A comparison study between power-split CVTs and a push-belt CVT

Transcription

1 A comparison study between power-split CVTs and a push-belt CVT Pablo Noben DCT Master s thesis Coaches: Supervisor: ir. T. Hofman dr. P.A. Veenhuizen prof. dr. ir. M. Steinbuch Technische Universiteit Eindhoven Department Mechanical Engineering Dynamics and Control Technology Group Automotive Engineering Science Group Eindhoven, August, 2007

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3 Abstract Since the ongoing discussion about the global warming of the earth, this is mainly attributed to the greenhouse gasses. Which on their part are produced by vehicles, by internal combustion engines to be more accurate. More and more car manufacturers and research institutes are investigating alternatives for internal combustion engines. However changing the fuel for vehicles is very difficult because this is a complex collaboration of governments, oil companies and car manufacturers. On top of this years and years of development has resulted in the current infrastructure of the gas stations. A first solution to decrease the fuel consumption of vehicles is to develop hybrid power trains. With a hybrid power train, a power train consisting of two power sources is meant here. Normally this is an internal combustion engine combined with one or more electric machines. The fuel consumption of a hybrid vehicle is lower compared to a conventional vehicle because electric machines can recover brake energy which can be stored in a battery or a similar electrical storage system. Later this electric energy can be used to power the electric machines and assist the internal combustion engine to power the vehicle and herewith decreasing the fuel consumption. To realize a hybrid power train the most commercially successful hybrid vehicle makes use of a power split transmission. This power split transmission contains of a kinematic chain and an electric variator. The electric variator controls the overall transmission ratio and herewith the working point of the internal combustion engine. In literature different methods can be found to investigate power split transmissions. In this thesis some methods are treated. Schulz and Villeneuve investigate both a specific power split transmission. Mattsson on the other hand investigates several power split transmissions. Eventually the method by Mattsson is used to investigate the Toyota Hybrid System and the Renault IVT concept power train. Both transmissions are alike, however the Toyota hybrid system is a single mode transmission and the Renault IVT is a dual mode transmission. To compare these transmission considering efficiencies, a simplified loss model is used. Finally the Toyota hybrid system, as hybrid power train, is compared to a push-belt CVT, as conventional power train. Hereto three cases are studied, first the working point efficiency of the ICE is considered only. Followed by the implementation of constant efficiencies for the power train components. At the end working point dependent efficiencies are implemented for the electric machines in case of the Toyota hybrid system and for the push-belt CVT in case of the push-belt CVT. Herewith the overall efficiency of both power trains are compared. iii

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5 Samenvatting Door de voortdurende discussie over de opwarming van de aarde, die voor het merendeel aan de broeikasgassen wordt toegeschreven. Die op hun beurt worden veroorzaakt door voertuigen, meer precies door verbrandingsmotoren. Steeds meer automobielfabrikanten en onderzoeksinstellingen zoeken naar alternatieven voor verbrandingsmotoren. Hoewel het erg moeilijk is om de brandstof van voertuigen te veranderen omdat dit wordt beïnvloed door de complexe samenwerking van regeringen, olie maatschappijen en automobielfabrikanten. Daarnaast is de huidige infrastructuur van tankstations door de jaren heen uitgegroeid tot een goed georganiseerd netwerk. Een eerste oplossing om het verbruik van voertuigen te verlagen is om een hybride aandrijflijn te ontwikkelen. Met een hybride aandrijflijn wordt hier een aandrijflijn bedoeld die door twee vermogensbronnen aangedreven wordt. Normaal gesproken is dit een verbrandingsmotor, gecombineerd met een of meerdere elektrische machines. Het brandstofverbruik van een hybride voertuig is lager ten opzichte van een conventioneel voertuig doordat de elektrische machines remenergie kunnen terugwinnen, wat opgeslagen kan worden in batterijen of een soortgelijk elektrisch opslag systeem. Naderhand kan deze elektrische energie gebruikt worden om de elektrische machines aan te drijven en de verbrandingsmotor assisteren, hierdoor daalt het brandstofverbruik. Het meest commercieel succesvolle hybride voertuig maakt gebruik van een vermogenssplit transmissie. Deze vermogenssplit transmissie bestaat uit een mechanisch gekoppelde keten van tandwielen en een elektrische variator. De elektrische variator regelt de transmissie ratio en hiermee ook het werkpunt van de verbrandingsmotor. In de literatuur kunnen verschillende onderzoeken gevonden worden met betrekking tot vermogenssplit transmissies. In dit verslag worden verschillende methodes behandeld. Schulz en Villeneuve onderzoeken allebei een specifieke vermogenssplit transmissie. Mattsson echter onderzoekt verschillende vermogenssplit transmissies. Uiteindelijk is de benadering van Mattsson gebruikt om het hybride systeem van Toyota en de Renault IVT te onderzoeken. Beide transmissies lijken op elkaar hoewel het hybride systeem van Toyota maar een mode heeft terwijl de Renault IVT twee modes heeft. Met een simpel rendementsmodel worden deze transmissies vergeleken met elkaar. Uiteindelijk is het hybride system van Toyota vergeleken met een duwband CVT. Hiervoor worden drie situaties bestudeerd, allereerst worden alleen de werkpunts afhankelijke rendementen van de verbrandingsmotor beschouwd. Gevolgd door de toevoeging van constante rendementen voor de transmissie componenten. En uiteindelijk worden de werkpunts afhankelijke rendementen van elektrische machines voor het hybride systeem van Toyota en van de duwband CVT voor de transmissie met duwband CVT. Hiermee wordt het totale rendement van beide transmissies met elkaar vergeleken. v

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7 Contents Abstract Samenvatting Nomenclature iii v ix 1 Introduction 1 2 Methodologies Method by Schulz Method by Villeneuve Method by Mattsson Discussion methodologies Analyzing IVTs Kinematics Toyota hybrid system Renault IVT Comparison THS & Renault IVT Mattsson Toyota hybrid system Renault IVT Efficiencies Detailed efficiency analysis Internal combustion engine Toyota hybrid system Case A - ICE efficiency Case B - Constant transmission component efficiencies Case C - EM working point efficiencies Push-belt CVT Case A - ICE efficiency Case B - Constant transmission component efficiencies Case C - CVT working point efficiencies Discussion ICE strategy Comparison case A, B & C Comparison THS & push-belt CVT Conclusion & recommendations Conclusion Recommendations vii

8 viii CONTENTS Bibliography 47 A Kinematics planetary gear 49 B Clarification of the method by Schulz 51 B.1 M-file for the method by Schulz C Clarification of the method by Villeneuve 55 C.1 M-file for the method by Villeneuve D Clarification of the method by Mattsson 59 E Kinematics THS 61 F Kinematics push-belt CVT 65 G Toyota Prius specifications 67

9 Nomenclature Abbreviations 2WD / 4WD AMT AT BER CO 2 CVT DNR ECU EM EMPAct CVT GNR HEV ICE IMA IVT OD SOC SOOL SUV THS e-line rpm 2 / 4 Wheel Drive Automated Manual Transmission automatic transmission Brake Energy Recovery Carbon dioxide Continu Variable Transmission Drive-Neutral-Reverse Engine Control Unit Electrical Machine Electro-Mechanical Pulley Actuation CVT Geared Neutral Ratio Hybrid Electric Vehicle Internal Combustion Engine Integrated Motor Assist Infinitely Variable Transmission Overdrive State Of Charge System Optimal Operation Line Sport Utility Vehicle Toyota Hybrid System economy line revolutions per minute Symbols Symbol Definition Unit P power [kw ] T torque [N m] loh level of hybridization [ ] r radius [m] r ratio [ ] v velocity [m/s] z number of teeth [ ] Φ power split ratio [ ] ix

10 x NOMENCLATURE η efficiency [ ] λ E power ratio [ ] ω rotational velocity [rad/s] Subscripts Subscript Definition A1 planetary gear A1 A2 planetary gear A2 B planetary gear B C planetary gear C C1 clutch 1 C2 clutch 2 CV T push-belt CVT EM Electrical Machine F 1 brake 1 F 2 brake 2 H higher shaft ICE Internal Combustion Engine L lower shaft MG1 motor / generator 1 MG2 motor / generator 2 c ev f fd gn pg prim r s sec tr v v in v out wls carrier electrical variator fuel final drive geared neutral planetary gear primary pulley ring gear sun gear secondary pulley transmission vehicle variator in variator out wheels

11 Chapter 1 Introduction Every year more discussions arise about the global warming of the earth. This again got an extra boost since the documentary An Inconvenient Truth is released. Many scientists dedicate the global warming to the production of to much carbon dioxide (CO 2 ) emissions. More voices say this is caused for a large part by the growing transportation sector. Passenger cars are a main part of this sector. People are urged to help solving this problem by using less fuel, e.g. drive more fuel economic cars. This is also encouraged by the rising oil prices. Which is caused by the oil getting scarce on one hand. On the other hand, events which attributed to previous spikes are the North Korea s missile launches, the crisis between Israel and Lebanon, the Iranian nuclear brinksmanship and the Iraq war. People especially notice these rising oil prices by the increasing gas prices. The gas price over the past years can be seen in Fig The gas price of the year 2007 is slightly lower compared to the year 2006, however the year 2007 is only covering the first quarter. Governments stimulate more and more to awaken the people to use less oil. With respect to vehicles, fuel consumption guides are composed, e.g. Brandstof Verbruiks Boekje [2]. Next to stimulating the people to drive more fuel efficient with tips like keep the revolutions of the engine under 2500 rpm, drive constant velocities (use the cruise control) and check the tyre pressure every month, e.g. Het Nieuwe Rijden [14]. Understandably small vehicles are more fuel efficient, however people are used to luxurious and spacious vehicles. With a hybrid power train, mid-sized vehicles can reach the fuel efficiency of conventional smaller vehicles. However the social acceptance of hybrid vehicles is still low because hybrid vehicles are assumed to be slow, to have high maintenance costs and to be dangerous because of the high voltages present. Nevertheless the sales figures of the hybrid vehicles are rising. Nowadays more and more car manufacturers are producing hybrid vehicles. Next to even more concept hybrid vehicles which are developed by car manufacturers. In this section first the different classifications for hybrid vehicles are discussed. Next the different configurations for hybrid power trains are described gas price [euro/100 l] Figure 1.1: Development of the gas price (euro95) over the past years, data obtained from CBS [4] 1

12 2 CHAPTER 1. INTRODUCTION Classifications Hybrid vehicles can be divided into different classifications, ranging from conventional vehicle to plugin hybrid vehicle. Normally a vehicle has no electric driving power, the higher the hybridisation, the more electric driving power the vehicle has. Like a start-stop system is not typically for only hybrid vehicles, because this can be realized by an alternation in the engine control unit (ECU) of mostly every conventional car. On the other hand, hybrid vehicles are generally spoken equipped with this feature, an example of a conventional vehicle with a start-stop system is the Citroën C3 Stop & Start [10]. In contrast to a plug-in hybrid vehicle which tends to a complete electric vehicle. Basically it should be possible to make a vehicle which is only powered by electric motors and refuels by plugging-in. The classification which ranges from conventional to plug-in hybrid vehicle can be divided in a conventional vehicle, muscle-, mild-, full- and a plug-in-hybrid vehicle. This classification is listed in Table 1.1 and is further described by D. Friedman [5]. A muscle hybrid vehicle is not designed to improve the fuel consumption a lot however has extra power which is generated with the electric machines. Compared to equally sized conventional vehicles it uses less fuel. A mild hybrid vehicle is designed to improve the fuel consumption however has a small electric machine. It is not able to run on electrical power only. A full hybrid vehicle is like a mild hybrid vehicle with bigger electric machines, it is possible to drive on electrical power only. The last category, and the highest level of hybridisation, is the plug-in hybrid vehicle. This is the closest to the full electric vehicle, it can be plugged in to recharge the batteries and has a large range to drive on electric power only. Table 1.1: Hybrid checklist: Is this vehicle a hybrid? From A New Road, The Technology and Potential of Hybrid Vehicles [5] conventional muscle mild full plug-in Does this vehicle... vehicle hybrid hybrid hybrid hybrid shut off the engine at traffic lights and in stop-and-go traffic use regenerative braking and operates above 60 V use a smaller engine than a conventional version with the same performance drive using only electric power recharge batteries from the wall plug and have a range of at least 30 km on electricity alone Configurations The power trains of hybrid electric vehicles can be divided into three different configuration types. These configurations are series, parallel and series/parallel power train. In Fig. 1.2 these configurations are graphically presented together with a comparison of the gained effects. Typical hybrid functions are electric drive off, full electric driving, recharging of the secondary power source (e.g. battery) while driving, power assist, brake energy recovery (BER) and engine shut-off when no driving power is required. Series hybrids A series hybrid system consists of an Internal Combustion Engine (ICE) which drives a generator. The electric power generated can be stored in a battery or can directly be used to power an electric

13 3 motor. The vehicle is powered by an electric motor which uses this generated electricity to drive the wheels. This is called a series hybrid system because the power flows to the wheels in series, i.e. the engine power and the motor power are in series. A series hybrid system can run a small ICE in the efficient operating region relatively steadily, generate and supply electricity to the electric motor and efficiently charge the battery. It has two electric motors, one functions as a generator and the other as an electric motor. The advantage of a series hybrid power train is the ICE can operate at a constant speed so the fuel consumption is low. This system is very flexible as well, because only the ICE and generator are mechanical coupled, the motors can be placed in the wheels or wherever necessary. Disadvantages are the power from the ICE always goes over two electric machines, which both have a certain efficiency and during highway driving this can result in a lower efficiency compared to a conventional, mechanical transmission. This system is used in the TNO Hybrid Carlab. Parallel hybrids In a parallel hybrid system, both the ICE and the electric machine drive the wheels, and the drive power from these two sources can be utilized according to the prevailing conditions. This is called a parallel hybrid system because the power flows to the wheels in parallel. In this system, the battery is charged by switching the electric machine to operate as a generator. To drive the vehicle with the electric power Battery Inverter Engine Generator Motor Reduction gear Drive wheels Battery Engine Transmission Inverter Motor/ generator Reduction gear Drive wheels Generator Battery Engine Power split device Inverter Motor Reduction gear Drive wheels Figure 1.2: Three major types of hybrid configurations used in hybrid vehicles currently on the market, from The Fifth Toyota Environmental Forum [15]

14 4 CHAPTER 1. INTRODUCTION stored in the battery, the electric machine operates as motor. Although it has a simple structure, the parallel hybrid system cannot drive the wheels from the electric machine while simultaneously charging the battery since the system has only one electric machine. When the battery needs to be recharged while driving, an amount of the power delivered by the ICE goes to the electric machine. This configuration is, among other configurations, applied by Honda in the integrated motor assist (IMA) system and by Torotrak in their hybrid infinitely variable transmission (IVT) system. Series/parallel hybrids A series/parallel hybrid system combines the series hybrid system with the parallel hybrid system in order to maximize the benefits of both systems. It has two electric machines, and depending on the driving conditions, uses only one electric machine or the driving power from both the electric machines and the ICE, in order to achieve the highest efficiency level. Furthermore, when necessary, the system drives the wheels while simultaneously generating electricity using one electric machine as generator. A disadvantage of this system is its complexity, because the power train needs to combine the power from the ICE and both the electric machines. The advantage of this system is it can cover all hybrid functionalities depending on the sizes of the electrical machines and the electrical storage system. This is the system used in a lot of hybrid systems nowadays, among with the Toyota Prius, Lexus GS450h, Ford Escape Hybrid and the Mercedes-Benz S-Classe Hybrid. Commercial hybrid vehicles More and more car manufacturers have hybrid vehicles in their range of products. Audi started in 1994 with the Audi 80 Duo, because the price was to high it could not be sold, some years later Audi introduced the A4 Duo. After selling 90 items for still a high price, Audi decided to stop production and to explore the possibilities of direct diesel injection to improve fuel consumption. The first commercially successful hybrid vehicles are the Toyota Prius and Honda Insight. The Toyota Prius, a four-door sedan, is equipped with the Toyota Hybrid System (THS), a series/parallel hybrid power train. Toyota also developed the THS-C (THS with a continue variable transmission (CVT)) for the Estima and Alphard minivan. Next to the THS-M (mild THS) in the Crown sedan. Over the years the THS is improved considering fuel consumption and driving performance which resulted in the THS II. This hybrid power train is on its turn adjusted to fit into larger vehicles. In several sport utility vehicles (SUVs) of Toyota and Lexus the THS II for SUVs is available now. These vehicles are available in a 2WD and 4WD model, the 4WD model is realized with an extra electric machine on the rear wheels. Lexus adapted the THS II for a front engine, rear-wheel driven vehicle, the GS450h. The Honda Insight, a small two-seater, is equipped with the IMA system, a parallel hybrid power train developed by Honda. The IMA is enlarged to reach the required driving performance for the Civic Hybrid and the Accord hybrid. The hybrid model by Ford is the Escape Hybrid. This has a similar power train as the THS II for SUVs however is designed by Ford itself. The Escape Hybrid is available in a 2WD and 4WD model. With the Mercury brand, Ford brought the Mariner Hybrid on the market which is a sibling of the Escape Hybrid, however only in a 4WD model available. Remarkable is the point of view from which a hybrid vehicle is developed, like Toyota and Honda developed a completely new vehicle. Toyota developed a mid-sized hybrid vehicle to reduce emissions, especially in urban driving. On the other hand, Honda developed a small hybrid vehicle to reach the best fuel economy as possible. Both Toyota and Honda optimized the power train for a new model and later implemented this power train into new versions of existing models. Other car manufacturers develop concept vehicles based on existing models equipped with hybrid power train concepts.

15 5 Another interesting point is the level of hybridisation (loh) of a hybrid vehicle. In Fig. 1.3 the level of hybridisation is shown for the commercially available hybrid vehicles. The level of hybridisation is defined as in Eq. (1.1). loh = P EM P ICE Where P EM stands for the maximum power delivered by the electric machine, when the power train consists of two electric machines the electric machine is depicted which mainly operates as motor. P ICE is the maximum power delivered by the ICE. Clearly Honda has a low level of hybridisation, combined with relatively low vehicle weight. The second generation Toyota Prius has the highest level of hybridisation and still low vehicle weight, especially compared to the vehicles with just a little lower level of hybridisation. These all have a higher vehicle weight. The most desirable region is the top left corner, here the vehicle weight is low and the level of hybridisation is high. Low vehicle weight is an important factor because the fuel consumption increases drastically with increasing vehicle weight. In the contrary a hybrid vehicle is heavier compared to a conventional vehicle. This is caused by the electrical storage system and the electric machines. However a hybrid vehicle gains more fuel efficiency compared to the costs of fuel economy caused by the extra vehicle weight. (1.1) loh [ ] Toyota Prius II Toyota Highlander4WD Lexus RX400h Toyota Highlander 2WD Ford Escape 2WD Toyota Prius Ford Escape 4WD Mercury Mariner Lexus GS450h Toyota Kluger Toyota Harrier Toyota Estima Audi A4 Duo Honda Civic Honda Insight Suzuki Twin Toyota Alphard Hond Accord Vehicle weight [kg] Figure 1.3: Level of hybridisation for commercially available hybrid vehicles Outline of the report Almost all car manufacturers have carried out studies or are investigating the possibilities of different hybrid power trains. Research institutes and automotive suppliers are investigating hybrid power trains as well. Some interesting power trains are the Bosch Dual-E transmission, the Renault IVT, the TNO Hybrid Carlab and the LuK power split CVT for instance. The Bosch Dual-E transmission is a six speed automated manual transmission (AMT) equipped with two electric machines to create a continuously ratio change between the gears, on top of this hybrid functions are gained. The Renault IVT is a dual mode IVT realized with a combination of planetary gears and two electric machines. Depending on the electrical energy storage capacity this power train ranges from pure transmission to a full hybrid power train. TNO realized a series hybrid vehicle based on a Volkswagen Beetle, herein a diesel ICE and two electric machines result in the power train. With this vehicle the influence of different control strategies and the size of different power train components is investigated. LuK on the other hand developed a power split transmission based on a chain CVT, a planetary gear and two fixed gear ratios. Next to an electric machine which can fulfill most hybrid functionalities.

16 6 CHAPTER 1. INTRODUCTION Since the oil is getting more scarce every year and the oil price is rising, it becomes more important to improve the fuel efficiency of vehicles. A hybrid power train is a viable solution to improve the fuel consumption of vehicles. To realize a hybrid power train different configurations are possible. The most used configuration is the series/parallel hybrid power train, which is realized by means of power split transmissions. The main goal of this thesis is to investigate the construction and functionality of different power split transmissions. And the emphasis lays on the influence of the power train components on the overall power train efficiency of a power split transmission compared to a conventional transmission. To achieve this goal first three methods to investigate power split transmissions are discussed. The transmission developed by Bosch is investigated by M. Schulz [13]. Especially he is interested in circulating power flow and how to determine the region where no circulating power flow occurs. This in order to develop a strategy leading to a fuel-efficient vehicle operation. The power split transmission developed by Renault is investigated by A. Villeneuve [17]. Who looks at the ratio between the electrical variator power and the ICE power to investigate the transmission. Which also gives an indication for the circulating power flow in the transmission, however Villeneuve tolerates some circulating power flow. In contrast to Schulz and Villeneuve, P. Mattsson [8] derived a method to determine suitable values of the basic speed ratios for a general CVT. In order to derive this method Mattsson first investigates several power split transmissions. In Chapter 2 these different methods are discussed. Next a closer look is taken at two power split transmissions, the THS and the Renault IVT. First the kinematics are derived for these transmission and secondly these transmission are described by the method derived by Mattsson. This is discussed in Chapter 3. At the end a detailed efficiency analysis is made. Hereto the THS and the push-belt CVT are investigated, especially the power train component efficiencies and their influence on the overall power train efficiency. This is discussed in Chapter 4. Finally, in Chapter 5 the conclusions and recommendations are given.

17 Chapter 2 Methodologies The most commercially successful hybrid vehicles are equipped with a power split transmission. Power split transmissions like the name suggests split the power in the transmission. This is applied to achieve high efficiencies combined with outstanding driving comfort. The efficiency is high because the mainstream of the power is transmitted through a kinematic chain, normally consisting of one or more planetary gears combined with some gear stages. The rest of the input power passes through a variator which controls the transmission ratio and herewith the working point of the ICE. In case of an electric variator, hybrid functionalities are easy to implement. In case of a mechanical variator, hybridisation is somewhat more complicated however not impossible. The driving comfort is characterized by the transmission ratio which is continuously variable and herewith considered to be very comfortable. In literature various power split transmissions are investigated, in this chapter three publications are discussed. First the hybrid power split transmission developed by Bosch is discussed, M. Schulz [13] investigates this transmission by means of power flow and especially circulating power flow. Next the hybrid power split transmission developed by Renault is discussed, A. Villeneuve [17] investigates this transmission by means of power flow as well, however in a different manner. Finally the publication of P. Mattsson [8] is discussed. This publication reports a general description of power split transmissions and how to quantify them. First some general notations used in this thesis are presented. The overall speed ratio used in this thesis is defined as the output speed over the input speed, Eq. (2.1). Where the wheels are the output of the transmission and the ICE functions as input. r tr = ω wls ω ICE (2.1) Where r tr stands for the overall speed ratio. The rotational speed of the wheels and ICE are represented by ω wls and ω ICE respectively. In power split transmissions normally the power is split over a kinematic chain and a variator path. An interesting parameter is the ratio between the variator input speed and the variator output speed. This is shown in Eq. (2.2). r ev = ω v out ω vin (2.2) Where r ev is the electric variator speed ratio. The rotational input and output speeds of the electric variator are represented by ω vin and ω vout respectively. Next to these speed ratios, power ratios are useful as well to indicate the power split transmissions. The power split ratio is defined as the electric variator input power over the ICE input power, Eq. (2.3). Φ = P v in P ICE (2.3) 7

18 8 CHAPTER 2. METHODOLOGIES Where Φ stand for the power split ratio and the power delivered by the ICE is represented by P ICE. The power which goes into the electric variator is indicated with P vin. This chapter reviews the literature concerning the usefulness of using the methods derived by M. Schulz, A. Villeneuve and P. Mattsson. 2.1 Method by Schulz The Robert Bosch GmbH company developed the Dual-E transmission, a hybrid power train based on a six speed automated manual transmission (AMT). This power train is investigated by M. Schulz [13]. In Fig. 2.1(a) the schematic representation of the Dual-E transmission is shown. Where the crankshaft is connected to the ICE and the output shaft is connected to the driven wheels. The loop-like arrange- MG2 r MG2 r A2 MG1 P MG1 C1 P1 L r A1 P C1 P L MG1 ICE wls P ICE P wls r MG1 C2 P C2 P2 P H H (a) Schematic representation of the Dual-E transmission MG2 P MG2 (b) Internal and external power flow of the Dual-E transmission Figure 2.1: Bosch Dual-E transmission, [13] ment of the shafts give the supposition circulating power may occur in this system. The knowledge of the region where circulating power occurs is essential for developing a fuel efficient strategy. Hereto first the power flow in the transmission is investigated and followed by the kinematics. In Fig. 2.1(b) the internal and external power flows are depicted. The energy balance can be formulated by the linear algebraic Eq. (2.4), herein the inertia effects, compliance of the members and the mechanical power losses are neglected. With Ax = b A = (2.4) (2.5) x = [ P C1 P C2 P L P H ] T (2.6) b = [ P ICE P wls P MG1 P MG2 ] T (2.7)

19 2.1. METHOD BY SCHULZ 9 Where x is the internal power flow and b is the external power flow. The ICE and the two electric machines provide the power input to the transmission, P ICE, P MG1 and P MG2 respectively. Together with the output power, P wls, they represent the external power flow. The power of the ICE is split into P C1 and P C2 driving the carriers of the two planetary gears P1 and P2 respectively. The outputs P L and P H from the ring gears of the planetary gears drive the two countershafts L and H. The coefficient matrix A is singular. An analysis shows that each solution can be expressed as a linear combination of three basic solutions and one solution which represents cyclic power flow. The internal power flow is not uniquely defined by Eqs. (2.4) to (2.7), a detailed investigation of the kinematics and dynamics of the transmission is necessary. The kinematics for a planetary gear are derived in App. A. Combining these equations with the constraints imposed by the meshing gears result in the equations for the rotational speeds of the EMs, which depend on the rotational speed of the ICE and the output shaft. This results in Eq. (2.8), an elaborate clarification can be found in App. B. [ ] ωmg1 = ω MG2 [ ] [ ] a b(l) ωice c d (H) ω wls The derivation of the constants a, b (L), c and d (H) can be found in App. B. Neglecting the mechanical losses and the inertia of the power train components, the relations for the torques result into Eq. (2.9). (2.8) [ ] [ TICE = T wls a b (L) c d (H) ] [ ] TMG1 T MG2 (2.9) Where the constants a and c are independent of the engaged gear. In contrast to the constants b (L) and d (H) which are dependent of the engaged gear. When the 1 st and 2 nd gear are engaged this results for the torque relations into Eq. (2.10). [ ] TICE = T wls [ ] [ ] TMG1 T MG2 (2.10) For a graphical representation of the operating range free from circulating power, the ratio of the total mechanical power of the EMs to the output power is introduced, Eq. (2.11). λ E = P MG1 + P MG2 P wls (2.11) λe [ ] st gear 2 nd gear 3 rd gear 4 th gear 5 th gear 6 th gear /r tr [ ] Figure 2.2: Overview of the power ratio for each discrete transmission gear

20 10 CHAPTER 2. METHODOLOGIES Where the power ratio is represented with λ E. The power from the electric machines is represented with P MG1 and P MG2, where the output power is given by P wls. In Fig. 2.2 the power ratio is plotted against the inverse of the overall speed ratio. The inverse of the overall speed ratio is taken because Schulz opts for this variable to indicate the circulating-power-free region. Each line represents one discreet ratio of the six speed automated manual transmission used in the Bosch Dual-E transmission. The region where no circulating power flow occurs is in between two half lines, e.g. in between the lines representing the 1 st and the 2 nd gear (the two top-right lines). When the transmission is in the 1 st gear, T MG2 is zero. So when the transmission is purely in the 1 st gear the electric power is only delivered or consumed by MG1. In contrast to the line which represents purely the 2 nd gear where T MG1 is zero. In between the the two half lines both the EMs are operating. The half line representing the 3 rd gear, again T MG2 is zero, analogously for the rest of the discreet gear ratios. A more elaborate clarification about determining the circulating-power-free operating range can be found in Schulz [13]. When λ E is zero, the output power is completely delivered by the ICE. If the half line of a gear intersects with the line where λ E is zero, both the EMs do not cooperate. In the other hand, in between two half lines and on the line where λ E is zero, the sum of the powers generated by the EMs is zero so the power generated by one EM is completely consumed by the other EM. On the basis of this knowledge, a fuel-efficient operating strategy can be developed, taking into account that circulating power leads to high mesh losses. 2.2 Method by Villeneuve Renault studied the possibilities of power split automatic transmission architectures in order to select the most flexible and efficient variator. Their conclusion is an electric variator based upon two electric machines is one of the best solutions considering the existing technologies. At first a single mode transmission was developed, however the ratio range is limited and the EMs have to be large to cope with the power passing through the variator. The drawback of large EMs is they are heavy and expensive. Hereto a dual mode power split transmission is designed, one mode is dedicated to the low vehicle speed range and the second mode to the high vehicle speed range. This reduces the power passing through the variator and herewith the size of the EMs. The mode change has to be Electric Machine 1 F2 F1 C r 2 B A2 A1 r 1 Damper ICE r fd r 3 Electric Machine 2 wls Differential wls Figure 2.3: Schematic representation of the Renault IVT

21 2.2. METHOD BY VILLENEUVE 11 transparent and seamless to the driver because it is not really a gear change and is not made at the driver s request. Hereto a set of rules and conditions are developed to optimise the mode change. In Dual mode electric infinitely variable transmission [17] A. Villeneuve describes the development of the dual mode Renault IVT. The resulting design is shown in Fig The transmission can be divided in a kinematic chain and an electric variator. The kinematic chain consists of gear stages and planetary gear sets. This kinematic chain has two inputs and two outputs, when two input speeds are set the output speeds can be calculated according to Eq. (2.12). [ ] ωice = ω wls [ a b c d ] [ ] [ ] ωmg1 ωmg1 = M ω MG2 ω MG2 (2.12) When the inertia effects, compliance of the members and the mechanical power losses are neglected, the torques can be calculated according to Eq. (2.13). [ ] [ ] TMG1 = M T TICE (2.13) T MG2 T wls Because the Renault IVT is a dual mode transmission, the matrix M needs to be defined for each mode. The elaborate clarification can be seen in App. C. For mode 1 this results in Eq. (2.14) and for mode 2 this results in Eq. (2.15). [ ] M 1 = (2.14) M 2 = [ ] (2.15) As can be seen, the constants b and d are the same for each mode. This corresponds to the rule which ensures the power through the electric variator is zero during mode change. Since ω MG1 = ω MG2 = 0. Other rules are the overall in- and output speed should continue during mode change which implies the mode change should occur at a given transmission ratio. The overall transmission ratio is the same at this point for mode 1 and mode 2. Next to the rule of continuity of the in- and output speed of the electrical variator during mode change. Table 2.1: Power circulation in the Renault IVT Φ < 0 1 < Φ < 0 negative power recirculation Φ < 1 Φ > 0 0 < Φ < < Φ < 1 true power split Φ > 1 positive power recirculation

22 12 CHAPTER 2. METHODOLOGIES To analyze the Renault IVT, the power split ratio defined in Eq. (2.3) is used. When the variator input is working as a motor, P vin is negative. When the variator input is working as a generator, P vin is positive. The possible power flows are listed in Table 2.1. Negative circulating power flow is undesirable because this implies larger EMs and a lower efficiency of the power train. The desired operating range is true power split to keep the size of the power train components relatively small and ensure the transmission efficiency. However little negative power recirculation is tolerated in order to obtain a sufficient ratio range. When the Renault IVT purely operates as transmission the electrical storage system is omitted. This is investigated with Fig As can be seen, the power split ratio does not exceed the value ± 0.5. This means the power through the electric variator is less then half the power delivered by the ICE. Only at low transmission ratios the power split ratio tends to infinity. However no losses are taken into account here. If losses will be implemented, the power split ratio will no longer tend to infinity. This is caused by the ICE power which is no longer equal to zero. The advantage is the ICE can not deliver zero power when rotating, driving the power output to zero is possible by organising the losses in the transmission to exactly compensate the ICE power. Logically the ICE power is as low as possible in this situation. At low transmission ratios it can also be seen the power split ratio is negative which implies negative power recirculation. However the first node, where the power ratio is equal to zero, is designed to be as close as possible to a transmission ratio of zero. Herewith the transmission will spend only limited time in negative power recirculation mode. With increasing transmission ratio the power split ratio increases as well. The power split ratio increases up to nearly 0.5, which means almost half the power delivered by the ICE is transmitted through the electrical variator. When the transmission ratio increases further, the power split ratio decreases and becomes even zero. In this point the transmission switches from mode 1 to mode 2. In mode 2 the power split ratio is negative and reaches nearly a value of 5, which means almost one quarter of the power delivered by the ICE recirculates via the electrical variator in negative sense. At increasing transmission ratio, the power split ratio increases and becomes positive again. This means the transmission reaches true power split mode Φ [ ] r tr [ ] Figure 2.4: The power split ratio versus the overall transmission ratio for the Renault IVT

23 2.3. METHOD BY MATTSSON 13 v in variator v out in kinematic chain out Figure 2.5: General power split transmission 2.3 Method by Mattsson In order to model continuously variable power split transmissions, P. Mattsson analysed the speed and torque relations in a general matter for several power split transmissions [8]. In Fig. 2.5 the schematic representation of a power split transmission is shown. The transmission is assumed to be a loss-free transmission with linear speed and torque relations. It has two speed degrees of freedom and two torque degrees of freedom. The speed relations can be written according Eq. (2.16). [ ] [ ] [ ] [ ] ωvin a b ωin ωin = = I ω vout c d ω ω (2.16) out ω out The torque relations can be written as Eq. (2.17). [ ] [ ] [ Tin = I t Tvin a c T ω = out T vout b d ] [ Tvin T vout ] (2.17) The overall transmission ratio is defined as in Eq. (2.1). With the speed relations defined as in Eq. (2.16) and the variator ratio defined as in Eq. (2.2) this results in Eq. (2.18). r tr = a r ev c b r ev d (2.18) The power split ratio can also be described with the relations in Eqs. (2.16) and (2.17), this results in Eq. (2.19). The elaborate clarification can be found in App. D. Φ = P v in P in = T v in ω v in T in ω in r ev = a r ev c a d b c b r ev d (2.19) Assume that a power split transmission is designed so that the amount of power transmitted through the variator is always less than the input power. It can be shown that the overall speed ratio range of the transmission will be smaller than the speed ratio range of the variator. Hereto it is important to investigate the variator transmission ratio and the power split ratio. An elaborate derivation is given in App. D.

24 14 CHAPTER 2. METHODOLOGIES 2.4 Discussion methodologies In this section three methods are discussed. Schulz and Villeneuve are each subjected to one specific power split transmission. On the other hand Mattsson uses his method in a much more general manner, this is applicable for any kind of power split transmission in a straight forward manner. On top of this Mattsson evaluated his method with a simplified loss model as well. When the general equations for a power train are derived the efficiencies are easily to implement. Mainly therefore this method is used in the next section to investigate the THS and the Renault IVT. Because for both power trains the same method is adopted, the power trains can be compared with each other. All three methodologies discuss the importance of circulating power flow. The method by Schulz is to determine the region where no circulating power flow occurs. In his opinion circulating power highly influences the overall transmission efficiency and is therefor undesirable. The method by Villeneuve on the other hand investigates the amount of circulating power. The transmission is designed in such a way this circulating power is within proportion and the overall speed ratio is reasonable. The main difference between the Bosch Dual-E transmission and the Renault IVT is, Bosch has five driving ranges and Renault has only two driving modes. The method by Mattsson is comparable to the method used by Villeneuve. However the variator used by Mattsson is not an electric variator necessarily, this can also be a mechanical variator like a push-belt CVT. The main goal of Mattsson is to determine the dimensions of the transmission considering the power split ratio combined with the overall speed ratio and the variator speed ratio.

25 Chapter 3 Analyzing IVTs In the previous chapter each method was used to analyze a different power split transmission. In this chapter two transmissions are investigated by the method derived by Mattsson. The two transmissions are the Toyota hybrid system (THS) and the Renault IVT. The method by Mattsson is chosen because herewith a simple analysis can be made without losses and on top of this efficiencies can be implemented in a very straightforward manner. However to have a benchmark, initially the kinematics of the two transmissions are derived and analyzed. 3.1 Kinematics In order to analyze the THS and the Renault IVT the kinematics are derived. The dynamics are neglected, thus no inertias and spring-damper effects are considered. This means considering the in- and output power these are equal to each other. First the THS is analyzed using the kinematics, followed by the Renault IVT Toyota hybrid system The THS is shown in Fig. 3.1(a) with the planetary gear enlarged. The electrical system, like battery, supercapacitors and inverter, is not shown here. In this thesis the THS is investigated at constant vehicle speeds only. When the THS operates at a constant vehicle speed, in a steady state point, the battery is not discharged or recharged. When the battery would be recharged in a steady state operating point, the battery would be recharged completely. As a consequence the operating point of the power train c s pg r MG1 in batt MG2 r fd out (a) Schematic representation of the THS, [16] (b) Simplified representation of the THS electric path mechanical path Figure 3.1: Toyota hybrid system 15

26 16 CHAPTER 3. ANALYZING IVTS would change because the battery can not obtain more electric power. Correspondingly is the situation when the battery would be discharged in a steady state operating point. The control strategy would notice the battery depleting and at a certain state of charge (SOC) level the working point would be changed to recharge the battery. The electrical energy storage system (e.g. battery) is not taken into account because only steady state operation points are considered. This means the power generated by one EM is completely consumed by the other EM, considering the efficiencies to be 100 %. As one EM operates as motor, the other operates as generator. If losses are taken into account the generator has to compensate the losses for both the EMs. The generator in Fig. 3.1(a) is referred to as MG1 and the motor is referred to as MG2 because both the EMs can operate as motor and generator. The planetary gear is often referred to as the power split device. By definition the sum of the powers acting on the planetary gear is always equal to zero. Hereto the power is split into two paths or brought together from two paths. In Fig. 3.1(b) a simplified representation of the THS is shown. The kinematics of a planetary gear are derived in App. A, in Eq. (3.1) these are listed to recapitulate. r pg = zr z s ω s + r pg ω r (1 + r pg ) ω c = 0 r pg T c + (1 + r pg ) T r = 0 T c + (1 + r pg ) T s = 0 T r r pg T s = 0 (3.1) Where r pg is the planetary gear ratio, with z the number of teeth of a gear, ω stands for the rotational speed. The subscripts refer to the different parts of the planetary gear, with r the ring gear, s the sun gear and c the planet carrier. With MG1 the working point of the ICE is influenced via the planetary gear. In Fig. 3.2 two engine operating points at identical vehicle speed are schematically represented in a nomograph. In Fig. 3.2(a) the sun gear has positive rotational speed, hence MG1 operates as generator. In Fig. 3.2(b) the working point of the ICE (connected to the carrier) is influenced by lowering the rotational speed of MG1 (connected to the sun gear) compared to Fig. 3.2(a). Because the electrical energy storage system is not taken into account and no losses considered, the ICE provides the road load power. The power on the carrier is for both situations the same. Because the rotational speed of the carrier is lowered, the torque on the carrier increases. With Eq. (3.1) the torques acting on the rest of the planetary gear are calculated. For both the sun gear and the ring gear the torques increase. The situation in Fig. 3.2(a) corresponds with the situation shown in Fig The situation in Fig. 3.2(b) corresponds with the situation shown in Fig. 3.5(b). To drive in reverse with the ICE turned on, the carrier of the planetary gear has a positive rotational sun carrier ring gear gear s c r sun carrier ring gear T r gear s c r T s T r T c 0 + torque, speed r pg 1 (a) Positive speed of the sun gear T s 0 + torque, speed r pg 1 T c (b) Negative speed of the sun gear Figure 3.2: Nomographs of the planetary gear during forward driving with the ICE on

27 3.1. KINEMATICS 17 sun carrier ring gear gear s c r T s sun carrier ring gear gear s c r T r 0 T r + torque, speed T s 0 T c + torque, speed T c r pg 1 (a) Planetary gear relations during reverse driving r pg 1 (b) Planetary gear relations in the geared neutral ratio Figure 3.3: Nomographs of the planetary gear during reverse driving and in geared neutral ratio speed. The ring gear needs a negative rotational speed to drive in reverse, so the generator needs to compensate the velocity difference, thus always has a positive rotational speed and operates as a generator. This is shown in Fig. 3.3(a). The speed of the sun gear increases very fast when the carrier speed only increases a little. In Fig. 3.5(a) the situation is shown, corresponding to the situation in Fig. 3.3(a). The THS is designed to drive reverse on electric power only, normally the ICE will not be started. Another interesting situation is the geared neutral ratio (GNR). This is the transmission ratio for which the power only is transmitted via the mechanical path. For the planetary gear this means no power goes via the sun gear. This is realized by putting the rotational speed of the sun gear to zero. This is shown in Fig. 3.3(b). However the torque acting on the sun gear is not zero. The GNR for the complete power train of the THS is given by Eq. (3.2). r gn = (1 + r pg) r pg r fd (3.2) Where r gn stands for the geared neutral ratio and r fd stands for the final drive ratio. The power flow in the THS can be divided into several situations. During normal driving, the engine delivers power and is assisted by the electric motor as shown in Fig In this situation the battery can be charged or discharged, whatever necessary. When cruising, driving a constant speed, the ICE delivers the power to drive the wheels. The power generated by MG1 is consumed by MG2 to assist the ICE. To recharge the battery when cruising the ICE delivers more power then necessary and the extra power is converted into electric energy by MG1 which is stored in the battery. Another situation can be seen in Fig. 3.5(b), here circulating power flow occurs. This means power circulates inside the transmission. Circulating power flow is undesired because the overall transmission efficiency will decrease drastically. Therefore this situation is avoided in the THS. c s pg r in batt MG1 MG2 fd out electric path mechanical path power Figure 3.4: Hybrid vehicle propulsion