Fast crank-angle based 0D simulation of combustion engine cold tests including manufacturing faults and production spread.
During series production of modern combustion engines a major challenge is to ensure the correct operation of every engine part. A common method is to test engines in end-of-line (EOL) cold test stations, where the engines are not fred but tugged by an electric motor. In this work we present a physically based 0D model for dynamic simulation of combustion engines under EOL test conditions. Our goals are the analysis of manufacturing faults regarding their detectability and the enhancement of test procedures under varying environmental conditions. Physical experiments are prohibitive in production environments, and the simulative approach reduces them to a minimum. This model is the first known to the authors exploring advanced engine test methods under production conditions. The model supports a wide range of manufacturing faults (with adjustable magnitude) as well as error-free production spread in engine components. Modeled effects include engine gas dynamics and mechanics, variable valve lift and -timing and the special cold test conditions. The challenge is to simulate a large number (i.e. >1000) EOL tests to cover a realistic production scenario. Compared to maximum-precision development tools, our 0D model has the advantage of high computational speed and the ease with which a wide range of faults can be introduced. As a use-case, a modern 2.0 liter four cylinder four stroke SI engine was modeled using only data readily available from the development process. Compared to real EOL measurements and a 1D model from engine development, the 0D simulation reproduced all relevant dynamics.
CITATION: Wiederer, J., Leitner, L., Endisch, C., and Reiss, H., "Fast Crank-Angle Based 0D Simulation of Combustion Engine Cold Tests including Manufacturing Faults and Production Spread," SAE Int. J. Passeng. Cars - Mech. Syst. 9(1):2016.
Long-term business success in the automotive industry strongly depends on customer satisfaction . High product quality and durability result in a small rate of breakdowns in the field and strengthen the image of the original equipment manufacturer (OEM). The consequences are low costs for recalls and continuous customer retention. OEMs rely on the zero-defects principle in production to generate high quality vehicles.
The complexity of combustion engines, which are still the main powertrain component of motorized vehicles, is rapidly increasing. Multiple sensors and actuators aim for high power at low emission levels over the entire operating range. Examples for actors are variable valve timing and -lifting as well as wastegates in turbocharged engines. With the quantity of components the possibilities of faults increase accordingly. The optimal interaction between all engine components already has to be proofed during the production and assembling process. The EOL test is used to check the performance at the end of the assembling procedure of modern combustion engines. State of the art EOL tests are realized as cold test stations, where the combustion engine is not fred, but turned by an electric motor. In comparison to hot test cells the cold test possesses several ecological and economic advantages. Low exhaust gas and noise emissions establish a comfortable working situation and drop required investments for environment safety. Cold tests captivate with a higher rate of fault detection and test cycles of short duration and therefore enable a test coverage of 100% production volume . During the cold test procedure the automated test bench is connected to the engine by adapters for electrical signals to control actuators and measure sensor signals. A clutch connects the crankshaft to a speed controlled electrical motor. While tugged without combustion in the operating cylinders, over 100 signals of thermodynamic, mechanical, electric and acoustic nature are dynamically measured in certain test stages with varying actuator configurations and rotational speed. Through comprehensive evaluation of the recorded signals the engine under test is classified as error-free or faulty. To be classified as error-free every single signal has to satisfy predefined characteristics within certain xranges. Figure 1 shows a condition that checks whether the signal-maximum in given x-boundaries lies within the given y-boundaries.
Covering the production spread the definition of the x/y-boundaries determines the balance between false alarms and detected faults. It is the cold test engineer's responsibility to find a reasonable compromise between undetected faulty engines (boundaries are too wide) and a high false alarm rate (boundaries are too tight). The determination of the boundaries fully relies on real measurement data from cold tests. This is because typical engine simulation models neither cover the special operating conditions the tugged engines are exposed to, nor the production spread of engine components. To improve the test procedure and boundaries, e.g. to check whether a certain fault can be detected reliably, physical experiments have to be conducted. However, physical experiments in full-scale production environments are highly prohibitive due to their cost. In this work we present a simulation model of combustion engines under EOL test conditions including production spread and engine production faults to resolve this.
In powertrain development, engine modeling has been an essential method in optimizing performance and building up control structures for several decades. Approaches supporting different depths and simulation speed have been derived . Literature illustrates the widespread application of engine models in the development process, while references about modeling in the manufacturing context are very rare. [4, 4, 5] are dealing with cold test simulation and fault modeling to some extent, but only consider a Diesel engine in a elementary set-up stage composed of cylinders and valves covering valve train and sensor faults without an elaborate validation. In this paper a model describing the entire intake and exhaust system is explicitly derived in the cold test environment aiming for comprehensive fault studies. To reproduce a realistic production scenario, a large number of EOL tests (i.e. >1000) has to be simulated. Therefore a high simulation speed is desirable. To keep the simulation time as low as possible while still providing engine dynamics, the model has been built based on the 0D approach in crank-angle resolution. Recently 0D models gained back interest caused by the opportunity on solving them in real time systems. A lot of models regarding engine control have been developed using this technique [7, 8, 9, 9]. The model presented in this paper is the first known to the authors, which is used to explore advanced engine test methods under production conditions observing a completely assembled engine. Our model simulates mechanical and thermodynamic cold test signals and represents all relevant physical effects in the intake and exhaust gas system caused by the individual cylinders. In comparison, a mean value approach can't provide the requested system dynamics [11, 12, 13].
The rest of this paper is structured as follows. In section "Special EOL Conditions and Engine Configuration" we give a detailed description of the operating conditions during cold testing. The model itself is derived in section "Generalized 0D Model Equations for Simulation in Crank Angle Resolution". As a use case we showcase the model in section "Implementation in Matlab/Simulink" for a modern 2.0 liter four cylinder four stroke SI engine from Audi ([14, 15] describe the 1.8 l version). Simulin[k.sup.[R]] is used to implement the model equations, and simulation control is executed by a user-friendly structured Matlab[R] program. Finally, a validation of simulated cold test signals is performed with real data of EOL test benches as well as with a 1D GT-Suit[e.sup.[R]] model. Both error-free and faulty engines with adjustable production spread are covered.
SPECIAL EOL CONDITIONS AND ENGINE CONFIGURATION
Building up a model simulating cold test signals, the special engine conditions in the EOL test stations have to be considered. The following description refers to the Audi four cylinder engine production line located in Gyor (Hungary). In engine production advanced monitoring systems are applied, but consistent prevention of manufacturing faults is still not possible. In an extensive EOL test missed faults such as deviations in manufacturing tolerances (e.g. in shape cutting processes), missing or wrongly assembled parts (e.g. missing roller levers or valve springs), faults in actuator excitation (e.g. offset in throttle excitation) or sensor measurement (e.g. offset in crankshaft encoder signal) must be invariably revealed.
Before starting the cold test routine, the test bench automatically connects to the engine using an electronic adapter for actuator excitation and sensor signal logging, a multifunctional coupling disk supplying necessary operating media (e.g. oil) and a mechanical clutch linking the electric motor to the crankshaft. While oil lubrication is guaranteed by the test bench, no engine cooling fluid is used during the test process. Flow restrictions in terms of orifices at the inlet (inlet orifice diameter [d.sub.i,o] = 1 mm) and the outlet (outlet orifice diameter [d.sub.o,o] = 2.5 mm) of the air path constitute another specialty in engine cold testing (cp. Figure 2). The pressure drop caused by air flow through the orifices is used to make charge cycle effects in the intake and exhaust manifold measurable. For exact orifice attachment and positioning one relies on an industrial robot. The nomenclature cold test already implicates the unfred engine operation caused by missing fuel injection and ignition. Passing different test stages at variable actuator configuration and crankshaft speed, physical engine quantities are measured. Figure 2 shows the engine constitution and the sensor locations recording mechanical (i.e. engine torque) and thermodynamic signals (i.e. intake and intake manifold pressure, intake manifold temperature and exhaust gas pressure) dynamically over time or crank angle. Low rotational speed along with high restriction through the orifices in most of the test stages precludes the rotation of the exhaust turbocharger turbine. For this reason, the turbocharger dynamics are not included in the presented model. In  a thermodynamic and fluid-dynamic turbocharger model approach is shown.
Simulating mechanical and thermodynamic cold test sensor signals requires consequent inclusion of the mentioned EOL conditions.
Furthermore, engines in real production environments have an individual production spread, resulting from manufacturing tolerances of all engine parts. The model supports this effect and in addition a wide range of manufacturing faults. In the next section generalized 0D elementary models for engine components, which are used to build up the engine simulation tool in the subsequent step, are derived based on previous works and accounting for the EOL characteristics.
GENERALIZED 0D MODEL EQUATIONS FOR SIMULATION IN CRANK-ANGLE RESOLUTION
Like in control oriented modeling the application elaborated in this paper also calls for high simulation speed to represent a real production environment in short time. Since simulating multidimensional models is time-consuming, the zero dimensional approach with lumped parameters is used [9, 16]. The basic assumption for zero dimensional models is that thermodynamic states in a fixed volume are seen as location independent. Unlike mean value models for real time applications no simplifications, which renounce the proper reproduction of physical effects to the benefit of time saving, are allowed. All signals are persistently simulated over a crank-angle scale, which leads to consideration of all engine gas dynamic effects for individual cylinders, but without the requirement of real-time capability.
Nowadays in 0D engine modeling two techniques have been established, called "Filling and Emptying" (F&E) and "Quasi-Steady-Flow" (QSF) method . The gas path is considered as an alternating sequence of gas storages (e.g. manifold) and flow resistances (e.g. throttle). The F&E approach is based on physical laws in terms of mass and energy conservation as well as the ideal gas law in differential form, which result in ordinary differential equations (ODEs) [9, 11, 18]. Gas storages, which can be seen as control volumes, are the typical usage of the F&E method. None-volume parts, i.e. flow resistances, are described by QSF models using algebraic equations [8, 9, 17, 18, 19]. Combining the distinct models for storages and flow resistances yields the process model of the entire engine gas dynamic . The dynamic engine torque generation includes the gas and the mass torque. Through the kinetic of the crank drive the gas and mass torques are calculated and subsequently summarized [9, 20].
To sufficiently predict the influences of manufacturing faults and spread on simulated state variables all specialties regarding EOL tests mentioned in section above have to be included in the models. In the following, elementary models for generalized engine components (i.e. storage, cylinder, resistance) using the lumped parameter approach based on literature are derived and presented. A short outline of the gas and mass torque calculation method is also given.
An engine consists of several gas storages such as the intake manifold, ducts or the exhaust gas manifold. In a narrow sense, the engine cylinders are a kind of storage, but due to volume alteration in time they are treated in a separate section. In this regard storages are characterized by a constant control volume with mass and energy permeable boundaries in order that the equations for thermodynamic open systems hold. One or more inlet and outlet mass flows transport internal energy over the control surface and cause a change of storage state variables (i.e. pressure [p.sub.st], temperature [T.sub.st] and mass [m.sub.st]) (cp. Figure 3). Using the F&E approach one obtains the differential equations of the three state variables.
The mass balance of a gas storage with an arbitrary number of inlet and outlet flows provides the first ODE :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
Based on the first law of thermodynamics the energy balance can be formed correspondingly :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [U.sub.st] is the internal energy of the stored air, [h.sub.st,in] and [h.sub.st,out] are the specific enthalpies of the mass flows and d[Q.sub.st,w]/dt is the heat flow through the storage walls. Neglecting the heat transfer is reasonable due to the missing engine cooling and the unfred operation in the cold test application. Together with the assumption of a permanent validity of the ideal gas law and constant specific heat capacities c and [c.sub.v] , the differential equation for the air temperature is (The exact derivation can be found in the appendix) :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
Solving the ideal gas law in the differential form for the pressure changing and inserting eq. (3) results in the last intended gas storage ODE (The exact derivation can be found in the appendix) :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
with the ratio of specific heat capacities [kappa] and the specific gas constant of the air R. The mass flows and their temperatures are provided by the adjacent flow resistances using the QSF method. Integrating eqs. (1), (3) and (4) delivers the state variables of the gas storage as functions of time.
This section derives three equations for the description of the cylinder behavior in four stroke engines during EOL testing on the basis of the single-zone approach as presented in . In contrast to engine development models, a combustion model is not necessary for the given cold test application. Since a cylinder is nothing else than a gas storage whose volume has a time dependency, the F&E approach can be used again. The control volume of the cylinder and its system boundary shows Figure 4. The three state variables are [p.sub.cyl], [T.sub.cyl] and [m.sub.cyl]. Depending on the mass flow in and out of the cylinder through the valves [m.sub.iv] and [m.sub.ov], the volume change dV and the heat transfer through the cylinder walls [Q.sub.cyl,w] the stored energy is changing.
The main difference in the model derivation in comparison to the storage model from the previous section is the volume change, which has to be taken into account. Mass and energy conservation together with the ideal gas law in differential form yield the three state equations, while heat transfer through the cylinder walls is not evaluated (for the exact derivation of the temperature and pressure ODE it is referred to the appendix):
* Cylinder mass for a cylinder with r inlet and s outlet valves:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
* Cylinder temperature allowing for volume changes d[V.sub.cyl]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
* Cylinder pressure:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
* with the specific enthalpies of the inlet and outlet mass flow [h.sub.iv] and [h.sub.ev] estimated by the following relationship :
h = [c.sub.p] * T (8)
The cylinder volume as a function of time follows from engine kinetics [20, 23]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
* [omega] is the angular velocity of the crankshaft.
* [A.sub.piston] is the pistons cross-sectional area.
* [r.sub.cs] is the eccentricity of the crankshaft
* [lambda] is the connecting rod ratio.
Eqs. (6), (7), (8) and (9) are applied to all working cylinders taking the particular fring distance angles [[phi].sub.0] into consideration.
Flow resistances are model as non-volume elements using the QSF method to estimate the mass flows and their specific temperatures for the adjacent storage or cylinder models (cp. section "Storages" and "Cylinders") and cause pressure drops between consecutive volumes. Figure 5 shows the conjunction of two storages by one flow resistance and the associated nomenclature of the state variables.
Based on the algebraic flow functions for compressible fluids the air mass [m.sub.res] streaming through a flow restriction in subcritical condition is calculated as a function of the prevailing pressure ratio [8, 9, 19, 24]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
In eqs. (10) and (11) [psi] is the outflow function depenending on the pressure ratio. The discharge coefficient [c.sub.d] including friction losses and contraction effects  and the reference flow area [A.sub.ref] follow from experimental messurements. According to Figure 5 T1 and p1 are the upstream stagnation temperature and pressure. Assuming negligible pressure recovery, which is reasonable for sharp edged restrictions , [p.sub.2] is equal to the pressure of the succeding air reservoir. When the velocity of the air mass in the contraction reaches sound velocity, the outflow function [psi] attains a constant value, which depends on the isentropic exponent exclusively, and a simplified equation for the mass flow holds :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
The crucial quanity is the pressure ratio. For choked flow, i.e. the pressure ratio is less than or equal the critical value 
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
eq. (12) is appropriate for the mass flow calculation. Especially at flow resistances with small flow diameters high pressure losses result in high flow velocities near or at sonic speed . In accordance with  for small pressure differences a isothermal change of state is assumed, which leads for the mass flow temperature [T.sub.res] to:
[T.sub.res] = [T.sub.1] (14)
A separate approach for heat transfer in the resistance is not used, since heat transfer does not pertain to the primary function of the flow resistances (e.g. orifices, valves and leakages) in the considered engine . The model equations are used for every occuring flow restriciton in the system.
Many analytical formulations estimating engine torque exist in open literature [9, 20]. The total engine torque [M.sub.eng], i.e. the drive troque of the electric engine [M.sub.el], is composed of several individual parts :
* gas force torque [M.sub.g]
* oscillating masses torque [M.sub.m]
* friction torque [M.sub.f]
* auxiliary drive torque [M.sub.aux]
* valve train torque [M.sub.v]
* mass moment of inertia [M.sub.J]
Summarizing these constituents, while the gas force torque is the only treated as positive, yields :
[M.sub.eng] = [M.sub.el] = [M.sub.g] - [M.sub.m]-[M.sub.f]-[M.sub.v]-[M.sub.aux]-[M.sub.J] (15)
The presented model comprieses the gas force and the oscillating mass toque, as they amount to the main parts, so that eq. (15) simplifies to:
[M.sub.el] =[M.sub.g]-[M.sub.m] (16)
The internal combustion engine handbook of Basshuysen  provides all relevant equations derived from the crank drive geometry and kinematics to calculate the gas force and mass torque. For an engine with [n.sub.cyl] cylinders the gas torque as a function of time is :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)
and for the mass torque one optains :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)
IMPLEMENTATION IN MATLAB/SIMULINK
There are many software solutions available to simulate the behavior of dynamic systems with mathematical models, e.g. O-Matrix, Octave and Matlab/Simulink. Since Matlab[R] with the integrated simulation tool Simulink[R]  is one of the most popular applications with a user-friendly interface, it is utilized in this work for the implementation of the model eqations derived in the previous section. As a use case a four cylinder engine is considered equipped with variable valve timing at the inlet and outlet. Additionally it provides a variable two-stage lifting in terms of the Audi valvelift system (AVS) at the outlet valves, which offers highest charge cycle flexibility in real operation , and a continuous throttle adjustment. As the combustion process is irrelevant in matters of cold tests, further considerations are resigned. Table 1 lists the main engine characteristics.
The developed simulation tool can be devided into two functional parts. A Simulink block diagramm containing and solving the combined model equations with regard to the special cold test engine settings represents the first part. The user-friendly, flexible parametrization and control of the Simulink block diagram for error-free as well as for faulty engines is ensured by a structured matlab script, which represents the second part.
The benefit of the Matlab program is manifiested in the easy introduction, parametrization and simulation of production spread and manufacturing faults. Furthermore, in the entire development process of the simulation tool great attention was paid to high simualtion speed and the fully automated simulation of a user defined number of error-free and faulty engines.
Applying the mathematical equations on system components and implementing them into software starts with the division of the entire engine into functional elements following the 0D approach. According to this, volume (i.e. storages and cylinders) and non-volume (i.e. flow resistances) elements are distinguished. The intake manifold, a short duct and the exhaust manifold are treated as storages with a constant volume, while the orifices at the inlet and the outlet, the throttle as well as the inlet and outlet valves are considered to be flow resistances. Figure 6 depicts the block diagram one receives by summarizing the elementary models and combining them using their boundary conditions. On the one hand the surrounding storages provide the upstream and downstream pressure and temperature for the intermediate restrictions and on the other hand the algebraic equations of the flow restriction models emit the mass flow and mass flow temperature for the adjacent volume elements.
In this figure the environment is seen as an air source delivering air without pressure and temperature changes. Again, the exhaust gas turbocharger is not included.
Building up on the described block diagram the Simulink model is developed using only blocks of the basic Simulink library to stay independent of specific toolboxes (cp. Figure 7). Two switches allow removing the orifices at the inlet and outlet for the simulation of certain test stages. In addition, according to the real production environment the model includes leakages in every single volume element, which are modeled as resistances emptying into environment, to simulate possible faults.
In the following we go into some details of our Simulink model. In order to configure the graphical block diagram for volume elements, one has to be aware, that the temperatures of the inlet and outlet mass flows are determined by the flow direction depending on the pressure gradient [p.sub.2]/[p.sub.1] (cp. eqs. (10) and (12)). The outflow function of a flow resistance as a function of the pressure ratio [p.sub.2]/[p.sub.1] in eq. (11) is only valid for [p.sub.2]/[p.sub.1]<1 and thus only enables positive flow in this form. To account for both flow directions, e.g. from the intake manifold to the cylinder and vice versa, a one dimensional lookup table (LUT) was synthesized (Figure 8). It supports both flow directions by combining the original outflow function in eq. (11) (in the range [p.sub.2]/[p.sub.1] from 0 to 1) and the negative outflow function as a function of [p.sub.1]/[p.sub.2] for pressure ratios [p.sub.2]/[p.sub.1] greater than 1 and also respects critical and over critical pressure ratios following eq. (13). As a side-effect this step leads to the benefit of a high simulation speed, since one can relinquish a switch block switching frequently back and forth between two outflow function (each for one flow direction). This is especially important for approximately equal adjacent pressures, which slows the simulation down due to Simulink's zero crossing detection . Discharge coefficients for the valves and the throttle were identified experimentally and tabulated over valve lifts and throttle angle, respectively. During simulation the current discharge coefficient of a valve is chosen using firstly a valve lift over crank angle lookup table covering one operating cycle (i.e. up to 720 [degrees] crank angle) and secondly a discharge coefficient over valve lift lookup table. The current crank angle for the valve lift LUT is calculated by a sawtooth signal generator out of simulation time. This signal is characterized through an amplitude reaching from 0 to 720 [degrees] crank angle and a period of one operation cycle. That means, depending on the sawtooth signal, which is exclusively used for the valve actuation, the valves are either opened or closed. Shifting this signal in x direction the valve timing is changed relating to the individual piston fring angles and leads to variable camshaft phasing.
Finally, the total engine torque is estimated by summing up the results of the individual cylinder gas and mass torques. In view of simulating faulty engines a simplified approach for increased piston speed dependent piston ring friction torque is additionally included in the Simulink model .The piston ring friction torque magnitude as well as every other simulation parameter is adjustable within the Matlab script described in the next section. Regarding solver settings, the accelerated mode of the Simulink solver is used together with the continuous ode45 solver with a variable step size. The variable step solver rapidly adapts the time steps to the model dynamics to satisfy the requested accuracy . Through a To-Workspace block signals, relevant for the cold test application, are collectively transferred to the Matlab environment as a structure of timeseries, where the post processing and the graphical evaluation take place (cp. Figure 7).
Model Parametrization and Control Using a Structured Matlab Program
The 0D model approach minimizes experimental parameter identification during the model setup phase. For the main geometric engine parameters a fast parameterization based on drawings and data sheets is possible. Test bench measurements are only necessary for the determination of throttle and valve discharge characteristics. Next to parameter settings the Matlab program proceeds with the automatic simulation of multiple error-free and faulty engines. Comparable outcomes for all simulation runs are ensured by a steady state condition being checked for all 21 state variables before the simulation is stopped. Concerning the integration of production spread our model consists of a unique feature which distinguishes it from other developments in this domain. Furthermore it is possible to implement a multitude of conceivable production faults (i.e. over 100) with adjustable magnitudes. The modeling of production spread and faults are considered in the following two sections.
Every dimension of the engine components has an associated tolerance caused by the limited precision of the underlying production processes. These imprecisions, which result in measurable deviations from the nominal dimensions, reflect in the recorded cold test signals (Figure 9). In order to emulate a real production environment and investigate the influences of globally and individually increasing and decreasing production spread, the simulation needs to include this phenomenon. Changes in manufacturing precision describe a realistic scenario, in case of introducing new manufacturing technologies.
Two options are conceivable to incorporate production spread. First, the engine parameters can be modified slightly for every engine simulation. Second, simulated signals can be post-processed to add variance after the simulation was finished. The parameter modification mirrors the natural production process. Therefore this option is put into practice. A cylinder and valve individual parameter nomenclature provides the basis for a modification of all engine parameters. Before starting a simulation every reference parameter value (i.e. [x.sub.f]) defined by the user is modified using a deviation within a predefined tolerance following this equation:
X = [X.sub.ref] + [x.sub.spread] * [X.sub.tol] (19)
where x is the afficted parameter. The parameter [x.sub.spread] is a random variable with standard normal distribution, limited to a range from -1 to 1 to comply with the stated symmetric tolerance [x.sub.tol] and prevents tolerance exceedance concurrently. The standard deviation of the normal distribution holds for all engine parameters, while the tolerances are parameter specific. A new random sample is generated for every individual engine parameter. From this it follows, that the user is able to vary the spread for the whole engine by adapting the random generation of [x.sub.spread] and just for some selected parameters by changing tolerances.
In the engine production process also the application of sophisticated quality management systems can't avert manufacturing and assembling faults entirely. Based on production expert knowledge numerous potential faults comprising all system components have been selected and included in the model. This concept allows for the choice and parametrization of faults in a Microsoft Excel[R] table. After reading and analyzing this Excel fle, Matlab conducts the designated parameter adaptions. The fault choices being available in the Excel file as well as the parameter adaptions performed in the Matlab program are:
* Clogged orifice at the inlet and/or outlet: Reducing the orifice diameter.
* Leakages in the gas storages of the model (e.g. intake manifold, cylinders): Enlarging the leakage diameters.
* Faults at the throttle actuator: Setting the throttle angle to a constant value or applying an angle offset.
* Damaged throttle plate: Modifying the throttle discharge coefficient lookup table.
* Faults in the variable camshaft phasing: Setting the camshaft position to a constant value or applying an angle offset.
* Missing roller levers resulting in a permanent closed valve: Setting the valve lift curve to zero.
* Missing valve springs resulting in a permanently open valve: Setting the valve lift curve to a constant value.
* Wrongly assembled camshaft: Modifying the valve lift curve.
* Leaking valves: Adding a constant value to the valve lift curve.
* Clogged valves: Scaling the valve discharge coefficient lookup table.
* AVS is not operating: Valve lift curve does not change when the AVS is actuated.
* Increased piston ring torque: Changing the amplitude of the piston ring torque.
The evaluation of the simulation results in steady state condition has been conducted by a comparison with existing cold test data and an established 1D GT-Suite model. The real cold test data originate from the Audi engine manufacturing located in Gyor (Hungary) and the 1D GT-Suite model was built and adapted to the cold test conditions based on an entire GT-Suite engine model for engine dimensioning. GT-Suite is a CAE tool specialized on modeling and simulations in the automotive industry using a 1D method, which leads to location-dependent state variables with more precise results, but also slows the simulation down.
For error-free engines results of two certain test stages at different rotational speeds (120 [min.sup.-1] and 1000 [min.sup.-1]) and for faulty engines results of a leaking outlet valve at 120 [min.sup.-1] are shown and compared in this section. According to real measurements the environment conditions are set to 1 bar and 300 K in all simulations.
Error-Free Engine Simulation
In the two test stages, in which the error-free validation takes place, the same actuator configurations are set (Table 2).
At first appearance, a comparison of the pressure in the intake and exhaust gas manifold and the engine torque at 120 [min.sup.-1] between Matlab/Simulink and real cold test data shows a sufficient agreement (Figure 10).
The low pressure in the intake (ca. 0.5 bar) and the temporary high over pressure in exhaust gas manifold (max. 1.2 bar) accrue from the pressure drop at the inlet and outlet orifices. Apparently, individual charge cycle effects are considerably represented in the pressure curves. Since the 0D model approach does not take the fluid inertia into account, high frequency changes in state variables, like in the exhaust gas manifold pressure, cannot be reproduced . The slight differences in the engine torque are caused by the effects neglected in the engine torque calculation (i.e. friction torque, auxiliary drive torque and valve train torque).
The cylinder state variables and the mass flow through and the lift of the inlet and outlet valves (1st cylinder) are not measured on the cold test benches. Therefore a simulation of the 0D model without leakages is contrasted with the GT-Suite results in Figure 11.
All curves show a good agreement with the reproduction of the main physical effects. At the beginning of the working cycle the first cylinder compresses the stored air to a maximum pressure of ca. 3 bar and expands again in the next stroke. Due to the engine curbing and the small air mass in the working chamber the maximum cylinder pressure is very small compared to normal engine operation. The subsequent exhaust stroke (open outlet vales) and induction stroke (open inlet valves) run at exhaust gas manifold pressure and intake manifold pressure, respectively. The cylinder mass is constant during compression and expansion (closed control volume). When opening the outlet valves, high pressure in the exhaust gas manifold causes a mass flow into the cylinder before the piston expels gas. A high cylinder pressure together with a low intake manifold pressure causes a negative mass flow through the inlet valves at the beginning of the induction stroke. The relatively high cylinder temperature is a result of the neglected heat transfer through cylinder walls.
Figure 12 exemplary shows the influence of spreading simulation parameters on the simulation results. The comparison to Figure 9 indicates a good emulation of production spread.
The pressure in the intake manifold shows again high accuracy, but the exhaust gas pressure differs from real measurements at this speed. Reasons constitute the neglected turbocharger, which states an additional flow resistance in the system, the missing heat transfer approach and the unknown magnitude of the leakages in real engines. The higher charge cycle frequency at 1000 [min.sup.-1] strengthens the restriction effects and creates very low pressure in the intake and great maximum pressure in the exhaust gas manifold (Figure 13).
Faulty Engine Simulation
Since real data of faulty engines is rare and experiments during the running production process are prohibitive, this section compares a faulty engine simulation of Matlab/Simulink with the GT-Suite results at 120 [min.sup.-1]. As an example one of the faults listed in the section "Fault Modeling" was chosen for the simulation. In this case an outlet valve at the fourth cylinder of the engine is permanently leaky, which is realized by adding the value 0.2 mm to the valve lift curve. This fault has a great impact on the system gas dynamics and strongly influences the state variables in the whole gas path (Figure 14). The Matlab/Simulink results show a good correspondence with the GT-Suite model and are physically explainable. Higher intake manifold pressure in the GT-Suite simulation results in a higher cylinder charge so that the maximum cylinder pressure at the end of the compression phase is higher.
SUMMARY AND CONCLUSIONS
A reliable evaluation of cold test signals demands optimal predefined signal test characteristics and boundaries to check them. Their determination currently relies fully on existing real production data of error-free and faulty engines. The model presented in this paper provides a tool to further analyze and enhance the EOL test without the interruption of real production processes. Simulating engines with different faults and production spread under varying environment conditions allows optimizing signal characteristics and boundaries used for engine testing. First, this applies to a cause-and-effect analysis between an existing fault and its effect on the engine signals. Secondly, new faults that did not appear in reality can be simulated and checked for their detectability during EOL tests.
The model was theoretically built up considering the engine gas dynamic as a sequence of gas storages and flow resistances using the common F&E and QSF methodology. Based on crank drive kinematics an engine torque approach was derived. During the model development great attention was paid on including all specialties of the EOL test procedure. A 2.0 liter four cylinder four stroke SI engine from Audi served as a first application of the mathematical model. The small set of geometric parameters and characteristic curves allows the model to be easily applied to other engine types when compared to CFD models. For this application an entire engine model was built in Simulink with different sub-models for volume and non-volume elements following the engine setup in a cold test bench and including variable valve lift and timing. A Matlab program conducts the simulation automatically and offers the possibility of simulating different engine faults and adjusting production spread by changing parameters.
In order to validate the mechanical and thermodynamic signals of error-free and faulty engines simulated in crank angle resolution comparisons to real cold test data and a 1D GT-Suite model were performed showing a high degree in qualitative and quantitative agreement. The simplicity of the 0D approach, the prevention of chattering in mass flow calculation and the accelerator mode of the Simulink solver together lead to ten times higher simulation speed compared with the GT-Suite simulation. At the same time the model integrates about 100 different fault sources.
For further developments in the area of cold test simulations, model improvements can be considered. Especially an inclusion of the turbocharger, a heat transfer approach and an isentropic change of state for the temperature calculation in the flow restrictions  can conduce to a greater accuracy.
[1.] Johnson, M. D., Herrmann, A., Huber, F., and Gustafsson, A., "Customer Retention in the Automotive Industry - Quality, Satisfaction and Loyalty," (Wiesbaden, Betriebswirtschaftlicher Verlag Dr. Th. Gabler GmbH, 1997), ISBN 3-409-12237-0.
[2.] Martyr, A. J., and Plint, M. A., "Engine Testing - The Design, Building, Modification and Use of Powertrain Test Facilities, Fourth Edition," (Oxford, Elsevier, Butterworth-Heinemann, 2012), ISBN-13 978-0-08-096949-7.
[3.] Wurzenberger, J., Heinzle, R., Deregnaucourt, M., and Katrasnik, T., "A Comprehensive Study on Different System Level Engine Simulation Models," SAE Technical Paper 2013-01-1116, 2013, doi:10.4271/2013-01-1116.
[4.] Wei, L., Xi, C., Jie, L., Wen, X., "Modeling and Simulation of System Dynamics for Cold Test," presented at IEEE Second International Symposium on Intelligent Information Technology Application, Shanghai, December 20-22, 2008, doi:10.1109/IITA.2008.507.
[5.] Wei, L., Kun, Z., Wen, X., Xi, C., "The Fault Simulation of Diesel Engine in Cold Test," presented at IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS), Xiamen, October 39-31, 2010, doi:10.1109/ICICISYS.2010.5658468.
[6.] Nyberg, M., "Model-Based Diagnosis of an Automotive Engine Using Several Types of Fault Models," IEEE Transactions on Control Systems Technology 10(5): 679-689, 2002, doi:10.1109/TCST.2002.801873.
[7.] Guzzella, L., and Onder, C., "Introduction to Modeling and Control of Internal Combustion Engine Systems," (Heidelberg, Springer-Verlag, 2010), ISBN 978-3-642-10774-0.
[8.] Gambarotta, A. and Lucchetti lng, G., "Control-Oriented "Crank-Angle" Based Modeling of Automotive Engines," SAE Technical Paper 2011-24-0144, 2011, doi:10.4271/2011-24-0144.
[9.] Eriksson, L., "Modeling and Control of Turbocharged SI and DI Engines," presented at IFP International Conference vol. 62, 2007, doi: 10.2516/ogst:2007042.
[10.] Isermann, R., "Engine Modeling and Control - Modeling and Electronic Management of Internal Combustion Engines," (Heidelberg, Springer-Verlag, 2014), doi: 10.1007/978-3-642-39934-3.
[11.] Schulten, P. and Stapersma, D., "Mean Value Modelling of the Gas Exchange of a 4-stroke Diesel Engine for Use in Powertrain Applications," SAE Technical Paper 2003-01-0219, 2003, doi:10.4271/2003-01-0219.
[12.] Hendricks, E. and Sorenson, S., "Mean Value Modelling of Spark Ignition Engines," SAE Technical Paper 900616, 1990, doi:10.4271/900616.
[13.] Gambarotta, A., Lucchetti, G., Fiorani, P., De Cesare, M. et al., "A Thermodynamic Mean Value Model of the Intake and Exhaust System of a Turbocharged Engine for HiL/SiL Applications.," SAE Technical Paper 2009-24-0121, 2009, doi:10.4271/2009-24-0121.
[14.] Eiser, A., Doerr, J., Jung, M., Adam, S., "The New 1.8 L TFSI Engine from Audi - Part 1: Base Engine and Thermomanagement," MTZ worldwide eMagazine 72(6):32-39, 2011, doi: 10.1365/s38313-011-0062-9.
[15.] Heiduk, T., Kuhn, M., Stichlmeir, M., Unselt, F., "The New 1.8 L TFSI Engine from Audi - Part 2: Mixture Formation, Combustion Method and Turbocharging," MTZ worldwide eMagazine 72(7):58-64, 2011, doi: 10.1365/s38313-011-0078-1.
[16.] Merker, G., Schwarz, C., Stiesch, G., Otto, F., "Simulating Combustion - Simulation of combustion and pollutant formation for engine-development," (Wiesbaden, B.G. Teubner Verlag, 2004), ISBN 3-540-25161-8.
[17.] Fiorani, P., Gambarotta, A., Tonetti, M., and Lanfranco, E., "A Real-Time Model for the Simulation of Transient Behaviour of Automotive Diesel Engines," SAE Technical Paper 2006-01-3007, 2006, doi:10.4271/2006-01-3007.
[18.] Harlock, J., Winterbone, D., "The Thermodynamics and Gas Dynamics of Internal-Combustion Engines, Volume II," (Oxford, The Estate of Rowland S. Benson, 1986), ISBN 0-19-856212-8.
[19.] Moskwat, J., Hedrick, J., "Automotive Engine Modeling For Real Time Control Application," presented at IEEE American Control Conference, Minneapolis, June 10-12, 1987.
[20.] Basshuysen, R., Schafer, F., "Internal Combustion Engine Handbook - Basics, Components, Systems and Perspectives," (Wiesbaden, Vieweg Verlag, 2002), ISBN 0-7680-1139-6.
[21.] Watson, N., Janota, M., "Turbocharging the Internal Combustion Engine," (London, Macmillan, 1982), ISBN: 0-333-24290-4.
[22.] Zahn, S., "Arbeitsspielaufigeloste Modellbildung und Hardware-in-the-Loop -Simulation von Pkw-Dieselmotoren mit Abgasturbolader," Ph.D. thesis, Fachbereich Elektrotechnik und Informationstechnik, Technische Universitat Darmstadt, Darmstadt, 2012.
[23.] Pulkrabek, W., "Engineering Fundamentals of the Internal Combustion Engine, Second Edition," (Upper Saddle River, Person Education Inc., 2004), ISBN 0-13-140570-5.
[24.] Canova, M., Fiorani, P., Gambarotta, A., and Tonetti, M., "A Real-Time Model of a Small Turbocharged Multijet Diesel Engine: Application and Validation.," SAE Technical Paper 2005-24-065, 2005, doi: 10.4271/2005-24-065.
[25.] Beucher, O. and Weeks, M., "Introduction to MATLAB & SIMULINK - A Project Approach, Third Edition," (Hingham, Infinity Science Press LLC, 2006), ISBN 978-1-934015-04-9
[26.] Huber, R., Klumpp, P., and Ulbrich, H., "Dynamic Analysis of the Audi Valvelift System," SAE Int. J. Engines 3(1):839-849, 2010, doi:10.4271/2010-01-1195.
[27.] The MathWorks, Inc., "Simulink User's Guide - MATLAB & SIMULINK," (Natick, The MathWorks, Inc., 2015).
[28.] Halsband, M., "Entwicklung reibungsoptimierter Kolbengruppen unter Anwendung spezifischer Messverfahren," (Dusseldorf, VDI-Verlag GmbH, 1994), ISBN 3-18-322112-8.
University of Applied Sciences Wurzburg
Lukas Leitner and Christian Endisch
Technische Hochschule Ingolstadt
[([p.sub.2]/[p.sub.1]).sub.crit] - critical pressure ratio
[A.sub.piston] - cross-sectional area of the piston
[A.sub.ref] - reference flow area of a flow resistance
[c.sub.d] - discharge coefficient
[c.sub.p] - specific isobaric heat capacity
[c.sub.v] - specific isochoric heat capacity
[d.sub.i,o] - inlet orifice diameter
[d.sub.o,o] - outlet orifice diameter
h - specific enthalpy
[H.sub.iv] - enthalpy of the mass flow through the inlet valves
[h.sub.iv,k] - specific enthalpy of the mass flow through the inlet valve k
[H.sub.ov] - enthalpy of the mass flow through the outlet valves
[h.sub.ov,l] - specific enthalpy of the mass flow through the outlet valve l
[h.sub.st,in,i] - specific enthalpy of the storage inlet mass flow i
[h.sub.st,out,j] - specific enthalpy of the storage outlet mass flow j
[m.sub.1] - upstream stagnation mass
[m.sub.2] - downstream stagnation mass
[M.sub.aux] - auxiliary drive torque
[m.sub.cyl] - cylinder mass
[M.sub.el] - drive torque of the electric engine
[m.sub.em] - exhaust gas manifold mass
[M.sub.eng] - total engine torque
[M.sub.f] - friction torque
[M.sub.g] - gas force torque
[m.sub.im] - intake manifold mass
[m.sub.iv,k] - mass flow through the inlet valve k
[M.sub.J] - mass moment of inertia
[M.sub.m] - oscillating masses torque
[m.sub.osc] - oscillating masses
[m.sub.ov,l] - mass flow through the outlet valve l
[m.sub.res] - mass flow through a flow resistance
[m.sub.st] - storage mass
[m.sub.st,in,i] - storage inlet mass flow i
[m.sub.st,out,j] - storage outlet mass flow j
[M.sub.v] - valve train torque
[n.sub.cyl] - number of cylinders
p - number of storage inlet mass flows
[p.sub.1] - upstream stagnation pressure
[p.sub.2] - downstream stagnation pressure
[p.sub.a] - ambient pressure
[p.sub.cyl] - cylinder pressure
[p.sub.cyl,n] - pressure in cylinder n
[p.sub.em] - exhaust gas manifold pressure
[p.sub.im] - intake manifold pressure
[p.sub.st] - storage pressure
q - number of storage outlet mass flows
[Q.sub.cyl,w] - heat through the cylinder wall
[Q.sub.st,w] - heat through the storage wall
R - specific gas constant of the air
r - number of inlet valves at one cylinder
[r.sub.cs] - eccentricity of the crankshaft
s - number of outlet valves at one cylinder
t - time
[T.sub.1] - upstream stagnation temperature
[T.sub.2] - downstream stagnation temperature
[T.sub.cyl] - cylinder temperature
[T.sub.em] - exhaust gas manifold temperature
[T.sub.im] - intake manifold temperature
[T.sub.res] - temperature of the mass flow through a flow resistance
[T.sub.st] - storage temperature
[T.sub.st,in,i] - temperature of storage inlet mass flow i
[T.sub.st,out,j] - temperature of storage outlet mass flow j
[U.sub.cyl] - internal energy of a cylinder
[u.sub.cyl] - specific internal energy of a cylinder
[U.sub.st] - internal energy of the storage
[V.sub.cyl] - cylinder volume
[V.sub.st] - storage volume
[x.sub.ref] - reference parameter
[x.sub.spread] - random variable with standard normal distribution (limited to a range from -1 to 1)
[x.sub.tol] - symmetric tolerance
[KAPPA] - isentropic exponent
[lambda] - connecting rod ratio
[[phi].sub.0] - fring distance angle
[[phi].sub.0,n] - fring distance angle of cylinder n
[psi] - outflow function
[omega] - angular velocity of the crankshaft
ATDC - after top dead center
AV S - Audi Valvelift System
BTDC - before top dead center
CAE - computer aided engineering
CFD - computational fluid dynamics
EC - exhaust valve closes
EOL - end-of-line
F&E - flling and emptying
IO - inlet valve opens
LUT - lookup table
ODE - ordinary differential equation
OEM - original equipment manufacturer
QSF - quasi steady flow
SI - spark-ignition
[degrees] - degree
[degrees]C - degrees Celsius
cc - cubic centimeter
g - gram
K - Kelvin
kg/s - kilogram per second
[min.sup.-1] - revolutions per minute
mm - millimeters
Nm - Newton meters
s - second
In the appendix the derivation of the ODE's for pressure and temperature of volume elements are considered. Since from a thermodynamic point of view a storage is a cylinder with a constant volume, only the derivation for a cylinder is described.
The second law of thermodynamics for a thermodynamic open system is :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)
* [H.sub.iv] is the enthalpy of the inlet mass flows.
* [H.sub.ov] is the enthalpy of the outlet mass flows.
* d[Q.sub.cyl,w]/dt is the heat flow through the cylinder wall.
Replacing the enthalpies by the summation of a product of the mass flows and their specific enthalpies and neglecting the heat transfer leads to :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)
The internal energy [U.sub.cyl] is calculated with the product of the air mass in the cylinder and its specific internal energy:
[U.sub.cyl] = [m.sub.cyl] * [u.sub.cyl] (22)
For the derivative of [U.sub.cyl] from eq. (22), which contains two time dependent variables, follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)
Assuming ideal gas, the caloric relations for the specific internal energy and its derivative hold :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)
In these equations the temperature dependency of the specific isochoric heat capacity is neglected. Inserting eq. (24) into eq. (23) and equalizing the result with eq. (21) yields:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)
After solving for the temperature change, the temperature ODE is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)
For the specific enthalpies the eq. (8) holds. In the case of a storage without volume change, d[V.sub.cyl]/dt becomes zero.
It is assumed, that the ideal gas law is always valid :
[P.sub.cyl] * [V.sub.cyl] = R * [m.sub.cyl] * [T.sub.cyl] (27)
For a storage with time-dependent volume the ideal gas law in differential form is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (28)
Solving this equation for the pressure change yields the pressure ODE:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)
By inserting eq. (26) for the temperature change, setting the volume change to zero and using the isentropic exponent [kappa]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (30)
the pressure ODE for a storage with constant volume can be developed.
Table 1. Main engine characteristics Firing order 1-3-4-2 Displaced volume 1984 cc Stroke 92.8 mm Bore diameter 82.5 mm Connecting Rod length 144 mm Compression ratio 9.6:1 Number of Valves 4 Variable valve timing (IO) 30[degrees] BTDC to 30[degrees] ATDC @ 1mm lift Variable valve timing (EC) 24[degrees] BTDC to 6[degrees] ATDC @ 1 mm lift AVS maximal valve lift 6.35 mm/ 10 mm Table 2. Actuator configuration for the two test stages at 120 and 1000 [min.sup.-1] Actuator Position Throttle 82.5 [degrees] (while 0[degrees] is closed) Variable valve timing (IO) 30[degrees] ATDC @ 1mm lift Variable valve timing (EC) 24[degrees] BTDC @ 1 mm lift AVS maximal valve lift 10 mm
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|Author:||Wiederer, Julian; Leitner, Lukas; Endisch, Christian; Reiss, Hans|
|Publication:||SAE International Journal of Passenger Cars - Mechanical Systems|
|Date:||Apr 1, 2016|
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