2, Kinematic Modeling of Engine Mechanism

From figure 2, mathematical model can be gover ned as

a vector equation below,

324r r r ! ««.. (1)

This equation can be derived to obtain the velocity of points along the line vector, such below

33224 xr xr r UU ! ««.. (2)

From this equation can be calculated the connecting

rod angular velocity such below,

2

33

22

3cossin

sincosU

F F

F FU

¹¹ º

¸©©ª

¨

!

x y

y x

r r

r r «« (3)

Equation (2), can be derived to give the equation of

acceleration of points motion along the cylinder axis can bewritten as below,

F

UUUU

cos

....2

3333

2

2222

4

x y x yr r r r

r

! « (4)

Calculation of angular acceleration of linkage 3 can be

derived and the result as below,

D

C B A !3U

««««« (5)

where :

222 .sincos U F F

y xr r

!

2

222 ).cossin( U F F y x

r r B !

2

333 ).cossin( U F F

y x r r C ! )cossin( 33

¡ ¡

x y r r D !

Through equation (1) to equation (5), the position.

velocity (linear and angular) and acceleration (linear and

angular) of pins and center of mass can be obtained.

2.2 Dynamic Formulation

Calculation of shaking forces in any of pins and existing

forces at center of mass of linkage, can be modeled as

figure 3 below [8].

F

Y

X

2

3

4

1

Figure 3, Dynamic Modeling of Engine Mechanism

This model can be solved by using Cartesian coordinate

method (vector analysis for dynamic systems) [9]. Thisengine mechanism can be modeled separately as follows.

2.2.1 Crankshaft Modeling

Ti

m2b.a2b

I2b

p2a

q2a

p2b

¢

2

-¢

3

m2c.a2c

-W2c

I2a 2

2

-W2a

-W2b

m2a.a2a

£

¤

¥

2 2 22, ,

¦ 2

§ igure 4, Modeling of ̈

rankshaft



3

Figure 4, shows a physical modeling of Crankshaft. In

this modeling, the crankshaft is separated into two parts,

that are crank and balancer. Center of rotation assumed

located at point A, therefore all of the moments refer to that

point.

The inertia torque22 .U

a I that is generated by rotation

of the crank and located at point A. The inertia torque

22 .Ub I that is generated by rotation of balancer and located

at point B. Reaction torque Ti is in put moment to the shaft

due to the reaction of combustion and inertia loads.

The vector 2

F is the reaction of the crankshaft to the

crank, while vector 3 F is the reaction force of crankpin to

the crank. The massa© 2

is of crank mass and generate the

inertia force of aa

a

22. and centered at point A. The

b© 2is the mass of balancer and generate the inertia force

of bb

a

22. and centered at point B. The mass

c

2is a

half mass of crankpin to the crank, this mass generate a

half of inertia force cc a© 22 . and centered at point C. In

this modeling, the distributed weight of linkage part are

included. W 2 is a half of weight of crankshaft. W 2a is the

weight of crank, W 2b is the weight balancer. W 2c is a half

of the weight of crankpin

2.2.2 Connecting rod Modeling

F3

m3.a3

I3

-F4

q3

p3

3

3

-W3

D

3

, 3 3,

Figure 5, Modeling of Connecting rod

Figure 5 shows a physical modeling of Connecting

rod. Center of rotation assumed to be located at point D.

The inertia torque33U I is generated due to the

rotation of connecting rod. The mass3m is the connecting

rod mass and generate the inertia force 33.am and centered

at point D. The vector F 3 is the reaction force of crankpin

to the connecting rod, while the force of F 4 is reaction of

piston pin to the connecting rod. The weight W 3 is

connecting rod weight and centered at point D.

2.2.3 Piston Modeling

m4.a4

F14

Fc

z

F4

F

-W4

E

4

1

Figure 6, Modeling of Piston

The vector 4

F is the reaction force of connecting rod to

the pin of piston. The mass4m is the sum of piston¶s pin

and piston mass itself and generated the inertia force

44.am and located at point E. The weight W 4 is the sum

of pin and piston weight. The vector 14

F is reaction force

of cylinder to the piston and located at the length of vector

z from the center of mass, and the vector c F is a force as a

result of the combustion process in the cylinder to the

piston.

2.3 Mathematical Equations

Mathematical modeling can be developed by using

vector analysis (Cartesian coordinate) method for engine

mechanism.

2.3.1 Equation for Crankshaft

Crankshaft mechanism is modeled by assumed that the

center of rotation located on point A and mass of each of

crank part located at the center of each part.

Equation of the forces equilibrium vector of the

Crankshaft,

ccbbaaamamam F F

22222232... ! «.. (6)

Equation of moment equilibrium vector of the Crankshaft,

J I H G F E

T x F p x F q iaa

! 3222

««. (7)

where:



4

bbaba xmq p E

2222.)( !

bab xW q p F 222 )( !

22 xW qG a!

ca xW p H 22!

ccaa xm p I

222.!

222 )( Uba I I J !

Equation (6) can be developed to give the force equations

in x and y direction, it mean give two rows of equation.

Equation (7) give the moment equations to the center of

rotation, after developing it using vector analysis, this

equation give a row of moment equation.

From equation (6) and (7) can result three rows of linear

equation to form matrix.

2.3.2 Equation for Connecting rod

Equation of the forces equilibrium vector of Connecting

rod,

33343 . W am F F ! «««««.. (8)

Equation of the moment equilibrium vector of Connecting

rod,

334333.U I x F p x F q ! «««««.. (9)

Equation (8) is developed to give two rows of the force

equations in x and y direction, and equation (9) give a row

of moment equation.

From equation (8) and (9) can result three rows of linear

equation to form matrix.

2.3.3 Equation for Piston

Equation of forces equilibrium of piston,

c F am F F ! 44144 . ««««« (10)

Equation of moments equilibrium,

014 ! z x F «««... «.. (11)

Equation (10) can be developed into two rows of the

force equation, in x and y direction, while equation (11)

can be developed to be a row of moment equation in x and

y.

These equations give three rows of linear equation to

form matrix.

2.3.4 Matrix Formation

The equation (6) to equation (11) that have nine of

linear equations and can be solved simultaneously by

matrix formation,

? A _ a _ab x A ! «««««. (12)

where, ? A A is a coefficient of symmetric matrix (9x9

matrix element), _ a x are the forces and torque parameter to

be solved (9x1 matrix element), while _ ab are the effective

inertia forces and moment (9x1 matrix element) due to the

moment and forces of inertia.

The forces and torque in matrix _ a x can be solved by

using Gauss-Jordan Elimination principle for solving

Simultaneously Linear Equation [10].

III. METHOD OF SOLUTION

This programming is divided in two category

calculation. Firstly, kinematic step and secondly, dynamic

system formulation. Compiler Visual C++ is used for

programming language [11].

Briefly, figure 7, shows a flow chart of programming.

Figure 7, Flow Chart of Programming

On the kinematic step, calculation of position, velocity,and acceleration of pins and center of mass of each link

were carried out. Vector of position was written as

equation (1). In this development vector 2

r and

3r considered as the length of crank and connecting rod, the

values are constant. Vector 4r considered as the length of

position between piston and the main bearing, this is an

unconstant variable. Equation (2) gives the linear velocity

of piston motion along the cylinder axis. Rotation of the

crank gives the angular velocity and acceleration of the



5

connecting rod,3U and

3U , it can be seen in equation (3)

and (5). For this purpose, the main bearing is fixed, and

body tilt angle is included as a parameter to ad just the

position of axis of piston to x (same as engine¶s body tilt

angle axis). Through this development, the effect of body

tilt angle F can be seen from the equation (3) to equation

(5). Equation (4) shows the linear acceleration of piston

motion along the cylinder axis.

Validation of kinematic calculations had been carriedout by comparing it to the hand calculation of polygon

method (see attachment-1 and attachment-2).

On the dynamics step, calculation of forces and

moments started of physical modeling of the crank and

balancer, connecting rod, and piston. Figure 3 shows the

physical dynamics modeling of engine mechanism.

Concept of Cartesian coordinate is used in accordance with

the vector analysis of forces and moments.

Crankshaft model, as showed at figure 4, can be derived

mathematically in accordance with d¶Alembert principle of

equilibrium. Equation (6) shows the vector for force

equilibrium, while equation (7) for moment equilibrium.

Connecting rod, as showed at figure 5, can be derived intothe forces and moments (equation (8) and (9)). Piston is

considered as the body motion along the cylinder axis.

Friction is neglected in this situation, because of the

complexity of calculation.

Matrix formation is used to collect the ninth of

equations had been developed from equation (6) to equation

(11). For detail explanation, see section 2.3 (Mathematical

Equations) for every step of modeling.

The data that are used for this solution is taken from

the size of diesel engine mechanism. Piston bore size d =

82.5 mm, stroke L = 92.5 mm, connecting rod length = 15

mm. Length of crank r a = 47 mm, balancer length r b = 78

mm. The inter nal pressure force data delivered to the

equation (10) depend on the crank angle of combustion [12].

Simultaneously linear equations in a matrix form can be

solved by using Gauss Elimination procedure, by inserting

pivot point algorithm. This solution gives the result of

parameters that are considered as the reaction forces of the

pins.

Validation of dynamics system had been carried out by

comparing it to the static equilibrium, by eliminating the

dynamic parameters, such the effective forces and moments

of inertia (see attachment-3 and attachment-4).

Validation for mass of piston carried out by getting its

weight. For connecting rod, the mass, centroid and mass

moment of inertia by calculation and getting its weight andcompare it, the parts are modeled as a volume combination

of the separately blocks. For crankshaft, calculation of

mass, centroid and mass moment of inertia carried out by

modeling its volume as the combination of many blocks

(same procedure with connecting rod).

IV. R ESULT AND DISCUSSION

Tilt Rx Ry

75

85

90

100

-12000

-10000

-8000

-6000

-4000

-2000

0

2000

4000

Force

Tilt Angle

Body Tilt Angle

75 80 85 87.72 90 95 100

Figure 8, Graphic of Tilt Angle to Shaking Force

Programming of this engine mechanism gives a

comparatively result, even for accuracy of calculation and

in accordance with the engine¶s body tilt angle, see figure8.

This angle result gives the minimum shaking force in

horizontal direction, Rx = 2.07 Newton, while for vertical

direction, R y = -11957.05 Newton. For diesel engine has

pressure 3,5 MPa, so inter nal pressure force F c = 18709.70

Newton, at 100 of crank angle. Rotation of engine is

constant, n = 4500 rpm. This condition is very important

consideration for the human body comfort characteristic.

The human body characteristic can stand for up and down

shaking motion, but for horizontal shake must be avoided

for a long period. The optimum tilt angle of engine¶s body

obtained072.87! F .

Validation of kinematic calculation, a good result was

reached. Calculation for n = 2000 rpm ( 4.209![

rad/sec),00! F , gives angular velocity for Connecting

rod 98.613 ![ rad/sec for calculation and 0.623 ![

rad/sec for polygon method. Angular acceleration

41.99363 !E rad/sec2 for calculation and 99403 !E

rad/sec2 for polygon method. Piston acceleration of

polygon method 9290!a ft/sec2 , for calculation

54.111435!a in/sec2 = 9286.3 ft/sec2 (see

attachment-1 and attachment-2).

For dynamics calculation, validation had been carried

out with a good result. The effective force and momentmust be eliminated (set to zero) to get static balance. For r 2

= 10 cm, r 3 = 20 cm,0

230!U gives the result for

manual calculation, for F c = 2500 N, obtained F 14y = 645.5

N, F 2 x = 2500 N, F 2y = -645.5 N, T i = -18090.19 N.cm. The

result of computer calculation, for F c = 2500 N, obtained

F 14y = 645.5 N, F 2 x = 2500 N, F 2y = -645.5 N, T i = -

18090.17 N.cm (see attachment-3 and attachment-4).

Validation for calculating the connecting rod mass and

centroid can be explained, total mass m = 0.79 kg,

045.0! y m, 00314.0! zz I kg-m2. By getting weight



6

procedure, it is obtained that mass m = 0.75 kg,

049.0! y m. By this validation procedure, it can be

assumed that the calculation value of crankshaft can be

accepted. For crank: mass ma = 0.5867 kg, centroid

0272445.0! y m, mass moment of inertia I zz =

0.000494 kg-m2 (one crank). For balancer: mass mb =

0.8829 kg, centroid 03988.0! y m, mass moment of

inertia I zz = 0.001028 kg-m2.

V. CONCLUSION

For revolution n = 4500 rpm, and maximum inter nal

pressure force F c = 18709.70 N, at crank angle of 100, it is

obtained the minimum horizontal shaking force of Rx =

2.07 N, and the vertical force Ry = -11957.05 N. By this

calculation, the optimum body tilt angle can be ad justed to

be072.87! F .

This programming has reached a good accuracy for

calculating dynamic system of engine mechanism.

VI. R EFERENCES

[1] A.K. Agarwal, Biofuel (alcohols and biodiesel)

applications as fuel for inter nal combustion engines,

Progress in Energy and Combustion Science 33

(2007) 233-271.

[2] A.S. Ramadhas, S. Jayara j, and C. Muraleedharan,

Use of vegetable oil as IC engine fuel: A review,

Renewable Energy 29 (2004) 727-742.

[3] A. Murugesan., A. Umarani, R. Subramanian., and

N. Nedunchezhian, Bio-diesel as an alter native fuel

for diesel engines, Renewable and Sustainable

Energy Reviews (2007).[4] Z. Geng, and J. Chen, Investigation into piston-slap-

induced vibration for engine condition simulation

and monitoring, Jour nal of Sound and Vibration

282(2005) 735-751.

[5] A.P. Garlucci, F.F. Chiara, and D. Laforgia, Analysis

of the relation between injection parameter variation

and block vibration of an inter nal combustion diesel

engine, Jour nal of Sound and Vibration, 295 (2006)

141-164.

[6] E. Brusa, Torsional Vibration of Crankshaft: Effects

of Non-Constant Moments of Inertia, Jour nal of

Sound and Vibration, 205(1997) 135-150

[7] A.L. Guzzomi, The effect of piston friction on the

torsional natural frequency of a reciprocating engine,

Jour nal of Mechanical Systems and Signal

Processing (2007) 2833-2837.

[8] A.R. Holowenko, Dynamics of Machinery, John Wiley

& Sons, 1955, pp. 184-237.

[9] F.P. Beer, and E.R. Johnston. Jr, Vector Mechanics

for Engineers, Dynamics, Sixth Edition, McGraw-

Hill, 1997, pp. 885-895.

[10] W.H. Press, Numerical Recipes in C++, The Art of

Scientific Computing, Second Edition, Cambridge

University Press, 2002, pp. 39-51.

[11] I. Horton, Beginning Visual C++ 6, Wrox Press,

1998

[12] J.B. Heywood, Inter nal Combustion Engine

Fundamentals, Mc Graw Hill, 1988, pp. 491-561.

ACKNOWLEDGMENT

Thanks to ANPCYT for supporting this event. Special

thanks to UTHM that has collaborated with UMP, UTeM,and UniMAP.

Unforgettable special thanks to my colleagues, Muhaimin

Ismoen and Dr. Waluyo A.S, who have given much support

and the efforts for this research development.

effect of engine position (full paper)

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