EP1585895B1 - Method for calculating pressure fluctuations in a fuel supply system of an internal combustion engine operating with direct injection of fuel and for controlling the injection valves thereof - Google Patents

Abstract

Pressure fluctuations can occur in internal combustion engines provided with direct fuel injection systems. This increases fuel consumption inter alia and has a negative effect upon exhaust gas properties. The invention provides a method for calculating pressure fluctuations in the fuel supply system, which is used as a basis for controlling the injection valves of the fuel injection system such that the above-mentioned disadvantages do not occur. The invention is based on the perception that the fuel injection system can be described as a closed high-pressure system which is exposed to injection-valve actuation as an external excitation source of fluctuation. Fourier analysis is used to analyse the thus excited liquid pressure fluctuation and correction values are calculated in order to enable the time of injection, duration of injection and/or the injection volume to be modified. The temporal dependency of the liquid pressure and/or liquid volume flow is calculated by means of a separate equation

Description

The invention relates to a method for calculating pressure fluctuations in a fuel supply system of a direct fuel injection internal combustion engine and for controlling these injectors.

It is well-known that vehicles with internal combustion engines with direct-injection fuel supply systems are becoming increasingly popular with customers. This is mainly because they have a much lower fuel consumption compared to conventional internal combustion engines. In addition, in diesel internal combustion engines, the diesel fuel is cheaper and now also known as so-called bio-diesel (RME diesel) to acquire, which is made from renewable resources and therefore does not further increase the CO ₂ pollution of the earth's atmosphere. In such direct-injection fuel supply systems, the best efficiency is achieved when the fuel pressure in the injection system has a constant high value.

In diesel internal combustion engines, in addition to the so-called pump-nozzle injection system, in particular the known common-rail injection system is used. At least for the latter are multiple injection known, with which to improve the mixture preparation and the Combustion process, the required for a work operation in an engine cylinder fuel quantity is injected in, for example, three partial injection operations. In this case, a pre-injection improves in particular the mixture preparation and thus the onset of combustion during the main injection. A post-injection of fuel is finally before all the improvement of the exhaust gas performance of the internal combustion engine.

In particular, when operating such common rail injection systems with multiple injection occur during the injection processes pressure waves in the lines leading to the injectors, which reduce the nominal value of the injection pressure in an unfavorable case and thus adversely affect the efficiency and reliability of the injection system of the internal combustion engine. Thus, it may happen that during an injection process at the injection nozzle, the required target injection pressure is not available and therefore the desired amount of fuel is not injected at a predetermined injection duration. Depending on the pressure wave phase, this may lead both to an oversupply and to an undersupply of fuel as well as to different injection pressures. As a result, the drive power and the nominal exhaust behavior of the internal combustion engine is deteriorated.

To solve this problem, it has been proposed in the unpublished DE 102 17 592, by means of a control device, to adapt the injection duration of a partial injection to the phase position of the injection in relation to the pressure wave, so that at least the fuel quantity provided for an undisturbed injection process, although it is injected over a longer injection duration in the cylinder of the internal combustion engine. In this method, however, you need knowledge about the time course and thus about the trigger and the frequency of the pressure wave. Although the trigger of the pressure wave is known by the previous partial injection, but the frequency of the pressure wave is dependent on the geometry of the fuel line and the speed of sound of the shaft in the fuel.

In addition, pressure waves are generated by all other actuation processes of the injection valves of the injection system, so that superimpose a plurality of partial pressure waves in the injection system. In addition, since the speed of sound is dependent on the type of fuel (summer diesel, winter diesel, RME diesel) not considered in this method and the fuel temperature, with the said control device for adjusting the injection duration of a fuel injection, the problem caused by the pressure waves in the fuel supply of the cylinder does not sufficiently solved.

Other known provisions for compensation of pressure waves in such fuel injection systems relate to devices such as the integration of additional fuel reservoirs in the vicinity of the injection nozzles or the installation of throttles between the supply line and the respective injection nozzles.

In the mentioned DE 102 17 592 a compensation device is additionally proposed in which a piezoactuator determines the frequency of a fuel pressure wave by converting the mechanical force exerted on this sensor, converted into an electrical signal and provides a control device available. This control device then uses this frequency information and the knowledge about the undisturbed start of injection and the undisturbed injection end of the injector to adjust the level of the injection pressure of the following injection process.

In addition, from WO 99/47802 a method for determining the injection time in a working with direct fuel injection internal combustion engine, with which occurring in the supply line to an injection valve pressure fluctuations during two consecutive injection operations within the same cycle of the cylinder with a mathematical Korrekturterm be taken into account. With the corrected pressure value, the activation time for the injection valves is then changed, so that the correct amount of fuel is injected. The correction term is determined by means of a so-called "least-squares estimator" which, depending on the geometric data of the fuel injection system, such as e.g. the length of the supply line from the common supply line to the injection valve, and the properties of the fuel estimates the likely injection pressure at the nozzle of the injection valve.

A disadvantage of the previously known methods or devices for compensating for the effects of pressure waves in the lines of direct injection fuel injection systems is that they cause increased device costs or is tuned only to a very specific injection system with all its geometric data and other physical constraints and the asked technical Therefore solve the problem only very imperfectly.

In addition, DE 199 50 222 A1 describes a method with which the defect-free functioning of components of this system should be detectable by Fourier analysis of the fuel pressure in a high-pressure fuel supply system of a direct-injection internal combustion engine. It is not about fuel pressure fluctuations, which are caused primarily or secondarily by a functionally correct operation of the fuel injection valves, but those that arise due to a faulty behavior of components in the fuel supply system.

In addition, the publication A.G. Favennec, P. Minier, M. Leburn, Renault / Imagine: "Analysis of the Dynamic Behavior of the Common Rail Direct Injection System", Forth JHPS International Symposium on Fluid Power, Tokyo 1999, 15-17 Nov. 1999, pp 543-548 that a common rail injection system using an Amesim software model described and the injection pressure of such a system can be subjected to a Fourier analysis.

Finally, DE 197 40 608 A1 discloses a method for determining at least one fuel-injection-related parameter for an internal combustion engine with common-rail injection system. In this method, the pressure in the common engine fuel injection system common to the engine combustion chambers is detected via a respective injection curtain for a respective combustion chamber in its course by means of a pressure sensor of the distributor pressure chamber. From this pressure curve, an associated pressure profile pattern is obtained, from which the at least one fuel-related parameter individually is determined for each combustion chamber and each injection process.

Against this background, the present invention seeks to provide a method for reducing the effects of the pressure waves described above, with the efficiency of the engine further increased and the reliability of the overall system of the internal combustion engine and fuel injection system is improved. This method should also be usable without major changes for different sized fuel injection systems.

The solution to this problem results from a method having the features of the main claim, while advantageous embodiments and further developments of the invention are the dependent claims.

The method according to the invention is based on the knowledge that the steady-state fuel pressure oscillations occurring in a directly injecting fuel injection system can be reliably described by means of a Fourier analysis.

For the mathematical analysis of this vibration behavior of the pressure wave, it is assumed that no non-linear effects occur in the injection system, or that these are linearizable when nonlinear effects occur. If, for example, the dynamic behavior of the fuel injection valves is liniearisierbar, so the drive signal (piezo signal) can be used for this valve for Fourier analysis. In addition, it is assumed that this signal or specifically this Fuel injection rate is associated with a fixed time dependence, which is why dynamic influences of the injection quantity as a result of actuation of the injection valve are disregarded. The fuel injection amount in the subsequently developed mathematical model, therefore, is simply proportional to the timing of the operation and duration of the injection valve. In addition, the following considerations assume that the dynamics of the fuel injection system depend on well-defined operating conditions in terms of injection pressure and engine speed.

The temporal fluctuations of the fuel pressure and thus the fuel flow with the injection valve open are also not considered for the entire fuel supply system, but only for predetermined fixed points in the line and for given volumes. These points are nodes in a one-dimensional lattice mindset in the injection conduit system and to which the continuum equations are applied to describe the temporal evolution of the system. By definition, the pressure swing analyzes used for these junctions also apply to all other locations in the considered injection system.

Under the abovementioned model requirements, the time variation of the pressure and / or the volume flow at the junctions, for example in a common rail system, can be described by first-order differential equations with time-dependent coefficients. It is legitimately assumed that after a few working cycles of the internal combustion engine, a steady state with respect to the pressure oscillations in the fuel distribution system is present, since the injection timing and injection quantities do not change at a constant engine speed. The dynamics of such a discrete system, hitherto assumed to be free from external disturbances, can be more generally represented as a superposition of vibrations at different frequencies, each frequency being a resonant frequency of that system.

However, due to the opening and closing of the injectors, the fuel injection system is not actually considered an isolated system. Rather, in addition to the typical in an isolated system oscillation also occur in the fuel injection system, which are generated by the external excitation of the valve actuation.

If, as here, the external excitation is periodic, because of the viscosity of the fuel present throughout the fuel injection system, the pressure of the fuel will also oscillate at its equilibrium value (the static pressure) with the same period as the external excitation source after a certain excitation time. The time dependence of this oscillation can be calculated using the mathematical method of Fourier transformation.

Accordingly, in order to determine a correction control time for changing the actuation time and / or the actuation duration of an injection valve in a direct-injection fuel injection system of an internal combustion engine, it is initially assumed that the injection system can be regarded as a high-pressure hydraulic system stabilized after a few operating strokes of the internal combustion engine, in which the geometric properties of the injection and the properties of certain types of fuel are constants. In addition, it is assumed that the actuation of the injection valves constitutes an external excitation source for the fuel pressure oscillations in the injection system.

In order to determine the fuel pressure oscillations arising in such an injection system, the transfer function method is used, whose response function indicates the sum of the amplitudes and phases of the pressure wave with which it oscillates around the desired pressure in the fuel supply system.

The pressure oscillation phases and pressure oscillation amplitudes thus calculated are then compared with desired values of the actuation times, the fuel injection pressure and / or the injection volume. In case of deviations of the achievable actual values in comparison to the specified values, at least one correction value for the originally provided actuation time, the originally provided actuation duration and / or the originally provided injection volume is then calculated from the deviation. Subsequently, at least one of the previous setpoint values is changed by applying a correction value for the next and / or all subsequent injection events to the effect that a compensation of the disadvantages resulting from the fuel pressure oscillation is achieved.

bestimmt. Die in dieser Gleichung genannten Konstanten und Variablen werden später hergeleitet und daher direkt nachfolgend nur kurz erläutert. So bedeutet X_k,0 den Gleichgewichtswert von der Komponente X_k der Zustandsvariablen X für den Druck und den Volumenstrom, 1 die Anzahl von Nicht-Null-Komponenten der Zustandsvariablen der äußeren Anregung F, $X_{k,n}^i$

die Fourier-Komponenten des Amplitudenwertes sowie ${\mathrm{\Phi }}_{k,n}^i$

die Fourier-Komponenten des Phasenwertes zwischen der k-ten Zustandsvariablen und der i-ten Steuerungsvariablen, $f_{c,n}^i$

und ${\phi }_{c,n}^i$

die Koeffizienten der Fourier-Transformation der Steuerungsvariablen i, t die Zeit, T die Periode einer Kraftstoffdruckschwingung, c und s die Koeffizienten der Kosinus- und Sinusanteile sowie n einen ganzzahligen Indexwert.In this method, moreover, the time dependence of the fuel pressure and / or the fuel volume flow with the aid of the equation $$X_k\left(\mathrm{t}\right)=X_{k.0}+{\displaystyle \underset{i=1}{\overset{l}{\Sigma }}{\displaystyle \underset{n=0}{\overset{\infty }{\Sigma }}{X}_{k.n}^i\left(f_{c.n}^i\cos \left(\frac{2\pi \cdot n\cdot t}{T}+{\phi }_{c.n}^i+{\mathrm{\Phi }}_{k.n}^i\right)+f_{s.n}^i\sin \left(\frac{2\pi \cdot n\cdot t}{T}+{\phi }_{s.n}^i+{\mathrm{\Phi }}_{k.n}^i\right)\right)}}$$

certainly. The constants and variables mentioned in this equation are derived later and therefore only briefly explained below. Thus, X _{k, 0} denotes the equilibrium value of the component X _{k of} the state variables X for the pressure and the volumetric flow, 1 the number of nonzero components of the state variables of the external excitation F, $X_{k.n}^i$

the Fourier components of the amplitude value as well ${\mathrm{\Phi }}_{k.n}^i$

the Fourier components of the phase value between the k th state variable and the ith control variable, $f_{c.n}^i$

and ${\phi }_{c.n}^i$

the coefficients of the Fourier transform of the control variables i, t the time, T the period of a fuel pressure oscillation, c and s the coefficients of the cosine and sine components and n an integer index value.

• Bestimmen von geometrischen Parametern des Einspritzsystems,
• Bestimmen von Eigenschaften des Kraftstoffs,
• Bestimmen der Zustandsvariablen F(t) der äußeren Anregungsquelle (z.B. Einspritzventilbetätigung; eingespritzte Kraftstoffmenge),
• Fourier-Entwicklung der i-ten Komponente der Zustandsvariablen F(t),
• Berechnen der Amplitude und Phase der Druckschwingung in dem Einspritzsystem durch Anwendung der Fourier-Transformation,
• Korrektur des Einspritzzeitpunktes und/oder der Betätigungsdauer für das jeweilige Einspritzventil derart, dass unter Beachtung der berechneten Amplitude und Phase der Druckschwingung der gewünschte Einspritzdruck und/oder die gewünschte Einspritzmenge für die jeweiligen Einspritzventile eingehalten wird.

A concrete control method can include the following method steps:

• Determining geometric parameters of the injection system,
• Determining properties of the fuel,
• Determining the state variable F (t) of the external excitation source (eg injector actuation, injected fuel quantity),
• Fourier evolution of the ith component of the state variable F (t),
• Calculating the amplitude and phase of the pressure oscillation in the injection system by applying the Fourier transformation,
• Correction of the injection time and / or the actuation duration for the respective injection valve such that the desired injection pressure and / or the desired injection quantity for the respective injection valves is maintained, taking into account the calculated amplitude and phase of the pressure oscillation.

The geometric parameters of the injection system and / or the properties of the fuel are preferably specified as constants, although these can also be determined by means of suitable measuring devices at predetermined time intervals.

worin A eine Matrix ist, die die geometrischen Parameter des Systems und die Flüssigkeitseigenschaften des Kraftstoffs angibt, während F(t) der Vektor des Betätigungsverlaufs der Einspritzventile oder speziell betrachtet z.B. der Vektor der eingespritzten Flüssigkeitsmenge an den jeweiligen Einspritzventilen ist.To compute the pressure and / or volumetric flow fluctuations in the fuel injection system, X shall be referred to as the vector indicating the pressure and volumetric flow rates at said nodal points of the injection system. The components X _k of the vector X are referred to as state variables of the fuel. For the derivation of the vector X after the time then applies $$\frac{dx}{dt}=\mathrm{A}\mathrm{x}+\mathrm{F}\left(\mathrm{t}\right)$$

where A is a matrix indicating the geometrical parameters of the system and the fluid properties of the fuel, while F (t) is the vector of the actuation history of the injectors or, specifically, for example the vector of the injected amount of fluid at the respective injectors.

The components of F (t) are periodic functions and are referred to as control variables, all of which have the same period T and typically have different phase relationships to each other.

wobei f _i (t) als periodische Funktion angesehen werden kann, die auf einen i-ten Einspritzvorgang zurückzuführen ist und in ihre Kosinus- und Sinus-Komponenten zerlegt ist.The Fourier evolution of the ith component of F (t) is $$f_i\left(\mathrm{t}\right)={\displaystyle \underset{n=0}{\overset{\infty }{\Sigma }}{f}_{c.n}^i\cos \left(\frac{2\pi \cdot n\cdot t}{T}+{\phi }_{n.c}^i\right)+f_{s.n}^i\sin \left(\frac{2\pi \cdot n\cdot t}{T}+{\phi }_{n.s}^i\right)}$$

where f _i (t) can be considered as a periodic function due to an ith injection process and decomposed into its cosine and sine components.

und $$f_{s,n}^i=\frac{2}{T}{\displaystyle {\int }_{-T/2}^{T/2}{f}_i\left(\mathrm{t}-{\mathrm{t}}_{\mathrm{i}}\right)\sin \frac{2\pi \cdot n\cdot t}{T}}$$

wobei t_i gegebenenfalls benötigt wird, um den Wertebereich des Variabilitätsbereiches von f(t) bis (-T/2, T/2) zu verschieben.The Fourier components of the excitation are determined by $$f_{c.n}^i=\frac{2}{T}{\displaystyle {\int }_{-T/2}^{T/2}{f}_i\left(\mathrm{t}-{\mathrm{t}}_{\mathrm{i}}\right)\cos \frac{2\pi \cdot n\cdot t}{T}}$$

and $$f_{s.n}^i=\frac{2}{T}{\displaystyle {\int }_{-T/2}^{T/2}{f}_i\left(\mathrm{t}-{\mathrm{t}}_{\mathrm{i}}\right)\sin \frac{2\pi \cdot n\cdot t}{T}}$$

where t _{i may} be needed to shift the range of values of the variability range from f (t) to (-T / 2, T / 2).

With the main theory of linear differential equations it can be shown that a sinusoidal excitation of a control variable with the frequency of f _n = n / T at one System equilibrium in the k-th component X _k of X a sinusoidal oscillation with an amplitude X _{k, n} and with a phase Φ _{k, n} induced. This relationship can be expressed by: $${\mathrm{f}}_{\mathrm{n}}\to {\mathrm{X}}_{\mathrm{k}.\mathrm{n}}.{\mathrm{\Phi }}_{k.n}$$

These amplitudes and phases of the oscillations can be calculated between the control variable and the state variable X _k at the frequency f _n with the formalism of the Fourier transform. The Fourier transform is always calculated numerically, even if in certain cases an approximate analytic expression for certain variables or constants could be given.

Each Fourier component of the injected flow thus induces an oscillation of the volumetric flow and the pressure at the considered node whose phase and amplitude are known. Since this system is linear, the time behavior of X _{k can be} considered as the sum of all the contributions of the Fourier components of the control variables.

worin X_k,0 der Gleichgewichtswert von X_k ist und 1 für die Anzahl von Nicht-Null-Komponenten von F steht. Dieser Gleichgewichtswert X_k,0 ist dabei nichts anderes als der statische Druck, unter dem der Kraftstoff in dem Einspritzsystem eingeschlossen ist. Um diesen Gleichgewichtswert des Drucks schwankt die Druckwelle mit den Kosinus- und Sinusanteilen der Anregungsschwingung.The already mentioned time dependence X _k (t) of the fuel pressure and / or the volume flow at a node in the injection system is therefore given by $$X_k\left(\mathrm{t}\right)=X_{k.0}+{\displaystyle \underset{i=1}{\overset{l}{\Sigma }}{\displaystyle \underset{n=0}{\overset{\infty }{\Sigma }}{X}_{k.n}^i\left(f_{c.n}^i\cos \left(\frac{2\pi \cdot n\cdot t}{T}+{\phi }_{c.n}^i+{\mathrm{\Phi }}_{k.n}^i\right)+f_{s.n}^i\sin \left(\frac{2\pi \cdot n\cdot t}{T}+{\phi }_{s.n}^i+{\mathrm{\Phi }}_{k.n}^i\right)\right)}}$$

where X _{k, 0 is} the equilibrium value of X _k and 1 represents the number of nonzero components of F. This equilibrium value X _{k, 0} is nothing more than the static pressure, under which the fuel is included in the injection system. Around this equilibrium value of the pressure, the pressure wave fluctuates with the cosine and sine components of the excitation oscillation.

und für ${\mathrm{\Phi }}_{k,n}^i$

werden aus der Fourier-Transformation zwischen der k-ten Zustandsvariablen und der i-ten Steuerungsvariablen berechnet, während $f_n^i$

und ${\mathrm{\Phi }}_n^i$

die Koeffizienten der Fourier-Transformation der Steuerungsvariablen i sind. Der Wert n gibt die Zahl des bei der Berechnung jeweils berücksichtigten Summanden an. Der Index s sowie der Index c stellen die Koeffizienten der Kosinus- und der Sinusanteile dar.The values for $X_{k.n}^i$

and for ${\mathrm{\Phi }}_{k.n}^i$

are calculated from the Fourier transform between the k th state variable and the ith control variable, while $f_n^i$

and ${\mathrm{\Phi }}_n^i$

are the coefficients of the Fourier transform of the control variables i. The value n indicates the number of addends considered in the calculation. The index s and the index c represent the coefficients of the cosine and sine components.

For the mathematical analysis of this vibration behavior of the pressure wave, it is assumed that no non-linear effects occur in the injection system or that these are linearizable when nonlinear effects occur. If, for example, the dynamic behavior of the fuel injection valves is liniearisierbar, so the drive signal (piezo signal) can be used for this valve for Fourier analysis. In addition, it is assumed that this signal or specifically this fuel injection rate is assigned a fixed time dependency, for which reason dynamic influences of the injection quantity as a result of actuation of the injection valve are disregarded. The fuel injection amount is therefore simply proportional in the mathematical model used from the time of actuation and the duration of operation of the injector. It is also believed that the dynamics of the fuel injection system depend on well-defined operating conditions in terms of injection pressure and engine speed.

With the described mathematical function [Eq. 7] was carried out a comparative calculation, with the accuracy of the considerations could be confirmed to the effect that the fuel injection system can be reliably described in the steady state with respect to the pressure oscillations occurring there by a Fourier analysis. First, a computer-aided simulation system called "Amesim" was supplied with all the necessary data on a common rail fuel injection system to be examined, in addition to the specific geometric information on the fuel line geometry and the properties of the injectors, their operating sequences and operating periods, the actuation target pressure and the Properties of the fuel used were entered. Subsequently, with this data, a program run was performed in a computer and the calculated pressure fluctuations in the fuel u.a. output in graphic form.

$$\mathrm{Q}\left(\mathrm{t}\right)={\mathrm{Q}}_{\mathrm{inj}}\mathrm{\hspace{0.17em}\hspace{1em}bei}\mathrm{\hspace{0.17em}}{\mathrm{\hspace{1em}t}}_{\mathrm{a}}<\mathrm{t}<{\mathrm{t}}_{\mathrm{a}}+\mathrm{\Delta }\mathrm{t}$$

$$\mathrm{Q}\left(\mathrm{t}\right)=0\mathrm{\hspace{1em}\hspace{0.17em}}\mathrm{bei\hspace{1em}\hspace{0.17em}}{\mathrm{t}}_{\mathrm{a}}+\mathrm{\Delta }\mathrm{t}<\mathrm{t}<\mathrm{T}$$

wobei t für die zwischen zwei Einspritzvorgängen am selben Einspritzventil vergangene Zeit, Δt für die Einspritzdauer und Q_inj für den maximalen Kraftstoffvolumenstrom am Einspritzventil steht. Die Einspritzdauer Δt und der maximale Volumenstrom Q_inj wurden dabei so eingestellt, dass die richtige Einspritzmenge am betrachteten Arbeitspunkt des Zylinders zur Verfügung stand. Der Zeitpunkt t_a, zu dem die Einspritzung des Kraftstoffs in den Zylinder erfolgt, wurde für jeden der Einspritzventile derart unterschiedlich gewählt, dass sich die richtige Einspritzreihenfolge ergab. Die Zyklusdauer T wurde zudem so berechnet, dass sich die gewünschte Motordrehzahl einstellte.Concretely, the analytical expression for the forced time response of the pressure and the volume flow to the excitation by the injector operation was tested in a computer program simulating a 4 and a 3-cylinder common-rail injection engine. The injected fuel flow rate Q (t) during an injection cycle duration T has been specified as a step function, for which the following relationships apply: $$\mathrm{Q}\left(\mathrm{t}\right)=0\mathrm{at}\mathrm{}0<\mathrm{t}<{\mathrm{t}}_{\mathrm{a}}$$

$$\mathrm{Q}\left(\mathrm{t}\right)={\mathrm{Q}}_{\mathrm{inj}}\mathrm{at}\mathrm{}{\mathrm{t}}_{\mathrm{a}}<\mathrm{t}<{\mathrm{t}}_{\mathrm{a}}+\mathrm{\Delta }\mathrm{t}$$

$$\mathrm{Q}\left(\mathrm{t}\right)=0\mathrm{}\mathrm{at}{\mathrm{t}}_{\mathrm{a}}+\mathrm{\Delta }\mathrm{t}<\mathrm{t}<\mathrm{T}$$

where t is the time elapsed between two injections on the same injection valve, .DELTA.t for the injection _duration and Q _inj for the maximum fuel _{flow rate} at the injection valve. In this case, the injection _duration Δt and the maximum volume flow Q _inj were set so that the correct injection _{quantity was} available at the considered operating point of the cylinder. The time t _a , at which the injection of the fuel into the cylinder takes place, was chosen differently for each of the injection valves in such a way that the correct injection order resulted. The cycle time T was also calculated so that the desired engine speed was set.

Fig. 1

den Verlauf des Kraftstoffdrucks berechnet mit dem Simulationsprogramm "Amesin" für ein Common-Rail-Einspritzsystem, sowie Druckwerte, die mit der erfindungsgemäßen Fourier-Transformations-Methode berechnet wurden, und in

Fig. 2

den graphisch aufgetragenen prozentualen Fehler zwischen den in Fig. 1 dargestellten Druckverläufen der Vergleichsberechnungen.

The accompanying drawings show in

Fig. 1

the course of the fuel pressure calculated with the simulation program "Amesin" for a common rail injection system, as well as pressure values, which were calculated with the Fourier transform method according to the invention, and in

Fig. 2

the graphically plotted percentage error between the pressure curves of the comparison calculations shown in FIG.

It can be seen clearly in FIG. 1 that the course of the fuel pressure at an engine speed of 1,250 rpm as previously described is that in the injection system oscillates in the simulation as a constant predetermined pressure of 600 bar and has a fluctuation range of 575 bar to 628 bar over the period of 5 milliseconds analyzed here.

While the continuous pressure curve line was calculated by the said simulation system "Amesim", the individual measuring points represent the results from the pressure calculation according to the invention by means of the Fourier analysis and the Fourier transformation. Even the simple graphical comparison shows that the calculation results are very close to each other ,

How well the agreement of the calculated pressure fluctuations between the complex simulation program "Amesim" and the much faster operating and less injection system data required method according to the invention is actually shown in Fig. 2, in which the percentage error between the two calculation methods for a common rail system Connection is shown with a four-cylinder internal combustion engine during a complete injection period with a length of 0.1 second. As this error history shows, this error does not exceed the value of 0.09%, so that a very good agreement between the results of both calculation methods can be found.

The proposed method for determining the pressure fluctuations can be used with advantage in control and regulating methods for actuating the injection valves of directly injecting fuel injection systems. These systems can be both common-rail and pump-nozzle injection systems.

Of particular advantage in the inventive calculation method is that the correction of the injection times can be calculated analytically with a formula that contains a clear and explicit dependency on the system geometry and the injection characteristic. The frequencies, amplitudes and phases used in this mathematical expression for calculating the pressure fluctuations and for the injection timing and possibly injection duration correction are predetermined a priori by the injection system and need not be determined by constantly repeated measurements.

Overall, the method is very fast and provides results that are in very good agreement with those of standard hydraulic system simulation tools. Therefore, the calculation time in the simulation of injection operations in stationary operating points of an internal combustion engine can be significantly reduced.

With sufficiently high computing power, this calculation can also be done with a vehicle computer, for example, during the first start-up or at predetermined intervals during operation of the vehicle. In the latter case, it will be preferable to determine only the viscosity of the fuel and to carry out a one-time simulation run.

Claims (5)

1. Method for calculating pressure fluctuations in a fuel supply system of an internal combustion engine operating with direct fuel injection and for control of its injection valves,
   in which the fuel supply system is defined as a high-pressure hydraulic system synchronized after a few operating cycles of the internal combustion engine,
   in which the geometrical characteristics of the fuel supply system and also the fuel properties for a specific type of fuel are specified as constants or are defined,
   in which the actuation of the injection valves represents an external source of excitation for fuel pressure fluctuations in the injection system,
   in which the method of Fourier analysis is applied to fuel pressure fluctuations arising in such an injection system,
   in which the response function of the Fourier analysis specifies the phases and the amplitude of the pressure fluctuation components at which the pressure fluctuation phases and pressure fluctuation amplitudes are compared with required values of the activation points of the fuel-injection pressure and/or of the injection volume for activating the fuel-injection valves,
   in which on deviation of the achievable actual values compared to the given required values, the envisaged activation duration and/or the injection volume is calculated from the deviation of the least one correction value for the originally intended activation point,
   in which at least one of the stated previous required values is changed by application of the correction value for the next and/or all subsequent injection processes to the extent that a compensation for the disadvantages arising from the fuel pressure fluctuation is achieved and in which the time dependency of the pressure and/or the volume flow is determined with the equation $$X_k\left(t\right)=X_{k,0}+{\displaystyle \sum _{i=1}^l{\displaystyle \sum _{n=0}^{\infty }{X}_{k,n}^i\left(f_{c,n}^i\cos \left(\frac{2\pi \cdot n\cdot t}{T}+{\mathrm{\phi }}_{c,n}^i+{\mathrm{\Phi }}_{k,n}^i\right)+f_{s,n}^i\sin \left(\frac{2\pi \cdot n\cdot t}{T}+{\mathrm{\phi }}_{s,n}^i+{\mathrm{\Phi }}_{k,n}^i\right)\right)}}$$

   

   
   in which X_k,0 stands for the equilibrium value of the component X_k of the status variable X for the pressure and the volume stream, 1 for the number of non-zero components of the status variable of the external excitation F, $X_{k,n}^i$

   

   for the Fourier components of the amplitude value and ${\mathrm{\Phi }}_{k,n}^i$

   

   for the Fourier components of the phase value between the kth status variables and the ith control variables, $f_{c,n}^i$

   

   and ${\mathrm{\phi }}_{c,n}^1$

   

   means the coefficients of the Fourier transformation of the control variables I, as well as t for the time, T for the period of a fuel pressure fluctuation, c and s for the coefficients of the cosine and sine components as well as n for an integer index value.
2. Method according to claim 1, characterized by following steps:

   - Determining geometrical parameters of the injection system,

   - Determining properties of the fuel,

   - Determining the status variables F(t) of the external excitation (e.g. injection valve actuation; injected fuel volume),

   - Fourier development of the ith component of the status variable F(t),

   - Calculating the amplitude and phase of the fuel pressure fluctuation in the fuel supply system by application of Fourier transformation,

   - Correction of the injection point and/or the injection period for the relevant injection valve such that, taking into account the calculated amplitude and phase of the pressure fluctuation, the desired injection pressure and/or the desired injection volume can be maintained for the relevant injection valves.
3. Method according to claim 2, characterized in that the geometrical parameters of the injection system and/or the properties of the fuel are specified as constants and/or determined by means of measuring devices at defined intervals.
4. Method in accordance with at least one of the previous claims, characterized in that the Fourier development of the ith component of the status variable F(t) of the injected fuel quantity is produced by the equation $$f_i\left(t\right)={\displaystyle \sum _{n=0}^{\infty }{f}_{c,n}^i\cos \left(\frac{2\pi \cdot n\cdot t}{T}+{\mathrm{\phi }}_{n,c}^i\right)+f_{s,n}^i\sin \left(\frac{2\pi \cdot n\cdot t}{T}+{\mathrm{\phi }}_{n,s}^i\right)}$$

   

   with $f_{c,n}^i$

   

   and $f_{s,n}^i$

   

   as Fourier coefficients, I as the ith injection process, t as the time, T as the period of an injection pressure fluctuation, c and s as coefficients of the cosine and sine components as well as n as an integer index value.
5. Method according to claim 4, characterized in that the Fourier coefficients are formed by $$f_{c,n}^i=\frac{2}{T}{\displaystyle {\int }_{-T/2}^{T/2}{\int }_i\left(t-t_1\right)\cos \frac{2\mathrm{\pi }\cdot n\cdot t}{T}}$$

   

   and $$f_{s,n}^i=\frac{2}{T}{\displaystyle {\int }_{-T/2}^{T/2}{\int }_i\left(t-t_1\right)\sin \frac{2\mathrm{\pi }\cdot n\cdot t}{T}}$$

   

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