otto engine design-2009

7/31/2019 Otto Engine Design-2009

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537 TECHNICAL UNIVERSITY OF CLUJ-NAPOCA

ACTA TECHNICA NAPOCENSIS

International Conference on Engineering Graphics and Design

12-13 June 2009

OTTO ENGINES DESIGN

Relly Victoria PETRESCU, Florian Ion PETRESCU

Abstract: The paper presents a few original elements about the dynamics and kinematics of piston

mechanism, used like motor mechanism from OTTO engines. One presents an original method to

determine the efficiency of the piston mechanism, used like motor mechanism. This method consists of

eliminating the friction modulus. One determines the efficiency of the piston mechanism in two ways: 1.

When the piston mechanism works like a motor; 2. When the piston mechanism works like a steam roller.

Finally one determines the total motor efficiency, for the four cycle engine and for two cycle engine. With

the relation of motor efficiency one optimizes the Otto mechanism, which is the principal mechanism

from the internal-combustion engines. This is the way to diminish the acceleration of the piston and to

maximize the efficiency of motor mechanism. One optimizes the constructive parameters: e, r, l, taking

into account the rotation speed of drive shaft, n. Key words: Efficiency, force, piston, crank, connecting-

rod, motor, stroke, bore.

1. INTRODUCTION

In this paper one determines the efficiency

of piston mechanism ( 2.) in two ways:

1.When the piston mechanism works like amotor; 2.When the piston mechanism works

like a steam roller. Finally one determines thetotal motor efficiency, for the four cycle engine

and for two cycle engine.

2. DETERMINING THE MECHANICAL

MOTOR EFFICIENCY

In figure 1 one can see the kinematical

diagram of the mechanism with crank -

connecting rod - piston [1, 2].The constructive parameters are: r, the

radius of crank; l, the length of connecting-rod;

e, the eccentricity between centre of crank

rotation and axis of piston guide. The

mechanism is positioned by the angle, , whichis representing the rotation angle of crank. Theconnecting rod is positioned by one of the two

angles, or (see picture 1). The variablelength between the centre of crank rotation and

the piston centre is yB.

2.1 The kinematics of Otto mechanismThe kinematical relations (see fig. 1) are the

following:

(1)

=+=+Bylrelr

sinsincoscos

0

0

O

A

B

l

r

e

yB

x

y

P

1

2

3

Fig. 1. The kinematical schema of Otto mechanism

From the first relation of the positions

system (1), one determines the value ofangle

(relation 2):

l

re

coscos

+= (2)

From the second relation of system (1) onecalculates directly the pistons displacement,

s=yB (see the relation 3):


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538 sinsin + lr== ys B (3)

One derivates the positions system (1) and

obtains the velocities system (4):

=+

=

Bylr

lr

&&&

&&

coscos

0sinsin(4)

From the first relation of system (4) one

calculates the angular velocity, & , (see the

relation 5), and from the second relation of

system (4) one determines the pistons linear

velocity, , (see the relation 6):By&

&&

=sin

sin

l

r(5)

coscos += &&& lryB (6)

One derivates the velocities system (4) and

obtains the accelerations system (7):

=+

=

Byllr

llr

&&&&&&

&&&&

cossinsin

0sincoscos

22

22

(7)

From the first relation of system (7) one

calculates the angular acceleration, && , (see the

relation 8), and from the second relation of

system (7) one determines the pistons linear

acceleration, , (relation 9):By&&

sin

coscos 22

+

=l

lr &&&& (8)

sinsincos 22 = &&&&&& lrlyB (9)The angle can be put in a function of the

angle, see the expression (10):90= (10)

One can now determine the trigonometric

functions of the angle:

=

=

cossin

sincos(11)

With the expression (2) and the second

relation of system (11), one determines sin ,

see the relation (12):

l

re

cossin

+= (12)

The pistons velocity takes the form (13):

sin)sin(

sin)sin(

)cossinsin(cossin

sin

cossincos

coscos

==

=

=

=

=

=+==

rr

r

rr

lryv BB

&

&

&&

&&&

(13)

2.2 Determining the mechanical efficiency

when the Otto mechanism works like a

motor mechanism

The Otto mechanism works like a motor

mechanism in a single cycle ( angle), when

the piston is moving from the near dead point tothe distant dead point (when the piston ismoving from an extreme position to another).

1

y

0

0

O

AI

BI

l

r

eP

1

2

3

I

I I

y

0

0

O

AII

BII

l

re

P

2

3

II

II

l-r

xx

l+r

II

l

near dead point

distant dead point

a - the crank is in prolongingwith the connecting-rod

b - the crank is overlappedon the connecting-rod

Fig. 2. The kinematical diagrams of Otto-mechanism in

the extremely positions

The efficiency of the pistons mechanism

when the piston works like a motor mechanismcan be determined, if one goes from the piston

to the crank, with the determining of forces (see

the figure 3), [2, 3]. The consumed motor force(the input force), Fm, is divided in two

components: 1)Fn - the normal force (in the

long of the connecting-rod); 2)F - thetangential force (perpendicular in B, on the

connecting-rod); see the system (14).

(14)

==

==

cossin

sincos

mm

mmn

FFF

FFF

Fn is a single force transmitted from B to A.

0

O

A

B

l

r

e

yB

x

y

P

-

Fm

Fn

F

Fn

Fu

Fc -

-

Fig. 3. The forces of Otto-mechanism,when the piston works like a motor mechanism


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539In A, the force Fn is divided in two

components too: 1. Fu the utile force; 2. Fc acompression force. See the system (15):

(15)

==

==

)cos(sin)cos(

)sin(sin)sin(

mnc

mnu

FFF

FFF

The utile power, Pu, can be written in form(16):

)sin(sin

=

===

rF

rFvFP

m

uAuu(16)

The consumed power, Pc, can be written inform (17):

sin

)sin( == rFvFP mBmc (17)

The momentary mechanical efficiency, i,can be written with the relation (18):

2

222 )cos(1cossin

sin

1)sin(

)sin(sin

l

re

rF

rF

P

P

m

m

c

u

i

+===

=

==

(18)

To calculate the mechanical efficiency, ,one can integrate the momentary efficiency, i,from near dead point to distant dead point, from

I to II (figure 2 ):

=

+=

)cos(2

)cos(

rl

ea

rl

ea

fII

iI

(19)

One determines approximately the efficiencywith the relation (20), only if we can determine

precisely the extreme angles, M and m:

)(2

cossincossin5.0

mM

mmMM

+= (20)

2.3 Determining the mechanical efficiency

when the Otto mechanism works like steam

roller

The Otto mechanism works like motor

mechanism in a single cycle (a angle), whenthe piston is moving from the near dead point tothe distant dead point, and it works like steamroller in the rest of the energetically cycle.

At the two cycle engines, the motor works

like steam roller, in a single cycle, when the

piston is moving from the distant dead point tothe near dead point.

At the four cycle engines, the motor

works like steam roller, in three cycle; twotimes the piston is moving from the distant

dead point to the near dead point, and in one

cycle (one time) the piston is moving from the

near dead point to the distant dead point.By a cycle (a angle), one understands a

time, a single time, precisely a semi

kinematical-cycle; a kinematical cycle has a 2.angle.

In figure 4 one can see the forces in Ottomechanism when the mechanism works like a

steam roller.

0

O

A

B

l

r

e

yB

x

y

P

-

Fm

Fn

F

Fn

Fu

Fr

-

-

Fig. 4. Forces, when the piston works like a steam roller

The input force (the consumed motor force),

Fm, perpendicular in A on the crank OA (r), isdivided in two components: 1. Fnthe normal

force, which is the active component, the only

components transmitted from couple A to joint

B; 2. Fthe tangential force, which can give a

couple, and can rotate the connecting-rod, orbend it, [2,3]; see the system (21):

=

=

)cos(

)sin(

m

mn

FF

FF(21)

In joint B, the transmitted force, Fn, isdivided in two components too: 1. Fu the

useful force; 2. Fr a force normal at the guideaxis; see the system (22):

=

===

=

===

cos)sin(

cossin

sin)sin(

sincos

m

nnr

m

nnu

F

FFF

F

FFF

(22)

The utile power can be written in form (23)

and the consumed power can be written in form(24):


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540

)(sinsin

)sin(

sin)sin(

2

=

==

rFr

FvFP

m

mBuu

(23)

== rFvFP mAmc (24)

The momentary mechanical efficiency when

the piston works like steam roller, can becalculated with the relation (25):

2

222

22

]sin)cos(cos)cos([

)(sin)(sin

l

rerel

rF

rF

P

P

m

m

c

ui

+++=

==

==

(25)

3. CONCLUSION

The momentary mechanical efficiency whenthe piston works like steam roller (25), is

different that the efficiency when the pistonworks like motor (18). Generally the steam

roller efficiency is lower that the motor

efficiency. The steam roller efficiency isapproximately 50% or a lower value and the

motor efficiency can be 60-99%, in function ofthe constructive parameters, e, r, l. The motor

efficiency increases when the ratio, =r/l,decreases. For a

otto engine design-2009

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