A Mean Value Internal Combustion Engine Model in MapleSim

Transcription

1 A Mean Value Internal Cobustion Engine Model in MapleSi by Mohaadreza Saeedi A thesis presented to the University of Waterloo in fulfillent of the thesis requireent for the degree of Master of Applied Science in Mechanical Engineering Waterloo, Ontario, Canada, 010 Mohaadreza Saeedi 010

2 AUTHOR'S DECLARATION I hereby declare that I a the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by y exainers. I understand that y thesis ay be ade electronically available to the public. ii

3 Abstract The ean value engine odel (MVEM) is a atheatical odel derived fro basic physical principles such as conservation of ass and energy equations. Although the MVEM is based on soe siplified assuptions and tie averaged cobustion engine paraeters, it odels the engine with a reasonable approxiation and gives a satisfactory aount of inforation about the physics of the fluid energy passing through an engine syste. MVEM can predict an engine s ain external variables such as crankshaft speed and anifold pressure, and iportant internal variables, such as voluetric and theral efficiencies. Usually, the differential equations used in MVEM will predict fuel fil flow, anifold pressure, and crankshaft speed. Because of its siplicity and short siulation tie, the MVEM is widely used for engine control developent. A ean value engine based on atheatical and paraetric equations has recently been developed in the new MapleSi software. The odel consists of three ain coponents: the throttle body, the anifold, and the engine. The new MVEM uses cobinations of causal and acausal coponents along with lookup tables and paraetric equations. Adjusting the paraeters allows the odel to be used for new engines of interest. The odel is forwardlooking and so benefits fro both Maple s powerful atheatical tool and Modelica s odern equation-based language. A set of throttle angle and ass flow data is used to find the throttle angle function, and to validate the throttle ass flow rates obtained fro the odel and the experient. iii

4 Acknowledgeents This work has involved help fro any people. I would like first of all to thank Professor John McPhee and Professor Roydon Fraser, y supervisors, who provided a great opportunity to work with the and their excellent teas. It was ainly their idea that I have expanded on in this work. Their patience, support, willingness to help, and enthusias ade this work possible. I a also grateful to Paul Goossens of Maple Inc. for his creative advice and entoring in the process of creating a new engine odel in MapleSi. Most of the ean value engine coponents were built during our exciting and fruitful bi-weekly sessions by bringing up a new idea and then ipleenting it inside the odel. I would like to thank Wilson Wong and other MapleSoft staff ebers for supporting this project. I want to express y extree gratitude to Dr. Nasser Lashgarian Azad and Dr. Chad Schitke for their any helpful discussions that we have had, and for their guidance during the validation and developent of the odel stages. As well, I would like to thank Chris Haliburton for his help with PSAT software and answering software-related questions. In addition, I want to thank to Joseph Loonaco fro Harley-Davidson Motor Co. for his support and the useful data he provided. I would also like to thank Mary McPherson of the grad Writing Centre for her editing advice on y thesis. Finally, I would like to thank y wife Mehranz for all her effort, tie, and support as she has helped e prepare this work, and y parents for all their long ter and never-failing support. iv

5 Table of Contents AUTHOR'S DECLARATION... ii Abstract... iii Acknowledgeents... iv Table of Contents... v List of Figures... viii List of Tables... x Noenclature... xi Chapter 1 Introduction Different Types of Engine Models Mean value and cylinder-by-cylinder engine odels Physical and Experiental odels Causal and Acausal Models Motivation and Goals Thesis Outline Contributions Docuent Structure... 7 Chapter... 8 Background and Literature Review Steady-state Models Regression Models Speed-Torque Tie Matrix Dynaic Models... 1 Chapter Powertrain Siulation Tools and Strategies Powertrain Strategies Backward Approach Forward Approach Cobined Backward-Forward Approach Siulation Tools Modelling by ADVISOR Modelling by PSAT Driver Model... 6 v

6 3... Engine Model Gearbox Model Wheel Model QSS Toolbox Matlab/Siulink and SiDriveline odels A Siulink Engine Model fro Matlab A Vehicle SiDriveline Model fro Matlab Dyola/Modelica Chapter Mean Value Engine Model Model Assuptions Coponents of the Engine Model Throttle Body Throttle Discharge Coefficient Throttle Area Models Pressure Function Models Throttle Angle Functions Intake Manifold Models Adiabatic and Isotheral Systes Voluetric Efficiency Fuel Dynaics Engine Models Theral Efficiency Rotational Dynaics Powertrain and Vehicle Models Chapter MapleSi Ipleentation Chapter Validation and Results Chapter Conclusions and Future Works Conclusions Future Work Appendices vi

7 Appendix A: Modelica Language Appendix B: Modelica Codes References..14 vii

8 List of Figures Figure.1 An Exaple of a Speed-Torque Tie Density Matrix [1] Figure. Carburetor in Dobner s Engine Model [17]... 1 Figure.3 The Dynaic Engine Syste and its coponents [19] Figure.4 Scheatic of a Mean Value Engine Figure 3.1 Siulation of a Conventional Drivetrain Configuration by ADVISOR [6]... 0 Figure 3. ADVISOR Input Window [6]... 1 Figure 3.3 ADVISOR Setup Window [6]... Figure 3.4 ADVISOR Result Window [6]... 3 Figure 3.5 Selecting the Configuration in PSAT... 4 Figure 3.6 A Coponent and Its Related Files in PSAT... 5 Figure 3.7 Top level of Driver odel in PSAT [30]... 7 Figure 3.9 Block C: Engine Torque Calculations in PSAT [30] Figure 3.10 Block C1: Wide Open Torque Curve in PSAT [30] Figure 3.11 Block D: Theral Model in PSAT [30] Figure 3.1 Top Level of a CVT Gearbox Model in PSAT [30] Figure 3.13 Torque Calculations in PSAT [30] Figure 3.14 Top level of Wheel Model in PSAT [30] Figure 3.15 Force Calculations in PSAT [30] Figure 3.16 Top Level of QSS Toolbox [34] Figure 3.17 Vehicle Calculations in QSS [34] Figure 3.18 Cobustion Engine Calculations in QSS [34] Figure 3.19 Tank Calculations in QSS [34] Figure 3.0 An Exaple fro Siulink Models: Top Level of an Engine with a Triggered Subsyste [39]... 4 Figure 3.1 An Exaple fro Siulink Models: Throttle Mass Flow Calculations [39] Figure 3. An Exaple fro Siulink Models: Intake Manifold Calculations [39] Figure 3.3 An Exaple fro Siulink Models: Engine Torque Calculations [39] Figure 3.4 An Exaple fro SiDriveline: Top Level of a Full Car Model [40] Figure 3.5 An Exaple fro SiDriveline: Torque Converter Block [40] Figure 3.6 An Exaple fro SiDriveline: The Transission in the Full Car Model [40] Figure 3.7 A Planetary Gear Set: Ring, Planet, Sun, and Carrier [40] Figure 3.8 An Exaple fro SiDriveline: Clutch Schedule [40] Figure 3.9 An Exaple fro SiDriveline: Final Drive, Wheel, and Road Calculations [40]. 50 Figure 3.30 Powertrain Coponents and Interfaces for a Conventional Autoatic Vehicle [4] 5 Figure 3.31 Engine Model in a Conventional Autoatic Vehicle [4]... 5 Figure 3.3 Theral Connectors in a Cylinder [43] Figure 3.33 A Sketch and Shifting Schedule for a Five-Speed Autoatic Gearbox [48] Figure 3.34 Gearbox Siulation for a ZF Autoatic Gearbox in Modelica [48] Figure 3.35 Engine on a Dynaoeter for a Four Cylinder Engine [49] Figure 3.36 Four Cylinders and Their Connections [49] Figure 3.37 The Cylinder Coponents in Siple Car [49] Figure 4.1 Discharge Coefficient in a Butterfly Valve [50] viii

9 Figure 4. Coparing Throttle Effective Areas of Two Models Figure 4.3 Effect of Throttle Pin Diaeter on Throttle Area Figure 4.4 Effect of Bore Diaeter on throttle Area Figure 4.5 Pressure Functions Coparison Figure 4.6 The Third- Degree-Cosine Function and Experiental Data... 7 Figure 4.7 Voluetric Efficiency Taylor s Model Figure 4.8 Voluetric Efficiency, Hendricks et al., 1st odel Figure 4.9 Voluetric efficiency, Hendricks et al., nd Model Figure 4.10 Voluetric Efficiency Map Figure 4.11 Bore-to-Stroke Ratio and Manifold Pressure Effects on Theral Efficiency Figure 4.1 Air-Fuel Ratio and Manifold Pressure Effects on Theral Efficiency Figure 4.13 Manifold Pressure and Engine Speed Effects on Theral Efficiency Figure 4.14 Displaced Volue and Engine Speed Effects on Theral Efficiency Figure 5.1 Top Level of the MapleSi Mean Value Engine Figure 5. Speed Controller in the MapleSi Model Figure 5.3 Throttle Body Model in MapleSi Engine Figure 5.4 Writing Equations in MapleSi Figure 5.5 Intake Manifold Model in a MapleSi Engine Figure 5.6 The Voluetric Efficiency Lookup Table in the Intake Manifold Model [5] Figure 5.7 Engine Model in the MapleSi Model Figure 5.8 Powertrain and Vehicle Model in the MapleSi Model Figure 6.1 Results for the Throttle Angle Figure 6. Throttle Air Mass Flow Results Figure 6.3 Manifold Pressure Results Figure 6.4 Voluetric Efficiency Results Figure 6.5 Theral Efficiency Results Figure 6.6 Net Power Results Figure A.1 Mass-spring-daper Syste in MapleSi ix

10 List of Tables Table 6.1 Percentages of the Errors in the MVEM Siulation Model x

11 Noenclature A p [ ] Piston area A thr [ ] Throttle area AF B [] C d Air-fuel ratio Cylinder bore Discharge coefficient C dvmax Maxiu discharge coefficient D [] d [] Throttle bore diaeter Throttle pin diaeter Eng _ Engine On-Off Switch On Off F aero [N] Aerodynaic resistance force F iner [N] Inertia resistance force F roll[n] Rolling resistance force F p [N] Piston force gear _ index Gear index: 0 for neutral gear, and 1,,3, and 4 for related gears H f [kj/kg] H l [kj/kg] J e [kg. ] Fuel heating value Lower fuel heating value Engine inertia l conrod [] Connecting rod length l crank[] Crankshaft length l p [] L v [] Displaced length of a piston Valve lift L VMax [] Maxiu valve lift K i K p [kg/s] e Integral gain Proportional gain Engine air ass flow rate xi

12 [kg/s] f Fuel ass flow rate fhot [kg/s] Fuel ass flow rate in hot-engine working condition fcold [kg/s] Fuel ass flow rate in cold-engine working condition [kg/s] Throttle air ass flow rate thr fi [kg/s] Injected fuel ass flow rate fv [kg/s] Evaporated fuel ass flow rate fw [kg/s] Wall fuel ass flow rate inertia [kg/s] Inertia ass of powertrain n e [RPM] or e [rad/s] P [Pa] P cc [Pa] P [Pa] P 0 [Pa] P f [W] Engine speed Cylinder pressure Crank case pressure Manifold air pressure Abient pressure Fuel heat power P ind [W] Indicated power P b [W] Brake power P loss [W] Engine loss power P friction [W] Engine friction power P puping [W] Engine puping power PW Brake Brake coand, varying fro 0 to1 PW cd Powertrain Coand, varying fro 0 to1 PW tep Engine war-up coefficient, varying fro 0 to 1 Q [W] Crank-angle-dependant heat release xii

13 Q Max [W] Maxiu crank-angle-dependant heat release q f [W] Heat energy released by fuel q fcold Heat-released-cold index q [W] Heat power rejected fro cylinders wall r H r w [N/] Copression ratio Wheel Radius S [] t s [s] t e [s] Piston stroke Cobustion starting tie Cobustion ending tie T dd [N.] Deand torque T _ [N.] Loss torque loss veh T [ o C] T o [ o C] Manifold teperature Abient teperature T cd [N.] Noralized coand torque T ax br [N.] Maxiu available brake torque T in [N.] Gearbox input torque T lossbr[n.] Torque lost by wheels T losstr[n.] Vehicle loss torque T out[n.] Gearbox output torque T var iation [N.] Variation torque T w [N.] Wheel torque T _ [ o C] Hot wide-open throttle torque value, wot cold T _ [ o C] Cold wide-open throttle torque curve value wot cold V c [ 3 ] V [ 3 ] V d [ 3 ] Clearance volue of a cylinder Manifold Volue Displaced Volue xiii

14 e [ rad/s ] Engine shaft rotational acceleration The specific heat ratio Noralized air-fuel ratio vol Voluetric efficiency th [Deg] Theral efficiency Throttle valve closed angle wheel [rad/s] Wheel Speed xiv

15 Chapter 1 Introduction In the last three decades, uch progress has been ade to iprove autootive engine efficiency, fuel econoy, and exhaust eissions. This progress is, in part, due to researchers ability to odel engines and thus exaine and test possible innovations. Modelling of an internal cobustion engine is a coplicated process and includes air gas dynaics, fuel dynaics, and therodynaic and cheical phenoena of cobustion. Even in a steady-state condition, in which an engine is hot and runs at a constant load and speed, the pressure inside each cylinder changes rapidly in each revolution, and the heat released by ignited fuel varies during the cobustion period. The ain focus in engine odelling is to clarify an engine s phenoena by establishing cause and effect dynaic relations between its ain inputs and outputs. The dynaic relations are differential equations obtained fro conservation of ass and energy laws. The input variables in engine odelling are usually throttle angle, spark advance angle (SA), exhaust gas recirculation (EGR), and air-fuel ratio (A/F). The output variables are engine speed, torque, fuel consuption, exhaust eissions, and drivability. The challenge in engine odelling is to find the relations between the engine input and output variables that best describe the odel and predict the output variables in different working conditions of the engine [1]. A four-stroke spark-ignition (SI) or diesel engine has four ain therodynaic processes - intake, copression, power and exhaust strokes- that occur in every two crankshaft revolutions of an engine in its operating condition. Each stroke refers to a half revolution of the crankshaft or full displaceent of a piston fro its top-dead-centre (TDC), the closest point of the piston top to the cylinder head, to its botto-dead-centre (BDC), the closest point of the piston top to the crankshaft or, in reverse, fro BDC to TDC. During the intake stroke, the intake valve is open and the piston oves fro TDC to BDC. The pressure inside the cylinder drops below the 1

16 atospheric pressure and forces the fuel and air ixture into the cylinder. Soeties, instead of ixing fresh air with fuel, a percentage of EGR is ixed with the air in the intake anifold to control the exhaust eissions. The copression stroke starts at angles close to the BDC, when both intake and exhaust valves are closed. The piston travels fro BDC to TDC, and gas in the cylinder is copressed. The ratio of cylinder volue before and after copression stroke is called the copression ratio, and is about 8 to 11 for ost SI engines. The power stroke starts when a piston is close to TDC, and the spark plug ignites the fuel. While both intake and exhaust valves are closed, the pressure inside the cylinder increases suddenly, forcing the piston downward to BDC and generating power. The exhaust stroke starts when the piston is close to BDC, and the exhaust valve is open, allowing the cobusted gas to flow out of the cylinder. Inlet and exhaust valves are usually opened shortly before or after TDC and BDC to allow axiu air into the cylinder or the axiu cobusted ixture to be swept out of the cylinder. Fuel can be directly injected into the cylinders, or it can be injected outside the cylinder into the intake port or throttle body. When it is injected outside of the cylinder, a fraction of the injected fuel strikes the wall, and the rest of the fuel evaporates and ixes with the air flowing into the cobustion chaber. This phenoenon is called wall-wetting. For central fuel injection, the injector is located at the top of the throttle valve, creating a fil ass that depends on the throttle angle. In siultaneous ultipoint injection and sequential fuel injection, the aount of fuel left on the wall is constant, regardless of the throttle angle []. The ignition angle is the angle of the crankshaft fro TDC at which a spark plug ignites the fuel. This angle is ainly a function of engine load and engine speed. Soeties a retarded ignition angle is used to copensate for high abient teperature or engine war-up conditions [3].

17 1.1 Different Types of Engine Models In the literature, engine odels are categorized by their coplexity, starting fro very siple transfer function odels to ean value engines, and then on to detailed cylinder-by-cylinder engines. The two latter engine types are discussed in Section Section 1.1. copares two types of physical and experiental odels. Section considers input, output, and variable relations in engine odels in causal and acausal odels. The types of equations usually used in physical and experiental odels are covered in Error! Reference source not found. and Chapter Mean value and cylinder-by-cylinder engine odels For the above-entioned engine events, the two ain odelling approaches are the cylinder-bycylinder engine odel (CCEM) and the ean value engine odel (MVEM). Cylinder-bycylinder odels are ore accurate than the MVEM odels and capture the details of instantaneous engine events such as pressure and teperature variations inside individual cylinders. CCEM odels can be used for evaluating eissions, engine diagnostics, fuel injection studies, and in-cylinder pressure, teperature, and fuel-consuption variations. Cylinder area, volue, pressure, and teperature, along with valve lift, fuel ass burning rate, and engine output power can be found and related to a specified crankshaft angle. Mean value engine odels are siple atheatical odels at an interediate level between siple transfer function engine odels and coplex cyclic siulation odels. Unlike the cylinder-by-cylinder engine odels that use a crank angle doain, ean value engine odels use tie scale doain. Tie scales in MVEM are ore than a single engine cycle and less than the tie that a cold engine needs to war up and coe in two types: instantaneous and tie 3

18 developing. Instantaneous scale involves a process that very quickly reaches equilibriu, siilar to the way that flow passes through the throttle valve. The instantaneous process is described by algebraic equations. Throttle air ass flow is an exaple of an instantaneous process. Tie developing processes are described by differential equations and reach equilibriu in one to three agnitude orders of engine cycles. An exaple is the equation for anifold pressure [] Physical and Experiental odels Physical odels are derived fro fundaental physical laws such as conservations of ass, oentu, and energy. The ain advantage of physical odels is that they are generalized and can be used for different systes. Filling and eptying of the air in a anifold, heat transfer, and crank shaft rotational dynaics are aong the physical processes odelled. In the absence of adequate knowledge to establish physical odels, and in soe phenoena like cobustion that are too coplex to be described by physical odels, relations between syste inputs and outputs are defined by experiental odels. These experiental odels are usually derived fro actual engine test data and thus can accurately predict engine s behaviour within the data range. Applying these odels to other types of engines or extrapolation of the data is eaningless. The large aount of data in such epirical odels needs to be processed, and polynoials or other types of experiental relations between input and output variables ust be introduced as equations. Paraeters and coefficients in equations are then fitted to the curves through the use of least square or other fitting ethods, and optial settings of input and output variables are obtained. In this work, both physical and experiental odels are used Causal and Acausal Models A causal odel is a syste of inputs, outputs, and variables, and the relations aong the. Inputs are introduced fro previous systes, or environents to predict the outputs, using a 4

19 relation defined in the syste. Inforation always flows into the syste (input) and out of the syste (output). Causal odels are best suited for explicit coputations. To build a siple physical odel in a causal syste, for exaple, a ass-spring-daper syste, different sets of blocks and connections are needed. However, the final syste and its coponents do not reseble the physical coponents, and it is hard to odify without detailed knowledge of the syste. In an acausal odel, each coponent is connected to other coponents by connecting nodes and lines. The nodes and lines between the coponents are very siilar to nodes and connections in physical systes. For exaple, in echanical coponents, the nodes can be described as echanical flanges, and the connecting lines as shafts that carry inforation such as force and displaceent. The direction of flow is not iportant, and coponents can be replaced or reused in other odels. This work uses both causal and acausal odels. The acausal odel is used ainly for echanical coponents after the engine output shaft and fored using Modelica [4] built-in language in MapleSi software. 1. Motivation and Goals Engine controllers need odels that are fast enough to interact with different engine sensors and actuators. The MVEM odels satisfy this condition. However adding any events to the odel, such as changes in the throttle angle, injection tiing, gear shiftings, road grade profiles, changing the fuel ratios, exhaust gas recirculation (EGR) percentage, vehicle acceleration and deceleration, and so on, adds too any details creating overwheling coplexity. The first goal of this thesis is to introduce a type of MVEM created with the new MapleSi [5] software. MapleSi is a ulti-doain odelling and siulation tool fro MapleSoft [6] and is ideal for engine phenoena, including cobustion, heat transfer, fluid echanics, and electrical doains. The second goal is to incorporate sybol-based equations into the engine odel facilitated by Maple software. This software enables one to write and to solve the equations in ways siilar to writing and thinking about atheatical equations. The third goal is to use replaceable engine coponents, a benefit of the Modelica equation-based language. Using 5

20 Modelica enables creation of physical coponents and equations in an equation-based for and in acausal forat. The latter can be used to create and to replace coponents quickly and easily, or change of coponents or equations are possible fro one odel to the next. The new coponents, then, can be introduced into the software library, and any types of engine configurations and coponents can be obtained. 1.3 Thesis Outline Using MVEM, this work develops a odel for engine gas dynaics. The odel is non-theral, in that it does not involve details of the cobustion process such as the fuel ass burning rate. Instead, it calculates the engine power and speed fro the throttle angle changed by a driver coand (pushing the accelerator pedal). The odel uses lookup tables, and physical and experiental equations. The ain coponents odeled are the throttle, intake anifold, and engine. The engine is considered to be naturally aspirated, which eliinates turbocharger and heat exchanger effects. EGR effect can be considered by introducing a percentage of exhaust gas that is ixed with fresh air in the anifold, but no eission and EGR effects are discussed in this thesis. 1.4 Contributions As entioned, odelling engines is a coplex task involving different doains. The first contribution of this thesis is to create an engine odel in the newly introduced MapleSi software in which odel coponents interact together in different doains. To odel such coplicated phenoena, an engine odel is broken down into three systes: physical, inputoutput odel, and causal and acausal. Physical odels are used for the parts of the coponents such as intake anifold pressure calculation and crankshaft rotational dynaics that are based on basic laws of echanics. The input-output odels are used for the parts of the coponents such as power loss and theral efficiency that are too coplicated to odel with a physical odel. 6

21 The second contribution is to use both lookup tables and paraetric equations inside the odel. Lookup tables can be replaced by paraetric equations, or the reverse, in this odel. Although paraeters of the input-output equations are defined for the engine of interest, they can be easily redefined inside the odel for new engines. The equations are defined inside each coponent in a sybolic anner by ebedded Maple inside the software. The sybolic equations can be changed and custoized for new coponents. The third contribution is the work s use of both causal and acausal odels. Although the acausal odels are used only in rotational dynaics, the introduction of gas connectors in future work should ake it possible to replace the causal throttle, intake, and engine coponents with acausal odels, which will help to replace and connect the odel coponents faster and ore easily. Finally, the thesis copares different throttle experiental equations by fitting curves to the engine data. For exaple, throttle angle function is obtained by reviewing siilar work in the literature, analyzing the actual data, and fitting the curve to the data. 1.5 Docuent Structure The engine odel in this thesis is discussed in following chapters: Chapter provides background on engine odels, including physical and experiental odels. Chapter 3 provides a review for current engine-and powertrain-siulation tools and software. Chapter 4 gives theoretical and atheatical equations for engine odels. Different types of engine odels for each coponent are discussed in this chapter. Chapter 5 presents the new MapleSi engine coponents and equations that are used in each coponent. Chapter 6 deonstrates the siulation setups and results. Chapter 7 sus up the conclusions of the thesis and akes recoendations for future work. 7

22 Chapter Background and Literature Review With new anti-exhaust eission legislation and increasing oil prices in the 1970s, the autootive industry adopted the goals of increasing fuel econoy and reducing eissions. Introduction of exhaust catalytic converters in 1975 helped to reduce carbon onoxide (CO), hydro-carbons (HC), and nitrogen oxides (NOx) eissions significantly. To increase fuel econoy, various strategies were ipleented, such as downsizing of vehicle and engine, increasing of engine, powertrain, and accessories efficiencies, and reduction of vehicular aerodynaic drag coefficient and rolling resistances. To achieve these goals required better odelling approaches for engine controllers. Controllers should be able to odel ain engine coponents in a fast and approxiate way. Better coputers in recent years have allowed ore coplex odelling of engine controllers. Engine odels can be divided into different types, such as physical or epirical, and dynaic or steady-state. However, there is no clear distinction between these types, and usually engine odels are a cobination. The early odels were based on steady-state test conditions and regression odels. Later, with advances in coputers, dynaic odels becae popular. Because the early odels usually used steady-state odels, and newer odels used dynaic and physical odels, the four engine types entioned above are cobined and discussed in two types: steady-state odels and dynaic odels. 8

23 .1 Steady-state Models Engine odels, until the 1970s, were ainly obtained fro steady-state tests at constant speed and torque conditions. Spark advance (SA), air-fuel ratio (AF), and exhaust gas recirculation (EGR) variables were changed slowly to deterine the best fuel efficiency and the lowest possible eission relations. Most of the odels were obtained by analyzing the effects of varying input variables on output variables, so they were called input-output odels [7]. Inputoutput odels were epirical and usually used either apping techniques or statistical correlations such as regression ethods to establish relations between input and output..1.1 Regression Models In a regression analysis ethod, epirical functions are approxiated by atheatical relations such as a Taylor series. A third order expansion of a Taylor series can be written for f as a function of three input variables: SA, AF, and EGR. f SA, AF, EGR 3 d f d f f df (. 1)! 3! The first derivative of the function can be written as df f f f SA AF EGR (. ) SA AF EGR By taking the second and third derivatives of the function and replacing the in the first equation f SA, AF, EGR k k SA k AF k EGR k SA k AF k EGR SA AF k SAEGR k AF EGR k SA k AF k k EGR k 14 SA AF k SA EGR k AF SA k AF EGR k EGR SA

24 EGR AF k SA AF EGR k 0 19 (. 3) Obviously, the above equation has any ters and it is hard to use it as an experiental equation. A statistical t-test can deterine the significance of each ter, and the ters that should be kept or eliinated fro the equation. Siplifying, obtains the final for of regression odel and the equation coefficients [8]. One of the first attepts to develop engine control optiization by a regression ethod was done by Prabhakar, et al. [9]. They used optiization ethods to find the relations between SA, AF, speed and torque variables with eissions and fuel consuption at steady-state conditions. However, the odel was not validated for a driving cycle. Mencik and Bluberg [8] used regression ethods for exhaust eissions. They concluded that the degree of a fitting polynoial depends on experiental data scatter. They also showed that the eission ass flows can be best presented by logarithic functions in that eissions can vary with the sae agnitude of order to the control variables. Delosh et al. [10] used a ixed regression and physical odel for total vehicle odelling. The odel was able to receive throttle and brake coands fro a driver, and thus followed a driving cycle..1. Speed-Torque Tie Matrix Bluberg [11] was able to reduce the tie and the costs of eission and fuel econoy tests over a driving cycle. His ethod involved using a tie distribution atrix of speed and torque over a driving cycle period. The driving cycle was divided into a few regions and representative points (8 to 13 points). The total tie spent in each region was considered as a weight factor for the representative point. Figure.1 shows an exaple of a tie atrix. Using this ethod, a driving cycle could be represented by a few points that could handle the drivetrain changes by adjusting the weight factors [1]. 10

25 Rishavy et al. [13] used a speed-torque atrix ethod involving a linear prograing ethod to reduce engine eissions. Cassidy [14] ipleented an on-line optiization ethod at selected points in a speed-torque atrix for engine calibrations. Auiler et al. [15] used dynaic prograing to allocate eission contributions at selected points. The ethod cobined the steady-state eissions with fuel flow data to iniize the fuel eissions. Figure.1 An Exaple of a Speed-Torque Tie Density Matrix [1]. 11

26 . Dynaic Models In a driving cycle, any transients such as shifting gears and changing the throttle angle can not be captured by steady-state tests. Advances in coputer technology and ore restrictions for fuel eissions led to dynaic odels becoing a general ethod for engine odelling. Dobner [16, and17] introduced a dynaic atheatical odel for an engine with a carburetor. The odel could be used for other engines with only a few changes in input paraeters. The control engine variables were SA, AF, EGR, throttle angle, and load torque, and the ain output variables were anifold pressure, engine net torque, and engine speed. The dynaics of the odel was presented by tie delays and integration of dynaic equations. The odel was a siple discrete odel in which coputations were done per each engine firing. The engine syste in the odel consisted of carburetor, intake anifold, cobustion, and engine rotational dynaics. Figure. Carburetor in Dobner s Engine Model [17] 1.

27 In the carburetor odel (Figure.), the fuel ass flow was calculated by using two individual lookup tables for noralized pressure ratio and throttle angle characteristic. The ethod of noralizing pressure and throttle angle function is still widely used in ass calculations of engines as lookup tables, or equation-based fors. The fuel flowing out of the anifold was calculated fro ass flow rate into the anifold and voluetric efficiency characteristics. By considering fuel delays as drops, wall, and gas contributions, the total fuel ass calculated, and air-fuel ratio was obtained. In the cobustion odel, the effects of SA, AF, and air charge density were perfored as functions of noralized torque in the lookup tables. The output values of these lookup tables were used to obtain the indicated torque. The odel used another lookup table for the friction added to the load torque and results were used in engine rotational dynaic to obtain engine speed. Using voluetric efficiency and engine speed, Aquino [18] presented an equation for of anifold pressure calculations based on continuity law. Unlike Dobner s, this odel was a continuous flow odel. The odel also gave a new set of equations for fuel dynaics. The odel tracked the fuel ass in the intake anifold by assuing that, for fuel injected into ports, a fraction of the fuel would evaporate and a fraction of it would be left on the port walls. After a delay, the fuel ass on the port wall is ixed with air and flows into cylinders. The fuel dynaic odel defined by Aquino can be easily used for other engines if the tie constant (τ) and fraction of injected fuel (X) paraeters are adjusted. Powell [19] introduced a nonlinear dynaic engine odel that included induction and an engine power syste. Figure.3 shows the configuration of the engine odel. The odel also considered EGR, fuel injection, and throttle valve dynaics. For intake anifold ass calculations, instead of using voluetric efficiency, which has an iportant role in transient conditions, he directly used a regression odel for ass flow changes as a function of engine speed and anifold pressure. The throttle ass flow was obtained fro an equation for pressure at choked and non-choked conditions, and a second degree polynoial was fitted for the throttle 13

28 angle function. The engine output torque was obtained by another regression equation as a function of engine speed, AF, and intake ass flow. Reference [7] gives ore inforation about siilar odels for intake ass flow calculation for various engine operation ranges. The paper also included inforation about induction-power and spark-power delays. Figure.3 The Engine Syste and its Coponents [19] Crossley and Cook [0] used an approach siilar to the Powell s but replaced the throttle angle approxiate function with a third degree polynoial and used engine output torque as a function of SA, AF, engine speed, throttle ass flow, and engine ass flow variables. Yuen and Servati [1] presented a dynaic engine odel siilar to the approach used in reference [16], replacing the throttle body with a carburetor in the engine odel. To generalize the odel for other engine applications for future, they did not use the throttle area characteristic ter, but instead used a noralized function for pressure and another noralized function by using Harington and Bolt s [] approxiation ethod. Unlike Dobner s, this odel considered intake anifold teperature changes and their effect on fuel evaporation and anifold pressure during the transient conditions. Engine eissions were obtained fro experiental tables as functions of cobustion paraeters. The odel could predict the ass generations of different pollutants as a function of the throttle ass flow and air-fuel ratio. 14

29 In actual engine operating condition, the air ass flow is closely related to throttle area geoetry and characteristics. Moskwa [3] introduced throttle area as a function of throttle angle, throttle pin diaeter, and throttle bore. The odel used friction, AF, and SA lookup tables for output torque calculation. Theral efficiency in the odel was a function of anifold pressure, copression ratio, and engine cylinder geoetries. A odel for the first tie called the ean value engine odel (MVEM), was introduced by Hendricks and Sorenson [4] and then described in ore detail in [5]. The idea was to capture engine dynaics in tie scales larger than an engine cycle. As shown in Figure.4, the odel included ain coponents of engine gas flow dynaics, fro the intake anifold to the exhaust syste. Hendricks and Sorenson introduced new equations for voluetric efficiency, theral efficiency, and pressure function. For fuel dynaics, they introduced a new odel that becae a copetitor to the Aquino odel. Unlike Aquino s fuel-ass-based calculations, the newer odel is based on fuel flow in the intake anifold. One of the advantages of Hendricks and Sorenson s odel is that ost of its paraetric equations, such as voluetric efficiency, theral efficiency, load, and loss power, are presented as functions of anifold pressure and engine speed that are obtained directly fro solution of differential equations in the anifold and engine. The engine paraeters can be easily adjusted and reused for other engines. 15

30 Figure.4 Scheatic of a Mean Value Engine [4] 16

31 Chapter 3 Powertrain Siulation Tools and Strategies Powertrain odelling and siulation software products are developed for various purposes and can be used for drivetrain analysis, vehicle perforance evaluation, or new powertrain developent. Powertrain siulation tools generally odel the coponents interactions on each other by coputing torque and speed values in each coponent. The powertrain strategies define the ethod and the direction of the power or torque, and speed flows in a siulation relative to the calculations. 3.1 Powertrain Strategies The power or torque flow in a powertrain starts fro the engine (upstrea), and ends with the wheels (downstrea). The flow of calculations can be either in the sae direction as the power flow, or in the reverse. Based on the direction of the power flow and direction of the calculations, vehicle siulation strategies are categorized as one of three types: backward, forward, or cobined backward-forward facing, all of which are described in following sections Backward Approach In a backward approach, calculations start fro wheels and end with the engine. In a powertrain, wheels are assued to be the front of the powertrain, and the engine end of the syste, leading to the ters backward or front-to-end, or wheel-to-engine approaches. In the backward ethod, the power required at the wheels is calculated back to the engine, and the related engine power is calculated. Calculations at the wheels start fro the tie-speed data fro a drive-cycle. 17

32 Drive-cycles, standard vehicle speed data regulated by different countries, are prepared to evaluate fuel efficiency and eissions of new vehicles, and used for various accelerating, decelerating, and stop conditions for different highway or in-city driving conditions. The vehicle is assued to follow the driving cycle with the sae speed at the wheels. Vehicle acceleration and travelled distance can be directly obtained by differentiating and integrating the velocity in each instant of tie of the driving cycle. The velocity and acceleration values are used to calculate tire roll losses, brake losses, and aerodynaic losses of the vehicle. The reactive force of the vehicle is assued to be equal to the su of these three losses. Tire radius, resistance forces, and vehicle velocity are used to calculate tire torque and rotational speed. Torque and speed in the final drive, driveshaft, gearbox, and torque converter (or clutch) are calculated fro the torque and speed of the previous downstrea coponents (closer to the wheels). The calculations are continued backward until the required power is obtained fro an efficiency lookup table. The calculations for vehicle losses and coponent efficiencies are siple; results have a siple integration and a fast siulation execution tie. One of the drawbacks of the backward approach is the assuption that the vehicle follows the drive-cycle with the sae speed at any instant of tie. In actual driving condition, the actual speeds of the tires are different fro the desired speed due to tire slip Forward Approach In the forward approach, the flow of calculation is in the sae direction as the power flow. The process starts when a driver pushes the acceleration pedal or brake. The controller receives this coand and translates it into throttle or brake coands, which are then translated to a required torque by calculating an error. The error that is the difference between the vehicle s desired and actual values is used to calculate the total deand torque. In the next step, the coputed torque is passed forward through powertrain coponents to the wheels. The forward approach is constructed in cause-and-effect for so it is desirable for detailed siulation. In each coponent instead of assuing required values, real torque and speed are 18

33 calculated. This approach gives very realistic results in particular for engine axiu output power calculations at wide open throttle conditions. The disadvantage of the forward approach is its long running tie for siulations. The calculations are based on integration of throttle anifold and powertrain speed state equations, resulting in high order integrations Cobined Backward-Forward Approach All coponents encounter liitations when they are working at their fully loaded conditions. Thus at soe levels, when power deand is increased upstrea of the coponent (i.e., coponents closer to the engine), the coponents reach a condition that can use only a part of the power or torque. In a forward-backward approach, siulation starts like a forward syste until the power or torque in the coponent reaches its axiu available liit. At this level axiu power or torque is fed back toward the engine, and siulation continues fro the engine to the wheels under new liitations [6]. 3. Siulation Tools Many tools are available for engine and powertrain odelling, both open source or coercial software. As exaples, advanced vehicle siulator (ADVISOR), powertrain syste analysis tool kit (PSAT), QSS toolbox, Matlab/Siulink, and Modelica are discussed in this chapter. The focus of the discussion is on how the odels work and which types of equations they use. The odels include different theral or non-theral, input-output or physical, forward or backward, and causal or acausal approaches. Depending on the level of details, the vehicle odel can be defined as steady state, quasi steady-state or dynaic. For exaple, ADVISOR is categorized as a steady-state odel, PSAT as quasi steady-state, and the odel in this work is a dynaic 19

34 odel. The ain advantage of using steady-state odels is their speed of coputation. However, they cannot predict dynaic conditions Modelling by ADVISOR Advanced vehicle siulator (ADVISOR) [6,7] is a siulation tool developed at the national renewable energy lab (NREL) in It was originally designed for hybrid electric vehicles (HEV) to iprove fuel econoy and vehicle perforance, but later on, developed for other configurations of vehicles. ADVISOR can be used for different applications, such as perforance and fuel econoy analysis, or eission control. The coponents of ADVISOR are created in Siulink. Using Siulink enables the coponent orders and their connections to be shown in a graphical way. Figure 3.1 presents an ADVISOR siulation for a conventional vehicle syste. The paraeters used in each Siulink block are defined in an associated Matlab -file. The odel inside each Siulink block and the Matlab -file can be redefined or replaced by new odels and paraeters. Figure 3.1 Siulation of a Conventional Drivetrain Configuration by ADVISOR [6] ADVISOR is open source code software. The odels inside the coponents can be scaled to atch other types of powertrains. ADVISOR provides three ain graphical user interface (GUI) windows: input, setup and result windows. Inside the input window (Figure 3.), various types of driveline coponents can be selected fro pull down enus. 0

35 Figure 3. ADVISOR Input Window [6] The values of the coponents such as engine power and all vehicle configurations can be edited and saved in this window. Upon loading any vehicle configuration, related data are loaded into the Matlab workspace, which are then used during the siulation. The characteristic ap of each coponent can be displayed for the selected configuration at the left side of the window. The value of coponents can be changed, and the Siulink block diagra of the coponent can be reached by Edit Var and View Block Diagra buttons. 1

36 Figure 3.3 ADVISOR Setup Window [6] The setup window (Figure 3.3) enables one to define different events such as running a siulation as a single or ultiple drive-cycles, or including the road grad or acceleration tests. The right side of the window is a portion showing user-defined paraeters and the left side window presents related graph inforation of selected paraeters. The result window (Figure 3.4) enables a review of the suary of results about the vehicle and its perforance at a specific tie or during a driving cycle [8].

37 Figure 3.4 ADVISOR Result Window [6] 3.. Modelling by PSAT The Powertrain Syste Analysis Tool (PSAT) was developed by the Argonne national lab and the US Departent of Energy (DOE) [9, 30, 31 3]. The software is based on Matlab/Siulink odelling environent with a graphical-user interface (GUI). The PSAT library has a large nuber of predefined echanical, hydraulic, and electrical coponents that can be accessed and reused. PSAT also has any predefined vehicle configurations in its library, such as conventional spark ignition (SI) and copression ignition (CI), electric, fuel cell, series hybrid, and parallel hybrid enabling users to siulate coplicated systes for different sizes of vehicles. It allows users to iport data into the odel coponents, or to define control strategies for the syste without needing to write any lines of code. PSAT can be used for various vehicle odelling strategies such as fuel econoy, engine perforance, drive-cycle studies, paraetric odelling, and controller design, but it cannot be used for calibration and drivability studies. Coponent controllers are controlled by the ain controller at the top level of the odel. 3

38 PSAT is a forward-looking odel that starts siulation by receiving brake and acceleration coands fro the driver. The controllers then receive these coands and distribute the into the coponent odels. The coponent controller decides which types of inforation should be sent to which coponent, for exaple, gear inforation goes to the gearbox, is gear ratio or gear nuber, or for the clutch is displaceent of its plates. Older versions had three ain windows, the sae as ADVISOR s, and for any additional tasks, a new window would be added to the odel, so it was confusing for the user to follow the process. Newer versions have only one window but with different tabs. In PSAT, the vehicle configurations are fixed, but coponents inside the configuration can be selected, odified, or replaced. Thus, for exaple, if a conventional SI engine is selected, the software allows choosing one of the predefined autoatic or anual configurations fro its subsyste. In all configurations, the order of coponents and their connection are fixed. In a conventional SI engine the order of the coponents starts fro the starter and engine, and ends with the wheel and the vehicle odel. The configuration can be selected fro the library list by dragging and dropping it into the work space (Figure 3.5). Figure 3.5 Selecting the Configuration in PSAT 4

39 In a siilar way, coponents can be selected fro the library list, and then its initialization file and related graph can be opened. The software allows access to the coponent Matlab -file for any paraeters odifications inside the odel (Figure 3.6). PSAT allows the choice of different accelerating, decelerating and shifting gear strategies fro the predefined strategies in the library. In newer versions, it is possible to odel the transient conditions of the coponents such as the engine or gearbox transition condition. Figure 3.6 A Coponent and Its Related Files in PSAT Soe of the ain coponents of PSAT and their odels are explained in the next sections. 5

40 3...1 Driver Model The driver odel calculates torque deand by converting the error that is the difference between vehicle actual and desired speeds. The vehicle desired speed is obtained directly fro a drivecycle that is used in siulation. Error calculations are shown at the top left corner of Figure 3.7 as V Error V V (3. 1) veh _ desired veh _ actual Error is used to calculate torque variation (block A). Tvar ition K p VError Ki VError dt (3. ) K p is proportional gain, which is the reaction of the syste to current error, and used for the transient portion of the torque deand that helps the vehicle to keep on the signal track during instant speed changes. The integral gain, K, is the reaction of the syste to the su of the errors i and used to eliinate errors reaining fro the steady-state working condition of vehicle. 6

41 A B Figure 3.7 Top level of Driver odel in PSAT [30] Vehicle losses, including rolling, aerodynaic, and grade resistance, are calculated by approxiating a second degree polynoial obtained fro dynaoeter experiental data as follows (block B). T loss _ veh veh _ desired veh _ desired r w a bv cv (3. 3) where rw is tire radius, and a, b, and c are experiental coefficients. Deand torque is the su of variation and vehicle loss torques. T dd T T (3. 4) variation loss_ veh 7

42 3... Engine Model This engine odel in PSAT calculates fuel consuption, output torque, and eissions in steadystate (hot) and transient (hot-cold) theral conditions. Figure 3.8 shows four blocks that calculate engine torque, engine theral paraeters, engine fuel rate, and exhaust eission flows in blocks C, D, E, and F respectively. Block C, shown in Figure 3.9, calculates engine torque by using a switch. To prevent excess injection of fuel when the engine speed is lower than idling speed (the tie when an engine is first switched on with a starter) the cut-off torque is calculated fro a lookup table, as shown at the top right of the window. In other conditions, engine torque is calculated fro function block as follows (block C1). T cd PW Eng, (3. 5) cd On _ Off e where PW cd is the coand coing fro the controller, varying fro 0 to 1. On Off Eng _ is a switch that has values of 0 when the engine ignition switch is off, and 1 when the engine is running. If T cd is zero, the output torque value calculated by the function block will be zero. If the engine speed is greater than zero and torque coand is equal or greater than zero, output torque is calculated in a function block by interpolation of wide open and closed throttle torque values fro following equation: T out T T T T, (3. 6) 1 cd ctt cd wot 8

43 where T wot is wide open throttle torque, and Tctt is closed throttle torque. C D E F Figure 3.8 Top level of Cold-Hot engine in PSAT [30] Block C1 (Figure 3.10), illustrates a wide open throttle torque curve ( T wot ), calculated by interpolation of the cold wide-open throttle curve and the hot wide-open throttle curves: T wott PW T PW T, (3. 7) 1 tep wot_ cold tep wot_ hot 9

44 where T wot _ cold is the cold wide-open throttle torque curve value, wot hot T _ is the hot wide-open throttle torque value, and PW tep is the engine war-up coefficient, equal to zero when the engine is cold, to 1 when the engine is hot, and between 0 to 1 during engine war-up. In a siilar way the closed-throttled torque is calculated in the block arked C. C1 C Figure 3.9 Block C: Engine Torque Calculations in PSAT [30] 30

45 Figure 3.10 Block C1: Wide Open Torque Curve in PSAT [30] Block D (Figure 3.11) calculates theral paraeters for the engine, including the war-up index, engine teperature, heat rejected power, and heat rejected energy. Figure 3.11 Block D: Theral Model in PSAT [30] 31

46 Knowing engine torque and engine speed, and heat power released by fuel per unit ass can be obtained fro the heat-released-hot and heat-released-cold indices lookup tables. q f tep q q q, PW (3. 8) fcold fhot fcold where q f is the heat power released by fuel per unit ass. Heat power rejected fro the cylinder walls or intake and exhaust valves is the power that is generated by fuel inus the power at the engine output shaft. q q T (3. 9) H f f e e The fuel rate is calculated by interpolation of the data fro hot and cold fuel rate lookup tables. f PWtep fhot fcold fcold (3. 10) Engine eissions including particulate atter (PM), hydrocarbons (HC), nitrogen oxides (NOx) and carbon onoxides (CO) are directly obtained fro a lookup table as functions of engine speed and torque data. 3

47 3...3 Gearbox Model Manual, autoatic, and continuous variable (CVT) are three types of transissions in PSAT. Figure 3.1 shows top level of a CVT gearbox odel that calculates speed, torque, and inertia. Figure 3.1 Top Level of a CVT Gearbox Model in PSAT [30] Output torque and speed are calculated by ultiplying or dividing input values by a gear ratio. Loss torque is considered in torque calculation by using a 3-D lookup table and three inputs: speed (ω in ), input torque (T in ), and a gear index. The gear index is calculated fro a lookup table 33

48 once the gear nuber is known. It is 0 for neutral gear, and 1,,3,4 for corresponding gears. A typical torque calculations is shown in Figure T out T T gear _ index (3. 11) in loss Figure 3.13 Torque Calculations in PSAT [30] Wheel Model Two types of wheel odel exists in PSAT. The first is the Single Wheel odel and is based on braking force calculations at each wheel individually, and adding inertias to all wheels. The second odel doesn t include the rolling resistance because it is already considered in the driver odel and because of three A, B, and C coefficients in the odel is called ABC odel. 34

49 The top corner of the wheel odel, displayed in Figure 3.14, includes three types of calculations: speed, force, and ass. The angular velocity of the wheel ( speed of the vehicle by the radius of the wheel ( r w ). wheel ) is calculated by dividing the V / r (3. 1) wheel veh w Figure 3.14 Top level of Wheel Model in PSAT [30] In force calculations block, torque loss for the wheel is calculated by ultiplying the brake coand value ( PW Brake ) by the axiu available brake torque. T lossbr PW T (3. 13) Brake ax br 35

50 The brake coand value varies fro -1 to 0, fro full brake pedal pushing to no-brake pedal pushing. The wheel losses are calculated in Figure 3.15 by a third-degree polynoial as a function of vehicle speed. T losstr 1 c V veh c3v veh 3 veh veh r w c c V g (3. 14) 4 where g is gravity acceleration, rwis wheel radius, and veh is ass of the vehicle. The output torque of the vehicle is obtained by subtracting the brake and wheel losses fro the input torque coing fro the final drive (Tin). T out T T T (3. 15) in lossbr losstr Finally the net force is calculated by dividing the output torque by the wheel radius ( r w ). T out Fout (3. 16) rw 36

51 braking torque 3 brake cd -Kax braking torque braking torque Eq. 14 wh trq out Eq info 1 spd in Eq. 15 veh spd Blending f(u) Rolling Resistance Calculation 4 trq in wh trq out -K- 1/radius force f(u) Speed dependent soothing -Kradius tire rollig resistance Sign Figure 3.15 Force Calculations in PSAT [30] Equivalent inertia ass of the powertrain ( inertia ) is calculated by adding the wheel inertia ( J wh) and upstrea inertia (J in ), and dividing the result by the wheel radius squared. inertia J J r (3. 17) in wh / w 3..3 QSS Toolbox A quasi-static siulation toolbox (QSS) is a discrete backward siulation odel that approxiates fuel consuption by using a fast and siple calculation algorith [33, 34]. The calculations start fro integration and differentiation of velocity in a driving cycle to obtain approxiations of vehicle travelled distance and acceleration. Figure 3.16 depicts the top level of QSS tool box. Various Aerican, European, and Japanese drive-cycles are available in the QSS library. Upon selection of a drive-cycle for a anual gearbox an associated shifting strategy vector file is loaded into the work space. Changing the gears is assued to be only a function of vehicle speed. 37

52 v v w_wheel w_wheel w_mgb w_gear dv i dw_wheel dv T_wheel Vehicle dw_wheel dw_mgb T_wheel T_MGB i Manual Gear Box dw_gear P_CE T_gear Cobustion Engine P_fuel x_tot Tank liter/100 k Display x_tot Driving Cycle Figure 3.16 Top Level of QSS Toolbox [34] As depicted in Figure 3.17, wheel rotational speed and torque can be obtained fro the following equations V (3. 18) w r w w T w aero roll iner r w F F F (3. 19) P (3. 0) w T w w where V w, r w, w, T w, and Pw are vehicle speed, wheel radius, wheel rotational speed, wheel torque, and power. F aero, F roll, and Finer are aerodynaic, tire rolling, and inertia forces. The vehicle is assued to be oving on a flat road, so grade loss is not considered in this odel. 38

53 1 v v v _a Average speed 1/r_wheel 1 w_wheel w_wheel 1/r_wheel dw _wheel P_wheel v F_roll Rolling resistance v F_aero Aerodynaic resistance r_wheel 3 T _wheel dv d_v F_iner Inertia Total resistances Wheel radius T_wheel P_roll P_aero P_iner Figure 3.17 Vehicle Calculations in QSS [34] Gear ratios are used to calculate gearbox input torque and speed in the gearbox block. In the engine block (Figure 3.18), fuel ass flow is obtained by a two-diensional ap and use of gearbox speed and torque inputs. Fuel power is obtained by P f f H f (3. 1) where H f is a constant fuel heating value. Finally, the required power level is obtained by adding the auxiliary vehicle equipent (such as air-conditioner) required power to the fuel power. 39

54 P P P (3. ) e f aux The QSS engine odel can also detect and control over load, over speed, idle and fuel cut-off conditions. w_ce T_CE 1 w_gear Lower liit (speed at idle ) w_ce Detect overload and overspeed 3 T_gear H_u dw_gear theta _CE Engine inertia Total torque Lower liit (fuel cutoff ) T_CE Engine consuption ap V = f(w, T) [kg/s] Fuel lower heating value P_CE_fuel w_ce P_CE P_CE_fuel T_CE Detect idle T_CE P_CE Detect fuel cutoff 1 P_CE P_CE P_aux Total power Figure 3.18 Cobustion Engine Calculations in QSS [34] Fuel liter per 100 kiloeters is calculated by integrating of fuel ass flow and dividing it by fuel density and distance travelled (Figure 3.19). 1 P_fuel P_fuel _fuel 1/rho _f x_tot Integration k_cs Factor for cold start 1e5 1 liter /100 k V_liter Figure 3.19 Tank Calculations in QSS [34] 40

55 3..4 Matlab/Siulink and SiDriveline odels Many exaples of Matlab [35] software exist in deo odels for engine and powertrain odelling. Soe of the exaple odels are created in Siulink [36], and others are in a Siulink extended tool called SiDriveline [37, 38] that odels the rotating dynaics of a drivetrain. The SiDriveline library contains different types of powertrain coponents such as transission, clutch, engine, tire, and vehicle odels A Siulink Engine Model fro Matlab In an internal cobustion engine, air continuously flows into the throttle and the intake anifold, but it is discretized by inlet and exhaust valve events. In theory, in a four-cylinder engine, each intake, copression, power, and exhaust stroke can be assued to happen every 180 degrees of the crankshaft. With this approxiation, valve tiing occurs at the end of the copression stroke and the beginning of the power stroke at TDC. Figure 3.0 deonstrates such an engine odel using a trigger block. For each cylinder, air induction occurs during a 180-degree of a coplete cycle (two revolutions of the crankshaft). The intake tiings for a four-cylinder, then, can be assued to be four individual intake processes separated by valve tiing events at every 180 degrees of the crankshaft. 41

56 ? Modeling Engine Tiing UsingTriggered Subsystes ThrottleAngle Throttle Angle Profiles (degrees ) edge180 valve tiing N 1 crank speed (rad /sec) Throttle Ang. ass(k) Air Charge Engine Speed, N ass(k+1) trigger Throttle & Manifold ass(k+1) trigger Copression Torque N Cobustion Load Teng Tload N Vehicle Dynaics 30 /pi rad /s to rp EngineSpeed Engine Speed (rp ) Drag Torque LoadTorque Copyright The MathWorks Inc. ThrottleAngle throttle deg (purple ) load torque N (yellow ) Figure 3.0 An Exaple fro Siulink Models: Top Level of an Engine with a Triggered Subsyste [39] The Siulink odel is based on the Crossley and Cook [0] engine odel and the Butts et. al [39] Siulink odel. The engine odel starts with a throttle valve coand. The throttle air ass flow is calculated as a function of the throttle angle and anifold to abient pressure ratio. As is shown in Figure 3.1, the throttle angle function is approxiated by an epirical thirddegree polynoial, and pressure function is obtained fro the ideal gas flow state in an orifice. thr (, P / P0) g( ) f P / P 0 (3. 3) 4

57 Throttle Angle, theta (deg ) 1 f(theta ) *u *u*u *u*u*u Manifold Pressure, P (bar ) in pratio g(pratio ) *sqrt(u - u*u) 3 Atospheric Pressure, Pa (bar ) 1.0 Sonic Flow 1 Throttle Flow, dot (g/s) flow direction Throttle Flow vs. Valve Angle and Pressure Figure 3.1 An Exaple fro Siulink Models: Throttle Mass Flow Calculations [39] In an orifice, back flow happens when pressure downstrea is higher than that upstrea. The block also considers back flow conditions by using a flow direction block. As deonstrated in Figure 3., Manifold pressure in the anifold block is calculated fro a differential equation as follows: P RT V thr e, (3. 4) where P, T, and V are anifold pressure, teperature, and volue, respectively; R is gas constant; and is obtained by an epirical equation as a function of anifold pressure and e engine speed. The above differential equation obtained fro the ideal gas law and will be discussed in ore details in chapter 4. 43

58 Manifold Pressure, P (bar ) 1 dot Input (g/s) RT /V N (rad /sec) 1 s p0 = bar *u[1]*u[] *u[]*u[1]*u[1] *u[1]*u[]*u[] Puping 1 dot to Cylinder (g/s) Intake Manifold Vacuu Figure 3. An Exaple fro Siulink Models: Intake Manifold Calculations [39] Engine torque is directly calculated fro another epirical equation as a function of spark angle, fuel ratio, engine air ass, and engine speed (Figure 3.3). 1 Air Charge 15.0 Spark Advance (degrees BTDC ) -K- Stoichioetric Fuel N *u[1] *u[1]/u[] - (0.85 *u[1]*u[1])/(u[]*u[]) *u[3] *u[3]*u[3] Torque Gen 0.07 *u[4] *u[4]*u[4] *u[4]*u[3] +.55 *u[3]*u[1] *u[3]*u[3]*u[1] Torque Gen Engine Torque 1 Torque Figure 3.3 An Exaple fro Siulink Models: Engine Torque Calculations [39] Engine speed is calculated fro an equation for engine rotational dynaics as T T e load e (3. 5) J e where e, e T, and J e are engine speed, torque, and rotational oent of inertia, respectively; T load is load torque. 44

59 3..4. A Vehicle SiDriveline Model fro Matlab An exaple of SiDriveline odelling is presented in Figure 3.4 so called Full Car Model [40]. The inputs for the odel are gear shifting, throttle coand, and brake signals. The output of the syste is the vehicle speed. SiDriveline ainly focuses on rotational coponent odelling. Varieties of transission odels, and advanced tire and vehicle odels, are defined and prepared in the library for users. Siulink environent also enables to ipleent different levels of coplexities for controllers. However, the engine odel is a very siple odel based on a one-diensional axiu torque lookup table as a function of engine speed. Clutch Hydraulics Prograed Brake Torque Torque Brake Torque Gear Sequence Gear P KPH Prograed Clutch Control Gear P In Out Drive Shaft Road Speed Throttle Throttle In Out Ipeller Turbine CR-CR 4-speed Vehicle Load - Wheels - Road - Power Scope Throttle Signal Gasoline Engine Engine Scopes Converter with Lockup Clutch Full Car Env Based on a CR-CR 4-Speed transission. Workspace variables are defined. Drive Ratio Scope Clutch Scopes Figure 3.4 An Exaple fro SiDriveline: Top Level of a Full Car Model [40] The throttle valve opening is a noralized signal varying fro 0 to 1, and it is ultiplied by the axiu torque value obtained fro the lookup table to calculate available torque. Except for signal blocks, coponents in SiDriveline can be connected to other coponents by physical connections. The physical connections work as a rotational shaft that can carry torque and speed. Physical connections cannot be connected to signal blocks and vice versa. The interediate blocks that connect the physical coponents to the signal blocks are actuators and sensors. Sensors are used to easure shafts speeds and torques, and actuators are used to receive signal 45

60 values and convert the into torques or speeds at an output connector that is considered to be a physical shaft. The coponent right after the engine is the torque converter. A torque converter is a coponent that couples engine rotational otion to drivetrain rotational coponents uch as a echanical clutch does. The ain difference between a clutch and a torque converter is that in a clutch the engine output shaft, is connected to other powertrain coponents by pressing the clutch disk together. When the clutch disks are pressed together, friction between the disk surfaces spins the driven shaft. A torque converter has three ain parts: the pup ipeller, stator, and turbine runner. The pup ipeller forces the fluid inside the torque converter to run into the turbine, and the hydrodynaic viscosity causes turbine to rotate. The stator is a part of the casing that directs the fluid fro the ipeller to the turbine. Figure 3.5 presents the torque converter block calculations. -1 Ipeller torque Ipeller speed ax -C- -C- ax 1 u in 1-D T (u) Ne/K u 1 Turbine speed speed ratio 1 K-factor 1 Turbine torque TORQUE CONVERTER 1-D T (u) Torque ratio Turbine torque Figure 3.5 An Exaple fro SiDriveline: Torque Converter Block [40] Speed ratio in a torque converter is calculated as below i t R in,, (3. 6) t i 46

61 where R is the speed ratio, i and t are the ipeller and the turbine speeds, respectively, and R is used to obtain the torque ratio ( R T ), and K-factor fro two lookup tables. The ipeller and turbine torques are calculated as follows: T i t i 1 i K (3. 7) T T R (3. 8) t i t The next powertrain coponent in the odel is the transission. The transission as depicted in Figure 3.6 consists of two planetary gears and five clutches. {B} {B} P B S M F SlipB ModeB SlipD ModeD S M F P B {D} {D} Clutch B R Clutch D Output Carrier /Input Ring Inertia C R In Input Carrier /Output Ring Inertia Input Planetary Gear S Input Sun Inertia Output Sun Inertia S Output Planetary Gear C v 1 Out SlipC v InSpeed {R} {R} P B Clutch R S M F {A} {A} SlipR ModeR P B Clutch A ModeC S M F SlipA ModeA S M F Clutch C P B {C} {C} Double -click to show Clutch Schedule {A} {B} {C} {D} {R} 5 5 Clutch Pressures OutSpeed 1 P Figure 3.6 An Exaple fro SiDriveline: The Transission in the Full Car Model [40] 47

62 The planetary gear is a set of gears including sun, carrier, planet, and ring gears (Figure 3.7). Fro the geoetry of the planetary gear, the following relations can be obtained: r c r r (3. 9) s p r r r r (3. 30) c p where r c, r s, r p, and r r are carrier, sun, planet, and ring radii. Planet Ring Sun Carrier Figure 3.7 A Planetary Gear Set: Ring, Planet, Sun, and Carrier [40] The kineatics of the gears gives the following relations: r r r (3. 31) c c s s p p 48

63 r r r (3. 3) r r c c p p The gear ratio can be defined as. T g T driven drive drive driven N N driven drive r r driven drive, (3. 33) where g is the gear ratio, T,, r, and N are the gears torque, rotational speed, radius, and nuber of teeth, respectively. The first planetary gear is the input planetary, and the second planetary gear is called the output planetary. The input planetary gear ratio, planetary gear ratio, nuber of teeth ratios. g i, and output g o, are defined as the ratios of the correspondent ring-to-sun radius or g g i o r r s r (3. 34) i r r s r (3. 35) o The two above entioned planetary gears are used with different cobinations of the five clutches in locked and free positions to define the total transission gear ratio that is the ratio of the output to the input of the transission. Figure 3.8 shows a shifting gear schedule for a four speed car. The clutches A, B, C, D, R can be set in the locked or the free positions depending on the gear selected. For exaple, in gear two, the A and C clutches are locked, but B, D, and R clutches are free. 49

64 Clutch Schedule Gear R L = Locked F = Free A B C D R Ratio L F F L F 1+go L F L F F 1+go/(1+gi) L L F F F F L L F F gi/(1+gi) F F F L L -gi gi=input planetary ring /sun gear ratio go=output planetary ring /sun gear ratio Figure 3.8 An Exaple fro SiDriveline: Clutch Schedule [40] Final drive, wheel, and road calculations are presented in Figure 3.9. Final drive can be considered to be a siple gearbox that changes the gear ratio. By using a torque sensor, the rotational speed at the final drive output (that is, the input of the wheel) is calculated. In the next step, the vehicle longitudinal velocity is obtained by ultiplying the wheel rotational speed and radius. Motion Sensor T v MPS to KPH Torque Actuator 3600 /1000 Vehicle Speed 1 KPH T B F Torque Sensor Linear Speed -K- Road Load rload 0 + rload*u^ 1 Drive Shaft B Forward Gear Power F Vehicle Effective Inertia Final drive power (Hpwr) Braking power (Hpwr) -K- -K- 0 1 Brake Torque <= Brake Torque STOP Stop Siulation Signed Load Figure 3.9 An Exaple fro SiDriveline: Final Drive, Wheel, and Road Calculations [40] 50

65 The road resistance torque, the su of the air, roll, and grade resistant forces ultiplied by tire radius, is approxiated by a second degree polynoial as a function of vehicle speed, and is added to the required torque for braking. The resultant torque is fed back into the syste as a negative torque. A ore advanced vehicle and wheel odels can be found in a SiDriveline exaple naed Coplete Vehicle [41] Dyola/Modelica Modelica is an object-oriented and equation-based odelling language that is suitable for physical odelling. Appendix A provides ore details about Modelica. Dyola is one of the siulation tools that uses Modelica language. Different types of doains such as electrical, echanical, hydraulic, theral, or control can be odelled in Dyola. It has various libraries of powertrain coponents, including engine, transission, drivelines, vehicle dynaics, and other coponents such as electrical otors, controllers, and hydraulics. Coponents are deonstrated in the sae way as physical odels. Each coponent contains equations inside its odel that can be reached and odified easily. Figure 3.30 shows the top level of a conventional vehicle and its coponents and interfaces [4]. The driver at the top sends acceleration, brake, and gear shifting coands to the driveline coponents. As shown in Figure 3.31, the engine in this odel is a very siple torque generator that is directly proportional to the throttle signal coand, and it also includes ounting effects as a coponent. 51

66 Figure 3.30 Powertrain Coponents and Interfaces for a Conventional Autoatic Vehicle [4] Figure 3.31 Engine Model in a Conventional Autoatic Vehicle [4] 5

67 An exaple of a theral doain is deonstrated in Figure 3.3, with red square shapes as theral connectors [43]. Heat is transferred fro the cylinder gas to the cylinder wall, the piston, the cooling water jacket around the cylinder block, the cylinder head, the vavletrain, the inlet and exhaust valves, and to the lubricant oil. The heat is transferred fro the cylinder gas to the engine block in convection for, and fro the cylinder block to the coolant water in conductive for of heat transfer. Figure 3.3 Theral Connectors in a Cylinder [43] Heat transfer odels are generally based on relations for convective heat transfer coefficients found in equations developed by Woschni [44] and Hohenberg [45]. The cobustion equation can be defined in different levels of coplexity fro zero diensional and single-zone odels to coplex three diensional and ulti-zone gas burning odels. To siulate the ass burning rate in the cobustion process, Wiebe [46] or a sigoid function can be used [47]. The echanical doain in powertrain odelling generally focuses on one-diensional dynaics. There are also ulti-diensional echanical odels that are used for vehicle dynaics and engine ounting systes [43]. Most of the engine dynaics such drivetrain rotational dynaics, and piston and valves translational dynaics can be assued and odelled as 1D dynaics. An exaple of a one-diensional rotational dynaics is depicted in Figure 3.33 for a five speed 53

68 gear box [48]. A gearbox consists of three planetary wheels and seven switches. The clutches are illustrated as A, B, C, with three D, E, and F brakes, and a freewheel FF. A shifting schedule at the right side of the figure defines which clutches in each gear selection are engaged. A Modelica odel of the gearbox is shown in Figure Figure 3.33 A Sketch and Shifting Schedule for a Five-Speed Autoatic Gearbox [48] Figure 3.34 Gearbox Siulation for a ZF Autoatic Gearbox in Modelica [48] An exaple of a ulti-doain odelling in Modelica, called Siple Car, is shown in Figure 3.35 for a 4-cylinder engine on a dynaoeter [49]. The throttle valve is adjusted by a signal coand. The anifold inlet and exhaust outlet are connected to abient air conditions, and both are connected to the engine by gas connections. The throttle valve discharge coefficient is defined by 54

69 C d sin (3. 36) 180 where is the throttle angle in degrees. The engine and the anifold can be considered control volues in which the air pressure, teperature, and volue inside the are changed based on the ideal gas law. The energy inside the control volue is based on the first law of the therodynaics. The ass of the gas and the gas species are obtained fro the conservation of ass law. Figure 3.36 shows the second level of the engine odel with gas connectors for the intake and exhaust valves, and echanical flange connectors for crankshaft and piston assebly. Figure 3.35 Engine on a Dynaoeter for a Four Cylinder Engine [49] The cylinders are identical except than a shift angle in crankshafts by 0, 360, 540, and 180 degrees for cylinder 1 to 4. Intake and exhaust valves opening and closing angles can be set as 55

70 paraeters. The engine in-cylinder pressure is odelled by a filling and eptying dynaics and relating the pressure changes to the cylinder volue that is changed by the piston oveent. Rotating of the cashaft echanis, cause the valves to open, and to close at predefined angles. The angles between opening and closing of the valves, define the aount of the gas that flows into the cylinder or out of it. The lift profile is calculated fro a noralized valve angle function as follows: L L v v 0 L vmax or o sin c o o c else, (3. 37) where L v and LVMax are valve lift and axiu valve lifts, and c and o are closed and open valve angles. The valve discharge coefficients are obtained directly fro the experientally obtained axiu discharge coefficient and axiu lift as C dvmax CdV Lv (3. 38) LVMax Figure 3.36 Four Cylinders and Their Connections [49] 56

71 where CdV and CdVMax are the valve and axiu valve discharge coefficients. The cashaft speed and torque are directionally proportional to the crankshaft speed and torque. (3. 39) ca crank ca crank (3. 40) The cylinder volue is changed by the up and down piston oveent. V V A l (3. 41) c p p where V is the cylinder volue for each position of the crank shaft rotational angle, Vc is the clearance volue, which is the sallest volue of the cylinder when the piston reaches to the TDC, Ap is the piston area, and l p is the displaced length of the piston in that its iniu is equal to zero at TDC, and its axiu is at BDC and is equal to the stroke l p S. At other angles, l p is calculated fro the following equation:, l l l cos l l sin l p conrod crank crank conrod crank (3. 4) where l conrod and l crank are the connecting rod and crank lengths. The force exerted on the piston is calculated fro the resultant pressure inside and outside the cylinder. F p A P P, (3. 43) p cc 57

72 where P and obtained at the crankshaft. Pcc are the cylinder and crank case pressures. The generated torque is the torque crank sin lcrank cos sin lcrank F p (3. 44) lconrod l crank sin Cobustion is approxiated by the following equation Q 0 Q Q Max t t s t ts Sin te t or t t s e else (3. 45) where Q and Q Max are heat and axiu heat release rates, and t s, and te are start and end ties of the cobustion period. Q Max is obtained by Q Max H l a 180 AF 1 e t t, e s (3. 46) where H l is the lower heating value of the fuel, Figure 3.37 shows a cylinder, its coponents, and their connections. a is air ass, and AF is the air-fuel ratio. 58

73 Figure 3.37 The Cylinder Coponents in Siple Car [49] 59

74 Chapter 4 Mean Value Engine Model To estiate intake air flow accurately, one ust be able to predict the engine output power and the engine eission. In MVEM, the air ass flow defines the actual air flowing into the engine that is used to calculate the fuel ass flow and air-fuel ratio. The engine output power is proportional to the fuel ass flow rate, and is calculated using the fuel heating value, a constant value for a specified fuel. A throttle valve controls the ass flow, operating as a restriction valve and dictating the aount of air ass flow upstrea of the valve. Depending on the engine geoetry, anifold pressure, and engine speed, the actual air ass flow into the engine is defined. The difference between the air ass flow into the engine and the air ass flow out of the throttle defines the anifold pressure of a gas state equation. Manifold pressure and engine speed are two ain paraeters used in ost of the ean value engine calculations, including voluetric efficiency, theral efficiency, throttle air ass flow, and engine load and loss calculations. Engine speed in MVEM is obtained by solving a crankshaft differential equation. 4.1 Model Assuptions The gas flow syste in an actual engine has nuerous coponents. When an engine is working, air is inducted into the air filters at atospheric pressure and teperature. Air filters reduce the air path, causing the air pressure to drop as it passes through. In the next step, air flows into the throttle body, which is assued to act as a restriction valve. If an engine is a turbocharged engine, soe part of the energy is lost due to the flow resistance in the copressor, intercooler, and turbine. The latter coponents change the pressure and teperature considerably. The intake anifold has a relatively large volue and can be considered as a gas container. Other pressure 60

75 drops occur as flow passes through pipes and connections between coponents. Intake and exhaust valves, catalytic converters, and ufflers also cause pressure drops. Because such coponents are not isolated copletely fro the environent, they lose heat to the environent, changing their teperature. For this odel, the following assuptions and siplifications are ade: The air filter effect is neglected By this assuption pressure drop in the air filter is neglected; therefore, the pressure and teperature in the throttle inlet are equal to the atospheric pressure and teperature. The engine is naturally-aspirated In naturally-aspirated engines, there is no turbocharger, thus eliinating copressor, intercooler, and turbine effects fro the odel. The pressure and the teperature at the output of the throttle body will be the sae as those at the intake anifold inlet. The intake anifold syste is isotheral The anifold input and output teperatures considered to be constant. This assuption neglects the teperature transition in the anifold. If considerable hot gas fro the exhaust syste is ixed with fresh air in the anifold, this approxiation does not atch with the actual teperature in the anifold. More details are given in the discussion of adiabatic and isotheral systes in Section 4...1in this chapter. Minor coponent effects are not odelled Intake and exhaust valves, pipes, connections, and the uffler are not odeled individually. Their effects can be luped together inside voluetric efficiency. The engine puping effect is odeled separately in engine odel. 61

76 The syste is continuous Manifold and engine gas systes can be best described by filling and eptying dynaics. The gas induction process should be considered as a discrete process rather than continuous. As the intake and exhaust valves open in every two revolutions of the crankshaft, a part of air stays in the anifold and a part of it is trapped in cylinders and is cut off fro the upstrea and downstrea flow. In an MVEM, the gas syste is approxiated by a continuous syste. Increasing the nuber of cylinders akes this approxiation ore realistic. 4. Coponents of the Engine Model Three ain coponents affect an MVEM engine and are discussed in this chapter: Throttle Body Intake Manifold Engine The ain dynaics of the odel that are discussed in this chapter are Air Dynaics Fuel Dynaics Rotational Dynaics 4..1 Throttle Body A throttle body is a part of engine syste that controls the air flow into the engine. Air flow is regulated by a throttle valve, usually an elliptical plate with a pin located at the centre, enabling the valve to rotate around it. When a gas pedal is released, the valve is closed. The plate is always left open in angles between 5 to 10 degrees fro the copletely closed position to prevent it fro binding. In an idle working condition, flow is directed through a bypass path valve. Traditional throttle bodies use a echanical linkage that transfers pedal input coands to the throttle valve. In newer types, called drive-by-wire, the pedal position is translated to an 6

77 electrical signal by a sensor. The electrical control unit (ECU) receives this signal and actuates an electrical otor connected to the valve axis. The drive-by-wire throttle type is ore precise than echanical linkages in ters of positioning of the valve and drivability 1. Throttle ass flow rate is ainly a function of the discharge coefficient, throttle area, and pressure ratio.. 0 thr C A f P / P (4. 1) d thr where C d is the discharge coefficient; abient pressure. A thr is the throttle area, P is anifold pressure, and P 0 is Throttle Discharge Coefficient The throttle discharge coefficient in a restriction is defined as a ratio of the actual ass flow downstrea of the restriction to the ideal ass flow at that point. C d is usually described as a function of pressure and geoetry of the restriction. In a throttle valve, the effective area is directly related to the throttle angle. Therefore, angle and pressure C d can be written as the contributions of throttle C d( 0 d d P0, P / P ) C ( ) C ( P / ) (4. ) Noralizing the geoetry and pressure variables provides a ap for exaple of a ap for a butterfly valve [50]. C d. Figure 4.1 shows an 1 Drivability can be defined as the quality of operating of an engine or vehicle driving condition in general. 63

78 Cd Throttle Body Discharge Coefficient Throttle Area Ratio Pressure Ratio (P0/P) 1.8 Figure 4.1 Discharge Coefficient in a Butterfly Valve [50] Throttle Area Models The throttle-effective area is the projected area of the throttle opening in the flow direction. Athr is the function of the throttle bore, D. The throttle pin diaeter is d and throttle angle is. Harington and Bolt [] introduced the following equation for A thr A thr d D 4 D d cos d 1 D cos o cos D arcsin a cos d cos 1/ o D cos a cos o arcsin cos o cos (4. 3) where d a and is the throttle angle at closed position. Moskwa [3] presented another D equation for A thr : 64

79 A thr dd 1 / dd cos D 1 a 1 a arcsin 1 a D cos cos arcsin 1 a cos cos cos 1 / 1 / 1 / (4. 4) As the throttle angle increases, at a specified angle, A thr reaches to its axiu, and is no longer affected by increases of the throttle angle. This angle is defined as arccos d D cos (4. 5) In this condition, A thr is calculated fro the following equation A thr 1/ dd 1 a 1 a 1/ D arcsin (4. 6) Both odels use a correction for sall throttle angles by introducing as (4. 7) Figure 4. copares the two odels as a function of throttle angle. The effects of throttle pin diaeters and bore diaeters are shown in Figure 4.3 and Figure

80 Throttle Area ( ) Throttle Area (3) 3.5 x Harington Moskwa Throttle Angle (Degree) Figure 4. Coparing Throttle Effective Areas of Two Models 3.5 x 10-3 Pin Diaeter Effect ; D= d= 6 d=8 d= Throttle Angle (Degree) Figure 4.3 Effect of Throttle Pin Diaeter on Throttle Area 66

81 Throttle Area ( ) 4.5 x 10-3 Bore Diaeter Effect ; d= D=40 D=50 D=60 D=70 D= Throttle Angle (Degree) Figure 4.4 Effect of Bore Diaeter on throttle Area Pressure Function Models Based on conservation of ass law for any restrictions such as a nozzle or a throttle valve, if pressure drops on one side of the restriction, velocity increases in the saller area. By decreasing pressure ore, the velocity at a saller area reaches sonic velocity, and its axiu flow rate. This flow condition is called choked or supersonic flow. In a choked condition, further decreasing pressure will not affect the ass flow. For air, a choked condition occurs at P 0.58 P. 0 A standard for of pressure equation for choked and non-choked conditions in a noralized for can be written as 67

82 68 1 / 0 1 / 0 1/ / 1 0 1/ 0 1/ / P P if P P if P P P P P P f (4. 8) where is the specific heat ratio. For air =1.4. An exaple of the above equation can be found in [3]. Equation (4.8) is soeties approxiated by the following equation in the literature (for exaple, Crossley and Cook [0]). 1 / o o P P for P P for P P P P P P f (4. 9) Hendricks [5] introduced another equation for pressure function c c p p n p P P if p P P if P P P P p P P f /, 1 /, / / 1 / 1 (4. 10) where 1 1/ 1 p p c p p p, 1 p c p c n p p p, 1 p =0.4404, p =.3143, and c p = Another equation for pressure function is given by Cho and Hedrick [51] 1 / 9 exp 1 / 0 0 P P P P f (4. 11)

83 All the above entioned pressure odels are copared in Figure 4.5. Figure 4.5 Pressure Functions Coparison Coparing Hendricks, Crossley-Cook, and Cho-Hedrick odel with the standard pressure odel (Moskwa) reveals that Crossley-Cook odel fits very well in the entire range of the pressure. Cho-Hedrick odel s error values for pressures lower than 0.9 bar are very low, but the error increases beyond 0.9 bar. The Hendricks odel has the highest error relative to the standard odel Throttle Angle Functions Throttle area, as discussed before, is a function of throttle geoetry ( D and d ) and throttle angle. Therefore, in a specified engine involving in Athr is only a function of throttle angle. Instead of being Athr calculations, throttle angle function can be obtained directly by cobining equations (4.1) and (4.). Mass flow is then obtained by noralizing the angle function: 69

84 thr P / P M thr g( ) f P (, P / P0) Cd. A ( ) f P (4. 1) thr 0 / 0 where g ( ) is the throttle angle function, and M thr M thr is the axiu ass flow rate at throttle. is characteristic of throttle body geoetry obtained at a fully opened throttle angle and choked flow conditions. Two types of throttle angle functions that are widely used in the literature are cosine and polynoial functions. As an exaple of cosine function, Harington and Bolt [] introduced a relatively siple function for g ( ) : g ( ) 1 cos (4. 13) Hendricks et al. [5] give a slightly different equation as 1 g ( ) 1 cos (4. 14)! where 1 =0.85. Reference [5] introduces the following equation g ( ) 1 cos 3 cos (4. 15) where = and 3 = Cho and Hedrick [53] used a piece-wise function 70

85 1 cos 4 5 for 6 g ( ) (4. 16) 1 for 6, where 4 = , 5 =1.06, 6 = Another type of equation for throttle angle function involves polynoial functions. Powell and Cook [54], introduced a second degree polynoial function for a 1.6 throttle bore as g ( ), (4. 17) where 7 =, 8 =1.8, and 9 =0.. Crossley and Cook [0] used a third-degree polynoial 3 g ( ) (4. 18) where 10=.81, 11= , 1= , 13= Notice that the latter odels are not noralized, and throttle angle functions in both odels include the lup effect of the discharge coefficient and noralized throttle angle. In this work by using a four-stroke test engine data, a third-degree cosine polynoial as follows is found to be the best fit for the throttle air ass flow calculations. 3 cos g ( ) 14 15cos cos (4. 19) 14= , 15=3.667, 16=-3.594, and 17 = Experiental data and third-degree polynoial are depicted in Figure

86 Fit Curve Third Order Cosine Function Third Order Cosine Function Throttle Noralized Mass Data Throttle Angle (Degree) Figure 4.6 The Third- Degree-Cosine Function and Experiental Data Cosine functions are usually a better fit to the throttle angle data. Polynoial data, especially with higher degrees, diverge very fast out of the data range. 4.. Intake Manifold Models The intake anifold is a part of an engine syste that directs a unifor flow of air to the intake ports. An intake anifold can be considered a control volue for containing inflow coing fro the throttle and outflow leaving the engine. Mass and energy conservation laws can be applied to the syste. According to the conservation of ass law, the ass change in the syste is equal to the net flow into and out of the syste. d dt cv i i o o (4. 0) 7

87 d where cv is the intake ass changes, i are inflows, and o are outflows. dt i If there is only one inflow fro the throttle, and one outflow to the engine, a continuity equation can be written as d dt o cv thr e (4. 1) If the inflow ass fro an EGR valve is considered, above equation becoes d dt cv thr EGR e (4. ) Based on conservation of energy law, the tie rate changes of energy inside a control volue are equal to the net heat transfer into the syste inus the work done by the syste plus the tie rates of the energy flowing into and out of the control volue [55]. d E dt cv Q cv W cv i i hi V i gz i e e he V e gz e, (4. 3) where d E cv, dt Q, and cv cv W are tie rate of control volue energy changes, net control volue heat transfer, and shaft or any other works done by changing control volue; h, V, and Z are the entering and existing flow enthalpy, velocity, and elevation of the syste; g is acceleration gravity. In an intake anifold there is no shaft work, and the volue of the intake is fixed, so the W cv ter becoe zero. Velocities and elevations of the fluid entering and existing the intake anifold are considered to be equal. Using the above assuptions, the conservation of energy equation is siplified into the following equation: 73

88 d E dt cv cv i i h h Q (4. 4) i e e e Energy changes are in the gas flow ainly due to the internal changes d E dt cv u du du cv d cv cv cv cv (4. 5) dt dt dt Where ucv is the internal energy of control volue per unit ass. Air flow in an intake anifold is considered to be an ideal gas. By this assuption, internal energy and enthalpy equations are siply proportional to the gas teperature, and the equations becoe sipler. According to the ideal gas law, PV RT, (4. 6) where, P, V,, and T are gas pressure, volue, ass, and teperature, and R is the gas constant equal to J K ol. Volue of the anifold has a constant value. By differentiating the ideal gas equation relative to the tie following equation can be obtained: PV d RT dt cv cv RT (4. 7) Internal and enthalpy can be written as u c T (4. 8) v h c T (4. 9) p 74

89 where c p and c v are specific heat ratios at constant pressure and teperature. Substituting equations (4.) and (4.6) for (4.9) in the equation (4.4) provides the following equation in general for for an intake anifold equipped with EGR valve [56]. P R V thr T thr EGR T EGR T e q c T p (4. 30) where thr, EGR, and are throttle, EGR, and engine air ass flow rates; is a specific heat e ratio; T thr, T EGR, and T are throttle, EGR, and anifold teperatures; volue. Siilarly another equation can be obtained for the anifold teperature: V is the anifold RT q T thr Tthr T TEGR T e 1 T (4. 31) EGR P V cv The two differential equations above are usually siplified by considering the process to involve adiabatic or isotheral conditions Adiabatic and Isotheral Systes In a therodynaic syste, adiabatic syste is one that is isolated fro its environent and so no heat is transferred fro the syste to the outside, or fro outside to the inside of the syste. Adiabatic assuption can be used for large anifolds. In adiabatic systes, the teperature of the flow entering into the anifold does not affect the intake anifold teperature, and teperature exiting the syste is assued to be equal to the control volue teperature, i.e., the intake anifold. Isotheral process is one for which teperature is constant for flow entering, exiting, and inside the syste. Isotheral assuptions are used when control volue is sall in 75

90 size, so the inflow teperature is considered to be the sae as the teperature of the control volue. Using these assuptions, Equations (4.9) and (4.30) can be siplified to Adiabatic Manifold: i.e., q =0 R P V thr T thr EGR T EGR T e (4. 3) RT T thr Tthr T TEGR T e 1T EGR P V (4. 33) Isotheral Manifold: i.e., T =0 and q =0 RT P thr EGR e (4. 34) V Tthr T (4. 35) In this work, an isotheral anifold assuption is used for engine odelling. By this assuption for the conditions that an EGR valve does not exist or is not open, the Equation (4.34) becoes RT P thr e, (4. 36) V 76

91 Pressure transitioning in the anifold can be calculated for the above equation. Since R, T, and V are all constant, pressure changes in the anifold are only related to the net ass entering and exiting the anifold. described as thr e calculations were discussed in detail earlier. N cyl vol V d 10 RT n e P, can be e (4. 37) where N cyl, vol, V d, and n e are the nuber of cylinders, voluetric efficiency, cylinder displaced volue, and engine speed in RPM. (4.36). P is obtained by replacing Equation (4.37) in P RT V thr N cyl vol V 10 V d n e P (4. 38) Engine speed calculations are discussed in the Engine Models section of this chapter. Voluetric efficiency definition and odels are discussed in the following section Voluetric Efficiency Voluetric efficiency is the ratio of actual air inducted into the cylinder to the theoretical air that is supposed to be inducted into the cylinder by displaceent of the piston fro TDC to BDC in an induction stroke. Taylor [57] introduces a siple equation for voluetric efficiency as a function of the pressure ratio and copression ratios. 77

92 ev 1 r P / P0 vol (4. 39) r 1 where r is the copression ratio, and =1.4. Figure 4.7 shows Taylor s odel for voluetric efficiency. As can be inferred fro the figure, the voluetric efficiency has values higher than unity. However, as Taylor has entioned in his book, voluetric efficiency is a function of various other variables such as gas teperature, engine geoetry, coolant teperature and so on. By diensional analysis, the reference categorizes the role of each variable set and introduces different correction factors for each set that can be obtain by different graphs. The actual voluetric efficiency is calculated by ultiplying the correction factors by the ideal voluetric efficiency Voluetric Efficiency- Taylor Model r=8 r=9 r=10 r= Pressure Ratio (P/P0) Figure 4.7 Voluetric Efficiency Taylor s Model [57] Hendricks et al. [5] introduced a regression-based odel for voluetric efficiency as functions of engine speed and anifold pressure e e P e n e n (4. 40) vol 1 3 e 4 e 78

93 where e 1 =0.696, e =0.16, e 3 =-0.06, and e 4 = P is anifold pressure in bar. The pressure ratio effect in this odel is shown in Figure 4.8. In the sae paper, Hendricks et al. give a second odel for voluetric efficiency by noralizing air charge per stroke as e6 vol e5, (4. 41) P where e 5=0.95, and e 6 = This odel is presented as a function of anifold pressure in Figure 4.9. It is notable that ultiplying both sides of the above equation by P should result in a linear function: P e P (4. 4) vol 5 e 6 Hendricks et al. showed that this result agrees well with experiental results for different engines. Equation (4.4) can be used in equation (4.37): P. RT V thr N cyl Vd n 10 V e N V n vol 5 6 V 10 V (4. 43) RT thr cyl d e P e P e 79

94 Voluetric Efficiency (ev) Voluetric Efficiency (ev) 0.9 Vouetric Efficiency -Hendricks et al. 1st. Model P/P0=0. P/P0=0.4 P/P0=0.6 P/P0=0.8 P/P0= Engine Speed (RPM) Figure 4.8 Voluetric Efficiency, Hendricks et al., 1st odel [5] 1 Voluetric Efficiency-Hendricks et al. nd Model Manifold Pressure (bar) Figure 4.9 Voluetric efficiency, Hendricks et al., nd Model [5] Another ethod for approxiating voluetric efficiency is using lookup tables or aps. Figure 4.10 shows an exaple of a lookup table ap. 80

95 Voluetric Efficiency % Voluetric Efficiency Map Engine Speed (RPM) Pressure (kpa) Figure 4.10 Voluetric Efficiency Map [5] Fuel Dynaics For direct fuel injection systes, fuel is injected inside the cylinders; in other types, fuel is ixed outside of the cobustion chaber. A fraction of injected fuel (x) strikes the cylinder wall, and the rest of the fuel (1-x) evaporates and ixes with the air flowing into the cobustion chaber. This phenoenon is called wall-wetting. The fuel fil on the wall is then heated and evaporated by the anifold after a tie constant fuel. The two odels introduced by Aquino [18], and Hendricks and Sorenson [4] are both very popular in the literature. Aquino s odel follows the track of the fuel left on the walls, while Hendricks and Sorenson odel follows the track of fuel ass flow. Aquino assued that injected fuel flow is proportional to the air flow, and the aount of the fuel that leaves the fil is proportional to the aount of fuel in the fil. He then derived following equations fro a continuity equation: 81

96 d dt fw 1 f fw x fi (4. 44) fv x (4. 45) fv fi x fi 1 (4. 46) fw f fv (4. 47) f and fw where fi, fv, are injected, evaporated, and wall fil ass flows respectively. fv is tie derivative of wall fil. The tie constant in the odel was inversely proportional to the anifold teperature that can be approxiated by the following function: f, f f1 exp T (4. 48) where 6 f 1 510, and f =0.0473; T is anifold teperature in K ; x is a linear function of crank angle x f 4, (4. 49) f 3 where f 3 = 46, f 4 = Hendricks and Sorenson obtained the following equations for fuel flow dynaics: fw 1 f x fi fw (4. 50) fv x fi 1 (4. 51) 8

97 (4. 5) f fv fw Where f and x are odeled as functions of anifold pressure and engine speed. f6 n f7 P f8 f9 n f10 11 f (4. 53), f 5 f where f 5 = 1.35, f 6 = -0.67, f 7 = 1.68, f 8 =-0.85, f 9 =-0.06, f 10 = 0.15, and f 11=0.56. x f (4. 54) 11 P f1n f13 where f 11= -0.77, f 1 = , and f 13=0.68. Tie delay due to the wall-wetting has a negative effect on fuel delivery systes that changes the fuel-air ratio in transient conditions. During engine controller design, this effect is eliinated by use of a copensator algorith. For defining the reverse odel, the aount of extra fuel due to the wall-wetting effect is calculated, and the aount of fuel needed to copensate is injected into the syste. More details are provided in [5,58] Engine Models In an internal cobustion engine, power is generated fro the conversion of fuel into heat energy. Air is ixed with fuel or fuel is directly injected into the cylinders by a ratio close to the stoichioetric value. The cobustion starts with ignition of the fuel by a spark at the end of the copression stroke in certain angles close to TDC. In actual cobustion, expansion of the gas in each cylinder is the ain source of power and varies as flae progresses and the piston oves downward. Details of the cobustion process are not of interest in MVEM; instead an average of 83

98 the convertible energy in each cycle is calculated. Since the fuel aount is directly proportional to the supplied air, it is easy to calculate the energy that can be extracted fro the fuel in each cycle. The axiu theoretical power that can be extracted fro fuel can be described so P f f H f, (4.55) where P f is fuel power; H f is a low heating value that is a constant value for fuels. For gasoline, H is about 43 MJ / kg. The fuel ass flow is f f and is defined by f e, (4.56) L th where is the noralized air-fuel ratio, that is, a ratio defined by dividing the actual air-fuel ratio to the stoichioetric air-fuel ratio. In odern engines, as it entioned, is close to stoichioetric fuel (i.e., 1). L th is stoichioetric noralization factor, for air-gasoline is equal to Soe part of the fuel power is dissipated by the coolant water flowing around the cylinder. Another part of a fuel s power is lost at the end of the exhaust stroke in the for of hot gas or unburned gas, and flows out of the cylinder. The reaining power is called indicated power and described as P ind P, (4.57) th f where th is theral efficiency, described in detail in the next section; P ind is indicated power, that is the axiu available power in any specific cylinders. However, soe part of this power is lost inside the cylinder due to the friction of the engines rotating coponents, and soe part is used for puping air into the cylinder. The power that is left is called brake power and is the available power at the engine output shaft. 84

99 P b Pind Ploss Pind P friction P puping (4.58) In ters of efficiency, the ratio of brake power to indicated power is called brake or echanical efficiency. P b (4.59) P ind In a siilar way, the efficiencies of other coponents of a powertrain, such as the torque converter, gearbox, differential, and wheel, can be defined as PTC TC ; P b P G G ; PTC P Dif Dif ; P G P w w, (4.60) P Dif where TC, G, Dif, and w are the torque converter, gearbox, differential, and wheel efficiencies, respectively, and P TC, P G, P Dif, and P w are torque converter, gearbox, differential, and wheel output powers. By cobining the above equations, the overall efficiency of the powertrain that is the ratio of the available power at the wheels to the fuel power, can be defined in this way Pind overall thtcgdif w Pb PTC PG PDif Pw Pw (4.61) P f Pind Pb PTC PG PDif P f In this work, only theral efficiency will be discussed in detail. 85

100 Theral Efficiency In an SI engine, ideal theral efficiency can be calculated fro an Otto air standard therodynaic cycle. An Otto air cycle assues that copression of the working fluid occurs fro BDC to TDC as an isentropic process, i.e., adiabatic and reversible. The cobustion process is replaced by an external source of heat that instantaneously adds heat to the air at a constant volue at TDC. The expansion process is considered to be another isentropic process where piston oves fro TDC to BDC. When the piston reaches BDC, the heat is rejected instantaneously. Following these assuptions, the ideal theral efficiency of air cycle can be expressed as 1 thi 1, (4.6) 1 r where r is a copression ratio. Heat transfer between the gas and the walls, and friction and puping effects are exaples of deviations of an actual SI cycle fro an ideal cycle. On the other hand, cobustion is not an instantaneous process, and soe part of cobustion heat is lost fro the cylinder walls, cylinder head, and piston during cobustion and expansion strokes. Intake and exhaust valves are opened and closed at different angles fro BDC and TDC. Theral efficiency in general is a function of any paraeters such as engine geoetry, 1 noralized air-fuel ratio (or equivalence fuel-air ), spark angle, and soe engine working paraeters such as engine speed and anifold pressure. In the following sections, two types of odels for theral efficiency are discussed. The first odel was developed by Chang [59] and the second, by Hendricks et al. [5]. Both odels are paraetric ones that can be adjusted and reused for other engines. 86

101 Chang s Theral Efficiency Model The Chang odel considers different paraeters affecting engine geoetry, such as the cylinder bore and stroke, fuel-air ratio, copression ratio, anifold pressure, and engine speed. Earlier than this work, Nitschke [60] had developed a odel for voluetric, theral efficiency, and engine puping work. The theral efficiency in Nitschke s odel had ost of the above entioned paraeters, but it was liited to a configuration of a special engine. Another shortcoing for Nitschke s odel was that the geoetry was not included in the odel explicitly. The Chang odel consists of sub odels for each paraeter. In order to find the coefficients of the odels, a cycle siulation data developed by Poulos [61] was used. Sub odels of Chang s theral efficiency odel can be described as follows: Copression Ratio e e r (4.63) cr 1 thi where e1 0.79; e Noralized Air-Fuel e3 P 85 P P 85kPa 85kPa (4.64) 4 e 5 e (4.65) where e.0419; e.30; e Manifold Air Pressure 87

102 where e 6 4.1; e7 4.36; e e 8 P P e6 e7 (4.66) Engine Speed e11 n e9 e10 n (4.67) where e.6; e 15.1; e Bore-to-Stroke Ratio B/ L 1 13 e B / L 14 e e (4.68) where e ; e ; e Displaced Volue where e.7; e 13.8; e e17 Vd e15 e16v d (4.69) The above six independent odels can then be integrated based on superposition law, and total theral efficiency is obtained thus: th c1 ccr c3 c4p c5n c6bl c7 (4.70) Vd where c ; c 0.96; c ; c ; c ; c ; c

103 Total Theral Efficiency % Theral Efficiency % Bore to Stroke Ratio and Manifold Pressure Effects 30 5 B/L=0.5 B/L=1 B/L= Manifold Pressure Figure 4.11 Bore-to-Stroke Ratio and Manifold Pressure Effects on Theral Efficiency [59] 45 Noralized Air-Fuel Ratio and Manifold Pressure Effects Labda=0.8 Labda=1 Labda= Manifold Pressure (kpa) Figure 4.1 Air-Fuel Ratio and Manifold Pressure Effects on Theral Efficiency [59] 89

104 Total Theral efficiency Total Theral Efficiency % 33 Manifold Pressure and Engine Speed Effects n=1000 RPM n=000 RPM n=3000 RPM n=4000 RPM n=5000 RPM Manifold Pressure (kpa) Figure 4.13 Manifold Pressure and Engine Speed Effects on Theral Efficiency [59] As shown in Figure 4.11 and Figure 4.1 increasing of bore-to-stroke ratio and noralized airfuel ration cause to decrease theral efficiency, but increasing the engine speed has positive effect of it (Figure 4.13 and Figure 4.14). Displaced Volue and Engine Speed Effects n=1000 RPM n=000 RPM n=3000 RPM n=4000 RPM n=5000 RPM Vd (Liter) Figure 4.14 Displaced Volue and Engine Speed Effects on Theral Efficiency [59] 90

105 The Hendricks et al. Model for Theral Efficiency The odel Hendricks et al. created is ore general, and it is not related to engine specifications such as the copression ratio or engine geoetry paraeters. Theral efficiency in this odel has four contributions: engine speed, anifold pressure, noralized air-fuel ratio, and spark angle. Engine Speed where h.558 ; h 0.39 ; h Manifold Pressure h3 thn h1 1 h n (4.71) thp 4 h5 P h6 P h (4.7) where h.9301; h ; h Noralized Air-Fuel Ratio h7 h8 h9 th (4.73) h10 h11 h1 h ; h ; h ; h ; h ; h Spark Angle th h h h bt 15 bt 91

106 n 47 h h n h 17 n h n h (4.74) 1 h18 P h19 n47 h0 P h1 n47 bt in 1, h ; h 0.39 ; h ; h ; h ; h h.99 ; h h 1.33 ; h h.741 ; h ; h.7 ; h ; h ; h.7 ; h 4. 8 ; h h.614 ; ; ; h 0 h1 h Total Theral efficiency in this odel can be obtained by the products of sub-odel contributions th thnthp th th (4.75) The Hendricks et al. theral efficiency odel is used in this work, and details of siulations are discussed in the next chapters Rotational Dynaics Engine speed transitions can be obtained fro crankshaft rotational dynaics (the power available at the wheels). Soe part of the fuel-generated power is lost as friction, and soe part of it is used to pup air into the cylinders. Another part, called the load power, uses the available 9

107 power at a shaft to rotate the powertrain coponents, including the torque converter, gearbox, drive-shafts, final drive, and wheel assebly. The part that reains is considered to accelerate the powertrain. I e e Pb Pload Pf Pfriction Ppup Pload (4.76) where I is the powertrain s oent of inertia and is the angular velocity of the powertrain rotating parts that is related to engine speed by e n e (4.79) 60 e Power and torque are connected by angular velocity P (4.80) e T e e Frictional power occurs as energy is lost during the contacts between engine s oving parts, including the pistons and cylinders, crankshaft bearings, piston asseblies, and vavletrain assebly. At idle speed, all power is directed to overcoing engine frictional power, 93 P friction. In reference [5] is given by approxiating a second degree polynoial for engine frictional torque and relating to frictional power friction where p 1 =1.673, p =0.7, p 3 = P e 1 p ne p3 ne n p (4.81) Puping losses are due to the required air induction power during the intake and exhaust strokes. In naturally aspirated engines, the pressure in the induction stroke is less than the exhaust pressure. In turbocharged engines, the pressure in the intake process is ore than the exhaust pressure, so extra power is added to the syste. Reference [5] introduces the following equation for puping loss power as a function of anifold pressure

108 P pup where p , p And the powertrain load power is approxiated by e p p n P, n (4.8) 4 5 e load 3 6 ne P p (4.83) 4.3 Powertrain and Vehicle Models The power required to thrust the vehicle is transitted fro the powertrain coponents to the wheels. When an engine is engaged, each coponent of the powertrain rotates with a rotational speed proportional to the engine speed. Torque in each coponent is obtained fro corresponding power and speed. Speed and torque are aplified or reduced when they pass through the transission and final drive. The transission, also called gearbox, reduces the engine speed and increases the torque by a ratio called the gear ratio where 60 n. T GR T driven drive drive driven n n drive driven (4.84) A gearbox has different sets of gears that enable it to provide different torques at different working conditions of the vehicle. The power lost in each coponent reduces the power, and hence the torque in that coponent, but this loss has no influence on speed reduction. For each coponent, torque and speed can be obtained as follows [6]: Torque-converter 94

109 T Tc T I T I n Tc e e e Tc e e e, (4.85) 60 where or ntc ne ; and Tc e (4.86) Tc e where T e, e, n e and I e are an engine s torque fro dynaoeter data at a given speed, rotational acceleration, speed, and oent of inertia. T Tc torque at gearbox input, efficiency, and speed., Tc, and n Tc are the torque-converter s Transission T Gb T Tc IGb e Gb GRGb (4.87) e GRGbGb or ne GRGb ngb ; and e GR Gb Gb (4.88) where T Gb is torque at the gearbox output, or at the driveshaft input. Gb I, Gb, n Gb, Gb and GR Gb are the oent of inertia, efficiency, rotational speed, rotational acceleration, and ratio of the gear box. Final Drive T Ax T Gb I d d Fd GRFd Fx rw I w w (4.89) Gb GR or n GR n ; and GR (4.90) Fd Ax Gb Fd Ax Gb Fd Ax where FD and GRFD are the final drive efficiency and gear ratio; T ax, n ax, and ax are the axle torque, speed, and rotational acceleration; I d and rotational acceleration. r w, I w, and 95 d are the driveshaft oent of inertia and w are the wheel radius, oent of inertia, and rotational

110 acceleration; Fx is tire traction force at contact point with the ground. Traction force can be obtained by cobining the above equations: F x Te Gb Fd G r w Gb G Fd ax I e IGb G GbGFd Id GFd Iw r w. (4.91) 96

111 Chapter 5 MapleSi Ipleentation The ean value engine odel in this work consists of a throttle body, a anifold, and an engine as ain coponents of the syste (Figure 5.1). The powertrain siulation uses a forwardlooking strategy starting with a driver speed coand and copares it with a calculated engine speed. The engine at this level is considered to be on a dynaoeter. Therefore, the load is added to the syste as a negative torque to the syste. Figure 5.1 Top Level of the MapleSi Mean Value Engine 97

112 The MapleSi MVEM is a paraetric odel. The paraeters can be defined by a block, as shown at top left of the window. The paraeters at this level are global and accessible fro any other subsyste coponents. Paraeters also can be defined inside each sub-odel. Probes can easily be attached to any connecting lines to easure the data flowing fro one coponent to another. The PID control in Figure 5. outputs throttle angle deand based on an engine s actual speed and driver-required speed. Figure 5. Speed Controller in the MapleSi Model The air ass flow rate in the throttle coponent (Figure 5.3) is calculated in two blocks: one for the throttle area calculations and the other for the air ass flow calculations. Throttle air ass flow is obtained by thr (, P / P P 0 ) Cd. Athr ( ) f P / 0 (5.1) where, the throttle effective area is obtained fro Equation (4.4), and the pressure function fro Equation (4.8). The discharge coefficient is a function of the throttle angle and anifold pressure. For siplicity, both are considered to be constant. These blocks are created by using custo coponents in Maple, and can be accessed by double-clicking on the coponents. 98

113 Figure 5.3 Throttle Body Model in MapleSi Engine Figure 5.4 shows the throttle effective area equation in a MapleSi custo coponent docuent. Various types of equation forats are available for use with such algebraic and differential custo coponents. Depending on the application, each of these coponents can be opened and replaced with new equations. The input or output connectors can be added to or deleted fro the coponent. It is also possible to introduce paraeters to a odel of the coponent, as is shown for throttle bore and pin diaeters at the figure s botto line. 99

114 Figure 5.4 Writing Equations in MapleSi The anifold block calculates air flow into the engine and anifold pressure. The input to the intake anifold block includes the ass inflow that is calculated in the throttle body coponent, the engine speed that is calculated in the engine block, and the voluetric efficiency (Figure 5.5). Figure 5.5 Intake Manifold Model in a MapleSi Engine 100

115 Manifold pressure is calculated fro a differential equation derived fro conservation of ass and ideal gas laws. RT P thr e, (5.) V where P, T, and V are anifold pressure, teperature, and volue; R is the gas constant; is air ass flow into the engine. e e v N cylvd P n, 10RT (5.3) where, v, N cyl, V d, and n are voluetric efficiency, nuber of cylinders, displaced volue, and engine speed. Voluetric efficiency is obtained fro a lookup table (Figure 5.6). Figure 5.6 The Voluetric Efficiency Lookup Table in the Intake Manifold Model [5] 101

116 The engine odel (Figure 5.7) calculates indicated, brake, and loss powers. A sensor easures powertrain angular speed and load power. The load power is then fed back into the engine odel and is used for power calculations. The engine speed is calculated fro a differential equation (Equation 4.76). The losses are the su of the pup and friction losses, and are obtained fro an epirical function for anifold pressure and engine speed variables. p1 p n p3n np4 p np P loss P friction P pup n 5 (5.4) Figure 5.7 Engine Model in the MapleSi Model The connector at the output of the sensor at the right end of the Figure 5.7 Engine Model in the MapleSi Model is a physical shaft that drives the drivetrain coponents downstrea of the engine, as deonstrated in Figure 5.8. The drivetrain in this odel consists of a siple rotational inertia for the driveshaft and differential, and a rotational to translational gear for the wheel odel. Roll, grade, and air resistance forces are introduced as a drag force on the syste. The 10

117 drag force is added to the dynaoeter load and result is the total negative power in the vehicle odel. The vehicle velocity is easured at the wheels by a translational speed sensor. Figure 5.8 Powertrain and Vehicle Model in the MapleSi Model 103

118 Chapter 6 Validation and Results An engine configuration siilar to the one shown in Figure 5.1 is used to run the siulations. A set of throttle angle and ass flow data is used to find the throttle angle function and used in a siulation odel, and another set of air ass flow data at angles different fro the previous angle data is easured and used as an experiental odel. The air ass flow in the siulation odel is calculated by following equations: thr (, P / P0) M thr g( ) f P / P (6.1) 0 where M thr =0.18 kg/s is the axiu air ass flow passing through a throttled and widely open throttle conditions. The pressure function is obtained by P P Po for P f P / 0 0 P P P 0 (6.) Po 1 for P The throttle angle function is defined by a third-degree cosine function cos 1.093cos g ( ) cos (6.3) The air ass flow for the experiental ass flow is obtained fro a one-diensional lookup table by changing the throttle angle valve gradually and easuring the air ass flow rate at the throttle upstrea. Both the siulation and experiental odels are then siultaneously run and results are copared. 104

119 The engine odel has two inputs: a step signal for the driver and another one for the drivetrain load. Step signals enable the capture of both dynaic and steady-state conditions of a syste. The input signals to the syste can be considered as the ideal level of a variable, and can be as siple as a step signal for gas acceleration or brake deceleration pedals in a driver odel, or ore coplicated signals such as drive-cycle data with uch accelerating, decelerating and stopping. If a drive-cycle is used, the actual velocity at the wheels is coputed and copared with the drive-cycle velocity, but if the engine is on a dynaoeter, engine speed data can be copared with reference speed data. The engine speed can also be copared directly with the drive-cycle speed data if the transission and final drive gear ratios are known in each instance of tie. A controller, such as a PID controller in this odel, receives the input signal, copares it with the calculated value fro the syste, and outputs a signal coprised of the two. The controller s output in this odel is a throttle valve angle varying fro 7 degrees for copletely closed to 90 degrees for the wide-open valve angles. The selected input variable for siulations are engine speed and drive train load actuating at t=60 s and t=100 s respectively, and all siulations are run for 10 s The speed step values are set at n=000 rp for the initial values of all siulations, and n=3000, 3500, 4000, and 5000 rp for the offset values after the speed is raped up. Running the experiental and siulation odels siultaneously and depending on the load and speed data for each siulation, the controller projects a throttle angle signal profile for the siulation and another for the experiental odel that differ fro each other. The throttle air ass flow is then calculated fro the throttle signal, and then other variables such as anifold pressure and engine power are obtained fro it. The engine for the study is a four-stroke SI engine with 85 and 100 bore and stroke diensions. The throttle valve pin and bore diaeters are 8 and 64, respectively. As shown in Figure 6.1, at ties t=0 s to t=60 s the engine speed is set to n=000 rp and the controller tries to adjust the throttle angle to about 1., and 9.8 degrees for the siulation and experiental odels, respectively. Changing the engine speed abruptly to n=3000, 3500, 4000, 105

120 and 5000 rp at t=60 s causes the controller to leave the valve in a copletely open position for a few seconds. The tie that the valve is copletely open increases with the increase of the engine speed set point. Figure 6.1 Results for the Throttle Angle Siulation (Solid Lines) and Experiental (Dash-dot Lines) After transition responses of the siulation and experiental odels have died out, steady-state responses of the throttle angle signal appear as values offset fro one another. These values are 106

121 then used to calculate the error percentages of the odels. At t=100 s, the tie that the dynaoeter load is connected to the engine, the throttle angle is decreased to copensate for this effect by supplying ore fuel power. Figure 6. Throttle Air Mass Flow Results Siulation (Solid Lines) and Experiental (Dash-dot Lines) The throttle ass flow (Figure 6.) and anifold pressure (Figure 6.3) have alost the sae trends as the throttle angle, in that increasing the throttle angle increases the air ass flow rate. 107

122 At angles higher than 8 degrees and pressure lower than 5 kpa, both experiental and siulation throttle ass flows show constant values equal to the axiu air flow. Figure 6.3 Manifold Pressure Results Siulation (Solid Lines) and Experiental (Dash-dot Lines) At the beginning of the siulation, that throttle angle is set at a copletely closed position, and the air deand fro the engine causes the anifold pressure to drop drastically, to about 10 kpa for both odels. The anifold pressure is increased by increase of the engine speed and throttle valve angle. 108

123 Figure 6.4 Voluetric Efficiency Results Siulation (Solid Lines) and Experiental (Dash-dot Lines) However, the voluetric efficiency, which is based on a D pressure-speed lookup table, shows different behaviour than the above variables (Figure 6.4). The higher values of the voluetric efficiency are obtained at n=3000 to n=4500, and at P= 30 kpa to P=50 kpa at t=0 to t=0 and at t=60 to t=80 s, which are the transition regions of the speed and anifold pressure. For any given speed and anifold pressure a value for voluetric efficiency is deterined by the 109

124 table. Because the rate of speed and pressure changes is too high, the voluetric efficiency values show excessive fluctuations in this region. Theral efficiency is a function of spark angle, noralized fuel-air ratio, engine speed, and anifold pressure. Fixing the first two variables as constants, theral efficiency becoes a function of only engine speed and anifold pressure. As shown in Figure 6.5, theral efficiency shows to be less sensitive to engine speed. However, for engine speeds equal to or lower than 000 rp, theral efficiency drops rapidly. Increasing the anifold pressure up to 65 kpa increases the theral efficiency, but increasing the pressure to higher than 65 kpa has the reverse effect on theral efficiency. 110

125 Figure 6.5 Theral Efficiency Results Siulation (Solid Lines) and Experiental (Dash-dot Lines) The net power at the wheels, the power needed to overcoe the vehicle resistances and to accelerate the vehicle, is obtained by subtracting the loss and load powers fro the indicated power. The load power in this odel is approxiated by a polynoial function of the thirddegree of the speed, and the loss power by a third degree of speed and linear function of anifold pressure. As shown in Figure 6.6, at ties t=5.5 to 16.0, and t=64.5 to 69.5 s, if engine 111

126 speed is increased suddenly, the su of the lost power and load power becoes greater than the indicated power, resulting in the net power becoing negative. Figure 6.6 Net Power Results Siulation (Solid Lines) and Experiental (Dash-dot Lines) The error percentage for the engine variables are calculated fro the following relation: Siulation Experiental Error % 100 (6.5) Siulation 11