The mathematical modelling of the electronic injection gasoline.

Blaga, Vasile ; Bara, Camelia ; Bara, Vasile 等

1. INTRODUCTION

The working of the curled engine with lambda transmitter and catalyst, makes coefficient [lambda] to be mentioned as close as possible to [lambda] = 1 (ideal dosage) (Bat.aga, 2000).

On the base of a personal model the author realized analytic calculation of pressure in the manifold [p.sub.ga] and the admission pressure [p.sub.a], the calculation of engine pressure regulator and the duration [t.sub.i] of the electromagnetic injector.

For the modeling cycle engines with spark lighting with engine injection are noticed the initial dates. All these expression were analytic calculated and correlated among them in order to be introduced in the calculator. The calculator gets the command to repeat this operation till the getting of the imposed error of the engines with spark lighting parameters (Turcom et al, 1987).

It is calculated the mechanical theoretic work proposed [L.sub.tp], the average pressure proposed [p.sub.tp], theoretical proposed efficiency and the mechanical loosing of the cycle.

The calculation of algorithm is made up of the following steps:

1) The initial parameter relation [T.sub.ao], [T.sub.zo], [T.sub.uo] si [k.sub.co], [k.sub.vo], [k.sub.uo], [k.sub.do], [k.sub.eo] for one revolution.

2) The cycle is going through, obtaining new values for k coefficients and [T.sub.a], [T.sub.z], [T.sub.u] temperatures.

3) It is made differences between old and new calculated values ([DELTA]k, [DELTA]T).

4) If the differences between ([DELTA]k, [DELTA]T) are lower than the imposed error, then the new calculated values are valid and they are going to the next revolution value and 1-4 points are repeated.

5) If the differences ([DELTA]k, [DELTA]T) are above the imposed errors then the cycle is going through by the recalculation of the adiabatic coefficient values and temperature, considered new value as initial parameter. This re-going through is realized until the descend of the differences ([DELTA]k, [DELTA]T) under the imposed errors.

2. THE OPTIMUM CALCULATION OF THE PRESSURE REGULATOR

Pressure regulator maintains constant pressure injection in supplying installation (Blaga, 2005). Calculation scheme of the pressure regulator is presented in figure 1.

[FIGURE 1 OMITTED]

Static balance equation of regulator membrane is given by the following relation (Negrea & Sandu 2000):

[F.sub.a] = [F.sub.ga] + [F.sub.b],

where: [F.sub.a] = [K.sub.a] x f

[F.sub.ga] = [pi] x [D.sup.2.sub.r]/4 x [P.sub.ga]; [F.sub.b] = [pi] x [D.sup.2.sub.r]/4 x [p.sub.b];

and [K.sub.a] is elastic constant springs; f--spring arrow; D-diameter of the regulator membrane; [F.sub.a]-power pressure of spring; [F.sub.ga]--pressure power from manifold; [p.sub.ga]--pressure from the manifold; [p.sub.b]--gasoline pressure in masterly of the injection; [F.sub.b] --the gasoline injection power.

[pi] x [D.sup.2.sub.r]/4 x [p.sub.b] = [K.sub.a x f] + [pi] x [D.sup.2.sub.r]/4 x [p.sub.ga],

After the changing, relation (1) becomes:

[p.sub.b] = 4/[pi] x [D.sup.2.sub.r] x [K.sub.a x f] + [p.sub.ga];

or:

[p.sub.b] = [K.sub.r] + [p.sub.ga];

where:

[K.sub.r] = 4 x [K.sub.a] x f/[pi] x [D.sup.2.sub.r]; [K.sub.r] = 1..4 (2)

Kr--is the constant regulator.

3. THE OPTIMUM CALCULATION OF THE ELECTROMAGNETIC INJECTION

The section of the passing pulverization hole is determined by the following relation (Bajaga, 2000):

[A.sub.a] = [pi] x [[bar.A].sub.c][d/2 + (d/2 - [[bar.A'].sub.c])] = [pi] x [s.sub.a] sin([beta]/2)(d-1/[s.sub.a] x sin [beta]); (3)

where: [A.sub.I]-passing section offered by conic top needle; [s.sub.a]-raising up needle; [d.sub.v]-diameter of the needle in top zone; [beta]-cone angle tight; [d.sub.p]-sack diameter.

Rising up needle [s.sub.a] is considered to be constant.

It was marked with [A.sub.I] the area of the leaking section near the needle top of injector with conic top (Grunwald, 1980).

[A.sub.i] = f([s.sub.a], [beta], d) = ct; [A.sub.i] = [pi]([d.sub.p] - 0,5 [s.sub.a] sin[beta])[s.sub.a] sin [beta]/2; [s.sub.a] = 0,15 mm; [d.sub.p] = l ... 1,2 mm; [beta] = 60[degrees].

Discharge of gasoline which passes the injector leaking section is calculated by the relation:

[Q.sub.b] = [[mu].sub.i] x [A.sub.i] [square root of 2([p.sub.b] - [p.sub.ga])/[[rho].sub.b]]; (4)

where [[mu].sub.I] coefficient of discharge in the section offered by the needle;

[[mu].sub.i] = 0,8 - 0,93;

Taking in consideration relation (2):

[Q.sub.b] = [[mu].sub.i] x [A.sub.i] [square root of 2[K.sub.r]/[[rho].sub.b]] (5)

where: [A.sub.i] is the leaking section at the injector; [p.sub.b]--gasoline pressure at the entrance of injector; [p.sub.ga]--air pressure from the manifold; [[rho].sub.b]--gasoline density; [K.sub.r]--constant regulator pressure; [Q.sub.b]--discharge of the gasoline.

In the other hands it is LAN own from the relation of the discharge definition that is the leaking fuel volume during a time unit.

Maybe written:

[Q.sub.b] = [V.sub.b]/[t.sub.i] = [m.sub.cb]/[[rho].sub.b] x [t.sub.i] (6)

From the equality of relation (5) and (6) results un duration of the injection, [t.sub.i]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII];

Where [xi] is the coefficient which represents the ratio between necessary air quantity for burning moor and the mixed quantity fuel accepted [m.sub.ad].

Results:

[t.sub.i] = [xi] x d x [m.sub.ad]/[[mu].sub.i] x [A.sub.i] x [square root of 2[K.sub.r]] x [[rho].sub.b] (7)

Where: [m.sub.cb] is the volume of the fuel; [m.sub.aer]--the volume of the air aspirated by the engine; [m.sub.ad]--quantity of mixed fuel admitted; d--proportioning. In figure 2 is represented the variation of the duration of injection [t.sub.i] with the revolution and the temperature of the environment surroundings.

[FIGURE 2 OMITTED]

4. CONCLUSIONS

The engines with spark lighting modeling cycle with the gasoline injection proposed by the author consist of the presentation of the initial dates of the calculation program, calculation and the correlation between the engines with spark lighting parameter expression with the gasoline injection for the achievement of the program calculation. The engines with spark lighting cycle calculation proposed, with gasoline injection is an helping cycle for the simulation on the calculator of the gasoline injection. The simulation on the calculator permit the determination of the theoretical economical-technical parameters proposed; mechanical work theoretical proposed corresponding to the diagram, theoretical pressure proposed, theoretical efficiency, theoretical specific consumption proposed. The loosing mechanical pressure and the pumping are calculated, the theoretical economical-technical parameters of the engine. Sing the proposed model by the author the volume of the fuel is calculated which reset of the engine cycle in function with the revolution of the total load, the debit of the gasoline which goes through the electromagnetic section of the injection, reaching the aim in view, the determination of the injection duration with the revolution in total load. It is conceived the calculation of the pressure regulator and of the electromagnetic injector. It was made the calculation of the injection duration [t.sub.i] with the revolution and load which represents the model proposed by the author . It was effectuated a engines with spark lighting program for the calculation of parameters with the gasoline injection with the under--program: the calculation program of engines with spark lighting parameters (depending on n and [lambda] at [t.sub.o] = -35 ... + 45[degrees]C and [p.sub.o] = 1 x [10.sup.2] kPa), the calculation program of engines with spark lighting parameters (depending on n and [t.sub.o] at [lambda] = 1 and [p.sub.o] = 1 x [10.sup.2] kPa) (Blaga, 2005).

5. REFERENCES

Bajaga, N. (2000). Driving with inward alight, The Didactic and Pedagogical Publishing House, 973-9471-20-X, Bucharest.

Blaga, V. (2005). Engine with gasoline injection, The Publishing House of University Edition Oradea, ISBN 973--613-981-6, Oradea.

Grunwald, B. (1980). The Theory, calculation and construction engine's for road motor vehicle, The Didactic and Pedagogical Publishing house, Bucharest.

Negrea, V.D. & Venetia Sandu (2000). The combating of medium pollution in motor vehicle, The Technical Publishing House, ISBN 973-31-1455-3 Bucharest.

Turcoiu, T., Boncoi, J. & Time, Al., (1987). Equipment's from injection for engine with internal burning, The Technical Publishing House, Bucharest.