DE102019203312A1 - Method for modeling a pressure in a cylinder of an internal combustion engine - Google Patents

Abstract

The invention relates to a method for modeling a pressure (p) in a cylinder of an internal combustion engine, with fuel being injected into the cylinder via at least one injector and a piston in the cylinder being driven cyclically via a shaft. The method has the following steps: First, an injected fuel mass (m) is determined from a model (10) for the at least one injector. The injected fuel mass (m) then passes through a filtering (12) in order to determine a fuel mass (m) available for combustion and to determine the rate of combustion of the fuel. In addition, the probability (W) for a start of the combustion is determined as a function of an injection angle (Φ) and an accumulated injected fuel mass (m). In addition, a time before the combustion starts is determined as a function of injection angles (Φ) and an initial pressure (p) in the cylinder using Wiebe lengths (WL, WL1, WL2) for all injections (E, E1, E2). Then a fuel mass (mcomb) burned during the combustion is calculated from the fuel mass (mba) available for the combustion, the probability (W) for the start of the combustion and from the Wiebe length (WL) (40). Finally, the modeled pressure (p) is determined from the burned fuel mass (m).

Description

The present invention relates to a method for modeling a pressure in a cylinder of an internal combustion engine. The invention also relates to a computer program that executes each step of the method when it runs on a computing device, as well as a machine-readable storage medium that stores the computer program. Finally, the invention relates to an electronic control device which is set up to carry out the method according to the invention.

State of the art

Nowadays there are efforts with regard to internal combustion engines to reduce the tolerances in the injections of fuel into a cylinder of the internal combustion engine by means of an injector, which results in very precise individual injections. For this purpose, a control strategy for the injector, the so-called “Needle Closing Control” (NCC), was developed. This control strategy includes a pre-control, the so-called “Back Pressure Precontrol” (BPP), which primarily affects the pressure in the cylinder. A change in the pressure in the cylinder can have various effects on the behavior of the injector, which can result in an imprecise metered fuel mass. In order to carry out a suitable correction, the pressure in the cylinder is required. There are already models for this which model the pressure in the cylinder. These models are mostly based on injections that are considered separately from one another. The configuration changes for each injection and the model is recalculated each time.

An example of such a model is “polyfit”, which is based on several tables of values and takes into account the number of pre, main and post injections, their injection angle and the combustion air ratio of the exhaust gas, the pressure of the common fuel reservoir and the pressure in an intake manifold.

Models are known in which a Wiebe function is determined for each injection pattern (determined from the angle and quantity for all injections). A conventional Wiebe function can be derived from the "Prediction of In-Cylinder Pressure, Temperature, and Loads Related to the Crank Slider Mechanism of IC Engines: A Computational Model", Carlos Alberto Romero Piedrahita et al., Conference Paper of conference SAE 2003 World Congress, at Cobo Center, Detroit, USA, March 2003 , can be taken.

Disclosure of the invention

A method for modeling a pressure in a cylinder of an internal combustion engine is proposed. Fuel is injected into the cylinder via at least one injector. A piston in the cylinder is driven cyclically by a shaft and increases or decreases the volume of the combustion chamber in the cylinder. In order to model the pressure in the cylinder, the burned mass of the fuel is calculated beforehand at all the necessary angles. The procedure consists of the following steps:

A fuel mass injected by the at least one injector is determined from a model for the at least one injector. For this purpose, a model known per se can be provided for the at least one injector, with which the fuel flow can be described. The fuel flow can then be integrated to obtain the injected fuel mass at all calculation steps over a cycle. The injected fuel mass is filtered in order to determine a fuel mass available for combustion and to describe a fuel distribution in a combustion chamber of the cylinder and to determine the rate of combustion of the fuel.

In particular, when filtering the fuel flow, a combustion speed is calculated as a function of exhaust gas, which is returned to the internal combustion engine through exhaust gas recirculation and through the combustion itself. The recirculated exhaust gas and the fresh air mass have an influence on the pressure development in the cylinder, especially during combustion. In addition, a high proportion of exhaust gas in the cylinder slows the combustion rate. The oxygen molecules are literally shielded from the fuel molecules by the exhaust gas. The effects of the exhaust gas can be included as a multiplicative factor in the filtering strength. The higher the exhaust gas rate, the larger the factor and the higher the time constant during the filtering. The factor can be stored in a characteristic curve depending on the exhaust gas rate.

Furthermore, the probability of starting a combustion of the fuel in the combustion chamber is designated as a function of an angle of the shaft during the injection, and the cumulative injected mass of fuel. The angle of the shaft at each start of injection is known as the “injection angle” and is specified as 0 ° starting from top dead center. At very early injection angles, therefore below -40 ° CA ("crank angle"), and at late injection angles, therefore above + 10 ° CA, the probability of starting the combustion is significantly lower. Even in the event that a small mass of fuel is injected, the likelihood of starting the combustion is reduced. This is especially true if no injection has previously taken place. Particularly in the event that a small mass was injected at a very early injection angle or at a late injection angle, the probability of the start of the combustion is very low. An unintended or incorrect start of the combustion can lead to a drastic increase in emissions. On the other hand, the probability of the start of the combustion is particularly high if the injection takes place in a range between -10 ° CA and 0 ° CA, hence the top dead center. In the case of several injections, the respective injected fuel masses are added up to form the accumulated fuel mass. Accordingly, the probability of the start of the combustion of the current fuel mass also changes as a function of the previous injections of the same cycle of the cylinder.

Injections that occur very late, but within the same cycle, therefore from + 80 ° CA, can be interpreted as independent injections.

The probability of the start of the combustion as a function of the injection angle and the injected fuel mass is preferably recorded in advance and stored in a characteristic map. This means that the probabilities can be called up directly without the need for an additional calculation.

In addition, a time before the combustion starts is calculated as a function of the injection angles using Wiebe lengths for all injections. In the case of an injection, especially if the pressure is low at the start of compression, it can be observed that the pressure in the cylinder suddenly drops after a certain period of time to a pressure that would be reached if all of the fuel had been injected and was instantly completely burned. The Wiebe lengths are not calculated separately for each injection, as is conventional, but the Wiebe lengths are determined for all injections independently of one another using a combustion enabling function. The combustion release function is a like-like correlation; H. it simulates the course of the Wiebe function and represents the above-mentioned specific duration and the instantaneous combustion. The Wiebe length is defined as the time until the probability of the start of the combustion (see above) is reached and thus corresponds to this specific time period. Consequently, the Wiebe length indicates the length of time between the injection and the expected start of combustion. The Wiebe length depends on the one hand on the initial pressure in the cylinder when the valves of the cylinder are closed: the lower the initial pressure in the cylinder, the greater the Wiebe length. On the other hand, the Wiebe length depends on the injection angle: the closer the injection is to top dead center, the smaller the Wiebe length.

The similar combustion release function can be determined in the case of several successive injections, as long as no complete release has been achieved at the currently calculated angle. This means that calculation steps can be saved.

The Wiebe-like combustion release function is preferably calculated in advance and the determined Wiebe lengths are stored in a characteristic map as a function of the injection angles and the initial pressure. This means that the Wiebe lengths can be called up directly without the need for an additional calculation.

The fuel mass burned during the combustion is calculated from the fuel mass available for combustion (see above), the probability of the start of the combustion and the Wiebe length. For this purpose, the current injected fuel mass is multiplied by the probability of starting the combustion. The Wiebe length ensures a delayed start of the combustion.

For several successive injections in a cycle, the probability of the start of the combustion of the current injections, as described above, is dependent on previous injections. The Wiebe length is adjusted for each injection. Once complete release of combustion is achieved, then combustion is maintained through the further injections until the cycle ends.

Finally, the calculated burned fuel mass flows into a known model for determining the pressure in the cylinder, so that the modeled pressure is determined.

By means of this method, the modeling of a pressure in a cylinder of an internal combustion engine can be carried out in an electronic control device in a time-saving and resource-efficient manner.

The fact is preferably taken into account that the metered fuel evaporates and has to reach the place where the fuel is burned. The time for evaporation of the metered fuel and the time until the metered fuel reaches the place where the fuel is burned can be taken into account as a waiting time when calculating the time before the combustion starts. The Wiebe length is then extended by this waiting time. This results in a more accurate model.

According to one aspect, when calculating the burned fuel mass, heat transport from the combustion chamber of the cylinder is only taken into account in a predeterminable area around the top dead center of the internal combustion engine. Otherwise the heat flow from the combustion chamber can be neglected. This makes the calculation easier without integrating too large an error into the model.

In addition, it can be provided that a torque of the internal combustion engine is calculated using the method and the variables determined therein.

From the time before the combustion starts, i.e. H. A start of the combustion after the injection can be determined by means of the Wiebe length. Starting from the start of the combustion, an end of the combustion can then be determined from the speed of the combustion and the burned fuel mass. Before the start of the combustion and after the end of the combustion, the change in the combustion chamber caused by the piston - i.e. the compression and decompression during a cycle - when the valves of the cylinder are closed can be described as an adiabatic change in state.

Provision can be made to calculate the torque of the internal combustion engine using the above-described modeled pressure in the cylinder. Especially with compression and decompression in the cycle, when an adiabatic change of state takes place, the modeled pressure can be calculated in one way with the aid of the adiabatic equation. This offers the advantage that the adiabatic coefficients were already calculated during the determination of the modeled pressure.

The invention enables the torque to be calculated for a high pressure loop. The total torque essentially corresponds to the torque during the adiabatic change of state, therefore before the start of the combustion or after the end of the combustion and during the combustion.

The computer program is set up to carry out each step of the method, in particular if it is carried out on a computing device or control device. It enables the implementation of the method in a conventional electronic control unit without having to make structural changes to it. For this purpose it is stored on the machine-readable storage medium.

By uploading the computer program to a conventional electronic control unit, the electronic control unit is obtained, which is set up to model the pressure in the cylinder.

Figure list

• 1 zeigt ein Ablaufdiagramm zur Ansteuerung von Injektoren für Zylinder einer Verbrennungsmaschine in einer Übersicht.
• 2a zeigt ein Druck-Volumen-Diagramm in doppellogarithmischer Darstellung für einen Zyklus der Kompression, Verbrennung und Dekompression in einem Zylinder.
• 2b zeigt das Zerlegungsprinzip zwischen zwei konsekutiven Berechnungswinkeln bei der Verbrennung in einem Druck-Volumen-Diagramm in einem Zylinder.
• 3 zeigt ein Ablaufdiagramm zur Ermittlung einer verbrannten Kraftstoffmasse gemäß einer Ausführungsform des erfindungsgemäßen Verfahrens.
• 4 a und b zeigen jeweils ein Diagramm eines Kraftstoffflusses bei der Einspritzung eines Injektors.
• 5 zeigt die Wahrscheinlichkeit für den Start einer Verbrennung in Abhängigkeit vom Einspritzwinkel und von der eingespritzten Kraftstoffmasse.
• 6 zeigt ein Diagramm der Wiebe-Länge in Abhängigkeit vom Einspritzwinkel und vom anfänglichen Druck.
• 7 zeigt ein Diagramm einer eingespritzten Kraftstoffmasse, einer für die Verbrennung zur Verfügung stehende Kraftstoffmasse und einer verbrannten Kraftstoffmasse für eine Einspritzung in der oberen Hälfte und die Wahrscheinlichkeit für den Start einer Verbrennung und eine Verbrennungsfreigabefunktion mit einer Wiebe-Länge für diese Einspritzung in der unteren Hälfte.
• 8 zeigt ein Diagramm einer eingespritzten Kraftstoffmasse, einer für die Verbrennung zur Verfügung stehende Kraftstoffmasse und einer verbrannten Kraftstoffmasse für zwei aufeinander folgende Einspritzung in der oberen Hälfte und die Wahrscheinlichkeit für den Start einer Verbrennung und eine Verbrennungsfreigabefunktion mit einer Wiebe-Länge für diese Einspritzungen in der unteren Hälfte.
• 9 zeigt in einem Diagramm des Drucks über dem Einspritzwinkel gemessene Drücke und den modellierten Druck gemäß einer Ausführungsform des erfindungsgemäßen Verfahrens.

Exemplary embodiments of the invention are shown in the drawings and explained in more detail in the description below.

• 1 shows an overview of a flow diagram for controlling injectors for cylinders of an internal combustion engine.
• 2a shows a pressure-volume diagram in a double logarithmic representation for a cycle of compression, combustion and decompression in a cylinder.
• 2 B shows the decomposition principle between two consecutive calculation angles during combustion in a pressure-volume diagram in a cylinder.
• 3 shows a flow chart for determining a burned fuel mass according to an embodiment of the method according to the invention.
• 4 a and b each show a diagram of a fuel flow during the injection of an injector.
• 5 shows the probability of starting a combustion as a function of the injection angle and the injected fuel mass.
• 6th shows a diagram of the Wiebe length as a function of the injection angle and the initial pressure.
• 7th shows a diagram of an injected fuel mass, a fuel mass available for combustion and a burned fuel mass for an injection in the upper half and the probability of starting a combustion and a combustion release function with a Wiebe length for this injection in the lower half.
• 8th shows a diagram of an injected fuel mass, a fuel mass available for combustion and a burned fuel mass for two successive injections in the upper half and the probability of starting a combustion and a combustion release function with a Wiebe length for these injections in the lower half Half.
• 9 shows in a diagram of the pressure over the injection angle measured pressures and the modeled pressure according to an embodiment of the method according to the invention.

Embodiments of the invention

In 1 an overview of the control of injectors for cylinders of an internal combustion engine is shown in a flow chart. The following models and functions as well as the control take place in an electronic control unit. With the exception of the model according to the invention 3 for the pressure in the cylinder (cylinder pressure model 3 ) the other models and functions are known per se. It becomes a model 1 for the air flowing into the cylinders, a pressure p _AK on an intake manifold, the combustion air ratio λ of exhaust gas, which is returned to the cylinder by exhaust gas recirculation, and a mass of air m _A , which is measured by an air mass sensor, into the model 1 flow in. There is also an evaluation 2 of pressure p _rail provided in the common high pressure accumulator of the injectors. To control the injectors, an injected fuel mass required for the current operation of the internal combustion engine is also required m _{inj, d, i} for each injection and a desired injection angle Φ _{d, i} for each injection at which the desired injected fuel mass m _{inj, d, i} is to be injected, specified.

With the cylinder pressure model 3 a modeled pressure is produced by means of the method according to the invention p _m determined in the cylinder of the internal combustion engine. This is described in detail below. The modeled print p _m flows into a Back Pressure Precontrol (BPP) 4th for the injectors and is used therein to carry out a suitable correction in the control of the injectors. Based on the BPP 4th the injector is then driven 5.

About the modeled print p _m To determine the cycle of compression, combustion and decompression of the cylinder is considered. In 2a shows a pressure-volume diagram in double logarithmic representation (logp-logV diagram) for the cycle. At point I, recirculated exhaust gas and air are let into the cylinder. The compression takes place between point I and point II, during which the valves of the cylinder are closed. This is an adiabatic change of state, ie work is done, but no heat is exchanged.

Shortly before point II, fuel is injected into the cylinder through the injector. Point II marks the start of the combustion and point III the end of the combustion. Between the two following calculation angles between point II and point III, the combustion can be broken down according to 2 B calculate: it changes first between points II _{a, i} - II _{b, i} the pressure at constant volume, ie no work is done, but heat is exchanged. Between the points II _{b, i} - II _{a, i + 1} an adiabatic change of state takes place again. The determination of the modeled pressure p _m is divided into two sections in accordance with the thermodynamic processes during combustion. Another adiabatic change of state takes place between point III and point IV.

In the cylinder pressure model 3 it is assumed that the gas mixture in the cylinder can be approximated by the ideal gas equation in formula 1, even for the maximum compression. $$p\cdot V=n\cdot \mathrm{R.}\cdot T$$

The pressure p is then determined from the volume V, the number of molecules n, the gas constant R and the temperature T.

The enthalpy H is given by formula 2, with the internal energy U: $$H=U+p\cdot V$$

The variation in enthalpy dH is according to formula 3: $$dH=d\left(U+p\cdot V\right)=dU+d\left(n\cdot \mathrm{R.}\cdot T\right)=n\cdot {\mathrm{C.}}_p\left(T\right)\cdot dT+dn\cdot \mathrm{R.}\cdot T$$

C _p (T) is the heat capacity at constant pressure. dn is the variation in the number of molecules caused by combustion.

ist: $$C_{p,Luft}\left(T\right)=\mathrm{6,69}{T}^{*3}-\mathrm{83,8}{T}^{*2}+359T^{*}+973$$

$$C_{p,Abgas}\left(T\right)=\mathrm{4,97}{T}^{*3}-\mathrm{61,2}{T}^{*2}+264T^{*}+932$$

The heat capacities C _p (T) depend on the temperature and these are approximated according to the following formulas 4 and 5 for air (C _{p, air} ) and for exhaust gas (C _{p, exhaust gas} ) for temperatures below 3500 K with a third degree polynomial , in which $T*=\frac{T}{1000}$

is: $${\mathrm{C.}}_{p,\mathrm{L.}uft}\left(T\right)=6.69T^{*3}-83.8T^{*2}+359T^{*}+973$$

$${\mathrm{C.}}_{p,\mathrm{A.}bGas}\left(T\right)=4.97T^{*3}-61.2T^{*2}+264T^{*}+932$$

The variation in enthalpy results from the sum of the changes in each energy type, hence the change in heat δQ, the change in work δW and chemical energy, as the number of fuel molecules burned dN _comb multiplied by the calorific value H ₀ , that for diesel for example 43 MJ / kg. The change in heat δQ, i.e. the heat loss on the cylinder wall, can be determined from test bench measurements in overrun mode and saved in a characteristic curve: $$dH=\delta Q+\delta \mathrm{W.}+d{N}_{cOmb}\cdot {\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="DE102019203312A1\_0020.png,DE102019203312A1\_0021.png"\; state="\{\{state\}\}">H</figure-callout>}}_0$$

If you combine Formula 3 and Formula 6, you get Formula 7: $$dH=n\cdot {\mathrm{C.}}_p\left(T\right)\cdot dT+dn\cdot \mathrm{R.}\cdot T=\delta Q+\delta \mathrm{W.}+d{N}_{cOmb}\cdot {\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="DE102019203312A1\_0020.png,DE102019203312A1\_0021.png"\; state="\{\{state\}\}">H</figure-callout>}}_0$$

By splitting the calculation of the pressure into two sections, simplifications can be assumed for each section.

No work is performed during the combustion between point II and point III, therefore: δW = 0.

It is assumed that the heat capacity does not change between two calculation steps that are close to one another. Therefore, the molar heat capacity n · C _p (T) can be converted into a mean mass-dependent specific heat 〈m · c _p 〉.

It is also assumed that the fuel is equivalent to heptadecane molecules. The variation in the number of molecules is when heptadecane molecules are burned to form carbon dioxide and water 8th . With a molar mass of 240 g / mol, the variation in the number of molecules corresponds to 33.34 times the mass of the combusted fuel m _comb .

Based on the assumptions shown, formula 7 results in a temperature T _III at point III according to formula 8: $$T_{\mathrm{I.}\mathrm{I.}\mathrm{I.}}=\frac{〈m\cdot c_p〉\left(T\right)\cdot T_{\mathrm{A.}}+\delta Q+d{m}_{cOmb}\cdot {\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="DE102019203312A1\_0020.png,DE102019203312A1\_0021.png"\; state="\{\{state\}\}">H</figure-callout>}}_0}{〈m\cdot c_p〉\left(T\right)+\mathrm{R.}\cdot 33.34\cdot m_{cOmb}}$$

An adiabatic change of state takes place between point I and point II and between point III and point IV. The adiabatic coefficient κ (T) is taken from the previously performed calculation step and is therefore: $$\kappa \left(T\right)=\frac{〈m\cdot c_p〉}{〈m\cdot c_v〉}$$

During the adiabatic change of state, no heat is exchanged and no molecules burn, therefore: δW = 0 and dN _comb = 0.

Accordingly, formula 7 is simplified to formula 10, with C _v (T) as the heat capacity at constant volume: $$dU=\delta \mathrm{W.}=-p\cdot dV=n\cdot {\mathrm{C.}}_v\left(T\right)\cdot dT$$

And thus: $$\frac{n\cdot \mathrm{R.}}{V}\cdot dV=-\frac{n\cdot {\mathrm{C.}}_v\left(T\right)}{T}$$

It is assumed that C _v (T) and n are constant.

This results in: $$\begin{array}{l}-\frac{\mathrm{R.}}{{\mathrm{C.}}_v}\frac{1}{V}dV=\left(1-\kappa \right)\frac{1}{V}dV=\frac{1}{T}dT\\ =\left(1-\kappa \right)\cdot \text{log}\left(\frac{V_2}{V_1}\right)=\text{log}\left(\frac{T_2}{T_1}\right)\end{array}$$

And thus $$\frac{T_2}{{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="DE102019203312A1\_0019.png,DE102019203312A1\_0020.png"\; state="\{\{state\}\}">T</figure-callout>}}_1}\text{=}{\left(\frac{V_2}{V_1}\right)}^{1-\kappa }={\left(\frac{V_1}{V_2}\right)}^{\kappa -1}$$

The temperature T _II at point II can be calculated from the initial temperature in point I if this is used as T ₂ and the initial temperature as T ₁ in formula 13. Likewise, the temperature T _IV at point IV can be calculated by using this as T ₂ and the temperature T _III at point III calculated above as T ₁ in formula 13. Intermediate temperatures can be calculated in the same way.

To calculate the pressure p, the temperatures are inserted into the ideal gas equation (formula 1) transformed according to the pressure p.

It can be seen that, on the one hand, the start of the combustion and the end of the combustion must be known and, in addition, the burned fuel _mass m _comb must be calculated.

3 shows a flow chart for determining the burned fuel _mass m _comb according to an embodiment of the method according to the invention. First is the injected fuel mass m _inj determined. For this a model 10 used for the injector, which is used below in connection with the 4a and 4b will be described in detail.

The 4a and 4b each show a diagram of a fuel flow f over time t during injection with an injection duration Δ. In 4a If the maximum possible fuel flow fmax, which depends, among other things, on the design of the injectors, is above the fuel flow f achieved during this injection. During the injection, the injector is opened first and the fuel flow f increases. The injector is then closed again and the fuel flow f decreases. As a result, the course of the fuel flow f assumes the shape of a triangle. In 4b the fuel flow f reaches the maximum possible fuel flow fmax. Here, too, the injector is opened first during the injection and the fuel flow f increases until the fuel flow f reaches the maximum possible fuel flow fmax. The injection is then continued with the maximum possible fuel flow fmax. The injector is then closed again and the fuel flow f decreases. As a result, the course of the fuel flow f assumes the shape of a trapezoid. The area below the fuel flow f gives the injected fuel mass m _inj again.

In the flowchart in 3 the fuel flow f becomes from the model 10 for the injector consequently integrated 11 over the injection duration Δ to the injected fuel mass m _inj to obtain.

After the fuel has been injected into the cylinder, it evaporates and spreads in space before it reaches the place where it is burned. Filtering is required to take this propagation process into account 12 first order with a time constant and a waiting time t _{w are} provided. The time constant depends mainly on the pressure p _rail in the common high pressure accumulator. The greater the pressure p _rail in the common high-pressure accumulator, the smaller the time constant. At a pressure p _rail In the common high-pressure accumulator from 1200 to 1500 bar, the time constant is typically in a range between 200 and 300 µs. The waiting time t _w represents the time for evaporation and the time until the location at which the fuel is burned is reached. The waiting time t _{w will be} discussed again below. By means of filtering 12 a fuel mass m _ba available for combustion and the rate of combustion of the fuel are determined.

In addition, an exhaust gas factor F _{EG is} provided that corresponds to the time constant of the filtering 12 is multiplied. This exhaust gas factor FEG represents the influence of exhaust gas, which is returned to the cylinder by exhaust gas recirculation and which arises from the combustion. The recirculated exhaust gas mass m _EG , the mass m _{fA of} the fresh air and their temperatures have a great influence on the pressure p in the cylinder during compression, combustion or decompression. Formula 14 describes the relationship between the recirculated exhaust gas mass m _EG , the mass m _A the air, the mass of the fresh air m _fA , the exhaust gas mass m _EG and the mass m _{uncomp of} the _unburned fuel and the mass m _{comp of} the burned fuel in stationary operation, where η can be determined from the previous cycle: $$\begin{array}{c}\left[\begin{array}{c}{m}_{\mathrm{A.}}\\ m_{\mathrm{E.}G}\\ m_{uncOmb}\end{array}\right]={\left[\begin{array}{c}{m}_{f\mathrm{A.}}\\ 0\\ 0\end{array}\right]}_{\mathrm{F.}riscHluft}+\frac{1}{1+14.6\Lambda }\cdot \left[\begin{array}{c}14.6\left(\Lambda -\eta \right)\\ 15.6\eta \\ 1-\eta \end{array}\right]\cdot m_{\mathrm{E.}G\mathrm{R.}}\\ \begin{array}{cc}mit\Lambda =\frac{m_{f\mathrm{A.}}}{14.6\cdot m_{cOmb}},& \eta =\frac{m_{cOmb}}{m_{inj}}\end{array}\end{array}$$

The rate of combustion is reduced by a high exhaust gas rate, since the oxygen molecules are literally shielded from the exhaust gas from the fuel molecules. The exhaust gas factor FEG is stored in a characteristic curve.

In addition, a map is created in advance 20th for the probability W for a start of the combustion as a function of the injection angle Φ and of a cumulative fuel _mass m _kum , in which the injected fuel mass from previous injections was added up. Such a map 20th for the probability W for a start of the combustion is in 5 shown. On the one hand, the probability W for a start of combustion is greatest for injection angles Φ between -20 ° CA (crank angle) and + 10 ° CA and decreases for injection angles Φ less than -40 ° CA and for injection angles Φ greater than + 10 ° CA from. On the other hand, the probability for small accumulated fuel _masses m _kum decreases. If a first injected fuel mass is not sufficient to start the combustion, it nevertheless increases the probability W for the start of the combustion in a subsequent second injection.

The time before the combustion starts is also considered. For this purpose, combustion release functions CEF are used for all injections. The combustion release function CEF is a wiebe-like correlation and simulates the course of the Wiebe function. The course represents the Property that the pressure p in the cylinder suddenly drops after a certain period of time to a pressure that would be reached if all of the fuel had been injected and was instantly completely burned. Wiebe lengths WL for all injections can be determined from the combustion release functions CEF. The Wiebe length WL is defined as the time until the probability W for the start of the combustion is reached and thus corresponds to this specific time period. The Wiebe lengths WL are in a map 30th as a function of the injection angle Φ and an initial pressure p _A in the cylinder when the valves are closed, i.e. the pressure p _A at point I in the diagram in 2 B , saved. Such a map 30th for the Wiebe lengths WL is in 6th shown. The smaller the initial pressure p _A in the cylinder, the greater the Wiebe length WL. The closer the injection angle Φ is to top dead center at 0 ° CA, the smaller the Wiebe length WL.

In order to obtain the burned fuel mass, the fuel mass m _ba available for the combustion is multiplied 40 by the probability W for the start of the combustion, the Wiebe length WL representing the time until the combustion starts.

In the 7th and 8th is the relationship between the injected fuel mass m _inj , the fuel mass m _ba available for combustion (shown in the upper half of the diagram) and the burned mass as well as the probability W for the start of combustion and the Wiebe length WL (shown in the lower half of the diagram). In terms of 7th an injection E is provided. In terms of 8th are two consecutive injections E1 and E2 intended.

In 7th an injection E takes place. After the injection E, the injected mass increases m _inj on. As in relation to 3 already described, a waiting time t _{w is} provided until the injected fuel has evaporated and it has reached the place where the fuel is burned. This effectively makes the time course for the injected mass m _inj moved back by the waiting time t _w . The fuel mass m _ba available for combustion increases after the waiting time tw and the time curve differs from the time curve for the injected mass m _inj . The time course of the fuel _{mass mba} available for combustion is determined by the filtering described above 13 receive. On the basis of the injection, the combustion release function CEF with the Wiebe length WL is provided for this injection. The course of the combustion release function CEF shows a sharp increase in the probability W for the start of the combustion after the waiting time t _w . In this case, the probability W that the combustion will start after the Wiebe length WL is 100%. The time profile of the burned fuel _mass m _comb can be interpreted as a combination of the two time profiles of the fuel mass m _ba available for combustion and the combustion release function CEF. Although the fuel mass m _ba available for combustion has already increased, the burned fuel _mass m _comb does not change. Only when the combustion release function CEF has risen to a probability of approx. 90% does the burned fuel _mass m _comb rise very sharply. The time profile of the burned fuel _mass m _comb then follows the time profile of the fuel _mass m _ba available for combustion. As in connection with 3 already described, the burned fuel _mass m _comb can be multiplied by 40 of standing for the combustion of available fuel mass m _ba with the probability W, are calculated for the start of combustion resulting from the combustion of released function CEF with the Wiebe length WL as time lag.

In 8th finds a first injection E1 instead of. As described above, a waiting time t is _w1 for this first injection E1 intended. The time course of the fuel mass m _ba available for the combustion results for the first injection E1 In analogy to 7th from filtering 13 . Starting from the first injection E1 becomes the first combustion release function CEF1 with the first Wiebe length WL1 for this injection E1 provided. In this case, the probability W that the combustion will start after the first Wiebe length WL1 is 50%. Here, too, there is a very strong increase in the burned fuel _mass m _comb only when the first combustion release function CEF1 has risen to a probability W of approx. 40%. The time profile of the burned fuel _mass m _comb then follows the time profile for half of the fuel mass m _ba available for combustion (dashed line).

A second injection then takes place E2 instead, so that the injected fuel mass m _inj increased, still some of that in the first injection E1 injected fuel mass m _inj is present in the cylinder. Again, there is a wait t _w2 for this second injection E2 intended. The time course of the fuel mass m _ba available for the combustion results for the second injection E2 also from the filtering 13 Here, too, a part of the is available for combustion standing fuel mass m _ba from the first injection E1 is available. Starting from the second injection E2 becomes the second combustion release function CEF2 with the first Wiebe length WL2 for this injection E2 provided. The probability W that the combustion will start after the Wiebe length WL is now 100%, since there is a greater fuel _{mass mba} available for the combustion from both injections E1 and E2 is available. In turn, there is only a very strong increase in the burned fuel _mass m _comb when the second combustion release function CEF2 has risen to a probability W of approx. 90%. The time profile of the burned fuel _mass m _comb then follows the time profile for the fuel _mass m _ba available for combustion.

9 shows a comparison between the modeled pressure p _m and a maximum measured pressure p _measmax and a minimum measured pressure p _measmin for different injection angles Φ between -60 ° CA and + 60 ° CA. The modeled print p _m is almost always between the two measured pressures p _measmax and p _measmin or corresponds to these. The course of the pressure is reproduced exactly and the incision at 0 ° CA can be clearly seen.

The method can be used to generate a torque M. to calculate. In 2a As already described, the cycle of compression, combustion and decompression in the cylinder is shown in a pressure-volume diagram with logarithmic axes (logp-logV diagram). The point II at which the combustion starts is determined from the Wiebe length WL and the point III at which the combustion ends is then calculated from the speed of the combustion and the burned fuel _mass m _comb . As also in connection with 2a and 2 B already described, an adiabatic change of state takes place between point I and point II and between point III and point IV. These are shown in the double logarithmic representation in the diagram in 2a shown as straight lines. The torque M. the high pressure loop is the area within the curves between points I, II, III and IV.

Several pressures are modeled before the start of combustion p _m1 , p _m2 ... p _mk determined by means of the adiabatic equation (see above), the adiabatic coefficients already in connection with 2 B were calculated when determining the modeled pressures. Here the torque can M. can be formed by adding up. During the combustion, i.e. between point II and point III, as in 9 shown, significantly more modeled pressures determined. The torque is integrated here. After the end of the combustion, several pressures are modeled again p ' _m1 , p ' _m2 ... p ' _mk determined by means of the adiabatic equation, the adiabatic coefficients also already in connection with 2 B were calculated when determining the modeled pressures. Here the torque can M. can also be formed by adding up. The adiabatic equation allows several modeled pressures p _m1 , p _m2 ... p _mk , p ' _m1 , p ' _m2 ... p ' _mk can be determined in a simple manner. The torque can simply be added up in these areas.

Below is a formula for determining the torque according to the method mentioned: $$〈\mathrm{M.}〉=\frac{N_Z}{\mathrm{4th}\pi }\left(\begin{array}{c}{\displaystyle \sum _{\{\begin{array}{c}{\Phi }_i={\Phi }_{\mathrm{S.}tar{t}_{calc}}\\ {\Phi }_{i+1}={\Phi }_i+\Delta \Phi \end{array}}^{{\Phi }_{\mathrm{S.}tar{t}_{inj}}{}^{-\Delta \Phi }}p\left({\Phi }_i\right)\cdot V{\left(\Phi \right)}^{{\kappa }_i\left(V_i\right)}{\frac{V{\left(\Phi \right)}^{1-{\kappa }_i\left(V_i\right)}}{1-{\kappa }_i\left(V_i\right)}]}_{{\Phi }_i}^{{\Phi }_{i+1}}}\\ +{\displaystyle \underset{\mathrm{S.}tar{t}_{inj}}{\overset{\mathrm{E.}n{d}_{cOmb}}{\int }}p\left(\Phi \right)dV\left(\Phi \right)}\\ {\displaystyle \sum _{\{\begin{array}{c}{\Phi }_i={\Phi }_{\mathrm{E.}n{d}_{cOmb}}\\ {\Phi }_{i+1}={\Phi }_i+\Delta \Phi \end{array}}^{{\Phi }_{\mathrm{S.}tar{t}_{calc}}{}^{-\Delta \Phi }}p\left({\Phi }_i\right)\cdot V{\left(\Phi \right)}^{{\kappa }_i\left(V_i\right)}{\frac{V{\left(\Phi \right)}^{1-{\kappa }_i\left(V_i\right)}}{1-{\kappa }_i\left(V_i\right)}]}_{{\Phi }_i}^{{\Phi }_{i+1}}}\\ -p_{env}\cdot (V\left({\Phi }_{\mathrm{E.}n{d}_{calc}}\right)-V\left({\Phi }_{\mathrm{S.}tar{t}_{calc}}\right)\end{array}\right)$$

The pressures p (Φ _i ), the volumes V (Φ) and the adiabatic coefficients κ _i (V _i ) are already in the cylinder pressure model mentioned above 3 has been calculated.

The term for the combustion can be further simplified by using a Riemann integral. $${\displaystyle \underset{\mathrm{S.}tar{t}_{inj}}{\overset{\mathrm{E.}n{d}_{cOmb}}{\int }}p\left({\Phi }_i\right)dV\left(\Phi \right)={\displaystyle \sum _{\{\begin{array}{c}{\Phi }_i={\Phi }_{\mathrm{S.}tar{t}_{inj}}\\ {\Phi }_{i+1}={\Phi }_i+\Delta \Phi \end{array}}^{{\Phi }_{\mathrm{E.}n{d}_{cOmb}}{}^{-\Delta \Phi }}\frac{p\left({\Phi }_i\right)+p\left({\Phi }_{i+1}\right)}{2}\left(V\left({\Phi }_{i+1}\right)-V_i\left({\Phi }_i\right)\right)}}$$

Such a calculation of the torque can be carried out in the electronic control unit.

QUOTES INCLUDED IN THE DESCRIPTION

This list of the documents listed by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Non-patent literature cited

• "Prediction of In-Cylinder Pressure, Temperature, and Loads Related to the Crank Slider Mechanism of IC Engines: A Computational Model", Carlos Alberto Romero Piedrahita et al., Conference Paper of conference SAE 2003 World Congress, at Cobo Center, Detroit, USA, March 2003 [0004]

Claims (11)

Method for modeling a pressure (p _m ) in a cylinder of an internal combustion engine, wherein fuel is injected into the cylinder via at least one injector and a piston in the cylinder is cyclically driven via a shaft, characterized by the following steps: Determination of an injected fuel mass ( m _inj ) from a model (10) for the at least one injector; - Filtering (12) of the injected fuel _mass (m _inj ) in order to determine a fuel _mass (m _ba ) available for the combustion and to determine the speed of combustion of the fuel; - Determining the probability (W) for a start of the combustion as a function of an injection angle (Φ) and an accumulated injected fuel mass (m _kum ); - Determination of a time before the combustion starts, depending on the injection angles (Φ) and an initial pressure (p _A ) in the cylinder by means of Wiebe lengths (WL, WL1, WL2) for all injections (E, E1, E2); - Calculating (40) a fuel _mass (m _comb ) burned during the combustion from the fuel mass (m _ba ) available for the combustion, the probability (W) for the start of the combustion and from the Wiebe length (WL); and - determining the modeled pressure (p _m ) from the burned fuel mass (m _comb ). Procedure according to Claim 1 , characterized in that the Wiebe lengths (WL) are stored in a map (30). Method according to one of the preceding claims, characterized in that the probability (W) for the start of the combustion is stored in a characteristic map (20). Method according to one of the preceding claims, characterized in that the time for the evaporation of the metered fuel and the time until the fuel reaches the place at which the fuel is burned as waiting time (t _w ) when determining the time before the combustion starts is taken into account. Method according to one of the preceding claims, characterized in that when calculating the burned fuel _mass (m _comb ), heat transport from the combustion chamber of the cylinder is only taken into account in a predeterminable area around the top dead center of the internal combustion engine. Method according to one of the preceding claims, characterized in that a combustion speed is calculated as a function of the recirculated exhaust gas (m _EG ) and is included in the filtering (12) of the fuel flow. Method according to one of the preceding claims, characterized in that a start of the combustion is determined from the time before the combustion starts and an end of the combustion is determined from a speed of the combustion and the burned fuel _mass (m _comb ). Method according to one of the preceding claims, characterized in that a torque (M) of the internal combustion engine by means of the modeled pressure (p _m , p _{m, 1} , p _{m, 2} , p _{m, k} , p ' _{m, 1} , p _{m, k} ) is calculated in the cylinder. Computer program which is set up, each step of the method according to one of the Claims 1 to 8th perform. Machine-readable storage medium on which a computer program is based Claim 9 is stored. Electronic control device which is set up to use a method according to one of the Claims 1 to 8th to model the pressure in the cylinder of an internal combustion engine.

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