mm IFToMM ARoTMM
THE NINTH IFToMM INTERNATIONAL SYMPOSIUM ON THEORY OF MACHINES AND MECHANISMS BUCHAREST, ROMANIA, SEPTEMBER 1 - 4, 2005 SYROM 2005
AN ORIGINAL INTERNAL COMBUSTION ENGINE Florian Ion PETRESCU Relly Victoria PETRESCU
Department of Mechanisms and Robots, University “POLITEHNICA” of Bucharest, 313 Splaiul Independentei, 77206 Bucharest, ROMANIA E-mail: tiberiuionro@yahoo.com Department of Descriptive Geometry and Engineering Graphics, University “POLITEHNICA” of Bucharest, 313 Splaiul Independentei, 77206 Bucharest, ROMANIA E-mail: victoriap@emoka.ro
ABSTRACT: The paper presents a new and original internal-combustion engine. It is presenting a method in determining the kinematics and the efficiency of a new mechanism, MF1, proposed (designed) to work and be tested like an internal-combustion engine. One determines the mechanical momentary efficiency, when the mechanism works like a steam roller and when the mechanism works like a motor. The determined efficiency is different in the two described situations. One presents an original way to determine the dynamic efficiency too. The dynamic momentary efficiency is the same in the two situations: when the mechanism works like a steam roller and when it works like a motor. One determines the efficiency without friction, but one can anytime add the effect of friction modulus. One presents the dynamic kinematics of this mechanism too: the dynamic velocity and the dynamic acceleration. When the constructive parameters are normal, the dynamic velocities take the same values like the classical speeds and the dynamic accelerations take the same values like the classical accelerations.
Keywords: Motor, connecting-rod, dynamic-velocity, dynamic-acceleration, dynamic-efficiency. 1. INTRODUCTION The paper shortly presents a new and original internal-combustion engine. The originality consists in the way of determining the mechanical and dynamic efficiency and in the way of determining the dynamic velocities and accelerations. 2. PRESENTING THE KINEMATICS OF MF1 In picture number 1, one can see the kinematics outline of the mechanism of the new presented motor (Motor Florio 1), [2,3]. The first modification of this model, having in view the classical model (Otto engine mechanism), is the use of two connecting-rod, (2 and 3) and the use of B couple, a dual couple: of rotation and translation. This motor mechanism is a new mechanism and his functionality will be different from the classical mechanism’s functionality. The great advantage of this mechanism is that it can be regulated to have a bigger zone with constant acceleration at the piston (the element number five). The efficiency of this mechanism is the same like the Otto mechanism. The structural group 2-4 (a dyad) can improve the motor functionality without damage of power. The kinematics relations are the following (1-11): a 2 = l02 + l12 − 2 ⋅ l0 ⋅ l1 ⋅ sin ϕ1
l1 ⋅ cos ϕ1 a e − l1 ⋅ cos ϕ1 − l2 ⋅ cos ϕ 2 cos ϕ3 = l3 cos ϕ 2 = −
(1) (2) (3)
y
MOTOR FLORIO1-MF1 © 2003 Florian PETRESCU The Copyright-Law Of March, 01, 1989 U.S. Copyright Office Library of Congress Washington, DC 20559-6000 202-707-3000
5 D
3
l3 0
φ3 C e
b
2
yD
B 4 0
1
a l0 O
l2 l1
A
ϕ2
φ1
x
0
Fig. 1. The MF1 kinematics outline y D = l1 ⋅ sin ϕ1 + l2 ⋅ sin ϕ 2 + l3 ⋅ sin ϕ3 l1 ⋅ cos(ϕ1 − ϕ 2 ) ⋅ ω1 a l ⋅ l ⋅ ω ⋅ cos ϕ1 a& = − 0 1 1 a
ω2 = −
ω3 =
(5) (6)
l1 ⋅ ω1 ⋅ [l0 ⋅ cos ϕ1 ⋅ sin(ϕ3 − ϕ 2 ) + b ⋅ cos(ϕ1 − ϕ 2 ) ⋅ cos(ϕ3 − ϕ 2 )] a ⋅ l3 y& D = ω1 ⋅ l1 ⋅ cos ϕ1 + ω2 ⋅ l2 ⋅ cos ϕ 2 + ω3 ⋅ l3 ⋅ cos ϕ3
(8)
l1 ⋅ ω1 ⋅ (ω1 − ω2 ) ⋅ sin(ϕ1 − ϕ 2 ) − ω2 ⋅ a& a
(9)
ε2 = ε3 =
(4)
l1 ⋅ ω1 ⋅ [−l0 ⋅ ω1 ⋅ sin ϕ1 ⋅ sin(ϕ3 − ϕ 2 ) + l0 ⋅ (ω3 − ω2 ) ⋅ cos ϕ1 ⋅ cos(ϕ3 − ϕ 2 ) − a ⋅ l3
a& b ⋅ (ω1 − ω2 ) ⋅ sin(ϕ1 − ϕ 2 ) ⋅ cos(ϕ3 − ϕ 2 ) − b ⋅ (ω3 − ω2 ) ⋅ cos(ϕ1 − ϕ 2 ) ⋅ sin(ϕ3 − ϕ 2 )] − ⋅ ω3 a &y&D = −ω12 ⋅ l1 ⋅ sin ϕ1 − ω22 ⋅ l2 ⋅ sin ϕ 2 + ε 2 ⋅ l2 ⋅ cos ϕ 2 − ω32 ⋅ l3 ⋅ sin ϕ3 + ε 3 ⋅ l3 ⋅ cos ϕ3
(7)
(10) (11)
3. DETERMINING THE MOMENTARY MECHANICAL EFFICIENCY WHEN THE MECHANISM WORKS LIKE A STEAM ROLLER One can determine the momentary mechanical efficiency, when the mechanism works like a steam roller, if one determines the distribution of forces, from the crank to the piston (figure 2); relations (12-19) [2,3]: ⎧⎪ Fn = Fm ⋅ sin(ϕ 2 − ϕ1) ⎨ F = F ⋅ cos(ϕ − ϕ ) ⎪⎩ τ A m 2 1 a a Fτ C = ⋅ Fτ A = ⋅ Fm ⋅ cos(ϕ 2 − ϕ1 ) b b
(12) (13)
⎧ FnI = Fn ⋅ cos(ϕ 2 − ϕ3 ) ⎪ ⎨ I ⎪⎩ Fτ C = Fτ C ⋅ sin(ϕ 2 − ϕ3 )
(14)
FT = FnI + FτIC = Fn ⋅ cos(ϕ 2 − ϕ3 ) + Fτ C ⋅ sin(ϕ 2 − ϕ3 ) = a = Fm ⋅ sin(ϕ 2 − ϕ1) ⋅ cos(ϕ 2 − ϕ3 ) + ⋅ Fm ⋅ cos(ϕ 2 − ϕ1) ⋅ sin(ϕ 2 − ϕ3 ) = b a = Fm ⋅ [sin(ϕ 2 − ϕ1 ) ⋅ cos(ϕ 2 − ϕ3 ) + ⋅ cos(ϕ 2 − ϕ1) ⋅ sin(ϕ 2 − ϕ3 )] b ⎧ FU = FT ⋅ sin ϕ3 ⎨ ⎩ FR = FT ⋅ cos ϕ3 a FU = Fm ⋅ sin ϕ3 ⋅ [sin(ϕ 2 − ϕ1 ) ⋅ cos(ϕ 2 − ϕ3 ) + ⋅ cos(ϕ 2 − ϕ1 ) ⋅ sin(ϕ 2 − ϕ3 )] b l2 ⋅ cos ϕ 2 ⋅ cos(ϕ1 − ϕ 2 ) vU = vm ⋅ [cos ϕ1 − + a l0 ⋅ cos ϕ1 ⋅ sin(ϕ3 − ϕ 2 ) + b ⋅ cos(ϕ1 − ϕ 2 ) ⋅ cos(ϕ3 − ϕ 2 ) ⋅ cos ϕ3 ] a F ⋅v a ηiC = U U = sin ϕ3 ⋅ [sin(ϕ 2 − ϕ1) ⋅ cos(ϕ 2 − ϕ3 ) + ⋅ cos(ϕ 2 − ϕ1) ⋅ sin(ϕ 2 − ϕ3 )] ⋅ Fm ⋅ vm b
l2 ⋅ cos ϕ 2 ⋅ cos(ϕ1 − ϕ 2 ) + a l ⋅ cos ϕ1 ⋅ sin(ϕ3 − ϕ 2 ) + b ⋅ cos(ϕ1 − ϕ 2 ) ⋅ cos(ϕ3 − ϕ 2 ) + 0 ⋅ cos ϕ3 ] a
(16) (17)
(18)
(19)
⋅ [cos ϕ1 −
FU
(15)
FT
ϕ2 ϕ2-ϕ3
Fn
FτC C
φ3
b
B Fn ϕ2-ϕ1 a
Fm MOTOR FLORIO1-MF1 © 2003 Florian PETRESCU The Copyright-Law Of March, 01, 1989 U.S. Copyright Office Library of Congress Washington, DC 20559-6000 202-707-3000
FτA O
φ3
D
ϕ2 A φ1
FR 0
φ1
x
Fig. 2. The MF1 distribution of forces, when the mechanism works like a steam roller 4. DETERMINING THE MOMENTARY MECHANICAL EFFICIENCY WHEN THE MECHANISM WORKS LIKE A MOTOR One can determine the momentary mechanical efficiency, when the mechanism works like a motor, if one determines the distribution of forces, from the piston to the crank (figure 3); relations (20-25) [2,3]:
⎧ FN = Fm ⋅ sin ϕ3 ⎨ ⎩ FR = Fm ⋅ cos ϕ3 ⎧⎪ Fn = FN ⋅ cos(ϕ 2 − ϕ3 ) ⎨ F = F ⋅ sin(ϕ − ϕ ) ⎪⎩ τ C N 2 3 b b Fτ A = ⋅ Fτ C = ⋅ Fm ⋅ sin ϕ3 ⋅ sin(ϕ 2 − ϕ3 ) a a ⎧⎪ Fu1 = Fn ⋅ sin(ϕ1 − ϕ 2 ) ⎨ F = − F ⋅ cos(ϕ − ϕ ) ⎪⎩ u 2 τA 1 2 b Fu = Fu1 + Fu 2 = Fm ⋅ sin ϕ3 ⋅ [cos(ϕ 2 − ϕ3 ) ⋅ sin(ϕ1 − ϕ 2 ) − ⋅ sin(ϕ 2 − ϕ3 ) ⋅ cos(ϕ1 − ϕ 2 )] a b − sin ϕ3 ⋅ [cos(ϕ 2 − ϕ3 ) ⋅ sin(ϕ1 − ϕ 2 ) − ⋅ sin(ϕ 2 − ϕ3 ) ⋅ cos(ϕ1 − ϕ 2 )] a μiM = l0 cos ϕ1 sin(ϕ3 − ϕ 2 ) + b cos(ϕ1 − ϕ 2 ) cos(ϕ3 − ϕ 2 ) l2 cos ϕ 2 cos(ϕ1 − ϕ 2 ) cos ϕ1 + cos ϕ3 − a a MOTOR FLORIO1-MF1 © 2003 Florian PETRESCU The Copyright-Law Of March, 01, 1989 U.S. Copyright Office Library of Congress Washington, DC 20559-6000 202-707-3000
FτC
ϕ2
FN φ3
(22) (23) (24)
(25)
ϕ3
FR
Fm
C
0
b
FN B A
(21)
ϕ3
D ϕ2-ϕ3
(20)
a
Fn
ϕ2 φ1
Fu2
FτA ϕ1-ϕ2
Fu1
Fn
φ1 O
x
Fig. 3. The MF1 distribution of forces, when the mechanism works like a motor 5. DETERMINING THE MOMENTARY DYNAMIC EFFICIENCY The dynamic efficiency of the mechanism is the same, anytime (when the mechanism works like a steam roller and when it’s working like a motor). It can be determined approximately with the relation (26): D D ⎧μiD = μiM = ηiC = sin 2 ϕ3 ⋅ sin 2 τ ⎪ ⎨ ⎪with : τ = 2 ⋅ ϕ 2 − ϕ1 − ϕ3 ⎩
(26)
One can determine the exactly momentary dynamic efficiency of the mechanism, if one takes in calculation the dynamic velocities (in this case the speeds distribution is the same like the forces distribution), see the relations (27-29):
−
Fu b = sin ϕ3 ⋅ [sin(ϕ 2 − ϕ1) ⋅ cos(ϕ 2 − ϕ3 ) + ⋅ sin(ϕ 2 − ϕ3 ) ⋅ cos(ϕ 2 − ϕ1)] Fm a
(27)
−
vu a = sin ϕ3 ⋅ [sin(ϕ 2 − ϕ1 ) ⋅ cos(ϕ 2 − ϕ3 ) + ⋅ sin(ϕ 2 − ϕ3 ) ⋅ cos(ϕ 2 − ϕ1 )] vm b
(28)
μiD = sin 2 ϕ3 ⋅ {sin 2 (ϕ 2 − ϕ1 ) ⋅ cos 2 (ϕ 2 − ϕ3 ) + sin 2 (ϕ 2 − ϕ3 ) ⋅ cos 2 (ϕ 2 − ϕ1) + +
a 2 + b2 ⋅ sin[2 ⋅ (ϕ 2 − ϕ1)] ⋅ sin[2 ⋅ (ϕ 2 − ϕ3 )]} 4⋅a⋅b
(29)
6. THE DYNAMIC KINEMATICS OF THE MECHANISM One can determine now the dynamic velocity (30) and the dynamic acceleration of the piston (31): Din vD = l1 ⋅ ω1 ⋅ sin ϕ3 ⋅ [sin(ϕ 2 − ϕ1 ) ⋅ cos(ϕ 2 − ϕ3 ) +
a ⋅ sin(ϕ 2 − ϕ3 ) ⋅ cos(ϕ 2 − ϕ1)] b
(30)
a ⋅ cos(ϕ 2 − ϕ1) ⋅ sin(ϕ 2 − ϕ3 )] + b + sin ϕ3 ⋅ [cos(ϕ 2 − ϕ1 ) ⋅ cos(ϕ 2 − ϕ3 ) ⋅ (ω2 − ω1) − sin(ϕ 2 − ϕ1 ) ⋅ sin(ϕ 2 − ϕ3 ) ⋅ (ω2 − ω3 ) − Din aD = {ω3 ⋅ cos ϕ3 ⋅ [sin(ϕ 2 − ϕ1) ⋅ cos(ϕ 2 − ϕ3 ) +
a a ⋅ sin(ϕ 2 − ϕ1) ⋅ sin(ϕ 2 − ϕ3 ) ⋅ (ω2 − ω1) + ⋅ cos(ϕ 2 − ϕ1) ⋅ cos(ϕ 2 − ϕ3 ) ⋅ (ω2 − ω3 ) + b b a& a ⋅ a& + ⋅ cos(ϕ 2 − ϕ1) ⋅ sin(ϕ 2 − ϕ3 ) + 2 ⋅ cos(ϕ 2 − ϕ1 ) ⋅ sin(ϕ 2 − ϕ3 )]} ⋅ l1 ⋅ ω1 b b −
(31)
7. DISCUTION If the values of the constructive parameters of the mechanism are normal, the dynamic speeds and the dynamic acceleration of the piston (30-31), are practical the same like the classical kinematics values (811), see the picture number (4, 5 and 6):
ηD =20.503427825
MOTOR FLORIO 1
a[m/s ];n=5000[rot/min];l1=0.01;l2=0.3;l3=0.5;l0=0.15;e=0 3000 2000 1000 0 -1000 0
100
200
300
400
-2000 -3000 -4000
Fig. 4. The MF1 piston acceleration, when the constructive parameters are normal
n=5000[rot/min];l1=0.01;l2=0.3;l3=0.5;l0=0.15;e=0
n=5000[rot/min];l1=0.01;l2=0.3;l3=0.5;l0=0.15;e=0
1.5
3000 V(Din)/(l1.w) V(Cin)/(l1.w)
1 0.5
2000 0
0 -0.5
aD(D) aD(Cin)
1000
0
100
200
300
400
-1000 0
100
200
300
400
-2000
-1
-3000
-1.5
-4000
Fig. 5. The kinematical and dynamic velocities
Fig. 6. The kinematical and dynamic accelerations
When the values of the constructive parameters are different from the normal, the dynamic speeds and the dynamic acceleration of the piston (30-31), are not the same like the classical kinematics values (8-11), see the picture number (7 and 8):
n=5000[rot/min];l1=0.08;l2=0.3;l3=0.5;l0=0.15;e=0
50000
n=5000[rot/min];l1=0.08;l2=0.3;l3=0.5;l0=0.15;e=0
2
1.5
0
V(Din)/(l1.w) V(Cin)/(l1.w)
1
-50000
0.5 0 -1
-100000 400 -150000
-1.5
-200000
-0.5 0
100
200
300
0
100
200
300
400
aD(D) aD(Cin)
-2
Fig. 7. The kinematical and dynamic velocities
Fig. 8. The kinematical and dynamic accelerations
8. CONCLUSION Some mechanisms have the same parameters for the classical and for the dynamic kinematics (gears, cams with plate followers, the planar tetra-later mechanism, etc…). Others don’t. At the presented mechanism, the dynamic-kinematics is different from the classical-kinematics, but, if the constructive parameters are normal, the dynamic velocities practically take the same values like the classical speeds and the dynamic accelerations take the same values like the classical accelerations. Structurally, the mechanism has two dyad, when it works like steam roller and it generates a triad, when works like motor. REFERENCES 1. Pelecudi, Chr., ş.a., Mecanisme. E.D.P., Bucureşti, 1985. 2. Petrescu, V., Petrescu, I., Randamentul cuplei superioare de la angrenajele cu roţi dinţate cu axe fixe, In: The Proceedings of 7th National Symposium PRASIC, Braşov, vol. I, pp. 333-338, 2002. 3. Petrescu, F.I., Petrescu, R.V., Câteva elemente privind îmbunătăţirea designului mecanismului motor, In: The Proceedings of 8th National Symposium on GTD, Braşov, vol. I, pp. 353-358, 2003.