Graduation Project Report Torque Vectoring

Scource: http://mercedesbenzblogphotodb.wordpress.com/2009/04/20/20042009-mercedes-benz-at-auto-shanghai-2009/torque-vectoring-brake/ (03-08-2011)

Enhanced Improvement Of Vehicle Dynamic Enhanced Improvement Of Vehicle Dynamic Behaviour By Applying Torque Vectoring BehaviourViewed From The By Vehicle Applying Dynamic And Torque Powertrains Vectoring Perspective Viewed From The Vehicle Dynamic And Powertrains Perspective

Enhanced Improvement Of Vehicle Dynamic

Behaviour By Applying Torque Vectoring Viewed From The Vehicle Dynamic And Powertrains Perspective

Source: [40]

10/01/2012| Graduation Project | S.J. Koster (Joost) & S. Nada (Shady)

Graduation Project Report

Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Contact Information

Placement company: Educational institution: TNO Automotive HAN University of Applied Sciences Steenovenweg 1 HTS Autotechniek 5708 HN Helmond Ruitenberglaan 29 T 088 866 57 29 6826 CC Arnhem F 088 866 88 62 T(024) 353 05 00E [email protected] [email protected]

Company supervisors; Ir. S.T.H. Jansen Ir. L.J.M. van Eeuwijk T +31 (0)88 866 57 43 T +31 (0)88 866 09 13 M +31 (0)65 388 94 82 M +31 (0)6 - [email protected] [email protected]

Educational supervisors: Ir. A.J. van Breugel Ing. I. de Gijsel T +31 (0)26 384 93 47 T +31 (0)26 384 93 39 M +31 (0)63 626 25 64 M +31 (0)61 489 85 87 [email protected] [email protected]

Graduates: S.J. Koster S. Nada M +31 (0)62 000 88 11 M +31 (0)62 734 06 05 [email protected] [email protected] [email protected] [email protected]

S. Nada and S.J. Koster I Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

List Of Acronyms And Abbreviations

Abbreviations in alphabetic order;

Abbreviation Full Meaning 2-DOF Two Degree of Freedom AC Alternating Current Alnico Aluminum-Nickel-Cobalt (magnet) AWD All Wheel Drive BMS Battery Management System CarLab Car Laboratory (Test Vehicle) CTRL Control (inverter) DC Direct Current DFL Drive Force Limiter (controller) DYM Direct Yaw Moment (controller) ECU Electronic Control Unit EM Electric Motor EMF Back Electromotive Force FD Final Drive FWD Front Wheel Drive HEV Hybrid Electric Vehicle ICE Internal Combustion Engine IM Induction Motor MF Magic Formula NdFeB Neodyium-Iron-Boron (magnet) NS Neutral Steer OS Over Steer PM Permanent Magnets PM Sync Permanent Magnet Synchronous (electric motor) PT Powertrain QSS TB QuasiStatic Simulation Toolbox RWD Rear Wheel Drive SmCo Samarium Cobalt (magnet) SRM Switch Reluctant Motor TE Tyre Estimator® TNO Netherlands Organization for Applied Scientific Research (Company) TR Traction (controller) TV Torque Vectoring US Under Steer VD Vehicle Dynamic

S. Nada and S.J. Koster II Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Vehicle dynamic related acronyms in alphabetic order;

Symbol Parameter Unit Track of the car

Frontal area surface of car

Lateral acceleration Cornering stiffness front wheel Cornering stiffness rear wheel Air drag resistance – Final drive reduction – Longitudinal force Longitudinal force rear right wheel Longitudinal force rear left wheel Lateral force Lateral force rear left wheel Lateral force rear right wheel Vertical force Vertical force rear left wheel Vertical force rear right wheel Gravity Height of central of gravity Tyre radius Inertia around x-axis Inertia around y-axis Inertia around z-axis Wheelbase Length: front wheels to central of gravity Length: rear wheels to central of gravity Vehicle mass Momentum around z-axis Pedal stroke Yaw-rate Corner radius Friction contact area certain tyre Rear left friction contact area Rear right friction contact area Longitudinal velocity Lateral velocity Side slip angle front wheel Side slip angle rear wheel Steer angle of the wheels Tyre friction coefficient –

Density of air Slope of normalized tyre characteristic –

S. Nada and S.J. Koster III Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Powertrain related acronyms in alphabetic order;

Symbol Parameters Unit Temperature coefficient magnets Required electrical energy Final gear ratio Moment of Inertia

Moment of inertia of EM

Moment of inertia of FD Back Electromotive Force (EMF) Torque Friction Electric motor inductance Maximum EM speed crossing signal Required electrical power Mechanical power

Maximum regenerative power Electrical resistance Temperature Specified Temperature The torque the EM provides with response delay

The requested torque from the EM

Provided torque on EM Shaft

FD torque at constant rotational speed

Required torque to overcome moment of inertia of EM

Required torque to overcome moment of inertia of FD Maximum possible torque

Maximum available torque of requested torque Torque provided on the FD output shaft Efficiency of EM

Efficiency factor Efficiency of FD Electrical time constant of the motor Mechanical time constant of the motor Rotational speed EM

Maximum predefined rotational speed Rotational speed of the wheel

S. Nada and S.J. Koster IV Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

List Of Figures And Tables

FIGURES FIGURE 1 | TARGET VEHICLE MODEL [24] ...... 2 FIGURE 2 | CIRCLE OF KAMM (FRICTION CIRCLE) [38]...... 4 FIGURE 3 | SCHEMATIC REAR VIEW OF THE VEHICLE MAKING A RIGHT HAND TURN [1]...... 4 FIGURE 4 | TOP VIEW OF THE TYRES WITHOUT USE OF ACTIVE DIFFERENTIAL IN A RIGHT HAND TURN...... 5 FIGURE 5 | EFFECT OF TORQUE VECTORING...... 5 FIGURE 6 | TYRE ESTIMATOR® FLOWCHART ...... 7 FIGURE 7 | THE PRIMARY (MAIN) COMPONENTS OF AN ELECTRIC VEHICLE POWERTRAIN [41] ...... 9 FIGURE 8 | CROSS SECTIONS OF THE ELECTRIC DIRECT CURRENT (DC), INDUCTION (IM), SWITCH RELUCTANT (SRM) AND PERMANENT MAGNET SYNCHRONOUS (PM SYNC) MOTORS [27] ...... 10 FIGURE 9 | TYPICAL ELECTRIC TRACTION CHARACTERISTIC [6] ...... 12 FIGURE 10 | TYPICAL IM TORQUE-SPEED CHARACTERISTIC [6]...... 15 FIGURE 11 | TYPICAL TORQUE-SPEED CHARACTERISTIC OF A SYNCHRONOUS PM [6] ...... 15 FIGURE 12 | TORQUE-SPEED CHARACTERISTIC OF A SYNCHRONOUS PM WITH CONDUCTION ANGLE CONTROL [6] ..... 16 FIGURE 13 | IN-WHEEL PM SYNCHRONOUS MOTOR (2) ...... 16 FIGURE 14 | TYPICAL TORQUE-SPEED CHARACTERISTIC OF AN SRM [6] ...... 17 FIGURE 15 | MECHANICAL TIME CONSTANT MULTIPLIER AS FUNCTION OF THE TEMPERATURE ...... 19 FIGURE 16 | VEHICLE MODEL DESIGNED IN MATLAB® SIMMECHANICS® ...... 23 FIGURE 17 | EXAMPLE PLOTS OUTPUT OF THE DESIGNED VEHICLE MODEL AND TYRE ESTIMATOR ® ...... 23 FIGURE 18 | STEER CHARACTERISTIC, STEER ANGLE VERSUS LATERAL ACCELERATION [2] ...... 24 FIGURE 19 | TYRE FORCES IN A STEADY STATE TURN [2] ...... 25 FIGURE 20 | NORMALIZED AXLE CHARACTERISTICS AND HANDLING CURVES. (1= FRONT AXLE, 2= REAR AXLE) [23] .... 26 FIGURE 21 | TORQUE VECTORING CONTROLLERS ...... 27 FIGURE 22 | TE AXLE CHARACTERISTIC, USED TO CALCULATE THE VEHICLE CORNERING STIFFNESS...... 28 FIGURE 23 | FIRST LAYER DIRECT YAW MOMENT CONTROLLER ...... 29 FIGURE 24 | VEHICLE MOTION DATA OF VALIDATION SIMULATION...... 30 FIGURE 25 | ACTUAL (REAL) AND THE CALCULATED IDEAL YAW-RATE...... 30 FIGURE 26 | ACCELERATION (ACC) CONTROLLER (ACC) CONTROLLER ...... 31 FIGURE 27 | TOP AND FIRST LAYER OF THE TRACTION (TR) CONTROLLER ...... 32 FIGURE 28 | THE TRACTION CONTROL DRIVE FORCE CORRECTION...... 32 FIGURE 29 | REDUCTION OF TYRE FORCES TO CONTROL THE CORNERING POWER ...... 33 FIGURE 30 | TOP AND FIRST LAYER MOTOR CONTROLLER ...... 34 FIGURE 31 | TOP AND FIRST LAYER OF THE DRIVERS INPUT SUBSYSTEM ...... 35 FIGURE 32 | FIRST LAYER OF AUTO STEER CONTROLLER ...... 36 FIGURE 33 | FLOWCHART WHEN USING THE REPLAY MODEL ...... 37 FIGURE 34 | THE TOP LAYER OF THE ELECTRIC MOTOR MODEL PRESENTED AS A SUBSYSTEM ...... 39 FIGURE 35 | SUBSYSTEM ‘GENERATED TORQUE’ ...... 40 FIGURE 36 | THE CONTENT OF SUBSYSTEM 'GENERATED TORQUE' ...... 40 FIGURE 37 | CONTENT OF SUBSYSTEM 'TORQUE-SPEED LIMITS + RESPONSE DELAY' ...... 41 FIGURE 38 | EMBEDDED MATLAB FUNCTION BLOCK 'HOLD ZERO VALUE' ...... 42 FIGURE 39 | EMBEDDED MATLAB SCRIPT WHICH WILL KEEP THE OUTPUT VALUE ZERO ONCE IT BECOMES ZERO ...... 42 FIGURE 40 | SUBSYSTEM 'REQUIRED ELECTRICAL POWER' ...... 45

S. Nada and S.J. Koster V Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

FIGURE 41 | CONTENT OF SUBSYSTEM 'REQUIRED ELECTRICAL POWER' ...... 45 FIGURE 42 | CAUSALITY REPRESENTATION OF A MOTOR /GENERATOR FOR QUASISTATIC MODELING [8] ...... 46 FIGURE 43 | TWO QUADRANT EFFICIENCY MAP FOR A 'TYPICAL' ELECTRIC MOTOR [8] ...... 47 FIGURE 44 | EM MODEL VALIDATION USING THE QSS TOOLBOX ...... 48 FIGURE 45 | ENERGY FUNCTION OF THE EM MODEL AND THE EM MODEL OF THE QSS AS FUNCTION OF THE TIME .... 49 FIGURE 46 | THE TOP LAYER OF THE FINAL DRIVE MODEL ...... 50 FIGURE 47 | FIRST LAYER OF THE FINAL DRIVE MODEL...... 51 FIGURE 48 | VEHICLE MOTION DATA OF ‘VEHICLE STEER CHARACTERISTIC’ SIMULATION ...... 53 FIGURE 49 | THE STEER CHARACTERISTIC OF THE DESIGNED VEHICLE MODEL WITH AND WITHOUT ACTIVE TORQUE VECTORING ...... 53 FIGURE 50 | VEHICLE MOTION DATA OF ‘STEADY STATE’ SIMULATION ...... 54 FIGURE 51 | THE VEHICLES POSITION DRIVING A CIRCLE WITH A CONSTANT STEER ANGLE AND CONSTANT LONGITIDINAL VELOCITY...... 55 FIGURE 52 | THE YAW-RATE OF THE VEHICLE DURING THE STEADY STATE SIMULATION ...... 55 FIGURE 53 | VEHICLE MOTION DATA, INFLUENCE RESPONSE DELAY ELECTRIC MOTORS ...... 56 FIGURE 54 | DIFFERENCE IN TORQUE REQUEST AND GIVEN OUTPUT RESPONSE WHEN THE RESPONSE DELAY OF THE ELECTRIC MOTOR IS ENLARGED BY 100 X NORMAL MOTOR DELAY...... 57 FIGURE 55 | THE VEHICLE YAW-RATE WITH DIFFERENT ELECTRIC RESPONSE DELAY VALUES ...... 58 FIGURE 56 | ELECTRIC MOTOR DELAY WITH THE REQUESTED TORQUE AND THE ACTUAL OUTPUT TORQUE ...... 58 FIGURE 58 | HOCKENHEIM DRIVE CYCLE ‘HIGHER’ SPEED ...... 60 FIGURE 57 | HOCKENHEIM DRIVE CYCLE ‘LOWER’ SPEED ...... 60 FIGURE 60 | THE ENERGY CONSUMPTION AS FUNCTION OF TIME OF THE 'HIGHER’ SPEED DRIVE CYCLE WITH AND WITHOUT APPLYING TORQUE VECTORING (TV)...... 61 FIGURE 59 | THE ENERGY CONSUMPTION AS FUNCTION OF TIME OF THE 'LOWER’ SPEED DRIVE CYCLE WITH AND WITHOUT APPLYING TORQUE VECTORING. (TV)...... 61 FIGURE 61 | VEHICLE MOTION DATA WITH STEADY STATE 'FIGURE OF 8' SIMULATION ...... 62 FIGURE 62 | THE ENERGY CONSUMPTION AS FUNCTION OF TIME OF THE ‘FIGURE OF 8’ SIMULATION WITH AND WITHOUT APPLYING TORQUE VECTORING (TV)...... 62 FIGURE 63 | REPLAY MOTION DATA OF A FIGURE OF 8 MANOEUVRE (RADIUS 100M) ...... 63 FIGURE 65 | WHEEL TORQUE, AS IS SHOWN THE WHEEL TORQUE OF THE REPLAY AND TV MODEL ARE THE SAME...... 64 FIGURE 64 | REPLAY MOTION DATA OF FIGURE EIGHT CIRCLE, RADIUS 100M...... 64

TABLES TABLE 1 | ELECTRIC PROPULSION APPLIED IN ELECTRIC VEHICLES WHERE; EV = ELECTRIC VEHICLE, HEV = HYBRID EV ...... 10 TABLE 2 | ELECTRIC MOTOR EVALUATION (1-5 WHERE 5 MEANS THE BEST COMPARED TO THE OTHERS) ...... 20 TABLE 3| M-SCRIPT DIRECT YAW MOMENT (DYM) CONTROLLER ...... 29

S. Nada and S.J. Koster VI Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Summary

Torque Vectoring applies a different amount of torque to each driven wheel which creates an additional yaw-moment to steer or control a vehicle during under-and oversteer situations. Vehicles with individual electric motors can easily adapt Torque Vectoring control for improvement of the vehicle handling performance. TNO (Netherlands Organization for Applied Scientific Research) has developed several algorithms for handling improvement in the simulation environment and is considering of building a CarLab (test vehicle) for Torque Vectoring research purposes. To do so, first a literature study has been conducted taking into account two perspectives; vehicle dynamics and powertrains. From the vehicle dynamic perspective a study is conducted on the control and required controllers for the application of Torque Vectoring. From the powertrain perspective a study on the electric motor in relation to the (anticipated) vehicle performance is conducted. Finally a method for evaluation of the vehicle performance, in the form of simulations, was established for development and demonstration purposes. The results of this research should serve as an introduction to related further assignments in which this study will be used for the construction of an Torque Vectoring CarLab. To apply Torque Vectoring (TV), in this study a so called Direct Yaw Moment (DYM) controller is created. Aiming to keep the vehicle stable in all situations, also a Traction (TR) controller is created and a Drive Force Limitation (DFL) controller is recommended. Combined they form the Torque Vectoring (TV) controller. Simulation results show that the main improvement of applying Torque Vectoring is that the steer characteristic of the vehicle moves more toward a linear steer characteristic. And by applying a shift in longitudinal tyre forces, the inner rear wheel will have more margin to transfer lateral tyre forces. To ensure that the Tyre Estimator®, a programme developed by TNO to generate axle characteristics, can cope with Torque Vectoring, some additions have to be applied to the required measured vehicle data so the extra yaw-moment from Torque Vectoring can be calculated. Also additions have to be applied to the vehicle models, i.e. the vehicle model used in the State Estimation and Replay model of the Tyre Estimator®. The best way is to calculate the yaw-moment, which is created by the difference in torque or longitudinal forces, and apply this extra yaw-moment on the z-axis (perpendicular to the road) of the vehicle. The Induction motor is considered particularly well suited when applying Torque Vectoring, especially because it is very robust. Also it can adjust its magnetic field strength, extending the control capabilities, and the purchase cost of an Induction motor is usually lower with respect to, for example, a ‘similar’ Permanent Magnet Synchronous motor. The electric motor that is used in this study is applied with an enlarged electrical time constant taking critical temperature influences into account. Because the response delay of the electric motor did not show any influence on vehicle behaviour in the performed simulation results, it is therefore not expected that, with what type of electric motor whatsoever, this delay will cause a problem for the control of Torque Vectoring. A strong conclusion about the exact quantity of difference in consumption cannot be drawn. This is because it strongly dependents on the operating points of the electric motor. Simulation results showed that the energy consumption may increase but also can decrease by as much as 1%.

S. Nada and S.J. Koster VII Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Samenvatting (Dutch)

Torque Vectoring past een verschillende hoeveelheid koppel toe op de aangedreven wielen wat een giermoment creëert om het voertuig te sturen of regelen (corrigeren) tijdens onder- en overstuur situaties. Voertuigen met individuele elektrische motoren kun gemakkelijk uitgebreid worden met Torque Vectoring voor de verbetering van het voertuig weggedrag. TNO (Nederlandse Organisatie voor toegepast-natuurwetenschappelijk onderzoek) heeft diverse algoritmes ontwikkeld om het weggedrag te verbeteren in een simulatie omgeving en overweegt nu om een CarLab (test voertuig) te bouwen voor Torque Vectoring onderzoek doeleinden. Om dat te doen is er eerst aan een literatuuronderzoek uitgevoerd kijkende naar twee perspectieven; voertuig dynamica en de aandrijflijn. Vanuit het voertuig dynamische perspectief is er een onderzoekt verricht naar de regeling en de benodigde regelaars voor de toepassing van Torque Vectoring. Vanuit het aandrijflijn perspectief is er een onderzoek verricht naar de elektrische motor in relatie tot de (verwachte) voertuigprestaties. Tenslotte is er een methode voor de evaluatie van de voertuigprestaties, in de vorm van simulatie testen, vastgesteld voor ontwikkeling en demonstratie doeleinden. De resultaten van dit onderzoek zullen moeten dienen als inleiding voor gerelateerd verdere opdrachten waarin dit onderzoek zal worden gebruikt voor de ontwikkeling van de Torque Vectoring CarLab. Om Torque Vectoring toe te passen, is in dit onderzoek een zogenaamde Direct Yaw Moment (DYM) regelaar gemaakt. Om er naar te streven het voertuig stabiel te houden in alle situaties, is er ook een Traction (TR) regelaar gemaakt en een Drive Force Limitation (DFL) regelaar aanbevolen. Gezamenlijk vormen ze de Torque Vectoring (TV) regelaar. De simulatie resultaten tonen aan dat de voornaamste verbetering van het toepassen van Torque Vectoring is, dat de stuur karakteristiek van het voertuig meer nijgt naar een lineair stuur karakteristiek. En door de verschuiving van longitudinale band krachten, heeft het binnenste wiel meer marge om laterale band krachten over te brengen. Om ervoor te zorgen dat de Tyre Estimator®, een programma ontwikkeld door TNO om askarakteristieken te genereren, om kan gaan met Torque Vectoring, zullen er aanpassingen moeten worden gedaan aan de benodigde gemeten voertuig data zodat het extra giermoment, veroorzaakt door Torque Vectoring, kan worden berekend. Ook moeten de voertuig modellen worden aangepast, d.w.z. het voertuig model die gebruikt wordt in de State Estimation en het Replay model van de Tyre Estimator®. Als beste kan het giermoment worden berekend, welke gecreëerd wordt door het verschil in koppel of longitudinale krachten, en worden toegepast op de z-as (haaks op het wegdek) van het voertuig. De Inductie motor wordt beschouwd als uitermate geschikt bij de toepassing van Torque Vectoring, speciaal omdat deze erg robuust is. Ook kan het deze zijn magnetische veldsterkte aanpassen, een uitbreiding van de regelingsmogelijkheden, en zijn de aanschaffingskosten zijn doorgaans lager met respect tot, bijvoorbeeld, een gelijkwaardige Permanente Magneet Synchrone motor. De elektromotor die gebruikt was is voor dit onderzoek is toegepast met een vergrote elektrische tijd constante rekening houdende met kritieke temperatuursinvloeden. Omdat de responsie vertraging van deze elektromotor geen zichtbare invloeden vertoond op het voertuig dynamisch gedrag in de uitgevoerde simulatie resultaten, wordt er daarom niet verwacht dat, met wat voor type elektromotor dan ook, dit een probleem zal veroorzaken voor de regeling van Torque Vectoring. Een sterkte conclusie over de exacte hoeveelheid van verschil in energieverbruik kan niet worden getrokken. Dit omdat dit sterk afhankelijk is van het werkpunt van de elektromotor. Simulatie resultaten tonen aan dat het energieverbruik kan toenemen maar ook kan afnemen met maar liefst 1%.

S. Nada and S.J. Koster VIII Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Preface

In this preface we (Joost and Shady) would like to devote some personal words concerning this final internship. First the personal experiences concerning the internship are discussed and subsequently it closes with words of thanks and acknowledgements.

Before graduation we both were working hard on arranging a graduation assignment abroad. Because negotiations in a very late stage yet failed we came in contact with TNO Automotive with the aid of our dean Mr. van Breugel. At TNO a final graduation project was available in the subject of Torque vectoring. Obviously, we were grateful to have found a suitable placement in such a late stage. Even better though, at our first acquaintance and during the course of this project we both realized that our graduation turned out to be more interesting than expected, since, unlike the prospect abroad, we got involved in a very interesting and up to date subject. We, by means of this report, have set a foundation for the construction of a Torque Vectoring CarLab (test vehicle) which will be used by TNO to perform real life tests. For us this is very exciting because of the prospect that our work will be used for this research. Looking back, we are very satisfied concerning our stay and guidance at the TNO Automotive where we have gained a lot of new knowledge at a high level and have a preview in the work that TNO is performing.

We would like to thank our dean Mr. van Breugel for assisting us in the late stage of arranging this placement and for straightening out the placement and our Plan of Approach approval. Also we would like to give special thanks to Mr. Jansen and Mr. van Eeuwijk for their guidance and time in our graduation project and for our stay at TNO.

Most sincerely,

Joost Koster and Shady Nada

S. Nada and S.J. Koster IX Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Contents

Contact Information ...... 1I List Of Acronyms And Abbreviations ...... 2II List Of Figures And Tables ...... 5V Summary ...... 7VII Samenvatting (Dutch) ...... 8VIII Preface ...... 9IX

Introduction ...... 1

1. Torque Vectoring Research ...... 2

1.1 Vehicle Dynamic Behaviour by Applying Torque Vectoring ...... 2 1.1.1 Vehicle Configuration ...... 2 1.1.2 Electronic Differential ...... 2 1.1.3 Maximum Tyre Force ...... 3 1.1.4 The Tyre Estimator® ...... 7

2. Powertrains Drive Selection For Torque Vectoring Carlab ...... 9

2.1.1 Electric Powertrain ...... 9 2.1.2 Electric Motors ...... 9 2.1.3 Selection Criteria ...... 11 2.1.4 Operating Principle Of An Electric Motor ...... 11 2.1.4.1 Direct Current Motors ...... 12 2.1.4.2 Alternating Current Motors ...... 12 2.1.4.3 Induction Motor ...... 13 2.1.4.4 Permanent Magnet Synchronous Motor ...... 13 2.1.4.5 Switched Reluctant Motor ...... 13 2.1.5 Comparative Study Overall Architecture...... 13 2.1.5.1 Direct Current Motors Versus Alternating Current Motors ...... 13 2.1.5.2 Induction Motor Versus PM Synchronous Motor ...... 14 2.1.5.3 Switch Reluctant Motor ...... 16 2.1.5.4 Regenerative Braking ...... 17 2.1.5.5 Response Delay Time ...... 17 2.1.6 System Evaluation ...... 19

S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

3. Vehicle Dynamic Models ...... 22

3.1 Vehicle Model ...... 22 3.1.1 Requirements For The Control Systems ...... 24 3.2 Torque Vectoring Controller ...... 27 3.2.1 Direct Yaw Moment Controller ...... 28 3.2.1.1 Validation Of Direct Yaw Moment Controller ...... 30 3.2.2 Acceleration Control ...... 31 3.2.3 Traction Control ...... 31 3.2.4 Driving Force Limitation Control ...... 33 3.2.5 Motor Control ...... 34 3.3 Drivers Input ...... 35 3.4 Replay Model ...... 36 3.4.1 Additions To The Tyre Estimator® ...... 36 3.4.2 Replay Model Used In This Study ...... 37

4. Powertrain Models ...... 39

4.1 Electric Motor Model ...... 39 4.1.1 Electric Motor Model Operation ...... 40 4.1.1.1 Generated Torque ...... 40 4.1.1.2 Required Electrical Power ...... 44 4.1.1.3 Validation Using The QSS Toolbox ...... 48 4.2 Final Drive Model ...... 50 4.2.1 Final Drive Model Operation ...... 50

5. Simulation Results ...... 52

5.1 Vehicle Steer Characteristic ...... 52 5.2 Steady State ...... 54 5.3 Influence Of Response Delay Of The Electric Motor ...... 56 5.4 Consumption When Using Torque Vectoring ...... 59 5.5 Replay Model ...... 63

6. Conclusions ...... 65

7. Recommendations ...... 66

8. References ...... 68

S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Appendix 1 - Vehicle Model ...... 71 Appendix 2 - Validation Designed Vehicle Model Using Tyre Estimator® ...... 75 Appendix 3 - M-File Of Electric Motor And Final Drive Models ...... 86 Appendix 4 - Electric Motor Model ...... 88 Appendix 5 - Final Drive Model ...... 98 Appendix 6 – Direct Yaw Moment Controller Validation...... 100 Appendix 7 - M-File Drivers Input ...... 102 Appendix 8 - M-File Run File ...... 105 Appendix 9 - Vehicle Characteristic ...... 107 Appendix 10 - Motor Response ...... 109 Appendix 11 - Steady State With DYM Controller On And Off ...... 112 Appendix 12 - Energy Consumption (Dynamic Drive Cycle, ‘Lower’ Speed) ...... 114 Appendix 13 - Energy Consumption (Dynamic Drive Cycle, ‘Higher’ Speed) ...... 116 Appendix 14 - Energy Consumption (Steady State Drive Manoeuvre, ‘Figure of 8’) ...... 118 Appendix 15 - Replay Model (Orignal Tyres) ...... 120 Appendix 16 - Replay Model (MF-Tyre Estimated Tyres) ...... 122 Appendix 17 - Electric Motor Glossary ...... 124

S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Introduction

Torque Vectoring (TV) applies a different amount of torque to each driven wheel which creates an additional yaw-moment to steer or control a vehicle during under- and oversteer situations. Vehicles with individual electric motors can easily adapt TV control for improvement of the vehicle handling performance. TNO (Netherlands Organization for Applied Scientific Research) has developed several algorithms for handling improvement in the simulation environment and is considering of building a CarLab (test vehicle) for Torque Vectoring research purposes. The specifications for the components have to be defined in relation to the (anticipated) vehicle performance. Additionally, a method for evaluation of the vehicle performance is required for development and demonstration purposes. This resulted in two related assignments where Torque Vectoring is approached from two different perspectives; vehicle dynamics and powertrains. The main purpose of this report is to answer a number of key questions with regard to Torque Vectoring. This then should serve as an introduction to related further assignments in which this study will be used for the construction of the Torque Vectoring CarLab. The key questions to be answered are drawn from the two mentioned perspectives;

From the vehicle dynamic perspective; 1. What kinds of controllers are required to correctly apply Torque Vectoring? 2. What kind of improvement can be accomplished by applying Torque Vectoring? 3. Which changes need to be made to the Tyre Estimator® to cope with a vehicle equipped with Torque Vectoring?

From the powertrains perspective; 1. Which types of powertrain components are best suited for the application of Torque Vectoring? 2. Does an electric motor have a sufficient rapid response for the appliance of Torque Vectoring? 3. Will the appliance of Torque Vectoring influence the energy consumption with respect to an electric vehicle which does not use Torque Vectoring?

The report is built up in three parts; the Introduction, the main content and the closure of the report. The main content itself can be in turn divided into three parts where Section 1 and 2 discusses the obtained information using multiple literature references, Section 3 and 4 discussing the models and Section 5 discussing simulation results of the complete model. The closure part includes; the conclusions, the recommendations, the used references and the reports corresponding appendices.

1 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

1. Torque Vectoring Research

To understand the meaning and operation of Torque Vectoring (TV) a literature study has been performed taking into account two perspectives; Vehicle Dynamics (VD) and Powertrains (PT). The VD part focuses on the vehicle dynamic behaviour and the influence of TV on this behaviour. The PT part focuses mainly on one of the main powertrain components, the Electric Motor (EM) where the different EM characteristics and the influences of these characteristics on the appliance of TV are discussed. Also superficially the corresponding controllers are taken into account. Both the VD and the PT part are combined into this single report.

1.1 Vehicle Dynamic Behaviour by Applying Torque Vectoring This section discusses the vehicle dynamic improvement and the limitations when applying Torque Vectoring (TV). Also it superficially discusses the by TNO designed Tyre Estimator® which is used to validate the build vehicle model.

1.1.1 Vehicle Configuration In this report a vehicle setup is used with two independent Electric Motors (EM’s) on the rear axle as is illustrated in Figure 1. By utilizing the possibility to control the torque output a positive effect can be obtained on vehicle performance.

Figure 1 | Target vehicle model [24]

1.1.2 Electronic Differential To corner with a vehicle, a differential is required between the driven wheels which makes it possible to have different wheel speeds, since in a corner the outer wheel has a larger circle radius compared to the inner wheel. In the used vehicle setup of independent EM’s, no mechanical differential is applied but an ‘electronic differential’. There are two options to use an electronic differential. One option is to apply the exact same amount of torque to each rear wheel. In a corner it will function as a mechanical differential, called an open differential, where the outer wheel is free to have a higher rotational speed. The second option is to use the electronic differential as an active differential and actively change the torque output to each rear wheel, and (Figure 1).

2 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

A significant improvement can be made when using an active differential instead of its mechanical counterpart. This by means of applying TV while cornering by shifting force to the wheel with a potentially higher grip. When applying TV, a different amount of torque is applied to each driven (in this study rear) wheel. This creates an additional yaw-acceleration to the vehicle which is used to steer or control a vehicle during understeer (US) and oversteer (OS).

Advantages of Torque Vectoring [1] are: ∙ Control under and over steer situations ∙ Improvement of vehicle response ∙ Cheap to realize ∙ Maintenance free ∙ Unlimited setup options

A conventional rear wheel drive vehicle uses a mechanical differential. An advantage of this kind of setup is that it makes it possible to distribute the driving force, up to 100% of the total amount of available driving force, between each of the two rear wheels. Whereas, when using two EM’s, this is limited to 50% of the total available driving force. So, when the vehicle is driving on its maximum torque, it may occur that there is not enough remaining torque to apply TV without the loss of the total torque, i.e. forward momentum. An attention point when applying TV, is that there is the possibility to saturate the maximum tyre force when applying more torque to one of the wheels in order to create a yaw moment. Because when this happens, a vehicle can become unstable. Further explanation is given in Section 3.1.1.

1.1.3 Maximum Tyre Force A tyre can only transfer a certain amount of force on the road mainly depending on the vertical tyre load and the friction coefficient between tyre and road surface. To visualize the maximum amount of force a tyre can transfer, the circle of Kamm, also known as the friction circle, is used which is illustrated in Figure 2. The friction circle can be related to the tyre road contact surface area, and the acting tyre forces. The outer edge, largest circle, represents the friction limit of the tyre. If the product of the longitudinal and lateral tyre forces exceeds the outer edge, the tyre will slip. The friction limit (circle radius) of a tyre can be increased or decreased depending on the two main variables, vertical tyre load and friction between tyre and road surface according to the expression;

Eq. (1)

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Sum of forces Fx, longitudinal force Fy, lateral force

1 = dry road surface 2 = wet road surface 3 = snow/ice

Figure 2 | Circle of Kamm (friction Circle) [38].

Figure 3 | Schematic rear view of the vehicle making a right hand turn [1]. Note: For understanding the Free Body Diagram and Kinetic Diagram are combinded.

When a vehicle makes a turn, a weight transfer occurs. For example, when a vehicle makes a right hand turn, a weight transfer to the left takes place which will increase the left vertical forces

and decrease the right vertical forces as is shown in Figure 3. The vertical load acting on the tyres can be calculated using the following expressions [2];

Eq. (2)

Eq. (3)

Where exists due to the weight transfer according;

Eq. (4)

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Where;

Eq. (5)

Substituting the expressions gives;

Eq. (6)

Eq. (7)

The result of a larger vertical force is a larger contact surface, i.e. tyre footprint, between tyre and road surface making it possible to transfer a larger force on the road.

Figure 4 | Top view of the tyres without use of active differential in a right hand turn.

Subsequently, the result is that due to the weight transfer the outside tyre is capable of transferring a larger amount of forces than the inner tyre. The friction boundaries of each tyre can by calculated according to:

Eq. (8)

Eq. (9)

Figure 5 shows the maximum friction forces of the left and right tyres. Due to the weight transfer the left tyre has a larger friction circle then the right tyre. (A) shows the driving forces without applying TV and (B) shows the driving forces when TV is applied.

In case of (A) the maximum friction force is assumed to be equal to the driving force ( ), where the right tyre is only capable of transferring the longitudinal force without exceeding the friction circle. This means that the left tyre has to transfer all the lateral forces. In case of (B) the total driving force is divided, , where some of the driving force of the right tyre is taken and given to the left tyre making sure there is no loss of forward force according Eq.‎ (10).

Fxrl Fx Fx Rl F Fxr Rl x r Rr

Fy Fyr Fyr

ll r

(A) Top view of the tyres without Torque Vectoring. (B) Top view of the tyres with Torque Vectoring.

Figure 5 | Effect of Torque Vectoring. 5 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Eq. (10)

Where:

Eq. (11)

Eq. (12)

By decreasing the driving force of the right tyre, it will also be possible to transfer a lateral force. In that case both tyres can transfer a lateral force without saturating the maximum tyre forces. With this variation in , the vehicles maximum (total) lateral force is increased which can be described as [3];

Eq. (13)

Where;

Eq. (14)

Eq. (15)

Eq. (16)

This equation represents a function where, when is increased from zero, the maximum value is achieved when [3];

Eq. (17)

This means that by applying TV, the maximum lateral force is increased and as a result the vehicles cornering limit is raised. The extra yaw acceleration which is created, improves the vehicle response. This yaw acceleration can be described as [1];

Eq. (18)

Where;

Eq. (19)

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1.1.4 The Tyre Estimator® The Tyre Estimator® (TE) is used to validate the vehicle model made for Torque Vectoring (TV). The TE is a tool to derive tyre forces from vehicle motion data and in this section, for understanding, the operation of the TE is superficially explained.

Nowadays a tyre is mounted on a specially designed truck where the tyre is forced on to the road and measurements in all directions are taken while driving. During these measurements, changes on the tyre can be made such as the angles and position. Also brake forces can be applied [4]. The lateral force as function of the slip angle, which is called a tyre characteristic, is considered to be most interesting. The objective of the TE, developed by TNO, is to determine the tyre characteristics corresponding to the tyres fitted on the vehicle by which the manoeuvre is performed. The TE needs a minimum number of measurement instruments installed on the vehicle and thereby making the TE useful for many applications. By these measurements the TE can determine the vehicle state. For the best results of the TE, care has to be given to the performed manoeuvre. The best manoeuvre is considered to be a ‘pure’ sideslip manoeuvre because the TE is made to predict only the lateral forces as function of the side-slip angles of the tyres. For that reason the usual test is a sinus test. When driving a sinus with a constant speed, there is none or almost none combined slip and the measurement range is quite large in both directions.

In the following diagram the TE is superficially explained.

Figure 6 | Tyre Estimator® flowchart

Inside the TE a vehicle model is used in the State Estimation. The input variables (measured vehicle data) for this model are a steer angle and the vehicles forward velocity. The vehicle model will start a simulation with these two input variables and will estimate variables (output) such as the yaw-rate, the lateral acceleration and the body slip angle. The estimated output variables will be fitted by the Magic Formula (MF) and will create a Tyre Property File. To validate the estimated tyre properties, the Tyre Property Files are placed in the Replay model. The Replay model is an exact same vehicle model as used in the State Estimation and will run the exact same manoeuvre using the same input variables (steer angle and forward velocity). It will also estimate the same output variables as the vehicle model. When the measured vehicle data

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and the replay estimated output variables are (almost) the same, the conclusion can be made that the estimated Tyre Property Files are correct. In this research the TE is used to validate the vehicle model which is used to perform research on TV. By comparing the output variables of the TE with the estimated output variables of the vehicle model made for TV, the designed TV vehicle model can by validated.

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2. Powertrains Drive Selection For Torque Vectoring Carlab

This section describes a comparative research to one of the primary (main) electric powertrain components, the Electric Motor (EM), and this for the purely Electric Vehicle (EV) powertrain application fitted with Torque Vectoring (TV). This chapter is written based on an extensive study of various EM’s with as standpoint their properties, mutual differences and the pros and cons mainly regarding the criteria for the applicability of TV. Their corresponding controls are in some cases superficially discussed as well. Specific technical terms which are used in this section are explained in Appendix 17.

2.1.1 Electric Powertrain An electric powertrain can be divided into primary and secondary components. The EM, the inverter and the battery are considered to be the primary components. Components like fuses, contactors and the Battery Management System (BMS) are considered to be secondary components. This is because they are not considered necessary but more as an added value in terms of safety, reliability and performance.

Figure 7 | The primary (main) components of an Electric Vehicle powertrain [41]

2.1.2 Electric Motors In the world of Internal Combustion Engine powered vehicles, engines are not identical. Beside the Otto and Diesel types there are also different configurations such as straight, opposed, V- configurations and so on. One would have thought that someone by now would have figured out which was best, so that it would have ended all choices and only the best type of engine would be in production. However, that is unlike the reality where there is no best engine type, rather than different types to suit different requirements. The same goes for EV’s and their EM’s [5]. The automotive industry is still seeking for the most appropriate electric-propulsion systems for EV’s. The key features in this case are efficiency, reliability, costs and power density. The process of selecting the appropriate EM’s however is difficult and should be carried out on system level [6]. In this case, building a Torque Vectoring (TV) Car Laboratory for research purposes, it mainly depends on vehicle constrains such as, for example, the available mounting space and TV applicability. With these considerations it can be stated that the motor operating point is not tightly defined which makes choosing the most appropriate EM a challenging task.

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EM’s come in many different types, sizes and shapes. The major types which are adopted or under serious consideration for EV’s are; the Direct Current (DC), the Induction (IM), the Permanent Magnet Synchronous (PM Sync) and the Switched Reluctant (SRM) motors [6] [7] of which for all four types cross sections are shown in Figure 8 [6]. Beside the general EM’s there are exotic types but they are disregarded in this research due to their immature technology. Based on an extensive web research it is observed that IM’s and PM Sync motors are dominant in the application for EV’s and Hybrid EV’s, proved by Table 1.

Figure 8 | Cross sections of the Electric Direct Current (DC), Induction (IM), Switch Reluctant (SRM) and Permanent Magnet Synchronous (PM Sync) Motors [27]

Nissan Leaf (Japan) Volvo C30e (Sweden) Mini Cooper E (UK) Tesla Roadster (USA) EV EV EV EV

PM Sync. Motor PM Sync Motor Induction Motor Induction Motor Fisker Karma (USA) Honda Insight (Japan) Toyota Prius (Japan) Linkoln MKZ (USA) HEV HEV HEV HEV

Induction Motor PM Sync Motor PM Sync Motor PM Sync Motor

Table 1 | Electric Propulsion Applied in Electric Vehicles where; EV = Electric Vehicle, HEV = Hybrid EV

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2.1.3 Selection Criteria The main requirements of the Electric Vehicle (EV) drive system, based on the applicability of Torque Vectoring (TV) and the foreseen development of the TV Car Laboratory (CarLab), summarized on the degree of priority are; 1. Fast response 2. High reliability and robustness for various conditions (Fault tolerant) 3. High power density 4. Good control capabilities 5. Good applicability of regenerative braking 6. High efficiency 7. Low costs

Notice that efficiency and costs are listed at the bottom stating that their degree of priority is low. Although these are very important criteria for the automotive industry, for this particular research application they are considered less significant. The criteria are drawn up, like stated before, based on the applicability of TV and the foreseen development of the TV CarLab. The main priority in all selecting criteria is a fast response which is necessary since from the vehicle dynamic and the controller’s point of view, the torque should be instantly available does it want to have any impact whatsoever. If this condition is satisfied, it is essential as well that the EM is fault tolerant, seen that tests are often operated in the critical working areas of the applied components. From the CarLab point of view, it’s desirable that the Electric Motor (EM) is compact and has a high power to weight ratio. Good control capabilities are required for accurate control of high performance tests. The applicability of regenerative braking is interesting to monitor the TV influences on the energy consumption, beside that other test disregarding TV can also be performed with the same CarLab. The EM’s are discussed taking into account the above stated criteria where some, in respect to the others, more comprehensive. It should be kept in mind while reading this report that the general characteristics of the EM’s can be, in a certain degree, influenced by the control strategies. However, this report discusses only the general characteristics like presented in different references.

2.1.4 Operating Principle Of An Electric Motor Figure 9 illustrates the standard characteristics of an Electric Motor (EM) [6]. It can be seen that the EM has a constant torque over the speed range until the base speed (rated speed). Past the rated speed the torque will lower proportionally with speed, resulting in a constant power output. Eventually the constant power region degrades past the maximum speed, in which the torque decreases proportionally with the square of the speed.

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Figure 9 | Typical electric traction characteristic [6]

EM’s can be roughly categorized into two main categories; Direct Current (DC) and Alternating Current (AC). All types of EM’s have a stationary part and a rotating part which are called a stator, respectively rotor. The rotor is connected to the output shaft on which the generated motor torque is acting. The electricity is provided by the energy supply, such as batteries, through the controller (power inverter) at the EM’s terminals. From there an electromechanical conversion takes place as a consequence of the laws of Faraday and Lorentz. Faraday describes the induction of an Electromotive Force (EMF) in conductors being in relative motion with respect to a magnetic field. Lorentz describes the force generated on a current-carrying conductor lying in a magnetic field [8].

2.1.4.1 Direct Current Motors In DC motors, the rotor consists out of a number of rotor windings (conductors) which terminate with a collector. Due to the DC voltage applied to the rotor windings, using carbon brushes which are in contact with the collector, a magnetic field is generated whose polarity is continuously changed by contact communication. At the same time a stationary magnetic field is generated in the stator by permanent magnets or using field windings. The rotation of the motor is caused by the interaction of the two magnetic fields. [8]

2.1.4.2 Alternating Current Motors In AC motors the magnetic field is generated in the stator by stator windings. Three-phase motors have one or more sets of three windings in their stator where the number of these sets is called the number of poles in the motor. A magnetic field is generated when a three-phase AC voltage is applied to the stator which changes its orientation according to the sign of the current flowing in the windings. Since this is continuously varying, the orientation of the magnetic field keeps varying, resulting in a rotating magnetic field. The speed of this rotating field is called the synchronous speed which equals the pulsation of the three-phase AC voltage divided by the number of poles [8]. Three current forms of AC motors are the Induction, the Permanent Magnet Synchronous and the Switch Reluctant motors

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2.1.4.3 Induction Motor IM’s belong to the category ‘AC asynchronous motors’ where the rotor consists of a set of conductors with end rings, a setup known as ‘squirrel cage’. A current, and thereby an EMF, is induced in the rotor windings by the interaction of the conductors with the rotating magnetic field generated by the stator. The rotor becomes an electromagnet with alternating poles attracted by those of the stators rotating magnetic field. In order for a torque to be produced, the speed of the rotor must be different from that of the rotating magnetic field, hence the name ‘asynchronous’ [8].

2.1.4.4 Permanent Magnet Synchronous Motor Permanent Magnet Synchronous (PM Sync) motors are synchronous AC motors where the rotor operates at the same speed as the rotating magnetic field. This synchronization is achieved by using permanent magnets which generate their own magnetic field which interacts with the rotating magnetic field generated by the stator windings. These motors are often referred as brushless DC motorsI [8].

2.1.4.5 Switched Reluctant Motor In SRMs both the stator and rotor are designed with ‘notches’ and ‘teeth’ referred to as salient poles where each stator pole carries an excitation coil. Opposite coils are connected to form one ‘phase’, while the rotor has no windings. When a DC voltage is supplied to a phase, the rotor rotates in order to minimize the reluctance of the magnetic path. Many topologies are adopted where the most popular is the one with six stator poles, i.e. three phases, and four rotor poles. Reference [9] discusses this more extensively.

2.1.5 Comparative Study Overall Architecture 2.1.5.1 Direct Current Motors Versus Alternating Current Motors Direct Current (DC) motors have been prominent in electric propulsion because they are simpler and less expensive, since they can be easily controlled by varying the current and voltage applied to them fed by a DC supply which is already present in a vehicle [8]. Also their torque-speed characteristic suits the traction requirement well. However, they have several disadvantages such as a low power density, low efficiency, low reliability and they have a high need of maintenance due to the presence of the mechanical commutator (brushes). Therefore the commutatorless motors, such as the Induction (IM) and Permanent Magnet Synchronous (PM Sync) motors are more attractive for electric propulsion since high reliability and maintenance-free operation are prime considerations. Nevertheless, with regard to the cost of the inverter, DC motors are attractive for lower power ratings where the commutator is used as inverter and therefore the

I The AC PM Sync motor develops a sinusoidal back EMF where that of the DC brushless is trapezoidal [39]

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power electronics can be kept relatively simple and inexpensive. An example of a large manufacture who has applied a DC motor as electric propulsion is Citroën who introduced it in the 1999 Berlingo model which is a Hybrid Electric Vehicle called Dynavolt [6] [10].

2.1.5.2 Induction Motor Versus PM Synchronous Motor Among AC motors, IM’s are generally characterized by a higher specific power compared to Permanent Magnet (PM) motors. This has also been shown in an analysis discussed in reference [8], where five IM’s and 11 PM motors were compared to have a power density of 0.76 [kW/kg] for IM’s against 0.66 [kW/kg] for PM motors. In contrast the PM motors showed a higher peak efficiency of 92,5% against 90,5% for the IM’s, where the efficiencies of the respective controllers were included. This could explain why IM’s are preferred for high power applications, such as sportive electric cars, while PM motors are preferred for parallel Hybrid EV’s where fuel economy is a key point [8]. Another interesting difference is that based on the same analysis cited above, the IM’s can generally bear higher rotational speeds. Where the IM’s were ranging from max. 7.500 up to max. 13.000 rpm, the PM Sync motors varied from max. 4.000 up to max. 8.500 rpm. In an ideal Permanent Magnet Synchronous (PM Sync) motor, the strength of the magnetic field produced by the PM’s would be adjustable in such a way that when the maximum torque is required, the magnetic field should be at its maximum. This so that the inverter and motor currents are maintained at their lowest possible value which minimizes the so called ‘current-square resistance’ (I²R) losses and thereby optimizes the efficiency. Likewise, when low torque is required, the strength of the magnetic field should be reduced such that the so called ‘eddy’ and ‘hysteresis’ losses, explained in reference [11] respectively [12], due to the magnetic field strength are also reduced. So basically, the ideal situation would be if the magnetic field strength can be adjusted such that the sum of the eddy, hysteresis, and I²R losses is minimized, which unfortunately is, as far as known, not possible with PM’s [5]. IM’s, in contrast, can adjust their magnetic field strength, since it is proportionate to (voltage to frequency) due to the absence of PM’s. This means that the inverter can reduce the voltage such that the magnetic losses are reduced and thereby the efficiency is maximized. Hence, in terms of efficiencies, the IM can gain in this case another advantage over the PM Sync motor, as long as operated with a ‘smart’ inverter, i.e. one that can control this magnetic field strength. If performance is increased, such as for sportive EV’s or series Hybrid EV’s, this becomes very important. This is because with PM’s, as machine size grows, the magnetic losses of a PM motor increase proportionately and part load efficiency drops. On the other hand, with IM’s, as size grows, losses do not necessarily grow. Hence, the peak efficiency will be a little less, but the average efficiency may actually be better compared to the PM Sync motor [5]. That explains why IM’s may be the favoured approach where high-performance is desired, which applies for the EV, Tesla Roadster and the series Hybrid EV, Fisker Karma which are both equipped with IM’s for their electric propulsion.

Figure 10 shows the typical torque-speed characteristic of an IM [6]. The visible extended speed range operation with a constant power beyond the base speed is accomplished by flux weakening, explained in reference [13]. The breakdown of torque limits the constant-power

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operation. At the critical speed, which generally is, for a conventional IM, around two times the synchronous speed, it reaches the ‘break down’ torque. If the motor is operated at the maximum current beyond the critical speed, it may stall the motor.

Figure 10 | Typical IM Torque- Speed characteristic [6]

Figure 11 shows the typical torque-speed characteristic of a PM Sync motor [6]. Notice the short constant power region which is caused due to their limited field weakening capabilities, explained in reference [13]. To increase the speed range and improve the efficiencies, the so called ‘conduction angle’ of the power converter can be controlled above the base speed. Figure 12 shows a torque-speed characteristic of a PM Sync motor performed with conduction angle control of which the speed range may be extended three to four times over the base speed [6]. An interesting quality about the PM Sync motor is that it is particularly well suited for the wheel direct-drive motor application as is shown in Figure 13 [6]. Finally, PM’s are quite expensive, like Neodymium-Iron-Boron which is currently (year 2011) about $40/kg [14]. This means that IM’s will probably have a cost advantage over PM motors. Also, due to the field weakening capabilities of IM’s, inverter ratings and costs seem to lower. However, a point of concern is that IM’s are more difficult to control. Achieving stability over the entire torque-speed range and over temperature is more difficult compared to the PM Sync motor, which means more development costs [5].

Figure 11 | Typical Torque-Speed characteristic of a synchronous PM [6]

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Figure 12 | Torque-Speed characteristic of a synchronous PM with conduction angle control [6]

Figure 13 | In-wheel PM Synchronous motor (2)

2.1.5.3 Switch Reluctant Motor The SRM is gaining much interest because of their advantages. They have a cost effective simple and rugged construction, are fault tolerant and have a high efficiency. Moreover, they have an interesting torque speed characteristic since they inherently operate with a very long constant- power range as is shown in Figure 14. However, beside these advantages, they have also several disadvantages which, in many applications, outweigh the advantages. The major disadvantages are acoustic noise generation, no uniformity of operation due to torque ripples depending on the number of phases, they require a special converter topology [9], and electromagnetic- interference noise generation [6] and [8].

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Figure 14 | Typical Torque-Speed characteristic of an SRM [6]

2.1.5.4 Regenerative Braking Beside the ‘normal’ brakes applied in conventional vehicles, converting the vehicles kinetic energy into heat where it is wasted, EV’s are mostly also applied with regenerative braking. In this case the vehicles kinetic energy is converted into, stored, electric energy, which can be used later to propel the vehicle. It is called ‘braking’ because it slows the vehicle down by doing so. It is called regenerative because the energy is recaptured, mostly in the batteries, where it can be used again [15]. Electrically this is achieved through the use of a generator, which is nothing more than the EM with the terminals reversed, and an energy storage device such as batteries. With the DC motors this is very simple, since the PM’s do not need to be energized. However, unlike the DC motor which is brushed, AC motors, i.e. IM and PM Sync motors, provide regenerated energy more efficient. Almost at the same efficiency as when used as a motor. And moreover, it comes at no extra costs to the controller [16]. For SRM motors this is more complex [17] where also many controllers are available, like the ones described in reference [18], with all their own particular pros and cons.

2.1.5.5 Response Delay Time The response time of an EM can be divided into two time constants; electrical and mechanical time constant. Unlike what their name implies, these parameters are not a “constant” value. In fact a very significant influence factor on these constants is temperature. Hence they are both functions of the motor’s temperature. In addition, the mechanical time constant only applies, according to its definition, for an unloaded motor. This while a certain load will significantly increase this time. As defined by multiple sources such as [19] and [20]; the motor’s electrical time constant is the time required for the current to reach 63,2% of its final value after a zero source impedance stepped input voltage is applied to a motor maintained in its locked rotor or stalled condition (i.e., ).

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Mathematically, the motor’s electrical time constant is defined as:

Eq. (21)

Subsequently, [19] [20] define the motor’s mechanical time constant as the time required for an unloaded motor to reach 63.2% of its final velocity after a zero source impedance stepped input voltage is applied to the motor. Mathematically, the motor's mechanical time constant is defined as:

Eq. (22)

Notice that the resistance , the back Electromotive Force (EMF) and the Torque friction depend on, or better said change with, temperature.

In case of EM’s with permanent magnets there is an additional effect that the temperature has on the motor’s mechanical time response. As shown Eq.‎ (22), the mechanical time constant of the motor inversely changes with the temperature of the motor, back EMF and torque friction.

According to reference [19], both and have the same functional dependence on the magnetic flux density produced by the magnets in the EM. All permanent magnets are subject to both reversible and irreversible demagnetization. In the case of irreversible demagnetization, it applies that it can occur at any temperature and must be avoided by not exceeding the motor’s peak current value which can permanently reduce the motor's and . If it does, this will increase the motor’s mechanical time constant permanently. Reversible thermal demagnetization however, depends on each specific magnet material. Presently, there are four different magnet materials being used in PM motors [19]: ∙ Aluminum-Nickel-Cobalt (Alnico) ∙ Samarium Cobalt (SmCo) ∙ Neodymium-Iron- Boron (NdFeB) ∙ Ferrite or Ceramic

Within the temperature range of; , all four magnet materials show linear reversible thermal demagnetization where the magnetic flux density produced by each magnet decreases linearly with increasing temperature. Hence, similar to electrical resistance, the expression for both and with increasing magnet temperature is:

Eq. (23)

Eq. (24)

Where the temperature coefficient of the four stated materials is [19]: ∙ Alnico = 0.0001/˚C ∙ SmCo = 0.00035/˚C ∙ NdFeB = 0.001/˚C ∙ Ferrite or Ceramic = 0.02/˚C

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Using Eq.‎ (23) learns that an increase of 100˚C in the magnet temperature will cause a reversible

and decrease of 1% for Alnico, 3.5% for SmCo, 10% for NdFeb and up to 20% for Ferrite or Ceramic magnets. Figure 15 shows the factor of increase, i.e. , with which the mechanical time constant increases as function of the temperature. Notice that the specified ambient temperature is 25˚C. The function is the multiplier due to the change of electrical resistance and occurs in every EM. The resistance of every electrical winding, at a specified temperature, is determined by the length, the profile and the material of the winding. The primary winding in the majority of industrial applications is constructed using ‘annealed copper magnet wire’ [21]. And based on the International Electrical Commission standard, the linear temperature coefficient of electrical resistance for ‘annealed copper magnet wire’ is 0.00393/˚C [19] [21]. Therefore, knowing the resistance at a specified temperature, the resistance at temperatures above or below this specified temperature is given by:

Eq. (25)

The remaining four show the combined effect of thermal demagnetization, for the four discussed magnetic materials, as well.

Figure 15 | Mechanical time constant multiplier as function of the temperature

2.1.6 System Evaluation Table 2 shows an evaluation for the four discussed types of EM’s where a score of 5 means the best compared to the other evaluated motors. The score values are based on the gathered information from multiple references. For this table in particular, similar evaluations are used from references [6] and [22], which correspond to the characteristic of the EM’s given by the different multiple references.

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Propulsion system

Characteristics (EM + CTRL.) DC PM Sync IM SRM Response Time 4,5 4,5 5 5

Robustness/Reliability 2,5 4 5 5 Power Density (kW/kg) 2,5 4 5 4,5

Power Density (kW/m3) 3,5 5 3,5 4,5 Control capabilities 4 5 5 5 Regenerative braking 4,5 5 5 4 applicability Efficiency(mean) 2,5 4,5 5 4,5 Purchase Costs 5 3,5 5 3,5

Table 2 | Electric Motor evaluation (1-5 where 5 means the best compared to the others)

Response Time As explained above, the response time can be divided into two time constants; electrical and mechanical time constant. The latter one will increase with rising temperature of the permanent magnets due to reversible thermal demagnetization where the magnetic flux density produced by each magnet decreases linearly with increasing temperature. However, since the quantity of demagnetization depends on the type of magnetic material, it might be considered insignificant, which is the case for Alnico magnets.

Robustness/Reliability The IM and SRM are well known for their rugged construction, since they do not have magnets which can demagnetize at high temperatures and their maintenance-free operation.

Power Density Power Density can be examined from two different perspectives. Power to weight and power to volume ratio. IM’s are generally characterized by higher specific power to weight ratio compared to PM motor due to the absence of magnets. However, induction motors are mostly larger because the absence of magnets, they need to be larger to generate a similar starting torque with respect to a PM Sync motor.

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Control Capabilities When it comes to control capabilities all EM’s have, especially the AC drives have multiple possibilities. The DC drive has a certain limitation due to the susceptibility of the mechanical commutator. With regard to IM’s, they can adjust their magnetic field strength, since it is proportional to (voltage to frequency) due to the absence of PM’s. Regenerative Braking Capabilities IM and PM Sync motors, unlike the brushed DC, provide regenerated energy more efficient. Almost at the same efficiency as when used as a motor and moreover, it comes at no extra costs to the controller. For SRM motors this is more complex and many controllers are available with all their own particular pros and cons.

Efficiency IM’s, in contrast to PM motors, can adjust their magnetic field strength due to the absence of PM’s. This means that the inverter can reduce the voltage such that the magnetic losses are reduced and thereby the efficiency is maximized. If performance is increased, this becomes very important because with PM’s, as machine size grows, the magnetic losses of a PM motor increase proportionately and part load efficiency drops. On the other hand, with IM’s, as size grows, losses do not necessarily grow. Hence, the peak efficiency will be a little less, but the average efficiency may actually be better compared to the PM Sync motor.

Costs PM’s are quite expensive which means that IM’s will probably have a cost advantage over PM motors. Also, due to the field weakening capabilities of IM’s, inverter ratings and costs seem to be lower.

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3. Vehicle Dynamic Models

The Vehicle Dynamic (VD) model is the complete model used to study the influence of Torque Vectoring (TV) on the VD behaviour. The complete model means it includes the parts of the VD and the Powertrains (PT) model which are build in MATLAB® Simulink® and SimMechanics® . The model consists out of a vehicle model and multiple control systems including two electric motors.

3.1 Vehicle Model The first step in building the Vehicle Dynamic (VD) model was designing a vehicle model in SimMechanics®. Thereafter the vehicle model is extended with controllers to apply Torque Vectoring (TV). After validating the vehicle model it subsequently is used to research the influence of TV. First of all, a model is designed without taking TV into account. Figure 16 shows a screenshot of the vehicle model. For validation, the output of vehicle model is compared with the output of the replay model of the, by TNO designed, Tyre Estimator® (TE).

The inputs of the designed vehicle model and the TE replay model are: ∙ Steer angle (δ)

∙ Vehicle speed ( )

Subsequently, the outputs of both models are: ∙ Yaw-rate (r) ∙ Body slip (β)

∙ Lateral velocity ( )

∙ Lateral acceleration ( )

∙ Lateral tyre force ( )

∙ Tyre load ( ) ∙ Slip angle tyres (α)

In Appendix 1 the vehicle model structure and M-file are shown. Appendix 2 shows the validation results of the vehicle model with the TE. Figure 17 shows a selection of the results. The blue lines represent the output result of the designed vehicle model whereas the red lines represent the output result of the TE replay model. Because both lines lie on top of each other, it can be concluded that the outputs of both models are equal. The vehicle model is extended as described in Section 1.1.1. Additions to the basic vehicle model are two electric motors each connected to one rear wheel. Next the controllers were designed to make use of the advantages and control the limitations of TV as previously described in Section 1.1.2.

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Figure 16 | Vehicle model designed in MATLAB® SimMechanics®

Figure 17 | Example plots output of the designed vehicle model and Tyre Estimator ® Note: The legend is visible in the right bottom corner of the top plot.

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3.1.1 Requirements For The Control Systems As described previously, a yaw-moment to control a turning motion can be generated by applying a difference in driving forces between both (in this study) rear wheels. To do so, a control system has to be designed which is called the Direct Yaw Moment (DYM) controller. Even when the DYM controller is active and working properly, there is the possibility that the behaviour of the vehicle becomes unstable. To visualize the stability of the vehicle in this study, a steer characteristic is used. To express the vehicles steer characteristic in the linear part of the axle characteristic, an under steer gradient (η) is introduced.

Eq. (26)

Where;

Eq. (27) (i notes the front or rear axle)

Here denotes the cornering stiffness respectively of the front and rear axle. There are three types of characteristics: under steer (US), neutral steer (NS) and over steer (OS). Out of Eq.‎ (26) a vehicle can be defined as:  neutral steered when η = 0  understeered when η > 0  oversteered when η < 0

As shown in Figure 18, a vehicle with US characteristic has to increase the steer angle when driving a constant radius while increasing the vehicle speed, and therefore the lateral acceleration. A vehicle with NS characteristic can keep the steer angle constant and a vehicle with OS characteristic has to decrease the steer angle to maintain the same turning radius [23]. Also see Eq.‎ (28) and Eq.‎ (29). If is equal to zero, the steer angle is equal to , i.e. constant, which means neutral steered.Eq.‎ (28)

Figure 18 | Steer characteristic, steer angle versus lateral acceleration [2]

Eq. (28)

Eq. (29)

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As can be derived from Eq.‎ (26), the rear axle of an understeered vehicle has a larger cornering stiffness with respect to the front axle. This means that the rear axle can transfer a larger lateral force at the same slip angle with respect to the front axle. Here out follows the first control requirement. As described in Section 1.1.3, each tyre has a maximum of tyre forces it can transfer between the tyre and the road. The boundary of the maximum tyre forces is called the friction limit. Beyond this boundary the tyre is not able to transfer more tyre forces. So for example, when a vehicle is cornering, the tyres have to generate lateral forces to keep the vehicle on the track, as is demonstrated in Figure 19, situation A. To maintain the forward velocity (V), longitudinal forces are applied on the rear tyres, situation B. If the result of the tyre forces on the rear axle will reach the friction limit by excessive driving forces, the lateral tyre forces will be limited, situation C. The cornering stiffness of the rear axle will decrease, i.e. the vehicles characteristic will change towards OS and eventually become oversteered. The direct solution to avoid this, is to limit the motor torque, i.e. the longitudinal forces to the rear tyres. In that case, the lateral forces can be maintained the same, situation D.

Figure 19 | Tyre forces in a steady state turn [2]

Even when the vehicle is stated to be understeered as described above, the vehicle characteristic can change when the lateral acceleration is increased [23]. Figure 20 shows in the left part four different axle characteristics. The right part of the figure shows the corresponding handling curve (a 90˚ anti-clock wise turn of the steer characteristic as in Figure 18). The topmost axle characteristic A, is in the first linear part understeered. At a larger slip angles the vehicle becomes oversteered. This is caused by the decrease of the slope of the normalized rear axle characteristic with respect to the front axle. The axle characteristic B is always understeered, characteristic C is always oversteered and the last characteristic D is at first oversteered and at larger slip angles the vehicle becomes understeered.

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Figure 20 | Normalized axle D characteristics and handling curves. (1= front axle, 2= rear axle) [23]

Here from can be concluded that there not only has to be looked at the cornering stiffness of the axle characteristic. But there also has to be looked at the slope of the normalised axle characteristic at a given level of lateral acceleration. The following equation is used to calculate the slope of the normalised axle characteristic.

Eq. (30) (i notes the front or rear axle)

The vehicle is considered to be stable when the following equations apply [23].

Eq. (31)

Eq. (32)

So when designing a controller for Torque Vectoring (TV), these potential problems should be taken into account. Therefore other controllers have to be designed as well, which are a Traction (TR) control and a Drive Force Limitation (DFL) control. Combined these controllers form the TV controller. To translate the throttle pedal signal set by the driver into a torque, and thereby longitudinal speed, an Acceleration (ACC) control is designed. In the next sections the construction and operation of the controllers will be explained.

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3.2 Torque Vectoring Controller Like stated previously, the Torque Vectoring (TV) controller is a combination of the Direct Yaw Moment Controller, the Traction Controller, the Acceleration Controller and a Drive Force Limitation controller. Figure 21 shows the outer layer of the TV model and the controller’s subsystems as used in this study.

Figure 21 | Torque Vectoring controllers

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3.2.1 Direct Yaw Moment Controller The heart of the TV controller is the Direct Yaw Moment (DYM) controller. The DYM controller determines the ideal torque difference between the two electric motors. For the calculation of the ideal torque difference, the vehicle yaw-rate and a calculated ideal yaw-rate is used. A yaw- rate is generated when a vehicle makes a manoeuvre. This does not have to be the ideal yaw-rate corresponding to the manoeuvre, i.e. corresponding to the longitudinal speed and steer angle. The DYM controller is used to minimize the difference between the actual and ideal yaw-rate by moving the actual yaw-rate more toward the ideal yaw-rate, i.e. target yaw-rate. The ideal yaw- rate is calculated using Eq.‎ (33) [2].

Eq. (33)

From the target yaw-rate the actual yaw-rate is subtracted which gives a yaw-rate error expressed as;

Eq. (34)

Where becomes small when the vehicle reaches its target yaw-rate.

Figure 22 shows the second layer of the DYM controller where subsystem A calculates the ideal yaw-rate. Linked to this is a Feed Forward (FF) controller with is designed to follow the target yaw-rate and a Feed Back (FB) controller which is designed to follow the yaw-rate error. The FB controller is a Proportional and Integral (PI) controller and the FF controllers is a derivative (D) controller. To generate the cornering stiffness of the front and rear axle ( ) the Tyre Estimator® (TE) is used. This is required to gain the understeer gradient (η), calculated using Eq.‎ (26), for the use in Eq.‎ (33).

Figure 22 | TE axle characteristic, used to calculate the vehicle cornering stiffness.

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Subsystem ‘Direct Yaw Moment Control’, top layer

Figure 23 | First layer Direct Yaw Moment controller

%% ======DYM controller ======%%

DYM = 1 ; % on/off (1=on & 0=off) DYM_delay = 0 ; % delay DYC controller to by active

% FF controller P_dym_ff = 0 ; % - I_dym_ff = 0 ; % - D_dym_ff = 0.4 ; % derivate is used

% FB controller P_dym_fb = 10 ; % proportional is used I_dym_fb = 0.6 ; % integrator is used D_dym_fb = 0 ; % -

factor = 150 ; % factor for Yaw error

n = (((Mass_f*g)/C1)-((Mass_r*g)/C2)); % understeer coefficient

Table 3| M-script Direct Yaw Moment (DYM) controller

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3.2.1.1 Validation Of Direct Yaw Moment Controller Like explained previously, when the wheels have almost no slip, the calculated yaw-rate, i.e. the ideal yaw-rate corresponding to the steer angle and longitudinal velocity, should be almost the same as the actual yaw-rate of the vehicle. To validate the calculations performed by the Direct Yaw Moment (DYM) controller, a test manoeuvre is preformed where the steer input is kept small and the speed of the vehicle is gradually increased from 10 up to 100 km/h. During this manoeuvre the slip angles of the wheels are kept small due to the low lateral acceleration, as shown in Figure 24. Figure 25 shows that the calculated ideal yaw-rate is almost the same as the actual yaw- rate of the vehicle model. From this can be concluded that the calculations performed by the DYM controller are correct.

Figure 24 | Vehicle motion data of validation simulation.

Figure 25 | Actual (real) and the calculated ideal yaw-rate 30 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

3.2.2 Acceleration Control In the Acceleration (ACC) controller a simple FF controller is used to determine the driving torque proportional to the position of the acceleration pedal.

Eq. (35)

Extra is the cruise control. This controller is made for maintaining a constant speed instead of a constant torque.

Eq. (36)

Subsystem ‘ACC control’, top layer.

Figure 26 | Acceleration (ACC) controller (ACC) controller

3.2.3 Traction Control To control the possible saturation of the tyres forces like explained in Section 3.1.1, a Traction (TR) controller is made. The TR controller is used to limit the driving forces of the electric motors. The following expression is used to calculate the maximum driving force:

Eq. (37)

Eq. (38)

These variables are calculated in subsystem A of Figure 27. The calculated maximum torque values are used as saturation points in B. In addition, if the driving force on one side is limited, the driving force on the opposite side must also be reduced. This is performed in C, so the torque difference between both wheels set by the DYM controller is maintained as is illustrated in Figure 28.

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Subsystem ‘Traction control’, top layer.

Figure 27 | Top and first layer of the Traction (TR) Controller

Figure 28 | The traction control drive force correction

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3.2.4 Driving Force Limitation Control The Drive Force Limitation (DFL) controller is not used in this study due to the lack of time. In this section it is explained how the controller should be made in theory.

To avoid the vehicle getting an oversteer characteristic as is explained in Section 3.1.1, where the vehicle can become unstable at high accelerations, a DFL controller is designed. The DFL controller will prevent that the slope of the normalised axle characteristic of the rear axle becomes and stays larger than the slope of the front axle. A direct solution is to reduce the driving forces to the rear wheels which will be performed equally to both the rear wheels as shown in Figure 29.

Figure 29 | Reduction of tyre forces to control the cornering power

Stability Of A Turning Motion Eq.‎ (39) and Eq.‎ (40) represent a two Degrees Of Freedom (2-DOF) model to study the vehicle turning motions where the forward velocity is held constant. In these equations the tyre forces are replaced with the values; and [24].

Eq. (39)

Eq. (40)

As described in Section 1.1.2, to maintain an understeer characteristic the vehicle conditions must satisfy the following expressions [24];

Eq. (41)

Eq. (42)

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3.2.5 Motor Control For explanation of the Electric Motor (EM) model (A) and final Drive model (B) shown in Figure 30, see Section 4.

For the overall model, an addition is applied to the electric motor model which is named ‘torque correction left-right’ presented in subsystem C. It acts when one of the electric motors is not capable of delivering the requested torque. And does so by limiting the output of the other EM as well to maintain the torque difference set by the DYM controller. Figure 30 shows the first layer of the motor controller.

Normally, the following expression applies;

Eq. (43)

If it does not apply, the following applies;

Eq. (44)

Subsystem ‘Motor control’, top layer

A B

Figure 30 | Top and first layer Motor controller C

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3.3 Drivers Input For easy use of the Torque Vectoring (TV) model and gain a clear overview, a subsystem named ‘Driver input’ is designed. In this subsystem all the so-called driver inputs for the vehicle and controllers are processed, which are; ∙ Acceleration pedal position or speed selection ∙ Steer position (fixed steer angles or auto steer) ∙ Controllers activation signals

Subsystem ‘Drivers input’, top layer

Figure 31 | Top and first layer of the Drivers input subsystem

When the vehicle has to make a turn with a set radius, the ‘auto steer’ function, subsystem A, will calculate the steer angle required for this radius and keeps on adjusting the steer angle until the vehicle is driving the desired turning radius. The steer angle is calculated using Eq.‎ (45) [2].

Eq. (45)

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Figure 32 shows the first layer of the auto steer controller. With the ideal steer angle, calculated in subsystem A, a yaw-rate is calculated, in subsystem B, in the same manner as in the Direct Yaw Moment (DYM) controller using Eq.‎ (33). From the target yaw-rate the actual yaw-rate is drawn which is also expressed as in the DYM controller using Eq.‎ (34). Where becomes small when the vehicle reaches its target yaw-rate. This means that if the vehicle is not generating the ideal yaw-rate, the steer angle will be increased until becomes zero. Appendix 7 shows the drivers input M-file.

A B

Figure 32 | First layer of auto steer controller

3.4 Replay Model As explained in Section 1.1.4, the Tyre Estimator® (TE) uses a vehicle model to estimate the vehicle motion data such as the yaw-rate, the lateral acceleration and the vehicle slip angle with as input the steer angle and the forward velocity of the vehicle. With the estimated variables (motion data) the Magic Formula (MF) creates Tyre Property Files for the rear and front axle. These Tyre Property Files are then loaded into the Replay model which is also a vehicle model that uses the measured steer angle and forward velocity as input. The estimated variables of the Replay model are than compared with the measured vehicle motion data to validate the Tyre Property Files.

When a vehicle is applying Torque Vectoring (TV), an extra yaw-moment is created by the differences in driving forces between the, in this study, rear wheels. So the yaw-rate that is generated when using TV is not only created by the front wheel steer angle but also by a difference in driving forces.

Within the TE, the vehicle model used in the State Estimator and the Replay model uses only the measured steer angle and forward velocity to estimate variables such as the yaw-rate. Therefore the estimated variables of these models will not correspond with the measured variables of a vehicle applied with TV. This means that some additions have to be made on the vehicle models used in the TE, i.e. the vehicle model used in the State Estimation and Replay model.

3.4.1 Additions To The Tyre Estimator® To prepare the TE so it can deal with TV, additions have to be made to: ∙ The required measured vehicle data ∙ The input of the vehicle models used to estimate the vehicle motion variables so they can follow the measured vehicle data.

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To create the extra yaw-moment that is needed for the vehicle models to follow the measured vehicle variables, the torque or longitudinal forces applied on the vehicles wheels needs to be measured.

There are three ways to use the measured torque of longitudinal forces in the vehicle models: 1. Apply the measured torque or forces in the vehicle model on the same place as measured, i.e. left front, left rear wheel etc. whereby creating a longitudinal velocity and when TV is applied, an extra yaw-moment. In addition the measured speed can be used to correct the deviation of the vehicle model speed and measured speed. 2. Measure the applied torque or forces and just look at the difference between left and right. Apply, in the same way as above described, the difference in torque or forces on the vehicle to create the extra yaw-moment when using TV. Hereby not changing the way that the TE follows the longitudinal velocity. 3. Calculate the yaw-moment which is created by the difference in torque or the longitudinal forces and apply this extra yaw-moment on the z-axis (perpendicular to the road) of the vehicle.

The third option is the most usable option because in that case the vehicle model, i.e. the TE, can still be used for vehicles without TV and without the requirement to measure the motor torque. This because in this way the measurement of torque is optional. A second advantage of the last option is that there are no longitudinal forces applied on the tyres and therefore the TE is able to calculate purely the lateral forces. To use the third option, some research has to be conducted on how the torque applied on the wheels can be selected from the vehicle computer (ECU) or being measured in the vehicle. Also there has to be looked at the measured location and unit, i.e. force [N] or torque [Nm]. In some cases the final drive and wheel radius has to be taken into account as well.

3.4.2 Replay Model Used In This Study The Replay model used in this study is somewhat different then the Replay model described above. This because due to the lack of time, the TE being a ‘black box’, and because initially it only has to work for this study. For that reason the vehicle model that is designed for the use of TV as described in Section 2.1 is used.

Figure 33 | Flowchart when using the replay model 37 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

The TV model is a vehicle model which requires a steer angle input and a torque input for each rear wheels. The tyres inside the vehicle model use a standard Tyre Property File provided by the TE (TNO_car205_60R15.tir). With this TV model, including the TV controllers, a manoeuvre is simulated. During these simulations vehicle motion data is measured and afterwards processed so it can be loaded into the MF-Tyre/MF-Swift. Only the MF-Tyre is used, for more information about the MF-Tyre/MF-Swift see reference [25]. With the MF-tyre a Tyre Property File is made with the measured motion data for the front and the rear axle. These Tyre Property Files are loaded into the tyres of the designed Replay model and will replay the same manoeuvre, i.e. steer angle and wheel torque, as measured in the simulation of the TV model. The only differences between the Replay and TV model are the Tire Property Files. If these Tire Property Files are correct, the replay motion data should be the same as the motion data measured during the simulation with the TV model.

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4. Powertrain Models

One of the main components in an electric powertrain is the Electric Motor (EM). To study the influence of the EM on the application of Torque Vectoring and in turn the effect of TV on the energy consumption, a model of the EM is created taking into account features such as electrical response delay and efficiencies. Also a Final Drive (FD) model is created where the efficiencies and the moment of inertia are taken into account. This section will discuss the operation of the complete EM and FD models. In order to keep a clear overview, the overall model structures are shown in the appendices attached to the report and the meaning, including units, of the used expressions are shown in Section ‘List of acronyms and abbreviations. The corresponding M-File of the models is shown in Appendix 3.

4.1 Electric Motor Model The Electric Motor (EM) model is part of the overall Torque Vectoring (TV) model, i.e. the Vehicle Model and all other corresponding control systems as was visible in Figure 30, Section 2.2.5. A key feature in this model is that the EM is modelled just based on the torque output and the required power where the main characteristics, such as response delay and efficiencies are used. This approach is chosen since for this study a detailed, and thereby complex, model is unnecessary. The model has a total of two inputs and four outputs.

Model Input

∙ is the instantly desired torque on the output shaft of the EM by the driver.

∙ is the resulting (measured) wheel speed of the wheel connected to the EM.

Model Output

∙ is the torque provided on the EM output-shaft. ∙ is the actual speed of the EM derived from the measured wheel speed. ∙ is the required power applied to the EM to deliver the total torque which consists of the torque on the EM shaft plus the torque required to overcome the EM’s moment of Inertia. Where the latter will have a value of zero if the motor speed is constant.

∙ is the maximum torque the EM can provide as function of the rotational speed.

Figure 34 | The top layer of the Electric Motor model presented as a Subsystem

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4.1.1 Electric Motor Model Operation Above is explained what the different input and output signals represent. This next section will explain the operation of the model using the applied equations and used approaches. For the understanding they will be discussed from the initial inputs toward the final outputs.

Electric Motor Speed The speed input provided to the Electric Motor (EM) by the vehicle is the measured wheel speed

. Since the model works with the speed of the EM itself, it is converted to using the expression;

Eq. (46)

4.1.1.1 Generated Torque Within the EM model different subsystems are processed in the first layer of the model. The first subsystem is ‘Generated Torque’ which provides three torque related outputs as function of the two initial model inputs shown in Figure 35.

Figure 35 | Subsystem ‘Generated Torque’

The content of this Subsystem is shown in Figure 36 where the following expression is applied;

Eq. (47)

Figure 36 | The content of Subsystem 'Generated Torque'

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Notice that the torque generated by the EM should also overcome its own moment of Inertia

which is expressed as;

Eq. (48)

The content of the subsystem ‘Torque-Speed Limits + Response Delay’, itself in turn consist out of three subsystems, visible in Figure 37. The first two subsystems check if and do not cross their maximum values and intervene, i.e. perform a certain action, if so. The final subsystem provides the torque output and simulates a Response delay due to the electrical time constant which proceeds according an exponential function.

Figure 37 | Content of Subsystem 'Torque-Speed Limits + Response Delay'

Overspeed Protection

Once the maximum rotational speed is crossed, there will be results generated which are improbable. To avoid making conclusions using those results, assuming the maximum speed crossing stays unnoticed, the simulation should be stopped. However, in some scenarios performing multiple simulation this approach may be undesirable since the complete simulation will stop. Therefore instead a method is used where, if the maximum speed is crossed, the EM stops generating torque permanently during the remaining simulation for which the first subsystem ‘Overspeed Protection’ is applied. This subsystem checks and acts, by giving a ‘zero’ or ‘one’ output which will be multiplied with the torque output explained further on. The ‘Overspeed Protection’ goes according the expressions;

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Eq. (49)

Eq. (50)

To avoid the EM giving a torque output as soon as the rotational speed drops below the maximum speed, an embedded MATLAB function, containing a script, is applied which will keep the output value of permanently zero for the remaining simulation. The Simulink Function block and the script are shown below in Figure 38 and Figure 39.

Figure 38 | Embedded MATLAB function block 'Hold zero value'

%%______function y = fcn(u)

% Embedded MATLAB Function: % The output value (y) is equal to the input value (u) if (u)= 1 % Once the input value becomes zero, it will stay zero the for % entire remaining simulation time

persistent g; y = u; if isempty (g) g = 0; end

if (u == 0) y = 0; g = 1; end

if (g == 1) y = 0; end %%______

Figure 39 | Embedded MATLAB script which will keep the output value zero once it becomes zero

Maximum Available Torque The subsystem ‘Max. Available Torque’ provides the maximum torque as a function of the rotational speed expressed as; and which is defined by the EM manufacturer. Although the Torque-Speed characteristic, in most cases, is only provided for the first quadrant of

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the EM, i.e. motor mode and and not for the second quadrant, i.e. II generator mode and , the model is applied with two 1D look-up tables,

and , which give a torque output as function of the speed input in [rpm]. The reason to apply two tables instead of one, where the first quadrant is just mirrored to the second one, is because it may be desired to modify the regenerative torque behaviour. To give an example, below a certain speed the regenerative torque drops rapidly. This feature could be taken into account using a separated regenerative table. If no modifications are desired it is of course possible to just mirror the first quadrant characteristic by multiplying it with (-1). And if no regenerative torque is desired at all, a value of zero torque over the entire motor speed should be applied.

Also for the maximum speed crossing is of influence according to the expression;

Eq. (51)

Where;

Eq. (52)

Eq. (53)

Torque Limitation

The subsystem ‘Torque Limitation’ is the last process in giving its final output . Three sub- processes are performed in this subsystem. First it provides the so called; , which is determined by checking if the requested torque is equal or less than the maximum torque available as function of the speed. If this is not the case, the value will be saturated to the maximum torque which goes according the following expression;

Eq. (54)

Eq. (55)

The second sub-process performed is the ‘torque stop’ where the output torque will be zero if the maximum speed is crossed using the expression;

Eq. (56)

Where;

Eq. (57)

Eq. (58)

II Since driving in reverse is meaningless for the Torque Vectoring study, the third and forth quadrant are not discussed here.

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Response Delay Like discussed in Section 1.2, the requested torque of the EM will not be delivered instantly due to two main time constants; the electrical and mechanical time constant. As defined by references [19] [20] the electrical time constant is the time required for the current to reach 63,2% of its final value. This after a zero source impedance stepped input voltage applied to a motor maintained in its locked rotor or stalled condition, i.e., . Mathematically, the motor’s electrical time constant is defined as:

Eq. (59)

Subsequently, references [19] and [20] defines the mechanical time constant of the motor as the time required for an unloaded motor to reach 63.2% of its final velocity after a zero source impedance stepped input voltage is applied to the motor. Mathematically, the motor's mechanical time constant is defined as:

Eq. (60)

To simulate the response delay due to the electrical time constant, the model is performed with a first order transfer function which is considered ideal since it simulates the progress according its corresponding exponential function. The transfer function is processed as the last sub-process in the subsystem ‘Torque Limitation + Reponse Delay’ and expressed as;

Eq. (61)

The Mechanical time constant isn’t separately processed in the model since the delay influence of it is already obtained due to the implementation of the expression; of which the value depends on . Notice that the largest influence factor for is , especially when a load is applied to the motor.

4.1.1.2 Required Electrical Power The subsystem ‘Required Electrical Power’ shown in Figure 40 gives as output the required electrical power, which is consumed or recaptured, to provide the EM’s output. It goes according to Eq.‎ (62), which is clearly visible in the subsystems second layer shown in Figure 41.

Eq. (62)

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Figure 40 | Subsystem 'Required Electrical Power'

To calculate the required power the model uses a reversed cause-and-effect relationship approach of the dynamic system which is based on the ‘quasistatic approach’ of the QSS Toolbox [26]. This approach means that, rather than calculating the torques from given inputs, the model first calculates the torque outputs and then determines the corresponding necessary inputs, in this case the required electrical power.

Figure 41 | Content of Subsystem 'Required Electrical Power'

Required Mechanical Power The Subsystem ‘Required Mechanical Power’ calculates the mechanical power using the expression;

Eq. (63)

Where is equal to zero if is constant.

Power Efficiency Factor

The subsystem ‘Power Efficiency Factor’ determines the factor with which should be multiplied to obtain the required electrical power. To do so an efficiency map of the EM is processed in the model. This map is presented in a 2D look-up table where the efficiencies are given as function of the Torque in [Nm] and the Speed in [rpm]. Since the efficiencies of an EM are usually only well defined for the first quadrant of the motor and not for the second quadrant, these efficiencies have to be determined. For the

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understanding of this approach first the general principle according to reference [27] will be explained, using a ‘causality’ representation of a Motor/Generator.

In Figure 42 the relationship between and can be calculated without a detailed model of the system when a stationary map of the EM efficiencies as function of the input variables is available.

Figure 42 | Causality representation of a Motor /Generator for quasistatic modeling [8]

In such a case the input power required is evaluated as;

Eq. (64)

Eq. (65)

For the efficiencies in generator mode two methods are proposed in reference [27]. The first method consists of mirroring the efficiency, assuming that;

Eq. (66)

The second method consists of mirroring the power losses expressed as;

Eq. (67)

These are evaluated from the energy balance in the defined motor range and then are mirrored to the second quadrant so that; . Using Eq.‎ (64), the efficiency in the generator range is expressed as;

Eq. (68)

Obviously, the two methods give different results. In general, according to reference [27], the result of a mirroring operation does not coincide with the data that can be obtained by measuring the motors efficiency also in generator range, where the difference is typically more important for induction motors for which is referred to reference [28]. Figure 43 shows an efficiency map in which neither the efficiencies nor the power losses are mirrored in the generator range. It seems that the average efficiencies are lower in the generator range. Therefore preference was given to the mirroring of the power losses approach of which the values are more critical, i.e. lower efficiency values.

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In the model the expressions for motor and generator operation are expressed as;

Eq. (69)

Eq. (70)

Notice that the efficiency factor in Eq.‎ (69) and Eq.‎ (70) is larger than one in normal operation which can be confusing since it may seem impossible. However, it is possible because of the before discussed reversed cause-and-effect relationship approach. The power input obviously should be larger than the output due to the efficiency, making it necessary to multiply it with a factor larger that one. For regenerative braking, the power that is recaptured (negative power input) is less than the kinetic power (negative power output) due to the efficiencies, making it necessary to multiply it with a factor less than one.

Figure 43 | Two quadrant efficiency map for a 'typical' electric motor [8]

Regenerative Power Limitation Due to the current flow limitation of the batteries and the fast increasing temperature of the EM while performing as a generator, the model is performed with a regenerative power limitation which saturates the power flowing back to the battery by a predefined value. This value differs for

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the type of EM and Battery. A common value is around 30 kW which is also used for the EM in the Torque Vectoring model. The saturation goes according;

Eq. (71)

Eq. (72)

4.1.1.3 Validation Using The QSS Toolbox The QuasiStatic Simulation ToolBox (QSS TB) is a toolbox designed in MATLAB® Simulink® by the Swiss Federal Institute of Technology in Zurich, Switzerland. It is designed to estimate the fuel consumption for many powertrains such as the electric powertrain. To validate the Electric Motor (EM) model, the power output is compared to that of the Electric motor from the QSS TB, assuming that the QSS TB is correct. Using the same Drive Cycle, Vehicle model and transmission as is shown in Figure 44, the power output of both models is converted to the used energy . This is then converted from joule [J] to kilo Watts per hour [kWh] according to the following expression;

Eq. (73)

Figure 44 | EM model validation using the QSS ToolBox 48 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Both EM models have the same efficiency values implemented and the parameter in the EM model should be a value of one, since the QSS TB transmission output provides already . The functions of both and as function of the runtime are presented in Figure 45. Notice that both functions lie on top of each other and therefore the conclusion can be drawn that, again assuming the QSS TB model is correct, the EM model is also correct. Also notice that the slope of the functions can be negative which presents the recaptured energy due to regenerative braking.

Figure 45 | Energy function of the EM model and the EM model of the QSS as function of the time (NEDC drive cycle)

Differences Between The QSS TB Motor Model And The EM Model That both lines in Figure 45 lie on top of each other, is to be expected as the basis of determining the required power in the EM model is similar to that of the QSS TB [26]. This does not mean they are completely similar. The main differences, considering this specific part and in the overall EM model, are;

a. The QSS motor only calculates the used power whereas the EM model also provides a torque output considering the maximum available torque and the electrical time constant response delay. Also an additional regenerative lookup table is applied in the EM model where the regenerative torque as function of the rotational speed is defined. b. The efficiency map of the QSS model is a 2D-lookup table where the regenerative efficiencies are already included according to one of the two methods; efficiency mirroring or power losses mirroring discussed in Section 4.1.1.2. Which exact one is not clear. This method has one large disadvantage which does not apply for the EM model. Namely, that it takes more work to process the efficiencies in the QSS look-up table where the additional time to test multiple EM’s can be very large with respect to how it’s processed into the EM model.

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c. The QSS will stop the complete simulation if the torque or the rotational speed values becomes larger that the predefined maximum values. Whereas the EM model saturates the torque output, avoiding it crossing its maximum value in the first place and will stop providing torque when the maximum speed is crossed. d. Additionally, the EM model is equipped with a function which saturates, and thereby limits, the regenerative power according to a predefined maximum.

4.2 Final Drive Model Electric Motors (EM’s) have a relatively large rotational speed range. Combined with their interesting Torque-Speed characteristic, such as maximum torque at zero speed, mostly there is no need for a gearbox with multiple gears. Obviously this is interesting for vehicle manufactures since it will save potential mass, efficiency losses and costs. However, a final gear is still in many cases applied, so that smaller EM’s can be applied as should be also the case for (as far as known at the moment) the Torque Vectoring Car Laboratory (CarLab). This is the reason why in the model also a final drive with a single gear is modelled of which the properties such as efficiency and the moment of inertia are taken into account. The Final Drive (FD) model is presented as a subsystem shown in Figure 46 and has two inputs and one output.

Model Input

∙ is the torque provided on the Electric Motor (EM) output-shaft. ∙ is the current speed of the EM derived from the measured wheel speed.

Model Output

∙ is the torque provided on the FD output-shaft.

Figure 46 | The top layer of the Final Drive Model

4.2.1 Final Drive Model Operation Above is explained what the different inputs and output signals represent. This next section will explain the operation of the FD model using the applied equations and used approaches.

The first layer of the Final Drive (FD) model is shown in Figure 47. In this layer two subsystem are processed which provide and where the latter is zero if is constant. The applied expressions are;

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Eq. (74)

Eq. (75)

The torque provided by the Electric Motor (EM) to the FD should also overcome its moment of inertia. Eq.‎ (74), Eq.‎ (75) and Figure 47 show that if the EM provides a positive torque and

, it should overcome the moment of inertia for which is required. Meaning:

. The same applies if . Only when; , the first expression does not apply since its corresponding sign is changed due to the minus sign, i.e. .

Therefore in that case it will just provide where the value and sign only depend on .

Figure 47 | First layer of the Final Drive Model

Torque Final Gear In the subsystem ‘Torque Final gear’ the torque provided by the EM is converted to the torque that the final drive will provide according to the following expression;

Eq. (76)

Inertia Torque Final Gear In the subsystem ‘Inertia Torque Final gear’ the torque required to overcome moment of inertia of the FD is provided according to the following expression;

Eq. (77)

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5. Simulation Results

This section discusses the main results of the simulations performed using the Torque Vectoring (TV) model and conclusions are drawn with regard to the influence of TV on a vehicle. For understanding, every new section discussing a particular simulation starts with presenting the so called ‘motion data’. It presents several parameters as function of the time from which the vehicle behaviour during the particular test can be derived. To keep a clear overview, only a selection of plots is shown in this section. All (other) plots are shown in the appendices attached to the report. The meanings, including units, of the used expressions are explained in the beginning of the report in section ‘List of acronyms and abbreviations’.

5.1 Vehicle Steer Characteristic Vehicle manufactures strive to keep the vehicle behaviour stable and predictable to the driver. This applies as well to the vehicles steer characteristic which can, as explained in Section 3.1.1, be defined as; oversteer (OS), neutral steer (NS) and understeer (US), where US is considered to be most stable and predictable, and therefore safe, to the driver. Through the use of Torque Vectoring (TV) it is intended to increase the vehicle performance. One of these performances is the compliance of the vehicle on the steer input of the driver. The driver will steer the vehicle towards a desired point and must adjust his input as a result of the compliance of the vehicle. If a vehicle is neutrally steered, the driver does not have to adjust his steer input. However, if the vehicle is linear steered, the driver has to change his input proportionally, i.e. if the forward velocity increases by a certain factor, the steer input has to increase with the same factor. In this case, the steer input will have to be less adjusted and the steer characteristic of the vehicle can maintain understeered, keeping the vehicle stable and predictable to the driver. For this study such a linear steer characteristic is desired. Figure 49 shows the steer characteristic of the designed vehicle model where the distinction is made between an active and inactive Direct Yaw Moment (DYM) controller, i.e. with or without the use of TV. This test is performed at different fixed speed steps of 10 km/h up to 150 km/h where the steering angle is, at every fixed speed step, gradually increased and decreased. Notice that the vehicle stays understeered, and with the use of TV, the steer characteristic tends to be more linear.

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Figure 48 | Vehicle motion data of ‘Vehicle Steer Characteristic’ simulation

Figure 49 | The steer characteristic of the designed vehicle model with and without active Torque Vectoring

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5.2 Steady State As explained in Section 3.2.1, there belong an ideal yaw-rate to each vehicle manoeuvre corresponding to the steer angle and longitudinal velocity. However, this yaw-rate is often not achieved. The Direct Yaw Moment (DYM) controller is used to minimize the difference between the actual and ideal yaw-rate by applying Torque Vectoring (TV). To demonstrate this, a steady state simulation is performed where the input of the driver is held constant, i.e. a constant steer angle (2˚) and a constant longitudinal velocity (100 km/h) as is visible in the motion data Figure 50. Figure 51 demonstrates that when TV is activated, after the vehicle has driven multiple circles without TV and the vehicle behaviour is considered stable, the circle radius becomes smaller. The activation point at which the Direct Yaw Moment (DYM) controller is turned on is indicated by a dot (small circle) as is shown in the legend. Figure 52 shows the yaw-rate of the vehicle during the test where initially the DYM is inactive and subsequently is activated at time = 400s. It is clearly visible that with TV the yaw-rate of the vehicle moves toward the ideal yaw-rate corresponding to the steer angle and longitudinal velocity.

Figure 50 | Vehicle motion data of ‘Steady State’ simulation with initially the Direct Yaw Moment (DYM) controller inactive and subsequently activated at t=400s.

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Figure 51 | The vehicles position driving a circle with a constant steer angle and constant longitidinal velocity. Initally without Torque Vectoring (TV) and subsequently, after the activation piont, with TV (inner circle)

Figure 52 | The yaw-rate of the vehicle during the steady state simulation where the DYM is initially turned off and subsequently turned on at t=400s 55 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

5.3 Influence Of Response Delay Of The Electric Motor As discussed in Section 2.1.30‎ , the main priority in the selecting criteria of the Electric Motor (EM) is a fast response. This is necessary since from the vehicle dynamic and the controller’s point of view, the torque should be instantly available if it wants to have any impact whatsoever. To show what the influence of the EM electrical response delay on the vehicle behaviour is, a simulation has been performed showing results with, without and with an enlarged electrical response delay.

The response delay is enlarged by multiplying the electrical time constant , Section 2.1.5.5, times 100, which gives a value of; = 0.46 seconds. The simulation performed can be best described in two steps after the vehicle drives for a time of 10 seconds a straight path with a longitudinal velocity of 100 km/h; 1. The vehicle forward velocity is held at a constant value of 100 km/h 2. The steer angle is applied according a sinus input with a value of; where the steer input frequency changes from 0.1 up to 1 Hz. The reason to perform the simulation with increasing steer frequency, as described above, is that it is expected that when the response delay of the EM is enlarged a phase difference will be visible.

Figure 53 | Vehicle motion data, influence response delay electric motors Note: Extra delay in motor = 100 x normal motor delay

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As is visible in Figure 54, Figure 56 and Figure 55, showing the torque output of the motors, the yaw-rate and the EM torque output delay, the normal delay of the EM has so little effect on the results that both lines, i.e. ‘normal motor’ and ‘no delay in motor’ lie practically on top of each other. When the electrical response delay of the EM was enlarged by 10 times, the effect became barely visible, for which these results are not presented. However, if the response delay is enlarged by 100 times the normal delay, the effect becomes visible. It shows in the three mentioned figures that the extra response delay has a phase and end value difference with respect to the output signals ‘no delay’ and ‘normal motor’ delay. Figure 54 shows the differences in motor torque output. The phase difference is a direct result of the response delay of the EM. Because the response delay is large, the torque output response is slow and therefore the vehicle response will be slower as well. Figure 55 shows the torque request and motor torque output of the EM. As is visible, the motor is not able to generate the requested torque value at the requested time. As a result, the yaw-rate error (Section 3.2.1) is not satisfied, i.e. not equal to zero. Therefore the torque differences that the DYM controller requests, is larger with respect to the torque request when the EM has a ‘normal motor’ delay. And when the steer input frequency becomes larger, the EM will be less able to generate the requested motor torque and the end value will become lower. This means that with an enlarged delay of 100 times the normal motor delay, the DYM controller is not capable anymore to control the yaw-rate of the vehicle toward the ideal yaw-rate at high steer frequencies. This is confirmed by Figure 55 , which shows that the requested torque value, which is requested by the DYM controller, cannot be obtained and also not on the requested time (phase difference).

Figure 54 | Difference in Torque request and given output response when the response delay of the Electric Motor is enlarged by 100 x normal motor delay.

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Figure 56 | The vehicle yaw-rate with different electric response delay values of the electric motor with the Direct Yaw Moment (DYM) controller active. Note: extra delay = 100 x normal motor delay

Figure 55 | Electric motor delay with the requested torque and the actual output torque

Because in the model itself the electric time constant has already been enlarged, taking temperature influences into account, it is therefore not expected that, with what type of EM whatsoever, it will cause a problem for the control of Torque Vectoring.

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5.4 Consumption When Using Torque Vectoring When using Torque Vectoring (TV), both Electric Motors (EM’s) operate in different operating points. Whereas using ‘conventional’ electric propulsion, i.e. without the use of TV, both EM’s work practically in the same operating point providing the same amount of torque. Because the efficiencies differ in each operating point, it seems possible that the energy consumption would also differ with respect to conventional electric propulsion. Seen that the range of electric vehicles (EV’s) is already very limited with respect to conventional Internal Combustion Engine (ICE) vehicles, a change in energy consumption could have a large impact. To find out if TV has influence on the energy consumption and, if so, in which quantity, two drive cycle simulation have been performed. These simulations consisted out of a ca. 6 minute during drive cycle where the longitudinal velocity and the steering angles varied constantly. The first test that was simulated is considered to be of the category; ‘lower’ speed, where as shown in the motion data Figure 58, the forward velocity is kept modest. The second test that was simulated is considered to be of the category; ‘higher’ speed, where as shown in the motion data Figure 57, the speed is enlarged. Obviously, in the second test TV had to engage more often and in a higher degree.

Figure 60 and Figure 59 show the used energy in [kWh] for both performed drive cycles. As is visible, the difference in energy consumption between driving with and without TV during the ‘lower’ speed drive cycle can be considered to be equal to zero (<0.1% increase). For the ‘higher’ speed drive cycle it’s it shows clearly that with active TV, the consumption increases gradually where after 350 seconds the increase is circa 1% with respect to conventional electric propulsion.

A strong conclusion about the exact quantity of difference in consumption cannot be drawn. This is because the operating points of the EM, and thereby the corresponding efficiencies, strongly dependent on the rotational speed and the requested torque of the EM. Meaning, if the EM speed and the requested torque differ, the quantity of energy consumption differs as well. This applies for both with and without TV, but also for the difference between the two. As expected, the energy consumption will increases by using TV mainly depending on the driving style of the driver. The reason why an increase in consumption is expected is because the energy required to generate more torque on one EM, is likely higher than the energy saved by lowering the amount of torque on the opposite EM. So, when driving calm and on a lot of straight paths, TV will barley engage meaning that’s it’s very likely there will be no difference in consumption. But when driving more dynamic with a lot of accelerations and rapid increasing steer angles, TV will engage more often resulting in higher energy consumption.

To confirm that the energy consumption with TV is not necessarily higher with respect to conventional electric propulsion, results of a steady state ‘Figure of 8’ simulation are presented (Figure 61 and Figure 62). It shows that the energy consumption with conventional electric propulsion gradually increases with respect to the consumption when TV is active. After 200 seconds, the energy consumption when using TV is circa 1% lower with respect to conventional electric propulsion.

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Figure 58 | Hockenheim drive cycle ‘lower’ speed

Figure 57 | Hockenheim drive cycle ‘higher’ speed 60 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Figure 60 | The energy consumption as function of time of the 'lower’ speed drive cycle with and without applying Torque Vectoring. (TV). ‘Lower’ speed It shows there is very little difference (TV < 0,1% extra) in energy consumption with or without TV for this particular drive cycle

Figure 59 | The energy consumption as function of time of the 'higher’ speed drive cycle with and without applying Torque Vectoring (TV). It shows that with TV the energy ‘Higher’ speed consumption increases by ca. 1% for this particular drive cycle

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Figure 61 | Vehicle motion data with steady state 'Figure of 8' simulation

Figure 62 | The energy consumption as function of time of the ‘Figure of 8’ simulation with and without applying Torque Vectoring (TV). It shows that with TV the energy consumption decreases by ca. 1% for this particular drive cycle

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5.5 Replay Model To recommend about the changes that have to be made in the Tyre Estimator® (TE) when using the motion data of a vehicle with Torque Vectoring (TV), a replay model is designed as described in Section 3.4.2. After simulating a manoeuvre with the TV model including the TV controllers, the measured motion data is loaded into the MF-Tyre where Tyre Property Files are created for the front and rear axle. These are then loaded into the designed Replay model.

If the Tyre Property Files are correct, the motion data of the Replay model and the TV model will be the same. To validate the designed Replay model, the used Tire Property Files in the TV model are loaded into the Replay model, meaning that the Tire Property Files in the TV model and Replay model are the same, namely TNO_car205_60R15.tir. In this case the motion data of both the models are almost the same, so the Replay model is considered to be correct (see Figure 63 for the replay motion data). To validate the Tyre Property Files made by the MF-tyre, the new Tyre Property Files, made from the original motion data, are loaded into the tyres of the designed Replay model. The results of the replay simulation are shown in Figure 65 and Figure 64. As can be seen, the results of the Replay and TV model are not the same, not even close. The reason they deviate so much from each other is not yet clear. It might be that the script used to modify the motion data from the TV model, so it can be used by the MF-Tyre, is not working correctly and therefore the Tyre Property Files made by de MF-tyre are not correct. This means there has to be looked into this problem so that the Replay model can be used to validate the Tyre Property Files made by the MF-tyre.

Figure 63 | Replay motion data of a Figure of 8 manoeuvre (radius 100m). It shows that the replay data is almost the same. Note: the Tyre Property Files used in these replay are the original as used in the TV model. 63 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Figure 65 | Replay motion data of figure eight circle, radius 100m. It shows that the replay data is deviating from the original motion data. Note, the Tyre Property Files used in these replay are estimated by the MF-Tyre.

Figure 64 | Wheel torque, as is shown the wheel torque of the Replay and TV model are the same.

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6. Conclusions

The main purpose of this report is to answer a number of key questions with regard to Torque Vectoring. This then should serve as an introduction to related further assignments in which this study will be used for the construction of the Torque Vectoring CarLab (test vehicle). Below the key questions are answered in the order asked in the introduction. To apply Torque Vectoring (TV), in this study a so called Direct Yaw Moment (DYM) controller is created. Aiming to keep the vehicle stable in all situations, also a Traction (TR) controller is created and a Drive Force Limitation (DFL) controller is recommended. Combined they form the TV controller. The DYM controller is used to create the torque difference for TV. However, even when the DYM controller is active and working properly, there is the possibility that the behaviour of the vehicle becomes unstable. Therefore the other two controllers are designed as well. The main improvement of applying TV is that the steer characteristic of the vehicle moves more toward a linear steer characteristic. This means that driver has to adjust the steer input less when cornering a vehicle due to the extra yaw-moment. Another improvement due to applying TV is the shift in longitudinal tyre forces and therefore the inner rear wheel will have more margin to transfer lateral tyre forces. To ensure that the Tyre Estimator® (TE) can cope with TV, some additions have to be applied to the required measured vehicle data so the extra yaw-moment from TV can be calculated. Also additions have to be applied to the vehicle models, i.e. the vehicle model used in the State Estimation and Replay model of the TE. The best way is to calculate the yaw-moment, which is created by the difference in torque or longitudinal forces, and apply this extra yaw-moment on the z-axis (perpendicular to the road) of the vehicle. The Induction Motor (IM) and Permanent Magnet Synchronous (PM Sync) motor are best suited for Electric Vehicles including the applicability of TV. The IM is considered particular well suited especially because it is more robust. Also it can adjust its magnetic field strength and the purchase cost of an IM is usually lower with respect to a ‘similar’ PM Sync motor. Research considering controllers (inverters) and batteries are unfortunately not discussed in this report due to a lack of time. For this please refer the recommendations. Because in the model itself the electric time constant has already been enlarged, taking temperature influences into account, and it did not show any influence in the performed simulations, it is therefore not expected that, with type of EM whatsoever, it will not cause a problem for the control of TV. A strong conclusion about the exact quantity of difference in consumption cannot be drawn. This is because it strongly dependent on the operating points of the EM. Simulation results showed that the energy consumption during a dynamic drive cycle may increase when using TV with ca. 1% with respect to conventional electric propulsion, i.e. no TV. However, with a steady state it showed that the consumption can also decrease by as much as 1%.

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7. Recommendations

After the studies carried out, there are still issues that should be answered for an optimal construction of the Torque Vectoring Car Laboratory (CarLab). Also in this case a division is made between the vehicle dynamic perspective and the powertrains perspective.

Vehicle Dynamic Perspective 1. In this report the influence of Torque Vectoring is studied when applied on a rear wheel drive (RWD) vehicle. There are however more configurations possible such as front (FWD) and all- wheel drive (AWD). In several papers such as reference [29] it is demonstrated that the beneficial effect of applying Torque vectoring on RWD and FWD vehicles depend strongly on the driving manoeuvre. Whereas Torque Vectoring applied on AWD vehicles, i.e. each wheel is individually propelled, shows to be most effective in every performed drive manoeuvre. It is therefore recommended to study the potential and expected improvement of Torque Vectoring applied on all four wheels. This possibly in means of extending the present Torque Vectoring model.

2. The Drive Force Limitation (DFL) controller is not used in this study. In this report it is explained how the controller should be made in theory. It is recommended to apply a functioning DFL controller in the Torque Vectoring controller for improved vehicle dynamic behaviour.

3. In the current model the tyre sides in the vehicle model are set to be ‘symmetric’ which is a simplification compared to the reality. To make the vehicle model more realistic, each wheel should be assigned a specific side, i.e. right wheel and left wheel. When doing so, the lateral forces generated by the tyres when driving in a straight path and the effects of this on the Torque Vectoring controllers should be taken into account. This with the Traction control in particular.

4. The result gained so far may be optimized by the tuning the Torque Vectoring controllers. It is therefore recommended to tune the controls for an improved Torque Vectoring response in a wider range of vehicle manoeuvres.

Powertrains Perspective 1. In this report no attention given to the energy storage unit, taking into accounts the Torque Vectoring application. The electrical energy storage units for a conventional electric vehicle, i.e. without Torque Vectoring application, need to be sized so that they store sufficient energy, provide adequate peak power for a specified acceleration performance and have the capability to meet appropriate driving cycles [30]. However, for a vehicle applied with Torque Vectoring, it is required as well that the batteries provide adequate peak power to provide Torque Vectoring. Obviously, the normative applies for which the higher peak power value is required.

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Another thing that need to be taken into account, is that batteries in purely Electric Vehicles, and thereby assuming as well in the to build Torque Vectoring CarLab, are regularly deep discharged and recharged. Hence, the cycle life for deep discharges is a key consideration and it is essential that the batteries meet specified minimum requirements. The use of ultra-capacitors should be reviewed as well because of the potential interesting possibilities they provide to fast recapture energy and subsequently fast provide a high peak power.

A couple of references which may provide useful information about this topic are; ∙ [30], ‘Batteries and Ultracapacitors for Electric, Hybrid, and Full Cell Vehicles’ ∙ [31], ‘Safe lithium-ion battery with ionic liquid based electrolyte for hybrid electric vehicles. Also reports about the TNO Hybrid CarLab (VW Beetle) may provide useful information in this topic.

To extend the Torque Vectoring overall model with a battery model a few of potential useful references are; ∙ [27], ‘Vehicle Propulsion Systems’ ∙ [26], ‘The QSS Toolbox Manual’ ∙ [32], ‘Modelling of Lithium-Ion Battery for Energy Storage System Simulation’

2. In this report only very superficial attention given to the inverter (controller) of the EM’s taking into accounts the Torque Vectoring application. It is recommended to study the basic operation of inverters and the potential property influences on the application of TV. Also it is recommended to research if extensive inverters are available on the current market which could extend the control capabilities of the EM with respect to the provided (recommended) inverters by the electric motor manufactures.

A couple of references which may provide useful information about this topic are reports written by Ir. F. Rentmeester working as a research scientist at TNO Automotive Helmond, department Powertrains; ∙ [33], ‘literatuuronderzoek, Drive topologieën’ ∙ [34], ‘Literatuuronderzoek, Modulatietechnieken’

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8. References

[1] L.J.M. van Eeuwijk, “Control of Active Electronic differential in Formula Student Electric Race Car,” Eindhoven, TU/e, 2010. [2] I. Besselink, “Vehicle dynamics (lecture notes),” TU/e, Eindhoven University of Technology, 2008. [3] Y. U. Kaoru Sawase, “Improvement of Vehicle Dynamics by Right-and-Left Torque Vectoring System in Varioas Drivetrains,” Drivetrain Engeneering Dept., Development Engineering Office, Japan, 2008. [4] TNO automotive, [Online]. Available: http://www.beyondsafe.com/tyre-testing. [Accessed 22 December 2011]. [5] W. Rippel, “Teslamotors.com,” Tesla Motors, 9 January 2009. *Online+. Available: http://www.teslamotors.com/blog/induction-versus-dc-brushless-motors. [Accessed 20 September 2011]. [6] M. Zeraoulia, M. El Hachemi Benbouzid and D. Diallo, “Electric Motor Drive Selection Issues for HEV Propulsion Systems: A Comparative Study,” IEEE, VOL 55, NO 6, November 2006. [7] K. Chau, C. Chan and L. Chunhua, “Overview of Permanent-Magnet Brushless Drives for Electric and Hybrid Electric Vehicles,” IEEE, VOL 55, NO 6, June 2008. [8] L. Guzzella and S. Antonio, “Vehicle Propulsion Systems,” Springer Berlin Heidelberg, Zürich, Switzerland, 2005. [9] F. Bordry, “Power converters: definitions, classification and converter topologies,” CERN, Geneva, Switzerland, 2007. [10] “Citroënnët,” *Online+. Available: http://www.citroenet.org.uk/passenger- cars/psa/berlingo/berlingo-dynavolt.html. [Accessed 25 Oktober 2011]. [11] T. Pavlic, “PhysLink.com,” *Online+. Available: http://www.physlink.com/education/askexperts/ae572.cfm. [Accessed 25 Oktober 2011]. [12] “HyperPhysics,” Georgia State University, *Online+. Available: http://hyperphysics.phy- astr.gsu.edu/hbase/solids/hyst.html. [Accessed 25 Oktober 2011]. [13] “scholar.lib.,” *Online+. Available: http://scholar.lib.vt.edu/theses/available/etd-031899- 212402/unrestricted/3.2.3FLUX-WEAKENING.PDF. [Accessed 25 oktober 2011]. [14] “MaximumEV,” *Online+. Available: http://maximumev.blogspot.com/2009/06/rare-earths- and-neodymium.html. [Accessed 25 Oktober 2011]. [15] G. Solberg, “Teslamotors.com,” Tesla Motors, 29 June 2007. *Online+. Available: http://www.teslamotors.com/blog/magic-tesla-roadster-regenerative-braking. [Accessed 26 September 2011]. [16] “DIY Electric Car,” Green Web Publishing, LCC, 2 November 2008. *Online+. Available: http://www.diyelectriccar.com/forums/showthread.php?t=8848. [Accessed 26 September 2011]. [17] G. Hongwei, G. Yimin and M. Ehsani, “A Neural Network Based SRM Drive Control Strategy for

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Regenerative Braking in EV and HEV,” Texas A&M University, IEEE, College Station, Taxes, USA, 2001. [18] L. Xiaoyu, L. Chuang, L. Ming and L. Diji, “Regenerative Braking Control Strategies of Switched Reluctance Machine for Electric Bicycle,” University of Aeronautics & Astronautics, IEEE, Nanjing, China, 2009. [19] G. W. Younkin and R. H. Welch Jr., “How Temperature Affects a Servomotor's Electrical and Mechanical Time Constant,” IEEE, 2002. [20] “Engineers Edge,” Engineers Edge, LLC, 2011. [Online]. Available: http://www.engineersedge.com/motors/motors_definitions.htm. [Accessed 13 Oktober 2011]. [21] J. T. Connor, “Copper Wire Tables,” National Bureau of Standards, Washington D.C., USA, February, 1966. [22] L. Chang, “Comparison of AC Drives for Electric Vehicles - A Report on Experts’ Opinion Survey,” University of New Brunswick, IEEE, Fredericton, NB, Canada, 1994. [23] H. B. Pacejka, Tyre and Vehicle Dynamics, Rotterdam: Butterworth-Heineman, 2002. [24] T. Sugano, H. Fukuba and T. Suetomi, “Vehicle System Dynamics,” Hiroshima Japan, Oktober, 2010. [25] TNO automotive, “MF-Tyre/MF-Swift 6.1.2.1, Help Manual,” TNO automotive, Helmond, the Netherlands, 2010. [26] L. Guzzela and A. Amstutz, “The QSS Toolbox Manual,” ETH Swiss Federal Institute of Technology Zurich, Zurich, Switzerland, 2005. [27] L. Guzzella and S. Antonio, “Vehicle Propulsion Systems,” Springer Berlin Heidelberg, Zürich, Switzerland, 2005. [28] R. Apter and M. Präthaler, “Regeneration of power in Hybrid Vehciles,” IEEE 55th Vehicular Technology Conferance, Birmingham, UK, 2002. [29] K. Sawase and Y. Ushiroda, “Improvement of Vehicle Dynamics by Right-and-Left Torque Vectoring System in Various Drivetrains,” Mitsubishi Motors Technical Review, Japan, 2007. [30] A. F. Burke, “Batteries and Ultracapacitators for Electric, Hybrid, and Fuel Cell Vehicles,” IEEE, Calfornia, USA, 2006. [31] L. Damen, M. Lazzari and M. Mastrago, “Safe lithium-ion battery with ionic liquid based electrolyte for hybrid electric vehicles,” vol. 196, 2011. [32] S. Chen, K. Tseng and S. Choi, “Modeling of Litium-Ion Battery for Energy Storage System Simulation,” IEEE, Wuhan, Hubei, China, 2009. [33] F. Rentmeester, “Literatuuronderzoek, Drive topologieën,” 2011. [34] F. Rentmeester, “Literatuuronderzoek, Modulatietechnieken,” 2011. [35] P. Yadamale, “Brushless DC (BLDC) Motor Fundamentals, AN885,” Microchip Technology Inc., 2003. [36] “TOOLINGU,” Tooling University, LLC., *Online+. Available: http://www.toolingu.com/. [Accessed 2011 September 23].

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[37] Clint Verwoert, “SearchMobileComputing.com,” TechTarget, July 2000. *Online+. Available: http://searchmobilecomputing.techtarget.com/definition/electromagnetic-interference. [Accessed 23 September 2011]. [38] BMW group, “Driving Physics,” BMW group, 2006. [39] “All About Circuits,” *Online+. Available: http://www.allaboutcircuits.com/vol_2/chpt_13/6.html. [Accessed 28 Oktober 2011]. [40] “Autopressnews.com,” *Online+. Available: http://www.autopressnews.com/2007/cars_tech_06/zf_torque/ZF_torque_vector_drive2.jpg. [Accessed 12 December 2011]. [41] Keio University, [Online]. Available: http://www.eliica.com/English/images/project/motor.png. [Accessed 2011 December 22].

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Appendix 1 - Vehicle Model

Vehicle model designed in MATLAB® SimMechanics®

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SimMechanics M-file

%% Torque Vectoring SimMechanics model (vehicle model) % Program: SimMechanicsData.M % TNO Automotive % Year: sept, 2011

g = 9.81 ; % [m/s^2] gravitational acceleration

%% vehicle parameters %front axle

Mass_Fa = 200 ; % [kg] mass vehicle front axle Mass_tyre_f = 10 ; % [kg] mass front tyre M_unspr_f = (Mass_Fa+(2*Mass_tyre_f)); % [kg] mass unspring mass I_xyz_f = eye(3) ; % [kg*m^2] inertia axle body ha_f = 0.295 ; % [m] height of c.g. axle front hf = 0.1007 ; % [m] height of front axle centre fr_f = 0.3 ; % [m] free rolling radius tyre front

%rear axle Mass_Ra = 200 ; % [kg] mass vehicle rear axle Mass_tyre_r = 10 ; % [kg] mass rear tyre M_unspr_r = (Mass_Ra+(2*Mass_tyre_r)); % [kg] mass unspring mass I_xyz_r = eye(3) ; % [kg*m^2] inertia axle body ha_r = 0.295 ; % [m] height of c.g. axle rear hr = 0.1007 ; % [m] height of rear axle centre fr_r = 0.3 ; % [m] free rolling radius tyre rear

% Front spring parameters massf = 7471.72; % [N] mass front spring spring_f = 50000 ; % k spring front demper_f = 5000 ; % c damper front offset_f = -0.17 ; % spring offset front rot_s_f = 66000 ; % k spring body roll front rot_d_f = 2050 ; % c damper body roll front

% Rear spring parameters massr = 7498.34; % [N] mass rear spring spring_r = 50000 ; % k spring rear demper_r = 5000 ; % c damper rear offset_r = -0.17 ; % spring offset rear rot_s_r = 66000 ; % k spring body roll rear rot_d_r = 2050 ; % c damper body roll rear

% Tyre parameters front

f_u_x = 1 ; % longitudinal friction

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f_Cfx = 1 ; % longitudinal slip stiffness f_u_y = 1 ; % lateral friction f_Cfa = 0.9; % cornering stiffness f_Cfc = 1 ; % camber stiffness f_t = 1 ; % pneumatic trail f_Cmy = 1 ; % camber torque stiffness

% Tyre parameters rear u_x = 1 ; % longitudinal friction Cfx = 1 ; % longitudinal slip stiffness u_y = 1 ; % lateral friction Cfa = 1 ; % cornering stiffness Cfc = 1 ; % camber stiffness t = 1 ; % pneumatic trail Cmy = 1 ; % camber torque stiffness tyre_left = 3104 ; % tyre code left tyre_right = 3104 ; % tyre code right

C1 = 99208 ; % front tyre lateral stiffness C2 = 116589 ; % front tyre lateral stiffness % generated with the Tyre Estimator

% Body Mass_f = 1004-(2*Mass_tyre_f) ; % [kg] mass vehicle front Mass_r = 1002-(2*Mass_tyre_r) ; % [kg] mass vehicle rear Mass = Mass_f+Mass_r ; % [kg] mass vehicle Mass_body = Mass-(M_unspr_r+M_unspr_f); % [kg] mass vehicle

Ix = 0 ; % [kg*m^2] yaw inertia X-axis Iy = 0 ; % [kg*m^2] yaw inertia Y-axis Iz = 4159.6 ; % [kg*m^2] yaw inertia Z-axis I_xyz = [Ix 0 0 ; ... 0 Iy 0 ; ... 0 0 Iz]; % [kg*m^2] inertia body

% Body Dimentions L = 2.888 ; % [m] distance between front and rear axle Lf = 1.44256 ; % [m] distance between cg and front axle Lr = 1.44544 ; % [m] distance between cg and rear axle Sf = 1.55/2 ; % [m] distance between front wheels Sr = Sf ; % [m] distance between rear wheels h = 0.295 ; % [m] radius of wheels ht = 0.3135 ; % [m] unloaded tyre radius hb = 0.1 ; % [m] unloaded tyre radius H = 0.54 ; % [m] height of c.g.

% Drag related

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rho = 1.22 ; % [kg.m^3] Air density A = 2.11 ; % [m^2] Frontal area Cw = 0.35 ; % [-] Aerodynamic drag coefficient

% Drive train fd = 3 ; % [-] Final drive

% initial speed Speed_IC = IC_speed/3.6 ;% [m/s] initial speed vehicle body wheel_speed = Speed_IC/ht ; % [rad/s] initial wheel speed

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Appendix 2 - Validation Designed Vehicle Model Using Tyre Estimator®

Validation data of designed vehicle model using the Tyre Estimator®. In all motion data; Est. (red) = Tyre Estimator®, Meas. (blue) = vehicle model.

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Input Tyre Estimator®

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Appendix 3 - M-File Of Electric Motor And Final Drive Models

1. %% File name: Torque Vectoring (TV), ELECTRIC MOTOR (EM) & FINAL DRIVE 2. (FD) Model 3. % Autor: S.J. Koster & S.Nada 4. % University: HAN University of Applied Sciences, HTS- Autotechniek 5. % Company: TNO Automotive, Efficient Powertrains (EPT) 6. % Year: 2011 7. 8. clc; 9. close all; 10. clear all; 11. 12. 13. %% ELECTRIC MOTOR (EM) INCL. CONTROLLER (CTRL); 14. 15. % Manufacturer and Type EM: UQM, PowerPhase HPM125 16. % Manufacturer and Type CTRL: UQM, DD45-500L 17. 18. %% CONSTANT PARAMTERES 19. 20. % EM PARAMETERS 21. J_EM = 0.0112; % Inertia Electric Motor [kg*m^2] 22. rpm_EM_max = 8000; % Max speed of EM [rpm] 23. P_reg_max = 30; % Max. regnerative power salvage [kW] 24. 25. tau_e = 5.7; % Electrical time constant (L/R) [ms] 26. temp_tau_e = 25; % At specified temperature [^oC] 27. temp_critic = -25; % Min. critical operation temp. [^oC] 28. % NOTE: If specified temperature is unknown, choose: 25 29. % If minimum critical temperature is unknown, choose: -25 30. 31. % FD PARAMETERS 32. J_gear = 0.002; % Inertia Transmission [kg*m^2] 33. i_gear_f = 4; % Final drive ratio [-] 34. eta_gear = 0.98; % Final drive transfer efficiency [-] 35. 36. %% REQUIERED CONVERSIONS / CALCULATIONS 37. 38. % Conversion [kW] to [W] 39. P_reg_max = P_reg_max * 1000; 40.

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41. % Most critical elec. time constant as function of temp. in [sec] 42. tau_e = tau_e * (1/1+0.00393*(temp_critic - temp_tau_e)); 43. 44. % Elec. time constant conversion [msec] to [sec] 45. tau_e = tau_e * 10^(-3); 46. 47. %% VARIABLE PARAMETERS 48. % Torque-Speed characteristics (NORMAL & REGNERATIVE) 49. % Efficiency map of EM incl. CTRL 50. 51. % Load Peak Torque vector, Torque-Speed charac. [Nm] 52. %'T_EM_max' 53. load UQM_HPM125\T_EM_max; 54. 55. % Load Speed vector,Torque-Speed charac. [rpm] 56. %'rpm_EM' 57. load UQM_HPM125\rpm_EM; 58. 59. % Load Generative Peak Torque vector, Torque-Speed charac. [Nm] 60. % 'T_EM_reg_max' 61. load UQM_HPM125\T_EM_reg_max; 62. 63. % Load Generative Speed vector,Torque-Speed charac. [rpm] 64. %'rpm_EM_reg' 65. load UQM_HPM125\rpm_EM_reg; 66. 67. % Load Efficiency map (Torque, speed) [-] (1 = 100%) 68. %'eff_EM_map' 69. load UQM_HPM125\eff_EM_map; 70. 71. % Load Torque vector, efficiency map in [Nm] 72. %'eff_EM_T_row' 73. load UQM_HPM125\eff_EM_T_row; 74. 75. % Load Speed vector, effciency map in [rpm] 76. %'eff_EM_rpm_col' 77. load UQM_HPM125\eff_EM_rpm_col; 78. 79. %% END

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Appendix 4 - Electric Motor Model

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Subsystem: Generated Torque

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Subsystem: Torque-Speed Limits + Response Delay

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Subsystem: Inertia Torque

Subsystem: Overspeed Protection

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Subsystem: Max. Available Torque

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Subsystem: Torque Limitation + Response Delay

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Subsystem: Required Electrical Power

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Subsystem: Required Mechanical Power

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Subsystem: Power Efficiency Factor

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Subsystem: Torque Limitation + Response Delay

Subsystem: Power to Energy Conversion

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Appendix 5 - Final Drive Model

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Subsystem: Torque Final Gear

Subsystem: Inertia Torque Final Gear

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Appendix 6 – Direct Yaw Moment Controller Validation.

To validate the Direct Yaw Moment (DYM) controller, a test manoeuvre is preformed where the steer input is kept small and the speed of the vehicle is gradually increased −0.1˚ < < 0.1˚ from 10 up to 100km/h. This is performed in such a way that the slip angles are kept small. If the calculated ideal yaw-rate is almost equal to the actual yaw-rate, the calculations performed in the DYM controller are assumed to be correct.

Vehicle Motion Data

) 0.1 δ DYM off 0 DYM

[deg] on

steeangl( −0.1 0 10 20 30 40 50 60 70 80 90 100 100 ) x

50 [km/u] Speed(v 0 10 20 30 40 50 60 70 80 90 100 0.5 0

[deg/s] −0.5 Yaw rate (r) 0 10 20 30 40 50 60 70 80 90 100 ) y 0.2 ] 2 0

[m/s −0.2 Lataccl (a 0 10 20 30 40 50 60 70 80 90 100 0.1 ) β 0.05 0 [deg]

Beta ( −0.05

0 10 20 30 40 50 60 70 80 90 100 time t [sec]

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DYM 0.6 off DYM on ideal

0.4

0.2

[deg/s] Yaw rate (r)

−0.2

−0.4

−0.6

0 10 20 30 40 50 60 70 80 90 100

Front Axle

DYM off DYM 0.05 on

0 Fy/Fz [−]

−0.05

−0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 alpha α [deg]

Rear Axle

DYM off DYM 0.05 on

0 Fy/Fz [−]

−0.05

−0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 alpha α [deg] 101 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Appendix 7 - M-File Drivers Input

%% Torque Vectoring, DRIVERS INPUT

% Author: Joost Koster, HAN-A % TNO Automotive, IS % Year: nov, 2011

% Use this script 'drivers_input_v..' to give your drivers input. % Make a choice in runtime, manoeuvre, speed or pedal position % and filename.

% When you run the file or press F5 a change is made to the m-file % 'run_file_v..' press run or F5 again and the simulation is started.

% After completing the run a selection of motion data is shown and saved. % Location, '..\simulations\{filename}\figures' (your selected filename). % If u wish to make new or change in the plots, open the script % ‘plot_file_v..'. % To use the motion data in the Tyre-Estimator see % '..\simulations\{filename}\TE_files'. % Also a TDX file is made for use in the Magic Formula. See location % ‘..\simulations\{filename}\TDX_files\’. clear all ; close all ; clc; %% model = ( 'TVmodel_v15' ) ; % change this name if you make a new model. open (model) ; % this will open the selected model

%% data selection if data is used as input % data = open ('C:\TNO Delft-Tyre\Tyre_Estimator... 1.0\Examples\nurburgring.mat');

%% drivers selection runtime = 50 ; % runtime for simulation % runtime = data.vdxdata.mRUNTIME; % data example

% steer input selection (1 = on, 0 = off) pass_step = 0 ; % step steer input pass_sin = 1 ; % sinus steer input steady_state = 0 ; % steady state pass_data = 0 ; % input from file

% step input steertime = [0 10 11 runtime] ; % [sec] time steer input steerin = [0 0 2 2] ; % [deg] steer input

% sinus input Steersin = 0.1 ; % [deg] steer input for sinus input 102 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Freq = pi/10 ; % [1/s] freq for sinus input delay_sin = 10 ; % [sec] delay for start sinus input

% steady state input timeR = [0 runtime] ; % [sec] time steady state R = [50 50] ; % [m] radius steady state

% steer input for data file (use if data is loaded) STRRATIO = 15 ; % steer wheel ratio delay_data = 0 ; % [sec] steedata = ([0,0]) ; % select if no data is used % steedata = ([data.steering_angle_time,data.steering_angle]); % data example

%% speed selection % ======% == lookup table vehicle speed [motor torque 300Nm] == % speed[km/u] = IC input[m/s], pedal[%],

% S= 150; I= 151.02; P= 0.1993; % S= 120; I= 120.96; P= 0.105; S= 100; I= 100.8; P= 0.1018; % S= 80; I= 80.352; P= 0.0742; % S= 50; I= 50.22; P= 0.04 464; % S= 10; I= 0; P= 0;

% (select the speed input) % ======% initial vehicle speed IC_speed = S ; % [km/h] initial vehicle speed % use S if you use the Cruise Control % and I if you use a Pedal input % pedal postition acctime = [0 runtime] ; % select the time belonging to accin accin = [0 0] ; % select the pedal position

%% Cruise control input Cruise = 1 ; % cruise control (1=on & 0=off) cruise_time = [0 runtime] ; % [sec] cruise control speed time cruise_in = [S S] ; % [km/h] cruise control speed speed_file = ([0,0]) ; % select if no data is used % [km/h] speed from file % speed= ([data.speed_time,data.speed]);% data example

%% file name stringname = ([pwd, '\simulations\']) ; % Location for file

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name = ( 'example' ) ; % filename (change for new test) filename = ([stringname,name]) ; % do not change, this will make mkdir(filename) ; % a new file with your filename mkdir([filename, '\figures' ]) ; % ... save ( 'filename' ,'filename' ) ; % ...

%% Model drivers inputs run 'input_TVmodel_BMW_v6' ; % name of latest model input run 'Parameters_EM_FD_models_v02' ; % name of latest powertrain input open 'run_file_v5' ; % name of latest run file

%% end

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Appendix 8 - M-File Run File

%% Torque Vectoring RUN FILE

% Autor: Joost Koster, HAN-A % TNO Automotive, IS % Year: sept, 2011

% In this m-file you can select when and which controller is ON or OFF. % It is also possible to have a controller turn on later on in a simulation % to make the change visible. clear all ; close all ; clc ;

%% SimMechanics model %% TR on & DYM off run 'drivers_input_v5'

DYM = [0 0 0 0] ; % on/off (1=on & 0=off) DYM_delay = [0 1 1 runtime] ; % delay TR controller to by active

TR = [0 0 1 1] ; % on/off (1=on & 0=off) TR_delay = [0 1 1 runtime] ; % delay TR controller to by active

DFL = [0 0 0 0] ; % on/off (1=on & 0=off) DFL_delay = [0 1 1 runtime] ; % Delay DFL controller to by active sim (model,runtime) ; % start simulation

%% Data save TR on, DYM and DFL off cd (filename) ; save( 'DYMoff' ,'m*' ,'c*' ); % saves the data starting with a 'm' and 'c'. cd ..\.. ; run 'TDX_data_off_v2' ; % makes a file in .TDX format to use in the % Magic Formula.

%% TR & DYM on run 'drivers_input_v5' ;

DYM = [0 0 1 1] ; % on/off (1=on & 0=off) DYM_delay = [0 1 1 runtime] ; % delay TR controller to by active

TR = [0 0 1 1] ; % on/off (1=on & 0=off) TR_delay = [0 1 1 runtime] ; % delay TR controller to by active

DFL = [0 0 0 0] ; % on/off (1=on & 0=off) DFL_delay = [0 1 1 runtime] ; % delay DFL controller to by active sim (model,runtime) ; % start simulation 105 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

%% Data save TR, DYM on and DFL off cd (filename) ; save( 'DYMon' ,'m*' ,'c*' ) ; % saves the data starting with a 'm' and 'c'. cd ..\.. ; run 'TDX_data_DYMon_v2' ; % makes a file in .TDX format to use in the % Magic Formula.

%% Save file and plot results clear all ; close all ; clc; filename = open ( 'filename.mat' ); cd (filename.filename);

I = open ( 'DYMoff.mat' ); % opens the data all off II = open ( 'DYMon.mat' ); % opens the data DYM on save ( 'I' ); % saves I & II so you can use when you save ( 'II' ); % like to run the plot files again cd ..\.. ; run 'TE_data_save_DYMonoff' ; % save the run data for use in the TE run 'plot_file_v6' ; % plot all runs in single figures

%% end

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Appendix 9 - Vehicle Characteristic

Through the use of Torque Vectoring (TV) it is intended to increase the vehicle performance. One of these performances is the compliance of the vehicle on the steer input of the driver where in this study a linear steer characteristic is desired. This simulation is used to study the effect of TV on the vehicle characteristic and is performed at different fixed speed steps of 10 km/h up to 150 km/h where the steering angle is, at every fixed speed step, gradually increased and decreased.

Vehicle Motion Data ) δ 1 [deg]

steeangl( 0 0 100 200 300 400 500 600 700

) 150 x 100 50 [km/u]

Speed(v 0 0 100 200 300 400 500 600 700 10 5 [deg/s]

Yaw rate (r) 0 0 100 200 300 400 500 600 700 ) y

] 6 2 4

[m/s 2

Lataccl (a 0 0 100 200 300 400 500 600 700

) 0 β −2

[deg] −4 Beta ( 0 100 200 300 400 500 600 700 150 100

[Nm] 50 0 0 100 200 300 400 500 600 700 Motor Torque (T) time t [sec]

107 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

DYM off DYM on ideal 10

6 [deg/s] Yaw rate (r)

0 0 100 200 300 400 500 600 700

Handeling Curve 2 Neutral characteristic DYM 1.8 off DYM on

1.6

1.4

1.2

/g)[−] 1 y (A

0.8

0.6

0.4

0.2

0 −2 −1.8 −1.6 −1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 α −α [deg] f r 108 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Appendix 10 - Motor Response

The test performed to study the influence of the EM response delay on the vehicle behaviour can be best described in two steps, after the vehicle drives for a time of 10 seconds a straight path with a longitudinal velocity of 100 km/h; 1. The vehicle forward velocity is held at a constant value of 100 km/h 2. The steer angle is applied according a sinus input with a value of; where −1˚ < < 1˚ the steer input frequency changes from 0.1 up to 1 Hz.

The reason to perform the simulation with increasing steer frequency, as described above, is that it is expected when the response delay of the EM is enlarged a phase difference will be visible.

Vehicle Motion Data

) 1 δ normal motor 0 no delay in motor

[deg] extra delay in motor

steeangl( −1 0 5 10 15 20 25 30 35 40 45 50 55 100.5 ) x 100 99.5 [km/u] 99 Speed(v 0 5 10 15 20 25 30 35 40 45 50 55 10

0 [deg/s]

Yaw rate (r) −10 0 5 10 15 20 25 30 35 40 45 50 55 ) y

] 2 2 0 [m/s −2 Lataccl (a 0 5 10 15 20 25 30 35 40 45 50 55

) 1 β 0 [deg]

Beta ( −1 0 5 10 15 20 25 30 35 40 45 50 55 time t [sec] 109 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Vehicle Yaw rate 10 normal motor no delay in motor 8 extra delay in motor

Yaw rate [deg/s] −2

−4

−6

−8

−10 0 5 10 15 20 25 30 35 40 45 50 Time [sec]

The following four plots show the actual torque output of the Electric Motors (EM’s) against the (by the DYM controller) requested torque. It is divided in two times two plots where the upper two plots are with a ‘normal motor’ delay ( = 4.6 ms) and the bottom two plots are with an enlarged delay of 100 times the ‘normal motor’ delay ( = 0.46 s). In turn the two plots are divided in to two single plots where the upper plots are without the use of Torque vectoring (TV) and the bottom plots with the use of TV.

110 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Right Motor Delay (DYM ) on

150 Torque request Torque output Without Torque vectoring 100

[Nm] 50 R

0 torque T −50

−100

0 5 10 15 20 25 30 35 40 45 50 55 time t [sec]

Left Motor Delay (DYM ) on

150 With Torque vectoring 100

[Nm] 50 L

0 torque T −50

−100 0 5 10 15 20 25 30 35 40 45 50 55 time t [sec]

↑ Normal motor delay ↓ Enlarged delay (100 times ‘normal delay’ )

Right Motor Delay (DYM ) on

Torque request 200 Torque output Without Torque vectoring

100 [Nm] R 0 torque T −100

−200 0 5 10 15 20 25 30 35 40 45 50 55 time t [sec]

Left Motor Delay (DYM ) on

200 With Torque vectoring

100 [Nm] L 0 torque T −100

−200 0 5 10 15 20 25 30 35 40 45 50 55 time t [sec] 111 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Appendix 11 - Steady State With DYM Controller On And Off

The Direct Yaw Moment (DYM) controller is used to minimize the difference between the actual and ideal yaw-rate by applying Torque Vectoring (TV). To demonstrate this, a steady state simulation is performed where the input of the driver is held constant, i.e. a constant steer angle (2˚) and a constant longitudinal velocity (100 km/h).

Vehicle Motion Data )

δ 2 DYM 1 off

[deg] DYM on

steeangl( 0 0 100 200 300 400 500 600 700 800 900 1000 ) x 100 50 [km/u]

Speed(v 0 0 100 200 300 400 500 600 700 800 900 1000

10 5 [deg/s]

Yaw rate (r) 0 0 100 200 300 400 500 600 700 800 900 1000 ) y

] 6 2 4

[m/s 2

Lataccl (a 0 0 100 200 300 400 500 600 700 800 900 1000 0 ) β −2 [deg]

Beta ( −4 0 100 200 300 400 500 600 700 800 900 1000

DYM 50 on (Right)

[Nm] DYM on (Left) 0 DYM 0 100 200 300 400 500 600 700 800 900off 1000 Motor Torque (T) time t [sec]

112 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Yaw Rate 14

6 yaw rate [deg/s]

2 DYM off DYM on ideal 0 0 100 200 300 400 500 600 700 800 900 time [sec]

Vehicle Position

DYM off 250 DYM on DYM activation point

200

150

distance [m] 100

150 200 250 300 350 400 450 distance [m] 113 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Appendix 12 - Energy Consumption (Dynamic Drive Cycle, ‘Lower’ Speed)

To find out if TV has influence on the energy consumption and, if so, in which quantity, the following dynamic drive cycle of ca. 6 minutes is simulated. This first test, out of the three performed consumption tests, is considered to be a dynamic ‘lower’ speed test.

Vehicle Motion Data )

δ 5

0 [deg]

steeangl( −5 0 50 100 150 200 250 300

) 150 x 100 50 [km/u]

Speed(v 0 0 50 100 150 200 250 300 10 0

[deg/s] −10 Yaw rate (r) 0 50 100 150 200 250 300 ) y

] 2 2 0

[m/s −2 Lataccl (a 0 50 100 150 200 250 300 )

β 1 0 [deg] Beta ( −1 0 50 100 150 200 250 300 100 0 −100 [Nm] −200 0 50 100 150 200 250 300 Motor Torque (T) time t [sec]

114 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Vehicle Yaw Rate 20 DYM off DYM on 15

0 yawrate r [deg/s] −5

−10

−15

−20 0 50 100 150 200 250 300 350 time t [sec]

Used Energy [kWh] 0.9 DYM off DYM on 0.8

0.7

0.6

0.5

0.4

energy E [kWh] 0.3

0.2

0.1

−0.1 0 50 100 150 200 250 300 350 time t [sec] 115 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Appendix 13 - Energy Consumption (Dynamic Drive Cycle, ‘Higher’ Speed)

To find out if TV has influence on the energy consumption and, if so, in which quantity, the following dynamic drive cycle of ca. 6 minutes is simulated. This second test, out of the three performed consumption tests, is considered to be a dynamic ‘higher’ speed test.

Vehicle Motion Data ) δ 5 0

[deg] Used Energy [kWh] −5

steeangl( 3 DYM 0 50 100 150 200 250 off 300

) 150 DYM

x on

100 2.5 50 [km/u]

Speed(v 0 0 50 100 150 200 250 300 2 20 0

[deg/s] −20 1.5 Yaw rate (r) 0 50 100 150 200 250 300 ) y ]

5 Energy [kWh] 1 2 0

[m/s −5 Lataccl (a 0 0.5 50 100 150 200 250 300

) 5 β 0 0 [deg] −5 Beta ( 0 50 100 150 200 250 300 −0.5 200 0 100 200 300 400 500 600 700 800 900 1000 0 Time [sec] [Nm] −200 0 50 100 150 200 250 300 Motor Torque (T) time t [sec]

116 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Yaw Rate (DYM ) off 30 real ideal 20

−10 yaw rate r [deg/s] −20

−30

0 50 100 150 200 250 300

Yaw Rate (DYM ) on

30 real ideal 20

−10 yaw rate r [deg/s] −20

−30

0 50 100 150 200 250 300 time t [sec]

Used Energy [kWh] 3.5 DYM off DYM on 3

2.5

1.5 energy E [kWh] 1

0.5

−0.5 0 50 100 150 200 250 300 350 time t [sec] 117 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Appendix 14 - Energy Consumption (Steady State Drive Manoeuvre, ‘Figure of 8’)

To find out if TV has influence on the energy consumption and, if so, in which quantity, the following steady state drive manoeuvre of ca. 3 minutes is simulated. This second test, out of the three performed consumption tests, is considered to be a steady state ‘Figure of 8’ test.

Vehicle Motion Data ) δ 2 0 [deg] −2 steeangl( 0 20 40 60 80 100 120 140 160 180 200

) 150 x 100 50 [km/u]

Speed(v 0 0 20 40 60 80 100 120 140 160 180 200 10 0

[deg/s] −10 Yaw rate (r) 0 20 40 60 80 100 120 140 160 180 200 )

y 5 ] 2 0 [m/s

Lataccl (a −5 0 20 40 60 80 100 120 140 160 180 200

) 2 β 0 [deg] Beta ( −2 0 20 40 60 80 100 120 140 160 180 200 40 20 [Nm] 0 0 20 40 60 80 100 120 140 160 180 200 Motor Torque (T) time t [sec]

118 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Yaw Rate (DYM ) off

real 10 ideal

−5 yaw rate r [deg/s] −10

0 20 40 60 80 100 120 140 160 180 200

Yaw Rate (DYM ) on

real 10 ideal

−5 yaw rate r [deg/s] −10

0 20 40 60 80 100 120 140 160 180 200 time t [sec]

Used Energy [kWh] 0.9 DYM off DYM on 0.8

0.7

0.6

0.5

0.4

energy E [kWh] 0.3

0.2

0.1

−0.1 0 50 100 150 200 250 300 350 time t [sec] 119 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Appendix 15 - Replay Model (Orignal Tyres)

To advise the changes that have to be made to the Tyre Estimator® when using motion data of a vehicle with Torque Vectoring (TV), a replay model is designed. After simulating a manoeuvre with the TV model including the TV controllers, the measured motion data is loaded into the MF-Tyre. With the MF-Tyre Tyre Property Files are made for the front and rear axle. These are then loaded into the designed Replay model. To demonstrate that the designed Replay model works correctly the original tyres are loaded into this Replay model.

Vehicle Motion Data

) 2 δ org 0 replay [deg]

steeangl( −2 0 20 40 60 80 100 120 140 160 180 200 )

x 80.5 80 79.5 [km/u] 79 Speed(v 0 20 40 60 80 100 120 140 160 180 200 10

0 [deg/s]

Yaw rate (r) −10 0 20 40 60 80 100 120 140 160 180 200

) 5 y ] 2 0 [m/s

Lataccl (a −5 0 20 40 60 80 100 120 140 160 180 200 2 ) β 0 [deg] Beta ( −2 0 20 40 60 80 100 120 140 160 180 200 time t [sec] 120 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

TorqueTorque OutputOutput Motors

150150 orgorg replayreplay [Nm] [Nm] R R 100100

50 50

torque motor right T torque motor right T 0 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200

150 org 150 replayorg replay [Nm] L

[Nm] 100 L 100

50 50 torque motor left T

torque motor left T 0 0 20 40 60 80 100 120 140 160 180 200 0 0 20 40 60 80 time100 t [sec]120 140 160 180 200 time t [sec]

121 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Appendix 16 - Replay Model (MF-Tyre Estimated Tyres)

The designed Replay model may be used to validate the Tyre Property Files made by the MF-Tyre. These are loaded into this designed Replay model.

Vehicle Motion Data

) 2 δ org 0 replay [deg]

steeangl( −2 0 20 40 60 80 100 120 140 160 180 200 ) x 100 90 [km/u]

Speed(v 80 0 20 40 60 80 100 120 140 160 180 200 10

0 [deg/s]

Yaw rate (r) −10 0 20 40 60 80 100 120 140 160 180 200

) 5 y ] 2 0 [m/s

Lataccl (a −5 0 20 40 60 80 100 120 140 160 180 200 2 ) β 0 [deg] Beta ( −2 0 20 40 60 80 100 120 140 160 180 200 time t [sec]

122 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Torque Output Motors

150 org replay [Nm] R 100

50 torque motor right T

0 0 20 40 60 80 100 120 140 160 180 200

150 org replay [Nm] L 100

50 torque motor left T

0 0 20 40 60 80 100 120 140 160 180 200 time t [sec]

123 S. Nada and S.J. Koster Hogeschool van Arnhem en Nijmegen HTS-Autotechniek

Appendix 17 - Electric Motor Glossary

This appendix explains the used terms with regard to Electric motors. [35] [36] [37] Air gap Uniform gap between the stator and rotor Asynchronous Motor Type of motor in which the flux, generated by the stator and rotor, have different frequencies Current Ripple Characterized by a varying value. Unlike the constant values of DC, the average value of an AC output constantly ripples Back Electromotive Force Back Electromotive Force (EMF) The potential generated by a current carrying conductor when it is exposed to magnetic field. EMF is measured in volts Electro Magnetic Interference Electro Magnetic Interference (EMI) is the disruption of operation of an electronic device when it is in the vicinity of an electromagnetic field Rated Speed Speed specified on the name plate of a motor Rotor Rotating part of the motor Single-phase Single set of distributed windings in the stator of the motor Slip Speed Defined by the corresponding frequency difference between the stator and rotor magnetic fields (applies only to induction motors) Stator Stationary part of the motor Synchronous Motor Type of motor in which the flux generated by the stator and rotor have the same frequencies. The phase may be shifted Synchronous Speed Speed of the motor corresponding to the rated frequency Three-Phase (3-Phase) Three sets of distributed windings in the stator of the motor Torque Rotating force in Newton-Meters Torque ripple The amount of torque measured by subtracting the minimum torque during one revolution from the maximum torque from the same motor revolution 124 S. Nada and S.J. Koster