L 01 petrescu florian ion v engine by Ion Tiberiu

TECHNICAL UNIVERSITY OF CLUJ-NAPOCA ACTA TECHNICA NAPOCENSIS

International Conference on Engineering Graphics and Design 12-13 June 2009

V ENGINE DESIGN Florian Ion PETRESCU, Relly Victoria PETRESCU Abstract: V engines in a characteristic aside, their reply kinematics-dynamic (operating in a dynamic viewpoint) is closely linked to constructive parameters of the engine, especially the constructive angle. For this reason, as generally constructive value angle was chosen randomly, after various technical requirements constructive or otherwise, inherited or calculated by various factors (more or less essential), but never got to discuss crucial factor (which takes account of the intimate physiology of the mechanism) angle that is constructive with his immediate influence on the overall dynamics of the mechanism, the actual dynamics of the mechanism with the main engine in the V suffered, the noise and vibration are generally higher compared with the similar engines in line. This paper aims to make a major contribution to remedy this problem so that the engine in V can be optimally designed and its dynamic behavior in the operation to become blameless, higher than that of similar engines in line. Theoretical calculations are difficult and complex, but the alteration constructive required of them is simple, consisting of the imposition of a list of constructive values of the angle from which you can select the most convenient for each engine builder in V. Key words: Efficiency, force, piston, crank, connecting-rod, motor, stroke, bore, dynamic-velocity, dynamic-acceleration, dynamic-efficiency, V engines, dynamics, kinematics.

1. INTRODUCTION The V Motors’ kinematics and dynamics synthesis can be made optimally by the value of constructive angle (α). For this reason, as generally constructive value angle was chosen randomly, after various technical requirements constructive or otherwise, inherited or calculated by various factors (more or less essential), but never got to discuss crucial factor (which takes account of the intimate physiology of the mechanism) angle that is constructive with his immediate influence on the overall dynamics of the mechanism, the actual dynamics of the mechanism with the main engine in the V suffered, the noise and vibration are generally higher compared with the similar engines in line. This paper aims to make a major contribution to remedy this problem so that the engine in V can be optimally designed and its dynamic behavior in the operation to become blameless, higher than that of similar engines in line.

Theoretical calculations are difficult and complex, but the alteration constructive required of them is simple, consisting of the imposition of a list of constructive values of the angle from which you can select the most convenient for each engine builder in V. 2. V MOTOR’S SYNTHESIS 2.1. Presentation In the picture number 1 (see the detail in the picture number 2) one can see the kinematics schema of the V Engine. The crank 1 has a trigonometric rotation (ω) and actions the connecting-rod 2 which moves the piston 3 along the slide bar ΔB and actions the second connecting-rod 4, which moves the second piston 5 along the slide bar ΔD. There is a constructive angle α between the two axes ΔB and ΔD. The same constructive angle (α) is formed by the two arms of the connecting-rod 2; first arm has the length l, and the second (which transmits the movement to the second

connecting-rod 4) has the length a; this length a, add with the length b of the second connecting-rod 4 must gives the length l of the first connecting-rod. FCm

ΔD

4 b

α-β

γ+β

ΔB

FCn B

FCn

a FBm

FCm α

π/2-ϕ-β ||ΔB

= x ⋅ Fm ⋅ sin(ϕ + β ) ⋅ cos β

α/2

FB A

FBm

From the element 2 (first arm) to the first piston (element 3) one transmits the force FB (5) and the dynamic velocity vBD (6).

FB = FBm ⋅ cos β =

(4)

β 3

π/2+ϕ+β-α

+ϕ + β −α] = 2 = y ⋅ v m ⋅ sin(α − ϕ − β )

vCm = y ⋅ v m ⋅ cos[

(5)

r ϕ

v B = v Bm ⋅ cos β =

= x ⋅ v m ⋅ sin(ϕ + β ) ⋅ cos β

O V Motors’ Kinematics and Dynamics Synthesis by the Constructive Angle Value (α); Forces Distribution, Angles, Elements and Couples (Joints) Positions; a+b=l

Fig. 1. V Motor’ Synthesis

The crank motor force Fm is perpendicular at the crank length r, in A. A part of it (FBm) is transmitted to the first arm of connecting-rod 2 (along l) towards the first piston 3. An other part of the motor force, (FCm) is transmitted towards the second piston 5, by (along) the second arm of first connecting-rod 2 (a).

The kinematics (known) velocity (imposed by the linkage) is given by the relation 7. v B = v m ⋅ sin(ϕ + β ) ⋅

DB = x ⋅ cos 2 β

(8)

Where,

(2)

2.2. Forces and velocities A percent (of motor force Fm) x is transmitted towards the first piston (element 3) and the percent y is transmitted towards the second piston (element 5); the sum between x and y is 1 or 100%. The dynamic velocities have the same direction like forces:

v BD = D B ⋅ v B

(9)

vm = r ⋅ ω

(10)

The second Motor’ outline can be solved now. In C, FCm and vCm are projected in FCn and vCn:

FCn = FCm ⋅ cos(γ + β ) = = y ⋅ Fm ⋅ sin(α − ϕ − β ) ⋅ cos(γ + β ) vCn = vCm ⋅ cos(γ + β ) = = y ⋅ v m ⋅ sin(α − ϕ − β ) ⋅ cos(γ + β )

v Bm = x ⋅ v m ⋅ cos[ − (ϕ + β )] = 2 = x ⋅ v m ⋅ sin(ϕ + β )

(7)

(1)

+ϕ + β −α] = 2 = y ⋅ Fm ⋅ sin(α − ϕ − β ) FCm = y ⋅ Fm ⋅ cos[

1 cos β

To force the first piston velocity equalises the dynamic value, one introduces a dynamic coefficient DB (8):

FBm = x ⋅ Fm ⋅ cos[ − (ϕ + β )] = 2 = x ⋅ Fm ⋅ sin(ϕ + β )

(6)

(11)

(12)

(3) The transmitted force along of the second connecting-rod (FCn) is projected in D on the

ΔD axe in FD: FD = FCn ⋅ cos γ = = y ⋅ Fm ⋅ sin(α − ϕ − β ) ⋅

(13)

⋅ cos(γ + β ) ⋅ cos γ

3. DYNAMIC ANALYSIS

The dynamic velocity in D is: v D = vCn ⋅ cos γ = = y ⋅ v m ⋅ sin(α − ϕ − β ) ⋅

The value of x was determined from the imposed condition to have a single dynamic coefficient for the mechanism.

(14)

⋅ cos(γ + β ) ⋅ cos γ

The dynamic analysis made with the presented systems indicates some good values for the constructive angle (α), which allow the motor in V works normally without vibrations, noises and shocks (see the table 1): Alfa angle values in grad

The velocity of D imposed by the joint is (15): vm ⋅ cos γ ⋅ l ⋅ cos β ⋅ [l ⋅ cos β ⋅ sin(γ + α − ϕ ) − s& D = v D =

(15)

− a ⋅ cos ϕ ⋅ sin(γ + β )]

2.3. The dynamics coefficient The dynamic coefficient in D is (16): N ⎧ ⎪D D = n ⎪ ⎪ N = (1 − x ) ⋅ l ⋅ sin( α − ϕ − β ) ⋅ ⎪ 2 ⎨ ⋅ cos( γ + β ) ⋅ cos γ ⋅ cos β ⎪ n = l ⋅ cos β ⋅ sin( γ + α − ϕ ) − ⎪ ⎪ − a ⋅ cos ϕ ⋅ sin( γ + β ) ⎪ ⎩

α [GRAD] 0–8 12 – 17 23 – 25 155 – 156 164 – 167 173 – 179

4. CONCLUSION

With α indicate in the table 1 one can make V Engine work without vibrations. (16) 5. REFERENCES

One put the condition to have a single dynamic coefficient of the mechanism, D:

Nx ⎧ ⎪ D = DD = DB ⇒ x = n x ⎪ ⎪ N x = l ⋅ sin(α − ϕ − β ) ⋅ ⎪ 2 ⎪⋅ cos(γ + β ) ⋅ cos γ ⎪ 2 ⎨n x = l ⋅ cos β ⋅ sin(γ + α − ϕ ) − ⎪− a ⋅ cos β ⋅ cos ϕ ⋅ sin(γ + β ) + ⎪ ⎪l ⋅ sin(α − ϕ − β ) ⋅ cos(γ + β ) ⋅ cos 2 γ ⎪ 2 ⎪ D = DB = x ⋅ cos β ⎪ ⎩

Table 1

(17)

[1] Pelecudi, Chr., s.a. Mecanisme, E.D.P., Bucuresti, 1985. [2] Petrescu, F.I., Petrescu, R.V., Câteva elemente privind îmbunătăţirea designului mecanismului motor, Proceedings of 8th National Symposium on GTD, Vol. I, p. 353-358, Brasov, 2003. [3] Petrescu, F.I., Petrescu, R.V., An original internal combustion engine, Proceedings of 9th International Symposium SYROM, Vol. I, p. 135-140, Bucharest, 2005. [4] Petrescu, F.I., Petrescu, R.V., Determining the mechanical efficiency of Otto engine’s mechanism, Proceedings of International Symposium, SYROM 2005, Vol. I, p. 141146, Bucharest, 2005.

FCm

ΔD

4 b

α-β

γ+β

ΔB

FCn B

FCn

a FBm

FCm α

π/2+ϕ+β-α

FB A

FBm

α/2

π/2-ϕ-β ||ΔB

r ϕ

ω O

V Motors’ Kinematics and Dynamics Synthesis by the Constructive Angle Value (α); Forces Distribution, Angles, Elements and Couples (Joints) Positions; a+b=l

Fig. 2. V Motor kinematics schema.

DESIGNUL MOTOARELOR ÎN V Rezumat: Motoarele în V au o caracteristică aparte, răspunsul lor cinematico-dinamic (funcţionarea lor din punct de vedere dinamic) fiind strâns legat de parametrii constructivi ai motorului, în special de valoarea unghiului constructiv. Din acest motiv, cum în general valoarea unghiului constructiv a fost aleasă aleator, după diferite cerinţe tehnico-constructive ori de altă natură, moştenite sau calculate după diferiţi factori (mai mult sau mai puţin esenţiali), dar niciodată nu s-a luat în discuţie factorul hotărâtor (care ţine cont de fiziologia intimă a mecanismului) adică unghiul constructiv cu influenţa lui nemijlocită asupra dinamicii mecanismului per ansamblu, dinamica reală a mecanismului principal împreună cu cea a motorului în V a avut de suferit, nivelul zgomotelor şi vibraţiilor fiind în general mai ridicat comparativ cu motoarele similare în linie. Prezenta lucrare îşi propune să aducă o contribuţie majoră la remedierea acestei probleme, astfel încât motorul în V să poată fi proiectat optim, iar comportamentul său dinamic în funcţionare să devină ireproşabil, superior celui al motoarelor similare în linie. Calculele teoretice sunt dificile şi complexe, însă modificarea constructivă cerută de ele, este simplă, constând în impunerea unei liste de valori ale unghiului constructiv, din care se poate selecta valoarea cea mai convenabilă pentru fiecare constructor de motoare în V.

Authors: Petrescu Florian Ion, PhD. Eng. Assistant Professor at Polytechnic University of Bucharest, TMR Department (Theory of Mechanisms and Robots Department), petrescuflorian@yahoo.com, 0214029632; Petrescu Relly Victoria, PhD. Eng., Lecturer at Polytechnic University of Bucharest, GDGI Department (Department of Descriptive Geometry and Engineering Graphics), petrescurelly@yahoo.com, 0214029136.