Dynamics of multispeed transmissions for electric vehicles modelling analysis and validation

14 1.5 Range Model of Electric Vehicles with Multi-speed Transmissions.. 74 6 Range Model of Electric Vehicles with Multi-speed Transmissions 79 6.1 Range Model Formulation.. Appli-catio

Dynamics of Multi-speed Transmissions for Electric Vehicles: Modelling, Analysis and

Validation

Yuhanes Dedy Setiawan Liauw

Department of Mechanical Engineering

McGill University Montreal, Canada May 2018

A thesis submitted to McGill University in partial fulfillment ofthe requirements for the degree of Doctor of Philosophy

© 2018 Yuhanes Dedy Setiawan Liauw

2018/05/15

Abstract

Electric vehicles (EVs) are growing in importance One promising technique to improve theperformance and efficiency of EVs is the introduction of multi-speed transmissions (MSTs).Multiple speed ratios can maintain the traction motor at the most efficient operation region,especially for medium- and heavy-duty EVs In order to support the optimum design andcontrol of MSTs for EVs, a thorough dynamics analysis is needed However, a completemathematical model of MSTs for EVs has not yet been developed This model is needed

to analyze and optimize the gear-shifting events such that a swift, seamless shifting can beachieved This task is currently conducted by means of simplified dynamics models Thework reported here includes the formulation of a detailed model of a novel modular MSTfor EVs that takes into account discontinuities brought about by backlash and dry friction

in the gear pairs The dynamic response of gear-shifting was simulated for validation, theresults were verified experimentally on an in-house developed testbed of the novel MST

In addition, multi-speed transmissions undergo topology changes during gear-shifting.Nevertheless, this important phenomenon has been overlooked in transmission-model for-mulation, which results in an inaccurate prediction of the dynamic response To fill thisgap, a topology-change model was formulated to address the topology change in vehicletransmissions during gear-shifting The velocity jump brought about by topology changes

is given due attention A case study is included, whereby the model is implemented in anovel modular MST for EVs Both simulation and experimental tests were conducted forvalidation A good agreement between simulation and experimental results was achieved,which verifies the pertinence of the model It was concluded that the topology-change modelimproves the capability of transmission mathematical models in predicting the transmissiondynamic response during gear-shifting

Furthermore, the transmission model was used in a range-prediction model of EVs withMSTs Most range models are solely available for EVs with fixed gearing Moreover, trans-missions are assessed solely with a constant efficiency in EV range-prediction proceduresavailable in the literature A simple and accurate range model for EVs with MSTs isproposed in this dissertation In order to predict the range of EVs with MSTs reliably,the actual transmission efficiency was computed by means of a transmission model Acase study aimed at predicting the range of the GM EV1 with a two-speed novel modulartransmission is included Moreover, a simulation test with constant transmission efficiency,

intended to underline the advantages brought about by the actual transmission efficiency

in range-prediction, is provided The results indicate that the range of the two-speed GMEV1 simulated with constant transmission efficiency is 7.73% longer than the range of thestandard GM EV1 Nevertheless, this number could actually reach up to 13.09% whenthe range is predicted with the actual efficiency This result was verified by means of thedetailed model created in this dissertation that estimated a 12.76% of range improvement

In summary, this thesis highlights the advantages of realistic models that lead to a reliableprediction of the transmission efficiency and the range of EVs with MSTs

R´ esum´ e

Les v´ehicules ´electriques (V´E) sont de plus en plus r´epandus Une avenue prometteuse pouram´eliorer les performances et l’efficacit´e des V´E est l’utilisation des transmissions multivitesses (TMV) Des rapports de vitesse multiples permettent de maintenir le moteur detraction dans sa zone de fonctionnement le plus efficace, en particulier pour les v´ehicules

´electriques de moyenne et de grande puissance Pour arriver `a une conception et unecommande optimales des TMV destin´ees `a des V´E, une analyse dynamique approfondie estn´ecessaire Cependant, un mod`ele math´ematique complet des TMV pour V´E n’a pas `a cejour encore ´et´e ´elabor´e Ce mod`ele est n´ecessaire pour analyser et optimiser les changements

de vitesse de sorte qu’un changement rapide et continu puisse s’effectuer Cette tˆache estactuellement men´ee `a l’aide de mod`eles dynamiques simplifi´es Le travail pr´esent´e ici aborde

la formulation d’un nouveau mod`ele pour les TMV qui prend en compte les discontinuit´esprovoqu´ees par des jeux et le frottement sec au niveau des pairs d’engrenages La r´eponsedynamique du changement de vitesse a ´et´e simul´ee pour ˆetre valid´ee, les r´esultats ont ´et´ev´erifi´es exp´erimentalement sur un banc d’essai maison de la nouvelle TMV

De plus, les transmissions multi vitesses subissent un changement de topologie lorsdes changements de vitesse Toutefois, cet important ph´enom`ene a ´et´e n´eglig´e dans lesformulations des mod`eles de transmission, se soldant en une pr´ediction inexacte de lar´eponse dynamique Pour r´epondre `a cette probl´ematique, un mod`ele des changements detopologie a ´et´e con¸cu pour pr´evoir ces derniers `a l’int´erieur de la transmission des v´ehiculeslors des changements de vitesse Le saut de vitesse caus´e par ces changements a donc re¸cuainsi l’attention n´ecessaire Une ´etude de cas est incluse, o`u le mod`ele est impl´ement´e surune nouvelle TMV modulaire pour V´E Des simulations ainsi que des tests exp´erimentauxont ´et´e men´es pour validation Une bonne concordance entre les r´esultats exp´erimentaux et

de simulations a ´et´e observ´ee, ce qui confirme la pertinence du mod`ele Il a ´et´e conclu que

le mod`ele de changements de topologie am´eliore la capacit´e des mod`eles math´ematiques detransmission de pr´evoir la r´eponse dynamique de cette derni`ere durant les changements devitesse

Finalement, le mod`ele de transmission est utilis´e pour pr´edire les distances pouvant ˆetreparcourues par les V´E munis de TMV Les mod`eles actuels n’existent que pour les v´ehicules

`a engrenages fixes De plus, au travers de la litt´erature disponible, ces transmissions sont

´evalu´ees en consid´erant seulement un rendement constant en ce qui concerne la pr´ediction

de distances Un mod`ele simple et pr´ecis pouvant servir `a cette fin pour les V´E munisd’une TMV est propos´e dans cette dissertation Pour pouvoir pr´edire avec fiabilit´e ladistance pouvant ˆetre parcourue, c’est-`a-dire l’autonomie, le rendement r´eel est calcul´e `al’aide d’un mod`ele de la transmission Une ´etude de cas portant sur l’autonomie de la

GM EV1 avec une nouvelle transmission modulaire `a deux vitesses est incluse De plus,une simulation avec un rendement de transmission constant, effectu´ee pour souligner lesavantages de prendre en compte le rendement r´eel dans la pr´ediction d’autonomie, est

´egalement fournie Les tests permettent de conclure que l’autonomie de la GM EV1 `a deuxvitesses pr´edite avec un rendement constant est 7,73 % plus ´elev´ee que celle de la GMEV1 standard Cependant, ce nombre pourrait dans les faits atteindre 13,09 % lorsque ladistance atteignable est pr´edite avec le rendement r´eel Ce r´esultat a ´et´e v´erifi´e `a l’aided’un mod`ele d´etaill´e cr´e´e pour cette th`ese qui estime que l’am´elioration de l’autonomieest de l’ordre de 12,76 % Bref, cette th`ese met en lumi`ere les avantages de mod`eles plusr´ealistes qui permettent de mieux pr´edire le rendement et l’autonomie des V´E munis deTMV

Acknowledgments

I would like to express my most sincere gratitude to all those who helped me during mystudy and meaningful life in Canada First of all, I would like to give my highest praise toGod for all the help and guidance that I have received, to allow me to finish all my researchand thesis in the PhD program

Second, I would like to express my deepest gratitude to my supervisor, Professor JorgeAngeles, who has helped me significantly in completing my PhD program I really appre-ciate the kindness and support that he provided to me during my study in his excellentlaboratory

I would also like to express my sincere gratitude to the members of my thesis committee,Professors Jozsef K¨ovecses and Arun Misra, for their helpful comments and suggestionsthroughout my work

Furthermore, I would like to express my profound gratitude to Mehdi Roozegar, Dr.Ting Zou and Dr Alexei Morozov for their great help and advice that allowed me to finish

my research project and my PhD thesis

Last but not least, I would like to express my deepest gratitude to my father, Joeng JiLiauw, my mother, Erlani Go, my sister, Ciska Yuni Setiawan Liauw and all my relativesfor their love, endless prayers, encouragement and support for me not only in completingthe PhD program but also in the whole of my life

Contents

1.1 Background 1

1.2 Multi-speed Transmissions for Electric Vehicles 4

1.3 Mathematical Models for Multi-speed Transmissions 13

1.4 Topology Changes in Multi-speed Transmissions 14

1.5 Range Model of Electric Vehicles with Multi-speed Transmissions 16

1.6 Research Plan: Description and Objectives 17

1.7 Claims of Originality 18

1.8 Thesis Organization 18

2 A Novel Modular Multi-speed Transmission 21 2.1 Design Principles 21

2.1.1 The Underdrive Gear Train 28

2.2 Testbed Set-up 32

3 Formulation of the Mathematical Model 37 3.1 A Multi-speed Transmission 38

3.2 Linear Complementarity Problem Formulation 47

3.3 Backlash Modelling 50

3.4 Friction Modelling 51

3.5 Model Parameterization 52

3.6 Modal Analysis 54

3.7 Simplified Model 54

4 Gear-shifting Analysis 57

4.1 Simulation 57

4.1.1 Gear-shifting Mechanism 57

4.2 Experimental Validation 62

5 A Topology-change Model 65 5.1 Model Formulation 65

5.2 Case Study 68

5.3 Experimental Work and Simulation 69

5.3.1 Velocity-jump Calculation 70

5.4 Model Implementation 74

6 Range Model of Electric Vehicles with Multi-speed Transmissions 79 6.1 Range Model Formulation 79

6.2 Case Study: An Electric Vehicle with a Two-speed Transmission 83

6.3 Gear-shifting Schedule 84

6.3.1 Range Simulation 85

6.4 Transmission Efficiency 86

6.5 Range Simulation with the Actual Transmission Efficiency 88

7 Conclusions and Recommendations for Further Research 91 7.1 Conclusions 91

7.2 Recommendations for Future Research 92

List of Figures

1.1 Public electric bus in Montreal, Canada [10] 2

1.2 Tesla Semi truck [12] 3

1.3 Pure EV configuration [23] 5

1.4 MHEV powertrain (FG = fixed gearing, M = motor, D = differential) [24] 5 1.5 Typical electric motor characteristics [25] 6

1.6 Tractive effort: single-speed vs two-speed EVs [26] 7

1.7 Efficiency maps: 1-speed vs 2-speed [27] 8

1.8 A seamless two-speed transmission for EVs [40] 11

1.9 Two-speed dual-clutch transmission for EVs [7] 12

1.10 A two-speed dual-brake transmission for EVs [45] 13

2.1 (a) A simple PGS; (b) a diagram of the MST 22

2.2 Transmission modules: (a) underdrive, (b) overdrive 23

2.3 The novel modular MST concept 24

2.4 The novel modular MST 26

2.5 The iconic model of the novel modular MST, with all clutches open 27

2.6 Functional representation of the novel modular MST 27

2.7 Graph representation of the transmission when all clutches are open 28

2.8 The first operation mode: (a) functional and (b) graph representation 29

2.9 Functional representation of the underdrive gear train 29

2.10 Lever analogy of the underdrive gear train 30

2.11 Speed analysis with the simplified lever analogy 31

2.12 In-house developed testbed of the novel modular MST 32

2.13 Multi-disk clutch 33

2.14 Multi-disk clutch diagram [114] 33

2.15 Ring clutch 34

2.16 Control system diagram of the novel modular MST testbed 35

2.17 Testing site 36

2.18 Electronic box 36

3.1 The iconic model of the novel modular MST 39

3.2 Representation of vector q and its associated matrices (M, C or K) 46

3.3 (a) a simple gear pair, (b) backlash in the gear teeth, (c) backlash model 51

3.4 Friction-torque characteristics 52

4.1 The iconic model of the underdrive gear train of the novel modular MST 58 4.2 Simulink file of the comprehensive model 58

4.3 Simulink file of the simplified model 59

4.4 Control system block diagram to simulate the comprehensive model 59

4.5 Control system block diagram to simulate the simplified model 60

4.6 Gear-shifting algorithm in simulation phase 1 60

4.7 Experimental verification of the models 63

4.8 Comparison of the angular velocities of the planet gears 63

4.9 Comparison of the angular velocities of the ring gears 64

5.1 Functional representation of the underdrive gear train of the modular MST 69 5.2 Flow chart of simulation phase 1 69

5.3 Simulation phase 1 results 72

5.4 (a) Clutch torque capacity, (b) speed ratio 72

5.5 (a) The applied torques f , (b) τ 73

5.6 Flow chart of simulation phase 2 74

5.7 Gear-shifting algorithm 75

5.8 Simulation phase 2 results 76

5.9 Angular velocities of (a) planet gears, (b) ring gears 76

6.1 EV range modelling [13] 80

6.2 GM EV1 [132] 83

6.3 SFUDS [13] 84

6.4 Gear-shift schedule 85

6.5 Gear-shift time 86

List of Figures xi6.6 Transmission angular velocities and torques 876.7 Transmission efficiency of a two-speed novel modular transmission for SFUDS 88

List of Tables

1.1 Performance comparison between Tesla Semi and a comparable diesel truck 3

1.2 Specific energies of common batteries and fossil fuels [22] 4

2.1 Clutch state configuration of the novel modular MST (× denotes closed) 27

2.2 Clutch state configuration of the underdrive gear train (× denotes closed) 30 2.3 Testbed servo motor specification 32

3.1 Coefficient definition 56

4.1 Tuned PID gains 60

6.1 GM EV1 parameters [13] 84

6.2 Single- vs two-speed GM EV1 range comparison 89

A.1 Parameter definition 95

A.2 Simulation parameter values 96

List of Acronyms

AMT Automatic Manual TransmissionCVT Continuously Variable TransmissionDAE Differential Algebraic EquationDCT Dual-clutch Transmission

EV Electric VehicleFFV Fossil-fuel VehicleFUDS Federal Urban Driving ScheduleICEV Internal Combustion Engine VehicleMHEV Medium- and Heavy-duty Electric VehicleMST Multi-speed Transmission

NEDC New European Driving CyclePCC Planet-carrier Clutch

PGS Planetary Gear SetPGT Planetary Gear TrainSFUDS Simplified Federal Urban Driving Schedule

As a consequence, EVs have grown rapidly in the last decade.

The significant growth of EVs in the market stems from numerous advantages of EVsover FFVs or internal-combustion-engine vehicles (ICEVs) First and foremost, EVs do notdepend on non-renewable sources of energy as ICEVs do Second, EVs are more efficientthan their counterparts [4] Electric vehicles are propelled by highly efficient electric mo-tors and consume minimum amounts of energy during idling periods, as in the presence oftraffic jams In addition, EVs benefit from a regenerative braking feature that transformsthe motor into a generator that decelerates the vehicle and recharges the battery simul-taneously [5] Third, an EV configuration is simpler, hence easier and more economical

to maintain [6] Last, EVs are more user-friendly than ICEVs regarding pollution andnoise [7–9]

As a result of the advantages above, the concept of EV has broadened to and heavy-duty electric vehicles (MHEVs), such as buses and trucks In fact, larger energysavings can be gained from these types of vehicles because they carry higher loads and travel

medium-Fig 1.1: Public electric bus in Montreal, Canada [10]

longer distances Consequently, MHEVs have been implemented for public transportation

in major cities, such as Montreal, Canada, as depicted in Fig 1.1 Three electric buses arecurrently running in the city of Montreal, the size of the fleet gradually increasing to achievethe Montreal transportation goal of purchasing solely fully electric buses by 2024 [11] Itgoes without saying that the transportation industry is heading towards replacing fossil-fuelbuses with MHEVs

Another type of MHEVs that plays an important role in transportation is electric trucks.Trucks in general have been utilized widely for short- and long-haul delivery Unlike theirbus counterparts, trucks carry heavier loads and travel longer distances As a consequence,electrification and hybridization have been attractive options due to the high energy con-sumption and gas emission in trucks Moreover, electrification of trucks promotes significantadvantages in terms of energy and time, which translate into cost reduction A substantialnumber of electric trucks has been operating under tens of thousands of pounds of goodsfor hundreds of miles More than eight companies all over the world currently manufac-ture MHEVs Furthermore, Tesla, one of the pioneers in EVs, unveiled a new heavy-duty

electric truck Semi in November 2017, as captured in Fig 1.2.

Semi is foreseen to outperform diesel trucks to a great extent For starter, Semi is

reportedly 20% more cost-effective than diesel trucks Table 1.1 lists the performance

prediction of Semi in comparison to a diesel truck, under similar conditions, that Tesla

1.1 Background 3

Fig 1.2: Tesla Semi truck [12]

Table 1.1: Performance comparison between Tesla Semi and a comparable diesel truck

Performance Tesla Semi Diesel truckAcceleration 0–60 mph (without a trailer) 5 s 15 s

Acceleration 0–60 mph (with 80,000 lb load) 20 s 60 s

Top speed at 5% grade (maximum gross) 65 mph 45 mph

CEO, Elon Musk, highlighted in the Semi introduction event The major advantage of

electric motors over internal combustion engines in terms of performance is that the formerare able to exploit the maximum torque from the beginning Thus, this brings about

significant benefits on the acceleration performance of Semi in comparison to a comparable diesel truck Moreover, Semi is aerodynamically designed with a drag coefficient as low as

that of a sports car, hence more energy-saving The production is expected to debut in

2019, which signifies the importance of MHEVs in the transportation industry

To accommodate the long-term growth of MHEVs, or EVs in general, sizeable R&Dinvestment has been announced In fact, R&D of EVs commenced since EVs were firstcommercialized by the end of the 19th century [13] The main purpose of the R&D work

in this context was to replace fossil-fuel engines with electric motors, in order to reducegreenhouse-gas emissions and improve efficiency [14] Consequently, extensive investigation

to improve the efficiency in EVs have been conducted [14–21] Nevertheless, an inevitableconcern is still present when replacing fossil-fuel vehicles with EVs, namely, range pho-bia or anxiety of the range that EVs can travel Table 1.2 compares the specific energies

Table 1.2: Specific energies of common batteries and fossil fuels [22]

Energy Storage Type Sub-type Specific Energy (Wh/kg)

of common batteries and fossil fuels Apparently, the range that EVs can reach before

a need to recharge is still limited In addition, EVs are not as convenient as fossil-fuelvehicles because charging stations are not yet as widely distributed as gas stations There-fore, contemporary R&D in EVs primarily aims to improve the energy efficiencies withoutcompromising the performance One promising approach is to implement a multi-speedtransmission (MST)

The research work in this dissertation is concerned with the dynamics of multi-speedtransmissions in medium- and heavy-duty electric vehicles, such as trucks and buses Threeprimary tasks were carried out, namely, the formulation of a comprehensive model of MSTsfor EVs, analysis of the topology changes of MSTs upon gear-shifting, and the range-prediction of EVs with MSTs In the following sections, the application of MSTs to EVs

is explained After this, the transmission mathematical-modelling scene is surveyed Next,the topology changes of MSTs upon gear-shifting are studied Lastly, the description ofthe range-prediction of EVs with MSTs follows

1.2 Multi-speed Transmissions for Electric Vehicles

The configuration of pure EVs is depicted in Fig 1.3, where the thin and thick arrows count for the signal and power flows, respectively Unlike the configuration of ICEVs, mostmechanical components are replaced with electronics, which incidentally leads to lower en-ergy losses The driver inputs on the accelerator and brake are delivered electronically tothe controller, with significant gains in higher precision Energy and auxiliary systems man-age the energy and auxiliary components in the vehicles In addition, the inputs from thedriver can be manipulated by the controller to achieve a more efficient operation A powerconverter is needed for the controller to send signals to the motor because of different volt-age operation Subsequently, the motor operates according to the signal from the controller

ac-1.2 Multi-speed Transmissions for Electric Vehicles 5

Fig 1.3: Pure EV configuration [23]

Fig 1.4: MHEV powertrain (FG = fixed gearing, M = motor, D = differential) [24]

Mechanical transmissions may include fixed gearing or multi-speed transmissions

Two main MHEV powertrain configurations are displayed in Fig 1.4 Some MHEVsadopt single-speed transmission or fixed gearing, as electric motors are believed to be suffi-cient in providing all required power The powertrain configuration for this type of MHEVs

is illustrated in Fig 1.4(a) Each wheel has a motor equipped with a fixed gearing In parison, another group of MHEVs has one primary motor that provides the torque for thewhole vehicle instead of smaller motors in each wheel, as indicated in Fig 1.4(b) Theconcept is similar to the ICEVs, with a differential to distribute the power to the wheels.Either fixed gearing or a multi-speed transmission is utilized between the motor and differ-

com-Fig 1.5: Typical electric motor characteristics [25]

ential to manipulate the energy In the case of MHEVs with a multi-speed transmission,the energy flow can be better managed in the presence of a number of gear ratios

Without a multi-speed transmission, MHEVs must be equipped with cumbersome tric motors to compensate their heavy loads, which is not feasible economically Appli-cation of MSTs can come to the rescue by downsizing the motors and their accessories.Several companies, such as EMOSS, Electric Vehicle International and Balqon, have pro-duced MHEVs with a multi-speed transmission On the contrary, other companies, such

elec-as Hytruck, Motiv Power Systems, and Smith Electric Vehicles, have dispensed with speed transmissions in their MHEVs on the basis that electric motors have a wide range

multi-of operation, as required by MHEVs, thereby obviating multi-speed transmissions This

is, therefore, still a controversial issue because it is unclear whether the application ofmulti-speed transmissions in MHEVs, or EVs in general, is necessary at all [24]

The performance improvement of EVs by application of MSTs can be investigated byexamining the effects of the MST application on the efficiency maps of the EV motors A

1.2 Multi-speed Transmissions for Electric Vehicles 7

Fig 1.6: Tractive effort: single-speed vs two-speed EVs [26]

typical efficiency map of EV is given in Fig 1.5 A straight line on the high torque thatdeclines at a speed of around 1,500 rpm to the right vertical axis is the power envelopethat indicates the limit at which the motor can operate Moreover, the efficiency levels ofthe motor are represented by isocontours, with the numbers indicating efficiency level ofthat particular torque-speed state As revealed in the figure, 90% is the highest efficiencyregion, located in the medium torque and lower medium speed In other words, in order todrive efficiently, the vehicle cannot travel with a high speed, which is not convenient

By means of the application of MSTs, the vehicle performance can be manipulated

to drive efficiently with relatively higher speed, as justified in Fig 1.6 that compares thetractive efforts between a standard (single-speed) EV and a comparable EV with a two-speed transmission When the two-speed vehicle operates in the first gear, the attainabletorque is amplified by the gear ratio, as indicated in the figure This is advantageous forMHEVs because a high torque is required at the start-up Furthermore, the second gear

of the transmission allows a vehicle to travel at a higher speed, which enables the vehicles

to reach the destination sooner than its single-speed counterparts Equally important, theapplication of MSTs permits the vehicle to take advantage of the above benefits whilemaintaining the operation in the high-efficiency region More specifically, the application

of MSTs adjusts the efficiency region of the motor in accordance with the MST gear ratios.Figure 1.7 exemplifies the efficiency map adjustment due to the application of MSTs

to EVs The top figure displays the efficiency map of EVs with a single-speed The

Fig 1.7: Efficiency maps: 1-speed vs 2-speed [27]

vehicle efficiency is represented by the isocontours and is indicated proportionally by thebrightness intensity, where the darker the isocontour, the higher the efficiency In contrast,the characteristics of EVs with a two-speed transmission are depicted in the bottom figure.With such a transmission, the vehicle has two different efficiency regions that are beneficial

1.2 Multi-speed Transmissions for Electric Vehicles 9

in some particular cases For example, the efficiency region of the first gear contains thehighest efficiency region around the high torque and low speed, which is best exploitedduring start-up or low-speed operation In comparison, the highest efficiency region ofthe second gear is situated around the low torque and high speed, which fits perfectly inhigh-speed operations Moreover, in light of major advancements in vehicle transmissioncontrollers, the foregoing merits are complemented with automatic gear-shifting that yieldsthe highest possible efficiency throughout the operation The automatic gear-shifting isperformed by a gear-shifting schedule, as detailed in Section 6.3 Undoubtedly, these multi-speed features are unattainable in single-speed EVs, where the vehicle solely possesses afixed efficiency map and the chance to maintain the vehicle operating at a high efficiencysolely depends on the driver’s skill

Furthermore, EVs should be complemented with MSTs for a number of other compellingreasons First, as made apparent in Fig 1.5, motor efficiency in general is poor at lowspeeds, which leads to high energy consumption and heat generation This is particularlydangerous when EVs either climb a slope or maintain a low speed due to a traffic jamfor example Significant amounts of heat will be generated because of a high current

in the electric motor low-efficiency region [4] Second, although many researchers haveattempted to extend the EV range and to substantially distribute charging stations, afeeling of anxiety/phobia still exists among EV drivers [28, 29] People love EVs for manyreasons, but they cannot rely on them because the battery energy density is much lowerthan that of the tank of fossil fuels, as highlighted in Table 1.2 In other words, EVs stillhave limited range (and chargers) that make them not as convenient as ICEVs for long-haultravel For this reason, MSTs can be exploited to increase the efficiency of the drivelineand the range [30, 31] Third, bulky and expensive electric motors and power electronicsare required for MHEVs [32] In fact, current electric motors cannot meet the requiredtorque levels during start-up and high-torque operations in MHEVs because of heavy loadand frequent stops [33] Last, consumers dream of EVs that are comparable to ICEVs interms of dynamic and economic performance [9, 34–37] Up to date, most developments inEVs boil down to efficiency improvement Equally important, it is desirable to have EVsthat possess identical performance as ICEVs

In spite of the four above reasons, a large number of players disagree with the application

of MSTs to MHEVs Most of the reasons stem from additional MST weight to the EVdriveline, which reduces the achievable range [25, 38–42] In addition, the application

of MSTs will increase the cost, volume and losses in the driveline, the main item to beminimized as much as possible Furthermore, electric motors are believed to be sufficient

in operating over a wide range of conditions and at higher efficiency than ICEVs; R&D inthis field is vast at this moment [43–45]

Despite the objections in question, extensive work has confirmed the contribution ofmulti-speed transmissions to the improvement of EV performance [35, 40, 45–50] Fromexperiments conducted to verify transmission performance in EVs, Roberts [51] discoveredthat MSTs could maintain electric-motor operation at an efficiency level higher than 90%.Besides, Roberts’ tests demonstrated that the transmission increased the efficiency by 15%under the New European Driving Cycle (NEDC) Moreover, the application of MSTs to EVsdownsizes the requirements on battery and electric-motor performance, while extendingthe motor and inverter life spans [52, 53] The dynamics performance of EVs, such asgradeability, top speed, and acceleration, is also improved and balanced with the economicperformance offered by MSTs [44] As well, the performance improvement was verified inexperimental testing of actual EVs with MSTs [54–56]

Up to date, commercial MSTs available for MHEVs are those intended for ICEVs.MHEVs compatible with these MSTs notwithstanding, MSTs custom-tailored to MHEVsare actually more profitable with respect to energy consumption Evidently, multi-speedtransmissions for ICEVs function optimally for ICEV purposes An important parameter

in the ICEV transmission design is the efficiency region of the engines, which resembles ahill By implementing ICEV transmissions on EVs, the performance of EVs would not beoptimal because the efficiency region of EVs is clearly different from that of ICEVs Hence,MSTs must be fabricated specifically for EVs such that EVs with MSTs can perform inthe best possible efficiency region during operation

MSTs for EVs have evolved for one decade with at least 16 different EV MSTs, ing the novel modular MST originated in our research group, as recorded in the literature

includ-In the following paragraphs, the evolution of MSTs for EVs is recorded chronologically onwhen and how the transmission was invented The application of MSTs in EVs started in

2008, where a team from Beijing Institute of Technology, China implemented an automaticmanual transmission (AMT) in an electric bus [56] The purpose was solely to prove theperformance improvement from the application of AMT Improvements in drivability, effi-ciency and operability were catalogued Eventually, the AMT was installed in 50 electricbuses for the Beijing Olympic Games in 2008 Xi’s seminal work laid the foundations for

1.2 Multi-speed Transmissions for Electric Vehicles 11

Fig 1.8: A seamless two-speed transmission for EVs [40]

the application of MSTs to EVs that triggered other researchers to embark on investigatingthe MST concept for EVs Continuously-variable transmissions (CVTs) were tested in EVs

in 2009 and 2013 [57, 58] However, CVTs are not optimal for medium- and heavy-dutyEVs because the CVT belts or chains cannot transfer heavy loads In 2010, a novel clutch-less automatic manual transmission (CLAMT) was proposed by a laboratory in NationalPingtung University of Science and Technology, Taiwan [35, 48, 59, 60] As implied byits name, this transmission dispenses with clutch, hence leading to a simpler structure, alower cost and a higher efficiency compared with their counterparts supplied with clutches.Nevertheless, torque interruption is unavoidable in this design during gear-shifting [61].Moreover, three MSTs were established in 2011 First, a novel seamless two-speed MSTwas conceptualized by a collaboration between University of Surrey, UK and two automotivecompanies, Oerlikon Graziano Drive Systems and Vocis Driveline Controls [39, 40] Thedesign has a simple mechanical layout as portrayed in Fig 1.8 In the same year, a two-drive-transmission was invented at TU Darmstadt [62, 63] Lastly, an AMT without synchronizerand clutch was implemented in a battery electric bus in Jilin University, China [64, 65]

In 2012, four new MSTs emerged First, Antonov Automotive Technologies in Warwickintroduced a new two-speed dual-clutch transmission (DCT) for EVs [51] The researchproject was supported by Jaguar and Mira; the transmission was validated experimentally.Second, a research group at the University of Surrey, UK devised a novel four-speed trans-mission with dual motor [66, 67] The second motor fills the torque hole to accomplish a

Fig 1.9: Two-speed dual-clutch transmission for EVs [7]

seamless gear-shift However, this design is regarded as uneconomical because of its ple motors and the accessories that are required [61] Third, an inverse automated manualtransmission (i-AMT) was proposed by another research group from Jilin University [9, 34].The terminology “inverse” underlines the transmission design, as the clutch is mounted

multi-in the rear of the transmission (as opposed to the front) to compensate the traction multi-terruption Last, a two-speed dual-clutch transmission was examined at the University ofTechnology, Sydney [50, 61, 68–78] Figure 1.9 depicts the transmission In 2013, anothertwo-speed MST with two motors was devised at the University of Technology, Sydney [7, 71].Furthermore, a two-speed transmission was investigated for an electric bus in 2014 [79]

in-In the same year, a seamless dual-brake transmission was invented at the in-Industrial tomation Laboratory at McGill University for a national project, Automotive PartnershipCanada, that aimed to advance multi-speed transmissions for EVs [20, 30, 31, 44, 45, 80].Figure 1.10 displays the dual-brake transmission

Au-In 2015, another research group at McGill University came up with a novel modularMST for medium- and heavy-duty EVs, such as buses and trucks [5, 47, 81, 82] Thetransmission is modular, with the number of gear ratios adjustable according with thevehicle needs The principle, design and testbed set-up are expounded in Section 2 In thefollowing year, a two-speed uninterrupted mechanical transmission consisting of a planetarygear set, centrifugal clutch and a band brake was studied [8] It was reported that thetransmission offers a better comfort and dynamic performance than an optimized AMTwith the same gear ratios In the same year, a three-speed transmission with dual motors

1.3 Mathematical Models for Multi-speed Transmissions 13

Fig 1.10: A two-speed dual-brake transmission for EVs [45]

and one-way clutch was proposed [4] The transmission is compact for an in-wheel driveunit Furthermore, the clutch does not need external energy to operate, which makes itreliable and efficient

1.3 Mathematical Models for Multi-speed Transmissions

Although many research efforts in MSTs for EVs have been reported, thorough ics analyses that support the design and control of MSTs for EVs are still to appear inthe literature These analyses represent an important stage in transmission design anddevelopment to understand the dynamic response of the transmission and to determine, bysimulation, whether the transmission will work effectively within the intended operationrange and under the given conditions Extensive dynamics analyses to achieve optimalMST design started since the inception of ICEVs These analyses could be a reference forthe analyses of MSTs in EVs, but are not entirely applicable, because MSTs for ICEVsand those for EVs are inherently different, primarily because of the differences in the en-ergy source This leads to several different features in MSTs for EVs, such as regenerativebraking, no clutch/torque converter between motor and MSTs, and no reverse gear

dynam-For the above reasons, the dynamics analysis of MSTs in EVs under gear-shifting rants investigation The first step of this analysis is to develop the system mathematicalmodel aimed at predicting the dynamic response of MSTs in EVs under gear-shifting Thedynamic response of the system is important to support optimal transmission design, gear-

war-shifting analysis and vibration analysis [83] In addition, these studies are intended to bebeneficial to researchers and/or engineers for the development and validation of shiftingschedules and control systems.

Transmission models consist of inertial elements, gear meshing, and elements that arecapable of either storing or dissipating energy Transverse-torsional models have beenformulated for planetary gear sets [84–89]; they have been proven effective for representingthe PGS dynamic response However, transversal motion may be dispensable for vibrationanalysis when the supporting-bearing stiffness is tenfold larger than mesh stiffness [90],meaning that gears are not allowed to float Another way to assess planetary gear sets

is by means of finite element analysis [29, 91–93] However, for the purpose of this study,lumped-parameter models are utilized, as they have been proven effective for representingPGSs [88] Our study is based upon torsional lumped-parameter models

Kahraman [94] formulated a set of torsional-dynamics models of compound gear sets

by means of a Lagrangian formulation to predict free-vibration characteristics under ferent transmission topologies To account for backlash in the gear system, Al-shyyab andKahraman [95] expanded Kahraman’s model by including a periodic variation of gear back-lash Torsional springs were then added to represent the component coupling between twoadjacent gear sets [96, 97] Furthermore, Inalpolat and Kahraman [98] used Kahraman’smodel [94] in an application to automatic transmissions where a generalized model for itsmulti-stage planetary gear trains is produced However, backlash is not included in theirevaluation, and the mathematical models were not validated experimentally

dif-1.4 Topology Changes in Multi-speed Transmissions

Multi-speed transmissions have a significant influence on the vehicle performance and ciency Transmission development has improved largely due to the advancement of simula-tion techniques and the means that support them Compared to traditional transmissiondevelopment, simulation will not only reduce cost and shorten the development stage, butwill also improve its accuracy and help understand the dynamics of the transmission Thetransmission mathematical models play an important role in simulation tests intended topredict the transmission dynamic response to various inputs and conditions The usefulness

effi-of simulation results largely depends on the fidelity effi-of the transmission models

Many transmission models have been formulated as explained in Section 1.3 However,

1.4 Topology Changes in Multi-speed Transmissions 15

one important phenomenon has been overlooked that results in unreliable prediction ofthe dynamic response A multi-speed transmission is a mechanism with variable topologybecause its connectivity changes during gear-shifting The dynamic behaviour, in turn,follows the current gear ratio Modelling this type of system is challenging because differentmodels and constraints need to be imposed for different topologies [99–102] Furthermore,topology changes in transmissions happen in a short period, since gear-shifting needs to

be as swift as possible This phenomenon adds another complexity in calculating thesystem internal forces and velocity jumps during topology changes, a matter that has notbeen thoroughly considered in the formulation of multi-speed transmission mathematicalmodels

Topology changes occur frequently in mechanical systems [103] One topology-changemodel established on contact/impact mechanics utilizes spring-damping systems to repre-sent the contact/impact area [104, 105] The influence of topology changes can be under-stood by means of this model Furthermore, the full history of contact/impact forces duringtopology changes can be predicted Another model is based upon the impulse-momentumrelation and the coefficient of restitution [106, 107] This model can calculate the dis-continuous response upon topology changes Nevertheless, this model still has numericalproblems in coping with discontinuous jumps in the system state [101]

A topology-change model was formulated by K¨ovecses and Font-Llagunes [102, 103, 108–111] The model employs bilateral impulsive constraints to decouple the kinetic and kine-matic quantities during topology changes Energy redistribution and velocity change can beanalyzed when the topology change occurs Two case studies on mechanical systems withvariable topology, bipedal walking and a dual-pantograph robotic prototype, were carriedout for validation in the foregoing reference Furthermore, a new and simple model to com-pute discontinuous jumps in the system velocity during topology changes was proposedrecently [101] The model utilizes the impulse-momentum relation and the Lagrangianequations of the first kind, namely, the system differential-algebraic equations (DAEs).The dynamics equations are integrated over the topology-change period to establish theimpulse-momentum relation that allows the calculation of the discontinuous jumps in thesystem velocity The constraint violation elimination was given due attention for the accu-racy of post-topology-change simulation

1.5 Range Model of Electric Vehicles with Multi-speed

In a typical range-prediction simulation, transmissions are assessed solely with a constantefficiency, transmission dynamics being completely ignored This may be acceptable forrange-prediction of EVs with fixed gearing However, recent trends incorporate MSTs,extensive work has confirmed the contribution of MSTs to the extension of EV range, asdetailed in Section 1.2

In the case of range-prediction for EVs with MSTs, the dynamics of the transmissionsubsystem needs to be incorporated to evaluate the actual transmission efficiency such thatthe EV range can be predicted accurately A constant transmission efficiency is an over-simplification because efficiency varies depending on the dynamics conditions In addition,unlike fixed gearing transmissions, MSTs consist of several gears that are engaged and dis-engaged in accordance with the shift schedule The gear-shifting of MSTs influences thetransmission efficiency that cannot be neglected in range-prediction Gear-shifting is a dy-namic process that involves the main transmission components, such as clutches and gears.The gear-shifting event happens frequently and quickly in EVs; therefore, the dynamics

of gear-shifting is to be taken into account Moreover, gear-shifting alters the topology ofthe transmission, as indicated in the preceding section, the underlying model thus varyingaccording to the current gear ratio On the whole, the gear-shifting event is vitally impor-tant for range-prediction A range model for EVs with MSTs that takes into account thedynamics of gear-shifting is proposed in this dissertation

The transmission efficiency of MSTs for EVs has been approached primarily from twoperspectives, power-loss models [72–74, 113] and experimental investigation [70] In theformer, all losses of the clutch, gear windage and churning losses are investigated Inthe experimental investigation, expensive torque and speed sensors are required to find

1.6 Research Plan: Description and Objectives 17

the actual transmission efficiency Both approaches are not practical because of growingcomplexity in the computational algorithm or, correspondingly, in the sensory subsystem

In this dissertation, a simpler approach to calculating the efficiency from the transmissionmodel is documented Efficiency is evaluated for a typical driving cycle This yields amore accurate range, especially upon gear-shifting, compared with range-prediction under

a constant efficiency The efficiency calculation is verified with the comprehensive modeldeveloped in Chapter 3 that was validated experimentally, as reported in Chapter 4

1.6 Research Plan: Description and Objectives

This dissertation aims to develop gear-shifting strategies that optimize the performance andefficiency of electric vehicles with multi-speed transmissions First, a mathematical model

of multi-speed transmissions for electric vehicles is formulated Simulation and tal tests were conducted for verification Gear-shifting was then analyzed based upon themodel thus developed Furthermore, a topology-change event of multi-speed transmissions

experimen-is modelled such that the actual motion of the transmexperimen-issions during thexperimen-is event could beestimated Moreover, the range of electric vehicles with multi-speed transmissions is pre-dicted The transmission efficiency was assessed by means of the transmission model.The objectives of the thesis follow:

1 To develop a mathematical model of multi-speed transmissions for electric vehiclessuch that the dynamic response of the physical system can be predicted

2 To validate the transmission model in simulation and experimental tests

3 To analyze the gear-shifting of multi-speed transmissions for electric vehicles

4 To model the topology changes of multi-speed transmissions during gear-shifting

5 To verify the topology-change model in simulation and experiments

6 To analyze the topology changes of multi-speed transmissions during gear-shifting

7 To predict the range of electric vehicles with multi-speed transmissions

2 Simulation and experimental validation of the model on an in-house developed testbed

of a novel modular multi-speed transmission

3 Range-prediction model and simulation of electric vehicles with multi-speed sions

transmis-4 Significant improvement on the prediction of transmission efficiency of multi-speedtransmissions for electric vehicles

1.8 Thesis Organization

An outline of the dissertation follows:

In Chapter 2, a novel modular multi-speed transmission for medium- and heavy-dutyelectric vehicles is introduced First, the project under which novel multi-speed transmis-sions were developed is outlined The milestones of the project are highlighted chronolog-ically Second, the working principle of the transmission developed for the work reportedhere is explained, along with a description of its components In addition, the design pro-cess is documented Finally, an in-house developed testbed intended for experimental tests

is described

Chapter 3 is devoted to the mathematical model formulation of multi-speed sions for electric vehicles The transmission model is developed in agreement with theassumptions and the approach Discontinuities, brought about by gear-shifting, backlashand friction, are included Thereafter, the model parameterization for simulation tests isprovided Finally, a modal analysis is conducted

transmis-In Chapter 4, gear-shifting is analyzed by means of the model formulated in Chapter 3.Simulation was conducted and the results validated experimentally Both simulation andexperimental test procedures are explained

1.8 Thesis Organization 19

Chapter 5 is concerned with the topology changes in multi-speed transmissions upongear-shifting A case study was conducted on the prototype of the multi-speed transmissionmentioned above Simulation in MATLAB/Simulink was conducted to verify the modelthus developed Experimental results follow to validate the simulation results Procedures

of both simulation and experimental tests are described Finally, discussion and conclusionsare included

In Chapter 6, a scheme is introduced, under which the range of electric vehicles withmulti-speed transmissions is predicted The gear-shift schedule is first devised The trans-mission efficiency is calculated, by means of our mathematical model, to increase the range-prediction accuracy The range model is then exemplified in a case study for the GM EV1with the two-speed novel modular transmission A simulation test is conducted to highlightthe effectiveness of the range model The results are discussed to conclude the chapter.Finally, Chapter 7 includes conclusions and recommendations for future research

Chapter 2

A Novel Modular Multi-speed

Transmission

A novel modular MST for medium- and heavy-duty electric vehicles is introduced here

To begin with, this MST was developed in the context of a Canadian national project,Automotive Partnership Canada, that started in late 2012, for a four-year period Theproject focused on maturing MSTs for EVs and was conducted by a collaboration of sev-eral research groups at McGill University and three Canadian companies, Linamar, TM4,and Infolytica The McGill University groups consisted of several teams from two maindepartments, mechanical engineering and electrical engineering Together with the partnercompanies, the McGill University groups developed two novel MSTs for EVs, one of which,the modular MST, is of interest to this dissertation

The author undertook the development of the testbed through experimental tests, butwas not involved in the first stages of the design work, for which reason the testbed design

is not claimed as a contribution in this dissertation The principles that guided the design

of the MST are not described in full detail in the sections that follow The interested reader

is referred to a conference paper [5] for details

Under-drive

Over-drive

Loadsun

ring

carrierplanet

Fig 2.1: (a) A simple PGS; (b) a diagram of the MST

To this end, a modular concept was selected, with the number of gear ratios adjustable inaccordance with the vehicle requirements

The modular MST utilizes a planetary gear set (PGS) system by virtue of its advantagesover countershaft transmissions, such as higher torque-to-weight ratios and finer teeth,which thus leads to a smoother operation [94, 98] For quick reference, a simple PGS isdepicted in Fig 2.1(a) The PGS is made of four components: a sun gear; a planet gear; aring gear; and a planet-carrier While these components revolve around the same centerline,projected as the center of the two larger circles in Fig 2.1(a), the axis of the planet geartranslates around the centerline The MST considered in this work comprises one input

motor, a load, and two identical planetary gear trains (PGTs), underdrive and overdrive,

joined by the planet-carrier [5] The gear train is activated by means of clutches, which arerepresented as switches in Fig 2.1(b)

The underdrive and overdrive transmission modules are displayed in Fig 2.2(a) and (b),respectively Two terms are introduced, planetary gear set and planetary gear train Theformer refers to one single planetary gear mechanism, the one shown in Fig 2.1(a), whichincludes one single planet, but in practice the set carries a plurality thereof In turn, a PGT

is a mechanical system composed of various PGSs For instance, a group of PGSs in theunderdrive modules is called the underdrive gear train Further, subscripts s, p, r, C, and

pc indicate sun gear, planet gear, ring gear, clutch, and planet-carrier, respectively Twosubscripts are utilized for the gear notation, alphabetical (first) and numerical (second).The former stands for the gear train, either o for overdrive or u for underdrive In a similar