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1 Re, Qiglia (2) Numerical Aalysis ad Modellig of Trasmissio Systems for Hybrid Electric Vehicles ad Electric Vehicles. Doctoral thesis, Uiversity of Suderlad. Dowloaded from: Usage guidelies Please refer to the usage guidelies at or alteratively cotact

2 NUMERICAL ANALYSIS AND MODELLING OF TRANSMISSION SYSTEMS FOR HYBRID ELECTRIC VEHICLES AND ELECTRIC VEHICLES QINGLIAN REN A thesis submitted i partial fulfillmet of the requiremets of the Uiversity of Suderlad for the degree of Doctor of Philosophy February 2

3 Cotets Idex for figures... iv Idex for tables... ix Idex for appedices... x Ackowledgemet... xi Abbreviatios...xii Aotatios...xiv Abstract... xv Itroductio.... Eergy cosumptio ad emissios....2 Need for research o hybrid electric vehicles....3 Need for research o electric vehicles Aim ad objectives Review of previous work Itroductio Hybrid electric vehicles Defiitio ad classificatio Hybrid vehicle developmet Hybrid vehicle aalysis Electric vehicles Trasmissio desigs Trasmissios for HEVs Trasmissios for EVs Cotrol strategies Importace of cotrol strategy Cotroller desig Discussio Methods to aalyse gearbox used o HEVs Descriptio of epicyclic gear set Lever aalogy Algebraic desig techologies Matrix method Cocludig remarks Aalysis of epicyclic trasmissios Itroductio Aalysis of a sigle epicyclic trasmissio Speed ad ratio aalysis Torque aalysis Aalysis of a twi epicyclic trasmissio The rotatio speed equatio group Torque ad efficiecy aalysis...52 i

4 3.4 Computer program for the aalysis of epicyclic trasmissios Trasmissio systems aalysis tool (TSAT) Use of TSAT to aalyze some complex PSDs Cocludig remarks Compariso of a sigle ad twi epicyclic gearbox Itroductio Mathematical model Results ad compariso Torque ad power split Power of MG ad MG Potetial beefits of the twi epicyclic gearbox Cocludig remarks Modelig hybrid electric vehicle (HEV) performace Itroductio Overview of Vehicle Models Egie model Trasmissio models Covetioal maual gearbox Sigle epicyclic gearbox model Twi epicyclic gearbox model Motor ad geerator model Cotrol strategy Cocludig remarks Compariso of HEVs fitted with sigle ad dual epicyclic trasmissios Itroductio Drivig cycles Simulatio results Fuel cosumptio Egie operatio poits, power flow ad battery SOC Mode selectio aalysis Motor ad geerator operatio poits Vehicle performace Top speed Acceleratio Drivig aggressiveess Cocludig remarks Electric vehicle with trasmissio system Itroductio Electric vehicle modelig Vehicle modelig Method of selectig motor operatio poit Results with a geeric motor EV with sigle trasmissio ratio EV with cotiuously variable gearig EV with a multispeed gearbox Effect of drive cycle Results with the practical motor...42 ii

5 7.4. Results from simulatios over the NEDC cycle Simulatio results for the USA FTP-75 cycle Effect of drivig cycle Compariso of the results from two motors Effect of drivability Cocludig remarks Coclusios ad future work Summary ad coclusios Future work...63 Refereces...65 Appedix...7 iii

6 Idex for figures Fig 2. Classificatio of hybrid electric vehicles... 7 Fig 2.2 Fig 2.3 Toyota Prius, THS arragemet...4 Trasmissio speed ratio limits of the THS system (Cho, Ah et al. 26a)...6 Fig 2.4 GM Alliso AHS arragemet... 6 Fig 2.5 Geeric dual mode + 4 fixed ratios arragemet... 7 Fig 2.6 GM two mode hybrid trasmissio with 4 fixed gear ratios... 8 Fig 2.7 Bosch Dual-E trasmissio (Schultz 26)... 2 Fig 2.8 Possible EV cofiguratios (Ehsai, Gao et al. 24)... 2 Fig 2.9 The geeric structure of a hybrid vehicle cotrol system Fig 2. Eergy paths for equivalet fuel cosumptio calculatio durig battery discharge...25 Fig 2. Eergy paths for equivalet fuel cosumptio calculatio durig battery charge...26 Fig 2.2 A simple ad a complex epicyclic gear set (Corey 23)... 3 Fig 2.3 Simple epicyclic gearset ad aalogous lever diagram... 3 Fig 2.4 Methodology of the Algebraic desig method (Raghava, Buckor et al. 26)...33 Fig 2.5 A example of a ecoded trasmissio (Tia ad Lu 997) Fig 3. Toyota Prius PSD (Ayers, Hsu et al. 24) Fig 3.2 Sigle epicyclic gearbox, three brach system Fig 3.3 Ecode of basic parts ad coected parts...4 Fig 3.4 Relatioship of trasmissio ratio ad motor geerator speeds for the sigle epicyclic gearbox...43 Fig 3.5 Effects of two values of α o the sigle epicyclic gearbox Fig 3.6 Twi epicyclic trasmissio...47 Fig 3.7 Ecode of basic parts ad coected part of the twi epicyclic trasmissio...48 Fig 3.8 Relatioship of trasmissio ratio ad motor geerator speeds for the 4 brach systems...5 Fig 3.9 Effects of two values of α o the twi epicyclic gearbox Fig 3. Effects of two values of α 3 o the twi epicyclic gearbox iv

7 Fig 3. Flowchart for the TSAT program Fig 3.2 Step : trasmissio cofiguratio Fig 3.3 Step 2: tooth umber of each gear Fig 3.4 Step 3: Coectio...58 Fig 3.5 GM Alliso AHS arragemet Fig 3.6 Simplified drawig of GM Alliso AHS arragemet Fig 3.7 GM Alliso AHS mode ad mode Fig 3.8 Geeric dual mode + 4 fixed ratios arragemet... 6 Fig 3.9 Simplified drawig of Geeric dual mode + 4 fixed ratios arragemet Fig 3.2 Geeric dual mode + 4 fixed ratios...62 Fig 4. Calculatio process...65 Fig 4.2 Sigle epicyclic trasmissio, torque ad power split Fig 4.3 Twi epicyclic trasmissio, torque ad power split Fig 4.4 Sigle epicyclic trasmissio, power of MG & MG2, o acceleratio Fig 4.5 Twi epicyclic trasmissio, power of MG ad MG2, o acceleratio Fig 4.6 Sigle epicyclic trasmissio, power of MG ad MG2, with acceleratio Fig 4.7 Twi epicyclic trasmissio, power of MG ad MG2, with acceleratio Fig 4.8 Trasmissio ratios ad speeds of MG ad MG Fig 4.9 Power of MG ad GM Fig 5. Overview of the covetioal ICE vehicle model Fig 5.2 Overview of the hybrid vehicle model...76 Fig 5.3 Top view of the egie model based o a cosumptio map Fig 5.4 Egie efficiecy map...78 Fig 5.5 Top level of the block Maual Gear Box...79 Fig 5.6 Sigle epicyclic gearbox as used i the Toyota Prius also referred to as a 3 brach system...79 Fig 5.7 Power flow of the sigle epicyclic system... 8 Fig 5.8 Mode : Motor aloe...8 Fig 5.9 Mode 2: Combied power...82 Fig 5. Mode 3: Cruise mode...83 Fig 5. Mode 4: Egie aloe...84 Fig 5.2 Mode 5: Regeerative brakig...85 Fig 5.3 Mode 6: Mechaical brakig...86 Fig 5.4 Mode 7: Stadstill charge...87 Fig 5.5 Mode 8: Drivig charge...88 Fig 5.6 Twi epicyclic gearbox as proposed by NexxtDrive - also referred to as a four brach system...89 v

8 Fig 5.7 Power flow of the dual epicyclic system Fig 5.8 Mode : Motor aloe...9 Fig 5.9 Mode 2: Combied power...92 Fig 5.2 Mode 3: Cruise mode...93 Fig 5.2 Mode 4: Egie aloe...94 Fig 5.22 Mode 5: Regeerative brakig...95 Fig 5.23 Mode 6: Mechaical brake...96 Fig 5.24 Mode 7: Stadstill charge...97 Fig 5.25 Mode 8: Drivig charge...98 Fig 5.26 Mode 9: High efficiecy mode...99 Fig 5.27 A flaw i QSS motor/geerator model... Fig 5.28 Top view of MG2 model... Fig 5.29 MG efficiecy map... Fig 5.3 MG2 efficiecy map... Fig 5.3 Data flow for HEV models... 2 Fig 5.32 Relatioship of trasmissio ratio ad motor geerator speeds for the twi epicyclic system...3 Fig 5.33 Rule based cotrol strategy for HEV with a sigle epicyclic trasmissio... 5 Fig 5.34 Rule based cotrol strategy for HEV with a twi epicyclic trasmissio... 6 Fig 6. Egie operatio poits, NEDC cycle, traditioal ICE vehicle... 2 Fig 6.2 Egie operatio poits, NEDC cycle, sigle epicyclic system... 3 Fig 6.3 Egie operatio poits, NEDC cycle, dual epicyclic system... 3 Fig 6.4 Egie operatig poits, FTP 75, traditioal ICE vehicle... 4 Fig 6.5 Egie operatio poits, FTP75 cycle, sigle epicyclic system... 4 Fig 6.6 Egie operatio poits, FTP75 cycle, dual epicyclic system... 5 Fig 6.7 Power flows i the HEV with the sigle epicyclic gearbox over NEDC drivig cycle...5 Fig 6.8 Power flows i the HEV with the dual epicyclic gearbox over NEDC drivig cycle...6 Fig 6.9 Power flows i the HEV with the dual epicyclic gearbox over FTP- 75drivig cycle...6 Fig 6. Power flows i the HEV with the dual epicyclic gearbox over the FTP- 75drivig cycle...7 Fig 6. Battery SOC over the NEDC5 cycle... 8 Fig 6.2 Battery SOC over the FTP-75 cycle...8 Fig 6.3 Mode selectio, Europe NEDC cycle... 9 Fig 6.4 Mode selectio, USA FTP-75 cycle...2 vi

9 Fig 6.5 Relative amout of time spet i each mode, NEDC cycle... 2 Fig 6.6 Relative amout of time spet i each mode, FTP-75 cycle... 2 Fig 6.7 Operatio of MG, sigle epicyclic system, NEDC cycle Fig 6.8 Operatio of MG, twi epicyclic system, NEDC cycle Fig 6.9 Operatio of MG2, sigle epicyclic system, NEDC cycle Fig 6.2 Operatio of MG2, twi epicyclic system, NEDC cycle Fig 6.2 Top speed for the covetioal vehicle (55.92m/s) Fig 6.22 Top speed for a HEV with a CVT...25 Fig 6.23 Maximum acceleratio versus vehicle speed Fig 6.24 /a versus vehicle speed...27 Fig 6.25 /a versus vehicle speed Fig 6.26 Speed versus time curve...28 Fig 6.27 Drivig cycles with differet drivig aggressiveess Fig 6.28 Sesitivity to drivig aggressiveess fuel cosumptio ormalized to the baselie ICE coditio...3 Fig 7. Block diagram of EV model...33 Fig 7.2 Schematic diagram of selectig motor operatio poit Fig 7.3 Motor operatio poits with o gearbox Fig 7.4 Motor operatio poits with cotiuously variable gear Fig 7.5 Gear ratios selected by optimisatio strategy Fig 7.6 Motor operatio poits with four gear ratios Fig 7.7 Motor operatio poits with two gear ratios Fig 7.8 NEDC cycle vehicle speed profile ad required torque at the differetial...43 Fig 7.9 Motor operatio poits with o gearbox NEDC cycle Fig 7. Motor operatio poits with a cotiuously variable gearbox NEDC cycle...45 Fig 7. Gear ratio selectio for maximum motor efficiecy for a costat acceleratio of.7 m/s Fig 7.2 Gear ratio selectio for maximum motor efficiecy for icreasig values of costat ruig speed...47 Fig 7.3 Gear ratio selectio show as a probability distributio over the NEDC cycle assumig a cotiuously variable gearbox Fig 7.4 Motor operatio poits with a 4 speed gearbox NEDC cycle Fig 7.5 Motor operatio poits with a 2 speed gearbox NEDC cycle... 5 Fig 7.6 USA FTP-75 cycle vehicle speed profile ad required torque at the differetial...5 vii

10 Fig 7.7 Motor operatio poits with o gearbox USA FTP-75 cycle... 5 Fig 7.8 Motor operatio poits with a CVT USA FTP-75 cycle Fig 7.9 Gear ratio selectio show as a probability distributio over the USA FTP75 cycle assumig a cotiuously variable gearbox Fig 7.2 Compariso of eergy cosumptio Fig 7.2 Compariso of the geeric motor with a CVT ad a 4 speed gearbox Fig 7.22 Compariso of the practical motor with a CVT ad a 4 speed gearbox Fig 7.23 Improvemet with a 4 speed gear box...56 Fig 7.24 Motor operatio poits with o gearbox Japa mode Fig 7.25 Improvemet with a CVT...57 viii

11 Idex for tables Table 2. Classificatio of HEVs...8 Table 2.2 Hybrid checklist: is this vehicle a hybrid?(friedma 23)... 9 Table 2.3 Predicted results usig VP-SIM for a 3 kw hybrid SUV over 6 stadard drivig cycles (Musardo, Rizzoi et al. 25)... 3 Table 4. Typical vehicle parameters ((Miller 24)...64 Table 4.2 Electric power for two trasmissio at the ode poit Table 4.3 The wheel ad egie speeds at the two typical vehicle speeds Table 4.4 Power of MG ad MG2 at 3m/s Table 5. Vehicle parameters (Miller 24) Table 6. Comparisos of fuel cosumptio for the hybrid vehicle fitted with the 3 ad 4 brach systems compared with a covetioal, maual gearbox vehicle over differet drivig cycles... Table 6.2 Percetage improvemet of the 4 brach over the 3 brach drivelie over differet drivig cycles... Table 6.3 Fuel cosumptios with differet drivig aggressiveess Table 7. Vehicle parameter data...35 Table 7.2 Efficiecy improvemets for differet gearboxes over the NEDC cycle... 4 Table 7.3 Comparisos of improvemets i eergy cosumptio over 6 differet drivig cycles...42 Table 7.4 Vehicle parameter data for the model with UQM motor Table 7.5 Eergy cosumptio over the NEDC cycle for differet fial drive ratios Table 7.6 Comparisos of improvemets i eergy cosumptio over 6 differet drivig cycles...49 Table 7.7 The average improvemet over 6 cycles...55 ix

12 Idex for appedices Appedix Matlab fuctio of Gauss-Jorda elimiatio... 7 Appedix 2 Matlab programme to get speed coefficiet matrix ad to get the rotatio speed relatioships for the sigle epicyclic gearbox Appedix 3 Speed coefficiet matrix A for the sigle epicyclic gearbox Appedix 4 Relatioship of rotatio speed for the sigle epicyclic gearbox Appedix 5 Matlab program to plot MG ad MG2 speed vs. trasmissio ratio for the sigle epicyclic gearbox Appedix 6 Matlab programme to get torque coefficiet matrix ad to get torque relatioships for the sigle epicyclic gearbox Appedix 7 Torque coefficiet matrix AT for the sigle epicyclic gearbox Appedix 8 Relatioship of torque for the sigle epicyclic system Appedix 9 Matlab programme to get speed coefficiet matrix ad to get speed relatioships for the twi epicyclic gearbox Appedix Speed coefficiet matrix A for the twi epicyclic gearbox... 8 Appedix Relatioship of rotatio speed for the twi epicyclic system... 8 Appedix 2 Matlab program to plot MG ad MG2 speed vs. trasmissio ratio for the twi epicyclic gearbox...82 Appedix 3 Matlab programme to get torque coefficiet matrix ad to get torque relatioships for the twi epicyclic gearbox Appedix 4 Torque coefficiet matrix AT for the twi epicyclic gearbox Appedix 5 Relatioship of torque for the twi epicyclic system Appedix 6 Matlab program to compare the sigle epicyclic gearbox ad the twi epicyclic gearbox...86 Appedix 7 Matlab program for the cotroller for the HEV with the sigle epicyclic gearbox...94 Appedix 8 Matlab program for the cotroller for the HEV with the twi epicyclic gearbox...99 x

13 Ackowledgemet I would like to express my gratitude to all those who gave me the possibility to complete this thesis. I wat to thak the Istitute for Automotive ad Maufacturig Advaced Practice (AMAP), Uiversity of Suderlad for givig me permissio to commece this thesis i the first istace. I have furthermore to thak my lie maager ad director of study, Mr. Adria Morris, who ecouraged me to go ahead with my thesis. Also I would like to thak Professor Wheatley for his assistace over the period of the research study. I am deeply idebted to my supervisor Prof. Dave Crolla, who gave me huge support ad helped me throughout the research project ad i writig up of the thesis. Especially, I would like to give my special thaks to my family whose love eabled me to complete this work. xi

14 Abbreviatios A-ECMS AMT BEC DP DO ECMS E-CVT EFC EV EVT FL FTP GA HEV HE-VESIM HSD ICE IMA ISA IVT LCV MG NEDC NN OEM OFC PHEV PI PSAT PSD Adaptive equivalet cosumptio miimisatio strategy Automated maual trasmissio Battery eergy chaged Dyamic programmig Dyamic optimisatio Equivalet cosumptio miimisatio strategy Electroically-cotrolled cotiuously variable trasmissio Egie fuel cosumpto Electric vehicle Electrically variable trasmissio Fuzzy logic Federal test procedure Geetic algorithm Hybrid electric vehicle Hybrid electric vehicle simulatio tool Hybrid syergy drive Iteral combustio egie Itegrated motor assist Itegrated starter alterator Ifiitely variable trasmissio Low carbo vehicle Motor geerator New europea drivig cycle Neural etwork Origial equipmet maufacturer Overall fuel cosumptio Plug-i hybrid electric vehicle Proportioal-itegral Powertrai system aalysis toolkit Power Split Device xii

15 PST QSS RB SOC SQP SUV THS TR TSAT TSB Power splittig trasmissios Quasistatic simulatio Rule based State of charge Sequetial quadratic programmig Sport utility vehicles Toyota hybrid system Trasmissio ratio Trasmissio systems aalysis tool Techology Strategy board xiii

16 Aotatios R S C CL Z α p f q x r A T r A T ρ Rig gear Su gear Carrier Clutch Rotatio speed (rpm) Tooth umber Gear ratio The umber of coected parts The degree of freedom The umber of basic parts The umber of gear uits Rotatio speed vector The speed coefficiet matrix Torque vector Te torque coefficiet matrix Fuel desity η Egie efficiecy eg D Drivig distace P a P Available power Required power F _ rr Rollig resistace force F _ ad Aerodyamic drag η t r V m e ω Efficiecy of the whole powertrai Radius of the tire Vehicle speed Equivalet mass of the vehicle Rotatio Speed (rad/s) xiv

17 Abstract Iterest i hybrid electric vehicles (HEVs) ad electric vehicles (EVs) has icreased rapidly over recet years from both idustrial ad academic viewpoits due to icreasig cocers about evirometal pollutio ad global oil usage. I the automotive sector, huge efforts have bee ivested i vehicle techology to improve efficiecy ad reduce carbo emissios with, for example, hybrid ad electric vehicles. This thesis focuses o oe desig area of these vehicles the trasmissio with the aim of ivestigatig the potetial beefits of improved trasmissios for HEVs ad EVs. For HEVs, a ovel trasmissio developed by Nexxtdrive based o a twi epicyclic desig is aalysed usig a matrix method ad its performace is compared with the more commo sigle epicyclic arragemet used successfully i the Toyota Prius. Simulatio models are the used to compare the performace of a typical HEV passeger car fitted with these two trasmissios over stadard drivig cycles. The coclusio is that the twi epicyclic offers substatial improvemets of up to 2% reductio i eergy cosumptio, though the beefits are sesitive to the drivig cycle used. For EVs, most desigs to date have used a sigle fixed ratio trasmissio, ad surprisigly little research has explored whether multi-geared trasmissios offer ay beefits. The research challege is whether it is possible to optimise the usage of the electric motor i its regio of high efficiecy by cotrollig the trasmissio. Simulatio results of two EV examples cofirm that eergy cosumptio beefits are ideed achievable of betwee 7 ad 4% depedig o the drivig cycle. Overall, the origial aspects of this work the aalysis ad modellig the twi epicyclic gearbox; the aalysis ad modellig the twi epicyclic system i a vehicle ad a compariso of the results with sigle epicyclic system; ad the aalysis ad modellig of EVs with ad without a trasmissio system of varyig levels of complexity have show that there are worthwhile performace beefits from usig improved trasmissio desigs for low carbo vehicles. xv

18 Itroductio. Eergy cosumptio ad emissios Oil plays a fudametal role i the world ecoomy. Although recet estimates vary, there is absolutely o doubt that global cocers about the fiite ature of our oil-based eergy reserves are well fouded (Hirsch, Bezdek et al. 25). Global eergy demad from all sources is expected to icrease by.3 percet per year o average from 25 to 23 (ExxoMobil 27). Apart from the shortage of oil storage, there is equal cocer about the growth i emissios ad terms such as greehouse gases ad carbo footprit are i the ews every day. Overall, the trasportatio sector accouts for aroud 2 percet of curret global fossil fuel CO 2 missios to the atmosphere secod oly to emissios from power productio (IPIECA 24). Accordig to the Techology Strategy Board (TSB), i the UK it is estimated that trasport accouts for 24% of the UK s carbo emissios. Road trasport accouts for 8% of this figure (IME 29). The automotive idustry has bee very resposive to both legislatio ad growig cosumer demads to reduce emissios..2 Need for research o hybrid electric vehicles Hybrid electric vehicles (HEVs) are cosidered to be a itermediate step towards purely electric drive (fuel cells or batteries) (Cole ad Ama 29). Commercial iterest i hybrid vehicle techology has grow at a much more dramatic rate tha was predicted a decade ago. Aroud that time, may idustry observers were substatially more optimistic about a major leap from curret petroleum based techology straight to hydroge, fuel cells ad bio fuel systems. However, it is ow widely accepted that hybrid vehicles will have a sigificat role to play over the ext couple of decades as these other techologies cotiue to be developed. The developmet of power splittig trasmissios (PST) has bee a crucial feature i the techological success of hybrid drivelie vehicles. They have played a key role i facilitatig the maagemet of the mechaical ad electrical power flows, esurig good driveability, providig improved ecoomy ad reducig emissios compared to covetioal iteral combustio egie vehicles.

19 Hybrid electric vehicle techology has made a massive impact over the past decade o the automotive egieerig idustry (Miller 26, Ehsai et al 25). The growth i iterest has bee fuelled by icreasig cocers about the eviromet ad fuel efficiecy savigs. But also, the market uptake of hybrid vehicles led maily by the Toyota Prius has bee much greater tha most observers origially predicted; this i tur has led most of the other origial equipmet maufacturers (OEMs) ad Tier Oe suppliers to develop their ow systems, ofte i collaborative parterships. Although may versios of hybrid vehicle have bee tried, by far the most commo layout is the series/parallel hybrid, i which a IC egie ad electric motor ca either work idepedetly or together. This meas that the trasmissio system must icorporate (a) a power combiig device ad (b) a regeeratio scheme so that the battery ca be recharged either by the egie or by the kietic eergy of the vehicle durig brakig. It is perhaps ot widely recogised, but the trasmissio desig has bee a crucial issue i the success of hybrid vehicles. These trasmissios are also ofte referred to as power split devices (PSD) ad the cotrol strategy to maage all the egie, motor geerator (MG) ad trasmissio elemets is also crucial to the goal of achievig improved fuel efficiecy from the hybrid vehicle compared with that available from covetioal vehicles..3 Need for research o electric vehicles There has bee a massive resurgece of iterest i electric vehicles (EVs) over the past decade. May observers ow see them as the log term solutio to reducig vehicle emissios ad CO 2 usage i compariso to alterative approaches such as hybrid vehicles, fuel cells or biofuels. The public perceptio of electric vehicles has chaged dramatically ad recetly aouced vehicles such as the Tesla roadster ad Chevrolet Volt have reiforced the idea that they are ow becomig seriously competitive products. Not log ago, electric vehicles were still see as iche products ad associated more with milk float techology rather tha a viable passeger trasport alterative (Cha ad Chau 2; Husai 23; Larmiie ad Lowry 23). 2

20 The massive advaces have occurred i battery techology although the progress has bee gradual ad sustaied so that it has ot commoly bee perceived as a major breakthrough. The vehicle rage available with moder battery sets such as Lithium Io is ow typically of the order of 2km, which makes electric vehicles acceptable for much urba use. High cost of the batteries is still a problem ad despite a reletless dowward price tred, the battery sets are ofte supplied o a leasig arragemet rather tha a straightforward purchase. As the electric vehicles market cotiues to grow, the vehicle maufacturers will place icreasig emphasis o searchig for efficiecy gais. This process of cotiual improvemet is cetral to vehicle developmet ad has occurred for example over recet decades with iteral combustio egies; the idustry has achieved fuel cosumptio ad CO 2 emissios figures that were cosidered impossible twety years ago. I all the gree solutios, battery electric cars have the best well-to-wheel efficiecy of both covetioal cars ad hydroge fuel-cell cars. For example, with MWh of electricity, a EV ca drive 5525 km; while usig the same amout of electricity to geerate hydroge ad to drive a fuel cell car, the distace is reduced to 79 km (Radall 29). The electric vehicle part of this research focuses o oe particular area i which efficiecy gais may be achievable for electric powertrais the additio of a gearbox. It is commoly argued that oe of the distict advatages of a electric motor as a motive uit is its torque characteristic; it ca deliver maximum torque from zero speed ad throughout the low speed rage typically up to aroud 2 rev/mi. The, the available maximum torque reduces with speed alog the motor s maximum power curve. This is a much better characteristic tha that associated with iteral combustio egies, which caot deliver useful torque at low speeds ad because of their relatively arrow torque ad power bads must be used with multispeed trasmissios i order to deliver tractive power to the vehicle i a suitable form. Typical electric motors have aother desirable feature their maximum itermittet power is cosiderably higher tha their rated cotiuous power for example, 75 kw compared to 45 kw for the example motor used here. The limitig factor is usually related to cotrollig the amout of heat build-up. Cosequetly, good acceleratio times ca be achieved providig they 3

21 are oly used for relatively short periods a situatio which fortuately is typical of ormal drivig..4 Aim ad objectives The proposed research is focused o trasmissios for hybrid ad electric vehicles. I the HEV part, the research is focused o the NexxtDrive system (Moeller 26) which is marketed as DualDrive for automotive ad off-highway applicatios. The trasmissio provides a cotiuously variable gearbox based o two epicyclic gear sets plus two electric motor/geerator uits. This uique, pateted scheme offers potetial efficiecy beefits over its competitors. It has a crucial beefit of providig two ratios at which the electrical path trasmits o power (ad therefore o losses). A key desig issue is to desig the trasmissio to match the vehicle applicatio such that these two poits occur at commo operatig speeds. The DualDrive system is covered by patet protectio ad potetially has applicatios i other idustrial drive situatios, bicycle drive uits, egie acillary uits etc. It is similar i priciple to the successful Toyota Prius uit, but differs i particular i that the Toyota scheme oly has oe epicyclic gear set. I the EV part, the research is focused o the effect of trasmissios o performace of electric vehicles. The efficiecy curves for a typical electric motor are highly depedet o both speed ad torque ad the motor efficiecy tails off rapidly at low speeds ad torques where its efficiecy might drop to say 5%, whereas i its mid speed ad torque rage it ca be as high as 93%. Cosequetly, it is of iterest to the eergy efficiet vehicle commuity to try ad quatify ay potetial gais from utilisig a gearbox i order to operate the motor for loger periods i its high efficiecy regio. The overall aim of the proposed research is to study the ew type of trasmissio for hybrid electric vehicles ad to ivestigate the effect of trasmissios o electric vehicles. This ca be broke dow ito the followig objectives:. Aalyze the behavior of the twi epicyclic gearbox ad the sigle epicyclic gearbox; 4

22 2. Compare the twi ad sigle epicyclic gear box ad ivestigate the potetial beefits of the twi epicyclic gearbox. 3. Build up Matlab/Simulik models of hybrid electric vehicles equipped with the sigle ad twi epicyclic gearboxes. 4. Compare the overall performace of HEVs fitted with the sigle ad the twi epicyclic trasmissio. 5. Model the powertrai of a geeric electric vehicle ad ivestigate whether the additio of a gearbox results i sigificat values of predicted efficiecy gais. The origial aspects of this work are:. The aalysis ad modellig the twi epicyclic gearbox. 2. The aalysis ad modellig the twi epicyclic system i a vehicle ad a compariso of the results with sigle epicyclic system. 3. Modellig ad aalyzig EVs with ad without a trasmissio system of varyig levels of complexity. 5

23 2 Review of previous work 2. Itroductio I this chapter, previous work o hybrid electric vehicles (HEVs), electric vehicles (EVs), trasmissios for HEVs ad EVs, ad cotrol strategies for HEVs are reviewed. The defiitios ad classificatios for HEVs are summarised ad the mai tools for HEV aalysis are itroduced. For EVs, the curret situatio ad the future treds are aalyzed. Trasmissios for HEVs have received a substatial amout of attetio ad several differet desigs have bee proposed over the past decade. Ad fially, the cotrol strategies for hybrid vehicles, a crucial feature i optimizig performace ad overall efficiecy are reviewed. 2.2 Hybrid electric vehicles 2.2. Defiitio ad classificatio Accordig to Ehsai (Ehsai, Gao et al. 24), A hybrid electric vehicle (HEV) is a vehicle with two or more eergy sources ad eergy coverters, oe of which is electrical. There are at least two power sources a primary power source ad a secodary power source. The primary power source is ormally a thermal eergy source, for example, petrol or diesel for a iteral combustio egie, or hydroge for a fuel cell stack. The secodary eergy source is ormally electricity i a battery or supercapacitors. There are several ways to classify HEVs. From the differet powertrai structure, or the differet eergy flow routes, HEVs ca be classified ito three kids: series hybrid, parallel hybrid, ad series-parallel hybrid (Vaugha 28). Some other authors separate the fourth kid of hybrid complex hybrid (Ehsai, Gao et al. 24; Cha 27). But the defiitios are ot uiversally agreed ad complicatios ca arise i the literature. The structure of each kid of HEV is show i Fig 2.. I series hybrid vehicles, the egie drives the geerator to geerate electricity, which either is stored i the battery, or is supplied to the motor to drive the car. There is o mechaical coectio from the egie to the drive wheels (Fig 2. a). By decouplig the egie from the drivig wheels, the egie ca always work at 6

24 its highest efficiecy poit. But, the eergy is coverted twice, amely mechaical to electrical i the geerator ad electrical to mechaical i the motor. So the efficiecy of these two processes is a major issue for series hybrid vehicles. I parallel hybrid vehicles, both the egie ad motor/geerator are mechaically coected to the drive wheels via two clutches. The propulsio power may be supplied by the egie, the motor, or by both (Fig 2. b). Compared to the series hybrid, the parallel hybrid eeds two propulsio devices the ICE ad the electric motor. But both egie ad motor ca be dowsized to get the same performace. I series-parallel hybrid vehicles, there is a additioal mechaical lik betwee the egie ad the motor, via a geerator. Hece, depedig o the coditios, part of the power from the egie ca be coverted ito electricity to either charge the battery or drive the electric motor (Fig 2. c). Obviously, the series-parallel is more complicated ad more expesive tha the previous two kids of hybrids. But it possesses the advatages of both series ad parallel hybrid. Fig 2. Classificatio of hybrid electric vehicles Accordig to the hybridizatio ratio, amely the level of electric power ad the fuctio of the electric motor, HEVs ca be classified as: micro hybrid, mild hybrid ad full hybrid (Cha 27). For a micro hybrid, the mai fuctio of the electric 7

25 motor, which usually is about 2.5 kw, is for start ad stop, ad the eergy savig may reach about 5% to %. I a mild hybrid, the motor is about -2 kw. The motor ca replace the origial flywheel of the egie, ad add to the propulsio as i the parallel hybrid system. A mild hybrid ca achieve eergy savig of amout 2% - 3%. For a full hybrid, which ca save eergy about 3%-5%, the motor power is about 5 kw. I this desig, the motor aloe mode is used for start up ad mid-rage speed drivig. A summary of classificatio of HEVs is show i Table 2.. Table 2. Classificatio of HEVs Drivetrai structure Hybridisatio ratio Positio of the motor ad the trasmissio The method of refuellig the eergy Classificatio Series hybrid Parallel hybrid Series-parallel hybrid Micro hybrid Mild hybrid Full hybrid Pre-trasmissio hybrid Post-trasmissio hybrid Petrol statio refuellig Plug-I hybrid (PHEV) Examples Toyota Coaster Hybrid bus, Chevy Volt Hoda Isight Ford Escape, Toyota Prius, Ferrari hybrid Citore C3, Chevrolet Silverado, GM Satur VUE Gree lie, ew BMW X & Smart MHD Hoda IMA (Itegrated Motor Assist) system (Civic, Isight), Toyota Crow, Chevy Malibu, BMW ED Nissa Tio, Toyota Estima, Toyota Prius & Ford Escape, Lexus RX I mild hybrid HEVs GM Autoomy(i-wheel motor) Most of curret HEVs BYD F3DM, Reault Kagoo Accordig to the positio of trasmissio ad motor, the hybrid ca be classed as pre-trasmissio (the motor is ahead of the trasmissio) ad posttrasmissio (the motor is behid the trasmissio) (Miller 24; Ehsai, Gao et al. 27). 8

26 Accordig to the method of the refuelig the eergy, HEVs ca be classified as gas statio refuelig ad plug i hybrid (PHEV)(Cha 27). PHEV is becomig a popular topic i recet years ad most of the global OEMs have developmet programmes. I December 28 i Chia, BYD Auto started sellig the world's first mass-produced plug-i hybrid vehicle, the BYD F3DM, produced for the domestic Chiese market. A Toyota plug-i hybrid is plaed to be available commercially i 29. (Friedma 23) summarised a checklist to check whether a vehicle is a hybrid or ot, which is show i Table 2.2. The vehicle that has two checkmarks is described as a muscle-hybrid, which is a America term, ad is similar i defiitio to a micro-hybrid. Geerally speakig, hybrids with more checkmarks obtai higher fuel savig rates ad less emissios. But the best way to judge a vehicle is the practical performace o ormal road coditios. Table 2.2 Hybrid checklist: is this vehicle a hybrid?(friedma 23) Hybrid vehicle developmet Hybrid vehicle techology is a relatively ew aspect of automotive egieerig; most of the developmets have occurred over the past 2 decades. The ladmark date was probably 997 whe Toyota itroduced the first commercial hybrid, the Prius. Despite its relative ewess i automotive techology, iterest has grow at a staggerig rate. This is reflected i the fact that there are several excellet textbooks o hybrids (Husai 23; Ehsai, Gao et al. 24; Miller 24; Guzzella 9

27 ad Sciarretta 27) ad the uderpiig electric vehicle techology (Cha ad Chau 2; Larmiie ad Lowry 23). Hybrid vehicle techology ievitably ivolves a systems-desig approach, based o a collectio of compoets such as: i) Petrol, diesel egies ii) Electric motor/geerator uits iii) Batteries iv) Supercapacitors, ultracapacitors v) Fuel cells vi) Electrical compoets, e.g. iverters Needless to say, there remais a vast rage of viewpoits about the relative merits of competig schemes. There have bee several excellet review papers published recetly (Chau ad Wog 22; Friedma 23; Miller 26; Va, Maggetto et al. 26; Cha 27; Ehsai, Gao et al. 27). Key topical questios iclude: i) Will fuel cells have a future give the hydroge storage/ifrastructure problems? ii) Ca telematics-eabled covetioal powertrais compete with hybrids (Mazie, Watso et al. 27)? iii) Are mild hybrids (highly efficiet diesels, itegrated starter alterator(isa), regeeratio) more cost-effective tha full hybrids (Cho ad Vaugha 26b; Chau ad Cha 27)? iv) Are plug-i hybrids becomig commercially attractive (Goder, Markel et al. 27; Shabashevich, Saucedo et al. 27)? Hybrid vehicle aalysis The worldwide debate about hybrid powertrais has led to a proliferatio of research i aalysig ad predictig vehicle performace. This i tur has led to the developmet of several software packages specifically aimed at modellig the eergy maagemet i hybrid drivelies (Gao, Mi et al. 27). The best kow of these is probably ADVISOR (Wipke, Cuddy et al. 999; Markel, Brooker et al. 22), developed i 999 by the US NREL ad based o Matlab/Simulik blocks.

28 Other well-kow codes iclude the QSS-Toolbox (QuasiStatic Simulatio Toolbox) (Rizzoi, Guzzella et al. 999) ad PSAT(Powertrai system aalysis toolkit) sposored by the US Departmet of Eergy (Argoe 27), both of which also use Matlab/Simulik. Further codes iclude PSIM, Simplorer ad V-ELPH (Gao, Mi et al. 27). 2.3 Electric vehicles The curret level of iterest i Electric Vehicles (EVs) could hardly be overstated as maufacturers ad govermets aroud the world appear to have icreased iterest at a substatial rate. The historical perspective of EVs is a fasciatig egieerig story; few people realise that they pre-dated Iteral Combustio (IC) egie powered vehicles ad were commercially available at the ed of the 9th cetury. A electric car eve held the world lad speed record i 899 ad was the first car to exceed oe mile per miute! At this time, for a give power output, oe oly had to compare the size ad complexities of three competig devices electric motor, IC egie ad steam egie to realise that the electric motor was a clear wier. Nevertheless, its dowfall whe deployed i a vehicle was the eergy storage usig rechargeable batteries; the specific eergy (Wh/kg) of gasolie is aroud 3 times higher tha that of the origial lead acid batteries. There are several excellet refereces (Cha ad Chau 2; Westbrook 2; Husai 23; Larmiie ad Lowry 23) recoutig the story of electric vehicle developmet up to the preset day. The resurgece of curret iterest i the early part of the 2st cetury has bee drive by both political ad techological developmets, amely a requiremet to cotrol global emissios ad the emergece of ew battery desigs with improved specific eergy, eergy desity ad rechargability properties. Oe of the great advatages of the electric motor is its torque characteristic; it provides maximum torque from zero up to low speeds, ad the it is govered by the maximum power available as motor speed icreases. This has two sigificat advatages over the typical torque-speed properties of the competig IC egie: i) It provides fudametally a more desirable characteristic spread of torque over the speed rage i cotrast to the peakiess of a IC egie.

29 ii) It removes the eed for ay additioal trasmissio clutch or gears. Cosequetly, the vast majority of curret EV desigs to date have exploited this advatage ad the motor is usually coected to the drive wheels via a sigle reductio ratio ofte icorporated i the differetial uit. This advatage of the electric motor is further helped by the fact that most motors have two ratigs a itermittet high power curve ad a lower cotiuous power curve, ormally costraied by heat dissipatio. So, high torques are always available for good acceleratio, particularly from low speeds, ad the vehicle top speed is cotrolled by the torque o the cotiuous power curve, so the fixed reductio gear is ormally selected to cotrol this. However, oe of the mai coclusios to emerge from the plethora of research work ito eergy efficiet vehicles is that it is ecessary to pursue every possible aveue for mior efficiecy gais. The poit is the that oly whe all these gais are added together does the vehicle begi to show worthwhile advatages. A classic case study to uderlie this coclusio is to compare two cotrastig approaches to eergy efficiet vehicles (i) a full hybrid, e.g. Toyota Prius ad (ii) a covetioal state of the art diesel vehicle, e.g. BMW8d. The Toyota Prius is a highly sophisticated hybrid desig usig a combiatio of a IC egie based o the Atkiso cycle, coupled with two electric motors ad a uique epicyclic gearbox. The BMW8d is a covetioal vehicle with a diesel egie modified for high efficiecies particularly at part load, a covetioal trasmissio, stop-start arragemet ad some regeeratio capability. For both these vehicles all the iput eergy derives from the fuel iput although they have very differet ways of maagig the efficiet usage of it but crucially they both support the key issue that research ito eergy efficiet vehicles depeds o the pursuit of all aveues of efficiecy gais together. Returig to the case of EVs, it is therefore of iterest to ivestigate whether it is possible to maage the efficiecy of the electric motor, so that by usig a itermediate gearbox the motor is operated more ofte i its higher efficiecy regio. I similar fashio to HEVs, plug-i EVs have also become a very topical subject. For example, the i MiEV from Mitsubishi Motors has bee commercially produced 2

30 ad 2 of these vehicles have bee put ito the UK for test drivig. Usig the oboard charger, the vehicle ca be charged with a V or 2 V power source i the home. The rage over oe of the drivig cycles, Japa -5, for oe charge is 6 km, which is eough for most commutig applicatios. For example, i the Uited States, half of U.S. households have a daily mileage of uder 3 miles per day; 78 percet of daily work commuters travel 4 miles or less (Babik 26). 2.4 Trasmissio desigs Cotiuously Variable Trasmissios (CVTs) have bee aroud for may years some authors claim that Leoardo da Vici sketched a desig cocept over 5 years ago. However, although the first patet was filed i 886, CVTs did ot have ay commercial impact util DAF produced a CVT car based o a pulley ad rubber belt priciple i 958. Iterest i the US followed much later i 989 whe the Subaru Justy offered a CVT because US vehicles had bee domiated by covetioal automatic trasmissio systems for may decades. The cost-beefit issues relatig to CVTs are well uderstood. The potetial advatages are improved performace, ecoomy ad emissios or more importatly a improved compromise betwee them. Their disadvatages have bee cost, complexity, oise ad drivig refiemet. Oly over the past five years or so has the developmet of CVTs reached a stage at which they are begiig to be geuiely competitive with the alteratives, e.g. covetioal, torque coverter automatics ad automated maual gearboxes, such as the twi clutch VW DSG system. There are several geeric approaches to CVT techology: i) Variable pulleys usig rubber or steel belts (e.g. DAF, Audi, GM, Hoda, Nissa) ii) Toroidal schemes usig the frictio betwee discs ad rollers (e.g. Torotrak, Nissa Extroid) iii) Hydrostatic usig variable displacemet pump ad motors (Torvec IVT) iv) Hydromechaical usig a cotrolled power split betwee mechaical ad hydrostatic compoets (e.g. agricultural, all-terrai vehicles) 3

31 v) Electromechaical usig epicyclic gears plus electric motor/geerator systems (e.g. Toyota Prius, NexxtDrive) 2.4. Trasmissios for HEVs The first successful electromechaical PSD trasmissio is geerally credited to TRW (Gelb, Richardso et al. 97). The key feature is to use a epicyclic gear to combie the power from the egie ad two MG (motor/geerator) uits. Note that two MG uits are required i order to exercise sufficiet cotrol of both speeds ad torques i the system. The trasmissio effectively has two fuctios it provides a cotiuously variable gear ratio over a certai rage ad it selects the balace of torques, ad hece powers, applied to ad from the drive wheels by the egie ad MG uits. The Toyota Prius, itroduced i Japa i 997, used this trasmissio desig, with a IC egie of 52 kw ad MG uits of 33 ad kw, ad is ow widely recogised as makig it commercially successful (Ioue, Kusada et al. 2; Miller ad Miller 25). Further developmets have occurred sice the Prius was itroduced, ad there are ow two geeric types of power splittig trasmissios used i hybrid vehicles the sigle ad dual mode desigs. Examples of these, icludig the latest developmets are discussed here. Toyota Prius, THS desig sigle mode Because of the commercial success of the Toyota Prius, this trasmissio arragemet is the most commo layout used i the idustry; it has already bee used by several other maufacturers i their hybrid vehicle desigs. The layout is show diagrammatically i Fig 2.2. I this research, R, C, S represet the rig gear, the carrier ad the su gear respectively. Fig 2.2 Toyota Prius, THS arragemet 4

32 The clever feature of this relatively simple lookig arragemet is that (a) it cotrols the split of power betwee the mechaical ad electrical paths ad (b) it offers a ifiitely variable trasmissio ratio by cotrollig the relative speed of the su, carrier ad rig gears of the epicyclic. A lot of the other challegig desig aspects which are ot show i Fig 2.2 relate to the cotrol of the differet elemets ad the ievitable compromise betwee achievig good driveability together with high levels of efficiecy. Basically, this system ca be characterized by five mai modes of operatio. i) Electric drive the IC egie is off ad the battery powers MG2 ad hece the vehicle. ii) iii) iv) Normal drive, cruisig the IC egie is o; the tractive power is a summatio of the mechaical path directly from the egie plus the electrical path from the MG2 motor. The egie also supplies power to drive MG which acts as a geerator to supply MG2. Power boost, acceleratio this is similar to mode 2 except that torque delivery to the drive wheels is give priority, so for example, the battery will be used to supply the MG uits for these periods. Battery charge, idle the IC egie simply drives MG as a geerator to supply curret to charge the battery, depedig o its state of charge (SOC). v) Negative split i this case, both MG ad MG2 ca act as motors, which results i a lower IC egie speed, or egie luggig, as a meas of optimizig fuel ecoomy. A example of the speed ratios for this system is show i Fig 2.3. The Trasmissio Ratio (TR) is defied as (iput speed/output speed) for the gearbox. Normally, the iput is coected directly to the egie ad the output is coected to a fial drive, differetial uit. There is oe poit o these curves which is of particular iterest, because at this poit all the power is trasmitted by the mechaical path. It occurs for the example show i Fig 2.3 at a TR of.72, at which poit the speed of MG is zero, ad although MG2 is still turig, it ca be cotrolled to spi freely. As a rough guide, the mechaical efficiecy of a typical gear set is aroud 98%, compared to a overall efficiecy of aroud 8% for the 5

33 electrical path. Hece, the desig choice of this ratio is extremely importat; it is usually chose to optimise ecoomy o oe of the established idustry-stadard drive cycles. Fig 2.3 Trasmissio speed ratio limits of the THS system (Cho, Ah et al. 26a) GM Alliso, AHS system dual mode The additio of clutches to a trasmissio based o two epicyclic gear uits opes up a opportuity to fudametally chage the power flow through the system (Miller ad Miller 25). A example is show i Fig 2.4. Fig 2.4 GM Alliso AHS arragemet Basically, the two modes of operatio are usually referred to as: i) Low rage iput power split ii) High rage compoud power split I the first of these iput power split, the trasmissio behaves i exactly the same way as the sigle mode system. I the secod compoud split mode the su gear (S) is coected via MG to rig gear 2 (R2). The ability to switch 6

34 betwee these two modes smoothly is a crucial aspect of this desig, ad this is usually referred to as sychroous shiftig. I other words, the clutches are shifted whe the MG speeds are zero, such that torque trasfers ca take place without ivolvig sudde speed chages. The beefits of this system are. i) A low ad high rage is available without the eed for a gear shift. The low rage is used for startig, low speeds ad reverse, whereas the high rage is used for highway operatio, grades ad towig. ii) The required speed rages of the MG uits are reduced. iii) The MG uits ca be iductio type machies. iv) I the compoud split arragemet, less power is trasmitted via the electrical path, so the motor size ca be reduced ad overall electrical losses reduced. Geeric dual mode + 4 fixed ratios systems A iterestig software package for geeratig ovel trasmissio desigs has bee developed by GM Research ad Developmet Laboratories (Raghava, Buckor et al. 26; Raghava, Buckor et al. 27). Oe of the examples described i these papers is a dual mode system which also offers four fixed gear ratios. The desig is show i Fig 2.5, ad it emphasises the potetial beefits of the software, because (a) this arragemet is rather complicated, (b) it is ot ituitively obvious to uderstad exactly how it will meet the performace specificatios ad (c) it is ot a desig that would aturally be proposed usig traditioal desig methods. Fig 2.5 Geeric dual mode + 4 fixed ratios arragemet GM/DC/BMW system - dual mode 7

35 Oe of the latest developmet of a dual mode system was aouced i 26 (Nitz 26a; Nitz, Truckebrodt et al. 26b), as the result of a cosortium agreemet betwee these three major vehicle maufacturers. It ivolves the additio of a third epicyclic gear uit ad a total of four clutches. The beefits of this additioal complexity are related to the additio of four fixed gear operatig modes as well as the retetio of two rages of cotiuously variable trasmissio capability. Overall, therefore this system offers six methods of operatio. i) Iput-split ecvt mode, or cotiuously variable mode, operates from vehicle lauch through the secod fixed gear ratio. ii) Compoud-split ecvt mode, or cotiuously variable mode 2, operates after the secod fixed gear ratio. iii) First fixed-gear ratio with both electric motors available to boost the iteral combustio egie or capture ad store eergy from regeerative brakig, deceleratio ad coastig. iv) Secod fixed-gear ratio with oe electric motor available for boost/brakig. v) Third fixed-gear ratio with two electric motors available for boost/brakig. vi) Fourth fixed-gear ratio with oe electric motor available for boost/brakig. Fig 2.6 GM two mode hybrid trasmissio with 4 fixed gear ratios Full details of this trasmissio buildig upo substatial experiece with oe ad two mode trasmissios were recetly released by GM (Grewe, Colo et al. 27). It is particularly suited to larger vehicles, such as full size SUVs (sport utility 8

36 vehicles) ad persoal trucks, where towig ad high cotiuous egie power coditios are importat aspects of the vehicle capabilities. The rage of fixed gear ratio optios meas that more reliace ca be placed o the mechaical power trasmissio path, thus reducig the extreme, cotiuous duty motor requiremets of other systems without sacrificig fuel ecoomy. These claims are supported (Grewe et al 27) by power ad ecoomy calculatios for a large GM SUV over the EPA Urba, EPA Highway ad US6 schedules. I the loger term, the cosortium believes that this arragemet will set a ew idustry stadard for hybrid vehicle trasmissios. Bosch Dual-E trasmissio Bosch have recetly aouced a ew prototype trasmissio system called Dual-E, which is described i a paper by Schultz (Schulz 24; Schultz 26). I Schultz s work, two separate epicyclic gear uits are coected with a 5 speed automated maual trasmissio (AMT). This differs from the NexxtDrive system studied here i which two epicyclic gear uits are directly coected together ad ot coected to a AMT. The Dual-E system is show i Fig 2.7. Each motor geerator uit plus epicyclic gear uit cotrols oe of the mai gearbox shafts. Hece, overall it offers a total of five fixed gear rages plus a ifiitely variable capability withi each rage. For a mid size saloo, the motor geerator uits are rated at 8 kw each. The beefits of this system are high efficiecy because the power used i the electrical path ca be miimised ad a wide rage of trasmissio ratios. Gear chages i the AMT whe ecessary are performed automatically without tractio iterruptio Trasmissios for EVs The possible cofiguratios of EVs are show i Fig 2.8 (Ehsai, Gao et al. 24), from which it ca be see that maily two types of trasmissios are used o EVs: multi-gear trasmissio ad sigle-gear trasmissio. Curretly, sigle gear trasmissios are used o most EVs. For example, o the Gulliver U5 desig from Tecobus, the trasmissio is a sigle gear with a fixed ratio of :4.37. For cofiguratios like Fig 2.8 (a) ad (b), a electric propulsio motor replaces the IC egie of a covetioal vehicle drive trai. The multi-gear trasmissios here were origially desiged for a egie, ot especially for electric motors. It is 9

37 perhaps surprisig, but there is very little published research o the potetial beefits from fittig trasmissios ito the drivelies of electric vehicles. Fig 2.7 Bosch Dual-E trasmissio (Schultz 26) Fig 2.8 Possible EV cofiguratios (Ehsai, Gao et al. 24) 2

38 Oe of the few published reports of work i this area was recetly published i Jue 29 (Hoeywill 29). It describes work by a UK compay, Vocis, o the developmet of a two speed gearbox suitable for a 7kW delivery va applicatio. It highlights oe of the importat problems of the actuator required to switch betwee gear ratios, assumig that this would be automated rather tha uder maual cotrol. The authors refer to simulatios idicatig a claimed 5 to % reductio i eergy cosumptio over the NEDC cycle. No details are give, but these figures appear to be i lie with the results reported later i this thesis. 2.5 Cotrol strategies 2.5. Importace of cotrol strategy Implicit i the desig of hybrid vehicles is the fact that there are o magic eergy sources! Hece, the desig philosophy is based o maagig the eergy from gasolie egies, electrical storage, fuel cells more effectively somehow. This overall effectiveess is usually judged agaist oe of the so-called stadard drive cycles i the EU, USA or Japa to eable fair comparisos to be made. Hece, the cotroller desig is absolutely cetral to the overall effectiveess of a hybrid powertrai. The aim of this sectio is to review recet cotributios (sice 2) ad summarise the curret state of the art i cotroller strategy ad desig. The review focuses o cotrol techiques ad their usefuless both for aalytical ad practical situatios. I the mai text of this sectio, little referece is made to authors claims about the performace improvemets of their systems. This is because they ca be misleadig; i order to make iformed judgmets about improvemets it is ecessary to kow all the details of the modelig, assumptios ad drivig cycles used. However, some overall commets about relative performace are icluded i sectio Cotroller desig The geeric structure of a hybrid vehicle cotrol system (Pagaelli, Ercole et al. 2; Koot, Kessels et al. 25; Pisu ad Rizzoi 27) is show i Fig 2.9. The first, ad by far the most commo hybrid vehicle cotrol system, is a rulebased approach largely based o egieerig ituitio. The potetial problem with 2

39 this approach is that it is difficult to fie-tue the rules without ay further help from more rigorous mathematical approaches. There have also bee several attempts to ehace this rule-based strategy by usig more formal techiques such as Fuzzy Logic (FL), or Neural Networks (NN). Fig 2.9 The geeric structure of a hybrid vehicle cotrol system The secod approach is usually referred to geerally as Static Optimisatio. This uses quasi steady coditios ad obtais poits which are optimum i some sese. This may, for example, be optimum fuel ecoomy with details of eergy usage betwee the electrical ad mechaical paths. However, because it is a relatively simple poit-wise approach, it is possible to exted the optimisatio to icorporate both ecoomy ad emissios for example. This is also ofte referred to as Sequetial Quadratic Programmig (SQP) ad has the potetial disadvatage that it is ot robust agaist disturbaces. The third, ad most sophisticated approach, is Dyamic Optimisatio. This deals with trasiet coditios typically over a specified time frame; i the case of vehicle studies this usually ivolves oe of the well kow idustry stadard drive cycles. There are a rage of detailed approaches to this particular problem uder the geeral headig of Dyamic Programmig (DP). Most recet cotributios agree that this approach is computatioally itesive ad that although it results i a global optimisatio of the cotrol problem, it is ot possible to directly implemet it as a real time cotroller. Some observers argue therefore, that it is ot a 22

40 practical approach, because it requires a priori kowledge of the iput profile speeds, acceleratios, grades etc i this case. However, others argue that it is valuable for two reasos. First, it provides a bechmark of the best performace that is achievable; hece other cotrol schemes ca be assessed agaist this yardstick. Secod, it ca lead to suggestios for improvemets i the rule-based strategies that may ot have bee apparet from egieerig ituitio. Ideed, there have bee several recet research projects which attempt to exploit a combied SQP ad DP aalysis to develop a practical rule-based plus fuzzy logic cotroller. Rule based (RB) cotrol The rule based approach is ofte described as a heuristic cotrol strategy. It has bee described i may recet papers (Li, Filipi et al. 2a; Li, Filipi et al. 24; Zhag, Li et al. 26; Zhu, Che et al. 26; Ah, Cha et al. 27; Hofma, Steibuch et al. 27a; Hofma, Steibuch et al. 27b), although most of these papers also cotai comparisos with other cotrol techiques. I the developmet of practical prototype vehicle systems, the majority have used rulebase cotrollers, although details are rarely published because of commercial aspects. Hece, it is curretly by far the most commoly implemeted o-lie approach. It is based o a set of rules, usually implemeted as ests of if-the-else statemets. The system compoets ca be described by parametric or empirically derived maps, ad the cotroller largely cotrols the switchig betwee differet modes, e.g. egie power, motor power, battery chargig or eergy regeeratio. Because the rules are specific to a particular applicatio they require cosiderable calibratio ad are ot usually trasferable. The work reported i (Zhag, Li et al. 26) is iterestig i that it applies a RB scheme to a hybrid vehicle fitted with a ovel trasmissio based o a sigle epicyclic gear, sigle motor/geerator uit ad 4 fixed gears. Predictios usig ADVISOR compare the results of this drivetrai with that of the stadard Prius ad show that over 6 typical drivig cycles, fuel ecoomy improvemets of aroud 2-5% are available. Rule-based plus Fuzzy Logic 23

41 The use of a fuzzy logic cotroller eables the rule-based approach to be improved sice it removes the restrictio for hard o/off type rules. It is well kow for its robustess ad ability to deal with o-liear systems ad timevaryig compoets ad hece, it appears well suited to the hybrid powertrai problem. Several recet papers have used fuzzy logic cotrol (Bauma, Washigto et al. 2; Wo ad Lagari 22) with a variety of views of how to set the membership fuctios to trade off acceleratio, power split, eergy/fuel usage, emissios ad battery state-of-charge. Refereces (Salma, Schoute et al. 2; Kheir, Salam et al. 24) used a set of 44 rules i a attempt to balace fuel usage ad emissios as a performace idex, ad also used the Matlab PSAT (Power System Aalysis Toolbox) rule-based cotroller for compariso. I (Rajagopala, G. et al. 23), the fuzzy logic cotroller was derived as a NREL(Natioal Reewable Eergy Laboratory, USA) project for use i the ADVISOR package. Rule-based plus Neural Network (NN) The Neural Network approach has bee used together with both rule-based ad DP systems. I (Suzuki, Yamaguchi et al. 27), the NN was traied o the hardware fitted to a light duty hybrid truck, i particular to model the fuel usage ad electric curret. This was the used to assist a covetioal rule-based cotroller i drivig coditios away from the ormal regios represeted i the stadard drivig cycles. I (Hug, Tsai et al. 27), the NN was tued usig the results from a DP cotroller over the 5 drivig cycles used i ADVISOR. The iputs were 4 idices velocity average ad stadard deviatio, acceleratio stadard deviatio ad stadstill time ad the outputs were 3 polyomial coefficiets. A very differet approach was used i (Arsie, Graziosi et al. 24) where a Recurret NN was used to cotiuously predict the vehicle load. It was argued that this iformatio could the effectively be fed to a DP cotrol algorithm, which could the be implemetable as a o-lie cotroller. Equivalet Cosumptio Miimisatio Strategy (ECMS) 24

42 This techique is based o the cocept of combiig the eergies from the IC egie ad electrical machies o the same scale, by defiig equivalet fuel cosumptio. I this way, a sigle cost fuctio ca be formulated i order to apply covetioal optimisatio techiques (Delprat, Guerra et al. 2; Sciarretta, Back et al. 24). The priciple behid this approach is show i Fig 2. for the case of battery discharge ad Fig 2. for the case of battery recharge (Musardo, Rizzoi et al. 25). The path o the left side of each figure shows the equivalet route by which eergy is stored ad restored to the system. Of course, there are losses ivolved i all the coversio processes, ad these losses are differet i the chargig ad rechargig directios; cosequetly there are some approximatios that eed to be made i this equivalece approach. The results for the HEV over 6 stadard drivig cycles are show i Table 2.3. Fig 2. Eergy paths for equivalet fuel cosumptio calculatio durig battery discharge 25

43 Fig 2. Eergy paths for equivalet fuel cosumptio calculatio durig battery charge Oe of the potetial difficulties is i dealig with the battery state of charge (SOC), which effectively provides costraits sice it should remai withi a fixed rage. Also, it is importat i calculatig comparative results that the fial ad iitial battery states are the same, i order that there are o hidde eergy losses or gais. I Pagaelli s research (Pagaelli, Guerra et al. 2b), the predicted results from a ECMS cotroller are compared favourably with results derived from a optimum cotroller (Delprat, Lauber et al. 24). I Pagaelli s research (Pagaelli, Guerra et al. 2b), a adaptive term is added to provide a A-ECMS cotrol scheme which deals with the battery state of charge by varyig a cotrol parameter based o a fuctio of the road load. Agai, the results are compared with those from a optimal DP solutio, but the authors make the iterestig poit that although they use a sophisticated vehicle model, based o the VP-SIM code (Rizzoi 2) for the A-ECMS calculatios, the DP code must use a much simpler vehicle model i order to restrict the computig times; hece, the two solutios are ot exactly comparable. I Hofma s research (Hofma, Steibuch et al. 27a; Hofma, Steibuch et al. 27b), a ovel cotroller (RB-ECMS) based o a combiatio of rule based ad 26

44 ECMS systems is itroduced. This overcomes the difficulties of each idividual approach i that they are sesitive to the iput topology. Effectively, the RB-ECMS provides a collectio of drivig modes selected through various states ad coditios. It is based o oe decisio variable the maximum propulsio of power of the secodary power source, i.e. motor/battery durig pure electric drivig. The proposed cotroller the requires o tuig of the threshold values ad variables ad is implemetable i real time. Simulatio results predicted usig ADVISOR for the Japaese cycle show that it achieves a 2% improvemet over the RB scheme ad achieves the same (withi % accuracy) of the performace of the optimum DP cotroller. Dyamic Programmig (DP) The overall eergy maagemet of a hybrid electric vehicle ca be viewed as a global optimisatio problem. The performace idex is liked to miimisig the fuel cosumptio ad emissios outputs. The cotroller specifies the commads ad settigs, e.g. power split betwee IC egie ad electric motor, which achieves this goal, withi certai costraits, e.g. battery state of charge. Sice a typical drivig cycle lasts several miutes, it is ecessary to repeat this calculatio may thousads of times. The DP techique is well suited to this problem. Also, the DP algorithm is based o a global solutio which requires a specific time frame over which the problem is kow. Thus, it appears highly appropriate for a specific drivig cycle where the complete iput profile is defied. However, as metioed previously, this comes with two mai drawbacks; (i) it is extremely computatioally itesive ad (ii) it caot be implemeted i real time sice it requires a priori kowledge of the iput. Applicatios of the Dyamic Programmig approach have bee reported may times i the literature over recet years (Li, Filipi et al. 2a; Li, Filipi et al. 24; Scordia, Besbois-Reaudi et al. 25; Zhu, Che et al. 26; Perez, Bossio et al. 26a; Perez, Bossio et al. 26b; Pu ad Yi 27). Ofte the results from the DP solutio have bee used as the bechmark agaist which to compare other implemetable, but sub-optimal, cotrollers. For example, at the Uiversity of Michiga (Li, Kag et al. 2b; Li, Kag et al. 23), the DP geerated results have bee cleverly used to iform the developmet of ear- 27

45 optimum rules which are the implemetable i a real time cotroller, usig their ow software package, HE-VESIM, a hybrid electric vehicle simulatio tool. Because of the argumet that the DP approach is ot implemetable sice its optimality is liked to a specific drivig cycle, further recet work at Uiversity of Michiga (Li, Filipi et al. 24) has expaded it to treat it as a ifiite horizo stochastic optimisatio problem. The power demad from the driver is treated as a radom Markov process. It is show how the optimal cotrol solutio ca de derived from this Stochastic DP techique, leadig to a full state feedback scheme which i priciple could be implemeted as a real time cotroller. Predicted results are geerated both for a hybrid diesel truck (Li, Filipi et al. 24) ad a fuel cell powered, medium size SUV (Li, Kim et al. 26). Others The Geetic Algorithm (GA) approach which is a probabilistic global search ad optimisatio techique, based o atural biological evolutio, has bee applied to the HEV drivelie maagemet problem. However, because it is ot suitable for costraied optimisatio, the costraits i the HEV model have, for example (Motazeri-Gh, Poursamad et al. 26) bee dealt with as pealty fuctios. I aother study (Ippolito, Loia et al. 23), a so called fuzzy clusterig criterio was used with GA to develop a kowledge based cotrol strategy. Fially, i yet aother versio (Wag 25), a Pareto domiace cocept was combied with GA to result i a multi objective optimisatio problem formulatio. However, o balace the cosesus is that GA techiques are ot well suited to the HEV cotrol case. Other variatios o the various detailed approaches to optimal cotroller desig have bee tried, e.g. Sequetial Quadratic Programmig (Oh, Mi et al. 27), simulated aealig (Pagaelli, Guerra et al. 2b), Pareto optimality (Ah, Cha et al. 27), Potryagi s miimum priciple (Wei, Guzzella et al. 27) ad direct trascriptio approach (Perez ad Pilotta 27) Discussio The recet work o HEV cotrol reviewed here is domiated by theoretical studies aimed at improvig cotroller desig over the early rule-based systems. It 28

46 is clear that there are two distictly differet types of modelig simulatio commoly referred to as backwards ad forwards facig. I the backwards approach, the vehicle speed is kow ad the required powers throughout the system are calculated. This techique clearly suits the HEV problem where comparisos are most commoly made usig oe of the stadard drivig cycles. I the forwards approach, the iput is a driver commad which the results i the vehicle performace as a output. This is clearly more represetative of the ormal drivig situatio ad is useful for predictig the performace of real time cotrollers. If this techique is used over a drivig cycle, the a driver model is eeded ofte a simple PI (proportioal-itegral) cotroller is used. Oe of the importat issues which is ot well covered i the literature is drivability. Of course, it is a difficult subject sice it relies heavily o driver subjective judgemets, but it is crucial i the commercial acceptace of ay cotroller which has primarily bee optimized aroud eergy maagemet ad emissios targets. A useful research goal would be to specify some objective targets which correlated well with driver subjective assessmets ad which could the be used to quatitatively assess cotroller desigs. Some work has bee doe i this area i relatio to Ifiitely Variable Trasmissios (IVT) (Cacciatori, Boet et al. 25a; Cacciatori, Boet et al. 25b) ad objective assessmets based o driver step iputs of various levels of throttle demad at (a) rest, (b) slow speed ad (c) deceleratio have bee suggested. Such assessmets would require a forwards facig simulatio approach. A related potetial problem of the much used backwards simulatios is that it is possible for the optimum solutio at each icremet to jump betwee solutio poits. I practice, this would imply o-smooth trasitios durig ormal drivig. I fact, this is recogized i (Sciarretta, Back et al. 24) ad a additioal pealty is icluded for the IC egie stoppig ad startig. Aother importat issue which is ot well covered is brakig behaviour. It is rather straightforward to aim for maximum eergy recovery i ay cotrol scheme. However, i ormal drivig this must be bleded smoothly with the covetioal brakes. It is aother key aspect of overall drivability. Also, there will ievitably be occasios whe regeeratio is ot possible because of the battery SOC or temperature. This issue is discussed i (Kim, Kim et al. 27) who also raise the 29

47 potetial problem of iteractio betwee the regeeratio algorithm ad the yaw stability cotroller. Table 2.3 Predicted results usig VP-SIM for a 3 kw hybrid SUV over 6 stadard drivig cycles (Musardo, Rizzoi et al. 25) Percetage improvemet i fuel ecoomy over the pure thermal (egie) mode Drivig cycle DP Tued ECMS (sigle parameter) FUDS FHDS ECE EUDC NEDC.7.7. JP Adaptive ECMS 2.6 Methods to aalyse gearbox used o HEVs 2.6. Descriptio of epicyclic gear set Epicyclic gearig, also called plaetary gearig, is widely used i vehicle trasmissio systems. For example, most covetioal automatic gearboxes utilise epicyclic gear sets. A plaetary gear trai is defied as ay gear trai cotaiig at least oe gear that orbits by rotatig about its ow axis ad also about the axis of a arm, or carrier (Corey 23). Examples of simple ad complex epicyclic gear sets are show i Fig 2.2. Fig 2.2 A simple ad a complex epicyclic gear set (Corey 23) There are three kids of compoets i a epicyclic gear trai: i) The su gear ii) Plaet gears ad the plaet carrier, or the arm iii) The rig gear, or the aulus 3

48 Each of the three kids of compoet ca be used as the iput, output, or kept statioary. Differet gear ratios ca be achieved by choosig each compoet to play a differet role. I a automatic trasmissio, clutches ad brake are used to hold differet compoets statioary ad chage the iput ad output, thus chagig the trasmissio ratio. Compared to the covetioal gearbox arragemet, the epicyclic gear set has may advatages, such as high speed reductio, gear shiftig while the vehicle is i motio, ad structural compactess (Tia ad Lu 997). The epicyclic gearig is also used i the Power Split Device (PSD) i hybrid vehicles. Toyota used the PSD i the hybrid model Prius, which was lauched i 997. A dual mode PSD similar to the Toyota Prius has also bee studied (Mashadi ad Emadi 29). Geeral Motors have also desiged several ew trasmissios based o the epicyclic gear set (Raghava, Buckor et al. 26) Lever aalogy A method to aalyze trasmissios called the lever aalogy was itroduced i 98 (Beford ad Leisig 98). I this method, a etire trasmissio ca usually be represeted by a sigle vertical lever. The iput, output ad reactio torques are represeted by horizotal forces o the lever, ad the lever motio, relative to the reactio poit, represets rotatioal velocities. Fig 2.3 Simple epicyclic gearset ad aalogous lever diagram The procedure for settig up a lever to a trasmissio is: replace each gearset by a vertical lever, the rescale ad coect levers accordig to the gearsets 3

49 itercoectios. The horizotal force ad the velocity relatioships of the lever are idetical to the torque ad rotatioal velocity relatioships of the gearset. For example, for a simple plaetary gearset show i Fig 2.3a; if the carrier is grouded, the lever diagram is show i Fig 2.3b. Because the lever diagram provides a ituitive way of aalyzig plaetary gear sets, it is widely used to aalyze trasmissios o vehicles, icludig hybrid electric vehicles. The advatage of this method is that it is simple, ad easy to uderstad. The disadvatage of it is that for differet trasmissios or the same trasmissio but with differet modes, differet lever diagrams have to be created. I additio, if use this method to aalyze trasmissios which cotai 3 or more plaetary gear sets, the lever diagram becomes very complex ad ot easy to read Algebraic desig techologies Researchers from Geeral Motors Research ad Developmet Ceter developed a method of creatio of ovel trasmissio mechaisms, both covetioal as well as hybrid, usig algebraic desig techiques (Raghava, Buckor et al. 26). To use the method, a upfrot decisio regardig the umber of plaetary gear sets ad clutches to be used i the proposed trasmissio is made. (Raghava, Buckor et al. 26) observed that: The desig process uses graph theory to hadle issues related to mechaism plaarity ad isomorphism. Followig the idetificatio of attractive trasmissio cadidates at the lever diagram level, we prepare layouts ad detailed stick diagrams, takig ito accout the packagig of bearigs, hydraulic circuitry, supportig shafts ad structures. The steps of the sythesis strategy are outlied i Fig 2.4. A detailed explaatio of the methodology ca be foud i the paper by (Raghava, Buckor et al. 26). 32

50 Fig 2.4 Methodology of the Algebraic desig method (Raghava, Buckor et al. 26) The advatage of the method is that it allows the desiger to geerate ad assess ovel desigs without relyig o ituitio ad prior experiece. Because the computer will cosider all possible coectios of the proposed trasmissio, the method may create some uusual arragemets which eve experieced desigers might overlook. Furthermore, because of the ever-icreasig requiremets o fuel ecoomy ad performace, the trasmissios for both covetioal vehicles ad HEVs are becomig more ad more complicated. This method is very useful for creatig this sort of trasmissio i this complex eviromet. The disadvatage is that the method itself is very complex, usig graph theory, lever diagram method, ad stick diagrams. Besides, the detailed procedure ad computig program have ot bee made publicly available yet Matrix method A matrix method for the aalysis of plaetary trasmissios was proposed i (Tia ad Lu 997). The method aalyzes both kiematics ad dyamics of a whole plaetary trasmissio system with a geeral program. First, the 33

51 trasmissio is broke ito fiite fuctio uits ad each basic part, such as a gear, a carrier, a clutch drum, or a brake disk, is eumerated. The basic parts that are always coected together are defied as coected parts. The basic parts from oe coected part tur at same speed. The, a represetig matrix is created, icludig a speed matrix ad a torque matrix, accordig to both the cofiguratio relatioships betwee those uits ad the trasmissio maipulatig characteristics. Oce these matrixes are geerated, the kiematic ad dyamic problems of the trasmissio ca be solved by meas of stadard matrix operatios. A example of a ecoded plaetary trasmissio is show i Fig 2.5. The advatage of this method is that it is described clearly the paper (Tia ad Lu 997), so that the readers ca follow ad uderstad the method. Also, the whole process of aalysis is stadardized to become very straightforward, makig it especially good for the developmet of a geeral-purpose plaetary trasmissio computer-aided-desig package. Oce the package is built up, it is very easy to aalyse ay give plaetary trasmissio. Fig 2.5 A example of a ecoded trasmissio (Tia ad Lu 997) I this research, the matrix method is used to aalyse two trasmissios for a HEV: a sigle epicyclic trasmissio ad a dual epicyclic trasmissio. Also, a uiversal software package to aalyze differet types of PSD for HEVs is developed. 34

52 2.7 Cocludig remarks HEVs ad EVs Iterest i HEVs ad EVs has icreased rapidly recet years, from both idustry ad academic viewpoits. Research ad developmet efforts have bee focused o developig ew cocepts ad low cost systems, but this has proved difficult primarily because of high battery costs. However, hybrid vehicles have bee successfully mass produced, e.g. Toyota Prius, ad at preset may maufacturers are tryig to put plug-i electric vehicles, ofte with some form of rage-exteder techology ito the market. Trasmissio desigs Curret desig treds i power splittig trasmissios have bee summarised. Historically, the role of the power splittig trasmissios i the overall developmet of hybrid vehicle techology has commoly bee uderestimated. But PSTs have actually played a crucial role i maagig the electrical ad mechaical power flows ad esurig good driveability ad efficiecy. It is cocluded that it has bee a area of rapidly chagig techology over the past decade. But perhaps more importatly, this is certai to cotiue over the ext decade. The overall coclusio about the curret picture is that whilst the first geeratio, sigle mode uits have proved to be adequate i the small/mid size passeger car sector, dual mode systems are set to become domiat i the large car, SUV ad commercial vehicle sectors. For EVs, the effect of trasmissios o the vehicle performace ad eergy cosumptio has ot yet received much attetio i the curret research. Cotrol strategies Although it is clear that may differet cotrol techiques have bee applied to the HEV problem, the overall coclusio is that oly three geeric types are likely to have a future i the short to medium term: i) Rule-based still at the heart of most practical ad prototype systems ii) Equivalet eergy methods a elegat simplificatio which eables ear-optimal performace to be obtaied iii) Dyamic programmig crucial i defiig the optimum performace ad useful i iformig rule-based system desig. 35

53 Almost all this recet work reviewed here has used stadard drivig cycles as a basis for comparisos. Whilst there are good reasos to justify this, it evertheless raises a fudametal global cocer of whether the idustry is desigig cars aroud arbitrarily selected drivig cycles rather tha aroud practical, cosumerdrive demads. There remais further scope for research ito drivability issues i the acceleratio ad brakig maoeuvres associated with ormal drivig. A sigificat goal of beefit to the idustry would be a better uderstadig of the subjective/objective correlatio of drivability. Methods to aalyse the epicyclic gear box There are three approaches used to aalyse the epicyclic gear box: the lever method, the algebraic desig method, ad the matrix method. I this research, the matrix method is chose maily because it is straightforward ad easy to program. 36

54 3 Aalysis of epicyclic trasmissios 3. Itroductio I this chapter, the sigle ad twi epicyclic trasmissios are aalyzed i detail ad the relatioships of speed ad torque of the egie, the motor ad the geerator are geerated. Computer programmes for the aalysis of epicyclic trasmissio based o a matrix method are developed ad examples of usig the programmes are give. 3.2 Aalysis of a sigle epicyclic trasmissio A typical ad successful example of a sigle epicyclic power split device (PSD) is the Toyota Prius, as show i Fig 3.. I the device, the iteral combustio egie (ICE) is coected to the plaet carrier. Whe the ICE rotates, the plaets mesh with ad ted to push both the su gear ad the rig gear i the same directio as the carrier. So the torque from the egie is split ito two directios. The rig gear is coected the reductio gear uit, which is coected to the differetial, the to the wheel. So the torque from the rig gear actually drives the car. The su gear is coected to oe of the motor geerators (MG), which largely acts as a geerator. The plaetary PSD is desiged so that the rig gets larger part of the egie torque, ad the su gear gets smaller part of the egie torque. The PSD is called E-CVT (Electroically-Cotrolled Cotiuously Variable Trasmissio). It combies the characteristics of a electric drive ad a cotiuously variable trasmissio, usig motor geerator uits i additio to toothed gears. I the PSD, MG2 is mouted o the driveshaft, ad thus couples torque ito or out of the driveshaft. So MG2 is sometimes called MG-T for Torque. MG is coected with the su gear ad is used to chage the su gear speed. So MG is sometimes called MG-S for Speed. Because MG2 is coected with the driveshaft, it caot chage speed ad torque freely. Hece there are three power iput/output braches i the system: the egie, MG, the output (MG2). Because the speed of the output shaft is decided by the speed of the vehicle, there is some limitatio o the cotrol strategy to achieve optimum performace. 37

55 Fig 3. Toyota Prius PSD (Ayers, Hsu et al. 24) The first geeratio of the Toyota Hybrid System (THS) is used i the Toyota Prius. After that, the secod geeratio, THS II, is called as Hybrid Syergy Drive (HSD). The HSD is used i Prius, Highlader Hybrid, Camry Hybrid, ad Lexus RX 45h automotives. The ame was chaged from THS to HSD, because some other car makers may use the power split techology. For example, Ford Escape Hybrid uses the hybrid syergy drive techology, ad it claims to be the most fuel-efficiet SUV o the plaet. Usually, a vehicle with a HSD is a full hybrid, because it ca drive usig oly electric power. Because the Toyota Prius PSD has oly oe set of epicyclic gears, it is called the sigle epicyclic trasmissio i this research. The sigle epicyclic system has three braches of power iput/output: i) Brach : the egie iput; ii) Brach 2: the MG iput/output, depedig o whether MG is actig as a motor or a geerator; 38

56 iii) Brach 3: the drivelie output, ad also the MG2 iput/output, depedig o whether MG2 is actig as a motor or a geerator. Hece, it is also called a three brach system. The simplified diagram of the sigle epicyclic system is show i Fig 3.2. The terms of a sigle epicyclic trasmissio ad a three brach system are distiguished from a twi epicyclic trasmissio ad a four brach system, which will be itroduced later. Fig 3.2 Sigle epicyclic gearbox, three brach system To use the matrix method to aalyse the trasmissio, each basic part is umbered, from to. There are 4 coected parts: I to IV. The coected part I icludes basic part, 5 ad 8; the coected part II iclude basic part 2, 7 ad 9; the coected part III icludes basic part 4 ad 6; the coected part IV icludes basic parts 3 ad. There are two gear uits X ad X2 The basic parts, the coected parts ad the gear uits are as show i Fig 3.3. I the matrix method, all the basic parts are umbered as, 2, 3, etc ad early all the basic parts are repeatedly amed. For example, umbers, 5 ad 8 poit to the same part: stads for iput shaft, 5 stads for the carrier of the gear mesh X ad 8 stads for the carrier of the gear mesh X2. The whole system has q basic parts: q = 2 + 3* = (3.) i which the last 2 parts are the rotor of MG ad the rotor of MG2. 39

57 Fig 3.3 Ecode of basic parts ad coected parts The umber of coected parts p is: The umber of degrees of freedom f is: where x is the umber of gear uits. p = 4 (3.2) f = p x = 4 2 = 2 (3.3) The gears tur i a ratio determied by the umber of teeth i each gear, where α is the gear ratio ad Z is the umber of teeth. α = Z / Z b a (iside egaged) ad α = Z b / Z a (outside egaged). Let α to α 3 represet the gear ratios of uits X ad X2 respectively. The tooth umber for the su gear, the piio gear ad the rig gear is 3, 24, ad 78 respectively. So the gear ratios for X ad X2 are Z 4 α = = 24 / 3 =.8 (3.4) Z 3 Z 7 Z 7 Z 3 + 2Z 4 (3.5) α = = = = Z Z Z α 2 =

58 where Z represets the tooth umber for gear defied by i Fig 3.3. I Equatio (3.5), α 2 is expressed i α, so there is actually oly oe parameter for the sigle epicyclic gearbox - α Speed ad ratio aalysis The followig describes the rotatio equatio group (3.6) for the sigle epicyclic trasmissio: Coected part : 5 = 8 = Coected part 2: 2 7 = 2 9 = Coected part 3: 3 = Coected part 4: 4 6 = Gear system uit X: α + α ) 3 4 ( 5 = Gear system uit X2: α + α ) (3.6) ( 2 8 = The above liear equatio group ca be writte i the followig vector form: r r A = (3.7) where: r equals [ 2 ] T ; A is the speed coefficiet matrix for the sigle epicyclic gearbox. Equatio (3.8) is the Itegratio of Equatios (3.6) ad (3.7). Equatio (3.8) ca be solved usig a stadard method, for example, the Gauss- Jorda elimiatio method. The computer programme (gjelim.m, Appedix ) of the Gauss-Jorda elimiatio method used i this research is from (Williams 27). 4

59 42 = α α α α (3.8) The Matlab program to obtai the speed coefficiet matrix A ad to derive the relatioship of rotatio speeds for each compoet is show i Appedix 2. From ruig the program, the speed coefficiet matrix A is show i Appedix 3, ad the relatioship of rotatio speeds for the sigle epicyclic gearbox is show i Appedix 4. The result show i matrix format is: = 5 3 / 5 8 / 65 / 2 45 / 2 65 / 2 45 / 5 3 / 5 8 / (3.9) The speed relatioships for MG ad MG2 with the egie ad the drivelie are: = + ( 3.) 2 9 = ( 3.)

60 This agrees with the equatio i Miller s presetatio (Miller ad Miller 25), i slide 3: k ( k + ) = (3.2) s + r c where k = Hece, this cofirms the accuracy of the matrix method ad the whole calculatio process. The egie speed is set to be as a referece poit so that the speed of part, amely =. The speed of each other part is actually the speed of that part relative to the speed of the egie. The trasmissio ratio of the system is defied as egie _ speed i = = = ( 3.3) output _ speed 2 The Matlab program to plot MG ad MG2 speed vs. trasmissio ratio for the sigle epicyclic gearbox is show i Appedix 5. From ruig the program, the result is show i Fig 3.4. Whe the trasmissio ratio is.72, the speed of MG is. This meas that at this poit, if MG2 does ot add torque to the wheels, zero power is trasmitted via the electrical path. The poit is called a ode poit. At the ode poit, the trasmissio efficiecy is higher. The desig of the powertrai should therefore make use of this ode poit. For example, this ode poit could be arraged to coicide with a vehicle speed aroud 7 mile/h, which is a typical cruisig speed o the highway, with a trasmissio ratio of Fig 3.4 Relatioship of trasmissio ratio ad motor geerator speeds for the sigle epicyclic gearbox 43

61 To study the effect of the parameter α o the speeds of MG ad MG2, two gear ratios are chose:.8 ad.2. The curves of speed of MG ad MG2 versus trasmissio ratio are show i Fig 3.5. Fig 3.5 Effects of two values of α o the sigle epicyclic gearbox With the icrease of the gear ratio α, the speed of MG vs. speed of egie also icreases. The speed of MG2 does chage with differet α. This is because MG2 is fixed with the output shaft, amely 9 = 2. From Equatio ( 3.3), the speed of MG ca be obtaied: 9 = ( 3.4) i Hece, the speed of MG does ot chage whe gear ratio α chages Torque aalysis While the system is ruig steadily, the sum of all the torques applied to a coected part should be zero. For example, coected part II i Fig 3.3 has a torque equatio like T + T + T, ad so o = For a gear system uit, the torque equatio would be: t α η T a + T b = ( 3.5) T T + T = ( 3.6) a + b c where T a, Tb ad T c are the torques applied to the coected part by the gear a, b, ad the carrier h. η t is the trasmissio efficiecy of the gear uit. If a is the drivig part, t = ; if a is the drive part, t =. 44

62 The torque equatio group ( 3.7) for the simple epicyclic gearbox is writte below: Coected part : T + T + T 5 8 = Coected part 2: T + T + T = Coected part 3: T + T 3 = Coected part 4: T + T 4 6 = t Gear uit X: α η T + T 3 4 = T 3 + T4 + T5 = t Gear uit X2: α η T + T = T + T + T ( 3.7) = At the momet, it has ot bee decided which gear is the drivig part ad which gear is the drive part. It is assumed at this stage that there is o loss i the trasmissio. I the later part of the simulatio studies, the efficiecy of the trasmissio is take ito cosideratio. I this case, the iput speed ad torque are kow for each idividual drivig coditio, so the directios of the power trasmissio are kow, thus the efficiecy ca be icorporated. The above liear equatio group ca be writte i the followig vector form: A T r = r T ( 3.8) where: T r equals [ T T 2 T ] T A T is the torque coefficiet matrix. Itegratig Equatios ( 3.7) ad ( 3.8) gives, 45

63 46 = T T T T T T T T T T t t η α α η (3.9) The Matlab program to get the torque coefficiet matrix T A ad to get the relatioship of torque for each compoet is show i Appedix 6. From ruig the program, the torque coefficiet matrix T A is show i Appedix 7, ad the relatioship of torque for the sigle epicyclic gearbox is show i Appedix 8. The result show i matrix format is: = 5 /8 3 /8 2 / 3 /8 9 2 / 2 / 9 2 / 5 / T T T T T T T T T T (3.2) The torque relatioships for MG ad MG2 with the egie ad the drivelie are: = + + T T T ( 3.2) 8 5 = + T T ( 3.22)

64 3.3 Aalysis of a twi epicyclic trasmissio I a twi epicyclic trasmissio system, which is preseted i this paper, there are two sets of epicyclic gear uits. The egie output shaft is coected to the carrier of the first epicyclic set. The carrier of the secod epicyclic set is coected to the rig gear of the first epicyclic set. The drivelie output is coected to the carrier of the secod epicyclic set. Neither of the motor geerator uits is mouted o the driveshaft or o the egie iput shaft, which gives more freedom ad beefits to the system which is show i Fig 3.6. Oe motor/geerator (MG) is coected to the su gear, ad the other motor/geerator (MG2) is coected with a rig gear. So there are four braches of power iput/output: i) Brach : the egie iput; ii) Brach 2: the drivelie output; iii) Brach 3: the MG iput/output, depedig o whether MG is actig as a motor or a geerator; iv) Brach 3: the MG2 iput/output, depedig o whether MG2 is actig as a motor or a geerator. Fig 3.6 Twi epicyclic trasmissio This type of four brach trasmissio system has bee described recetly by Moeller (Moeller 26) who proposed that it offers advatages i may automotive applicatios, icludig hybrid ad o-hybrid vehicles, such as light electric 47

65 vehicles or off-road vehicles. However, its usage i a hybrid electric vehicle drivelie will be aalysed here for the first time. Fig 3.7 Ecode of basic parts ad coected part of the twi epicyclic trasmissio The simplified structure ad the ecode of the 4 brach system is show i Fig 3.7. There are 6 basic parts which are umbered from to 6 respectively. There are 6 coected parts which are umbered from I to VI respectively. There are 4 gear uits which are umbered from X to X4 respectively. The umber of basic parts q for the whole system: q = 2 + 3* = 6 (3.23) i which the last 2 parts are the rotor of MG ad the rotor of MG2. The umber of coected parts is: The degree of freedom where x is the umber of gear uits. p = 6 (3.24) f = p x = 6 4 = 2 (3.25) Let α to α 4 represet the gear ratios of uits X to X4 respectively. Hece, α (3.26) = Z 4 / Z 3 48

66 α α 2 = 7 Z 6 = Z 7 / Z 4 = ( Z 3 + 2Z 4 ) / Z 3 = 2 / Z / α (3.27) α (3.28) 3 = Z / z9 4 = 3 Z2 = Z 7 / Z = ( Z 9 + 2Z ) / z = 2 / Z / α (3.29) 3 So actually there are 2 variables, α ad α 3 i the system. The values of α ad α 3 are both set to be The rotatio speed equatio group The speed equatio group for the twi epicyclic gearbox is writte below: Coected part : 5 = 8 = Coected part 2: 2 7 = 2 = 2 4 = Coected part 3: 3 = 3 6 = Coected part 4: 4 6 = Coected part 5: 2 = Coected part 6: 3 5 = Gear system uit X: α + α ) 3 4 ( 5 = Gear system uit X2: α + α ) ( 2 8 = Gear system uit X3: α + α ) 9 3 ( 3 = Gear system uit X4: α + α ) ( 3.3) ( 4 4 = I similar fashio to the aalysis for the sigle epicyclic gearbox, the above liear equatio group ca be writte i the followig vector form: r r A = ( 3.3) where: r equals [ 2 6 ] T A is the speed coefficiet matrix for the twi epicyclic. 49

67 5 Itegrate Equatios ( 3.3) ad ( 3.3) : = α α α α α α α ( 3.32) The Matlab program to obtai the speed coefficiet matrix A ad to derive the relatioship of rotatio speeds for each compoet for the twi epicyclic gearbox is show i Appedix 9. From ruig the program, the speed coefficiet matrix A is show i Appedix, ad the relatioship of rotatio speeds for the sigle epicyclic gearbox is show i Appedix. The relatioships MG ad MG2 with the egie ad the output shaft are: = + ( 3.33) = + ( 3.34) The Matlab program to plot the speeds of MG ad MG2 relative to the trasmissio ratio are show i Appedix 2. From ruig the program, the result is show is Fig 3.8. There are two ode poits for the twi epicyclic gearbox, whe the trasmissio ratios are.72 ad.72 respectively. I cotrast, for a sigle epicyclic gearbox, there is oly oe ode poit, whe the trasmissio ratio is.72 (Fig 3.4).

68 5 = 5 3/ 5 8 / 3/3 8 /3 3/3 8 /3 2 / 2 9 / / 5 8 / 4 3/ 4 9 / 4 3/ 4 9 / 5 3/ 5 8 / ( 3.35) Fig 3.8 Relatioship of trasmissio ratio ad motor geerator speeds for the 4 brach systems To study the effect of α, two differet values for α are chose, keepig a costat value of 8 3 =. α. Fig 3.9 shows the effect of α o the speeds of MG ad MG2. For the blue lies, α ad 3 α are both.8. For the red lies, 2 3 =. α

69 ad α 3 =. 8. The results show that for a icrease of α, the speeds of both MG ad MG2 icrease. Fig 3.9 Effects of two values of α o the twi epicyclic gearbox To study the effect of α 3, two differet values for α,.8 ad.2, are chose, keepig a costat value of α =. 8. The result is show i Fig 3.. Fig 3. shows chagig α 3 oly affects the speed of MG2 while the speed of MG keeps uchaged. The reaso is that the speed of MG is decided by the first epicyclic gear uit ad the speed of MG2 is decided by the two epicyclic uits (Fig 3.6). Because α is kept uchaged, so the curve of the speed of MG does ot chage. Fig 3. Effects of two values of α 3 o the twi epicyclic gearbox Torque ad efficiecy aalysis The torque equatio group (3.36) for the twi epicyclic gearbox is writte below: 52

70 Coected part : T + T + T 5 8 = Coected part 2: T + T + T + T = Coected part 3: T + T + T = Coected part 4: T + T 4 6 = Coected part 5: T + T 2 = Coected part 6: T + T 3 5 = t Gear uit X: α η T + T 3 4 = T 3 + T4 + T5 = t Gear uit X2: α η T + T T = 6 + T7 + T8 = t Gear uit X3: α η T + T T 3 9 = 9 + T + T = t Gear uit X4: α η T + T = T + T + T (3.36) = Agai at the momet, it has ot bee decided which gear is the drivig part ad which gear is the drive part. Hece, it is assumed that there is o loss i the trasmissio, so the aalysis ca be completed. The efficiecy of the trasmissio is take ito cosideratio i the later part of simulatio ad calculatio whe the iput speed ad torque are kow. The above liear equatio group ca be writte i the followig vector form: A T r = r T ( 3.37) where: T r equals [ T T 2 T 6 ] T A T is the torque coefficiet matrix. Itegratig Equatios (3.36) ad ( 3.37) gives, 53

71 54 = T T T T T T T T T T T T T T T T t t t t α η α η α η α η ( 3.38) The Matlab program to obtai the torque coefficiet matrix T A ad to obtai the relatioship of torque for each compoet is show i Appedix 3. From ruig the program, the torque coefficiet matrix T A is show i Appedix 4, ad the relatioship of torque for the sigle epicyclic gearbox is show i Appedix 5. From Equatio ( 3.38), the relatios of the torque of the electrical machies with the torque of the egie ad the torque of the output shaft are obtaied as the followig equatios = + + T T T (3.39) = + + T T T (3.4)

72 55 = 5 / / 3/ / 2 / 36 3/ 3/ / 9 2 / 3/ 8 2 / 36 3/ 9 2 / 3/ 8 5 / / 2 / 3/8 9 2 / 2 / 9 2 / 5 / T T T T T T T T T T T T T T T T (3.4) 3.4 Computer program for the aalysis of epicyclic trasmissios 3.4. Trasmissio systems aalysis tool (TSAT) The commo features of the may desigs proposed for power splittig trasmissios to date is that they all cotai epicyclic gear uits, clutches, brakes ad motor geerator uits, which are ofte itercoected i quite complicated ways. I this research, a software tool has therefore bee developed to allow a speedy aalysis of the wide variety of cadidate desigs. The user iterface requires the desiger to iput the data for all the compoets ad coectios i a straightforward structured fashio. The mathematical calculatios are based o the matrix aalysis approach which is coded i a MATLAB eviromet. Typical outputs iclude the speeds ad torques of all compoets from which the power flow details through the trasmissio elemets ca be calculated. The software is curretly upgraded to icorporate trasmissio efficiecies.

73 The procedure to obtai the relatioships of speed of a trasmissio usig TSAT is show i Fig 3.. Fig 3. Flowchart for the TSAT program There are maily 6 steps i the calculatio:. Ask the user to iput the cofiguratio of the trasmissio, amely the umber of epicyclic gear uits, clutches, brakes, ad motor/geerators (Fig 3.2); Fig 3.2 Step : trasmissio cofiguratio 56

74 2. Ask the user to iput the tooth umber of each gear. If the tooth umbers are ot available, you ca also iput the gear ratios for each gear uit (Fig 3.3); Fig 3.3 Step 2: tooth umber of each gear 3. Desigate a umber to each of the basic parts. The sequece is: the iput axle, the output axle, the gears, the clutch drums, the brake disks. Every plaetary gear uit has three basic parts. A clutch has two basic parts. A brake has oly oe basic part. The whole system has q basic parts: q = 2 + 3x + 2y + z (3.42) where : x is the umber of gear uits, y is the umber of clutches, z is the umber of brakes. 4. Ask the user to iput the coectios for all coected parts (Fig 3.4). The programme will list out all the basic parts, accordig to the iput from step. The the user selects which part is coected to which. 57

75 Fig 3.4 Step 3: Coectio 5. Calculate the speed of each part, assumig that the egie speed is, ad the output speed equals the egie speed divided by the trasmissio ratio. For all the basic parts i a coected part, the speeds of all basic parts are the same. For a gear uit, the kiematic relatioship betwee gears a, b ad the carrier h are: a α + ( α ) = (3.43) b h where a, b ad h are the speeds of rotatio of geasr a, b ad the carrier h respectively. α is the gear ratio. All the liear equatio group ca be writte i the followig vector form: r r A = (3.44) where: r is the speed vector; A is the speed coefficiet matrix. 6. Geerate the plot of motor/geerator speed vs. trasmissio ratio. The egie speed is set to be. So for ay trasmissio ratioi T, 58

76 egie i T = (3.45) output The speed of motor/geerator is calculated whe the trasmissio ratio chages Use of TSAT to aalyze some complex PSDs GM Alliso, AHS-2 system The arragemet of the GM Alliso, AHS-2 system is show i Fig 3.5. The additio of clutches to a trasmissio based o two epicyclic gear uits opes up a opportuity to fudametally chage the power flow through the system. Fig 3.5 GM Alliso AHS arragemet Fig 3.6 Simplified drawig of GM Alliso AHS arragemet 59

77 Basically, the two modes of operatio are usually referred to as: Low rage iput power split High rage compoud power split I the first of these iput power split - the clutches are set as: CL locked CL2 ulocked CL3 locked The trasmissio behaves i exactly the same way as the sigle mode system. I the secod compoud split mode, the clutches are set as: CL locked CL2 locked CL3 ulocked Thus, the su gear (S) is coected via MG to rig gear 2 (R2). The ability to switch betwee these two modes smoothly is a crucial aspect of this desig, ad this is usually referred to as sychroous shiftig. As metioed i Chapter 2, there is o sudde speed chages durig torque trasfer because the clutches are shifted whe the MG speeds are zero. The speed results for this system are show i Fig 3.7. I this example, the shift poit is arraged at a trasmissio ratio of.3. Fig 3.7 GM Alliso AHS mode ad mode 2 6

78 Geeric dual mode + 4 fixed ratios systems As metioed already i the itroductio, a iterestig software package for geeratig ovel trasmissio desigs has bee developed by GM Research ad Developmet Laboratories (Raghava, Buckor et al. 27). Oe of the examples described i this paper is a dual mode system which also offers four fixed gear ratios. This trasmissio is a full-fuctio EVT (electrically variable trasmissio) comprised of 3 simple plaetary gear sets, 2 rotatig clutches, statioary clutch, ad 2 motor-geerators, labelled MG ad MG2. It operates i Battery Reverse, EVT Reverse ad Forward, Battery-chargig Reverse ad Forward, ad has 4 fixed (i.e., all mechaical) speed-ratios. The desig is show i Fig 3.8, ad it emphasises the potetial beefits of the software, because (a) this arragemet is rather complicated, (b) it is ot ituitively obvious to uderstad exactly how it will meet the performace specificatios ad (c) it is ot a desig that would aturally be proposed usig traditioal desig methods. Fig 3.8 Geeric dual mode + 4 fixed ratios arragemet A simplified diagram of the desig is show i Fig 3.9 I mode, the clutches are set as: CL ulocked CL2 ulocked CL3 locked I mode 2, the clutches are set as: CL ulocked 6

79 CL2 locked CL3 ulocked Fig 3.9 Simplified drawig of Geeric dual mode + 4 fixed ratios arragemet The speeds ad torques of this desig have bee aalysed usig the TSAT software, ad the speed results for the ecvt modes ad 2 are show i Fig 3.2. Fig 3.2 Geeric dual mode + 4 fixed ratios 3.5 Cocludig remarks The speeds ad the torques for each compoet i the sigle epicyclic gearbox are aalyzed ad the relatioships of MG ad MG2 with the egie ad the output shaft are give. 62

80 The speeds ad torques for each compoet i the twi epicyclic gearbox are aalyzed ad the relatioships of MG ad MG2 with the egie ad the output shaft are give. A software package to aalyse epicyclic trasmissios, especially trasmissios for hybrid vehicles is developed ad examples of usig the software have bee described. 63

81 4 Compariso of a sigle ad twi epicyclic gearbox 4. Itroductio The aim of this chapter is to compare the behaviors of the sigle ad twi epicyclic trasmissios. I order to do this, the aalysis described i Chapter 3 is combied with a simple vehicle model. This eables typical torque, speed ad power results to be geerated, assumig these two gearboxes are fitted to a typical, medium sized passeger car. Two drivig coditios are examied: costat speed ruig ad acceleratig at a costat value of.8 m/s 2. This eables comparisos to be draw about the potetial beefits of the twi epicyclic trasmissio. 4.2 Mathematical model The behaviors of the sigle ad twi epicyclic systems are ow compared, by assumig they are fitted to a typical vehicle, which is about the same size, for example, as Toyota Prius (see Table 4.); the egie data is a simple look up table based o the idea of tryig to use the maximum fuel ecoomy lie. Two coditios are aalyzed: i) costat speed, steady ruig ii) acceleratio of.8 m/s 2 Table 4. Typical vehicle parameters ((Miller 24) Vehicle curb weight 33 kg Drag coefficiet, Cd.26 Frotal Area 2.29 m 2 Tire radius.3425 m Fial drive 4.: The mathematical model is built followig the 6 steps below:. Calculate the road load for the stated coditio; 2. Reflect the road load to the drivelie speed ad torque; 64

82 3. Assig the egie speed; 4. Use the plaetary gear speed equatio to determie the motor/geerator speed ad torque; 5. Calculate the egie mechaical path torque per the plaetary gear torque expressio; 6. Calculate all power flows for motor/geerators. The calculatio procedure is summarized i Fig 4.. Fig 4. Calculatio process A similar calculatio strategy is used for both the sigle ad twi epicyclic trasmissios. For the two systems, the value of the degrees of freedom is 2. These calculatios are repeated over the speed rage from m/s to 35 m/s (22 mile/h to 77 mile/h). The power for MG ad MG2 are calculated. Also the torque split, amely how much percet of the egie torque is directed towards the wheels is derived. The Matlab program to perform the calculatios is show i Appedix Results ad compariso 4.3. Torque ad power split For the sigle epicyclic trasmissio, the torque of egie is split betwee the wheels, via the rig gear, ad MG, via the su gear. Due to its structure, the ratio of the torque to the wheels ad the MG torque is fixed as 2.6:, which meas that /3.6 (28%) of the egie torque is set to the su gear (MG), ad 2.6/3.6 (72%) of the egie torque is set to the rig gear (the drivig wheels). But this does 65

83 mea that the power of egie is trasmitted to the wheels ad to the MG at a fixed rate, because the power is the product of torque ad rotatio speed. For the sigle epicyclic trasmissio, the torque split ad the percetage of the power through the electrical route are show i Fig 4.2. The percetage of the power through electrical route is defied as the power of MG relative to the power of the egie. The values are egative because, whe the power is iput to the system, it is defied as positive; whereas whe the power is draw from the system, it is defied as egative. I this simulatio, the power of MG is always egative, meaig that it acts as a geerator over the speed rage from m/s to 35 m/s (22 mile/h to 77 mile/h). Fig 4.2 Sigle epicyclic trasmissio, torque ad power split For the twi epicyclic trasmissio, the torque split ad the percetage of the power through the electrical route are show i Fig 4.3, from which it ca be see that the ratio of the torque to the wheels ad the torque to the MG is ot fixed. It varies whe the trasmissio ratio chages. Most of the torque split ratio for the twi epicyclic trasmissio is bigger tha 2.6:. Comparig the two lower curves i Fig 4.2 ad Fig 4.3, it ca be see that the absolute values of the power of MG vs. the power of the egie for the twi epicyclic trasmissio are much lower tha 66

84 for the sigle epicyclic arragemet, which meas for the twi epicyclic trasmissio, less percetage of egie power is trasmitted by the electrical path. Fig 4.3 Twi epicyclic trasmissio, torque ad power split Power of MG ad MG2 The results for the power i MG ad MG2, for costat speed ruig, i.e. o acceleratio are show i Fig 4.4 ad Fig 4.5 for the sigle ad twi epicyclic trasmissio respectively. For the sigle epicyclic trasmissio (Fig 4.4), MG2 is actig as a motor. The power demaded from MG icreases as the vehicle speed icreases, whereas the power used to drive MG2 stays fairly costat up util the higher speed. For the twi epicyclic trasmissio (Fig 4.5), the situatio is very similar: MG2 acts as a geerator ad MG acts as a motor. Also, their characteristics as the forward speed chages are rather similar to each other. The MG ad MG2 power results whe the vehicle is acceleratig at.8 m/s 2 are show i Fig 4.6 ad Fig 4.7 for the sigle ad twi epicyclic trasmissios. The power splits are ow very differet from the zero acceleratio case. For the sigle epicyclic trasmissio, MG2 acts as a motor, deliverig from aroud 8 to 3 67

85 kw as forward speed icreases. At the same time, MG acts as a geerator with a power demad from aroud -5 to -7 kw. Thus cosiderable power is trasmitted through the electrical route. Fig 4.4 Sigle epicyclic trasmissio, power of MG & MG2, o acceleratio Fig 4.5 Twi epicyclic trasmissio, power of MG ad MG2, o acceleratio 68

86 Fig 4.6 Sigle epicyclic trasmissio, power of MG ad MG2, with acceleratio Fig 4.7 Twi epicyclic trasmissio, power of MG ad MG2, with acceleratio 69

87 For the twi epicyclic trasmissio, the overall situatio is rather similar; MG2 acts as a motor ad MG as a geerator. However, the absolute power values are cosiderably lower. Thus, the twi epicyclic trasmissio demostrates clearly its potetial advatage, amely that less power is trasmitted via the electrical routes ad cosequetly, the overall trasmissio efficiecy will be higher. 4.4 Potetial beefits of the twi epicyclic gearbox More flexibility for cotrol For a sigle epicyclic trasmissio, MG2 is coected to the output shaft. So its speed is decided by the vehicle. I cotrast, for a twi epicyclic trasmissio, either of the electric machies is coected to the iput or output shaft, which gives a opportuity to choose the electric machie to work i its highest efficiecy area. Oe more ode where oe of the electric machies is at stadstill I a three brach system, there is oly oe ode poit. I the four brach system, two ode poits occur over the etire speed rage (Fig 4.8). Fig 4.8 Trasmissio ratios ad speeds of MG ad MG2 I the four brach trasmissio, at the ode, MG is at a stadstill; at ode 2, MG2 is at stadstill. So at ode poits the power via the electrical path goes to 7

88 zero, ad the system works at its highest efficiecy. By compariso, i a sigle epicyclic trasmissio, there is oly oe ode poit. There is potetial to improve efficiecy by desigig the cotroller to make the trasmissio work at the two ode poits. I this study, the two ode poits occur whe the trasmissio ratios are.72 ad.72 respectively. To show that it is possible to use the 2 ode poits to reduce the overall power, a example calculatio is doe: The egie speed is set to be 3 rad/s ad torque is set to be Nm. The trasmissio ratio is set to be.72. The powers of the electric machies are show i Table 4.2. Table 4.2 Electric power for two trasmissio at the ode poit 2 Power of MG, P_mg_3brach -7.4 kw sigle epicyclic trasmissio Power of MG2, P_mg2_3brach 22.2 kw sigle epicyclic trasmissio Power of MG, P_mg_4brach 4.8 kw twi epicyclic trasmissio Power of MG2, P_mg2_4brach twi epicyclic trasmissio Note: Postive power meas iput power ito the system, like a motor; Negative power meas power out of the system, like a geerator. Suppose the efficiecy of a motor takig power from the battery ad the efficiecy of geerator savig the eergy ito the battery are both.8, the the differece betwee a twi epicyclic trasmissio ad a sigle epicyclic trasmissio is: P _ 3brach = P _ mg2 _ 3brach /.8 + P _ mg_ 3brach*.8 = 3. 9kW P _ 4brach = P _ mg2 _ 4brach /.8 + P _ mg_ 4brach *.8 = 3. 9kW Hece, the differece betwee the two systems is = kw. For a vehicle operatig i the UK, it is likely that the two most typical speeds are 3 mile/h, i a city drivig, ad 7 mile/h, whe high speed cruisig. To make full use of the two ode poits, the desig of the powertrai should be arraged so that the two ode poits coicide with the speeds 3 mile/h ad 7 mile/h 7

89 respectively. With the vehicle parameters give i Table 4., the wheel speeds ad egie speeds at the vehicle speed of 3 mile/h ad 7 mile/h are give i Table 4.3. So whe selectig the egie, the best efficiecy area should be aroud 28 rad/s. Table 4.3 The wheel ad egie speeds at the two typical vehicle speeds Vehicle speed (mile/h) Trasmissio ratio Wheel speed (rad/s) Egie speed (rad/s) Smaller size of electric machies Itegratig Fig 4.6 ad Fig 4.7, whe acceleratig the typical car with.8 m/s 2 from to 35 m/s, the powers of MG ad MG2 for the two systems are show i Fig 4.9. Fig 4.9 Power of MG ad GM2 72

90 From Fig 4.9, it ca be see that the power of MG ad MG2 for a twi epicyclic trasmissio is smaller tha a sigle epicyclic trasmissio. For example, whe the vehicle speed is 3 m/s, the power of each machie is show i Table 4.4. Table 4.4 Power of MG ad MG2 at 3m/s Twi epicyclic trasmissio Sigle epicyclic trasmissio Power of MG Power of MG2 Power of MG Power of MG kw 5.67 kw kw 24.7 kw 4.5 Cocludig remarks The sigle epicyclic gearbox although used successfully o, for example, the Toyota Prius has the limitatio that oe of the MG uits is coected directly to the fixed drive, the twi epicyclic gearbox does ot have this restrictio, ad so it offers the opportuity of more freedom to cotrol the speeds of MG ad MG2. For the twi epicyclic gearbox, it has bee show over a limited rage of operatig coditios that it is possible to direct less power via the electrical route, thus offerig potetial efficiecy gais. Also, the twi epicyclic gearbox has tow ode poits, whereas the sigle epicyclic oly has oe. Agai, this offers potetial if these two mode poits are arraged to coicide with commo operatig speeds, say 3 ad 7 mile/h. The fial potetial beefit of the twi epicyclic gearbox is that it should be possible to dowsize the electric machies. However, this beefit must be weighed agaist the slight disadvatage of icreased complexity of the gear system. 73

91 5 Modelig hybrid electric vehicle (HEV) performace 5. Itroductio I this chapter, the modellig is further developed to ivestigate i more detail the effect of the sigle ad twi epicyclic gearbox whe fitted to a typical HEV. The modellig is therefore exteded to iclude all the subsystems ad the cotroller desig of a typical HEV, ad the vehicle is simulated over more typical drivig cycles. Three vehicle models are built up: a traditioal ICE vehicle, a HEV with sigle epicyclic gearbox, ad a HEV with twi epicyclic gearbox. Firstly, the subsystem models, such as the egie, trasmissio, ad motor/geerator are itroduced. The, the cotrol strategy for a HEV is studied ad cotrollers for 3 brach ad the sigle ad dual epicyclic systems are described i detail. The vehicle models are built based o the quasistatic approach (Guzzella, 27). This approach allows the fuel cosumptios of each vehicle uder differet drivig cycles to be calculated. The QSS toolbox (Guzzella ad Amstutz 25) is used for some of the system elemets such as drivig cycles, egie, ad battery model. 5.2 Overview of Vehicle Models The modellig of the hybrid electric vehicle performace is doe usig the QSS Toolkit (Guzzella ad Amstutz 25). This is a quasistatic simulatio package based o a collectio of Simulik blocks ad the appropriate parameter files that ca be ru i ay Matlab/Simulik eviromet. The traditioal ICE vehicle model itself is straightforward ad is show i Fig 5.. There are 5 sub-systems: the drivig cycle subsystem, vehicle subsystem, the gearbox subsystem, the combustio egie subsystem, ad the fuel tak subsystem. The data for the egie ad gearbox are take from geeric data i the QSS package. The fuctio of the egie subsystem is to compute the fuel cosumptio from a cosumptio map, accordig to the torque ad the rotatioal speed demad. The gearbox has 5 gears ragig from 3.84 to.63. the differetial gear ratio is The other vehicle data are show i Table 5.. It is ot iteded to represet ay specific 74

92 vehicle but rather to act as a geeric vehicle platform to focus attetio o the differeces obtaiable from the three vehicle models. Fig 5. Overview of the covetioal ICE vehicle model Table 5. Vehicle parameters (Miller 24) Vehicle curb weight 257 kg Drag coefficiet, Cd.29 Frotal Area m Tire radius.292 m Fial drive 3.95: The models for the 2 HEV vehicles are built based o the same baselie vehicle, with the same vehicle parameters, but differet trasmissios, as show i Fig 5.2. The iput to the model is oe of the stadard drivig cycles the NEDC ad USA FTP-75 cycles are used extesively i this work ad the solutio procedure is based o steppig through the drivig cycle at typically oe secod steps, calculatig the equilibrium coditio ad the collectig all the data for plottig at the ed of the cycle. Thus, the focus of attetio is o the overall efficiecy of the egie ad motor geerator uits ad the major issue of whether it is possible to improve overall eergy usage by operatig the whole system at or ear to the best efficiecy poits. 75

93 Fig 5.2 Overview of the hybrid vehicle model 76

94 5.3 Egie model The egie model from QSS Toolbox was used i this research. The fuctio of the egie model is to compute the fuel cosumptio from a cosumptio map. Iputs for the model iclude egie speed, egie acceleratio ad egie torque. The output of the model is the fuel cosumptio of the egie at each samplig poit. Fig 5.3 Top view of the egie model based o a cosumptio map The fuctio of overload ad overspeed detectio was built i the egie model. As soo as the egie torque or speed is over the limit, the simulatio is stopped. The similar detectio fuctio is built i the motor/geerator models. To fiish the simulatio with the whole drivig cycle, oce ay overload or overspeed is detected, the cotroller will reselect the related speed ad/or torque, to make sure every compoet, icludig the egie ad the motors, work withi these the speed-torque limit. The data for the fuel cosumptio map represets a small egie with maximum speed 5 rad/s ad maximum torque 8 Nm. There are 3 parameters for the map: a vector ( ) cotaiig the rotatioal speed, a vector ( m ) cotaiig the torque ad a efficiecy map ( m ) cotaiig the fuel efficiecy poit (kg/s) at each combiatio of speed ad torque. Fig 5.4 shows the egie efficiecy map used i the simulatio. 77

95 2 25 Egie torque (Nm) Cosumptio g/kwh Egie speed (rad/s) Fig 5.4 Egie efficiecy map 5.4 Trasmissio models 5.4. Covetioal maual gearbox The model of a 5-gear shift maual gearbox was take from oe of the stadard blocks i the QSS toolbox, the top level of which is show i Fig 5.5. The gear ratios from the first gear to the fifth gear are 3.84, 2.,.36,.86 ad.63 respectively. The differetial gear ratio is The efficiecy of the whole gearbox is set to be.9. The iputs of the block are wheel speed, wheel acceleratio, wheel torque, forward speed, ad gear umber. The gear umber specifies which gear to use ad it is geerated from the drivig cycles. The outputs of the block are speed of the fly wheel, acceleratio of the flywheel ad torque o the flywheel. The fuctio of the gearbox model is to reflect the road load to the output shaft of the egie, the to calculate the egie fuel cosumptio accordig to the rotatio speed ad the torque demad. 78

96 Fig 5.5 Top level of the block Maual Gear Box Sigle epicyclic gearbox model The layout of a sigle epicyclic gearbox is show i Fig 5.6. Fig 5.6 Sigle epicyclic gearbox as used i the Toyota Prius also referred to as a 3 brach system The power flow of the sigle epicyclic gearbox is show is Fig 5.7. MG, which is maily used as a geerator ad MG2, which is maily used as a motor, are coected to the battery, takig or savig electricity from or to the battery. The power of the egie is split ito two ways: to the wheel via the rig gear, ad to the MG. The vehicle ca be drive o egie aloe, the MG2 aloe, or both, depedig o the power required ad state of charge (SOC) of the battery. 79

97 Fig 5.7 Power flow of the sigle epicyclic system As described previously i Chapter 3, the speed ad torque relatios of the 3 brach system are: Speed relatioships: = (5.) mg e dl mg2 = dl (5.2) Torque relatioships: T mg = (5/8) T e (5.3) T mg = (3/8) T e T (5.4) 2 dl The speed ad torque for each elemet uder differet operatio modes are calculated based o the above equatios. The equatios for torques do ot take losses ito cosideratio at the momet. I the whole simulatio model, the trasmissio loss is take ito cosideratio for each specific iput speed ad torque. The efficiecy for each gear pair is set to be 98.5%. The acceleratios of each elemet, represeted as d, d mg ad d mg2, are also take ito e cosideratio. The relatios of acceleratio are simply derived from the relatios of the rotatio speed. Mode : Motor aloe mode (silet operatio, battery-ev) Whe the vehicle speed is low ad there is eough electricity is the battery, the egie ca be shut off ad the vehicle drive purely by electric motor. I Miller s aalysis (Miller ad Miller 25), the egie-off-speed is 3 mph; i Mi s study (Mi, 8

98 Zhag et al. 23), the speed is 35 mph. I this research, the egie-cut-off speed is set to be 35mph. I this mode, electricity is supplied to MG2, ad MG is locked. Because the egie is off, the car rus quietly. So this mode is ofte also referred to as silet mode. Of course, this situatio would also occur if the car rus out of fuel, ad the eergy i the battery is used as a emergecy to get to a gas statio. Fig 5.8 Mode : Motor aloe Output speed ad torque for all elemets are show i equatio group (5.5) : e d T e = e = = mg2 = dl d mg2 = d dl T mg2 = T dl mg = d mg = T mg = (5.5) Mode 2: Combied power (electric boost) Whe acceleratig at low speeds i ormal operatio, the egie turs more rapidly tha the wheels but does ot develop sufficiet torque. The extra egie 8

99 speed is fed to MG actig as a geerator. The electricity from MG is fed to MG2, which acts as a motor ad adds torque at the driveshaft. Whe hard acceleratio is eeded or o a uphill road, if egie has isufficiet power to meet the road load, extra power from the battery will be added via MG2. I this case, there are two sources of electricity for MG2: from MG ad from the battery. Fig 5.9 Mode 2: Combied power Output speed ad torque for all elemets are show i equatio group (5.6): e = e d = ( / ) d e T = e T e e mg2 = dl d mg2 = d dl T = T dl dl mg2 dl ( 3/8) Te = 2.6 * mg 3.6* e mg = 3.6* de d 2.6 * d dl dl T mg = (/ 3.6) T e (5.6) Mode 3: Cruise mode (ormal drivig) Cruise mode is used whe the vehicle is cruisig at high speed. At this time the egie turs more slowly tha the wheels but develops more torque tha eeded. 82

100 MG2 the rus as a geerator to direct the excess egie torque, producig power that is fed to MG actig as a motor to icrease the wheel speed. Fig 5. Mode 3: Cruise mode Output speed ad torque for all elemets are show i equatio group (5.7): e = e d = ( / ) d e T = e T e e dl mg2 = dl d mg2 = d dl T ( 2.6 / 3.6 T dl mg2 = ) e T dl 2.6* mg = 3.6* e mg = 3.6* de d 2.6* d T = (/ 3.6) mg T e dl dl (5.7) Mode 4: Egie aloe mode I this mode, MG2 rotates freely, ad MG is locked. All the power of the egie is trasmitted to the drivelie. The HEV operates i this mode whe the SOC of the battery is too low, so o electric machie should be used, or SOC is too high, so there is o eed to charge the battery. 83

101 Fig 5. Mode 4: Egie aloe Output speed ad torque for all elemets are show i equatio group (5.8): = (3/8) e dl d = ( / ) d e e T = (8/3) dl e T dl mg2 = d mg2 = T mg2 = dl mg = d mg = T mg = (5.8) Mode 5: Regeerative brakig Whe the vehicle is brakig, if the battery is ot fully charged, MG2, as a geerator, will absorb the eergy ad use it to charge the battery. The practical difficulty is i bledig the brakig torque obtaied via regeerative brakig with the brakig demaded by the driver through the brake pedal. The driver would prefer to have a seamless trasmissio betwee regeerative brakig ad applicatio of the ormal vehicle brakes for more severe stops. I this case, MG rotates freely. 84

102 Brake bledig for HEVs ad EVs is a importat feature of driveability ad is a topic for further research work i future. Fig 5.2 Mode 5: Regeerative brakig Output speed ad torque for all elemets are show i equatio group (5.9): e d T e e = = = mg2 = dl d mg2 = d dl Tmg2 = Mi( Tdl,iterp( ωmg2 _ row, Tmg2 _ max, ωmg2 )) where ω mg 2_ row is the speed of MG2 ad T mg 2_ max is the maximum torque of MG2. mg = d mg = T mg = (5.9) Mode 6: Mechaical brakig If the battery is fully chaged the acts MG2 as a geerator, absorbs the eergy, geeratig electricity ad shut it to MG. MG acts as a motor drivig the egie rapidly forward. The purpose of usig MG2 to draw power to MG is to reduce the 85

103 load for the ormal compressio brakig. So the size of the brake ca be dowsized ad brake liigs last loger tha for most cars of similar mass. Fig 5.3 Mode 6: Mechaical brakig Output speed ad torque for all elemets are show i equatio group (5.). The speeds ad the torques of MG ad MG2 are all set to be zero, because o electricity is savig or takig from the battery. e d T e e = = = mg2 = d mg2 = T mg2 = mg = d mg = T mg = (5.) Mode 7: Stadstill charge mode The sigle epicyclic gearbox ca be desiged to charge the battery whe the vehicle is statioary, by ruig the egie ad geeratig electricity from MG. 86

104 The egie operatio poit will be arraged accordig to the efficiecy of both MG ad the egie itself. I this study, the egie speed ad torque are set to be rpm ad 9 Nm. Fig 5.4 Mode 7: Stadstill charge Output speed ad torque for all elemets are show i equatio group (5.): e d T e e = 2 = = 9 mg2 = d mg2 = T mg2 = * mg = 3.6 e d mg = T mg = (/ 3.6) T e (5.) Mode 8: Drivig charge Whe drivig at high speed, if the battery state of charge is lower tha certai level, say, 5%, the egie will operate at the maximum power area. Both MG2 ad MG act as geerators, turig the extra power ito electricity to charge the 87

105 battery. I this case the egie does ot ecessarily work i the highest efficiecy area. Fig 5.5 Mode 8: Drivig charge The output speed ad torque for all elemets are show i equatio group (5.2): where e = e d = ( / ) d e e dl T = iterp( w e dl eg _ max, T eg _ max, w w eg _ max is egie maximum rotatio speed ad eg _ max maximum torque. mg2 = dl d mg2 = d dl T = ( T *.72 + T mg2 e dl ) e ) T is the egie = 2.6 * mg 3.6* e mg = 3.6* de d 2.6 * d T = (/ 3.6) mg T e dl dl (5.2) Twi epicyclic gearbox model The layout of the twi epicyclic gearbox is show i Fig 5.6. The structure is take from oe of pateted desigs from (Moeller 25). Compared to the sigle epicyclic gearbox, the twi epicyclic gearbox has two epicyclic gearsets. The carrier of the first epicyclic gearset is coected to the egie iput ad the carrier 88

106 of the secod epicyclic gearset is coected to the drivelie output. The purpose of addig oe more epicyclic gearset is to give the system more flexibility of cotrollig the speeds ad torques of MG ad MG2. Fig 5.6 Twi epicyclic gearbox as proposed by NexxtDrive - also referred to as a four brach system The power flow of the twi epicyclic gearbox is show i Fig 5.7. As before, MG is maily used as a geerator ad MG2 is maily used as a motor; both are coected to the battery, takig or savig electricity from or to the battery. The power of the egie is split ito two ways: to the wheel via the rig gear, ad to the MG. The vehicle ca be drive o egie aloe, the MG2 aloe, or combied power, depedig o the power required ad state of charge (SOC) of the battery. Fig 5.7 Power flow of the dual epicyclic system Followig o from the results i Chapter 3, the speed ad torque equatios of the dual epicyclic gearbox are: Speed equatios: 89

107 Torque equatios: mg + (8 / 3 ) * e (3 / 3 ) * dl = (5.3) (8/ 5)* (3/ 5)* (5.4) mg2 e dl = T (69/ 324) * T + (3/8) * T (5.5) mg + e dl = T (55/ 324) * T + (5/8) * T (5.6) mg2 + e dl = The speed ad torque for each elemet of the 4 brach system uder differet operatio mode are calculated based o the above equatios. Agai, the equatios for torques do ot take idividual losses ito cosideratio at the momet. I the whole simulatio model, the trasmissio loss is take ito cosideratio for each specific iput speed ad torque. The efficiecy for each gear pair is set to be 98.5%. By doig this, ay additioal losses of the twi epicyclic gearbox due to the icreased umber of gear pairs compared to the sigle epicyclic gearbox are take i to cosideratio. Agai, the acceleratios of each elemet are represeted as dω, mg e dω ad mg2 dω. The detailed descriptio of each operatio mode for the 4 brach system, some aspects of which are similar to the 3 brach system, will ot be repeated agai i the followig text. Oly the differeces will be metioed. Mode : Motor aloe mode (silet operatio, Battery-EV) This mode is used whe the vehicle starts from statioary ad the speed is lower tha 35 mph. The egie is shut dow, ad MG is locked. Electricity is supplied to MG2 to drive the car. I this mode, the vehicle is ruig purely o electricity, so it also called the battery EV mode, or silet mode operatio. 9

108 Fig 5.8 Mode : Motor aloe The output speed ad torque for all elemets are show i equatio group (5.7): e d T e = e = = (8/3) mg2 = dl mg2 = (8/3 d dl mg2 = (3/8 T dl d ) T ) mg = d mg = T mg = (5.7) Mode 2: Combied power (electric boost) Whe acceleratig or drivig o the uphill road, both the egie ad MG2 are drivig the vehicle. MG is a geerator, supplyig electricity to MG2. If more power is eeded, the battery will supply electricity to MG2 as well. 9

109 Fig 5.9 Mode 2: Combied power The output speed ad torque for all elemets are show i equatio group (5.8): e = e d = ( / ) d e T = e T e e dl (8/3) (3/3) dl mg2 = e + mg2 = (8/3) de + mg2 = (69/ 324) Te d (3/3) d T (3/3) T dl dl dl 2.6 * mg = 3.6* e dl mg = 3.6* de mg (55/ 324) Te d 2.6 * d dl T = (5/8) T (5.8) dl Mode 3: Cruise mode (Normal drivig) Whe the vehicle is cruisig at high speed, the egie is cotrolled to ru at a lower speed ad higher torque tha would be the case for a covetioal geared car. I this case, MG is cotrolled as a motor to chage the gear ratio ad icrease the output speed. MG2 acts a geerator to absorb the extra torque ad supply electricity to the battery ad MG. 92

110 Fig 5.2 Mode 3: Cruise mode The output speed ad torque for all elemets are show i equatio group (5.9): e = e d = ( / ) d e T = e T e e dl (3/3) dl mg2 = (8/3) e + mg2 = (8/3) de + mg2 = (69/ 324) Te d (3/3) d T (3/3) T dl dl dl = 2.6 * mg 3.6* e mg = 3.6* de mg (55/ 324) Te d 2.6 * d dl dl T = (5/8) T (5.9) dl Mode 4: Egie aloe mode Whe the battery SOC is too low or too high, the vehicle will drive oly o egie. I this mode, MG is locked ad MG2 rotates freely. The dual epicyclic system actually turs ito a sigle epicyclic system. 93

111 Fig 5.2 Mode 4: Egie aloe Output speed ad torque for all elemets are show i equatio group (5.2): = e e ( 3/8) e d = ( / ) d T = e e dl ( 8/3) Te mg2 = d mg2 = T mg2 = dl mg = d mg = T mg = (5.2) Mode 5: Regeerative brakig I this mode, the system acts i similar maer to the sigle epicyclic system, with MG locked ad MG2 supplyig power to the battery. 94

112 Fig 5.22 Mode 5: Regeerative brakig The output speed ad torque for all elemets are show i equatio group (5.2): e d T e e = = = mg2 = dl d mg2 = d dl Tmg2 = Mi( Tdl,iterp( ωmg2 _ row, Tmg2 _ max, ωmg2 )) where ω mg 2_ row is the speed of MG2 ad T mg 2_ max is the maximum torque of MG2. mg = d mg = T mg = (5.2) Mode 6: Mechaical brake If the battery is full, o electricity is eeded to be saved to the battery. But the MG2 will still act as a geerator to absorb the eergy from the rotatig wheel. The electricity will be shut to MG, which dissipatig the electricity by turig the egie. Whe the maximum torque MG2 ca provide less tha the eeded brake torque, the covetio bake o the car will provide the rest of it. The purpose of this is to absorb the brakig eergy as much as possible, thus to reduce the size or the ormal brake ad to prolog the life of the ormal brake. 95

113 Fig 5.23 Mode 6: Mechaical brake The output speed ad torque for all elemets are show i equatio group (5.22). The speeds ad the torques of MG ad MG2 are all set to be zero, because o electricity is savig or takig from the battery. e d T e e = = = mg2 = d mg2 = T mg2 = mg = d mg = T mg = (5.22) Mode 7: Stadstill charge mode For a 3 brach system, MG2 is coected to the output shaft, which meas it ca ot move whe the vehicle is statioary. So i the stadstill mode, oly MG ca be used as a geerator. This limitatio does ot exist for a 4 brach system. Both the two electric machies ca be used as geerators, chargig the battery more quickly. 96

114 Fig 5.24 Mode 7: Stadstill charge Output speed ad torque for all elemets are show i equatio group (5.23): e d T e e = 2 = = 9 2 = (8/3) d 2 = (8/3) T.78* mg e mg d e mg2 = T e * mg = 3.6 e d mg = T mg = (/ 3.6) T e (5.23) Mode 8: Drivig charge For most ormal drivig, the cotrol strategy for the HEV system attempts to operate the ICE i a optimum efficiecy area ad it maages MG ad MG2 withi the battery SOC costraits to achieve this ofte this meas operatig the ICE at a higher torque ad lower speed tha for covetioal geared vehicles. However, if the battery SOC becomes too low, the egie power will be icreased such that both MG ad MG2 might geerate electrical power to charge the battery. 97

115 Fig 5.25 Mode 8: Drivig charge Output speed ad torque for all elemets are show i equatio group (5.24): where e = e d = ( / ) d e e dl T = iterp( w e dl eg _ max, T eg _ max, w w eg _ max is egie maximum rotatio speed ad eg _ max maximum torque. mg2 = (8/3) e + mg2 = (8/3) de + mg2 = (69/ 324) Te (3/3) d (3/3) d T (3/3) T dl e dl ) dl T is the egie = 2.6 * mg 3.6* e dl mg = 3.6* de mg (55/ 324) Te d 2.6 * d dl T = (5/8) T (5.24) dl Mode 9: High efficiecy mode This is a mode that a sigle epicyclic system does ot have. As show i Fig 3.8, the twi epicyclic system has oe more ode poit whe the trasmissio ratio is.72. Whe the vehicle is cruisig at high speed, with the speeds of MG ad MG2 cotrolled i the reasoable rage, the trasmissio ratio is set to be.72 to get higher trasmissio efficiecy. I this mode, MG is a motor ad MG2 is a geerator, which are the same as i mode 3. 98

116 Fig 5.26 Mode 9: High efficiecy mode Output speed ad torque for all elemets are show i equatio group (5.25): e d T e = 2 e = = it erp( ω eg _ best, T eg _ best, w eg where ω is the egie s rotatio speed ad T eg _ best is the egie s best eg _ best efficiecy torque. mg2 = d mg2 = T mg2 = 2.9* mg = e ) d mg = T = (55/ 324) T (5/8) T (5.25) mg e dl 5.5 Motor ad geerator model I this study, both MG ad MG2 ca be used i 4 quadrats; this meas they ca act either as a motor or geerator i both the positive ad egative rotatio directios. Withi the motor quadrats, the electric power required ca be expressed as: P = ω T η ( ω, T ) (5.26) EM EM EM EM EM EM While i the geerator quadrats, the power geerated ca be expressed as: 99

117 P = ω T η ( ω, T ) (5.27) EM EM EM EM EM EM I QSS, it combies the two cases ito a sigle efficiecy map to avoid havig to keepig distiguishig betwee the two cases. This causes a fudametal flaw which may make the simulatio results ot precise eough. Whe calculatig the iterpolatio to get the motor efficiecy, it is possible to obtai urealistically high efficiecy poits aroud the zero torque area, which is obviously ot correct, as show i Fig Fig 5.27 A flaw i QSS motor/geerator model I this study, models for MG ad MG2 with separate motor ad geerator quadrats were built, usig S-fuctio blocks. The top view of the MG2 model is show i Fig The MG ad MG2 efficiecy maps are show i Fig 5.29 ad Fig 5.3. Fig 5.28 Top view of MG2 model

118 Torque (Nm) Speed (rad/s) Fig 5.29 MG efficiecy map Torque (Nm) Speed (rad/s) Fig 5.3 MG2 efficiecy map 5.6 Cotrol strategy The advatages ad disadvatages of differet cotrol strategies for hybrid vehicle have bee discussed i Chapter 2. I this research, the rule based cotrol strategy will be used i the modelig ad simulatio.

119 The data flow for the 2 HEV models is show i Fig 5.3. Durig the whole drivig cycle, for each samplig time, the drivelie speed ad torque (w_dl ad T_dl respectively) ca be calculated from the curret vehicle speed ad acceleratio. The pre-selected egie speed ad egie torque (w_e ad T_e respectively) are decided from the combied cosideratio of power required ad egie best efficiecy curve. Accordig to the curret vehicle speed, acc, egie speed ad torque, drivelie speed ad torque, ad the battery State of Chage (SOC), the CVT cotroller will decide the drivig mode, ad speed ad torque for each elemet, iclude MG, MG2 ad the egie. The, the results for curret fuel cosumptio ad updated battery SOC ca be obtaied. I the model, the acceleratio of MG, MG2 ad egie are also take ito cosideratio, because they are related to the eergy cosumptio or eergy geeratio. Fig 5.3 Data flow for HEV models I this study, there are 8 drivig modes which are used durig the simulatio for the HEV with the sigle epicyclic system:. Mode : Motor aloe mode 2. Mode 2: Combied power 3. Mode 3: Ccruise mode 4. Mode 4: Egie aloe mode 5. Mode 5: Regeeratio brakig 6. Mode 6: Mechaical brakig 7. Mode 7: Stadstill charge 8. Mode 8: Drivig charge 2

120 I the simulatio, the SOC is cotrolled to remai withi a reasoable rage: for example, as selected by (Mashadi ad Emadi 29). Because the egie is kept workig i the most efficiet area, the, if the required power is low, the extra eergy will be used to charge the battery. So the fial SOC maybe higher or lower tha the iitial SOC, depedig o the demad of the drivig cycles. This importat factor is allowed for later i the overall eergy or fuel cosumptio results. The cotrol strategy to decide the drivig mode for the HEV with sigle epicyclic system is show i Fig For the HEV with the twi epicyclic system, oe more mode is added: high efficiecy mode. This is because for a twi epicyclic system, there is oe more poit that the speed of oe of the motor/geerator is zero (Fig 5.32). This meas that at this poit, less power is trasmitted via the electrical route. To make full use of this, whe the trasmissio ratio fall withi the rage.5 to 2, MG2 is locked, ad the speed of the egie ad MG are adjusted to make the trasmissio ratio to be.72. I this mode, less power is coverted ito electricity ad the whole efficiecy of the powertrai is higher MG2 MG Speed of MG ad MG Trasmissio Ratio Fig 5.32 Relatioship of trasmissio ratio ad motor geerator speeds for the twi epicyclic system The coditio for the high efficiecy mode to be used is 58 < T is the procedure to describe this coditio is as follows: For MG, best speed rage is 5 to 6 rad/s < dl 5 < < 6 mg (5.28) 3

121 (5.29) mg = 2.9 e 7.77 < (5.3) < e To esure the egie always works aroud the optimum efficiecy area: < e < (5.3) (5.32) dl =.72 e 58 < dl <66.8 (5.33) Hece, there are 9 drivig modes used durig the simulatio for the HEV with the twi epicyclic system:. Mode : Motor aloe mode 2. Mode 2: Combied power 3. Mode 3: Cruise mode 4. Mode 4: Egie aloe mode 5. Mode 5: Regeeratio brakig 6. Mode 6: Mechaical brakig 7. Mode 7: Stadstill charge 8. Mode 8: Drivig charge 9. Mode 9: High efficiecy mode The cotrol strategy to decide the drivig mode for the HEV with twi epicyclic system is show i Fig

122 Fig 5.33 Rule based cotrol strategy for HEV with a sigle epicyclic trasmissio 5

123 Fig 5.34 Rule based cotrol strategy for HEV with a twi epicyclic trasmissio 6

124 5.7 Cocludig remarks Three vehicle models have bee developed; a covetioal IC egie vehicle with a maual gear box, a HEV with a sigle epicyclic gearbox, ad a HEV with a twi epicyclic gearbox. The models were derived usig a combiatio of the QSS toolbox together with additioal Matlab/Simulatio blocks. For example, it was coveiet to use the QSS software for some of the straightforward subsystems such as the IC egie ad battery, whereas ew Simulik blocks were writte for more specialized subsystems such as the epicyclic gearboxes. For the hybrid electric vehicle with the sigle epicyclic gearbox model, a total of eight drivig modes were idetified. While for the HEV model with the twi epicyclic gearbox, oe more mode was added to make a good use of the ode poit. Rule based cotrol strategies were derived for both the sigle ad dual epicyclic gearbox cases. For the modellig of the motor geerator uits, it was foud that the QSS software experieced difficulties at very low torques, so a ew Simulik S fuctio approach was proposed to overcome this problem. 7

125 6 Compariso of HEVs fitted with sigle ad dual epicyclic trasmissios 6. Itroductio I previous chapters, the sigle ad twi epicyclic gearbox arragemets have bee aalyzed ad modeled. The these gearbox models were combied with a hybrid electric vehicle model i Chapter 5. Results are ow geerated to ivestigate the performace of these two gearboxes i a hybrid electric vehicle (HEV). The results are calculated usig two of the commoly used drivig cycles the Europea NEDC ad USA FTP- 75cylces. The HEV results are also compared agaist a covetioal IC egie plus maual gearbox vehicle. The results focus o fuel cosumptio comparisos, but it is also show how the sigle ad twi epicyclic gearboxes use the egie ad motor geerator uits differetly. Fially, some observatios about drivability of the HEVs are made. 6.2 Drivig cycles Drivig cycles, which are produced by differet coutries ad orgaizatios, are stadardized drivig patters described by meas of a velocity-time table. Oe use of drivig cycles is to assess the performace of vehicles, such as fuel cosumptio ad emissio. I this case, the tests are usually performed o chassis dyamometers. Aother use of drivig cycles is i vehicle simulatios, especially used i propulsio system simulatios, as used i this research. I the simulatio, the drive system is modeled to predict performace of iteral combustio egies, trasmissios, electric drive systems, batteries, fuel cell systems, etc. There are two types of drivig cycle: modal drivig cycles ad trasiet drivig cycles. Modal drivig cycles ivolve protracted periods at costat speeds, while trasiet drivig cycles ivolves may chages, represetig the costat speed chages while drivig. 8

126 There are 3 groups of drivig cycles used aroud the world:. Europea drivig cycles, icludig ECE 5, EUDC, EUDCL, NEDC, HYZEM, etc. - these belog to the modal cycle category. 2. US drivig cycles, icludig FTP 72, SFUDS, FTP 75, HFEDS, IM24, LA 92, NYCC, US 6, etc. - these are trasiet cycles. 3. Japaese drivig cycles, icludig Mode, 5 Mode, -5 Mode, etc. - these are modal cycles. The choice of drivig cycles iflueces HEV desig decisios. Nearly all stadard drivig cycles are suggested to be less aggressive tha real-world drivig coditios. (Stobart ad Che 29) who also claim that desigig ew drivig cycles that are more represetative of real world drivig patters is a emergig research directio for HEV research. I this research, Europea NEDC ad the America FTP-75 will be used because they are relatively more represetative of real world drivig coditio tha other cycles, ad they are probably the most commoly used drivig cycles 6.3 Simulatio results 6.3. Fuel cosumptio For HEVs, the differece betwee the iitial ad fial battery SOC ca sigificatly affect the measuremet of fuel ecoomy. To elimiate this effect, the cocept of overall fuel cosumptio (OFC) was itroduced. The total additioal eergy stored or draw from the battery (kwh) is claculated ad the coverted ito how much fuel (liter) would be used for the egie to produced this amout of eergy. i) Egie fuel cosumpto (EFC, liter/km): actual fuel bured by the egie devided by the drivig distace; ii) Overall fuel cosumptio (OFC, liter/km): the fuel cosumtio after takig the battery eergy chaged (BEC) ito cosidio. BEC η OFC = EFC + eg / D (6.) ρ 9

127 i which ρ is the fuel desity (g/ml), η eg is the egie efficeecy(g/kwh) ad D is the drivig distace (m). The values for ρ ad η are.76 g/ml ad 24 g/kwh resepctively. I the simulatio, BEC is positive if eergy is draw from the battery ad egative if the eergy is stored ito the battery. So at the ed of each drivig cycle, if fial SOC is smaller tha the iitial SOC, amely the eergy is draw from the battery, overall fuel cosumptio is greater tha the egie fuel cosumptio, ad vice versa. It is very improtat to take accout of the battery SOC i the calculatios, because if it is differet at the ed of the drivig cycle from its value at the start the some et eergy has effectively bee lost or gaied i the vehicle calculatios. I several examples of results i the literature, it is ot clear whether this effect has bee accouted for. Also, some researches acutally use the cotrol system to esure that the battery start ad fiish coditios are exactly the same. However, this ca cause difficulties because the cotrol system is ot ecessaryly represetative of what it would be doig durig ormal practical drivig. The first set of results was used to compare the two PST arragemets with a baselie, covetioal vehicle equipped with a five speed gearbox (3.84, 2.,.36,.86 ad.63 with the same fial dive ratio). The cotrol strategies for the two PST arragemets were based o a rule-based approach to compromise betwee overall eergy efficiecy ad maitaiig the battery state of charge (SOC) uder cotrol. The vehicle models were ru over several differet drivig cycles, icludig the stadard NEDC ad USA FTP-75 drivig cycles, ad the overall fuel cosumptio results are show i Table 6.. Table 6. Comparisos of fuel cosumptio for the hybrid vehicle fitted with the 3 ad 4 brach systems compared with a covetioal, maual gearbox vehicle over differet drivig cycles Fuel cosumptio over drivig cycle, l/km Drivig cycle Traditioal Sigle epicyclic system Dual epicyclic system Egie FC Overall FC Egie FC Overall FC Europe NEDC USA FTP

128 Europe EUDC USA City I Japa Japa As expected, both hybrid vehicles show ecoomy advatages over the covetioal, maual gearbox vehicle. However, the improvemets are ot as great as published i some other studies, but this is uderstadable because the systems used here ad i particular their cotrollers have ot yet bee optimised. The mai aim of this work was rather to compare the 3 ad 4 brach drivelies uder exactly comparable coditios; this compariso is show i Table 6.2 ad it shows that the 4 brach system offers aroud sigificat improvemets over all the drivig cycles. The improvemets vary substetially with the differet cycles, varyig from 7.4% for the NEDC to 2% over the USA FTP-75 cycle. The reso for these substatial differeces is the suage of the mode 9 for the twi epucyclic gearbox. This is the high efficiecy mode which is oe of the potetial beefits of the twi epicyclic arragemet ad as show later i Figs 6.3 to 6.6 it is used more i the USA-FTP-75 drivig cycle. Oce agai, these results highlight the sesitively of efficiecy predictios to the assumptio about which drivig cycle to use i the calculatios Table 6.2 Percetage improvemet of the 4 brach over the 3 brach drivelie over differet drivig cycles Drivig cycle Percetage improvemet of 4 brach over the 3 brach drivelie (%) Europe NEDC 7.4 USA FTP Europe City 2.5 USA City I 7.2 Japa.5 Japa 9.

129 6.3.2 Egie operatio poits, power flow ad battery SOC The associated egie utilisatio maps are show i Fig 6. to Fig 6.6 for the baselie gearbox, the sigle epicyclic gearbox ad the twi epicyclic gearbox vehicles respectively. Each poit o the map of egie torque vs speed is the solutio at a sigle poit durig the NEDC cycle; the cycle defies iput from t = s to t = 22s. However, the NEDC cycle cotais a percetage of costat speed ruig coditios, so that several poits will sit o top of each other. First, these results highlight i Fig 6. ad Fig 6.4 the shortcomig associated with covetioal IC egie cars amely that they ievitably sped cosiderable time at part load coditios well away from the areas of maximum efficiecy. I cotrast, it ca be see i Fig 6.2 ad Fig 6.5 for the sigle epicyclic gearbox, that it maages the IC egie rather well through the combiatio of effectively its cotiuously variable gear ratio plus its ability to maage the electrical power flows i ad out of the battery. This results i the usage poits beig costraied aroud the area of maximum specific fuel cosumptio of the egie. Fially, i Fig 6.3 ad Fig 6.6 it ca be see that the dual epicyclic gearbox actually maages some further improvemet ad also reduces the use of the higher egie speeds. Fig 6. Egie operatio poits, NEDC cycle, traditioal ICE vehicle 2

130 Fig 6.2 Egie operatio poits, NEDC cycle, sigle epicyclic system Fig 6.3 Egie operatio poits, NEDC cycle, dual epicyclic system 3

131 Fig 6.4 Egie operatig poits, FTP 75, traditioal ICE vehicle Fig 6.5 Egie operatio poits, FTP75 cycle, sigle epicyclic system 4

132 2 25 Egie torque (Nm) Cosumptio g/kwh Egie speed (rad/s) Fig 6.6 Egie operatio poits, FTP75 cycle, dual epicyclic system Further isight ito the detailed behavior of the sigle ad dual epicyclic gearboxes ca be see i the time history plots i Fig 6.7 ad Fig 6.8 for the NEDC cycle ad Fig 6.9 ad Fig 6. for the USA FTP-75 cycle. The power utilizatio of the IC egie ad two motor geerator uits, MG ad MG2 are plotted alog with the vehicle speed profile specified i each of these drivig cycles. Fig 6.7 Power flows i the HEV with the sigle epicyclic gearbox over NEDC drivig cycle 5

133 Fig 6.8 Power flows i the HEV with the dual epicyclic gearbox over NEDC drivig cycle Fig 6.9 Power flows i the HEV with the dual epicyclic gearbox over FTP-75drivig cycle 6

134 Fig 6. Power flows i the HEV with the dual epicyclic gearbox over the FTP-75drivig cycle The results i Figs 6.7 to 6. also highlight the substatial differeces betwee the Europea ad USA stadard drivig cycles; the Europea versio cotais a much greater umber of statioary ad costat speed ruig evets, whereas the USA versio is almost cotiually chagig speed i its versio of a urba cycle. This reflects a fudametal difficulty withi the vehicle idustry whe it has to try ad make fair comparisos of competig drivelie techologies regardig their eergy cosumptio what actually costitutes a represetative drivig patter over which to make comparisos? The aswer is likely to vary across the three major global automotive markets Europe, USA ad the Far East. But the acceptace of a so-called stadard cycle also raises aother potetial problem that i the quest for the best headlie figures, the drivelie ad particularly its cotroller is actually optimised aroud the specific cycle. This ca lead to egieerig developmets based more aroud the stadard tha aroud a drivable, efficiet vehicle across a wider rage of operatig coditios. Battery SOC plays a importat role i the research of HEV performace ad all eergy maagemet strategies eed to take the SOC ito cosideratio. For example, keepig the SOC at the ed of drivig cycles the same as the begiig 7

135 of the cycle is the goal of some strategies. I this research, the SOC is kept i a reasoable rage, from.5 to.75. Fig 6. ad Fig 6.2 show example of the chage of SOC over the two cycles. Battery SoC Battery SoC, sigle epicyclic system Battery SoC, dual epicyclic system time Vehicle spd (m/s) time Fig 6. Battery SOC over the NEDC5 cycle.72 Battery SoC Battery SoC, sigle epicyclic system Battery SoC, dual epicyclic system time 3 Vehicle spd (m/s) time Fig 6.2 Battery SOC over the FTP-75 cycle 8

136 6.3.3 Mode selectio aalysis For HEVs with sigle ad twi epicyclic trasmissio, the selectio of drivig mode durig NECD ad FTP-75 cycle is show i Fig 6.3 ad Fig 6.4 respectively. The mai differece is that for twi epicyclic trasmissio, oe more mode: high efficiecy mode is selected. The percetage of time spet i each mode selected is show i Fig 6.5 ad Fig 6.6. For HEV with twi epicyclic trasmissio, durig NEDC cycle, the percetage of time spet i the high efficiecy mode is.7%, while durig FTP-75 cycle, this figure is 3.7%. This goes some to explaiig why the improvemet of fuel cosumptio over NEDC cycle is lower tha the improvemet over FTP-75 cycle (Table 6.). Drivig mode Drivig mode Vehicle spd (m/s) Sigle epicyclic trasmissio Twi epicyclic trasmissio time Fig 6.3 Mode selectio, Europe NEDC cycle 9

137 6 Drivig mode Sigle epicyclic trasmissio Drivig mode Vehicle spd (m/s) Twi epicyclic trasmissio time Fig 6.4 Mode selectio, USA FTP-75 cycle 2

138 Europe NEDC Sigle Epicyclic system Twi epicyclic system. Motor aloe Combied power Cruise mode Egie aloe Regeeratio brakig Mechaical brakig Stadstill charge Drivig charge High efficiecy Fig 6.5 Relative amout of time spet i each mode, NEDC cycle USA FTP Sigle Epicyclic system Twi epicyclic system..5 Motor aloe Combied power Cruise mode Egie aloe Regeeratio brakig Mechaical brakig Stadstill charge Drivig charge High efficiecy Fig 6.6 Relative amout of time spet i each mode, FTP-75 cycle 2

139 6.3.4 Motor ad geerator operatio poits For the HEV with the sigle epicyclic trasmissio, the operatio poits of MG ad MG2 over NEDC cycle are show i Fig 6.7 ad Fig 6.9. For the HEV with the twi epicyclic trasmissio, the operatio poits of MG ad MG2 over NEDC cycle are show i Fig 6.8 ad Fig MG Torque (Nm) MG Speed (rad/s) Fig 6.7 Operatio of MG, sigle epicyclic system, NEDC cycle MG Torque (Nm) MG Speed (rad/s) Fig 6.8 Operatio of MG, twi epicyclic system, NEDC cycle 22

140 For both MG ad MG2, the cotrol strategies were desiged that the motor/geerators work withi the maximum torque curve. If oe of the calculatio poits suggests that oe of the electric machies is overspeed or overload, the cotroller will chage the speed ad/or torque of the egie to make sure every elemet is workig i the correct operatio rage Torque (Nm) MG2 Speed (rad/s) Fig 6.9 Operatio of MG2, sigle epicyclic system, NEDC cycle Torque (Nm) MG2 Speed (rad/s) Fig 6.2 Operatio of MG2, twi epicyclic system, NEDC cycle 23

141 6.4 Vehicle performace 6.4. Top speed For covetioal IC egied vehicle, the top speed that ca be reached o level road with a give trasmissio ratio ca be foud by itersectig the curve of the available power at the wheels with that of the required power o level road (Geta ad Morello 28). The available power for gears I, II, III, IV ad V are calculated as: for the give gear ratio, assume the egie always works o the egie speed-maximum egie torque curve. P = η P = η ω T ( 6.2) a t e t eg eg _ max P = ( F + F ) V ( 6.3) rr ad where: P a is the available power; P is the required power; T eg _ max is the egie s miximum torque F rr is the rollig resistace force; Fad is the aerodyamic drag; ηt is the efficiecy of the whole powertrai; The vehicle speed uder each gear is V = i gear r is the radius of the tire; ω eg ( 6.4) r i differetial i gear is the trasmissio ratio of each gear; i differetial is the trasmissio ratio of the differetial. The power required ad the available power for each gear ratio are show i Fig 6.2. For the IC egied vehicle the top speed is 54.5 m/s (96.2km/h). For full hybrid vehicles, if the egie is ot dowsized, the vehicle is almost retai to have better overall performace compared with a covetioal vehicle (Cha 27). As far as the top speed is cocered, because the power split device is actually a CVT, it ca chage the trasmissio ratio to achieve the highest top 24

142 speed, as show i Fig the top speed for the HEV with a E_CVT is 58.6 m/s (2.9 km/h). 5 Power required Power available for I gear Power available for II gear Power available for III gear Power available for IV gear Power available for V gear Power (kw) Vehicle speed (m/s) 5 Fig 6.2 Top speed for the covetioal vehicle (55.92m/s) Trasmissio.6 Power (kw) Vehicle speed (m/s) Fig 6.22 Top speed for a HEV with a CVT 25

143 I practice, for a full HEV it is ormal desig practice to dowsize the IC egie. The challege for the cotroller desig is the to maximize the time spet by the egie toward its optimum efficiecy regio by cotrollig the power flows to ad from the battery. However, this should ot compromise overall performace ad drivability compared to the equivalet IC egie vehicle. So the cotroller exploits the cotiuously variable trasmissio ratio to address this compromise Acceleratio The maximum acceleratio a vehicle is capable of at various speeds is (Geta ad Morello 28): where dv dt η t Pe P η P ( F + F ) V ( 6.5) t e rr ad = = m V m ( V ) max e e + m e is the equivalet mass of the vehicle; P e is the egie power; P is the required power. The plot of maximum acceleratio versus vehicle speed of the traditio IC egied vehicle with a five speed gear box is show i Fig The miimum time eed to accelerate from speed V to V2 ca be calculated by itegratig Eq. ( 6.6), but usually umerical itegratio is performed I gear II gear III gear IV gear V gear Accleratio (m/s 2 ) Vehicle speed (m/s) Fig 6.23 Maximum acceleratio versus vehicle speed 26

144 A graphical iterpretatio of the itegratio is show i Fig 6.24, which plots (/acceleratio) vs. vehicle speed. The area uder the curve /a is the miimum time required for the acceleratio. Fig 6.24 /a versus vehicle speed The miimum time of acceleratio for a HEV with a PST (power split trasmissio) is show i Fig The dark area is the time to speed for a HEV with a CVT. Fig 6.25 /a versus vehicle speed. 27

145 The time-speed curve, as show i Fig 6.26 ca be obtaied by itegratig the dark area i Fig 6.24 ad Fig From Fig 6.26, it shows that the time to accelerate from to km/h (27.78 m/s) for a vehicle with a geared trasmissio ad a HEV with a PST is 2.3 s ad 4.4 s, respectively CVT Vehicle speed (m/s) Geared trasmissio Drivig aggressiveess time (s) Fig 6.26 Speed versus time curve A study at the Argoe laboratory demostrated that HEVs have a higher fuel cosumptio sesitivity to aggressive drivig (Sharer, Leydier et al. 27). They defie more aggressive drivig to mea more use of periods of higher acceleratios that idicated i the typical drivig cycles. I this study, the sesitivity of the two HEV models to drivig aggressiveess was calculated ad the results are show below. The FTP 75 drivig cycle is used as a baselie drivig iput for the comparisos. The, a simple multiplier factor of.8..9,. ad.2 was imposed to get cycles that represet differet drivig aggressiveess. The bigger the factor, the more aggressive the drivig cycle becomes sice the speeds ad hece acceleratios are simply icreased. Factor.8 meas the cycle is less aggressive tha the baselie cycle ad factor.2 meas the cycle is more aggressive tha the baselie cycle, as show i Fig

146 Fig 6.27 Drivig cycles with differet drivig aggressiveess The simulatio result is show is Table 6.3. Table 6.3 Fuel cosumptios with differet drivig aggressiveess Scalig Factor Traditioal ICE Sigle epicyclic system Dual epicyclic system Overall Fuel cosumptio Normalized Fuel cosumptio Overall Fuel cosumptio Normalized Fuel cosumptio Overall Fuel cosumptio Normalized Fuel cosumptio *Note: all the ormalized fuel cosumptios are ormalized to 3.64, which is the overall fuel cosumptio of the traditioal ICE with scalig factor. First, the overall beefits of the twi epicyclic over the sigle epicyclic ad the traditioal ICE are show to occur cosistetly over all limited rage of drivig aggressiveess tested here. The, the same results are plotted i Fig 6.28 showig the tred of the fuel cosumptio figures ormalized to the traditioal ICE at a scalig factor of. These curves provide iformatio o how sesitive each system is to drivig aggressiveess as idicated by the slope of the lies. The ICE case is show to be rather isesitive; the twi epicyclic is somewhat less 29

147 sesitive tha the sigle epicyclic as the drivig aggressiveess icreases above. this agai relates to the greater flexibility of maagig the power flows betwee the mechaical ad electrical paths..4 Normalized fuel cosumptio Scallig factor Sigle epicyclic system Dual epicyclic system Traditioal vehicle Fig 6.28 Sesitivity to drivig aggressiveess fuel cosumptio ormalized to the baselie ICE coditio 6.5 Cocludig remarks The four brach, dual epicyclic gearbox arragemet offers a sigificat performace beefit over the three brach, sigle epicyclic arragemet; fuel ecoomy improvemets of 7 ad 2% were show over the two mai Europea ad USA drivig cycles. The performace beefits arise from the greater flexibility of cotrol over the torques, speeds ad power flows through the two motor geerator uits available with the dual epicyclic scheme. For a HEV with a PST, which provides the beefits of a CVT gearbox, if the egie is ot dowsized, the HEV will have better drivability, amely higher top speed ad shorter acceleratio time. I practice, the ormal desig approach for a HEV is to dowsize the egie, ad improve overall fuel cosumptio, whilst exploitig the trasmissio ad cotroller properties to obtai similar performace to the equivalet ICE vehicle. 3

148 The four brach system is slightly less sesitive to icreased drivig aggressiveess tha the 3 brach system, because it ca cotrol the power flows better accordig to differet drivig coditios. I practice, further beefits are probably available; first, the dual arragemet has two odal positios at which zero electrical power circulates ad these ca be desiged to occur at coveiet speeds, e.g. i the UK, 3 mile/h i urba drivig ad 7 mile/h motorway cruisig. Secod, with the dual arragemet it is possible to dowsize the motor geerator uits to retai the same driveability but with reduced weght ad cost. Although the results preseted here have bee based o relatively simple vehicle models, it is likely that the promisig results for the twi epicyclic trasmissio could be further improved usig more sophisticated optimisatio strategies for the cotrol system. 3

149 7 Electric vehicle with trasmissio system 7. Itroductio The work o trasmissio performace for HEVs is exteded i this chapter to ivestigate the potetial role of trasmissio desig for EVs. As observed i the itroductio i Chapter, global iterest i EVs has grow at a dramatic rate particularly over the curret decade. May of the major OEMs, e.g. GM, Nissa, Reault will shortly be marketig commercial versios of EVs. I the UK, the govermet has bee very active i tryig to promote the EV idustry as part of its Low Carbo Vehicle (LCV) Techology programmes. This has resulted i may compaies becomig ivolved i developmet of EVs sometimes for iche markets i order to establish early leadership of the developig techology. Despite this high worldwide level of iterest i EVs some aspects of the vehicle techology have received little attetio. The trasmissio desig is oe such area ad perhaps it is uderstadable that the majority of research attetio has to date focused o the more obvious topics of batteries, motors ad power electroics. The aim of this chapter is to ivestigate whether there are ay potetial efficiecy or performace beefits for usig geared trasmissios for EVs. Predicted results are compared for a typical EV without a gearbox, with a CVT ad with a covetioal stepped gearbox. As for the HEV results, predictios are made over the stadard drivig cycles. Oe of the critical features i this study is the usage of the electric motor i its regio of high efficiecy. Cosequetly, two motors were modeled i this work i order to uderstad the sesitively of the results to the assumptios about motor efficiecy maps. These motors will be referred to as a theoretical motor derived from geeric equatios ad a practical motor which is effectively a look-up map from the maufacturers data. 32

150 7.2 Electric vehicle modelig 7.2. Vehicle modelig The modellig of the electric vehicle performace is also doe usig the QSS Toolkit (Guzzella ad Amstutz 25). This is a quasistatic simulatio package based o a collectio of Simulik blocks ad the appropriate parameter files that ca be ru i ay Matlab/Simulik eviromet. The vehicle model itself is straightforward ad is show i Fig 7.; it is a covetioal plug-i type EV with the additio of a gearbox i the power trai. Fig 7. Block diagram of EV model Two types of motors were used i this research: a geeric motor ad a practical motor. The geeric motor characteristics are iteded to represet a typical geeric motor of 4 kw. They were take from Larmiie s book (Larmiie ad Lowry 23) who presets a Matlab script to geerate a set of geeric motor properties based o assumptios about the losses withi the motor. The data of the practical motor were give by UQM ( 29), a America compay that develops ad maufactures high-performace, powerdese ad eergy-efficiet electric motors, geerators ad related power electroics. This motor was selected as beig represetative of a curret, off-theshelf motor suitable for electric vehicle applicatio. The iput to the model is oe of the stadard drivig cycles the NEDC cycle ad USA FTP 75 are used extesively i this work ad the solutio procedure is based o steppig through the drivig cycle at typically oe secod steps, calculatig the equilibrium coditio ad the collectig all the data for plottig at the ed of the cycle. The modellig assumptios are kept very simple i this iitial work, so that o accout is icluded of losses i the gearbox. Thus, the focus of attetio is o the motor efficiecy map ad the major issue of whether it is 33

151 possible to improve overall eergy usage by operatig at or ear to the best efficiecy poits Method of selectig motor operatio poit 25 2 (x, y ) Torque (Nm) 5 (x, y) Costat power lie, power = x * y Electric Motor Speed (rad/s) Fig 7.2 Schematic diagram of selectig motor operatio poit The schematic diagram of selectig motor operatio poit is show i Fig 7.2. For a geeric motor, the efficiecy of each poit is calculated as follows. For ay give poit ( x, y), Power = Power Power output = x * y ( 7.) kc * y + ki * x + kw * x CoL ( 7.2) iput output + η ( x, y) Power x * y output = = 2 3 Poweriput x * y + kc * y + ki * x + kw * x + CoL ( 7.3) where 2 kc * y, ki * x, 3 kw * x ad CoL are copper losses, Iro losses, widage losses ad costat motor losses respectively. I this study, kc, k, kw ad CoL are.2,.8,. ad 4 respectively. 34

152 Let x, ) represet ay poit alog the costat power lie o ( y which power = x * y, x * y = x * y ( 7.4) eta( x, y ) x * y = 2 3 x * y + kc * y + ki * x + kw * x + CoL ( 7.5) For Equatio ( 7.5), replace y with x * y, we ca obtai x eta( x, y ) = kw * x 5 + ki * x 3 power * x 2 + ( power + CoL) x 2 + kc * power 2 ( 7.6) Oce the expressio of efficiecy for ay poit alog the costat power lie is give, Matlab ca be used to search for the most efficiet poit. For the practical motor, the efficiecy of each poit is obtaied via iterpolatio of data give by the motor maufacturer, so effectively it is iput as a look-up table ad Matlab is used to iterpolate betwee the data poits to fid a specific operatig coditio. 7.3 Results with a geeric motor The vehicle parameters for the EV with the geeric motor are summarised i Table 7.; they are iteded to be represetative of a typical geeric vehicle rather tha ay specific desig. The motor rated power is 4 kw, ad the total vehicle mass is set to be 95 kg. Table 7. Vehicle parameter data Parameter, uits Value Total vehicle mass, kg 95 Wheel diameter, m.5 Aerodyamic drag coefficiet.22 Frotal area, m 2 2 Rollig resistace coefficiet.8 Motor maximum torque, Nm 24 Motor maximum speed, rad/s 8 Motor power, kw 4 Fial drive ratio

153 7.3. EV with sigle trasmissio ratio The first results show i Fig 7.3 refer to the baselie coditio of the vehicle with o gearbox. Each poit o the map of motor torque vs. speed is the solutio at a sigle poit durig the NEDC cycle; the cycle defies iputs from t = s to t = 22 s. The top half of the figure refers to coditios i which the motor is deliverig power ad the bottom half to coditios i which the motor acts as a geerator ad regeerates power which is fed back to the battery. The efficiecy lies i the top half are defied as (iput power required/output power delivered); the efficiecy lies i the lower half are defied as (power regeerated/iput power) From to 66.7 rad/s the maximum torque that the motor ca deliver is 24 Nm, ad after this poit the maximum power lie is show i Fig Torque (Nm) Electric Motor Speed (rad/s) Fig 7.3 Motor operatio poits with o gearbox I this case, the maximum power lie is actually the lie for rated power, which is 4 kw. O each poit of that lie, power = torque speed = 4kW ( 7.7) 36

154 This meas that if it is ru at this power, its temperature will settle dow to a safe level. Because it is fairly large ad heavy, it takes some time to heat up to a dagerous value. So if i ay case more power is eeded, it ca be ru i excess of 4 kw, as log as this is cotrolled less tha about miute. This is extremely useful for a electric vehicle as peak power may oly eeded for a short period of time, such as whe acceleratig (Larmiie ad Lowry 23) EV with cotiuously variable gearig The ext results assume that the gearbox is ifiitely variable so that ay ratio ca be selected; i fact upper ad lower limits are applied so that the ratio ca be ay value betwee 4 ad.6. The calculatio procedure is effectively a simplified optimisatio strategy. At ay poit i the drive cycle, the torque ad speed demaded of the motor are first calculated; the, for this power requiremet a search routie is used with the motor map to fid the poit of maximum efficiecy ad the appropriate gear ratio selected so that the motor ca operate at this poit ad still deliver the ecessary torque ad speed to the drivig wheels Torque (Nm) Electric Motor Speed (rad/s) Fig 7.4 Motor operatio poits with cotiuously variable gear 37

155 It is further assumed that the gearbox respose would be fast eough to follow these chagig requiremets. Thus, the results show i Fig 7.4 effectively describe the optimisatio of the motor usage over the selected NEDC drive cycle. It is clear from Fig 7.4 that the results follow the omial lie of maximum efficiecy of the motor. The gear ratios selected by the algorithm to achieve this are show i Fig Gear Ratio Time (s) Fig 7.5 Gear ratios selected by optimisatio strategy EV with a multispeed gearbox The results show i Fig 7.6 refer to the case i which it is assumed that a four speed gearbox is fitted i the trasmissio. The ratios are selected i a rather subjective fashio after ispectio of Fig. 4, ad are 2.5,.5, ad.8; i practice, the gear ratio selectio would be doe automatically rather tha maually as with a covetioal IC egie car. Here, a simplistic gear selectio strategy is used: i) For costat speed ruig the highest gear (lowest umerical ratio) is selected ii) Whe acceleratig, the ratio is based simply o speed such that the above ratios are selected for the speed rages -, -2, 2-3 ad 3-8 rad/s. 38

156 It is ot suggested that this is i ay way optimal, but this approach is chose to uderstad the sesitivity of the eergy usage predictios to practical desig issues Torque (Nm) Electric Motor Speed (rad/s) Fig 7.6 Motor operatio poits with four gear ratios Torque (Nm) Fig Electric Motor Speed (rad/s) Motor operatio poits with two gear ratios 39

157 The results are the repeated for two other gearboxes: i) 3 speed with ratios of 2, ad.8 ii) 2 speed with ratios of 2 ad.8 for the speed rages -3 ad 3-8 rad/s The motor operatio poits for the 2 gear system are show i Fig 7.7. The results are summarized i Table 7.2 showig the relative eergy cosumptios for the differet geared systems over the NEDC cycle. The improvemets resultig from fittig a additioal gearbox are actually rather modest over the NEDC cycle. The percetage improvemets would, i practice, be immediately cacelled out by the additioal efficiecy losses i the gearbox itself, which have iitially bee igored i this work. Oe of the potetial advatages of a geared trasmissio relates to possible improvemets i drivability. For example, the to km/h acceleratio time of the fixed gear vehicle is 8.3 s, whereas with just 2 gears, this time is reduced to 2.4 s. The top speed of 83 km/h of course remais uchaged. Table 7.2 Efficiecy improvemets for differet gearboxes over the NEDC cycle Eergy cosumptio per km (kwh/km) o gear CVT speed speed speed Improvemet % This raises the possibility that oe of the advatages of a simple geared system would be to dowsize the motor, but still retai the same drivability characteristics. Whether this is a practical propositio will deped largely o the specific vehicle applicatio, ad the detailed properties of the motor selected relative to the critical vehicle properties of mass, rollig resistace ad aerodyamic drag. For example, although the NEDC is widely used as a stadard drivig cycle, the peak power demaded from the motor is oly 2.9 kw. I practice, the peak power of the 4

158 motor would have to be aroud double this value i order to provide a sufficietly high level of acceleratio to meet customer demads Effect of drive cycle Oe of the fudametal problems ow facig the automotive idustry i their quest to develop eergy efficiet vehicles is a methodology which eables robust comparisos of competig desigs. The approach adopted to date has largely depeded o stadard drivig cycles. This is defesible from a scietific poit of view because vehicle desigs are the compared uder like-for-like iput coditios. But oe of the major issues is the what exactly costitutes typical drivig cycles which somehow represet ormal everyday drivig? Ievitably, this has led to the developmet of may so-called stadard drivig cycles ad these to some extet do reflect differet drivig patters i the three major world markets: Europe, USA ad Far East. Some idea of this problem is highlighted i Table 7.3, i which the EV results are repeated for six differet drivig cycles. These results are somewhat more promisig. Over four of the six cycles, the improvemet usig cotiuously variable gearig is betwee 9.6 ad 2.4%. Eve though some of these efficiecy gais would be lost through the losses i the trasmissio, there are still some worthwhile gais to be exploited. Of course, these would also be set agaist the additioal cost, weight ad complexity of the trasmissio system. However, small efficiecy gais of this order would be seriously cosidered i IC egied vehicles as part of the reletless quest for ay efficiecy gais possible. Hece, it is likely that as electric vehicles become more commo, compaies will be searchig for all potetial ways of improvig efficiecy. The two most represetative drivig cycles are the Europe NEDC ad the USA FTP-75; the Europe City ad USA City are actually oly subsets of these loger cycles ad the Japa cycles are rather short ad simple. The results for the USA FTP-75 are rather promisig; this cycle has less costat speed ruig ad iclude more acceleratio cycles up to the 4 to 5 km/h regio. So the effect of the cotiuously variable gearbox over these coditios is to offer a greater improvemet. 4

159 Table 7.3 Drivig cycle Comparisos of improvemets i eergy cosumptio over 6 differet drivig cycles No gearbox 4 speed gearbox Cotiuously variable gearbox Eergy cosumptio (kwh/km) Eergy cosumptio (kwh/km) Improvemet % Eergy cosumptio (kwh/km) Improvemet Europe NEDC Europe City USA FTP USA City I Japa mode Japa mode Results with the practical motor The vehicle parameters for the practical motor are summarised i Table 7.4. Compared with the parameters used for the previous motor, the vehicle is heavier ad has bigger drag coefficiet. This is because the data for the motor is from a 75 kw motor, which should be used o a larger vehicle. This does ot affect the usefuless of the results, because the primary objective is to ivestigate the potetial beefits of differet trasmissios i a typical EV applicatio. % Table 7.4 Vehicle parameter data for the model with UQM motor Parameter, uits Value Total vehicle mass, kg 2 Wheel diameter, m.5 Aerodyamic drag coefficiet.3 Frotal area, m 2 2 Rollig resistace coefficiet.8 Motor maximum torque, Nm 24 Motor maximum speed, rad/s 75 Motor power cotiuous, kw 45 Motor power maximum, kw 75 42

160 7.4. Results from simulatios over the NEDC cycle No gearbox The first set of results were all carried out usig the NEDC drivig cycle; this is remai the most commoly used drivig profile used i Europe, although as observed previously cosiderable cotroversy surrouds the idea of what are claimed to be stadard drivig cycles. The NEDC cycle ad the resultig torque demad or this vehicle are show i Fig Torque (Nm) Time (s) Vehicle speed (m/s) Time (s) Fig 7.8 NEDC cycle vehicle speed profile ad required torque at the differetial The first phase of the NEDC cycle comprises four repeats of a city phase, i which there are sigificat periods of low speed costat ruig. The secod phase is iteded to represet urba drivig ad cosists agai of substatial periods of costat speed ruig, this time at higher speeds. The required torque figures at the iput to the differetial assumig that the reductio gear would be icorporated here emphasise the low torque requiremet wheever the vehicle is ruig at costat speed. For the covetioal arragemet i which there is o gearbox, the choice of sigle reductio, fial drive ratio is importat; it is a compromise betwee acceleratio performace or more geerally the whole feelig of drivability ad overall eergy usage. Several fial drive ratios were tested over the NEDC cycle ad the results are show i Table 7.5. The ratio of 3.5 was selected o the basis 43

161 of a fairly subjective judgemet of miimisig eergy cosumptio whilst retaiig reasoable acceleratio capability Table 7.5 Eergy cosumptio over the NEDC cycle for differet fial drive ratios Fial drive ratio Eergy cosumptio per km (kwh/km) The motor operatio poits with o gearbox are show i Fig Torque (Nm) Electric Motor Speed (rad/s) 9 Fig 7.9 Motor operatio poits with o gearbox NEDC cycle Each poit is the result of a idividual calculatio at s itervals. However, some care must be used whe iterpretig this graph because i the costat speed ruig coditios, the required tractive motor torque is costat ad so may poits lie exactly o top of each other. Hece, the seve poits of low torque 44

162 below 25Nm are actually much more sigificat tha might appear, because each poit actually represets several secods of costat speed ruig; the exact data ca be extracted from Fig 7.8. But these poits are importat i overall eergy calculatios because they all lie i a regio of very low motor efficiecy. Of course, the overall effects o the total eergy losses are a combiatio of the facts that although the motor efficiecy is low, so too is the absolute value of torque delivered hece the overall effect may ot be as sigificat as it may first appear. Cotiuously variable gearbox The NEDC cycle is the repeated assumig a cotiuously variable gearbox is fitted i the trasmissio, ad the motor operatio poits are show i Fig 7.. These are simplified, idealised calculatios igorig at this stage ay efficiecy losses i the trasmissio itself Torque (Nm) Electric Motor Speed (rad/s) 9 Fig 7. Motor operatio poits with a cotiuously variable gearbox NEDC cycle 45

163 The calculatios are based o the followig procedure: for each torque demad sample the gear ratio is calculated which results i the motor torque ad speed beig optimised i terms of the motor operatig efficiecy. The calculatio requires some iterpolatio of the motor data poits which are show as joied-up curves i Fig 7.. Thus, the overall approach is effectively a simple optimisatio procedure, ad the results i Fig 7. show how the poits ow cogregate i the optimum motor efficiecy regio. I practice, the gear ratio selectio is a compromise betwee acceleratio capability more geerally referred to as drivability ad eergy usage or fuel cosumptio. This is, of course, the case for all vehicles, irrespective of their power source. Hece, two further sets of results to highlight the sesitivity of the gear ratio selectio are show i Fig 7. ad Fig 7.2. Gear ratio Time Vehicle speed (m/s) Fig 7. Gear ratio selectio for maximum motor efficiecy for a costat acceleratio of.7 m/s 2 46

164 Gear ratio Time Vehicle speed (m/s) Fig 7.2 Gear ratio selectio for maximum motor efficiecy for icreasig values of costat ruig speed I Fig 7. the vehicle is assumed to start from rest ad accelerate at a costat value of.7 m/s 2 up to its maximum speed. I Fig 7.2, the vehicle effectively does the same thig except that it also ow icludes a period of costat ruig at each icremet of 2.5 m/s. At first sight the values for selected gear ratio are ot as smooth as might be expected as the speed chages but this is simply a result of the iterpolatio required o the motor torque/speed/efficiecy map. However, two importat treds are highlighted; firstly, whe acceleratig, the selected gear ratio is early always aroud oe or higher at the lower speeds, ad secodly, for the vast majority of the costat speed coditios the gear ratio is aroud the.5 figure. The implicatio is that for the NEDC cycle, a simple trasmissio which just has two ratios may offer a combiatio of mechaical simplicity ad sigificat eergy improvemet. This idea is the tested by plottig out a probability distributio for the gear ratios selected by the cotiuously variable gearbox strategy durig the NEDC cycle (Fig 7.3). Each bar i Fig 7.3 represets a badwidth of.4 of the gear 47

165 ratio distributio. These results suggest that a gearbox based o just two ratios of aroud.6 ad may offer beefits Probability (%) Gear ratio Fig 7.3 Gear ratio selectio show as a probability distributio over the NEDC cycle assumig a cotiuously variable gearbox Four speed gearbox First however, the results are repeated assumig a rather covetioal four speed gearbox with ratios of.5,.8, ad.5 is fitted. Agai, it ca be see i Fig 7.4 that this results that motor operatio poits fairly well clustered aroud the optimum motor efficiecy regio. The overall eergy cosumptio results over the total NEDC cycle are compared with those for the cotiuously variable gearbox i the top row of Table 7.6. The improvemets over the o gearbox case are 8.7% for the CVT ad.4% for the four speed gearbox. These are clearly very sigificat improvemets, eve allowig for the mechaical efficiecies of the gearbox i practice. 48

166 Table 7.6 Drivig cycle Comparisos of improvemets i eergy cosumptio over 6 differet drivig cycles No gearbox Eergy cosumptio (kwh/km) Cotiuously variable Eergy cosumptio (kwh/km) gearbox Improvemet % 4 speed gearbox 2 speed gearbox Eergy cosumptio (kwh/km) Improvemet % (o acc:.5; acc: ) Eergy cosumptio (kwh/km) Improvemet % Europe NEDC Europe City USA FTP-75 USA City I Japa mode Japa mode Torque (Nm) Electric Motor Speed (rad/s) 9 Fig 7.4 Motor operatio poits with a 4 speed gearbox NEDC cycle 49

167 Two speed gearbox Next, the results are repeated for a two speed gearbox with ratios of.5 ad. A very simple gear selectio strategy is ow used; for costat speed ruig the value of.5 is used ad for all other coditios a value of is selected. The results i Fig 7.5 suggest that this approach leads to results similar to those obtaied for the four speed case. Ad the results i Table 7.6 cofirm this observatio; the overall improvemet for the two speed case is 9.2% compared with the.2% figure obtaied for the four speed case ad 8.7% for the CVT Torque (Nm) Electric Motor Speed (rad/s) 9 Fig 7.5 Motor operatio poits with a 2 speed gearbox NEDC cycle Simulatio results for the USA FTP-75 cycle No gearbox The USA FTP-75 drivig cycle alog with the required torque values for the vehicle data used i this study are show i Fig 7.6. Although this is similar i legth to the NEDC cycle, a major differece is apparet it ivolves hardly ay 5

168 costat speed ruig. The cosequeces of this are twofold; the improvemet offered by the CVT remais substatial at 9.2%, but the improvemets offered by the two ad four speed gearbox cases are sigificatly less tha for the NEDC coditios. 2 Torque (Nm) Time (s) Vehicle speed (m/s) Time (s) Fig 7.6 USA FTP-75 cycle vehicle speed profile ad required torque at the differetial Torque (Nm) Electric Motor Speed (rad/s) Fig 7.7 Motor operatio poits with o gearbox USA FTP-75 cycle 5

169 These differeces are see more clearly, for example, i Fig 7.7 which plots the motor operatio poits with o gearbox. Because the required acceleratio i the USA FTP-75 is cotiuously chagig, the motor operatio poits are much more widely spread tha those for the equivalet NEDC results i Fig 7.9. CVT gearbox The results usig the CVT arragemet are show i Fig 7.8 ad as before, it is clear how the simple optimisatio strategy works i cogregatig the poits aroud the optimum motor efficiecy regio. Fially, i Fig 7.9, the probability distributio of gear ratios for the USA FTP-75 is plotted usig a similar scale to the previous oe (Fig 7.3) for the NEDC cycle. The spread of gear ratio usage throughout the cycle is show to be sigificatly greater tha that for the NEDC cycle Torque (Nm) Electric Motor Speed (rad/s) Fig 7.8 Motor operatio poits with a CVT USA FTP-75 cycle Overall, these results highlight oe of the cocers facig the idustry ivolved i low carbo vehicle techology. Whilst it is perfectly reasoable form a scietific viewpoit to compare competig schemes over a stadard drivig cycle so the vehicle powertrais are subjected to exactly the same requiremets, it is also a 52

170 matter for debate as to what costitutes a reasoable ad represetative drivig cycle. Ad a further complicatio is that the aswer to this questio is likely to be substatially differet i differet markets aroud the world. There are obvious differece betwee trasportatio systems ad road ifrastructures across the three major automotive markets i Europe, USA ad Far East. Ad already it ca be observed that differet stadard drivig cycles have bee recogized i these markets Probability (%) Gear ratio Fig 7.9 Gear ratio selectio show as a probability distributio over the USA FTP75 cycle assumig a cotiuously variable gearbox Effect of drivig cycle The sesitivity of these results to differet drivig cycles is summarised i Table 7.6 usig those cycles which are available i the QSS software. The results are rather variable: the CVT arragemet early always results i sigificat improvemets but the results for the two ad four speed cases are ot as promisig. The results highlight a major issue which is relevat to all the work o comparisos of alterative propulsio systems the eergy usage results are highly sesitive to the drivig cycle used. This coclusio emphasises the eed for extreme cautio i iterpretig claimed improvemets with competig systems for eergy efficiet vehicles. 53

171 For the results calculated here, the NEDC ad USA FTP-75 cycles are probably the two most represetative cycles ivolvig a combiatio of city ad urba drivig over a substatial period. The Europe City ad USA City are actually subsets of these cycles ad the Japaese cycles are very short ad simple Compariso of the results from two motors The results of eergy cosumptio for the vehicle with a geeric motor are show i Table 7.3. The results of eergy cosumptio for the vehicle with a practical motor are show i Table 7.6. The ext stage is to aalyze the differece betwee the two motors. Fig 7.2 Compariso of eergy cosumptio Fig 7.2 shows the eergy cosumptio for the two motors over 6 drivig cycles. The vehicle with the practical motor has higher eergy cosumptio tha the vehicle with the practical motor. This is simply because some of the vehicle parameters are differet (Table 7. ad Table 7.4). But the treds over drivig cycles are the same USA City I is the highest ad Europe City is the lowest. It is obvious that, for both the geeric motor ad the practical motor, the vehicle with a CVT has higher improvemet tha the vehicle with a 4 speed gear box, which is show i Fig 7.2 ad Fig This is because with a CVT, more freedom of selectig the highest efficiecy operatio poit is available. 54

172 Fig 7.2 Compariso of the geeric motor with a CVT ad a 4 speed gearbox Practical motor 25 Improvemet (%) CVT 4 speed gearbox Fig 7.22 Compariso of the practical motor with a CVT ad a 4 speed gearbox The average improvemet over 6 drivig cycles for vehicles with differet combiatio of a trasmissio ad a motor is show i Table 7.7. The average improvemet of for vehicles with the two motors rages from 6.7% to 4.3%. Table 7.7 The average improvemet over 6 cycles CVT 4 speed gearbox Geeric motor 9.% 7.5% Practical motor 4.3% 6.7% 55

173 Fig 7.23 Improvemet with a 4 speed gear box Costat speed poits 5 Torque (Nm) Electric Motor Speed (rad/s) 9 Fig 7.24 Motor operatio poits with o gearbox Japa mode 56