Investigation of the transient nature of rolling resistance...

MASTERS THESIS

Investigation of the transient nature of rollingresistance on an operating Heavy Duty Vehicle

PETTER LUNDBERG

September, 2014

Masters thesis, Civilingenjrsprogrammet i teknisk fysik, Ume University.Petter Lundberg, [email protected].

Investigation of the transient nature of rolling resistance on an operating Heavy Duty Vehicleis a project done in the course Masters Thesis in Engineering Physics, 30.0 ECTSat the Department of Physics, Ume University.

Supervisor: Anders Jensen, YDMC - Fuel consumption, Scania CV AB.Examiner: Krister Wiklund, Department of Physics, Ume University.

What would an ocean be without monsters lurking in the dark?It would be like sleep without dreams.

Werner Herzog

AbstractAn operating vehicle requires energy to oppose the subjected driving resistances. This energy is suppliedvia the fuel combustion in the engine. Decreasing the opposing driving resistances for an operating vehicleincreases its fuel efficiency: an effect which is highly valued in todays industry, both from an environ-mental and economical point of view. Therefore a lot of progress has been made during recent years in thearea of fuel efficient vehicles, even though some driving resistances still rises perplexity. These resistancesare the air drag Fd generated by the viscous air opposing the vehicles propulsion and the rolling resistanceFrr generated mainly by the hysteresis caused by the deformation cycle of the viscoelastic pneumatic tires.

The energy losses associated with the air drag and rolling resistance account for the majority of thedriving resistances facing an operating vehicle, and depends on numerous stochastic and ambient para-meters, some of which are highly correlated both within and between the two resistances. To increasethe understanding of the driving mechanics behind the energy losses associated with the complexity thatis rolling resistance, a set of complete vehicle tests has been carried out. These tests were carried out onthe test track Malmby Fairground, using a Scania CV AB developed R440 truck equipped with varioussensors connected in one measurement system. Under certain conditions, these parameters can allow foran investigation of the rolling resistance, and a separation of the rolling resistance and air drag via explicitsubtraction of the air drag from the measured traction force. This method is possible since the aerodynamicproperty AHDVCd( ) to some extent can be generated from wind tunnel tests and CFD simulations.

Two measurement series that enable the above formulated method of separation were designed andcarried out, using two separate measurement methods. One which enables the investigation of the transi-ent nature of rolling resistance as it strives for stationarity, where the vehicle is operated under constantvelocities i.e. no acceleration, and one using the well established method of coastdown, where no drivingtorque is applied.

The drive cycles spanned a range of velocities, which allowed for dynamic and stationary analyses ofboth the tire temperature- and the velocity dependence of rolling resistance. When analysing the results ofthe transient analysis, a strong dependence upon tire temperature for given constant low velocity i.e. v 60 kmh1 was clearly visible. The indicated dependency showed that the rolling resistance decreased as thetire temperature increased over time at a given velocity, and vice versa, towards a stationary temperature andthereby rolling resistance. The tire temperature evolution from one constant velocity to another, took placewell within 50 min to a somewhat stationary value. However, even though the tire temperature had reachedstationarity, rolling resistance did not; there seemed to be a delay between stationary tire temperature, androlling resistance. The results did not indicate any clear trends for v 60 kmh1, where the results atv = 80 kmh1 were chaotic. This suggests that some additional forces were uncompensated for, or that thecompensation for air drag was somehow wrongly treated at higher velocities.

Several factors ruled out any attempts at proposing a new rolling resistance model. These included: thechaotic results for v = 80 kmh1, the delayed rolling resistance response upon tire temperature stabiliza-tion, and the lack of literature support for the observed tendency. The results from the coastdown serieson the other hand, showed good agreement with a dynamical model suggested in literature. The stationarytemperature behaviour for the considered velocity range at assumed constant condition is also supported inliterature.

Finally, an investigation of the aerodynamic property AHDVCd inspired by ongoing work in ACEA(European Automobile Manufacturers Association), was carried out assuming both zero and non-zero airdrag at low velocities. The results indicated surprisingly good agreement with wind tunnel measurements,especially when neglecting air drag at low velocities: as suggested by ACEA.

Keywords: Rolling resistance, Air drag, Heavy Duty Vehicles, Vehicle dynamics, Complete vehicle test,Coastdown, Effective radius, ACEA, Pneumatic tires, Driving resistances, Energy efficiency.

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SammanfattningFr att vervinna de motstnd som ett fordon utstts fr under drift krvs energi, vilket levereras genomfrbrnningen av brnsle. Genom att minska de krmotstnd som ett fordon utstts fr under drift, kanman ka dess energieffektivitet. Denna potential r idag hgt vrderad i fordonsindustrin, bde ur ett mil-jmssigt och ekonomiskt perspektiv. P senare r har stora framsteg gjorts inom omrdet energieffektivafordon, men fortfarande rder det frvirring kring de energifrluster som frknippas med luftmotstndFd och rullmotstnd Frr, dr luftmotstndet skapas av den omkringliggande visksa luften, medan rull-motstndet genereras av hysteresen som uppstr nr fordonets viskoelastiska pneumatiska dck utstts frdeformation.

De energifrluster som frknippas med luft- och rullmotstnd motsvarar den strsta delen av de mot-stnd som ett fordon pverkas av, och beror p en mngd stokastiska och yttre parametrar, varav vissar starkt korrelerade bde inom och mellan nmnda motstnd. Fr att frbttra frstelsen kring dessaenergifrluster, med fokus p frstelsen av rullmotstnd, har ett antal helfordonstest genomfrts. Dessagenomfrdes p provbanan Malmby Fairground med en R440 lastbil frn Scania CV AB, utrustad med enmngd sensorer sammankopplade i ett mtsystem.

Det uppbyggda mtsystemet mjliggjorde samtida mtningar av bl.a. drivande moment, motorvarv, for-donshastighet, dcktemperatur, omkringliggande lufts hastighet och dess riktning. Under specifika frhl-landen kan dessa parametrar mjliggra analys av rullmotstnd genom en explicit subtraktion av luftmot-stnd frn den uppmtta drivande kraften. Denna metod r mjlig tack vare en frhllandevis bra modell avekipagets aerodynamiska egenskap AHDVCd( ), som generats frn vindtunneltest och CFD simuleringar.

Tv krcykler som mjliggjorde ovan formulerade separation designades och genomfrdes. Dessa an-vnder tv skilda mtmetoder, varav den ena mjliggr analys av rullmotstndets vergende frlopp frndynamiskt till stationrt genom att hlla konstant hastighet. Den andra studerade det dynamiska frloppetgenom den vletablerade metoden utrullning, dvs. utan ngot drivande moment.

Dessa krcyklar genomfrdes, fr ett antal hastigheter, vilket mjliggjorde analys av bde hastighets-och dcktemperaturberoendet hos rullmotstnd, under dynamiska svl som stationra frlopp. Analysenav rullmotstndets dynamik i strvan mot stationra frhllanden visade p ett starkt temperaturberoen-de vid lga hastigheter dvs. v 60 kmh1. Beroendet visade p att rullmotstndet avtog med kandedcktemperatur och vice versa, tills dess att en ngorlunda stationr temperatur fr given hastighet upp-ntts. Dcktemperaturen stabiliserades till ett nytt stationrt vrde inom 50 min frn att hastigheten ndrats.Resultaten tyder dock p att ven om stationr dcktemperatur uppntts finns det en frdrjning i rullmot-stndets tidsspann innan rullmotstndet stabiliserat sig. Fr hgre hastigheter, dvs. v 60 kmh1, var dockinga klara trender synliga, varken i hastighet eller temperatur och resultaten vid v= 80 kmh1 var kaotiska.Detta antyder att man missat att kompensera fr ngon kraft vid hga hastigheter, alternativt att man pngot stt kompenserar fel fr luftmotstndet vid hgre hastigheter.

Flera faktorer hindrade frsk att fresl ngon ny rullmotstndsmodell. Dessa faktorer inkluderar detkaotiska resultatet vid v = 80 kmh1, tidsfrdrjningen mellan stationrt rullmotstnd och dcktemperatursamt att resultatet fr antagna stationra vrden inte finner std i litteraturen. Resultatet frn utrullnings-provet verstmmer dock bra med tidigare freslagen dynamisk modell, samt att resultaten av beteendethos stationr temperatur fr olika hastigheter ven de verensstmmer med och finner std i litteraturen.

Slutligen har en studie kring den aerodynamiska egenskapen AHDVCd , inspirerad av pgende arbeteinom ACEA (European Automobile Manufacturers Association) utfrts bde med antagandet av ett noll-skilt och med ett frsumbart luftmotstnd vid lga hastigheter. Resultatet visar p en verraskande godverensstmmelse med vindtunnelmtningar, framfr allt under antagandet av frsumbart luftmotstnd vidlga hastigheter i enlighet med frslagen metod frn ACEA.

Nyckelord: Rullmotstnd, Luftmotstnd, Tunga fordon, Fordonsdynamik, Helfordonstest, Utrullningstest,Effektiv radie, ACEA, Pneumatiska dck, Krmotstnd, Energieffektivitet.

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Acknowledgement

Even a smooth ride has its resistance and since life has its ups and downs I have found energy losses tobe a field worth to immerse myself in, both from an emotional and technical point of view. When giventhe opportunity to analytically work with the energy consumption of heavy duty vehicles, and extend thefundamental knowledgeable base of external energy losses, I was curious to see what I could bring to thetable. Being the passionate environmentalist that I am, I found myself eager to perform well and workthoroughly, so that my thesis work really could result in something useful. When it was decided that themethod of choice would be to rig and perform complete vehicle measurements, my eagerness increased: itwould challenge both my theoretical and practical engineering skills. Also, complete vehicle tests requiresone to leave the office and the comfort zone of suits, and thereby work directly side by side with themechanics; solving the problems arising in the workshop hands on. This really intrigued me! Therefore, Iwould hereby like to invite you to literary follow me into the complexity of vehicle dynamics and completevehicle measurements, with focus on the energy losses known as rolling resistance.

Within my thesis work I have had the great honour to have Anders Jensen as my guide and supervisor.Without him and the rest of my colleges at YDMC - Fuel Consumption I would still be standing still,stunned by the complexity facing me in my work. For all your help and willingness to discuss, I would liketo emphasise my gratitude and say thanks. I would also like to give a special thanks to Roger Palm for hispatience and expertise in the workshop; you really did decrease the resistance in my work.

As always, my family and friends; you really make my life easier, often just by picking up your phonesor inviting me for a long walk. I would especially want to direct my gratitude to Mattias Lindh, MariamShirdel and Emma Zll; for helping me with my grammar and layout. I could not be more thankful for yourwillingness to help, discuss and illuminate my mistakes. Thanks!

Finally, I would like to thank the Baltic Sea for always being by my side, enabling me to keep my headcold. Without you I would probably since long gone overheated.

Petter Lundberg,Bygde, Sweden,18 August, 2014.

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Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Disposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theory and approaches 52.1 Driving resistance of an operating HDV . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Simplified dynamics of a HDV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Pneumatic tires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Rolling resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4.1 Measurement methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4.3 Existing models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5 Effective radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Method 163.1 Measurement equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1.1 Vehicle specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.1.2 Sensors and experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Test track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3 Measurement series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3.1 Dynamic to stationary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3.2 Coastdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4.1 Theoretical simplifications and assumptions . . . . . . . . . . . . . . . . . . . . . 213.4.2 Signal processing and computing . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4 Results 264.1 Measurement data required for further analysis . . . . . . . . . . . . . . . . . . . . . . . 26

4.1.1 Test track data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.1.2 Anemometer data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1.3 Torque data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.1.4 Resulting effective radius Re . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.2 Transient temperature behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3 Transient analysis of rolling resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.3.1 Separation of the driving resistances . . . . . . . . . . . . . . . . . . . . . . . . . 324.3.2 Stationary effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.4 Coastdown verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.5 Multivariate data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

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CONTENTS

5 Discussion 405.1 Methods, conditions and considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.2 Result credibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2.1 Multivariate data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2.2 Transient temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.2.3 Separation between air drag and rolling resistance . . . . . . . . . . . . . . . . . . 43

5.3 Further studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6 Conclusions 47

7 Bibliography 48

A Test vehicle specifications 51A.1 Test vehicle illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51A.2 Axle and tire specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52A.3 Inertia specifications and calculation method for equivalent mass . . . . . . . . . . . . . . 53

B Experimental set-up specifications 54

C Multivariate data analysis 55

D Matlab scripts 57D.1 Test track parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57D.2 Averaging over measurement laps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59D.3 Transient separation of driving resistances . . . . . . . . . . . . . . . . . . . . . . . . . . 61D.4 Coastdown verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

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To my beloved nieces Elsa and Lilly

Chapter 1

Introduction

1.1 Background

Energy efficiency is an important topic for todays industries, not least the vehicle industry. The demandson fuel efficiency are becoming stricter, both from society, government and costumers, to keep the envir-onmental impact and fuel consumption to its minimum. One motive is that about 30% of the total lifecycle cost for an Heavy Duty Vehicle (HDV) is estimated to correspond to fuel consumption, motivatingthe desire from an economical point of view [1]. To cope with the standards of todays market and to be afrontier in energy efficiency it is important for Scania CV AB (Scania) to grasp how, why and where thetransitions of energy losses occurs. Understanding these transitions enables a deeper understanding of themechanisms behind fuel consumption and possible decreases.

In recent years, a lot of progress has been made in the field of energy efficient vehicles, both along thepower train, and within the techniques of active adaptiveness. Using on-board sensors, information gen-erated from wireless communications between vehicles, and from the Global Positioning System (GPS),smart features such as Scania Opticruise, Scania Active Prediction, and Scania Ecocruise, have been de-veloped along with the possibility of online-estimations of e.g., vehicle mass, and road grade, enabling fuelefficient gear shifts, and thereby fuel savings on topographical roads [2, 3].

However, the two driving resistances that alone accounts for around 60 80% of a HDVs fuel con-sumption, i.e. air drag and rolling resistance, still rises perplexity. The underlying mechanisms of theseresistances depend on numerous of parameters, many of which have a stochastic nature and correspondto ambient parameters that are hard to measure accurately or even quantify. There is also high levels ofcorrelations between these explanatory variables, both between and within the two resistances. Because ofthis complexity, separation and estimations of these two driving resistances remains problematic especiallywhile operating, and is therefore a high priority in the vehicle industry. This fact is emphasized not onlyby Scania, but also addressed within the European Automobile Manufacturers Association (ACEA) andthe project Models for rolling resistance In Road Infrastructure Asset Management Systems (MIRAIM),where among others the Swedish National Road and Transport Research Institute (VTI) is involved [4, 5].

Also, as the possibility and usefulness of vehicle simulations increases, both as a development tooland as a support for salesmen, programs such as: Scania Truck And Road Simulation (STARS), VehicleEnergy Consumption calculation Tool (VECTO) and Vehicle Optimizer (VO), has been developed. Dueto the major contribution, associated with rolling resistance and air drag, to vehicle dynamics as such, andenergy consumption in general, mathematical models have been developed to enable simulations of theseresistances [6, 7]. For air drag there exists a well established physical model, where the uncertainty liesin the input data of wind tunnel measurements, and Computational Fluid Dynamics (CFD) simulations aswell as the influences from ambient parameters. Rolling resistance on the other hand lack such a modeldue to its complexity. Hence all existing models of rolling resistance make more or less questionable as-sumptions, which has been proven to create shortcomings in many cases. These models are all based uponmeasurements, most in accordance with the standards stated by International Organization for Standardiz-ation (ISO) and Society of Automotive Engineers (SAE). These standards of measurement techniques areall performed in laboratory environments, on free rolling tires against test drums. Dependent on the choice

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CHAPTER 1. INTRODUCTION

of method, aerodynamic losses of the tire may or may not be included. They also lack connection to realoperating scenarios, such as realistic road surfaces and driving patterns; a problem which is addressed inMIRAIM [5, 8].

For ongoing work in ACEA a measurement method, called CO2-method, has been designed to enableseparation of the two driving resistances rolling resistance and air drag while operating. The fundamentalpurpose of the method is to express the air drag characteristics for different vehicle submodels categorisedin a tree of vehicles. This tree consists off vehicle families, categorised by different cabin lines. Each lineconsists of different models that are further divided into submodels. For each submodel, measurements ofdriving resistance and wind should be performed at one low and one high velocity during close to stationaryconditions, in order to express the sum of the two resistances of interest. Firstly, the rolling resistance isexpressed as the total driving resistance at the low velocity and assumed to be independent of velocity, i.e.constant in considered method. Secondly, the air drag is expressed as a second order fit of the remainingdriving resistance at the considered high velocity, after subtraction of the rolling resistance. Via this secondorder fit it is then possible to express submodel characteristics, i.e. the term AHDVCd in equation (2), afterconsiderations of ambient parameters, such as wind, has been conducted. These submodel characteristicswill then be used when simulating a vehicle unique energy declaration [4].

The need for further analysis regarding the effect of assuming a velocity independent rolling resistancein the method proposed by ACEA, has been emphasised by e.g. Pflug, H-C, who is highly involved with theongoing process in ACEA [9]. Using the velocities considered in the CO2-method designed by ACEA, ameasurement cycle has been suggested that should measure both the initial and stationary, i.e. after 90 min,driving resistance for considered high velocity, and then decelerate to the considered low velocity. At thelow velocity the same procedure as described above is considered, and after 90 min at a constant velocity,a final acceleration to the high velocity for a last driving resistance measurement is performed. Whenperforming this measurement cycle, both against a drum and outdoor on a single tire mounted in the centreof a trailer, one concluded that the rolling resistance differ both between the high and the low velocity,along the warm up and cool down phases at a constant velocities, and also between the two series of highvelocity [9]. It is this realisation that is the major foundation upon which my thesis objectives are based.

1.2 PurposeThe definitive purpose of this work was to address the possibility to distinguish the energy losses associatedwith the driving resistances air drag and rolling resistance, on an operating HDV. Preferably, online using"look-a-head" techniques1. This is however a vision of the future and the purpose of this thesis work is toanalyse such a possibility. The analysis should result in a deeper understanding around discussed energylosses, which requires exploration of their underlying driving mechanisms and physical nature.

1.3 ObjectivesSince the purpose stated above is rather vague a more quantifiable version follows, in the form of projectobjectives.

i) Compile previous work regarding the dynamics and physical nature of the energy losses occurringoutside the power train on an operating HDV, to encapsulate their driving mechanisms.

ii) Set up a measurement system that captures parameters which enables separation of these energy losses.The system should also consider potential explanatory variables of rolling resistance, enabling com-parison and hence validation of existing simulation models.

iii) Design and conduct a series of measurements that allow investigation of the transient nature of rollingresistance over a range of velocities under somewhat realistic operating conditions.

iv) Analyse this transient nature of rolling resistance, and compare correspondence with existing models.If feasible and suitable, suggest a new estimation model which encapsulates the nature of rollingresistance during real operating scenarios.

1i.e. using GPS and prior known roadway data to make adaptive changes while operating, decreasing the energy consumption.

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1.4. DISPOSITION

v) Compare the results of transient behaviour against those of a coastdown measurement series to verifythe potential possibility of energy loss separation and the correspondences between the two series.

1.4 DispositionThis thesis is divided into six chapters. In this introductory chapter a rather thorough background to thefield of energy efficient HDVs was given, introducing the perplexity of driving resistances in general androlling resistance in particular. Within this background a brief overview of ongoing work within the subjectas such was addressed, ending up in the definitive purpose and objectives of the project carried out.

To facilitate reading and orientation, a short description of the chapters at hand follows. Chapter 2addresses the physical background of vehicle dynamics and driving resistances, with a focus on the com-plexity that is rolling resistance. It includes the theory behind existing measurement methods, knowndependencies, and a few models of rolling resistance. With the theory from chapter 2 as a foundation,two measurement series have been carried out on an operating HDV; investigating the transient nature ofrolling resistance over a velocity span. The method, sensors and set-up of these are given in chapter 3, to-gether with the analysis procedure and considerations taken. The results from the performed measurementseries are shown in the subsequent chapter 4, upon which the discussion in chapter 5 is based. In chapter 5recommendations of future studies are also given before the thesis ends with a final chapter of conclusions.

Moreover, in appendix A specifications about the used HDV during the complete vehicle tests, bothits exterior and interior components, are given. Appendix B considers the specifications of the designedmeasurement set-up, whilst appendix C covers some covariance tables from the multivariate data analysis,as well as a set of scree plots from a principle component analysis carried out . Finally, appendix D containsa few Matlab-scripts used to analyse and handle the huge amount of data.

1.4.1 NomenclatureTo further facilitate reading, every equation and definition is enumerated. There is a consistent use ofnomenclature and notations throughout the thesis, e.g., the time derivative of is denoted , the indexi indicates force acting only on one wheel and denotes the time average of whilst denotes theequipage average. |=c denotes as the parameter is held constant at c. Also, each tire is referred toaccording to its corresponding axis and side of equipage, e.g., A3L is the left wheel of the third axis. Left ishere used as the notation for the port side of the vehicle and axis number 1 is the frontal axis. To introducethe terminology and ease the orientation within the theory, a nomenclature list of frequently used variablesfollows below in table 1.

Table 1: List of frequently used parameters.

Parameter Description Unit

Fd The total air drag acting on the entire HDV NFrr The total rolling resistance acting on the HDV, i.e. the sum of all wheels NFg The gradient resistance, due to gravitational force NFxi The traction force between a tire and underlying road surface NFzi The normal force from the roadway acting on one wheel Ni The applied torque to one wheel Nm

{v, vx} The velocity of the HDV and its corresponding longitudinal velocity m/s{vWind, vAir} The wind speed and resulting air velocity around the HDV m/s

The angular velocity of a rotating wheel rad/se The engine speed rpmg The gravitational acceleration m/s2

J The inertia of specified wheel or interior component kgm2

{R, Rl , Re} Free rolling, loaded and effective radius correspondingly mContinued on next page. . .

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CHAPTER 1. INTRODUCTION

ContinuedParameter Description Unit{M, mrot} The total mass of the HDV and its equivalent mass kg

m The portion of M+mrot corresponding to one wheel kgAHDV The effective projected frontal area of the HDV in the direction of m2hHDV The maximum hight between the roadway and the top of the HDV mhAne The height between the roadway and the anemometer m

lx The longitudinal distance travelled m

{x, y, h} The position in space from reference point m The road grade

{, } The wind and resulting yaw angle

Crri Coefficient of rolling resistance for given wheel kg/tonCd Air drag coefficient, unique for given aerodynamic shapeC f Viscous friction coefficient for specified tire kgm2/s

Air The density of the ambient air kg/m3PAir The pressure of the ambient air PaTAir The temperature of the ambient air C The relative humidity of the ambient air %

TTire The shoulder temperature inside the pneumatic tire CPTire The inflation pressure of the pneumatic tire bar

TTireAir The inflated air temperature of the pneumatic tire CTTire |vx=c The stabilization temperature for given tire at specified velocity vx = c C

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Chapter 2

Theory and approaches

2.1 Driving resistance of an operating HDV

It is a well known fact that a vehicle requires energy to operate. Energy which is supplied by the fuelcombustion in the engine. To increase the fuel efficiency of an operating vehicle one must grasp whereand why the energy losses, the so called driving resistances, occurs. As for all bodies, operating vehiclesexperiences inertial resistance while accelerating or decelerating opposing the change of velocity. Operat-ing vehicles also experience the driving resistances shown in figure 1 which illustrates an operating HDVof mass M driving on a slope of grade facing the driving resistances air drag Fd , gradient resistance Fgand rolling resistances Frr. The index i, seen in figure 1, indicates that each tire may experience differentrolling resistances which is further discussed in section 2.4 [5].

Fdv

Frr35

Frr2Frr1

Mg

Fg

Figure 1: An operating HDV of mass M driving with the speed v on a slope of grade , illustrating thevarious driving resistances air drag Fd , gradient resistance Fg and rolling resistances Frri .

Beside the above mentioned driving resistances, an operating HDV also experience energy losses inthe form of suspension loss, transmission loss and engine resistance, as well as energy losses in auxiliaryequipment e.g., air condition, and generator. These energy losses occur along the powertrain and dependson the choice of engine, gearbox etc. [10], and are not considered further within this report.

Focus instead lies on the driving resistances illustrated in figure 1. The road grade resistance Fg whichis due to existing road topography, is the gravitational force acting on the HDV. The road grade, or slope, is given by the change in altitude h over a finite longitudinal distance lx, i.e. tan() = h l1x , andhence changes along the road. The resistance force introduced by the grade is,

Fg = Mgsin() (1)

where g is the gravitational acceleration [11, 12].

5

CHAPTER 2. THEORY AND APPROACHES

The drag force Fd caused by the ambient viscous air surrounding the operating HDV, is defined by,

Fd =12

AirAHDVCdv2Air (2)

where Air is the density of the ambient air, AHDV is the effective area, Cd is the drag coefficient whichdepends on the vehicles aerodynamic design and vAir is the velocity of the air opposing the vehicle [13, 14].

Without any ambient wind, vAir equals the velocity of the operating HDV i.e. vAir = vx. AHDV is thensimply the projection of the frontal area in the direction of motion. In general there is however an ambientwind present of speed vWind at the attack angle as shown in figure 2, affecting both parameters. Theambient wind changes the opposing air speed according to the law of cosines, stated below,

vAir =

v2x + v2Wind +2vxvWind cos( ) (3)

where is the yaw angle seen in figure 2. The effective area AHDV becomes the projection of the frontalarea1 in the the direction of the airflow i.e. [14].

vx

vWind vAir

Figure 2: An HDV operating with the longitudinal velocity vx experiencing a meteorological wind ofvelocity vWind from the angle transforming the air velocity vAir to oppose at the yaw angle .

As illustrated in figure 1, each tire experiences a resistance force known as the rolling resistance Frri .This resistance is however so complex that it is covered in its own section, see section 2.4. It can still benoted that the rolling resistance is somewhat proportional to the vertical load on the tire i.e. axle load. Thetotal rolling resistance of the operating HDV Frr = ni Frri , where n is the number of tires, should in theorytherefore be independent of the distribution of vertical loads and hence the number of axles since it onlypartitions the vertical load over the tires [15, 7].

Knowing the driving resistances acting on the HDV, it is possible to state the equation of motion forthe complete vehicle as,

(M+mrot) vx = FxFgFdFrr (4)

where Fx is the total traction force generated by the driving wheels and mrot is the equivalent mass i.e. thecontribution to mass from the inertia of rotating parts both along the powertrain and the wheels [16].

2.2 Simplified dynamics of a HDV

As described in section 2.1 the dynamic nature of an operating HDV is rather complex. A commonly usedsimplification is to represent the whole vehicle by the longitudinal and rotational dynamics of a singlewheel, as the number of axles only partition the vertical load. Applying Newtons second law of motionto the simplified representation seen in figure 3, which illustrates one wheel on a horizontal plane surface,enables formulation of a force balance.

1Given that vx vWind.

6

2.2. SIMPLIFIED DYNAMICS OF A HDV

ivx

Fzi

Faxle load

R

Fdi Frri

Fxi

R

Rl

Figure 3: A simplified sketch over the forces acting on one wheel at a horizontal surface. The figureindicates velocities and the free rolling radius R as well as the loaded radius Rl .

The driving force on wheel i is the applied torque i which generates an angular wheel velocity .It is this rotation that drives the wheel forward with the longitudinal velocity vx [17]. If one introduces aroad grade to the simplified representation shown in figure 3, generating a gradient resistance Fgi , therotational and longitudinal equations may be written as,

Rotational: J = iRFxi C f (5a)Longitudinal: mvx = Fxi Fdi Fgi (5b)

where J is the in inertia of wheel i of radius R, C f is its corresponding viscous friction coefficient and m isthe portion of M+mrot corresponding to one wheel [12, 17]. The traction force Fxi describes the tire-roadinteraction driven by the applied torque,

Fxi = ( )Fzi (6)

where Fzi is the normal force from the roadway acting on the wheel. The friction coefficient ( ) dependson the slip ratio ,

= 1 vxR

(7)

for which there exist a numerous of empirical models [17].The road grade resistance Fgi and air drag Fdi in equation (5b) is, in this simplified model of one wheel,

the longitudinal partition of the the total resistance from respective force corresponding to that of onewheel. Noteworthy is that it is only the driven wheels, i.e. the wheels where the drive line apply the torquei, that contracts the driving resistances from air drag and gradient resistance.

If the single wheel illustrated in figure 3 was solid; this simplistic model described above would essen-tially be complete. However due to the deformability of the commonly used pneumatic tires, described insection 2.3, a rolling resistance often treated as a force opposing the direction of motion, as illustrated infigure 1 and figure 3 arises, as well as a non-uniformed radius. The concept of rolling resistance introducesa fictional force denoted Frri opposing the direction of movement. This force is addressed and defined insection 2.4, and includes the dissipating losses due to hysteresis, the viscous term C f R1e , where Re is theeffective radius considered in section 2.5, and some additional energy losses. The force balances expressedin equation (5) is therefore modified and expressed as stated below for a single driven wheel of the vehicle[18, 17, 19];

Rotational: J = iReFxi (8a)Longitudinal: mvx = Fxi Fdi Fgi Frri+ j (8b)

7


note that it is only the driven wheels that contracts the rolling resistance from the additional wheels, hencethe term Frri+ j where j indicates the portion of driving resistance from additional wheels deceleratingdriving wheel i.

2.3 Pneumatic tiresSince the late 1900s pneumatic tires have served as the interface between the vehicle and the road itoperates on, replacing the previously used solid rubber tires [18]. It is via the contact area between the tireand the road, all the forces for accelerating, braking, turning etc. is transmitted [20].

Simplified, the pneumatic tire consists of a tread with its crown creating the contact patch, and a bodyproviding the compartment for the compressed air together with the wheels rim. The science behindmodern tires are however a complex mix of polymers, fillers, softeners, sulphur, steel cords, bead wires,etc. It exists a wide range of tires on the market today, both from different manufacturers and of differentstyles. These can however be divided into three groups, i.e. diagonal bias, belted bias and radial tires.Whereof radial is the most commonly used today [18].

The tire is designed to ensure grip and comfort, withstand various weather and road conditions andact as a damping system for road irregularities. This is generated by the deformability of the pneumatictires where the tire deflect under the vertical load of the vehicle until the contact area pressure is balancedby the internal air pressure of the tire. As the wheel rotates each material element of the tire undergoes adeformation cycle. The tire experiences bending of the crown, sidewalls and bead area, compression of thetread and shearing of the tread and sidewalls. At the area of contact the curvature of the tire changes. Boththe maximum and minimum curvature occurs at this area.

When a surface element has been exposed to this deformation and stress it returns to its initial shapeafter a finite time, creating hysteresis. This is due to the viscoelastic nature of the pneumatic tire and thefact that the time it takes for the tire element to revert to its original shape is associated with dissipationof energy, in the form of heat. This energy dissipation caused by repeated deformation of a rotating tire iswhat causes the so called rolling resistance Frr, see section 2.4. It has been shown that the deformation ofthe crown is responsible for the most energy dissipation and alone stands for about 70% [18, 20].

2.4 Rolling resistanceAs described in section 2.3 it is the hysteresis in the deformation cycle of the tire that creates the energydissipation that give rise to the energy loss called rolling resistance. The concept of rolling resistance alsoinclude other energy losses associated with a rotating wheel under load. These are the aerodynamic dragaround the wheels, micro-slippage between the tread and the road, and the tire and the rim, and also energylosses occurring within the tire structure. The majority, around 80 95%, of this energy loss is howevercaused by the hysteresis [18]. Since rolling resistance is a pure energy loss it is adequate to define it assuch: for example the definition formulated by Schuring [21].

Definition 1 (Schuring, 1977, p31). Rolling [resistance] is the mechanical energy converted into heat bya tire moving for a unit distance on the roadway

As the definition 1 suggests the rolling resistance is given by energy over distance i.e. J m1. Since joulesmay be expressed as Nm, the dimension of rolling resistance is equivalent to that of a force, even though itcan not be an actual physical force [5].

Because of the nature of rolling resistance it is a scalar and not a vector. It can however be usefulto model rolling resistance as a physical force, enabling formulation of equilibriums as in equation (8b)[18]. Since it has been measured that there is a forward shift in the resultant normal force acting on arotating wheel under a vertical load, as shown in figure 4, such a formulation is arguable. This forward shiftgenerates a rolling resistant torque around the wheel centre, opposing the driving torque i from which analternative definition may be formulated [19, 7, 22].

Definition 2. The longitudinal force rolling resistance Frri is defined as the force required to keep a wheelat constant speed on a level roadway in spite of the resisting torque caused by the forward shift of theresulting normal force Fzi for a rotating wheel under a vertical load.

8

2.4. ROLLING RESISTANCE

vx

Faxle load

Fzi

Frri

Fxi

Re

i

Figure 4: The deformability of pneumatic tires causes a shift from the tire centre of the resultant normalforce Fzi , generating an opposing momentum modelled as the longitudinal force Frri .

It has been shown that the force defined in definition 2 is close to proportional to the axial load Fzi andtherefore it is common to express the following equation for rolling resistance;

Frri CrriFzi =Crrimgcos() (9)

that is, rolling resistance Frri is proportional to the normal force Fzi with Crr as the coefficient of rollingresistance [23, 24]. Since most road grades are quite small, i.e. a few degrees, it is possible to approxequation (9) even further;

Frri =Crrimgcos()Crrimg , for small (10)

this approximation is however seldom necessary, since is required for computing Fg [3].The coefficient of rolling resistance has been shown to be far from constant and depends strongly on

many parameters, some more or less unquantifiable. These properties, which are based on results from arange of measurement methods described in section 2.4.1, are further discussed in section 2.4.2. Furthermore some commonly used models to simulate rolling resistance, at e.g., Scania, are described in section2.4.3.

2.4.1 Measurement methodsWhen measuring rolling resistance the measurement usually considers one of two cases. Either at constanttire temperature; where measurements are performed directly after an alternation in conditions so that thetemperature of the tire is unchanged, and hence the measurement only captures the effect of the alternation,or after sufficiently long time under the same conditions; so that an equilibrium temperature is reached.There is of course also a third option, however less common: to measure continuously to capture thetransient effect on rolling resistance from an alternation in conditions. Some measurement methods alsoconsiders a so called regulated test, which means that potential inflation pressure changes are suppressedby connecting the tire to a pressure regulator, used as a version for direct measurements. A non-regulatedtest is called capped.

Standardized methods

As mentioned in section 1.1 there exist standardized test methods for measuring the rolling resistance of aspecific tire, specified by either SAE or ISO [25, 26, 27, 8]. These are all conducted in controlled laboratoryenvironments and only considers brand new tires free rolling under a specified load against a driven rotating

9


drum. Most standardized methods consider measurements at stationary conditions, i.e. a warm up period 180 min, for either a single-point or multi-point test. A single-point only includes one setting of tirepressure and load whereas a multi-point test considers various settings of these parameters [5].

A typical standardized measurement set-up is illustrated in figure 5, showing a test drum driven by amotor against which the test tire is held by a given load, applied by the actuating cylinder. For a set-up likethis, four standardized measurement methods exists:

Force method: Measures the resistive force at the tire centre.

Torque method: Measures the resistive torque on the drum hub.

Power method: Measures the power supplied to the motor to keep the drum rotating at constant speed.

Deceleration method: Measures the deceleration after the driving force to the drum is disconnected.

Depending on the choice of standard, some of the above described methods will not apply [5].

Actuating cylinder

Test tire

Test drum

Motor

Figure 5: A sketch of a typical standard test configuration for measuring rolling resistance [5].

Regardless of the choice of method, a correction of the aerodynamic drag, which alone can accountfor 15% of the laboratory result, should be done since it otherwise differs significantly from that of a realoperating scenario and hence gives an unrepresentative result. This is however not always done, due topractical limitations and hence not mandatory. Another correction is also required and that is to accountfor the effect of the drum curvature and hence improve the result accuracy. This is done according astandardized formula [18].

Nonstandardized methods

As stated in section 1.1 the standardized measurement methods of rolling resistance lack connection toreal operating scenarios, both considering the effect of road surface structure, aerodynamic drag around thewheels and possible transient effects. As stated in both definition 1 and 2, rolling resistance is caused by theinteraction between the tire and the road, a fact that is more or less neglected in the standardized methods.As an example, in real operating scenarios the paving can both cause local deflection which causes extraenergy loss, and also some of the rolling losses may be consumed in the paving rather than inside tire, i.e.heating and/or deformation of road.

Even if no standardized method for rolling resistance measurement under real scenarios exists, there isstill numerous nonstandardized methods that aim to include the effect of road surface, structure and henceclose in on real operating scenarios. Many of these techniques considers a so called fifth wheel, eithermounted on a special trailer designed to be towed by a passenger car or a single wheel mounted at thecentre of a truck trailer. The measuring method differs between these specially designed trailers, somemeasures the inclination angle between the wheel carrier and the trailer frame created as the fifth wheel ispulled back by the rolling resistance, whilst other may use specially designed hubs or rims to measure theactual torque on the wheel. However, all of these trailers consider the rolling resistance on one non-drivenwheel, and not the actual operating wheels of the driven vehicle.

One method aiming to establish measurement of more than one tire at the same time is to mount atrailer via a drawable force transducer, which enables measurements of the force required to tow the trailer.

10


This method then succeeds to measure the average rolling resistance for the number of trailer tires underreal operating scenarios, but still only for non-driven wheels, and not the actual tires of the vehicle [5].

Another commonly used method to measure the rolling resistance of the actual equipage tires is theso called coastdown method. By allowing the operating vehicle to coastdown, i.e. neutral gear and henceno applied torque nor traction force Fx, on a level roadway one can get an estimate of the decelerationvx caused by the air drag Fd and rolling resistance Frr, i.e. (M+mrot) vx = Fd Frr in accordance withequation (4). By estimating or measuring the air velocity vAir around the equipage, knowing its aerody-namic properties, one may estimate the average rolling resistance of the entire equipage by computing andsubtracting the air resistance according to equation (2). Since it requires the vehicle to coastdown, themethod only considers non-driven wheels under a decelerating event, and hence not under realistic drivingscenarios [28, 10].

As mentioned in section 1.1, ongoing work in ACEA has developed a measurement method to establishmeasurements of actual traction force while operating using torque sensors mounted either at the shaft, hubor rim. Measuring the applied traction force under a specified drive cycle enables, after some considerationsand assumptions, estimations of both the total rolling resistance and air drag for the entire equipage. Thisdesigned drive cycle considers both two low velocity measurement sections, where the velocity is keptconstant within the interval vx [10,15] kmh1, and a constant high velocity section, i.e. vx 85 kmh1held in between the two low velocity sections. These measurements shall be performed on a level dryroadway after a 90 min warm up section at vx 85 kmh1 to enable somewhat stationary tire conditions.By measuring ambient parameters such as temperature TAir, relative humidity etc., engine data, e.g.engine speed e, and the ambient air properties (vAir and Air) one may via an anemometer compute theaverage traction force needed to overcome the driving resistance caused by rolling resistance Frr, and airdrag Fd , over specified stretch of road [4].

The idea of the method specified by ACEA is to end up with a result similar to the sketched graphin figure 6, which indicates the traction force needed to keep a constant velocity in spite of the resistancecaused by rolling resistance and air drag. Assuming that the average traction force at considered lowvelocity vLow corresponds to the total rolling resistance, i.e. Fx|vx=vLow Frr and hence Fd|vx=vLow 0, i.e.low enough to be neglected. Then, by assuming that the rolling resistance is independent of velocityand hence constant in the considered case enable one to express the air drag as a second order fit of theremaining traction force after subtracting the assumed constant rolling resistance as indicated in the sketchgraph given in figure 6 [4].

The aim is then, as mentioned in section 1.1, to categorize HDV-submodels and for each submodelexpress its aerodynamic characteristics, i.e. the term AHDVCd in equation (2) after considerations of ambientparameters such as surrounding air flow velocity vAir, direction Air and density Air have been concluded.Hence, which is worth to emphasise, the pure goal of the method specified by ACEA, is not to study therolling resistance [4]. However, as it is a parameter that has to be considered in the designed measurementmethod it still counts as a method for estimating the average rolling resistance of the actual tires on theentire equipage while operating at constant low velocities, i.e. both the driven wheels and non-driven wheelsare accounted for.

2.4.2 Properties

As indicated by the strict restrictions of different parameters in the measurement methods described insection 2.4.1 the rolling resistance coefficient Crr does depend on a wide range of variables, e.g. inflationpressure Ptire, tire temperature Ttire, longitudinal velocity vx and the roughness of the roadway surfaceupon which the vehicle operates. These are often considered the most prominent parameters of rollingresistance, but many more parameters have shown to have a non negligible influence on rolling resistance.Some of these parameters are ambient parameters such as air temperature TAir, air pressure Pair and roadwaytemperature TRoad. Others are the type of tire, its dimension and vertical load Fzi

2 [10, 7, 29].When considering the above stated parameters one realises that many, if not all, of these parameters

are strongly correlated. For example, when driving on a road the roughness of the roadway may increasethe deformation of the pneumatic tire and hence increase the temperature in the tire material due to the

2Which somewhat contracts the previous stated property that the total rolling resistance Frr acting on a operating HDV should beindependent of the number of axles.

11


vx

Fd +Frr

15 90

Frr

Fd

Figure 6: The fundamental idea of the measurement principle specified in the ongoing work by ACEA isto enable energy classification of each unique vehicle, via simulations. To enable accurate data for thesesimulations every submodels aerodynamic properties AHDVCd is required and shall be based upon theaverage traction force needed to overcome the driving resistance caused by rolling resistance Frr and airdrag Fd for a considered low and high velocity [4].

increased hysteresis. This increase of tire temperature will increase the temperature of the inflated air andhence also the tire pressure. Dependent on the vehicle velocity, the deformation cycle is more or lessfrequent and hence also energy loss and therefore energy build up inside the tire.

Using the measurement methods described in section 2.4.1, much work have been carried out tryingto isolate the effect on rolling resistance from specific parameters. Starting with the velocity dependence,studies have shown that the rolling resistance increases with velocity, regardless if one considers dynamicalor stationary tire temperature measurements [30]. In figure 7 the two lines shown indicates the effect ofa velocity increase at equilibrium temperature for given velocity under capped conditions (dotted) and thecorresponding effect under regulated conditions, hence constant temperature measurement (dashed dotted).As indicated a velocity increase seems to have the most pronounced effect directly after an increase, i.e. atconstant temperature.3 The results from the study illustrated in figure 7 also suggest a linear behaviour inthe velocity span vx [40,80] kmh1 [30].

An explanation of this indicated result may be that as the velocity increases, it takes a certain timefor the tire temperature to stabilise under the alternated condition [31]. Since a higher velocity results ina higher deformation frequency, increasing the tire temperature and thereby the inflation pressure as timegoes, it will evidently decrease the magnitude of deformation and hence the rolling resistance [29, 32].Studies indicate that an increased initial inflation pressure generates a lower rolling resistance than for alower initial inflation pressure under the same conditions [30].

When considering the effect of road structure one enters a less easily quantifiable area. The effect ofroad structure is therefore often separated into unevenness i.e. irregularities 0.25 m and macrotexture i.e.irregularities within 103 101 m. Both parameters suggest that an increase in irregularities increasesthe rolling resistance. However studies indicate that macrotexture has a more significant effect on rollingresistance [33]. Also, dependent on the paving and structure of the roadway, more or less energy may betransferred into the roadway, e.g. heating of the road, and thereby affect the rolling resistance [34].

Ambient parameters such as temperature TAir, pressure PAir, direct sunlight, participation etc. will alsohave a non negligible influence on the rolling resistance coefficient. These parameters both directly affect

3Sadly, the study was not performed on the same tire, as shown in the legend of figure 7, which could hence have affected thepronounced result.

12


40 45 50 55 60 65 70 75 80

6.8

7

7.2

7.4

7.6

7.8

vx [km/h]

Crr

i[k

g /to

n]

Capped: 295/75R22.5Regulated: 385/65R22.5

Figure 7: The effect that a velocity change has on rolling resistance considering both a capped and regulatedmeasurement for two different kinds of tires [30].

the tire temperature and pressure and indirectly via heating of and/or cooling from the roadway.Considering the actual tires, studies have shown that a larger circumference of the tire generates a larger

rolling resistance, since it directly increases the area of contact between the roadway and the tire. Also,wear, or rather tread depth, have a pronounced influence on the rolling resistance. A brand new tire tendto have a larger rolling resistance then when it is worn down. Probably due to that the tire crown will haveless material and therefore less material will be deformed in the deformation cycle [30]. Of course thematerial design of the pneumatic tire also have a major influence on the rolling resistance, as it defines itsviscoelastic nature discussed in section 2.3.

2.4.3 Existing modelsDue to the complexity that is rolling resistance, mathematical models have to make one or more ques-tionable assumptions, as mentioned in section 1.1. Some of these models consider stationary conditionswhilst other aim to model the dynamical effects. Hence the numerous of models for the rolling resistancecoefficient of an HDVs tire available in literature. The simplest model suggested is a constant value forCrr, where different values have been suggested e.g. Crr = 7 kgton1. If available it is however custom touse the Crr-value according to the rolling resistance labelling on each tire4 [7, 35, 36].

The most commonly used models considers some kind of polynomial velocity dependence, whereof thesimplest models suggest a linear dependence. Such a model is implemented in e.g. VO and shown below,

Crr =Crr1 +Crr2vx (11)

where the coefficients Crr1 and Crr2 are empirically derived and account for both tire properties and roadsurface conditions [37].

Considering models of higher order, two commonly considered models are shown in equations (12).Both these models consider a second order velocity dependence and neither of the two consider any para-meters besides velocity. The two models do however differ, which is clearly visible in figure 8. The maindifference between the two models is that the one suggested by Wong, i.e. equation (12a), aims to modeldynamical changes in velocity, whilst the model suggested by Michelin, i.e. equation (12b), considersstationary tire conditions [38, 37];

CrrWong = 0.006+0.23 106v2 (12a)

CrrMichelin =Crriso +a(v2x v2iso

)+b(v viso) (12b)

4In accordance with the European tire labelling regulation EC/222/2009. Which refers to the ISO-standards.

13


in equation (12b); Crriso is the Crr-value according to the rolling resistance labelling for given tire in ac-cordance with EC/222/2009 and thereby ISO, where viso usually is 80 kmh1. The coefficients a and bare constant numerical values that are independent of wheel type [7].

0 10 20 30 40 50 60 70 80 90

6

6.5

7

7.5

8

vx [km/h]

Crr

i[k

g /to

n]

CrrWongCrrMichelin

Figure 8: A comparison between the two second order velocity dependent models suggested by Wong andthe manufacturer Michelin shown in equation (12) [7].

In an attempt to capture both dynamic and stationary effects and thereby better describe the actualrolling resistance behaviour during real operating scenarios, a rather advanced model has been developed,shown in equation (13). The model is based on physical principles and considers the velocity v and tiretemperature TTire to be the most dominant parameters that the coefficient of rolling resistance dependsupon. The model assumes that there is a corresponding steady-state temperature TTire for each velocity,resulting in a steady-state curve gsc(v), as expressed in equation (13d). By relating this curve to a stationarycoefficient of rolling resistance in combination with a dynamical model of second order,i.e. Crr = Crr0 + Crr1v

2 (similar to the one suggested by Wong in equation (12a)) and a thermodynamicmodel of the tire described in equation (13c) a complete model is achieved;

Crr(TTire,v) =Crr0(TTire)+Crr1(v2 v2sc

)(13a)

vsc = g1sc (TTire) (13b)dTTire

dt=1

(TTireTTire|v

)(13c)

TTire|v = gsc(v) (13d)

the model consists of two parameters; a velocity coefficient parameter Crr1 and a time constant , thatdescribes the time it takes for a given tire to reach TTire|v . The model also requires this steady-state curvegsc described in equation (13d), and thereby its inverse g1sc expressed in equation (13b) [32, 22].

2.5 Effective radiusWhen applying a vertical load to a deformable tire, such as a pneumatic tire, it causes the tire to compressat the area of ground contact, as illustrated in figure 3, until the average contact area pressure is balanced bythe internal air pressure of the tire [18]. This compression decreases the distance from the centre of the tireto the ground and is denoted loaded radius Rl . When driving, the rotational motion of the wheel creates acentrifugal force which forces the radius to grow, motivating one more radius definition. This non physical

14

2.5. EFFECTIVE RADIUS

radius is the so called effective radius Re illustrated in figure 4 [17]. The effective radius is defined as,

Re =vx

(14)

which in other words means that the effective radius is the radius at which the slip ratio equals zero i.e.no slip, as seen if inserted to equation (7). This fictive radius is often used in models enabling computationsand simulations that neglects slip. It can be shown that the effective radius is limited between the loadedradius Rl and the free radius R, i.e. Rl < Re < R [7]. Worth to notice is also that many of the parameters thataffect rolling resistance also influence the effective radius, due to their correlation with inflation pressure[15, 10].

15

Chapter 3

Method

To investigate the transient nature of rolling resistance on an operating HDV, a series of complete vehicletests have been designed and carried out. Throughout all measurements the same vehicle, measurementset-up, and test track have been used. Below follows a closer look at the equipment used, test track, andcycles driven, ending with a description of the analysis procedure of the measurement data.

3.1 Measurement equipment

3.1.1 Vehicle specificationsThe test vehicle used was a Scania developed truck, manufactured 2009. The most relevant truck specificsare tabulated in table 2.

Table 2: Vehicle specifications for the test truck used.

Parameter SpecificationChassis R440Cab CR19TEngine DC12 10Gearbox GRSO905RShift program OpticruiseAxle gear R780Rear axle ratio 3.08Wheel configuration 4x2

The equipage was completed with a semi-trailer with aerodynamic side-skirts connected to the test truck.The entire equipage, which is illustrated in figure 29 in appendix A.1, had a total weight of M = 40.17 tons.The equipage was equipped with four types of tires from three different manufacturers, all of which arespecified in table 6 in appendix A.2 together with their respective rolling resistance classification, momentof inertia and initial inflation pressure. Especially note that there were different types of tires on thedriving axle, as the right driving wheel was a Yokahama SuperSteel TY 607 whilst the left driving wheelwas a GoodYear Ultragrip WID. Also worth to emphasise is that all tires were radial pneumatic tires ofregroovable type, which had been used for a while and hence quite worn down.

3.1.2 Sensors and experimental set-upTo enable separation of the energy losses associated with rolling resistance and air drag, and prepare fora transient analysis of the rolling resistance the test vehicle described in section 3.1.1 was equipped witha range of additional sensors which together with existing sensors, the standard equipment of the HDV,made up the measurement system. All channels of the build up measurement system was logged via the

16

3.1. MEASUREMENT EQUIPMENT

Data Acquisition (DAQ)-system Dewe43, using the software DewesoftX1. The DAQ-system Dewe43 hadeight analogue channels and two isolated Controller Area Network (CAN)-bus entries, onto which allsensors, besides the used GPS1, was connected. The DAQ was set to ground via the banana plug on itsside decreasing its Signal to Noise Ratio (SNR) [39]. For a detailed description about the channel set-upof the DAQ see table 8 in appendix B. A more thorough description of each measurement device and theinformation taken from it follows below.

CAN

Information from the test vehicles control system was logged using the internal CAN-system. CAN is thestandard vehicle bus systems originally designed by Bosch, which connects numerous sensors and micro-controllers enabling them to communicate according to a sophisticated method without a host computer.The CAN-system at Scania is subcategorised into three buses, denoted green, yellow and red. These busessends information of different priority, i.e. green communicates information of lowest priority, whilst redhandles information of the highest priority [40].

For the measurement system used during the tests considered in this report the yellow CAN-bus wasactive. Connecting the yellow CAN from the diagnostic socket enabled the measurement system to log bothambient parameters such as ambient temperature TAir and pressure PAir, control system data such as enginespeed e and current gear and also monitor tire pressure via the Tire Pressure Monitor system (TPM), asspecified in table 8 in appendix B.

Worth to emphasise regarding the TPM is that it was disconnected on the right hand side of the testvehicle, hence only PA1L and PA2L{i+o} were monitored via the TPM. Also, TPM sends out stacked encryp-ted signals on CAN containing one variable that indicates pressure and another for which tire the pressureis given2. The tire variable is decimal encrypted for the otherwise hexadecimal language of CAN.

Anemometer

Ambient wind affects the energy losses associated with air drag, as described in section 2.1 in accordancewith equation (2). It was hence a highly valued parameter to estimate and therefore measure. This wascarried out by mounting an anemometer 1.45 m above the top of the test truck, at a height denoted hAne,see figure 29 in appendix A.1. This is to minimize the effect of velocity increase of surrounding air as thevehicle operates since it pushes the air in front of the vehicle over itself and hence measure a somewhatundisturbed flow.

The used anemometer was an ultrasonic wind sensor called Windsonic from Gill Instruments. Its work-ing principle was to measure the time of travel for an ultrasonic pulse between four transducers placed ateach cardinal axis, i.e. at {0, 90, 180, 360}, from which it could calculate the air velocity vAne anddirection Ane. The Windsonic sensor was connected to the DAQ via a coaxial cable, to decrease the SNR[41].

Torque sensors

Traction force Fxi and applied torque i relate to each other as expressed in equation (8a). The appliedtorque was therefore of interest and in considered tests measured in two ways. The first method measuredthe torque applied on the input shaft to the gearbox and hence the total applied torque, which was laterdistributed to the two driving wheels by the differential. This measurement was done via the non-invasivesensor Torductor from ABB. Torductor uses the fact that a ferromagnetic material changes its magneticproperty when subjected to a torsional force. Since it measures the torque on the input shaft, considera-tions to the current gear ratio had to be taken, hereafter denoted ABB which thereby includes the lossesdownstream the powertrain. The Torductor were also connected to the DAQ via a coaxial cable to lowerits SNR [42].

To aviod the need of expressing losses along the powertrain and thereby considerations of gear ratios,Scania developed torque hubs that enables measurement of applied torque on each driving wheel, usingstrain gauges mounted on the specially designed wheel hubs. These hubs were originally designed to

1Only a backup velocity reading was connected to the DAQ.2TPM sends out more parameters as well, but these are irrelevant for considered tests and hence disregarded.

17

CHAPTER 3. METHOD

measure the applied torque on the driving wheel i and the temperature inside the hub. The information wasthen wirelessly transmitted from the hubs to the measurement system using Dx telemetry from CAEMAX,which was connected to the DAQ via a coaxial cable.

For the test, the information about the temperature in the hub was irrelevant and therefore modificationsof each temperature sensor were made. Instead of measuring the hub temperature a thermocouple of Type Kwas drilled approximately 35 mm into the shoulder of each driving tire, using a drill of diameter 2.4 mm.Similar to what was done in Gamberg, M thesis work [31]. The thermocouple was then connected to thehub, replacing the pre existing thermocouple. This modification enabled transient measurements of therubber temperature inside each shoulder of the outer driven tire, denoted TA2(R/L) for right (R) and left (L)driving wheel respectively.

GPS

Position, velocity, elapsed time, and distance travelled are important factors of complete vehicle tests.These parameters were logged via a VGPS from Dewetron. The GPS-unit was magnetically mounted onthe cabin top and directly connected to the computer and software via a USB-port. The position parameterslogged from the GPS was longitude x, latitude y, and altitude h. Altitude was given in meters whereaslongitude and latitude were given in absolute values.3 Other logged parameters from the VGPS were thevehicle velocity v, acceleration a, distance travelled l, elapsed time since midnight UTC + 0 t, and thenumber of active satellites.

Miscellaneous sensors

Not all parameters were possible to log via the DAQ, since day-averaged ambient conditions such as hu-midity and temperature TAir were also of interest. Since no ground station was available, weather datafrom close by stations were taken from and supplied by the Swedish Meteorological and HydrologicalInstitute (SMHI), courtesy of Sjstedt, M. This in order to compute the ambient air density Air.

Also, since the mounted thermocouples turned out to be a bit shaky during performed pre-tests, asthey had a tendency to wear off and hence break as a result of the tire deformation, additional temperaturemeasurements were taken on intermittently occasions during the measurement series of constant velocityusing a Fluke 62 Mini Infrared Thermometer Gun. These measurements were taken both on the shoulderand crown for every tire, except the inner tires on the driving axle i.e. TA2{R+L}i.

3.2 Test trackAs consistency was an important factor for the designed tests described below, both for repeatability andcomparisons within and between each test cycle, the same test track was used and driven in a similarmanner throughout all tests. The test track used was Malmby Fairground, situated about 7 km south-eastof Strngns, Sweden at the old airbase with International Civil Aviation Organization ESKS.

The test track shown in figure 9 was asphalt coated, except at the corners where there was a concretepavement. The complete track driven was about 4 km long, whereof the straight part used for measurementaccounted for approximately 1.2 km. The track was consistently driven with the right hand outwards takingonly left turns, denoted LHT , besides during the coastdown measurement where, as explained in section3.3.2, also the opposite direction was driven, i.e. RHT . Noteworthy is that the measurement straight wasalmost level, but not sufficiently enough, so that road grade could be neglected.

3.3 Measurement seriesTwo measurement series were designed to capture and validate the transient nature of the average rollingresistance of the entire equipage used by explicit separation from air drag. The first and major series,described in section 3.3.1, was carried out over two days. The second series, described in section 3.3.2 was

3The quotient of absolute value/60 equals the number of degrees DD, whilst its modulus times 60 gives the number of minutes andseconds MM.SS, enabling the commonly used unit of expression DDMM.SS.

18

3.3. MEASUREMENT SERIES

175.88 176.00 176.12 176.24 176.36 176.48 176.60 176.72 176.84 176.96 177.085918.00

5918.30

5918.60

5918.90

5919.20

5919.50

Longitude

Latitude

Measurement straight

Rest of test track

Figure 9: The test track Malmby Fairground used throughout all measurement series, indicating the com-plete test track (dashed) driven as well as the straight used for measurements (bold), along which allmeasurements for rolling resistance analysis were taken.

carried out at the end of the first measurement day. Each test was performed at the Malmby Fairgroundtrack described in section 3.2 during April 17 and April 24, 2014.

The fundamental idea of the measurement series separation was to use known aerodynamic data i.e.AHDVCd( ), for the test equipage described in section 3.1.1 and illustrated figure 29, and via measurementsof air flow velocity and direction express the air drag Fd according to equation (2). Then by estimationsof both the total traction force Fx, via measurements of the applied torque at constant velocity alternativelywhile coasting in neutral, and the gradient resistance Fg according to equation (1) it was possible to expressthe equipage-average rolling resistance Frr as the remaining energy loss over distance, after subtraction ofair drag, gradient resistance, and possible inertial forces from the applied traction force. All in accordancewith equation (4).

3.3.1 Dynamic to stationarySince it has previously been shown that it takes time for the temperature of a pneumatic tire to stabilize, itwas possible to investigate the transient nature of rolling resistance with respect to the corresponding tiretemperature, by monitoring the temperature as well as the rolling resistance parameters continuously underotherwise close to stationary conditions. This was what the measurement series described below aimed for,over a set of velocities.

Drive cycles

If driving the same road, keeping a constant velocity on a limited area most parameters are constant, besidesthe tire temperature and the parameters affected by it, as well as stochastic parameters such as ambientwind. Therefore, by limiting the number of transient parameters as much as possible, i.e. keeping velocity,roadway properties, ambient parameters, etc. close to constant, one enabled a transient sampling over the

19

CHAPTER 3. METHOD

evolution of tire temperature and hence the parameters affected by its evolution such as tire pressure androlling resistance, as it strives for stationarity.

Using above stated principle, keeping a close to constant velocity for 90 min on given test track, mon-itoring the parameters described in section 3.1.2 continuously, enabled the looked for transient analysis.Then by altering the constant velocity and repeating the same procedure, a transient analysis as the systemof interest dynamically strived towards stationarity was achieved for the considered velocities.

The measurement series was divided into two cycles, where each cycle was performed on separatemeasurement days starting from cold tires as the vehicle had been standing still over night. The firstmeasurement cycle consisted of the velocities v = {20, 80, 20} kmh1, whilst the second measurementcycle considered the velocities v = {30, 60} kmh1 and another measurement at v = 80 kmh1. Eachvelocity was driven for an active driving time of approximately 90 min and held as close to constant aspossible.

During the five first velocities considered, stops were made about every fifteenth minute for about 2 minenabling measurements with the IR-gun as described in section 3.1.2. The velocity change between thesefive velocities were made as fast as possible, limiting the time of acceleration or deceleration. The twominute stops for measurements were not included in the total active driving time of approximately 90 min.

After the measurement at v = 60 kmh1 a break for about 30 min was made 4, measuring the tiretemperature decrease as the vehicle stood still, before making the last 90 min measurement section atv = 80 kmh1 without stopping to make measurements with the IR-gun.

Worth to emphasise is that for all considered velocities only a section of the test track described insection 3.2 and illustrated in figure 9, was considered for the analysis of rolling resistance. On this section,called measurement straight, a close to constant velocity was held, gear shifts were avoided, and also thedriving path was kept straight, minimizing lateral forces. This, as will be noticeable in section 4.2, wasnot possible on the entire track since it is a closed route, that hence includes some turns. These turns weresharp enough so that velocity decreases were required for velocities higher then v = 30 kmh1 and also,of course, when stopping to measure tire temperatures with the IR-gun. That said, as close to constantvelocity around the entire track was aimed for.

Even though measurements for analysis of rolling resistance only were considered on the measurementstraight, continuous measurements were taken around the entire track, besides for the first two consideredmeasurement velocities i.e. v = {20, 80} kmh1. All of this is visible in figure 15, in section 4.2.

Considered vehicle dynamics

As a constant velocity and a straight path was kept over the measurement straight, the velocity over thatpath was considered to be purely longitudinal i.e. v = vx and thereby acceleration assumed to be negligible,i.e. vx 0. By combining these assumptions with equation (8) it was possible to express the belowstated relation,

Fxi =iRe

(15a)

Frr = FxFdFg (15b)

in which all parameters were possible to express according to equations (1), (2) and (14) using measurementdata.

3.3.2 CoastdownA second, more traditional, measurement series was designed to verify and allow comparison with the onedescribed in section 3.3.1. This measurement series used the principle of coastdown described in section2.4.1, i.e. no applied torque and hence no traction force, i = 0 Fx = 0.

Drive cycle

For the considered coastdown test both directions, i.e. LHT and RT H, of the measurement straight wasdriven once for each considered initial velocity vxini . The starting velocities considered in both directions

4i.e. a reasonable time of a lunch break

20

3.4. ANALYSIS

were vxini = {80, 70, 60, 50, 40, 20} kmh1 for which the retardation was allowed along the measurementstraight, upon which the vehicle was kept in a straight path.

Firstly, the entire set of velocities were driven in the LHT -direction and directly after all velocities weredriven in the opposite direction. Both measurement sets started with the initial velocity vxini = 80 kmh

1

and worked subsequently down to vxini = 20 kmh1.

Considered vehicle dynamics

As the second law of motion is stated in equation (4) the change in velocity times the mass equals the sumof considered driving resistances, given that Fx = 0. By expressing the change of velocity as vx = lx t1and computing the contribution to mass from the inertia of rotating interior mrot, according to the data andexplanation in appendix A.3, it was again possible to express the equipage-average rolling resistance usingmeasurement data as shown below.

Frr =(M+mrot) vxFgFd (16)

Note that the contribution to the total equivalent mass mrot from the rotating parts along the powertrain wasrelatively small, i.e. approximately 4.1% and hence its influence quite negligible, motivating the simplifiedcalculations of e.g. gearbox inertia [4, 28].

3.4 Analysis

3.4.1 Theoretical simplifications and assumptionsConsidered dynamics

As described in section 3.3.1 and 3.3.2 no lateral forces were considered when expressing the dynamics,limiting the amount of algebra and measurement parameters required. This was motivated by keeping thevehicle on a straight path, minimizing lateral forces.

Another simplification required for the considered calculation was to neglect eventual slip, i.e. modelthe system as a no slip system. This was done by using the concept of effective radius and expressing Reas the vehicle velocity according to the GPS over the angular velocity of the driven axle and hence tires5

, which was attained from the the known relation to engine speed e stated below,

=e

FD CG 2

60(17)

using measurement data of current gear, since the gear ratio CG for active gear and final drive FD for theused gearbox was known, enabled one to compute the traction force according to equation (15a).

For the forces in equation (15b) and (16), only averages over each lap of the measurement straight wereconsidered, i.e. each parameter contributing to a force were consistently measured over the measurementstraight upon which respective force was calculated and averaged, besides the gradient resistance. Toexpress the gradient resistance, an estimation of the road grade was required and since no height profileexisted for the used test track a simplification was necessary. Using the height data h and the distancetravelled lx from the GPS it was possible to estimate the road grade as,

tan1(

hlx

)(18)

which together with equation (1) gave an estimation of Fg. Since the altitude data from the GPS wasinconsistent for some of the measurements laps, only a subset of laps were used to estimate a representativeroad grade. This road grade was then assumed constant throughout all computations and hence also thegradient resistance. To decrease the effect of this assumption only the last 600 m of the measurementstraight6 was considered since the slope was approximately constant for that subsection, see figure 11.

5Assuming no slip.6When driving LHT .

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CHAPTER 3. METHOD

A third assumption, mandatory for considered dynamics and analysis, was that the aerodynamic dataAHDVCd( ), for the used test equipage was known and adequate. This data was supplied by the seniortechnical manager of the aerodynamics group at Scania, Elofsson, P, as a third degree polynomial curvevalid for [0,10]. The curve was based on results from wind tunnel tests in combination with detailedconsiderations from e.g. CFD-analysis.7 This curve was an attempt to generate a generic curve and itassumes symmetry of the equipage, i.e. AHDVCd( )=AHDVCd( ). When assuming that the aerodynamicproperties of the equipage was known, computations of Fd was possible using measurement data, aftersome additional considerations of misalignment, misreadings and boundary layer effects were made. Allof which is described below.

Calibrations and measurement considerations

As for any measurement device, calibration is necessary. However for some devices, e.g. the anemometer,additional considerations were needed for a more accurate measurement representation, each time its po-sition was alternated. For the measurement set-up considered, see section 3.1.2, both the torque hubs andanemometer needed extra considerations. The torque hubs were required to be shunted to i 0, after acoastdown to stand still, i.e. v = 0, zeroing the device. This procedure was repeated at the beginning ofeach measurement day.

Another procedure repeated at each measurement day was measurement series for corrections of mis-alignment and velocity misreadings for the used anemometer. This was done by driving the measurementstraight both directions at a high velocity vx 80 kmh1, sampling data from the anemometer. A schem-atic sketch of what the anemometer measured is shown in figure 10, where both directions are illustratedon opposite sides as well as the vehicle velocity vxR/LHT , the wind velocity vWind and resulting anemometerreading of yaw angle and air velocity, i.e. AneR/LHT and vAneR/LHT .

vWindvxLHTvxRHT

vAneRHT vAneLHT AnemometerAneLHTAneRHT

Figure 10: A schematic sketch of the velocities of vehicle vxR/LHT , wind velocity vWind and correspondinganemometer readings, AneR/LHT and vAneR/LHT , when driving the measurement straight both direction underan assumed constant wind.

By assuming that the active wind was constant and weak enough, i.e. vWind 0, one could expressthe average misreading in air velocity vxfac caused when pushing the frontal air over the vehicle top, whichincreased the airflow velocity, by expressing the fraction of the vehicle velocity and anemometer reading forboth driven directions, according to equation (19a). This factor relates the measured air velocity vAneR/LHTwith the actual air velocity as vAir = vxfac vAne [4].

Under the same assumption, should be equal to zero when vWind 0 and aligned properly. Thereforea correction of misalignment was expressible, according to equation (19b).

vxfac =vxRHT + vxLHT

vAneRHT + vAneLHT(19a)

misalign =AneRHT +AneLHT

2(19b)

The anemometer readings still required further considerations, since wind velocity changes with height,as illustrated in figure 1. A well established method to express the wind over an open area is accordingto the logarithmic wind law, where the wind velocity increases exponentially above h = z0, Here z0 isthe surface roughness. However since no measurement of a shear velocity v?, nor measurements on twoheights were made, such a model is vague and requires unmotivated assumptions. Instead, in accordancewith ACEA, the power law boundary layer profile was used, with the exponent blexp = 0.2 [4].

7Due to confidentiality, aerodynamic data will not be given in this report.

22

3.4. ANALYSIS

The first computational step for the power law profile was to express the assumed undisturbed windvelocity both longitudinal vWindx and lateral vWindy components, at the anemometer height h = hAne wherethe air velocity is assumed to be undisturbed after correction for misreading, see equation (20) wheremisalign is the correction for misalignment computed according to equation (19b).

vWindx |h=hAne = vfac vAne cos(Ane +misalign) vx (20a)vWindy |h=hAne = vfac vAne sin(Ane +misalign) (20b)

Then by expressing the wind components according to the power law, i.e. decreasing with height, eachwind component became a function of height.

vWindx(h) = vWindx |h=hAne (

hhAne

)blexp(21a)

vWindy(h) = vWindy |h=hAne (

hhAne

)blexp(21b)

Finally, integrating the functions in equation (21) together with the airflow generated by the vehicle velo-city, between the ground h = 0 and top of the truck h = hHDV , a height averaged air velocity i.e. vAir andyaw angle was expressible.

vAir =1

hHDV

h=hHDVh=0

(Windx + vx)

2 + v2Windy dh (22a)

=1

hHDV

h=hHDVh=0

tan1(

vWindyvWindx + vx

)dh (22b)

Compensating for change in kinetic energy

Previous tests have shown that even small changes in vehicle velocity affect the measurement accuracy, dueto the large equipage weight and its effect on kinetic energy Ek. To compensate for this potential change inkinetic energy an average difference over the measurement straight was expressed, by comparing the kineticenergy coming into and out from the measurement straight divided by corresponding distance travelled,

M(v2out v2in)2 lx

FEk (23)

i.e. the average force acting on the equipage due to the change in kinetic energy. This force was onlycompensated for when considering the method of constant velocities, by adding FEk to the r

Investigation of the transient nature of rolling resistance...

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