Brake and roll-over performance of … · 2010. 3. 26. · Nomenclature Abbreviations DLTR dynamic load transfer ratio RA rearward ampliﬁcation SRT static roll-over threshold YDC

Brake and roll-over performance oflonger heavier vehicle combinations

M.PinxterenDCT 2009.063

Master’s thesis

Coach(es): Dr. Ir. I.J.M. Besselink (Eindhoven University of Technology)

Supervisor: Prof. Dr. H. Nijmeijer (Eindhoven University of Technology)

Members of committee: dr.ir.F.E. Veldpaus (Eindhoven University of Technology)N.A. Jongerius (DAF Trucks N.V.)

Eindhoven University of TechnologyDepartment of Mechanical EngineeringDynamics and Control Group

Eindhoven, March, 2010

Abstract

To overcome several economic and environmental challenges, the Dutch transport sector has intro-duced the so-called "Langere Zwaardere Vrachtautocombinations" abbreviated LZV’s and also knowas Ecocombi’s or Gigaliners, on the Dutch roads. After some experiments where LZV’s are allowed onDutch road under several restrictions, an unrestricted "phase of experience" is started in November2007.

This thesis contributes to the research done on the dynamic behaviour of LZV’s at the EindhovenUniversity of Technology since 2006. Previous research focussed on manoeuvrability and roll-overstability. The goal of this thesis is to gain insight on the braking performance of LZV’s and extensionof the roll-over research by means of multi-body models.

To evaluate braking performance and roll-over stability, the previously developed "TU/e-CommercialVehicle Library" is improved and extended with a brake system and several brake and roll-over sce-nario’s are defined. Scenario’s used for braking performance evaluation are braking in a straight lineon different road conditions, braking while driving a steady state circle and braking during a highwayexit. A steady state circle, a spiral, a single and double lane change are simulated to analyse roll-overstability.

After execution and evaluation of the braking scenario’s the conclusion is drawn that each LZVand conventional heavy vehicle obeys legal demands regarding brake force distribution with the im-plemented brake system. It is also shown that ABS improves the performance in critical situations byshortening the stopping distance on a dry, wet and µ-split road and by preventing jackknifing whenbraking on a µ-split road. For braking during a circle it is shown that the vehicles become oversteeredwhen the brakes are applied but no other conclusions can be draw because results contradict, the bestperforming vehicles regarding path deviation are the worst performing vehicles regarding neededsteer adjustments and vice versa. When comparing the braking performance between LZV’s mutuallyand conventional commercial vehicles, it can be concluded that braking performance of LZV’s is equalto the braking performance of conventional vehicles. No distinct differences are found.

Evaluation of the roll-over scenario’s show that the static roll-over thresholds are almost equal forall vehicles. By means of more dynamic roll-over scenario’s, distinct differences between vehicles areidentified. Vehicles having a low yaw damping perform worst regarding roll-over. When comparingLZV’s and conventional vehicles it can be concluded that LZV’s roll-over more easily. Another con-clusion is that all vehicles are most sensitive to roll-over when the frequency of the disturbance layswithin a band of 0.1 Hz and 0.6 Hz, which is well within the frequency band utilised by a human driverwhen performing a emergence steering manoeuvre. Steering frequencies above 2.5 Hz do not causeroll-over.

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iv

Samenvatting

Met het introduceren van de "Lange Zware Vrachtautocombinaties", afgekort als LVZ en ook bekendals Ecocombi of Gigaliner, op de Nederlandse wegen wil de Nederlandse transport sector een deel vande economische en milieutechnische problemen oplossen. Na eerdere experimenten loopt er sindsnovember 2007 er een zogenaamde ervaringsfase waarbij LZV’s gebruikmaken van de Nederlandsewegen. In deze ervaringsfase geldenminder strikte voorwaarden dan tijdens de eerdere experimenten.

Dit rapport is onderdeel van het onderzoek naar dynamisch gedrag van LZV’s uitgevoerd aan deTechnische Universiteit te Eindhoven sinds 2006. Eerder onderzoek had tot doel om de wendbaarheiden het kantelen van LZV’s te beoordelen. Dit onderzoek heeft als doel het verkrijgen van inzicht en hetbeoordelen van de remprestatie van LZV’s en het uitbreiden van het onderzoek naar het kantelen vanLZV’s. Tijdens het voorgaande en het hier beschreven onderzoek is gebruik gemaakt van multi-bodymodellen.

Voordat de remprestaties en het kantelgedrag van LZV’s konden worden onderzocht, is de eerderontwikkelde "TU/e-Commercial Vehicle Library" verbeterd en uitgebreid met een remsysteem. Hiernazijn remmen in een rechte lijn op verschillende ondergronden, remmen tijdens een steady-state cirkelen remmen tijdens het nemen van een afslag gesimuleerd om de remprestatie te beoordelen. Doormiddel van een steady-state cirkel met toenemende snelheid, een spiraal met constante snelheid, eenenkele en dubbele baanwisseling is het kantelen van de verschillende voertuigen beoordeeld.

Aangaande de remprestaties kan geconcludeerd worden dat zowel de LZV’s als de conventionelevoertuigen voldoen aan de wettelijk geldende eisen met betrekking tot de remkrachtverdeling. Daar-naast is er aangetoond dat ABS de remprestaties verbeterd tijdens kritische remmanoeuvres, wat re-sulteert in kortere remwegen tijdens het remmen op zowel een droog, een nat en een µ-split wegdek.Daarnaast wordt scharen tijdens remmen op een µ-split wegdek voorkomen. Omtrent het remmenin een bocht kan worden geconcludeerd dat het remmen in een bocht resulteert in een overstuurdvoertuig. Omdat de resultaten gevonden voor remmen in een bocht elkaar tegenspreken is het onmo-gelijk om verdere conclusies te trekken aangaande de remprestaties van de diverse voertuigen tijdenshet remmen in een bocht. In algemene zin geldt dat de resultaten van dit onderzoek geen duidelijkeverschillen aantonen tussen LZV’s onderling en tussen LZV’s en conventionele voertuigen.

Het onderzoek naar kantelen van LZV’s laat geen duidelijke verschillen zien in quasi-statischekantelgrens van de verschillende voertuigen. Uit de meer dynamische manoeuvres blijkt dat er weldegelijk verschillen aanwezig zijn wat betreft kantelen, de voertuigen met een lage gierdamping kan-telen het snelste. Ook kan geconcludeerd worden dat LZV’s sneller zullen kantelen dan conventionelevoertuigen. Uit de resultaten blijkt daarnaast dat alle voertuigen het gevoeligste zijn voor kantelen,wanneer de frequentie van de input, welke de rotatie rond de longitudinale as veroorzaakt, ligt tussen0.1 en 0.6 Hz. Deze frequentieband is ook de frequentieband welke een menselijke bestuurder intro-duceert tijdens sturen in een noodsituatie. Frequenties boven de 2.5 Hz zullen geen kantelen veroorza-ken.

v

vi

Contents

Abstract iii

Samenvatting v

Contents viii

Nomenclature ix

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Aim and scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Outline of the report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Literature survey 52.1 Theory behind braking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Brake/BFD models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 ABS logic and ABS models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Legislation regarding brake systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5 Roll-over of commercial vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 TU/e-Commercial Vehicle Library 213.1 Introduction into the "TU/e-Commercial Vehicle Library" . . . . . . . . . . . . . . . . 21

3.2 Dimensions and masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Tyres and tyre characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 Brake system module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.5 Driver model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4 Braking performance of LZV’s 334.1 Straight line braking without ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 Straight line braking with ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3 Braking while driving a circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.4 Braking while taking a highway exit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.5 Summary of braking performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5 Roll-over stability of LZV’s 515.1 Static roll-over threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.2 Dynamic roll-over, single lane change . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.3 Dynamic roll-over, double lane change . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.4 Dynamic roll-over, parameter study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.5 Summary of roll-over stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

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viii CONTENTS

6 Conclusions and Recommendations 696.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Bibliography 73

A LZV configuration A A–1

B LZV configuration B B–1

C LZV configuration C C–1

D LZV configuration D D–1

E LZV configuration E E–1

F LZV configuration F F–1

G LZV configuration G G–1

H Tractor semitrailer H–1

I Truck trailer I–1

J Truck drawbar-trailer J–1

K Tyre characteristics K–1

Nomenclature

Abbreviations

DLTR dynamic load transfer ratioRA rearward amplificationSRT static roll-over thresholdY DC yaw damping coefficientABS anti-lock brake systemBFD brake force distributionC.G. centre of gravityDOF degree of freedomLZV longer heavier vehicle combination

Symbols

Symbol Definition Unit

Ac brake chamber area [m2]Ai amplitude of cycle i [−]Cκ longitudinal tyre stiffness [N/m]Cφ roll-stiffness of suspension [Nm/rad]Fbr, fr brake force at front axle [N ]Fbr, re brake force at rear axle [N ]Fbr, tr brake force at trailer axle [N ]Fbr brake force per wheel [N ]Fx longitudinal force [N ]Fy lateral force [N ]Fz, axle actual axle load [N ]Fz, fr normal force at front axle [N ]Fz, re normal force at rear axle [N ]Fz, static static axle load [N ]Fz, tr normal force at trailer axle [N ]Fz vertical force [N ]Jwheel moment of inertia of wheel [kgm2]Jxx moment of inertia around x axis [kgm2]Jyy moment of inertia around y axis [kgm2]Jzz moment of inertia around z axis [kgm2]Kspring spring stiffness [N/m]M vehicle mass [kg]Mbr brake torque [Nm]Pc air pressure of brake chamber [bar]

ix

x NOMENCLATURE

Pl brake line air pressure [bar]Qfr brake force proportion coefficient of front axle [−]Qre brake force proportion coefficient of rear axle [−]Qst brake force proportion coefficient of semitrailer axle [−]Rdp effective radius through which µdp acts [m]Re effective tyre radius [m]Rtyre effective tyre radius [m]T track width [m]Vx longitudinal velocity of the vehicle [m/s]

d unit vector of direction vector of the vehicle [−]adesired desired deceleration [m/s2]ax, lock longitudinal deceleration at which wheel lock occurs [m/s2]ax longitudinal acceleration [m/s2]ay, peak lateral peak acceleration [m/s2]ay lateral acceleration [m/s2]d damping constant of suspension [Ns/m]dm mean fully developed deceleration [m/s2]g gravitational acceleration [m/s2]h height of chassis [m]hc.g.,rc height centre of gravity w.r.t. roll axis [m]hc.g. height of centre of gravity [m]hr height roll centre w.r.t. road [m]k required tyre road friction coefficient [−]kfr required tyre road friction coefficient for front axle [−]kre required tyre road friction coefficient for rear axle [−]ktr required tyre road friction coefficient for trailer axle [−]l length of chassis [m]ld look-ahead vector [m]n number of cycles [−]sspring spring deflection [m]sstop stopping distance [m]td total time delay of valves and pneumatics [sec]tla look ahead time [sec]w width of chassis [m]xfr position vector of front axle [−]xre position vector of rear axle [−]z dimensionless acceleration [−]

α side slip angle []δ logarithmic decrement [−]δs steering angle []ψ yaw velocity [/s]κaxle longitudinal slip of an axle [−]κ longitudinal tyre slip [−]µ friction coefficient [−]µdp friction coefficient between brake disk and brake pads [−]µh highest friction coefficient [−]µl lowest friction coefficient [−]Ω angular wheel speed [rad/s]φ roll angle []ψ yaw angle []τ time constant [sec]

Chapter 1

Introduction

1.1 Background

In recent years, the Dutch transportation sector was facing several economic and environmental chal-lenges. There is an increasing demand for transportation while there is a lack of truck drivers, theDutch and European roads are crowded and the pollution of the vehicle park has to decrease. To over-come these challenges, the Dutch transportation sector decided to introduce the so-called "longer andheavier vehicles" at the Dutch roads. These "longer and heavier vehicles" are already common on theScandinavian roads. The "longer and heavier vehicles" are also known as Ecocombi’s or Gigalinersand in the Netherlands common known as LZV’s.

The Dutch LZV’s are allowed to have a maximum length of 25.25 m and a maximum gross vehicleweight of 60.000 kg, instead of 18.75 m and 50.000 kg allowed by Dutch legislation for conventionalvehicle combinations. The number of turning points within these dimensions is restricted to a max-imum of two. Because of the bigger dimensions, LZV’s offer a more efficient transportation conceptthan the existing vehicle concepts. Several field experiments show that using LZV’s on the Dutchroads, leads to an average fuel reduction of 30 % when transporting the same amount of goods and areduction in air pollution between 3 and 5 %. Also the price per ton per kilometre decreases with 25 %and the number of traffic jams reduce with 0.7 till 1.4 % [28]. In November 2007 a so-called "phase ofexperience" has started. The phase of experience ends at the first of November 2011 and during thisphase the amount of LZV’s allowed on the Dutch roads is unrestricted.

In 2006, Eindhoven University of Technology started a project to analyse the dynamic behaviourof the different LZV configurations. By means of the multi-body package SimMechanics, a "TU/e-Commercial Vehicle Library" containing all possible LZV units was created. By connecting differentcomponents of the library all possible LZV and conventional vehicle can be modeled and analysed.The LZV configurations allowed on Dutch roads are shown in figure 1.1. G. Isiklar [18] uses this li-brary to build multi-body models and analyses the dynamic performance of the different LZV’s andalso compares the LZV’s with a conventional tractor semitrailer combination. The research consistsof a static analysis, a swept path analysis, and off-tracking at low and high speed. The roll-over perfor-mance of each LZV is examined by performing a steady turn with fixed radius and increasing velocityand a SAE lane change manoeuvre. In [18] it is concluded that LZV configuration B and F, see figure1.1, possess the worst swept path performance, both configurations have swept path widths in excessof 8 m which is the limit imposed by Dutch law. These configurations also show the worst low speedoff-tracking behaviour. Another conclusion is that LZV configuration E has the worst high speed off-track performance. With respect to roll-over performance, the conclusion is drawn that LZV G showsthe best steady state roll-over performance while LZV F performs the best and LZV E the worst atthe SAE lane. Afterwards, the "TU/e-Commercial Vehicle Library" was improved further by I.J.M.Besselink. By means of the study of Isiklar and the improved "TU/e-Commercial Vehicle Library" itcan be observed that there seems to be a tradeoff between manoeuvrability and roll-over stability, themost manoeuvrable LZV has the worst roll-over stability [17].

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2 CHAPTER 1. INTRODUCTION

Figure 1.1: the LZV congurations allowed on Dutch roads

1.2 Aim and scope

This thesis is divided into two parts, both have more or less the same aim, namely to get more insightin the dynamic behaviour of LZV by means of multi-body models. The aim of the first part is to getmore insight in the dynamics of LZV’s and conventional commercial vehicles during braking. The aimof the second part is to extend the knowledge about roll-over of LZV’s and conventional commercialvehicles. When achieving both aims, difference in braking performance and roll-over stability betweenLZV’s mutually and between LZV’s and conventional vehicles could be identified.To achieve above aims, the next steps are necessary:

• Check and, when necessary, improve the "TU/e-Commercial Vehicle Library" and themulti-bodymodels as described in [18].

• Implement a brake system into the multi-body models. After implementation of the brake sys-tem, braking performance of LZV’s and conventional commercial vehicles is analysed.

• Analyse roll-over stability of conventional commercial vehicles and LZV’s by means of quasi-static and dynamic manoeuvres which could lead to roll-over.

1.3. OUTLINE OF THE REPORT 3

1.3 Outline of the report

Chapter 2 contains a literature survey. The first subject of the literature survey is the braking system.The braking system part treats the theoretical background behind the brake force distribution forcommercial vehicles and anti-lock brake systems and it summarises legal demands regarding brakingof commercial vehicles. The second subject of the literature survey are the mechanics behind roll-overand roll-over stability of commercial vehicles.

Chapter 3 describes the most recent version of the "TU/e-Commercial Vehicle Library". The chap-ter starts with a short explanation about the library. After this explanation the chapter continuous anddescribes the modifications at the dimensions and masses of each unit of the library, modificationof the tyre properties. After this modifications, the development and implementation of the brakingsystem containing a brake force distribution part and an anti-lock brake system part, is described. Thelast subject of chapter 3 is the revised and improved driver model and its implementation.

In chapter 4 the braking performance of the conventional commercial vehicles and the LZV’s areevaluated. Manoeuvres studied are braking in a straight line without and with ABS on a dry, wet andµ-split road, braking when driving a circle and braking while taking a highway exit.

Roll-over stability is the subject of chapter 5. First, the static roll-over thresholds are determined bymeans of driving a circle with constant radius and increasing speed and a spiral with constant speedbut decreasing radius. After these quasi-static manoeuvres roll-over stability is evaluate for moredynamic manoeuvres. Manoeuvres studied are a single and double lane change, where the single lanechange is used also at a small parameter study in which the longitudinal velocity, the damping ratioand the roll stiffness of the vehicle is varied.

Chapter 6 finalises this report and it draws the conclusions of this research and it also gives therecommendations for future studies regarding the dynamic behaviour of LZV’s.

4 CHAPTER 1. INTRODUCTION

Chapter 2

Literature survey

This chapter presents the theoretical background behind brake force distribution and roll-over stabilityof commercial vehicles. Besides this theoretical background, the legislation regarding brake systemsof commercial vehicles is summarised and an overview of brake/brake force distribution and ABSmodels found in literature is given.

2.1 Theory behind braking

In their report R.W. Murphy et al [22] note that during braking, the kinetic energy of the vehicle isconverted into heat at the friction surface of the brake linings and at the tyre road contact. Accordingto this report, the deceleration achieved depends on the brake force developed by the brakes, the adhe-sion between tyre and road and the vertical force on the tyre which varies during braking because ofload transfer over the axles of the vehicle. Commercial vehicles are equipped with a pneumatic brakesystem. The fundamental principle utilised in pneumatic brake systems is pressure equalization be-tween two volumes, the volume of the air reservoirs and the sum of all brake chambers and connectingair pipe volumes respectively. A schematic drawing of a simplified pneumatic brake system is shownin figure 2.1.

Figure 2.1: simplied pneumatic brake system [22]

L. Segel et al [21] evaluate possibilities to come to a ideal brake force distribution, abbreviate asBFD, for a tractor semitrailer combination. They start the evaluation by formulating the equations ofmotion of a tractor semitrailer combination when braked. A free-body diagram of a tractor semitraileris shown in figure 2.2.

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6 CHAPTER 2. LITERATURE SURVEY

Figure 2.2: free-body diagram of a tractor semitrailer combination during braking

Via the free-body diagram, the equations of motion are derived as below.The vertical force balance of tractor semitrailer combination;∑

Fz, tractor semitrailer = 0

Fz, fr + Fz, re + Fz, st − (M g +Mst) g = 0 (2.1a)

The longitudinal force balance of tractor semitrailer combination;∑Fx, tractor semitrailer = 0

(M +Mst) ax + Fx, fr + Fx, re + Fx, st = 0 (2.1b)

Summing the moments about the fifth wheel coupling of the tractor yields;∑M5th wheel = 0

(Fx, fr + Fx, re) h5th + Fz, re (wb− x5th)− Fz, fr x5th+M g (x5th − xcg) +M ax (hcg − h5th) = 0 (2.1c)

and the sum of moments about the coupling pin of the trailer can be written as;∑Mpin = 0

Fx, st h5th + Fz, st wbst −Mst xcgst +Mst g ax (hcgst − h5th) = 0 (2.1d)

At the above equations of motion, the vertical and longitudinal tyre forces of the semitrailer are lumpedtogether in one vertical and one longitudinal force.

Fx, st =i∑Fx, st,i (2.2a)

2.1. THEORY BEHIND BRAKING 7

and

Fz, st =i∑Fz, st,i (2.2b)

where

i = number of axles

After deriving the equation of motion, a brake force distribution is introduced by means of;

Fx, fr = Qfr ax (M +Mst) (2.3a)

Fx, re = Qre ax (M +Mst) (2.3b)

Fx, st = Qst ax (M +Mst) (2.3c)

where

Qfr +Qre +Qst = 1Qfr = 1−Qre +Qst

A relation between Fz and Fx is introduced for each axle also. This relation is know as the requiredfriction k.

Fx, fr = kfr Fz, fr (2.3d)

Fx, re = kre Fz, re (2.3e)

Fx, st = kst Fz, st (2.3f)

According to [21], k is the minimum friction level between tyre and road needed to reach a given decel-eration with a specified fixed brake force distribution meaning a specified fixed set ofQfr,Qre andQst.By solving the equation of motions for a given deceleration and various brake force distributions, thusdifferent Qfr, Qre and Qst values, so-called "braking diagrams" are constructed. In these diagrams,the lines of equal kfr, kre and kst form triangle shaped regions and any brake force distribution layinginside a triangle will brake the tractor semitrailer at the given deceleration and level of k without wheellock. Figure 2.3 is an example of such a braking diagram, in this case for a laden tractor semitrailer dur-ing braking with −5.9 m/s2 or z = 0.6. The point in figure 2.3 where kfr = kre = kst = 0.6 intersect,indicated with a black dot, represents the ideal distribution of brake force for the specific case shownin [21]. This indicated brake force distribution is the only proportion which leads to ax = −5.9m/s2

on a road with µ = 0.6. If µ is interpreted as the peak of the µ− κ curve, then any set of Qfr, Qre andQst within the triangular region ki ≤ 0.7, can produce a deceleration of −5.9 m/s2 without locking ofone of the wheels at µ = 0.7.

By constructing braking diagrams for several decelerations and loading conditions, it is illustratedthat it is difficult or even impossible to meet braking requirements when using a fixed brake forcedistribution. In [21] the suggestion is made that the brake force distribution should vary with operatingconditions by means of a load sensing valve. To support this suggestion, ideal braking is assumed anddefined as;

Fx(i) = k Fz(i) (2.4a)

where

k =axg

= z (2.4b)


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Qfr [−]

Qre

[−]

kfr

kre

kst

0.80.70.60.50.4 0.9 1.0Qst

Qst

0.8 0.7 0.6 0.5 0.40.91.0

0.80.70.60.50.4

0.91.0

Figure 2.3: braking diagram for a tractor semitrailer, ax = −5.9 m/s2 [21]

Substitution of 2.4a and 2.4b into (2.3a), (2.3b) and (2.3c) yields to ideal brake force distribution,namely;

Qfr =Fz, frFz, total

(2.5a)

Qre =Fz, reFz, total

(2.5b)

Qst =Fz, stFz, total

(2.5c)

where

Fz, total = Fz, fr + Fz, re + Fz, st (2.5d)

The study of [21], result in the conclusion that ideal brake force distribution is accomplished if everyaxle brakes its own load, as stated by (2.5a), (2.5b) and 2.3c and that the axle loads depend on thedeceleration during braking.

Brake force distribution on commercial vehicles is also discussed by M. Haataja [14] and N.A Jon-gerius [19]. Although they use different approaches, both observe that ideal brake distribution canonly be accomplished when every axle brakes its own load. According to [14], ideal brake force dis-tribution is based on maintaining the steering response in all braking situations and to achieve theshortest stopping distance possible. Another target of the brake force distribution is to avoid unnec-essary wheel lock-up, providing stable vehicle behaviour and a minimum of tyre wear. This target isreached by balancing the brake force such, that all tyres simultaneously arrive at their longitudinal sliptop. The location of the slip top depends on vertical wheel load, lateral wheel load, tyre material, roadtype, etc. Thus a fixed brake force distribution is not suitable for heavy commercial vehicles becauseof the variation in loading conditions [19].

2.2. BRAKE/BFD MODELS 9

2.2 Brake/BFD models

M.W. Suh et al, [26], used mathematical models to developed a computer simulation to investigate theinfluence of the brake system design on the dynamic behaviour of a tractor semitrailer combination.One of the mathematical models of [26] describes the air pressure response of a pneumatic brakesystem by means of the first-order system of equation;

Pc =1

τs+ 1Pl, max (2.6)

where

Pc = air pressure of brake chamber [bar]τ = time constant [sec]Pl, max = maximum brake line air pressure [bar]

A slightly different approximation for the air pressure response is used by D. Cebon [3], as defined by;

Pc =Pl

τs+ 1e-tds (2.7)

where

td = total time delay of valves and pneumatics [sec]

The tractor semitrailer modeled in [26] is equipped with drum brakes, but most today’s commercialvehicles are equipped with disc brakes instead. The brake torque developed by disc brakes as functionof brake line air pressure is defined in [3] by;

Mbr = 2 Ac Pc µdp Rdp (2.8)

where

Ac = brake chamber area [m2]µdp = friction coefficient between brake disk and brake pads [−]Rdp = effective radius through which µdp acts [−]

The previous section has made clear that commercial vehicles needs a variable BFD to meet sufficientbraking performance under various conditions. P.Frank [12] develops a variable BFD for a two axleroad vehicle by using the difference in longitudinal tyre slip between axles. According to [24], thelongitudinal tyre slip is defined as;

κ = −Vx −Re ΩVx

(2.9)

where

κ = longitudinal tyre slip [−]Vx = longitudinal velocity of the vehicle [m/s]Re = effective tyre radius [m]Ω = angular velocity of wheel [rad/s]

(2.10)

The above definition holds for a single wheel. By taking the average of the longitudinal slip of the tyresmounted on an axle, the longitudinal axle slip is calculated.

κaxle =κleft + κright

2(2.11)


where

κaxle = longitudinal slip of an axle [−]κleft = longitudinal tyre slip at left wheel [−]κright = longitudinal tyre slip at right wheel [−]

By assuming that

Vx ≈ ReΩ

and that the angular wheel speeds are equal for each wheel of an axle, e.g. driving straight ahead, thedifference in longitudinal axle slip between the front and the rear axle of a vehicle can be calculated.

∆κaxle =Re,fr Ωfr −Re,re Ωre

Re,fr Ωfr(2.12)

where

fr = front axle

re = rear axle

The objective of the brake force distribution controlled by means of longitudinal slip of axles, is toachieve that the difference between axles is approximately zero. If this slip control is successful, theoperation point of the wheels in the Fx

Fz

- κ graph will coincide which means that the brake force isdistributed in such a way that every axle brakes its own load.

Besides using the longitudinal axle slip to balance braking forces, another solution is mentionedin [19]. This second approach is a more practical approach where an air valve regulates the pressureto the brakes an axle. The valve senses the axle load via the air pressure in the air bellows of thesuspension. This pressure is the control variable. A high pressure in the air bellows means a highaxle load thus a high brake line pressure is needed while a low air bellow pressure means a low axleload which results in a low brake line pressure. Load sensing valves have been in use on commercialvehicles for many years, since the mid 70’s until the mid 90’s. Around that time commercial vehicleswere equipped with ABS and angular wheel speed sensors and now days most commercial vehiclescontrol the brake force distribution based on the longitudinal slip approach.

2.3 ABS logic and ABS models

To prevent wheel lock and in this way unwanted vehicle behaviour, anti-lock brake systems abbreviatedas ABS, are developed. This section summarises the logic behind ABS and the ABS models found inliterature.

F.W Kienhöfer [20] explains the mechanics behind ABS by means of figure 2.4. The diagram atthe top left show the forces and moments on a braked wheel,which is used to derive the equations ofmotion for a braked wheel yielding;

Jwheel Ω = Mbr − Fx Re (2.13)

where

Jwheel = moment of inertia of wheel [kgm2]Mbr = brake torque [Nm]Fx = longitudinal force at tyre-road contact [N ]Re = effective tyre radius [m]

2.3. ABS LOGIC AND ABS MODELS 11

Figure 2.4: mechanics behind ABS [20]

Figure 2.4 also displays the road friction moment versus longitudinal tyre slip at the below left. Theright handed side of figure 2.4 displays time histories of several vehicle variables. The top right figuredisplays the longitudinal vehicle and the longitudinal wheel speed, the middle right figure shows theacceleration of the wheel and the bottom graph shows the brake torque. The nummers 1 till 4 in thefigure 2.4 indicate points of action for an ABS.

At point 1, the angular wheel acceleration is negative, so the right hand side of (2.13) is alsonegative which means Mbr > ReFx and the angular speed of the wheel will decrease. In otherwords, the wheel brakes and the operation point of the tyre shifts to the right in the longitudinal tyreslip curve, still maintaining a stable angular deceleration of the wheel till point 2. At operation point2, the tyre slip curve reaches its maximum and a further increase of the brake torque to the level of"Mbr2", leads to a rapidly decrease in angular wheel speed and wheel lock is imminent. The rapidlydecrease of the angular wheel speed is detected by the ABS algorithm because it exceeds the "predictionthreshold" and the ABS reduces the brake torque to the level of "Mbr3" level. At operation point 3, theleft hand side of (2.13) becomes positive again and the operation point of the tyre shifts back to theleft of the tyre slip curve. The wheel accelerates until it reaches the stable region of the tyre slip curveagain, indicated by operation point 4. At operation point 4 the acceleration of the wheel exceeds the"reselection threshold" and the brake torque is increased again by which the ABS control cycle startagain.

In [20] the "prediction" and "reselection threshold" are estimated by curve fitting of experimen-tally measured brake chamber pressures. The "prediction threshold" is exceeded at a deceleration of−22.6 m/s2 and the "reselection threshold" is exceeded when the angular wheel velocity exceeds thequotient of the acceleration of the vehicle and the effective tyre radius, thus when

Ω >VxRe

After derivation of these thresholds, they are implemented in a "bang-bang" controller to simulate anABS and verify the simulations results with experimental measurements. The remark is made that


controlling longitudinal tyre slip would improve ABS performance but no further details about such acontroller are mentioned in [20].

The report of D. Cebon [3] does describe an ABS which controls the longitudinal tyre slip, ac-tually his research results from the conclusions drawn in [20]. The ABS developed in [3] uses thesame pneumatic components but a gain-scheduled longitudinal tyre slip controller is used instead ofa "bang-bang" controller. A transfer function between the longitudinale tyre slip and the brake linepressure is derived. Derivation of this transfer function starts by taking the time derivative of thelongitudinal tyre slip (2.9) which results in;

κ =Re Ω− Vx

Vx(2.14)

When taking into account that the longitudinal velocity varies much slower than the other variablesinvolved, one can assume

Vx ≈ constant and Vx = 0

and by substituting (2.13) into (2.14) the tyre slip dynamics are obtained;

κ Vx =R2e

JwheelFx −

Re

JwheelMbr (2.15)

The lateral tyre force is linearised around a specific longitudinal tyre slip by stating

Fx = Cκ κ (2.16)

where

Cκ = longitudinal tyre stiffness at specified κ [N/m]

and by substitution (2.16), (2.8) and (2.7) into (2.15) the desired transfer function is obtained:

HPl, κ =e-tds

τs+ 1−Re

Vx Jwheel s− Cκ R2e

2 Ac µdp Rdp (2.17)

Because these plant dynamics vary with the longitudinal vehicle velocity, a gain-scheduled controlleris added to the ABS. The final block diagram of the gain-scheduled controller is shown in figure 2.5.

Figure 2.5: block diagram of gain scheduled ABS [3]

Comparison between the developed κ control strategy and the "bang-bang" strategy of [20] showsencouraging initial results. Although the stopping distance sstop increases with approximate 10 %because of poor ABS valve response, τ ≈ 1 sec, the mean fully developed deceleration increases by6 %.

2.4. LEGISLATION REGARDING BRAKE SYSTEMS 13

2.4 Legislation regarding brake systems

Regarding laws on brake systems of road vehicles, the European Commissions published CouncilDirective 71/320/ECC of 6 February 1970 [5] and Council Directive 98/12/EC 0f 27 Januari 1998[8]. Commission Directive 98/12/EC is a revision of Council Directive 71/320/ECC in which techni-cal progress in braking devices us taken into account. Commission Directive 98/12/EC defines themost recent definitions, functions and requirements for brake systems. Annex II of Council Directive98/12/EC [8] is called "braking tests and performance of braking systems" hold the legal demandsregarding braking performance of commercial vehicles, the relevant demands are summarized in thissection.

The performance of the brake system is based on the stopping distance and/or the mean fullydeveloped deceleration. The stopping distance, sstop, is the distance covered by the vehicle betweenactuation of the brake pedal and standstill of the vehicle. The mean fully developed deceleration, dm,is calculated with;

dm =v2b − v2

e

25.92 (se − sb)(2.18)

where

dm = mean fully developed deceleration [m/s2]vb = 0.8 v1 [km/h]ve = 0.1 v1 [km/h]v1 = initial vehicle speed [km/h]sb = distance traveled between v1 and vb [m]se = distance traveled between v1 and ve [m]

During the test the vehicle has to maintain its course, without abnormal vibrations and wheel lock isonly permitted when specifically mentioned. To pass the legal demands the brake system performancehas to satisfy the next requirements;

• The mean fully developed deceleration, dm, on a flat road and an initial velocity, Vx, of 60 km/hfor a loaded as well as an unloaded vehicle should be minimal 4 m/s2 when the engine is con-nected and minimal 5 m/s2 when the engine is unconnected. For the stopping distance, sstop, itholds that sstop ≤ 0.15 v1+ v12

130 with uncoupled engine and sstop ≤ 0.15 v1+ v12

103.5 with coupledengine respectively. The requirements on both the mean fully developed deceleration as well ason the stopping distance have to be met and during the test the force applied to the brake pedalshould not exceed 700 N

• The brake force has to be distributed among the axles of the vehicles in such a way that 0.15 <z < 0.30, if the adhesion utilisation curve for each axle is situated between the lines k = z+0.08and k = z − 0.08. For braking rates of z ≥ 0.3, the adhesion utilisation curve for each axle hasto stays below k = z−0.02

0.74 . Plotting these bounds results in the diagram shown in figure 2.6.These bounds hold for unladen as well as for laden vehicles.

Besides the above mentioned points, a vehicle has to fulfill a lot more requirements to pass legislationregarding brake system performance. For instance, the compatibility between a tractive unit and atrailer which is judged by means of diagrams where the air pressure send to the trailer is plottedagainst the dimensionless declaration, z. These other legislation requirements are not mentioned inthis report because the necessary parameters like for instance air pressure, are not an output of themulti-body models at this moment.

The legislation summarised till so far did not mention anything about legal demands on anti-lockbraking systems. Annex X of Council Directive 98/12/EC contains the definitions and the test require-ment for an ABS. Commission Directive 98/12/EC defines ABS as, "An anti-lock braking system is


Figure 2.6: legal z=k boundaries [7]

part of a service braking system which automatically controls the degree of slip, in the direction of ro-tation of the wheel(s), on one or more wheels of the vehicle during braking ". ABS can control a wheeldirectly or indirectly. Directly controlled wheels are defined as, "Directly controlled wheel means awheel whose braking force is modulated according to data provided at least by its own sensor" while"Indirectly controlled wheel means a wheel whose braking force is modulated according to dat pro-vided by the sensor(s) of other wheels" is the definition for a indirect controlled wheel. To pass legaldemands on ABS, the next requirements has to be fulfilled.

• The performance of the ABS shall be considered satisfactory if the utilisation of adhesion, ε, isequal or higher than 0.75. The adhesion utilisation is defined as;

ε =zmax

k(2.19)

The adhesion utilisation should be measured on surfaces with a µ of 0.4 or less and 0.8, with aninitial speed of 50 km/h and for both unladen as laden vehicles.

• Directly controlled wheels should not lock when the brake pedal is suddenly operated. On ahigh µ-roads, µ = 0.8, the initial velocity should be 80 km/h and only a laden vehicle has to beexamined. On a low µ-road, µ = 0.4, both an unladen and a laden vehicle have to examined, theinitial velocity must be set at 70 km/h.

• Directly controlled wheels should not lock when the brakes are applied and the right and leftwheels are situated on a different friction coefficients, the so-called µ-split road. The steeringadjustments during such a test should not exceed 120 in the first 2 seconds and 240 in total.An extra requirement for a laden vehicle on such a µ- split road is that z ≥ 0, 75 4 µl+µh

5 ≥ µl,where µl represents the low friction coefficient and µh the high friction coefficient

• At the above mentioned tests, directly controlled wheels are allowed to lock for a brief period.When Vx < 15 km/h directly controlled wheels are permitted to lock for an undefined period.

2.5. ROLL-OVER OF COMMERCIAL VEHICLES 15

For indirectly controlled wheels it holds that the may lock at any moment and for every periodas long it does not affect stability and steerability of the vehicle.

The above summary concludes this section about legal demands, these demands are used later on, inchapter 4 to evaluate and compare the braking performance of conventional commercial vehicles andLZV’s.

2.5 Roll-over of commercial vehicles

The report of C.B. Winkler et al [30] reviews the mechanics behind roll-over stability. There reviewstarts with a simple heavy vehicle model, on which tires and suspension are lumped into a single rollplane, which drives a steady state turn. By means of the free-body diagram in figure 2.7, it is possibleto derive an equilibrium of moments around half the track, yielding to;

Figure 2.7: free-body diagram of a rigid heavy vehicle in a steady turn [30]

M ay hc.g. +Mg ∆y = (Fz2 − Fz1)T

2(2.20)

where

M = vehicle mass [kg]hc.g. = height of C.G. [m]

ay = lateral acceleration [m/s2]∆y = lateral motion C.G w.r.t. rotation point [m]Fzi = vertical tyre force [N ]T = track width [m]


The moments at the left side of the equation destabilise the vehicle while the moment at the right sidewill stabilise the vehicle. The stabilising moment reaches it maximum when all load is transferredto one side of the vehicle, e.g. Fz1 = 0 and Fz2 = Mg. At that point, the stabilising moment has avalue equal toMg T

2 . By means of (2.20) and the assumption that the vehicle is rigid, so ∆y = 0, it isshown that the roll-over threshold of a vehicle in first principal is defined by;

ay =T

2hc.g.

By introducing tyres and suspension compliance, lash in suspension and couplings and multiple sus-pensions, the influence of those parameters on roll-over stability is evaluated.

Tyre compliance is introduced by representing vertical tyre stiffness as linear springs, which causesthe vehicle to roll around the half track point and the C.G. translates in lateral direction. Because ofthis lateral translation, a vehicle becomes roll unstable at a lower lateral acceleration compared to arigid vehicle. So, the effect of suspension compliance is similar to the influence of tyre compliancewith this difference that the axle still rotates around the half track point, but the chassis and body willrotate around a point above the ground, the so-called roll centre. Because of this extra compliance,the roll angle increases, thus the lateral translation of the centre of gravity increases. As a result thevehicle roll stability becomes worse. Placing the roll centre close to the centre of gravity is favourableto minimize the decrease of roll-over stability. The fact that a high place roll centre is favourable can beexplained by figure 2.8 which shows a vehicle with tyre and suspension compliance, driving a steadystate circle and where hc.g. is represented by hc.g., rr + h cosφ.

Figure 2.8: heavy vehicle in a steady turn, suspension compliance included [23]

By means of figure 2.8, (2.20) changes into;

May (hr + hc.g.,rccosφ) +Mg sinφ = (Fz2 − Fz1)T

2(2.21)

where

φ = roll angle []hr = height roll centre w.r.t. road [m]hc.g.,rc = height centre of gravity w.r.t. roll axis [m]


When the roll centre is placed close to the centre of gravity, hc.g.,rc is small. A small distance betweenthe centre of gravity and the roll centre results in smaller values for hc.g.,rc sinφ and hc.g.,rc cosφ. Inother words, for equal roll angle the destabilising moments at the left side of (5.3) are the smallestwhen the distance between the centre of gravity and the roll centre is small. With foregoing knowl-edge it becomes also immediately clear why a low centre of gravity, thus a small hc.g., is preferable.Regarding vertical tyre and suspension stiffness it is shown that an increase of stiffness will improveroll stability. An increase in tyre and suspension stiffness means a smaller roll angle which againresult in smaller destabilising moments.

In [30] the influence of multiple suspensions is judge also. The assumption that the the tyres andsuspension are lumped together and operate as a single suspension is abandoned and different levelsof roll stiffness for steer, drive and trailer axle of a tractor semitrailer are introduced instead. On a realvehicle, the trailer suspension has the highest roll stiffness followed by the driven axle suspension andthe steer axle suspension. The trailer tyres will lift of the first because the trailer suspension transferthe axle load the quickest to one side. At that point the roll stiffness of the trailer is lost, causing thetotal vehicle roll stiffness to decline however, the vehicle is still roll stable. The roll angle increasesfurther causing the tyres of the driven axle to be the next to lift from the ground and roll stiffnessif lost further. The remaining stiffness of the steer axle suspension is not enough to encounter thedestalibilsing roll moments and the vehicle becomes unstable and rolls over. By means of the aboveanalysis of multiple suspensions, it is concluded that roll stability is in general improved by stiffeningthe drive and steer axle suspension.

After covering multiple suspensions, other vehicle properties which effect roll stability are alsoidentified. Besides the tyre and suspension compliance, lateral and torsional compliance of the chassisand a lateral offset of the load are mentioned as properties which increase lateral travel of the C.G.,thus decreasing the roll stability. To finalise the evaluation of vehicle parameters effecting static rollstability, the conclusion is drawn that in general the roll stability of commercial vehicles typically canbe derived from

T

2 hc.g.

plus a large number of compliances and each compliance degrades roll stability further.Till now, roll-over of a vehicle is approach as a quasi-static event but according to [30], all roll-over

accidents in practice are dynamic events to some extent. Quasi-static roll-over is hard, if even possible,to accomplish when getting near the point of roll-over the driven wheels will lift from the groundcausing the vehicle to loose speed and the lateral acceleration will decline immediately. So, theremust be some dynamics involved which provides the energy to roll-over a vehicle. Several approachesto analyse a single vehicle are presented, including an analyse based on a constant lateral tip forceapplied to a rigid vehicle for a period of time, an analyse using a simplified 2 DOFmodel to predict theminimum lateral acceleration required for wheel lift and an analyse where the equations of motionsfor the same two DOFmodel are solved. The first approach supports the conclusion that static roll-overis the dominating factor regarding roll-over stability. The second approach results in the conclusionthat at highly transient manoeuvres, roll-over is possible for lower lateral accelerations than the staticroll-over threshold (STR) and that the resulting lateral acceleration depend highly on the amountof roll damping. The approach where the equations of motion are solved, shows that the responseto a sinusoidal excitation relates to roll natural frequency of a vehicle. The natural roll frequenciesrange from 2 Hz for a lightly loaded tractor semitrailer to 0.5 Hz for a heavy loaded combination, thushigh C.G., tractor semitrailer with a less than average suspension stiffness. The upper limit is wellabove the steering frequency which a driver can realise but the lower limit of 0.5 Hz is within therange of excitation frequencies observed at emergency manoeuvring. According to [30], the amountof roll stiffness and roll damping will determine dynamic roll stability of a heavy vehicle, high levelsof stiffness and damping are preferable. The level of stiffness should at least, place the roll naturalfrequency of the vehicle outside the range of steering frequency achievable by a driver.

Via rearward amplification (RA) and dynamic load transfer ratio (DLTR), two performance mea-sures to analyse dynamic roll stability for high frequency manoeuvres are introduced. Rearward am-plification is quantified by the ratio of the peak lateral acceleration of the last unit to that of the tractive


unit;

RA =ay,peak last

ay, peak rst(2.22)

where

RA = Rearward Amplification [−]

ay, peak last = lateral peak acceleration of the last unit [m/s2]

ay, peak rst = lateral peak acceleration of the first unit [m/s2]

Rearward amplification depends on the steering frequency at frequencies where RA peaks, roll stabilityis poor and a vehicle is expected to roll-over while for other frequencies the vehicle is roll stable. Anexample is shown in figure 2.9 for a "Western double" which consists of a full trailer connected to aconventional tractor semitrailer combination.

Figure 2.9: rearward amplication of a Western double [30]

A part of [10], evaluates the rearward amplification for a tractor semitrailer and of a truck full trailercombination by means of mathematical models. The effect of rearward amplification on roll stabilityfor a sudden lane change is evaluated by means of the next formula;

ay =SRT

RA(2.23)

Assuming a static roll-over threshold of 3.9 m/s2 and a rearward amplification of 1.73 , gives an esti-mated lateral acceleration of 2.25 m/s2 at which the vehicle will roll-over.

Evaluation of the parameters which could lower the rearward amplification of a vehicle, thus im-proving roll-stability, shows that reducing the vehicle speed, increasing the wheelbase of a full trailer,shorten the distance between C.G. and coupling of a towing unit and increasing the tyre corneringstiffness will have a positive effect on rearward amplification. Other improvements are using fewerarticulation points and roll coupling between units [15].

The dynamic load transfer ratio is a measure which quantifies load transfer from one side of avehicle to another, and is defined as;

DLTR =

∣∣∣∣ n∑i = m

FZLi − FZRi

∣∣∣∣∣∣∣∣ n∑i = m

FZLi + FZRi

∣∣∣∣ (2.24)


where

FzL, i = vertical force on the left side tyres of axle i [N ]FzR, i = vertical force on the right side tyres of axle i [N ]m = first axle of a roll unit [−]n = last axle of a roll unit [−]

In [30] the dynamic load transfer ratio for each roll unit of a vehicle is evaluated, where a roll unitis defined as a group of units which can roll independently of the rest of the vehicle, i.e. a tractorsemitrailer is one roll unit and a truck trailer are two roll units. When the dynamic load transfer ratiois equal to zero there is no load transfer while a dynamic load transfer ratio of one means that tyres atone side lift off, indicating that the roll-over threshold is reached.

To prevent roll-over, commercial vehicles can be equipped with a control system. Today’s commer-cially available control system all prevent roll-over by reducing the speed of the vehicle [1], [23] [25], [27].In general, these systems monitor the lateral acceleration and the angular wheel speeds of a vehicle.When the lateral acceleration exceeds a threshold, the brakes are applied. When angular wheel speedsat one side drop dramatically, the danger of rolling-over is present. By keeping the brakes applied, thespeed is reduced further which causes the lateral acceleration to decreases and thereby the danger ofroll-over. Another way to improve roll-over, especially when initiated by rearward amplification, is byactive trailer wheel steering which improves yaw stability [4], [23].


Chapter 3

TU/e-Commercial Vehicle Library

The subject of this chapter is the "TU/e-Commercial Vehicle Library" which is the basis for the multi-body models used in this research. The first section is a short introduction into the "TU/e-CommercialVehicle Library" in which some general information about the library is given. In the second section,modifications regarding dimensions and masses of the vehicle units are discussed and the third sec-tion treats the modification of the tyre characteristics. In the fourth and fifth section describe thenew systems added to the "TU/e-Commercial Vehicle Library". The fourth section describes the brakesystem while the improved driver model is the subject of the fifth section.

3.1 Introduction into the "TU/e-Commercial Vehicle Library"

Via the library, different vehicle combinations can easily be build by connecting tractive and trailingvehicles found in the library. By using a central library it is also possible to fast an easy modify a com-ponent of a vehicle without the need to modify every single multi-body model. If for example someoneneeds to evaluate another front wheel suspension, they just has to modify the suspension of the frontaxle block in the library and all tractors and trucks are automatically fitted with the modified front axlesuspension. Figure 3.1 shows the most recent version of the "TU/e-Commercial Vehicle Library". The"TU/e-Commercial Vehicle Library" is developed with the Matlab/Simulink toolboxes SimMechanicsand to fully exploit the possibilities of the "TU/e-Commercial Vehicle Library" the Stateflow and VirtualReality toolboxes are also required.

Every unit of the library has its own local coordinate system. The dimensions of each vehicle aremeasured from the local origin. For tractive units the origin of the local coordinate system is positionedat the point where a vertical line trough the centre of the steer axle and the ground intersect. For andfor trailing units the local origin is positioned at the point where a vertical line through the towingpin or eye intersect with the ground. Two examples are shown in figure 3.2, the left figure shows thedimensions for a truck and the right figure shows the dimensions for a drawbar-trailer.

When creating a certain combination, the units are positioned with respect to the origin of thetractive vehicles, thus contact point between ground and a line trough the center of the front axle,see figure A.1 at Appendix A. In other words, the library units are placed in a global axis system withorigin at the origin attached to the origin of the axis system attached to the tractive unit. All coordinatesystems used are right handed coordinate systems, the positive x axis points in forwards, the positivey axis points to the left side of the vehicle and the positive z axis points upwards.

21

22 CHAPTER 3. TU/E-COMMERCIAL VEHICLE LIBRARY

Figure 3.1: "TU/e-Commercial Vehicle Library"

Figure 3.2: dimensions of vehicles, using local coordinate system

3.2. DIMENSIONS AND MASSES 23

3.2 Dimensions and masses

Before including a brake into the "TU/e-Commercial Vehicle Library", the dimensions and the massesused in the previous library version are compared with data of manufacturers of towing and towedvehicles. No big dimensional deviations were found, but still the library is modified to create a morelogical placement of components of a vehicle, mainly axles. For example, in the previous library thefirst axle of a drawbar-trailer is placed with respect to the point where the drawbar is welded to thechassis, this welding point is positioned with respect to the towing eye of the drawbar-trailer. Inthe most recent library, the axle is directly placed with respect to towing eye of the drawbar-trailer,which is a more convenient an logical way to define the placement of the axle. In Appendix A till J theplacement of the axles and couplings for the LZV’s and the conventional commercial vehicles is shownvia schematic drawings. With the dimensions given in these drawings, the LZV’s and the conventionalcommercial vehicles fulfil the regulation of Council Directive 96/53 of the European Community [7],which defines boundaries for maximum combination and loading space length, maximum vehiclewidth and maximum vehicle height.

Previous versions of the "TU/e-Commercial Vehicle Library" did not include the fact that mass andinertia tensor of a chassis depend on the length of the chassis. So, a relatively short tractor chassis hasthe same mass and inertia tensor as a relatively long 8x4 truck, which is physically impossible whenlength is the only variable. Besides the influence of length, the number of cross-members mountedin the chassis is different for each vehicle and this will also affect the mass and inertia. Although, themass and inertia of a chassis will have a marginal, if any, effect on the results of this research, thechoice is made to include the influence of length in the most recent library. The mass of the chassisis estimated and the inertia tensor is determined by means of the moments of inertia of a rectangularbox having the mass, the length, the width and the height of the chassis;

Jxx =m

12(w2 + h2) (3.1)

Jyy =m

12(l2 + h2) (3.2)

Jzz =m

12(l2 + w2) (3.3)

Jxy = Jxz = Jyz = 0 (3.4)

Besides the chassis modification, the mass of the load is modified in such away that all studied con-figurations reach their maximum allowed gross vehicle weight, 60000 kg for an LZV [29]. At the sametime, the density of the load is decreased from 500 kg/m3 to 350 kg/m3 to create vehicles reachingboth the maximum vehicle weight and maximum dimensions. The load density is used to determinethe height of the centre of gravity. By decreasing the density of the cargo, the overall centre of gravityheight will increase which certainly has an effect on the dynamic behaviour of the studied vehicles andtherefore the results will differ from the results found by G. Isiklar [18].

The mentioned modifications do change the static axle loads of studied vehicles, The axle loadsfor each configuration using the most recent library version are listed in tables A.1, B.1, C.1, D.1, E.1,F.1, G.1, H.1,I.1 and J.1, given in Appendix A till J. The third column of these tables shows the legallyallowed axle loads, as formulated in Council Directive 96/53/EC [7]. Some remarks need to be madeabout these legal limits. First remark is that the legal limits depend strongly on the distance betweenaxles, which implies that the limits for the vehicles listed in the tables are only valid for the specificvehicle dimensions given in Appendix A till J. The second remark concerns the legal limit of a steeredaxle, within Council Directive 96/53/EC the load of a steered front axle can very for different vehicletypes up to amaximum of 10000 kg. In this research it is assumed that all steered axles have a technicalload limit of 7500 kg, which implies that the legal load limit is equal to the technical load limit. Furthermore, the assumption is made that the total axle load of the trailers is evenly distributed over the axle,so the legal limit for each axle is found by dividing the legal limit for the total axle load by the numberof axles, e.g. for a semitrailer with three axles the combined axle load has a limit of 24000 kg whichimplies a axle load limit of 8000 kg for every axle. Regarding axle loads, the dolly and semitrailer unitsof lZV D are judged as a trailer with tandem axles at the front and three axles at the rear.


Besides limitations on axle loads, the European Community also prescribes a limit to the verticalcoupling load when using a drawbar-trailer. Council Directive 94/20/EC states that the vertical cou-pling load is limited to a maximum of 1000 kg [6]. The resulting static coupling loads are also listedin axle load tables of Appendix A through J When evaluating the static axle and coupling loads found,it can be concluded that none of the vehicles violates the legal load limits.

3.3 Tyres and tyre characteristics

The "TU/e-Commercial Vehicle Library" contains three types of tyres, a tyre for a steered wheel, a tyrefor a driven wheel and a tyre for a trailer wheel. Compared to previous versions, the tyres of the mostrecent library are modified in two ways. Firstly, scaling of the tyre road adhesion is added to the tyreblocks and secondly the tyre properties are updated to get a more reasonable tire behaviour over thetotal vertical force range of the tyres.

To analyse the performance of the brake system, it is necessary to vary the adhesion between tyresand road, e.g. a dry or wet road and a µ-split road. Previously, varying the tyre road adhesion waspossible, but not as straightforward as one would expect and prefer. Different adhesions resulted ina extra multi-body model for each configuration where it is preferable to have one vehicle model onwhich the adhesion can be changed. By adding scaling to the tyre blocks of the models, the adhesionbetween road and tyre can be varied within a vehicle model. The scaling of the tyre road adhesion, isrealized by feeding back the lateral tyre position, "ycp", via a memory block and a look-up table to thetyre block as shown in figure 3.3.

VR

varinf

wheel

wheel velocity

wheel position

wheel force

wheel body

road

add signal names

VR_sensor

Scaling values

S-Function

MemoryIntegrator

wheel torque

varinf

ycp

Figure 3.3: tyre block including scaling of road tyre adhesion

The first column of the look-up table contains predefined lateral tyre positions and the second columncontains the corresponding scaling factor, 1 or 0.5 respectively. Table 3.1 lists the tyre position in thefirst column and the scale factors and the corresponding adhesion values in the remaining columns.The mentioned tyre road adhesion holds for static axle loads. The tyre road adhesion for a wet roadis half the adhesion for a dry road and at the µ-split road the tyres at the right of the vehicle, negativelateral tyre position, will have half the adhesion as the tyres at the left, positive lateral tyre position.

Besides the modifications mentioned above, the Magic Formula parameters which define the forceand moment characteristics of the tyres are modified. These Magic Formula parameters are based onmeasurements done in 2001. Houben [16] shows that fitting these measurements with the MagicFormula does not represent commercial vehicle tyre behaviour accurately outside the range of vertical

3.4. BRAKE SYSTEM MODULE 25

dry road wet road] µ-split road]lateral tyre position [m] scale µ scale µ scale µ

5.00 1.00 0.77 0.50 0.38 1.00 0.770.01 1.00 0.77 0.50 0.38 1.00 0.770.00 1.00 0.77 0.50 0.38 0.75 0.58

−0.01 1.00 0.77 0.50 0.38 0.50 0.38−5.00 1.00 0.77 0.50 0.38 0.50 0.38

Table 3.1: tyre road adhesion with respect to lateral tyre position

tyre force measured. By modifying the variation of µx and µy with Fz and by adding a self alignmentcoefficient the tyres used in this research, do represent the 2001 measurements and are also accuratewhen extrapolation the vertical tyre force. The force and moment characteristics of the used tyres areshown in Appendix K.

3.4 Brake system module

The library contains an brake system module which makes it possible to analyse braking scenarios.The brake system acts on local level meaning that every axle has its own brake system module insteadof a central brake system placed at tractor or truck as in reality. In this way, the flexibility to create newconfigurations, relatively simple and fast, is maintained. The brake module contains two subsystems,one system regulates the brake force distribution of the total vehicle and the second system is a anti-brake lock system which prevents locking of the wheels when braking. Both subsystems are describedseparately, starting with the brake force regulation system. Figure 3.4 shows the inputs, the outputsand the two subsystem of the brake system module.

brake_diag

3

Mbr_right

2

Mb_left

1

susp

1

LSV_valve

−a_desired Mbr

LSV_diagspring_defl

ABS_incl

ABS_moduleindependent

ABS_include

Mbr

omega_left

omega_right

Vx

Mbr_left

Mbr_right

ABS_diag

Vx

4

omega_right

3

omega_left

2

−a_desired

1

LSV_diag

ABS_diag

Figure 3.4: brake system module

The gain "ABS_incl" in the brake systemmakes it possible to disable or enable the ABS system depend-ing on the manoeuvre to analyse. The value of "ABS_incl"is set during initialization of a manoeuvre,when set to 1 ABS is included and wheels lock is prevented and when set to 0 , the ABS system isexcluded and it is possible to lock the wheels during a simulation.

Brake force distribution moduleLiterature mentions several ways to distribute brake force for commercial vehicles [12], [19]. One way isto use a controller which regulates the brake force distribution by minimizing the difference in wheelslip between axles. Another way to regulate brake force distribution is to measure spring deflectionwith load sensing valves, the amount of spring deflection is a measure for the load of an axle whichon its turn is a measure for the required brake force. Although nowadays most of the commercialvehicles have a wheel slip controller to distribute brake force, the brake system of the current library


uses load sensing valves. Load sensing valves are simple to implement and have a little to no effect onthe calculation time of simulations.

LSV_diag2

Mbr1

spring_defl1

s −> Fz

Fz −>Mbr

((u(1)/9.81)*Rtyre)/2−a_desired

1

LSV_Fz

delta_s

Mbr

Figure 3.5: load sensing valve

Figure 3.5 shows the implemented load sensing valve and its in- and outputs. Via input "spring_defl"the spring deflection is measured. This spring deflection is used as input of the look-up table "s -> Fz"which determines the vertical axle load by means of the next formula;

Fz, axle = Fz, stat + 2 sspring Kspring (3.5)

where

Fz, axle = actual axle load [N ]Fz, static = static axle load [N ]sspring = spring deflection [m]Kspring = spring stiffness [N/m]

Another input of the load sensing valve is the desired deceleration, "-a_desired". Via the vertical axleload and the desired declaration, the brake torque for each wheel is calculated by;

Mbr =z Rtyre

2Fz, axle (3.6)

which is derived by assuming z = k and by substituting

Fbr = zFz, axle

2

into

Mbr = Fbr Rtyre

where

Mbr = brake torque per wheel [Nm]

z =adesiredg

= dimensionless deceleration [−]

adesired = desired deceleration [m/s2]

g = gravitational acceleration [m/s2]Fbr = brake force per wheel [N ]Rtyre = effective tyre radius [m]


Note that the "LSV diag" output makes it possible to check the functionality of the load sensing valveif necessary. The performance of the load sensing valves is shown and analysed in section 4.1.

Anti-lock Brake moduleBesides the LSV valve, the brake systemmodule contains a subsystem called "ABS_module", as shownin figure 3.4. The ABS system is connected to the load sensing valve and modifies the brake torque iftyres enter the unstable wheel slip region and is an implementation the proces shown in figure 2.4. Todefine the wheel slip region during braking, the ABS system monitors the wheel speeds, "omega_left"and "omega_right", and the longitudinal velocity, "Vx" and calculate the longitudinal wheel slip, κ, withthese inputs. If the wheel starts to enter the unstable wheel slip region, the ABS starts to modify thebrake torque. Calculation of the wheel slip is done in the "signal processing" block of the ABS system,while the "brake_torque" blocks regulate the brake torque, see figure 3.6.

Figure 3.6: ABS module


The signal processing part, shown at the top of figure 3.6, calculates the longitudinal tyre slip via (2.9),which after rearranging of terms is defined as;

κ = −(1− Rtyre ΩVx

) (3.7)

The "brake_torque" block, the lower part of figure 3.6, is the controller part of the ABS system. Thecontroller knows five states namely, "no braking", "Mbr LSV", "Mbr hold","Mbr decrease" and "Mbr in-crease", which state is active depends on the longitudinal wheel slip calculated by the "signal processing"block. Which state is or becomes active is illustrated by means of figure 3.7 and 3.8 which show timehistories of ABS signals and flags during a certain braking manoeuvre. Figure 3.8 zooms in on thesignals when ABS is controllingMbr.

At t = 5 sec the brakes are applied for the first time. The ax demand is moderate, thus the lowerκ threshold, k ≤ −0.12, is not crossed. The ABS state is set to "Mbr LSV" meaning that ABS doesnot modify the brake torque and input 2, "Mbr", is connected directly to output 1, "Mbr_left", and 2,"Mbr_right", which are the brake torque outputs of the ABS. The brake torque is controlled by the loadsensing valve during this "Mbr LSV" state.

At t = 10 sec the brakes are released and at t = 11 sec the brakes are released completely and atthis point, ABS switches to the "no braking" state.

At t = 15 sec the brakes are applied again, but now the brake demand is such that the lower slipthreshold is exceeded at t = 15.9 sec. When crossing the lower slip threshold, the ABS switches from"Mbr LSV" to the "Mbr decrease" state. At this point, the "first cycle" flag is set also because ABSintervenes for the first time. When the "first cycle" flag is set, the connection between load sensingvalves and brake torque output of the ABS is disconnected and ABS starts to decrease the brake torque.The brake torque at the start of the ABS intervention is equal to the brake torque output of the loadsensing valve just before exceeding the lower slip threshold.

At t = 16.02 sec, the longitudinal wheel slip becomes bigger than the lower threshold. At this pointthe ABS states switch from "Mbr decrease" to "Mbr hold" and the brake torque is kept constant. In thiscase holding the brake torque constant results directly in a wheel slip which exceeds the upper slipthreshold of κ ≥ −0.08. Because the upper slip threshold is crossed, the ABS state switches from the"Mbr hold" state to the "Mbr increase" state and the ABS starts to increase the brake torque.

Increasing the brake torque causes the wheel slip to decline and the upper threshold is crossedfor the second time at t = 16.10 sec but now the wheel slip is lower than the upper threshold. TheABS states change again and now the state "Mbr hold" becomes active. When the declining wheelslip exceeds the lower threshold again at t = 16.15 sec, the brake torque needs to be decreased againand the cycle of decreasing, holding, and increasing brake torque starts all over again. At t = 18 secthe brakes are released and ABS stops controlling the brake torque and "first cycle" flag is reset. Theconnection between load sensing valve, input 1, and brake torque output of the ABS, output 1 and 2 isrestored.

At the shown manoeuvre, the brakes are applied again at t = 35 sec and at t = 35.9 sec the ABSstarts to intervenes again and the cycle of decreasing, holding, increasing and holding the brake torquestarts again. Not shown in figure 3.7 and 3.8 is that ABS is or becomes inactive when the longitudinalvelocity is of becomes lower than 1.5 km/h.

Next to the brake torque outputs, the ABS system contains a diagnostic output, "ABS_diag". Thisoutput has the same functionality as the "LSV_diag" output of the LSV module namely to outputdiagnostic signals.

The "TU/e-Commercial Vehicle Library" contains two ABS modules which both have the sameinputs and outputs and also use the same control logic. The difference lays in the approach how tocontrol the wheels, steer axle wheels are controlled in a select low approach while the drive and traileraxle incorporate independent wheel control. At the select low approach there is no difference in braketorque at the left or right wheel of an axle. If the lower slip threshold is exceeded at one of the wheels,the ABS becomes active on all wheels of that axle. At the independent wheel control each wheel iscontrolled separately, thus ABS interacts only at the wheel at which the lower slip threshold is crossed.Just as for the load sensing valve performance, the functioning of the ABS system analysed at chapter4.


0 5 10 15 20 25 30 35 40 45 50−5

0

5

ax [m

/s2 ]

demandreal

0 5 10 15 20 25 30 35 40 45 500

10

20

30V

[m/s

]

Vxω*R

0 5 10 15 20 25 30 35 40 45 50−0.2

0

0.2

κ [−

]

κlower thresholdupper threshold

0 5 10 15 20 25 30 35 40 45 500

5

10

15

Mbr

[kN

m]

Mbr

0 5 10 15 20 25 30 35 40 45 50no braking

Mbr LSV

Mbr decrease

Mbr hold

Mbr increase

ABS state

0 5 10 15 20 25 30 35 40 45 50reset

set

time [sec]

ABS, 1st cycle

Figure 3.7: ABS signals and ags during braking

14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19−5

0

5

ax [m

/s2 ]

demandreal

14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 190

10

20

30

V [m

/s]

Vxω*R

14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19−0.2

0

0.2

κ [−

]

κlower thresholdupper threshold

14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 190

5

10

15

Mbr

[kN

m]

Mbr

14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19no braking

Mbr LSV

Mbr decrease

Mbr hold

Mbr increase

ABS state

14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19reset

set

time [sec]

ABS, 1st cycle

Figure 3.8: ABS signals and ags during braking, zoomed


3.5 Driver model

During simulations, a vehicle drives a certain trajectory by controlling the steering wheel input. Thesteering inputs of the manoeuvres described in this report are controlled both open loop as well asclosed loop. At manoeuvres where steering is controlled open loop, the trajectory is driven by pre-scribing the steering wheel angles as function of time. At closed loop steering, a prescribed path isfollowed by means of a controller which calculates the steering wheel angles during a simulation andthereby representing a driver. The very basic driver model used in this research is a so-called "look-ahead path following driver model" as shown in figure 3.9.

Figure 3.9: "look-ahead" path following [2]

In previous research [18], a driver model is already implemented but in that driver model the "look-ahead" vector is represented by 2 joints and a bar. One side of the bar is connected to the vehicle whilethe other side physically connects the bar to the road and thereby connecting the vehicle physicallyto the road. With such a connection, there exists the possibility that the steering and overal vehiclebehaviour is affected by this connection during a manoeuvre. To exclude such effects, a new drivermodel is developed to replace the previous one.

The latest driver model is shown in figure 3.10. It has "driver signals" and "driver path’" as inputswhile "steer angle (rad)" is the only output. The input "driver signals" contains the position of front andrear axle and the longitudinal vehicle speed of the tractive unit.

steer angle (rad)

1

steer ratiosteer sens

−K−

low passfilter

1

0.01s+1

look aheadtime

−K−

frontaxle_pos

dist

driver_viewpoint

driver_pos

Product

Normalize Vector

Normalize

Gain1

−K− Fcn

f(u)

EmbeddedMATLAB Function

line

point

npoints

idx1

dist

pos

idx2

dist2line

driver_path’

Constant

10

Driver_signals

1rearaxle pos

frontaxle pos

Vx

Figure 3.10: driver model

With the axle positions a unit vector, d, is calculated. This unit vector contains the heading directionof the vehicle. By means of the vehicle velocity and the gain "look ahead time", the length of the look-ahead vector is calculated. Finally, the driver viewpoint is constructed by adding the multiplication ofthe unit vector and the look-ahead length to the front axle position.

3.5. DRIVER MODEL 31

The construction of the driver viewpoint is given by; (3.8).

driver viewpoint = dld + xfr (3.8)

where

d =xfr − xre|xfr − xre|

xfr = position vector of front axle

xre = position vector of rear axle

ld = look-ahead vector = Vxtla

tla = look ahead time

The "driver path’" input is an array containing the longitudinal, lateral and vertical coordinates of thedesired trajectory. The embedded Matlab function "dist2line" of the driver model calculates the dis-tance between the driver viewpoint and the desired trajectory. The first part of the "dist2line" function,determines which coordinates of the desired trajectory are the closest to the driver view point. Thesecond part of the "dist2line" function determines the distance between the driver view point and thedesired path by means of vector projection. Figure 3.11 shows a part of a desired trajectory and theposition vectors, ~a and ~b, used to determine the distance, (dist), between driver view point and thedesired path.

q

ar

br

dist

driver view point

trajectory

(a) θ < 90

q

ar

br

driver view point

trajectory

(b) θ ≥ 90

Figure 3.11: desired trajectory and vectors used by function "dist2line"

When the angle, Φ, between ~a and~b is smaller then 90, like depicted on the left side of figure 3.11, itis possible to project vector~b on vector ~a. This projection is equal to β~a and has a value between zeroand one. The factor β is found by

β =< ~a.~b >

< ~a.~a >(3.9)

and by substituting the value of β into

dist = |~b− β~a| (3.10)

the value of dist is determined. When the angle between ~a and ~b is equal of bigger then 90 likedepicted in the right side of figure 3.11, the distance between the viewpoint of the driver and thedesired path is equal to the length of position vector~b. In this case the following holds;

dist = |~b| (3.11)

After calculating dist, the next step is to determine its sign. In the "dist2line" function the sign of distis determined by means of the cross product between ~a and~b;

~c = ~a×~b (3.12)

dist = sign(~c)dist (3.13)


When the sign of ~c is positive the view point of the driver is located at the left of the desired path. Theopposite hold when the sign of ~c is negative, in that case the view point is located at the right of thedesired trajectory.

The signed dist value and the look ahead distance are fed into the function block "Fcn" whichcalculates the steering angle of the wheels by;

δs = arctan(dist

lb

)(3.14)

By multiplying the calculated angle with the steer ratio and steers sensitivity, the correction in steeringwheel angle is finally determined and sent to the vehicle. As an example, figure 3.12 shows the desiredpath, the actually driven path, the view point of the driver and the steering wheel angle during a singlelane change.

100 120 140 160 180 200 220 240 260 280 300 320 340−1

0

1

2

3

4

late

ral p

ath

[m]

driver model signals during a lane change

desired pathdriven pathviewpoint driver

100 120 140 160 180 200 220 240 260 280 300 320 340−10

−5

0

5

10

δs [o ]

longitudinal path [m]

δs

Figure 3.12: driver model signals during lane change

Chapter 4

Braking performance of LZV's

The subject of this chapter is the braking performance of conventional commercial vehicles and thedifferent LZV’s. The first section deals with straight line braking. In this section, fulfilment of legis-lation is examined by means of so-called "z=k" plots and (un)loading of axles and lock up of wheelsis analysed. Subject of the second section is the behaviour of the different commercial vehicles whenABS is switched on. Manoeuvres are again based on braking when driving straight ahead but the brakedemand is more severe or the road conditions are changed. Next to vehicle behaviour, the section isalso used to judge ABS performance and fulfillment of ABS legislation. At the third section the brakesare applied while driving a steady state circle and at the fourth section the vehicles brake while taking ahighway exit. The fifth section concludes this chapter and it holds a summary of the significant resultsregarding brake performance of conventional commercial vehicles and LZV’s.

4.1 Straight line braking without ABS

Subject of this section is the performance of the developed brake system with respect to legislation asmentioned in chapter 2 and the dynamic behaviour of the conventional commercial vehicles and theLZV vehicles when applying the brakes. Especially, fulfillment of the brake force distribution demandsis evaluated and also the (un)loading of axles and the wheel lock thresholds will be considered. Toexamine the fulfillment of legal demands, the scenario below is used;

1. Driving straight ahead with a velocity of 80 km/h a flat and dry road. The brakes are appliedafter 5 sec to achieve a deceleration of 6 m/s2 until standstill. The dry road has a road frictioncoefficient of 0.77 and during the complete manoeuvre ABS is switched off.

Commercial vehicles have tomeet legal requirements on brake force distribution as alreadymentionedin section 2.4. These legal requirements enforce boundaries on the maximum deviation from idealbrake force distribution. By constructing so-called "z=k" diagrams, see figure 2.6, the brake forcedistribution of each vehicles is examined, both for a laden as well as an unladen vehicle. Figure 4.1shows the legal borders, the thick black lines, and the brake force distribution for a tractor semitrailer.For LZV A, the legal borders and brake force distribution is given in figure 4.2, the diagrams for theremaining vehicles are given in Appendix A till J. By means of the brake force diagrams it becomesclear that all vehicles obey the boundaries on brake force distribution enforced by legislation. Howwell each vehicle approaches ideal brake force distribution, thus the dotted z = k line, is analysed bycalculating the absolute error with respect to the ideal z = k line.

33

34 CHAPTER 4. BRAKING PERFORMANCE OF LZV'S

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

tractor semitrailer (laden)

steer axledrive axlesemitrailer axle1semitrailer axle2semitrailer axle3Z = Klegal borders

(a) laden

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

tractor semitrailer (unladen)


(b) unladen

Figure 4.1: legal bounds and brake force distribution for laden/unladen tractor semitrailer

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV A (laden)

steer axledrive axlesemitrailer axle1semitrailer axle2semitrailer axle3dbtrailer axle1dbtrailer axle2Z = Klegal borders

(a) laden

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV A (unladen)


(b) unladen

Figure 4.2: legal bounds and brake force distribution for laden/unladen LZV A

In this research, the error with respect to ideal brake force distribution is calculated for decelerationsof 3 and 6 m/s2 by means of;

BFD,error = |1− z

k| (4.1)

where

BFD,error = deviation from ideal BFD [−]z = dimensionless deceleration [−]k = required friction [−]

The maximum errors found are placed in table 4.1, for both laden as well as unladen vehicles. Besidesthe brake force distribution diagrams, legislation on commercial vehicles also demands that non of the

4.1. STRAIGHT LINE BRAKING WITHOUT ABS 35

max. BFDerror

laden unladenconguration −3 m/s2 −6 m/s2 −3 m/s2 −6 m/s2

tractor semitrailer 0.012 0.025 0.196 0.157truck trailer 0.016 0.028 0.097 0.088

truck db trailer 0.021 0.030 0.162 0.135LZV A 0.014 0.027 0.174 0.122LZV B 0.019 0.030 0.181 0.131LZV C 0.037 0.049 0.185 0.164LZV D 0.023 0.031 0.257 0.241LZV E 0.021 0.031 0.148 0.112LZV F 0.015 0.025 0.195 0.165LZV G 0.023 0.024 0.150 0.109

Table 4.1: maximum brake force distribution error

wheels of a vehicle lock when the mean fully developed deceleration is lower than 5 m/s2 as alreadymentioned in section 2.4. Although simulation scenario 1 already fulfills this demand indirectly, thesimulation scenario below is executed to get an indication at which deceleration wheels start to lockand to identify which axle locks up first;

2. Driving straight ahead with a velocity of 80 km/h a flat and dry road. The brake are applied after5 sec to achieve a deceleration which increases until one of the wheels locks. The road frictioncoefficient is set to 0.77 and during the complete manoeuvre ABS is switched off.

The deceleration values found at which wheel locks starts to occur, for both laden and unladen vehicles,are summarised in the second and fourth column of table 4.2. The third and fifth column of the sametable identifies on which axle locks up first.

laden unladenconguration ax, lock [m/s2] locking axle ax, lock [m/s2] locking axletractor semitrailer −6.7 steer axle −7.4 steer axle

truck trailer −6.9 steer axle −7.4 steer axletruck db trailer −6.7 steer axle −7.4 steer axle

LZV A −6.8 steer axle −7.4 steer axleLZV B −6.8 steer axle −7.4 steer axleLZV C −6.6 trailer axle 1 −7.4 steer axle 1LZV D −6.7 steer axle −7.4 steer axleLZV E −6.7 steer axle −7.4 steer axleLZV F −6.7 steer axle 1 −7.4 steer axle 1LZV G −6.8 steer axle 1 −7.4 steer axle 1

Table 4.2: decelerations at which axle lock up occurs

From table 4.2 the conclusion can be drawn that wheels starts to lock around −6.7 m/s2 for a ladenvehicle and at −7.4 m/s2 for an unladen vehicle. Moreover, most of the times the first steer axle of avehicle locks first. The only exception is LZV C, where the first trailer axle locks just before the wheelsof the steered axle. So, the conclusion can be drawn that for every vehicle the first steered axle will lockfirst, which is preferable regarding directional stability of vehicles.

Next to above evaluation of legal demands and locking of the wheels, the changes in vertical tyreforces and vertical coupling force during braking are analysed. Combining the results of drivingstraight ahead without braking and the results of braking with 6 m/s2 during straight ahead driving,


yields to plots like figure 4.3 for the change in vertical tyre forces and figure 4.4 for the change invertical coupling forces. The left side of these figures shows the changes for a tractor semitrailer,while the right side shows the changes for LZV C.

tractor 1 tractor 2 semi 1 semi 2 semi 30

20

40

60

80

100

120

140

160

180

axle [−]

Fz

[kN

]

axle loads of tractor semitrailer (laden)

ax= 0 m/s2

ax= −6 m/s2

(a) tractor semitrailer

truck 1 truck 2 truck 3 truck 4 trailer 1 trailer 2 trailer 30

20

40

60

80

100

120

140

160

180

axle [−]F

z [k

N]

axle loads of LZV C (laden)

ax= 0 m/s2

ax= −6 m/s2

(b) LZV C

Figure 4.3: change in vertical axle forces, left: tractor semitrailer, right: LZV C

−180

−120

−60

0

60

120

180

[kN

]

Fx 5th−180

−120

−60

0

60

120

180

Fy 5th

coupling forces of tractor semitrailer (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz 5th

(a) tractor semitrailer

−180

−120

−60

0

60

120

180

[kN

]

Fx pin−180

−120

−60

0

60

120

180coupling forces of LZV C (laden)

Fy pin

[kN

]

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz pin

(b) LZV C

Figure 4.4: change in coupling forces, left: tractor semitrailer, right: LZV C

Table 4.3 summarizes the load transfer between axles of each vehicle. The values of this table are notthe absolute values but load transfer factors, determined by dividing the axle load during braking bythe axle load when the brakes are not applied.

fload =Fz, -6 (i)

Fz, 0 (i)(4.2)

4.1. STRAIGHT LINE BRAKING WITHOUT ABS 37

where

fload = load transfer factor [−]Fz, 6(i) = vertical axle force while braking for ith axle [N ]Fz, 0(i) = vertical axle force when brakes are not applied for ith axle [N ]

A load transfer factor larger than 1.00 means an increase in vertical tyre force at an axle, while a loadtransfer factor smaller than 1.00 means that the vertical tyre force declines during braking.

fload [−]conguration axle 1 axle 2 axle 3 axle 4 axle 5 axle 6 axle 7 axle 8tractor semitrailer 1.698 0.893 0.844 0.812 0.779 − − −

truck trailer 1.447 0.712 1.407 0.592 − − − −truck db trailer 1.595 0.983 0.830 0.763 0.860 − − −

LZV A 1.670 0.853 0.998 1.010 1.021 0.832 0.762 −LZV B 1.630 0.835 1.019 1.036 1.052 0.861 0.822 0.782LZV C 1.702 0.995 0.799 0.607 1.746 0.762 0.486 −LZV D 1.535 1.023 0.888 0.945 1.145 0.856 0.816 0.777LZV E 1.583 1.000 0.852 0.985 1.129 0.848 0.682 −LZV F 1.552 1.105 1.013 0.914 0.808 0.800 0.791 −LZV G 1.463 1.161 1.080 1.003 0.833 0.808 0.783 −

Table 4.3: load transfer factors

Evaluation of the load transfer factors shows that, in general, the vertical tyre force on the first axleis approximately 1.5 times the static tyre force during braking. The variation in vertical tyre force isalso the largest at the front axle. For all other axles the variation in axle load is a lot smaller, wherethe vehicles containing a full trailer like a truck trailer and LZV C are the only exceptions. For thesevehicles, the first trailer axles have a load transfer factors close to the first axle of the truck, which canbe explained by the fact that non of the forces acting on the trailer is transferred to the truck duringbraking. This phenomena is also observed later on, at the evaluation of coupling loads. The loadtransfer factors are a first measure to identify which wheels would lock first, the tyre properties ofsection 3.3 and Appendix K show that an increase in vertical tyre force leads to decreasing adhesioncoefficients, µx and µy, and together with the fact that the load sensing valve increases the braketorque, it will cause the wheels to lock. So, front wheels of each tractive unit are likely the first to lock.

To complete the overview of vertical tyre force variations for the studied vehicles, it is necessaryto study differences in coupling forces between the non braking and the braking situation. Espe-cially changes in vertical coupling forces are investigated because those forces have an effect on the(un)loading of the axles of a tractive unit. The mean coupling forces found at both the non brakingand braking manoeuvre are summarised in table 4.4. Orientation of the forces is such that positivelongitudinal forces point to the front, positive lateral forces point to the left and positive vertical forcespoint upwards at a pulling vehicle. The orientation of the coupling forces is also schematically shownin figure 4.5, in this case for a pin coupling used on a drawbar-trailer.

At both the non braking and the braking scenario, the lateral coupling forces are 0 kN becausethe vehicles follow a straight line thus no lateral forces act on the vehicles. The longitudinal forcesmeasured when driving straight ahead without braking are caused by the rolling resistance of thetyres, the more tyres locate behind the coupling the bigger the longitudinal coupling force. Whenapplying the brakes, the longitudinal coupling forces change sign and become positive. This meansthat a part of the brake force needed to brake the load of the trailing unit is applied by the leadingunit. Exceptions to this are the truck trailer and LZV C, where the sign of the longitudinal couplingforce does not change. This means that the trailers of those configurations fully brake their own load,which can be explained by evaluating the vertical coupling forces. The coupling of both the truck trailercombination and LZV C do not experience a change in vertical force when applying the brakes. So, the


Figure 4.5: orientation of coupling forces

Forces coupling 1 0 m/s2 −6 m/s2

conguration Fx [kN ] Fy [kN ] Fz [kN ] Fx [kN ] Fy [kN ] Fz [kN ]tractor semitrailer −1.4 0.0 −117.8 106.3 0.0 −153.0

truck trailer −1.2 0.0 0.0 −0.5 0.0 0.0truck db trailer −0.9 0.0 −4.4 19.7 0.0 −29.1

LZV A −2.7 0.0 −116.4 98.8 0.0 −143.0LZV B −2.8 0.0 −100.7 87.0 0.0 −126.3LZV C −1.9 0.0 0.0 −2.0 0.0 −0.1LZV D −2.3 0.0 0.0 20.5 0.0 −30.6LZV E −2.3 0.0 −2.9 19.4 0.0 −30.8LZV F −1.7 0.0 −125.3 110.6 0.0 −167.7LZV G −1.8 0.0 −5.7 37.4 0.0 −60.0

Forces coupling 2 0 m/s2 −6 m/s2

conguration Fx [kN ] Fy [kN ] Fz [kN ] Fx [kN ] Fy [kN ] Fz [kN ]LZV A −1.3 0.0 −5.1 31.0 0.0 −47.6LZV B −1.4 0.0 −118.1 101.2 0.0 −158.0LZV D −1.4 0.0 −114.8 95.5 0.0 −153.2LZV E −1.4 0.0 −4.9 28.5 0.0 −43.1

Table 4.4: coupling forces

total load of the trailer is carried only by the trailer axles. Because the brake system is designed suchthat every axle has to brake its own load, it is clear that the axles of the trailer provide the force to brakethe full trailer mass. In contrast to the truck trailer combination and LZV C, the other configurationsdo experience vertical coupling forces. This vertical forces also changes when the brakes of the vehiclesare applied. A distinct difference in vertical coupling forces is identified between a fifth wheel and apin coupling.

Evaluating the results presented in this section, the following conclusions can be drawn regard-ing the implemented brake system and braking performance. Firstly, the implemented brake systemcontrols the brake force distribution in such a way that all vehicles, both laden and unladen, obey leg-islation enforced by the European Community. Moreover, ideal brake force distribution is approachedwithin a maximum error of 4.9 % and 25.5 % for respectively laden and unladen vehicles. When com-paring the brake force distributions of the conventional commercial vehicles and the LZV vehicles, nodistinct differences are found. LZV’s created by coupling an extra trailing unit to a conventional con-figuration perform equal or even beter than the conventional vehicle, e.g tractor semitrailer and LZVA or truck drawbar-trailer and LZV E. Secondly, during braking the vertical tyre forces changes themost at the first axle. When braking with a deceleration of 6 m/s2, the vertical tyre forces are approxi-mately 50% higher then the static value, causing the steered wheels at the first axle to lock first. From

4.2. STRAIGHT LINE BRAKING WITH ABS 39

a stability perspective it is preferable that the steer axle wheels lock up first because than the vehiclewill remain stable, although no steering adjustment can be made. For laden vehicles the wheels lockaround −6.7 m/s2 and at −7.4 m/s2 when vehicles are unladen.

4.2 Straight line braking with ABS

The previous section evaluated the performance of the brake system, when ABS did not interact duringbraking. So, only the performance of the LSV part was taken into account. In this section the ABS isactive during braking and the ABS performance and the dynamic behaviour of the different vehiclesis evaluated for three braking scenarios. The first and second scenario at which ABS interacts duringbraking are described as;

3. Driving straight ahead with a velocity of 80 km/h on a flat and dry road. After 5 sec the brakes areapplied to achieve a deceleration of 8 m/s2 to come to standstill. The manoeuvre is performedtwice, the first time ABS is switched off and the second time ABS is switched on. The tyre roadadhesion of the dry road is 0.77 .

4. Scenario 3 where the dry road is replaced by a wet/icy road and the achievable deceleration ischanged to 6 m/s2. The wet/icy road has a adhesion coefficient of 0.38, like specified in table3.1.

To check if the implemented ABS prevents the wheel from locking, the angular wheel speeds in timeare analysed for scenario 3. Figure 4.6 shows the time histories of the angular wheel speeds for aladen truck drawbar-trailer. The figure reveals that the implemented ABS works correctly because thewheels don not lock when ABS is switched on.

4 5 6 7 8 9 10 11 12−10

0

10

20

30

40

50

time [sec]

Ω s

teer

axl

e

[rad

/sec

]

angular wheel speeds of truck wheels

no ABS leftno ABS rightABS leftABS right

4 5 6 7 8 9 10 11 12−10

0

10

20

30

40

50

time [sec]

Ω d

rive

axle

1

[ra

d/se

c]


4 5 6 7 8 9 10 11 12−10

0

10

20

30

40

50

time [sec]

Ω d

rive

axle

2

[ra

d/se

c]


4 5 6 7 8 9 10 11 12−10

0

10

20

30

40

50

time [sec]

Ω a

xle

1[r

ad/s

ec]

angular wheel speeds of drawbar−trailer wheels


4 5 6 7 8 9 10 11 12−10

0

10

20

30

40

50

time [sec]

Ω a

xle

2[r

ad/s

ec]


Figure 4.6: angular wheel speeds of truck drawbar-trailer wheels during braking on a dry road


Preventing wheel lock should result in a decrease in distance traveled between brake applicationand standstill, the so-called stopping distance which is indicate by sstop. The stopping distances withand without ABS for both laden as well as unladen vehicles on a dry road are summarised in table4.5 while table 4.6 summarises the results for a wet/icy road. The last row of both tables contains areference distance which is analytically determined substituting the longitudinal velocity and the roadadhesion coefficient of the dry and wet/icy road into

sstop,ref =V 2x −

2gµ+td2Vx (4.3)

where

td = time delay of valves and pneumatics = 1.5 sec

sstop on a dry road [m]laden unladen

conguration no ABS ABS ∆ no ABS ABS ∆tractor semitrailer 54.84 48.86 5.98 52.08 49.43 2.66

truck trailer 54.91 49.44 5.46 52.27 49.41 2.86truck db trailer 54.63 48.63 6.00 51.18 49.33 1.85

LZV A 54.97 49.07 5.90 51.76 49.26 2.50LZV B 54.77 49.17 5.61 51.24 49.28 1.96LZV C 54.74 49.31 5.44 51.65 49.07 2.58LZV D 54.64 48.50 6.13 50.78 49.34 1.45LZV E 54.87 48.81 6.06 50.59 48.94 1.65LZV F 54.63 48.43 6.20 51.14 49.03 2.12LZV G 54.74 48.52 6.22 50.85 48.88 1.97

reference sstop via (4.3) 49.35

Table 4.5: stopping distances with and without ABS for a dry road

sstop on a wet/icy road [m]laden unladen

conguration no ABS ABS ∆ no ABS ABS ∆tractor semitrailer 98.26 80.58 17.68 95.92 79.61 16.31

truck trailer 98.84 80.12 18.72 95.98 80.47 15.51truck db trailer 97.49 78.22 19.27 95.31 78.71 6.60

LZV A 98.92 81.00 17.91 95.80 80.13 15.67LZV B 98.37 81.46 16.91 95.71 80.39 15.33LZV C 98.77 79.17 19.60 95.35 79.48 15.87LZV D 97.77 79.05 18.73 95.23 79.06 16.17LZV E 98.39 78.95 19.44 95.36 79.74 15.62LZV F 97.76 78.61 19.15 95.17 77.76 17.41LZV G 98.18 79.09 19.10 95.16 79.08 16.08

reference sstop via (4.3) 82.90

Table 4.6: stopping distances with and without ABS for a wet/icy road

The results of tables 4.5 and 4.6 reveal that the stopping distance is reduced when ABS prevents wheellock, especially when a vehicle is laden and on a wet/icy road. Furthermore, it can be concluded that


there is no distinct difference between conventional vehicles and LZV’s and between LZV themselvesregarding reduction in stopping distance.

Besides a shorter stopping distance on a dry and wet or icy road, it is expected that vehicle direc-tional behaviour improves when ABS is active during braking on a µ-split road. Whether directionalbehaviour improves by implementing ABS, is investigated by the following manoeuvre;

5. Driving straight ahead with a velocity of 80 km/h on a µ-split road. After 5 sec the brakes areapplied to achieve a deceleration of 6 m/s2 to come to a stop. The specification of the road issuch that the road has a adhesion coefficient of 0.77 on the left side and 0.38 on the right side,like already mentioned in table 3.1. The manoeuvre is performed twice, the first time ABS isswitched off and the second time ABS is switched on.

For the µ-split scenario, one can expect more distinct differences between vehicles, because brakeforces developed at the left and right of an axle are different. This introduces additional moments onthe units of a vehicle and its couplings, which causes the vehicle to deviate to the high friction side ofthe road. The vehicle behaviour for the µ-split manoeuvre is analysed by evaluating the traveled pathand articulation angles. The longitudinal and lateral traveled path and the articulation angle for ladenLZV A and for LZV E are shown in figure 4.7. The left side of the figures represents LZV A and theright side LZV E. For the µ-split figures of the remaining configurations refer to Appendix A till J.

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV A (laden)

steer axle no ABSdrive axle no ABSsteer axle ABSdrive axle ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

semitrailer axle1 no ABSsemitrailer axle2 no ABSsemitrailer axle3 no ABSsemitrailer axle1 ABSsemitrailer axle2 ABSsemitrailer axle3 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

dbtrailer axle1 no ABSdbtrailer axle2 no ABSdbtrailer axle1 ABSdbtrailer axle2 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl2 no ABScpl2 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV E (laden)

steer axle no ABSdrive axle 1 no ABSdrive axle 2 no ABSsteer axle ABSdrive axle 1 ABSdrive axle 2 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

dbtrailer1 axle1 no ABSdbtrailer1 axle2 no ABSdbtrailer1 axle1 ABSdbtrailer1 axle2 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200

−150

−100

−50

0

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl2 no ABScpl2 ABS

Figure 4.7: path during braking on a µ-split road, left: laden LZV A, right: laden LZV E


Table 4.7 summarises the µ-split manoeuvre for the laden vehicles by mentioning the stopping dis-tance, the lateral course deviation, and the articulation angles for braking on a µ-split road with andwithout ABS. The result for µ-split braking with an unladen vehicle are placed in table 4.8.

sstop and lateral deviation [m] articulation angle []laden vehicles sstop lateral dev. cpl 1 / cpl 2 / turntableconguration no ABS ABS no ABS ABS no ABS ABStractor semitrailer 63.22 64.28 3.91 2.62 160.24 / - / - 3.16 / - / -

truck trailer 69.23 69.64 0.65 1.50 16.76 / - / 19.17 1.86 / - / 0.74truck db trailer 67.71 66.76 4.21 0.96 26.03 / - / - 0.48 / - / -

LZV A 62.49 63.90 3.83 2.51 165.36 / 8.28 / - 3.53 / 2.72 / -LZV B 62.46 63.95 4.37 1.83 139.61 / 5.12 / - 1.93 / 1.67 / -LZV C 68.70 70.85 1.15 1.13 11.03 / - / 14.90 1.45 / - / 1.02LZV D 66.39 67.11 1.89 1.86 4.01 / 5.60 / - 2.68 / 1.92 / -LZV E 67.23 65.52 3.77 0.62 21.14 / 8.75 / - 0.45 / 0.34 / -LZV F 66.85 66.88 4.62 0.93 24.30 / - / - 0.59 / - / -LZV G 66.79 67.08 3.11 0.16 12.90 / - / - 0.84 / - / -

Table 4.7: stopping distance, lateral deviation and articulation angles for laden vehicles with andwithout ABS, on a µ-split road

sstop and lateral deviation [m] articulation angle []unladen vehicles sstop lateral dev. cpl 1 / cpl 2 / turntableconguration no ABS ABS no ABS ABS no ABS ABStractor semitrailer 64.19 70.74 3.56 1.27 126.18 / - / - 1.23 / - / -

truck trailer 67.73 74.23 1.52 0.94 2.41 / - / 2.29 1.07 / - / 0.85truck db trailer 66.34 70.61 3.11 0.65 11.60 / - / - 0.24 / - / -

LZV A 64.24 69.89 3.48 1.24 135.84 / 3.88 / - 1.60 / 0.77 / -LZV B 64.67 71.10 3.73 0.85 120.63 / 1.84 / - 0.68 / 0.44 / -LZV C 68.01 74.12 1.78 0.70 1.85 / - / 1.96 1.02 / - / 1.07LZV D 67.43 71.59 2.50 1.14 3.59 / 4.33 / - 1.31 / 1.07 / -LZV E 66.95 70.02 3.39 0.55 17.48 / 1.65 / - 0.55 / 0.39 / -LZV F 66.60 70.21 2.80 0.80 6.13 / - / - 0.66 / - / -LZV G 67.47 72.05 2.22 0.16 3.92 / - / - 0.38 / - / -

Table 4.8: stopping distance, lateral deviation and articulation angles for unladen vehicles withand without ABS, on a µ-split road

At first glance the path deviations contradict, switching ABS on leads to an increase of the longi-tudinal path while the lateral path decreases. One explanation for the increase in longitudinal pathis found by taking the articulation angles into account. Large deviations in articulation angles meansthat the vehicle has a tendency to jackknife, especially when ABS is switched off. Switching ABS onprevents for jackknifing but because the stopping distance is measured at the front axle, the stoppingdistance increases. Analysing the articulation angles of tables 4.7 and 4.8 clarifies that especially ve-hicle containing a tractor and a semitrailer, have a tendency to jackknife. A second explanation for theincreased stopping distance, is that the ABS of the steered axles uses select low control. In this way,unwanted and uncontrollable steering moments are avoided but the road adhesion is not fully utilised.Replacing the select low control with "Modified Individual Control", abbreviate as MIR, could shortenthe stopping distance. "Modified Individual Control" is implemented in the ABS of steered axles ofmodern commercial vehicles and it monitors and compares the angular wheel speeds of the left andright wheel. By means of a difference between the wheel speeds of the left and right wheel, brakingon a µ-split road is identified. The "Modified Individual Control" starts with a select-low approach.


After a few seconds the brake force at the high µ-side is built up gradually. With "Modified IndividualControl" uncontrollable steering reactions due to brake force differences are avoid and the high µ-sideof the road is utilised better.

The results show that ABS improves the braking performance on a µ-split road and the next con-clusion can be drawn. LZV C needs the largest stopping distance followed by LZV E. Comparingconventional vehicles and LZV’s shows no distinct difference, LZV’s perform equal or even a bit bet-ter than conventional vehicles. Looking at lateral path deviation, a tractor semitrailer combinationperforms worst followed by LZV A and LZV G has the smallest deviation. Furthermore, brake per-formance of LZV’s created by coupling an extra trailing unit to a conventional configuration is equalor even beter than the conventional vehicle, e.g tractor semitrailer and LZV A or truck drawbar-trailerand LZV E. Legislation regarding ABS, see section 2.4, is partly fulfilled. Total fulfillment could beexpected, but can not be proven because the data sets of the performed simulations do not containall signals needed. For instance, steer angle adjustments to maintain course are not available becausesteering is controlled by a pre-defined steering angle, open loop steering, instead of a driver model,closed loop steering.

To conclude this section, a general conclusion about ABS performance of commercial vehicles isformulated. As mentioned earlier, the braking performance of commercial vehicles at critical brakesituations improves when they are equipped with ABS, so the existing type approval demand thatLZV’s should be equipped with ABS is confirmed.

(a) LZV A without ABS, the vehicle does jackknife

(b) LZV A with ABS, the vehicle does not jackknife

Figure 4.8: braking on a µ-split road with LZV A


4.3 Braking while driving a circle

The preceding sections evaluate braking performance for braking in a straight line. This section treatsbraking while driving a circle resulting in a vehicle which is subjected to both steering and braking.The main goal is to determine the path deviation for each vehicle. The manoeuvre driven is based onISO standard 14797:2003 [11] and is described below;

6. Driving a circular path with a velocity of 50 km/h on a dry and level road. The circular pathhas a radius of 100 m. Initially the steering input is 0, after 10.8 sec the steering input starts toincrease for 3 sec. From that point on, the steering input is kept constant and the vehicle startsto travel the circular path. The manoeuvre ends when 2 complete circles are covered or whenthe vehicle comes to a standstill. This manoeuvre is driven twice, namely without application ofthe brakes and a second time with application of the brakes to achieve a deceleration of 1.5 m/s2.At al simulations, ABS is switched on but it should not interact during braking.

At above scenario, the steering angle is prescribed in time. Therefore the steering input for eachvehicle must be determined in advance. By means of the desired velocity and the radius of 100 m, areference yaw velocity is calculated with;

ψref =360 Vx

2 π Rpath(4.4)

where

ψref = reference yaw velocity [rad/s]Vx = velocity of vehicle [m/s]Rpath = radius of circular path [m]

By comparing this reference yaw velocity with the yaw velocity signal during a spiral manoeuvre, theneeded steering input is found [16]. The spiral manoeuvre is described in more detail at section 5.1 asscenario 9.

The traveled path for LZV B is shown in figure 4.9, the left graph shows the global path and at theright graph there is zoomed in on the path deviation. The figures for the remaining vehicles can befound in Appendix A till J.

−100 −50 0 50 100

−100

−50

0

50

100

lateral path [m]

long

itudi

nal p

ath[

m]

path of steer axle, LZV B (laden)

0 m/s2

−1.5 m/s2

reference

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), LZV B (laden)

0 m/s2

−1.5 m/s2

reference

Figure 4.9: traveled path for LZV B, left: global path, right: zoomed in path

The path deviation figures show that applying the brakes during a circle, causes the vehicles to deviate

4.3. BRAKING WHILE DRIVING A CIRCLE 45

to a smaller cornering radius. This observation can be explained via the tyre behaviour, braking intro-duces longitudinal tyre slip which causes the cornering stiffness of the tyres to drop. Another aspectwitch occurs at the same time is the (un)loading of the tyres by load transfer, the drop in corneringstiffness is compensated at tyres which are laden but at unladen tyres the cornering stiffness dropsfurther. Consequently, the tyre side slip angle at the unladen tyres increases and the vehicle becomesoversteered.

To identify differences between the studied vehicles, the maximum path deviation is determined bycalculating the resulting radius when the vehicles had come to a stop. Table 4.9 contains the deviationsfor all vehicles, analysing the results leads to the following findings. Firstly, course deviation is the

path deviation [m]conguration laden unladentractor semitrailer 2.68 3.94

truck trailer 2.43 2.14truck db trailer 2.45 1.91

LZV A 2.97 4.20LZV B 3.62 4.42LZV C 2.88 2.03LZV D 2.75 1.61LZV E 2.55 2.10LZV F 2.22 2.04LZV G 1.71 1.74

Table 4.9: deviation from R = 100 m for braking in a turn

largest for LZV B and the smallest for LZV G, both in laden as well as unladen condition. The secondworst performing vehicle is LZV A, where it is remarkable that both LZV B and LZV A contain atractor coupled to a semitrailer. Secondly, when comparing track deviation between laden and unladenvehicles, LZV B, LZV A and the tractor semitrailer show an bigger deviation when unladen where allother vehicles show a smaller deviation when unladen, again it is remarkable that LZV B, LZV A arebased on a tractor semitrailer combination. Thirdly, LZV’s based on conventional vehicles performworst regarding course holding than the conventional vehicles where they are based on, as LZV Abased on a tractor semitrailer and LZV E based on a truck drawbar-trailer.

Besides maximum path deviation, also longitudinal acceleration, lateral acceleration, yaw velocityand articulation angles are evaluated in time. The longitudinal acceleration, the lateral accelerationand the yaw velocity are measured at the first axle of the vehicle, the placement of this axle is equalfor each vehicle thus measurements are not influenced by geometric differences. In contrast withpath deviation, longitudinal acceleration, lateral acceleration, yaw velocity and articulation angles areevaluated only by means of time histories for laden and unladen vehicles. Figure 4.10 show longitu-dinal acceleration, lateral acceleration, yaw velocity and articulation angles in time for LZV B, at theleft when laden and at the right when unladen. Once again, time histories of longitudinal accelera-tion, lateral acceleration, yaw velocity and articulation angels of the remaining vehicles can be foundin Appendix A till J. The time histories show that after applying the brakes at t = 60 sec, the decreasein radius dominates the change in lateral acceleration and yaw velocity. At t ≈65 sec the decrease inspeed becomes the dominate parameter of changes in lateral acceleration and yaw velocity. The timehistories also show that course holding of LZV B, LZV A and the tractor semitrailer are the most sen-sitive to application of the brakes, those vehicles show the biggest yaw velocity overshoot after applyingthe brakes.


50 55 60 65 70 75 80

0

20

40

60V

x [k

m/h

]braking in a turn, LZV B (laden)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

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ax [m

/s2 ]

0 m/s2

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input

50 55 60 65 70 75 80−1

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ay [m

/s2 ]

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reference

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yaw

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[o /s]

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reference

50 55 60 65 70 75 80−8

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art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

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time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −1.5 m/s2

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0

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Vx

[km

/h]

braking in a turn, LZV B (unladen)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

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input

50 55 60 65 70 75 80−1

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ay [m

/s2 ]

0 m/s2

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reference

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vel

[o /s]

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reference

50 55 60 65 70 75 80−8

−6.5

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art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −1.5 m/s2

Figure 4.10: signals during braking in a turn for laden/unladen LZV B

4.4 Braking while taking a highway exit

The previous section evaluated braking when driving a circle which is a useful experimental manoeu-vre. However, in reality a commercial vehicle will not encounter such a manoeuvre. This sectionevaluates the braking performance and vehicle behaviour for a more realistic manoeuvre, namelybraking while taking a highway exit. Braking on a highway exit appears for instance when a queue ofcars is waiting in front of a traffic light at the end of the exit. The driven highway exit is based on aexisting highway exit and is described below. Figure 4.11 shows the used highway exits, the left graphis the virtual exit while the right picture show the highway exit in reality.

7. The highway exit manoeuvre consist of several parts. The manoeuvre starts with driving ina straight line for 50 m, representing a lane of the highway. After 50 m a lane change starts,leading to a lateral movement of 3.5 m when the vehicle has travel a total longitudinal distanceof 150 m representing entering the exit lane. After the lane change, the vehicle maintains drivesin a straight line for 150 m, at this point the curvature part of the exit starts. The curvature partis half a circle with a radius of 150 m. The exit is completed by a straight line of 60 m. Thelongitudinal velocity of the vehicle during the complete manoeuvre is 65 km/h and again thismanoeuvre is driven twice, once without braking and the second time with application of thebrakes to achieve a deceleration of 3 m/s2. The brake application point lays at the 120 point of

4.4. BRAKING WHILE TAKING A HIGHWAY EXIT 47

the curvature part approximately, as indicated in figure 4.11. During this highway exit, ABS isswitched on and he steering wheel angle is controlled by the driver model described in section3.5.

0 50 100 150 200 250 300 350 400 450

−300

−250

−200

−150

−100

−50

0


late

ral p

ath

[m]

highway exit

desired pathdriven path

Brakeapplication

Figure 4.11: virtual and real highway exit [13]

The change in steering angle when applying the brakes, both the maximum change in steering wheelangle, ∆δs, and the rate of steering wheel angle change, are evaluated in this research because theyindicate if it is possible for the driver to maintain course. Table 4.10 holds the resulting maximumangles and the rate of change. The rate of steering angle change is found by fitting a first order polyno-mial through the steering wheel angle from the brake application point to the point where the changein steering wheel angle reached its maximum.

conguration max. ∆δs [] ∆δs rate [/s]tractor semitrailer 16.2 9.9

truck trailer 26.0 13.4truck db trailer 23.7 12.1


Table 4.10: maximum δs deviation and δs rate for highway exit

Besides the results of table 4.10, time histories of longitudinal acceleration, lateral acceleration, steer-ing wheel angle, articulation angles and coupling forces are analysed. Figure 4.12 shows the signalsfor LZV D, for the figures of the remaining vehicles Appendix A till J should be consulted.

By analysing the progress of the steering wheel angle and the articulation angles it is observedthat the vehicles become oversteered when the brakes are applied. Because of this oversteer tendency,the steering wheel angle is declined to maintain course. The largest change in steering wheel angleis found for LZV C, which is substantial larger than for all other vehicles. This can be explained bylooking at the intervention of ABS. At LZV C, ABS intervenes at the inner driven wheels thereby gen-erating a torque which amplifies the oversteer tendency. At the other configurations ABS intervenes at


the last inner wheels of the configuration having little to no effect on the course holding of the tractiveunit.

The rate of steering wheel angle change does not show big deviations between vehicles, so thesteering demand on the driver is more or less equal for each vehicle when applying the brakes whiletaking a highway exit. The average rate of change is 11/s which is within the range a driver canmaster.

0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

Vx

[km

/h]

signals during highway exit, LZV D

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ax [m

/s2 ]

0 m/s2

−3 m/s2

input

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ay [m

/s2 ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50

−8−6−4−2

02

yaw

vel

[o /s]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−80−60−40−20

020

δ s

[o ]

0 m/s2

3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −3 m/s2

Figure 4.12: signals during highway exit, LZV D

4.5. SUMMARY OF BRAKING PERFORMANCE 49

4.5 Summary of braking performance

This section contains an summary of the brake performance of conventional commercial vehicles andLZV’s. The significant conclusion drawn regarding brake performance are;

• Conventional commercial vehicles and LZV’s perform equal regarding brake force distributionand fulfillment of legalisation.

• LZV’s should be equipped with an Anti-lock Brake System. Preventing wheel lock improvesthe stopping distance on a dry and wet/icy road and it prevents jackknifing when braking on aµ-split road.

• When applying the brakes during a steering, commercial vehicles tend become oversteered. Thechange in steering angle necessary to maintain course is such that the changes are within thecapabilities of the driver.

Comparing the brake performance of all studied vehicles with the average brake performance givesthe classification of vehicles as in the table below.

brake performanceconguration legislation sstop µ-split steering and braking overalltractor semitrailer ++ + − + +

truck trailer ++ +− − − −truck db trailer ++ + + +− ++

LZV A ++ + − +− +−LZV B ++ +− − − +−LZV C ++ +− −− − −LZV D ++ ++ +− − +−LZV E ++ + + +− +LZV F ++ ++ + ++ ++LZV G ++ ++ + ++ ++

Table 4.11: summary of brake performance of conventional commercial vehicles and LZV's(++ = excellent, + = adequate, +− = moderate, − = inadequate, −− = poor)


Chapter 5

Roll-over stability of LZV's

This chapter discusses the roll-over stability of fully laden conventional commercial vehicles andLZV’s. In the first section roll-over of the different vehicles is evaluated in a quasi-static way by calcu-lating the static roll-over thresholds for a steady state circle and a spiral manoeuvre. The static roll-overthresholds provides a first indication about roll-stability of heavy commercial vehicles but to investigateroll-over more thoroughly, roll-over has to be approached as a dynamic event. This dynamic approachstarts at the second section, where a sinusoidal input with varying frequency is applied to the steeringwheel. By means of the dynamic load transfer ratio, the rearward amplification and the yaw damp-ing coefficient, roll-stability is evaluated for each vehicle. The dynamic approach is continued in thethird section by analysing the roll-over stability during a double lane change, representing an obsta-cle avoidance scenario. The fourth section deals with a parameter studie. In this section the vehiclespeed, roll stiffness and damping constant are varied and the effect of those changes on roll-stability isevaluated by driving the single lane change again. The fifth, and last, section of this chapter contains ashort summary of the significant results and conclusions regarding roll-over stability of conventionalcommercial vehicles and LZV’s.

5.1 Static roll-over threshold

In this section, roll-over is approached as a quasi-static event to get a first indication of the differencein roll-over stability between vehicles. The quantity used to compare between vehicles is the so-called"static roll-over threshold" abbreviated as SRT , which is nothing more than the value of lateral accel-eration, in m/s2, at which the vehicle rolls-over. The two manoeuvres driven to determine the staticroll-over threshold are a spiral and a circle manoeuvre, the exact descriptions are given below.

8. Driving a circular path with a radius of 100 m on a dry and level road. At the start of the ma-noeuvre the velocity is 60 km/h which is increased with an increment of 1 km/h until roll-overoccurs. The steering angles are prescribed in time, like already done at the braking while drivinga circle manoeuvre, manoeuvre 6 in section 4.3.

9. Driving a spiral path with decreasing radius at a velocity of 50 km/h on a dry and level road. Themanoeuvre starts with driving in a straight line for 10.8 sec. At that point the steering wheelangle is set to the value used to drive a circle with radius of 100 m. During the remainder ofthe manoeuvre the steering wheel angle increases till 200 at t = 200 sec. During the completemanoeuvre the velocity is kept constant by means of a cruise control.

The time histories of the velocity of the vehicle, the steering wheel angle, the lateral acceleration, theroll angle and the dynamic load transfer ratio, shortened as DLTR, during manoeuvre 9 and 8 areshown in figure 5.1 for LZV A. The left side represents the steady state circle signals and the right siderepresents the signals for the spiral.

51

52 CHAPTER 5. ROLL-OVER STABILITY OF LZV'S

0 50 100 150 20050

55

60

65

70

Vx

[km

/h]

steady state circle signals, LZV A

Vx

0 50 100 150 2000

25

50

75

100

δs[o ]

δs

0 50 100 150 2000

1

2

3

4

ay [m

/s2 ]

ay

0 50 100 150 2000

2

4

6

8

φ [o ]

front tractorrear tractorfront semitrailerrear semitrailerdbtrailer

0 50 100 150 2000

0.25

0.5

0.75

1

time [sec]

DLT

R [−

]

DLTR 1DLTR 2DLTR 3limit

0 10 20 30 40 50 60 70 80 90 1000

15

30

45

60

Vx

[km

/h]

steady state spiral signals, LZV A

Vx

0 10 20 30 40 50 60 70 80 90 1000

40

80

120

160

δs[o ]

δs

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

ay [m

/s2 ]

ay

0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

φ [o ]


0 10 20 30 40 50 60 70 80 90 1000

0.25

0.5

0.75

1

time [sec]

DLT

R [−

]

DLTR 1DLTR 2DLTR 3limit

Figure 5.1: signals in time for steady state circle and spiral, LZV A

The point in time where the dynamic load transfer ratio becomes larger then 0.9 for one of theunits of a vehicle is indicated as roll-over point and the corresponding lateral acceleration of the steeraxle is defined as the static roll-over threshold for that specific vehicle. The thresholds found for eachvehicle are represented in table 5.1 for both manoeuvres.

static roll-over thresholdconguration circle [m/s2] Vx [km/h] spiral [m/s2] R [m]tractor semitrailer 3.24 64.80 3.24 59.53

truck trailer 3.95 71.55 3.85 50.10truck db-trailer 3.44 66.77 3.33 57.93

LZV A 3.27 65.10 3.26 59.17LZV B 3.31 65.50 3.38 57.07LZV C 2.99 62.25 2.92 66.06LZV D 3.34 65.79 3.29 58.63LZV E 3.43 66.67 3.35 57.58LZV F 3.09 63.28 3.07 62.83LZV G 3.05 62.87 2.96 65.17

Table 5.1: static roll-over threshold for steady state circle and spiral

5.2. DYNAMIC ROLL-OVER, SINGLE LANE CHANGE 53

By means of the static roll-over threshold values of table 5.1, LZV C is identified as vehicle hav-ing the lowest threshold followed by LZV G and the highest roll-over threshold is found for the trucktrailer. Both LZV C and LZV G exist of a heavy loaded 8x4 truck coupled to a trailer or drawbar-trailerwhere the units are roll uncoupled, so there is no roll moment transfer between units. The dynamicload transfer ratio in time figures of LZV C and LZV G, see Appendix C and C, show that the heavyloaded truck reaches the roll-over point first. So at first glance, LZV C and LZV G could be marked asthe vehicles easiest to roll-over but they do not roll-over at all. At the roll-over point the driven wheelslift off and traction is lost, leading to a drop in vehicle velocity and thereby reducing the change ofrolling-over. In general, this observation holds for every scenario where the tractive unit is the firstunit to reach the roll-over point. Actually, roll-over will only occur when a trailing unit is the first toroll-over because in that case, traction is not lost and thereby the velocity can still increase.

To conclude this section, the threshold for the conventional vehicles are compared with the thresh-olds of the LZV’s. This comparison leads to the observation that there is no distinct difference in thestatic roll-over threshold between conventional vehicles and LZV’s although the load is increased from40 to 60 ton. An explanation can be found in the fact that although the total load is increased, the massof roll uncoupled units is kept equal thus the roll-over threshold for each roll uncoupled unit shouldbe equal too. The only difference between conventional commercial vehicles and LZV’s is the traveledradius of the units because of the differences in the spatial placement of the units.

5.2 Dynamic roll-over, single lane change

In the previous section, a first indication about roll stability of the different vehicles is given by eval-uating roll-over as a quasi-static event. However, in reality roll-over accidents are dynamic events inwhich yaw stability plays an important role [30]. So in this section, roll-over stability is quantified bymeans of the dynamic load transfer ratio, the rearward amplification and the yaw damping during amore dynamic manoeuvre. In addition to the quantification of the roll-over stability of each vehicle,this section also shows the influence of steering frequencies on roll-stability. The used manoeuvre isin essence nothing more than a single lane change, an exact description is given below.

10. Apply a single sinusoidal input at the steering wheel to drive a single lane change. The singlelane change is repeated for a frequency range of 0.1 until 3.0 Hz with an increment of 0.1 Hz.Because open loop steering is used, the amplitude of the steering input has to vary betweenvehicles so that each vehicle travels the same path at a specific frequency. During the lanechange, the velocity of the vehicle is kept constant at 80 km/h and the manoeuvre is driven withfully laden vehicles only.

As an example, the time histories of the steering wheel angle, the dynamic load transfer ratio for eachroll unit, e.g. DLTR1, DLTR2 and DLTR3, the lateral acceleration of the first and last axle and theroll angles during a single lane change with a input frequency of 0.3 Hz are show in figure 5.2, in thiscase for LZV E. By means of the time histories like figure 5.2, the maximal dynamic load transfer ratioand the rearward amplification for each frequency are calculated resulting in a serie of maximum loadtransfer ratios and and a serie of rearward amplifications for each vehicle. By plotting those maximumdynamic load transfer ratios and rearward amplifications against the range of frequencies it becomespossible to compare roll-stability between vehicles, to evaluate roll-stability for one specific vehicle andto analyse the influence of steering input frequency on roll-stability. Figure 5.3 shows the maximumdynamic load transfer ratio and the rearward amplification against input frequency for LZV E, the leftplot is the maximum load transfer ratio figure while the right plots represents the rearward amplifica-tion. The figures for the remaining vehicles are placed in Appendix A until J, just as before.

The maximum dynamic load transfer ratios and rearward amplifications for each vehicle are sum-marised in table 5.2 which also states the frequencies at which the dynamic load transfer ratio andthe rearward amplification peaks. When evaluating the dynamic load transfer ratio and the rearwardamplifications of table 5.2, the conclusion can be drawn that LZV E and LZV A have the worst roll-over stability. Both configurations are in origin a conventional vehicle to which a drawbar-trailer iscoupled to create a LZV. This extra drawbar-trailer causes the roll-stability to decline which becomes


0 5 10 15 20 25 30−40

−20

0

20

40

δ st

eer

[o ]

signals, LZV E @ 0.3Hz

δ steer

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2DLTR 3

0 5 10 15 20 25 30−5

−2.5

0

2.5

5

ay [m

/s2 ]

ay first axleay last axle

0 5 10 15 20 25 30−5

−2.5

0

2.5

5

time [sec]

φ [o ]

front truckrear truckdbtrailer1dbtrailer2

Figure 5.2: signals during a single lane change of 0.3 Hz, LZV E

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Dynamic Load Transfer Ratio, LZV E

DLTR 1DLTR 2DLTR 3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.5

1

1.5

2

2.5

3

3.5

freq [Hz]

RA

[−]

Rearward Amplification axles, LZV E

steerdrive1drive2dbtrailer1 axle1dbtrailer1 axle 2dbtrailer2 axle1dbtrailer2 axle2

Figure 5.3: DLTR and RA versus against frequency for a single lane change, LZV E

clear when the dynamic load transfer ratio and the rearward amplification of LZV A are comparedwith the tractor semitrailer values or when comparing LZV E and the truck drawbar-trailer. Next tothe values of table 5.2, the dynamic load transfer ratio and rearward amplification plots in Appendix


A and figure 5.3 show that the dynamic load transfer ratio and the rearward amplification are thehighest for the last drawbar-trailer. The above observations can be generalised to make a classi-

single lane changeconguration max. DLTR [−] f [Hz] max. RA [−] f [Hz]tractor semitrailer 0.621 0.1 1.402 0.3

truck trailer 0.484 0.2 2.211 0.6truck db-trailer 0.504 0.1 1.721 0.3

LZV A 0.878 0.3 2.489 0.4LZV B 0.568 0.1 1.486 0.3LZV C 0.710 0.3 2.400 0.4LZV D 0.519 0.1 1.917 0.3LZV E 1.000 0.3 3.365 0.3LZV F 0.640 0.1 1.517 0.3LZV G 0.699 0.2 1.841 0.3

Table 5.2: maximum DLTR and RA values and corresponding steering frequency

fication in configuration types, especially when the rearward amplifications are sorted. The highestrearward amplifications are found for configurations having two articulation points and one or moreroll-uncoupled units with short wheelbase, thus LZV E and LZV A, followed by the configurations hav-ing two articulation points and one or more roll-uncoupled units with a larger wheelbase, thus LZVC, truck trailer and LZV D. The lowest rearward amplifications are found for configurations with onearticulation point and roll-coupled units, thus LZV F, LZV B and a tractor semitrailer. This generali-sation enhances the trade-off between manoeuvrability and roll-over found during previous researchon the roll-over stability of LZV’s [18].

With above classification in mind and by comparing the dynamic load transfer ratios and the rear-ward amplification of conventional commercial vehicles and LZV’s, the conclusion can be drawn thatLZV’s roll-over more easily than conventional commercial vehicles. However, the best LZV performsbetter than the worst conventional commercial vehicle. The results in table 5.2, and the figures likefigure 5.7, also show that he dynamic load transfer ratio and the rearward amplification peaks between0.1 and 0.6 Hz. This frequency range is exactly the frequency band utilised by the driver. In otherwords, a steering adjustment by the driver can cause the vehicles to roll-over.

Besides the dynamic load transfer ratio and the rearward amplification, there is another quantifi-cation which can be useful to compare roll-over stability between vehicles, namely the yaw dampingcoefficient, abbreviated as Y DC. The amount of yaw damping will effect the rearward amplification,a low yaw damping coefficient will result in a high rearward amplification and vice versa. In this re-search, the yaw damping coefficient is calculated by means of the logarithmic decrement [9]. Thislogarithmic decrement represents the rate at which the amplitude of a free damped vibration declinesand can be calculated by

δ =1nln

Ai

Ai+n(5.1)

where

δ = logarithmic decrement [−]n = number of cycles [−]Ai = amplitude of cycle i [−]

and to calculate the yaw damping coefficients, the resulting logarithmic decrement value is substitutedinto;

Y DC =δ2√

(2π)2 + δ2(5.2)


To determine the yaw damping coefficient of each vehicle, the lateral accelerations of the first and lastaxle during a single lane change with a steering frequency of 0.3 Hz are used. The lateral accelerationsin time of each vehicle are shown in figure 5.4 and the resulting yaw damping coefficients are placedin table 5.3.

conguration Y DC [−]tractor semitrailer 0.726

truck trailer 0.250truck db-trailer 0.373

LZV A 0.073LZV B 0.592LZV C 0.129LZV D 0.440LZV E 0.002LZV F 0.684LZV G 0.320

Table 5.3: Y DC for a single lane change of 0.3 Hz

In essence, the yaw damping coefficient is nothingmore than ratio between yaw damping constant andcritical yaw damping constant, like the well-known damping factor. A yaw damping coefficient lowerthan one means that the vehicle is underdamped regarding yaw. So, according to table 5.3 all studiedvehicles are underdamped. This can also be concluded when evaluating the lateral accelerations infigure 5.4. For each vehicle, the accelerations of the last axles oscillates a certain time before reachingan equilibrium. LZV E, LZV A and LZV C have the lowest yaw damping coefficient, where LZV E hasalmost no yaw damping at all, and LZV F and the tractor semitrailer has the highest yaw dampingcoefficient.


0 10 20 30−6

−3

0

3

6

ay [m

/s2 ]

tractor semitrailer


0 10 20 30−6

−3

0

3

6

ay [m

/s2 ]

truck trailer


0 10 20 30−6

−3

0

3

6

ay [m

/s2 ]

truck dbtrailer


0 10 20 30−6

−3

0

3

6

ay [m

/s2 ]

LZV A


0 10 20 30−6

−3

0

3

6

ay [m

/s2 ]

LZV B


0 10 20 30−6

−3

0

3

6ay

[m/s

2 ]LZV C


0 10 20 30−6

−3

0

3

6

ay [m

/s2 ]

LZV D


0 10 20 30−6

−3

0

3

6

ay [m

/s2 ]

LZV E


0 10 20 30−6

−3

0

3

6

time [sec]

ay [m

/s2 ]

LZV F


0 10 20 30−6

−3

0

3

6

time [sec]

ay [m

/s2 ]

LZV G


Figure 5.4: lateral acceleration of rst and last axle, during manoeuvre 10 at 0.3 Hz


5.3 Dynamic roll-over, double lane change

Next to the single lane change, the roll-stability of the different vehicles is evaluated for a double lanechange, representing an avoiding an obstacle. Because the vehicle changes lanes two times, a doublelane change contains more dynamics than a single lane change, thus the change of roll-over is evenbigger. In contrast with the single lane change, the necessary steering adjustments are made by adriver model. An exact description of the double lane change manoeuvre is given below.

11. At this manoeuvre, a double lane change trajectory is prescribed which is followed by means ofthe driver model described in section 3.5. The speed of the vehicle is held constant at 80 km/hduring the complete manoeuvre and the manoeuvre is only driven with fully laden vehicles. Theprescribed path is shown in figure 5.5 as well as the path traveled by the front axle.

0 100 200 300 400 500 600 700−2

−1

0

1

2

3

4

5

6


late

ral p

ath

[m]

double lane change path, tractor semitrialer

desired pathdriven pathlane mark

Figure 5.5: double lane change manoeuvre

Again, roll-over stability of each vehicle is evaluated by calculating the dynamic load transfer ratiosand the rearward amplifications during manoeuvre 11. The maximum dynamic load transfer ratiosand rearward amplifications are summarised in table 5.4. Figure 5.6 shows the time histories of thesteering wheel angle, the dynamic load transfer ratio, the lateral acceleration, the articulation anglesand the roll angles for LZV E, the time histories for the remaining vehicles are shown in Appendix Atill J once again.

conguration max. DLTR [−] max. RA [−]tractor semitrailer 0.516 1.024

truck trailer 0.509 1.306truck db-trailer 0.515 1.219


Table 5.4: maximum DLTR and RA for a double lane change

The values in table 5.4 show that LZV E, LZV A and LZV G have the worst roll-over stability which

5.3. DYNAMIC ROLL-OVER, DOUBLE LANE CHANGE 59

matches with the findings at the single lane change. Roll-stability of LZV G is worst compared to thesingle lane change which is caused by the heavy drawbar-trailer. The conclusion that conventional ve-hicles perform better regarding roll-over stability than LZV’s is confirmed and the difference betweenthem become even more apparent by the results of the double lane change.

0 5 10 15 20 25 30−50

−25

0

25

50

δs [o ]

double lane change signals, LZV E

δs

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2DLTR 3

0 5 10 15 20 25 30−4

−2

0

2

4

ay [m

/s2 ]


0 5 10 15 20 25 30−6

−3

0

3

6

art.

angl

e [o ]

cpl 1cpl 2

0 5 10 15 20 25 30−6

−3

0

3

6

time [sec]

φ [o ]


Figure 5.6: signals during a double lane change, LZV E


5.4 Dynamic roll-over, parameter study

The previous sections analysed roll-stability of LZV’s and conventional commercial vehicles for differ-ent manoeuvres. This section contains a parameter study in which several vehicle parameters will bechanged. At the first part of this parameter study, the velocity of the vehicle, the damping ratio and theroll stiffness of the suspension are changed for each LZV and conventional commercial vehicle. Thesecond part of this parameter study only evaluates the roll-stability for LZV E. Different setups of LZVE are created by increasing the wheelbase of the drawbar-trailers, by placing the pin couplings closerto the centre of gravity of the tractive unit and by roll-coupling of the units of LZV E by removing therotational degree of freedom around the x axis.

First, the effect of damper and roll stiffness settings on roll stability is evaluated by driving thedriving the steady state circle of section 5.1 again. Before driving the steady state circle, the dampingconstants are set to 10 % of their original values or the roll stiffness is set to 50 % of its originalvalues. Afterwards, the static roll-over thresholds are determined again and compared with the originalthresholds. The thresholds determined for the three vehicle settings are summarised in table 5.5.

static roll-over threshold [m/s2]conguration original 50% of Cφ 10% of dtractor semitrailer 3.24 2.92 3.24

truck trailer 3.95 3.68 3.95truck db-trailer 3.44 3.10 3.44

LZV A 3.27 2.95 3.27LZV B 3.31 3.20 3.31LZV C 2.99 2.68 2.97LZV D 3.34 3.03 3.33LZV E 3.43 3.11 3.43LZV F 3.09 2.74 3.09LZV G 3.05 2.75 2.82

Table 5.5: static roll-over threshold for dierent vehicle settings

Evaluating the static roll-over thresholds of table 5.5 shows that changing the roll stiffness effects theroll-over stability certainly. Changing the damping ratio has an effect on roll-over stability, but theeffect is marginal and only visible for LZV C and LZV G. The lower static roll-over threshold when theroll stiffness is set to 50 % of its original values, can be explained by

May (hr + hc.g.,rccosφ) +Mg sinφ = (Fz2 − Fz1)T

2(5.3)

where

φ = roll angle []hr = height roll centre w.r.t. road [m]hc.g.,rc = height centre of gravity w.r.t. roll axis [m]

Lowering the roll stiffness results in a larger roll angle which on its turn results in a larger destabilisingmoment. A larger destabilising moment causes the vehicles to roll-over at a lower lateral accelerationthus at a lower static roll-over threshold.

Next to the steady state circle, the single lane change as described in section 5.2 is driven with fourdifferent vehicle settings. Besides the changed damping ratio and roll stiffness, the velocity of the vehi-cle is set to 50 km/h or 10 km/h instead of 80 km/h. The influence of those changes in velocity, damperand roll-stiffness settings is evaluated by determining the maximum dynamic load transfer ratios andrearward amplifications at each steering frequency, like already done in previous sections. Figures 5.7

5.4. DYNAMIC ROLL-OVER, PARAMETER STUDY 61

and 5.7 are a plots of the maximum dynamic load transfer ratios and the maximum rearward amplifi-cations against the steering frequency for LZV E. The peak values of the rearward amplification for theoriginal and modified vehicle settings are placed in table 5.6 together with the corresponding steeringfrequency. The same holds for the rearwards amplifications, those peak values and correspondingsteering frequency are placed in table 5.7.

single lane change, maximum DLTR [-] and corresponding steering input [Hz]original 50 km/h 10 km/h Cφ 50% d 10%

conguration DLTR freq DLTR freq DLTR freq DLTR freq DLTR freqtractor semitrailer 0.621 0.1 0.240 0.1 0.025 0.8 0.677 0.1 0.615 0.1

truck trailer 0.484 0.2 0.220 0.4 0.040 0.6 0.496 0.1 0.484 0.2truck db-trailer 0.504 0.1 0.208 0.2 0.033 0.5 0.566 0.1 0.504 0.1

LZV A 0.878 0.3 0.257 0.3 0.025 0.8 0.950 0.3 0.880 0.3LZV B 0.568 0.1 0.225 0.1 0.022 0.9 0.592 0.1 0.560 0.1LZV C 0.710 0.3 0.341 0.4 0.044 0.5 0.730 0.3 0.707 0.3LZV D 0.519 0.1 0.209 0.1 0.032 0.5 0.566 0.1 0.520 0.1LZV E 1.000 0.3 0.353 0.3 0.033 0.5 0.951 0.3 1.000 0.3LZV F 0.640 0.1 0.251 0.1 0.020 0.8 0.759 0.1 0.655 0.1LZV G 0.699 0.2 0.238 0.2 0.036 0.5 0.724 0.2 0.705 0.2

Table 5.6: maximum dynamic load transfer ratio and corresponding steering frequency

single lane change, maximum RA [-] and corresponding steering input [Hz]original 50 km/h 10 km/h Cφ 50% d 10%

conguration RA fr. RA fr. RA fr. RA fr. RA fr.tractor semitrailer 1.402 0.3 1.088 0.3 0.750 0.1 1.423 0.3 1.400 0.3

truck trailer 2.211 0.6 1.377 0.5 0.553 0.1 1.882 0.3 2.307 0.6truck db-trailer 1.721 0.3 1.205 0.3 0.546 0.1 1.546 0.3 1.701 0.3

LZV A 2.489 0.4 1.223 0.3 0.752 0.1 2.661 0.3 2.473 0.4LZV B 1.486 0.3 1.061 0.3 0.763 0.1 1.527 0.3 1.447 0.3LZV C 2.400 0.4 1.483 0.5 0.481 0.1 2.033 0.3 2.348 0.4LZV D 1.917 0.3 1.317 0.3 0.546 0.1 1.836 0.3 1.907 0.3LZV E 3.365 0.3 1.791 0.3 0.547 0.1 2.992 0.3 3.327 0.3LZV F 1.517 0.3 1.096 0.2 0.551 0.1 1.533 0.3 1.572 0.3LZV G 1.841 0.3 1.129 0.2 0.482 0.1 1.841 0.3 1.830 0.3

Table 5.7: maximum rearward amplication and corresponding steering frequency

By means of the results of the above parameter studie, it can be concluded that the longitudinalvelocity of the vehicle has the largest effect on roll-over stability. Both the height and the placement ofthe peak change when the velocity is lowered. Lowering the roll stiffness has a marginal effect on theroll-over stability during a single lane change. This is remarkable because the static roll-over thresh-olds are lower when the roll stiffness is decreased. So, there could be expected that decreasing theroll stiffness also would effect on the roll-over stability during more dynamic manoeuvres. Plottingthe roll-angles against steering frequency for LZV E, see figure 5.9, makes clear that the roll-angles dochange as expected because setting the roll-stiffness to 50 % of its original value leads to an increase ofroll-angles. Changing the damping ratio seems to have no or a marginal effect on the roll-over stabilityduring a single lane change.


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of LZV E, Vx= 80km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 50km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 10km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

d= 10%

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Croll= 50%

DLTR1DLTR2DLTR3

Figure 5.7: dynamic load transfer ratio for various velocities, damping ratios and roll stiness,LZV E


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]

rearward amplifications of LZV E, Vx= 80km/h

steerdrive1drive2dbtrailer1 axle1dbtrailer1 axle2dbtrailer2 axle1dbtrailer2 axle2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

freq [Hz]

RA

[−]

Croll= 50%


Figure 5.8: rearward amplication for various velocities, damping ratios and roll stiness, LZV E


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

2

4

6

8φ

[o ]

roll angle of LZV E, Vx= 80km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

2

4

6

8

φ [o ]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

2

4

6

8

φ [o ]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

2

4

6

8

φ [o ]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

2

4

6

8

freq [Hz]

φ [o ]

Croll= 50%


Figure 5.9: roll angle for various velocities, damping ratios and roll stiness, LZV E


Section 2.5 mentions several options to improve the dynamic load transfer ratio and the rearwardamplification of a commercial vehicle. Mentioned are, reducing the vehicle speed, increasing thewheel base of a trailing unit, shorten the longitudinal distance between C.G. and coupling of a towingunit and roll-coupling of units. The effect of speed reduction is already evaluated in the first part ofthis parameter study. The second part of this parameter study investigates the influence of increasedwheelbase of trailing units, of the coupling placement on a tractive unit and of roll-coupling of trailingunits on roll-over stability. Instead of evaluating all LZV and conventional configurations, only LZV Eis examined at this part of the parameter study. LZV E has the worst dynamic roll-over stability, thuswhen roll-stability of this configuration improves, it can be assumed that the roll-over stability of everyvehicle improves.

The original setting and the modifications of LZV E are mentioned in table 5.8. When the lon-gitudinal placement of the coupling is changed, the length of the drawbar is changed with the sameammount. So, besides the placement of the couplings, all parts of the vehicle are placed according tofigure E.1 at appendix E.

setting of LZV Ewheelbase [m] coupling 1 [m] coupling 2 [m] rotation of coupling [-]

original 1.80 −7.82 −15.32 x, y and z axislonger wheelbase 2.20 −7.82 −15.32 x, y and z axisshorter coupling placement 1.80 −7.12 −14.62 x, y and z axisroll coupling 1.80 −7.82 −15.32 y and z axis

Table 5.8: dierent setups of LZV E

Table 5.9 summarises the results found for a single lane change with different setups of LZV E.The table contains the maximum dynamic load transfer ratio, the maximum rearward amplificationand their corresponding steering frequency.

maximum DLTR and RADLTR freq [Hz] RA freq [Hz]

original 1.000 0.30 3.365 0.30longer wheelbase 1.000 0.30 3.367 0.30shorter coupling placement 0.814 0.30 2.540 0.30roll coupling 0.770 0.30 3.526 0.40

Table 5.9: maximum DLTR and RA for several setups of LZV E

Figure 5.10 shows the dynamic load transfer ratio against steering frequency and figure 5.11 shows therearward amplifications against the steering input for the different settings of LZV E.

From the result, it can also be concluded that shifting the pin couplings closer to the centre ofgravity of the tractive unit leads to the largest improvement in roll-stability. The maximum dynamicload transfer ratio goes from 1.000 to 0.814 and the maximum rearward amplification decreases from3.365 to 2.540. Roll-coupling of units is the second best option, the dynamic load transfer ratio dropsfrom 1.000 to 0.770 which is even beter then shifting the couplings but the maximum rearward am-plification increases to 3.526. Increasing the wheelbase of the two drawbar-trailers does not effectroll-stability for this particular manoeuvre.


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of LZV E, original setting

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

smaller C.G. to coupling distance

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

larger wb of dbtrailers

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

freq [Hz]

roll coupled units

DLTR1DLTR2DLTR3

Figure 5.10: dynamic load transfer ratio for various setups of LZV E


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]

rearward amplification of LZV E, original setting


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

smaller C.G. to coupling distance


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

larger wb of dbtrailers


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

freq [Hz]

roll coupled units


Figure 5.11: rearward amplication for various setups of LZV E


5.5 Summary of roll-over stability

To conclude this chapter about roll-over stability of conventional commercial vehicles and LZV’s, theresults are summarised in this section. The most important conclusions regarding the roll-over sta-bility of the studied vehicles are;

• In general, LZV’s are more likely to roll-over than conventional configurations. However, thebest LZV performs better than the worst conventional commercial vehicle. The trade-off be-tween manoeuvrability and roll-over found during previous research is enhanced [18].

• The conventional commercial vehicles and the LZV’s are the most sensitive to roll-over when inthe frequency range utilised by the driver when avoiding an obstacle.

• Lowering the longitudinal velocity has the largest effect on improvement of the roll-over stability.

The roll-over results shown in this chapter, make it possible to compare the studied vehicles to a vehiclehaving average roll-over stability yielding to the next classification.

roll-over stabilityconguration SRT single lane change double lane change overalltractor semitrailer − ++ + +

truck trailer ++ +− + +truck db trailer + + + +

LZV A +− −− −− −−ZV B +− + ++ +

LZV C −− − − −−LZV D +− +− +− +−LZV E + −− −− −−LZV F −− + +− +−LZV G −− +− −− −−

Table 5.10: summary of roll-over stability of conventional commercial vehicles and LZV's(++ = excellent, + = adequate, +− = moderate, − = inadequate, −− = poor)

Chapter 6

Conclusions and Recommendations

The aim of this research is to evaluate and compare the braking performance and roll-over stability of 7LZV configurations and 3 conventional commercial vehicles allowed on Dutch roads. Several brakingas well as roll-over manoeuvres are simulated and analysed in detail. Based on the results of thosemanoeuvres, conclusions regarding braking performance and roll-over stability are drawn in the firstsection of this chapter. The second section of this chapter gives recommendations for future researchregarding dynamic behaviour and performance of conventional commercial vehicles and LZV’s.

6.1 Conclusions

This section presents the conclusion of this research. Conclusions are drawn regarding axle loads,braking performance and roll-over stability to answer the question which configurations should beallowed on Dutch, and European, roads.

Static axle loads

• Except LZV F, all vehicles obey legal demands regarding static axle loads when the total vehicleweight has a maximum of 60 ton. The design of LZV F makes it difficult to evenly spread theload over the axles, the last 3 axles of the truck carry both the load of the truck and a part of thesemitrailer load. The 3 last axles of the truck violate legal axle loads while the semitrailer axleshave a margin of approximately 0.59 ton.

• All the vehicles obey legal demands regarding coupling forces. Legislation mentions especiallya restriction on the vertically coupling forces for drawbar-trailers.

Braking performance

• The brake system distributes the brake force satisfactory. All vehicles fulfil the legal demands re-garding brake force distribution in both laden as unladen condition. Laden vehicles approximatealmost ideal BFD while the maximum deviation for unladen vehicles is maximum 25 %.

• There is no difference in brake force distribution between LZV configurations existing of anextra drawbar-trailer coupled to a conventional combination, in other words LZV A and LZVE, and their corresponding conventional vehicle, tractor semitrailer and truck drawbar-trailerrespectively. The same holds for LZV versions of a conventional vehicles, in other words LZV Cand LZV D perform equal as the truck trailer and LZV G performs equal as the truck drawbar-trailer.

• Without ABS, laden vehicles experience wheel lock within a range of 6.6 -6.9 m/s2 and thewheels of the first steer axle are the ones to lock. The only exception is LZV C, where thewheels of the first trailer axle lock the first. For unladen vehicles it holds that the first steer axle

69

70 CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS

wheels at 7.4 m/s2 for all configurations. When taking into account the change in vertical tyreforces, it can be concluded that the axle on which the vertical tyre forces increase the most willlock first due to decreasing tyre-road adhesion.

• ABS improves the braking performance for critical braking manoeuvres. When ABS preventsthe wheels to lock, the stopping distance is reduced for all vehicles. This holds for a dry as wellas a wet/icy road and for both laden as well as unladen conditions. The amount of reduction instopping distance is equal for LZV’s and conventional vehicles.

On a µ-split road ABS prevents jackknifing of configurations containing a tractor and semi-trailer, it decreases lateral path deviation but stopping distance is not shortened. Configurationscontaining a tractor coupled to a semitrailer, both LZV as conventional, have the shortest stop-ping distance but the biggest lateral deviation, while the truck trailer configurations, both LZVas conventional, have the longest stopping distance but the smallest lateral path deviation.

• Applying the brakes during a corner results in a smaller cornering radius, thus the vehicle be-comes oversteered when the brakes are applied. Besides this observation, the results of thisresearch are not conclusive enough to identify a worst or best performing vehicle. A vehicleperforming worse regarding path deviation, belongs to the best performing vehicles regardingchanges in steering angle and rate of steering angle change and vice versa.

Braking performance of LZV’s is equal to the performance of conventional vehicles and based onjudged regulation, all LZV’s should be allowed. For braking manoeuvres in a straight line there is nodistinct differences between conventional commercial vehicles and LZV’s.

Roll-over stability

• The static roll-over threshold is approximately 3.3 m/s2 for both laden LZV’s and laden conven-tional commercial vehicles.

• In general, LZV’s are more likely to roll-over than conventional configurations. Configurationshaving a low yaw damping, LZV E, LZV A and LZV C, have the worst roll-over stability.

• The steering frequencies where the risk of roll-over is the highest, are within a region from0.1 to 0.6 Hz. This region is well within the frequency band utilized by a human driver whenpreforming a emergency steering manoeuvre. Furthermore, inputs frequencies above 2.5 Hz donot result in roll-over.

• The risk of roll-over is minimised the most by lowering the longitudinal velocity, while changingthe spring stiffness and the damping constant has little to no effect.

• Moving the coupling closer to the centre of gravity of the tractive unit is the most effectiveoption to improve the dynamic roll-stability of LZV E. The second best option is to roll coupletwo drawbar-trailers and the truck of LZV E.

OverviewThe results of the LZV research at Eindhoven University of Technologie till is used to come to anoverview of dynamic performance of LZV’s. The overview answers the question if a specific vehicleshould or should not be authorised.

6.2. RECOMMENDATIONS 71

conguration swept path [18], [17] braking roll-over overall authorisetractor semitrailer + + + + yes

truck trailer n/a − + +− yestruck db trailer n/a ++ + + yes

LZV A + +− −− − noLZV B −− +− + +− yesLZV C + − −− −− noLZV D +− +− +− +− yesLZV E ++ + −− − noLZV F − ++ +− + yesLZV G + ++ −− − no

Table 6.1: overall performance of conventional commercial vehicles and LZV's(++ = excellent, + = adequate, +− = moderate, − = inadequate, −− = poor)

To improve dynamical performance or to become authorised, the next improvements can be done,

conguration improvements and remarksLZV A improve roll-over stability of drawbar trailer to become authorisedLZV B improve manoeuvrabilityLZV C next to poor performance, the initial costs are high also.LZV D in some cases the dolly could become a bottleneckLZV E improve roll-over stability of drawbar trailer to become authorisedLZV F performs adequate but initial costs are highLZV G next to poor performance, the initial costs are high also.

6.2 Recommendations

This section contains the recommendations to consider for future research on the dynamic behaviourof LZV’s and/or conventional commercial vehicles.

General recommendations

• First, there is a need to validate the multi-body models.

• Narrow the number of configurations by excluding irrelevant configurations, see table 6.1 and6.1. For instance, LZV C, LZV F and LZV G contain an uncommon, very specific 8x4 truck. Inpractice, such vehicles will not be cost effective, so no transport company will buy such a vehicle.

• Evaluate dynamic behaviour under different loading conditions to identify worst-case loadingconditions. At this moment, the LZV’s are fully loaded or fully unloaded and the load is uni-formly distributed over the vehicle. Besides these loading conditions, other loading conditionsare likely to appear, for example a fully loaded unit coupled to an unloaded second unit, and viceversa.

• Investigate the possibilities to increase model complexity and to add extra (sub)models like forinstance a roll-over protection system, without increasing the calculation time needed to sim-ulate a certain manoeuvre. For instance, the ABS model could be modeled by means of thedifferent blocks of the Simulink library, switches, relational operators, logic operators, e.g. butthose blocks would cause the simulation time to explode. In this research a part of the ABSis build with the Stateflow toolbox of Simulink and by doing so, the simulation time is keptreasonable. Another option would be to "program" the ABS by using an "embedded Matlabfunction".

72 CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS

Brake system

• The load sensing valve currently implemented, controles the brake force for an axle in a dynamicway meaning that axle (un)loading during braking is into account. In reality it is commonpractice that only tractive units are equipped with such dynamic load sensing valves, the loadsensing valves on the remaining trailing units are static load sensing valves. Static load sensingvalves only take into account static axle loads to control brake force for an axle. Replacing thedynamic load sensing valve by static load sensing valves will change the brake force distributionfigures and thus the fulfillment of legalisation.

• The output of the current implemented brake system is braking torque, but in reality the outputof the brake system will be a brake pressure. Because of these different outputs it is currentlyonly possible to validate the implemented brake system by looking at a complete vehicle. Whenthe implemented model of the brake system also would have a brake pressure output, it wouldbe possible to validate the brake system on subsystem level.

• Replace the select low control of the ABS of steered axles by a modified axle control. This wouldbe closer to reality because modern commercial vehicles using the modified axle control strategyand it would improve ABS performance, especially at µ-split braking.

• Investigate delay in modern air brake system. Although most of the modern commercial vehi-cles are equipped with an electronic brake system, there is still a pneumatic part. This pneumaticpart still cause some delay between application of the brake pedal and the actual braking.

• Investigate delay in brake actuation between conventional commercial vehicles and LZV’s. Be-cause LZV’s are longer, signals may need more time to travel between sensors and actuators.

• Investigate the dynamic vehicle behaviour and performance for manoeuvres where both thebrakes and the steering is applied further. This research show that such manoeuvres are com-plicated to analyse because of the interactions between tyre behaviour, load transfer and couplingforces.

Roll-over stability

• Implement a system which prevents roll-over, for instance by applying the brakes when a lateralacceleration exceeds a certain threshold. Such systems are common on modern commercialvehicles and it will change the roll-over results of this research. For instance, LZV A wouldbecome authorised when the roll-over risk of the drawbar-trailer is reduced.

• Investigate possibilities to improve yaw damping of drawbar-trailers and trailers.

• Investigate possibilities to roll couple drawbar-trailers and trailers.

Driver model

• Improve driver model. When driving a curved traject, the steer angle output of the driver fluctu-ates. These fluctuations vary in amplitude and frequency when the grid of the desired trajectorychanges. A dense grid leads to smal amplitudes and frequencies.

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http://www.verkeerenwaterstaat.nl/actueel/nieuws/proefmetlangeenzwaarderevrachtwagens-\lzvspositief.aspx

http://www.verkeerenwaterstaat.nl/actueel/nieuws/proefmetlangeenzwaarderevrachtwagens-\lzvspositief.aspx

http://www.rdw.nl/nl/beroepsvervoer/LZV/

Appendix A

LZV conguration A

1. dimensions of LZV A

Figure A.1: dimensions of LZV A

LZV A consist of a 4x2 tractor, a 3 axle semitrailer and a 2 axle db-trailer. The front axle of thetractor is steered while the rear axle is driven. The tractor and semitrailer are coupled to eachother by means of a fifth wheel coupling which allows only allows rotation around the verticalaxis.The db-trailer is coupled to the semitrailer by a pin coupling which allows rotational DOF’saround vertical, lateral and longitudinal axis.

A1

A2 LZV conguration A

2. static axle loads and coupling forces

axle load [N ] load [ton] limit [ton]steer axle 73305 7.47 7.50drive axle 111627 11.38 11.50semitrailer axle 1 70623 7.20 8.00semitrailer axle 2 70840 7.22 8.00semitrailer axle 3 71057 7.24 8.00db-trailer axle 1 95676 9.75 10.00db-trailer axle 2 95473 9.73 10.00total 588602 60.00 60.00

coupling load [N ] load [kg] limit [kg]5th wheel Fx 0 0 −5th wheel Fy 0 0 −5th wheel Fz −116260 −11851 −pin Fx 0 0 −pin Fy 0 0 −pin Fz −5050 −515 −1000

Table A.1: static axle loads and coupling forces, laden LZV A

3. braking performance w.r.t legal demands

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV A (laden)


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV A (unladen)


Figure A.2: braking performance and legal demands, left: laden LZV A, right: unladen LZV A

4. load transfer

tractor 1 tractor 2 semi 1 semi 2 semi 3 dbtrailer 1 dbtrailer 20

20

40

60

80

100

120

140

160

180

axle [−]

Fz

[kN

]

axle loads of LZV A (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

[kN

]

Fx 5th−180

−120

−60

0

60

120

180

Fy 5th

coupling forces of LZV A (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz 5th

−180

−120

−60

0

60

120

180

Fx pin

[kN

]

−180

−120

−60

0

60

120

180

Fy pin−180

−120

−60

0

60

120

180

Fz pin

Figure A.3: axle (un)loading and coupling forces when braking, laden LZV A

LZV conguration A A3

5. ABS performance

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV A (laden)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl2 no ABScpl2 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV A (unladen)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl2 no ABScpl2 ABS

Figure A.4: path and articulation angles during µ-split braking, laden/unladen LZV A

6. brake while driving a steady state circle

50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV A (laden)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −1.5 m/s2

50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV A (unladen)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −1.5 m/s2

Figure A.5: ax, ay, ψ and articulation angles during braking at a circle, laden/unladen LZV A


20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), LZV A (laden)

0 m/s2

−1.5 m/s2

reference

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), LZV A (unladen)

0 m/s2

−1.5 m/s2

reference

Figure A.6: path deviation of steer axle when braking at a circle, laden/unladen LZV A

7. brake while taking a highway exit

0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

Vx

[km

/h]

signals during highway exit, LZV A

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ax [m

/s2 ]

0 m/s2

−3 m/s2

input

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ay [m

/s2 ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50

−8−6−4−2

02

yaw

vel

[o /s]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−80−60−40−20

020

δ s

[o ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −3 m/s2

Figure A.7: signals during braking at a highway exit, laden LZV A


8. roll-over: single lane change

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]Dynamic Load Transfer Ratio, LZV A

DLTR 1DLTR 2DLTR 3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.5

1

1.5

2

2.5

3

3.5

freq [Hz]

RA

[−]

Rearward Amplification axles, LZV A

steerdrivesemitrailer axle 1semitrailer axle 2semitrailer axle 3dbtrailer axle 1dbtrailer axle 2

Figure A.8: DLTR and RA against frequency of single lane change, laden LZV A

9. roll-over: double lane change

0 5 10 15 20 25 30−50

−25

0

25

50

δs [o ]

double lane change signals, LZV A

δs

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2DLTR 3

0 5 10 15 20 25 30−4

−2

0

2

4

ay [m

/s2 ]


0 5 10 15 20 25 30−6

−3

0

3

6

art.

angl

e [o ]

cpl 1cpl 2

0 5 10 15 20 25 30−6

−3

0

3

6

time [sec]

φ [o ]


Figure A.9: signals during a double lane change, laden LZV A


10. roll-over: parameter study

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of LZV A, Vx= 80km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 50km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 10km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

d= 10%

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Croll= 50%

DLTR1DLTR2DLTR3

Figure A.10: dynamic load transfer ratio for various velocities, damping ratios and roll stiness,LZV A


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]rearward amplification of LZV A, Vx= 80km/h

steerdrivesemitrailer axle1semitrailer axle2semitrailer axle3dbtrailer axle1dbtrailer axle2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

freq [Hz]

RA

[−]

Croll= 50%


Figure A.11: rearward amplication for various velocities, damping ratios and roll stiness, LZVA


Appendix B

LZV conguration B

1. dimensions of LZV B

Figure B.1: dimensions of LZV B

LZV B consist of a 4x2 tractor and two 3 axle semitrailer. The steer axle of the tractor is steeredwhile the rear axle is driven. The first semitrailer is coupled to the tractor and the second semi-trailer is coupled to the first, both couplings are fifth wheel couplings which only allow a rotationaround the vertical axis.

B1

B2 LZV conguration B

2. static axle and coupling loads

axle load [N ] load [ton] limit [ton]steer axle 70380 7.17 7.50drive axle 98950 10.09 11.50semitrailer1 axle 1 67604 6.89 8.00semitrailer1 axle 2 70859 7.22 8.00semitrailer1 axle 3 74114 7.55 8.00semitrailer2 axle 1 70913 7.23 8.00semitrailer2 axle 2 69225 7.06 8.00semitrailer2 axle 3 67538 6.89 8.00total 587895 59.93 60.00

coupling load [N ] load [kg] limit [kg]5th wheel1 Fx 0 0 −5th wheel1 Fy 0 0 −5th wheel1 Fz −100658 −10261 −5th wheel2 Fx 0 0 −5th wheel2 Fy 0 0 −5th wheel2 Fz −118016 −12030 −

Table B.1: static axle loads and coupling forces, laden LZV B


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV B (laden)

steer axledrive axlesemitrailer1 axle1semitrailer1 axle2semitrailer1 axle3semitrailer2 axle1semitrailer2 axle3semitrailer2 axle3Z = Klegal borders

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV B (unladen)

steer axledrive axlesemitrailer1 axle1semitrailer1 axle2semitrailer1 axle3semitrailer2 axle1semitrailer2 axle3semitrailer2 axle3Z = Klegal borders

Figure B.2: braking performance and legal demands, laden/unladen LZV B

4. load transfer

tractor 1 tractor 2 semi1 1 semi1 2 semi1 3 semi2 1 semi2 2 semi2 30

20

40

60

80

100

120

140

160

180

axle [−]

Fz

[kN

]

axle loads of LZV B (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fx 5th1−180

−120

−60

0

60

120

180

Fy 5th1

coupling forces of LZV B (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz 5th1

−180

−120

−60

0

60

120

180

Fx 5th2

[kN

]

−180

−120

−60

0

60

120

180

Fy 5th2−180

−120

−60

0

60

120

180

Fz 5th2

Figure B.3: axle (un)loading and coupling forces when braking, laden LZV B

LZV conguration B B3

5. ABS performance

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV B (laden)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

semitrailer1 axle1 no ABSsemitrailer1 axle2 no ABSsemitrailer1 axle2 no ABSsemitrailer1 axle1 ABSsemitrailer1 axle2 ABSsemitrailer1 axle3 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl2 no ABScpl2 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV B (unladen)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl2 no ABScpl2 ABS

Figure B.4: path and articulation angles during µ-split braking, laden/unladen LZV B


50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV B (laden)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −1.5 m/s2

50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV B (unladen)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −1.5 m/s2

Figure B.5: ax, ay, ψ and articulation angles during braking at a circle, laden/unladen LZV B


20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), LZV B (laden)

0 m/s2

−1.5 m/s2

reference

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), LZV B (unladen)

0 m/s2

−1.5 m/s2

reference

Figure B.6: path deviation of steer axle when braking at a circle, laden/unladen LZV B


0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

Vx

[km

/h]

signals during highway exit, LZV B

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ax [m

/s2 ]

0 m/s2

−3 m/s2

input

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ay [m

/s2 ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50

−8−6−4−2

02

yaw

vel

[o /s]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−80−60−40−20

020

δ s

[o ]

0 m/s2

3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −3 m/s2

Figure B.7: signals during braking at a highway exit, laden LZV B



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]Dynamic Load Transfer Ratio, LZV B

DLTR 1DLTR 2DLTR 3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.5

1

1.5

2

2.5

3

3.5

freq [Hz]

RA

[−]

Rearward Amplification axles, LZV B

steerdrivesemitrailer1 axle1semitrailer1 axle2semitrailer1 axle3semitrailer2 axle1semitrailer2 axle2semitrailer2 axle3

Figure B.8: DLTR and RA against frequency of single lane change, laden LZV B


0 5 10 15 20 25 30−50

−25

0

25

50

δs [o ]

double lane change signals, LZV B

δs

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2DLTR 3

0 5 10 15 20 25 30−4

−2

0

2

4

ay [m

/s2 ]


0 5 10 15 20 25 30−6

−3

0

3

6

art.

angl

e [o ]

cpl 1cpl 2

0 5 10 15 20 25 30−6

−3

0

3

6

time [sec]

φ [o ]

front tractorrear tractorfront semitrailer1rear semitrailer1front semitrailer2rear semitrailer2

Figure B.9: signals during a double lane change, laden LZV B



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of LZV B, Vx= 80km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 50km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 10km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

d= 10%

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Croll= 50%

DLTR1DLTR2DLTR3

Figure B.10: dynamic load transfer ratio for various velocities, damping ratios and roll stiness,LZV B


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]rearward amplification of LZV B, Vx= 80km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

freq [Hz]

RA

[−]

Croll= 50%


Figure B.11: rearward amplication for various velocities, damping ratios and roll stiness, LZVB


Appendix C

LZV conguration C

1. dimensions of LZV C

Figure C.1: dimensions of LZV C

LZV C consist of a 8x4 truck and a 3 axle full trailer. The first and second axle of the truckare steered while the third and fourth axle are driven. The trailer is coupled to the truck with apin coupling which allows rotation around a vertical, a lateral and a longitudinal axis, so the 3rotational DOF’s are allowed.

C1

C2 LZV conguration C


axle load [N ] load [ton] limit [ton]steer axle 1 72328 7.37 7.50steer axle 2 73589 7.50 7.50drive axle 1 83806 8.54 9.50drive axle 2 84211 8.58 9.50trailer axle 1 91560 9.33 10.00trailer axle 2 91560 9.33 9.00trailer axle 3 91560 9.33 9.00total 588614 60.00 60.00

coupling load [N ] load [kg] limit [kg]pin Fx 0 0 −pin Fy 0 0 −pin Fz 0 0 −

Table C.1: static axle loads and coupling forces, laden LZV C


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV C (laden)

steer axle1steer axle2drive axle1drive axle2trailer axle1trailer alxe2trailer axle3Z = Klegal borders

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV C (unladen)

steer axle1steer axle2drive axle1drive axle2trailer axle1trailer alxe2trailer axle3Z = Klegal borders

Figure C.2: braking performance and legal demands, laden/unladen LZV C

4. load transfer

truck 1 truck 2 truck 3 truck 4 trailer 1 trailer 2 trailer 30

20

40

60

80

100

120

140

160

180

axle [−]

Fz

[kN

]

axle loads of LZV C (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

[kN

]

Fx pin−180

−120

−60

0

60

120

180coupling forces of LZV C (laden)

Fy pin

[kN

]

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz pin

Figure C.3: axle (un)loading and coupling forces when braking, laden LZV C

LZV conguration C C3

5. ABS performance

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV C (laden)

steer axle1 no ABSsteer axle2 no ABSsteer axle1 ABSsteer axle2 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

drive axle1 no ABSdrive axle2 no ABSdrive axle1 ABSdrive axle2 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

trailer2 axle1 no ABStrailer2 axle2 no ABStrailer2 axle3 no ABStrailer2 axle1 ABStrailer2 axle2 ABStrailer2 axle3 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

turntable no ABSturntable ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV C (unladen)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]


Figure C.4: path and articulation angles during µ-split braking, laden/unladen LZV C


50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV C (laden)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

turntable 0 m/s2

turntable −1.5 m/s2

50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV C (unladen)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

turntable 0 m/s2


Figure C.5: ax, ay, ψ and articulation angles during braking at a circle, laden/unladen LZV C


20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle 1 (zoom), LZV C (laden)

0 m/s2

−1.5 m/s2

reference

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle 1 (zoom), LZV C (unladen)

0 m/s2

−1.5 m/s2

reference

Figure C.6: path deviation of steer axle when braking at a circle, laden/unladen LZV C


0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

Vx

[km

/h]

signals during highway exit, LZV C

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ax [m

/s2 ]

0 m/s2

−3 m/s2

input

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ay [m

/s2 ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50

−8−6−4−2

02

yaw

vel

[o /s]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−80−60−40−20

020

δ s

[o ]

0 m/s2

3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

time [sec]

art.

angl

e [o ]

turntable 0 m/s2

turntable −3 m/s2

Figure C.7: signals during braking at a highway exit, laden LZV C



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]Dynamic Load Transfer Ratio, LZV C

DLTR 1DLTR 2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.5

1

1.5

2

2.5

3

3.5

freq [Hz]

RA

[−]

Rearward Amplification axles, LZV C

steer1steer2drive1drive2trailer axle1trailer axle2trailer axle3

Figure C.8: DLTR and RA against frequency of single lane change, laden LZV C


0 5 10 15 20 25 30−50

−25

0

25

50

δs [o ]

double lane change signals, LZV C

δs

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2

0 5 10 15 20 25 30−4

−2

0

2

4

ay [m

/s2 ]


0 5 10 15 20 25 30−6

−3

0

3

6

art.

angl

e [o ]

cpl 1

0 5 10 15 20 25 30−6

−3

0

3

6

time [sec]

φ [o ]

front tractorrear tractorfront trailerrear trailer

Figure C.9: signals during a double lane change, laden LZV C



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of LZV C, Vx= 80km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 50km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 10km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

d= 10%

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Croll= 50%

DLTR1DLTR2

Figure C.10: dynamic load transfer ratio for various velocities, damping ratios and roll stiness,LZV C


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]rearward amplification of LZV C, Vx= 80km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

freq [Hz]

RA

[−]

Croll= 50%


Figure C.11: rearward amplication for various velocities, damping ratios and roll stiness, LZVC


Appendix D

LZV conguration D

1. dimensions of LZV D

Figure D.1: dimensions of LZV D

LZV D consist of a 6x4 truck, a 2 axle dolly and a 3 axle semitrailer. The front axle of the truckis steered while the second and third axle are driven. The dolly is coupled to the truck by apin coupling which allows 3 rotational DOF’s, the semitrailer is connected to the dolly with afifth wheel coupling which only allows a rotation around a vertical axis. The combination ofsemitrailer and dolly can rotate freely with respect to the truck.

D1

D2 LZV conguration D


axle load [N ] load [ton] limit [ton]steer axle 73567 7.50 7.50drive axle 1 90761 9.25 9.50drive axle 2 90769 9.25 9.50dolly axle 1 66075 6.74 9.00dolly axle 2 66228 6.75 9.00semitrailer axle 1 67080 6.84 8.00semitrailer axle 2 67070 6.84 8.00semitrailer axle 3 67060 6.84 8.00total 588610 60.00 60.00

coupling load [N ] load [kg] limit [kg]pin Fx 0 0 −pin Fy 0 0 −pin Fz −27 3 −5th wheel Fx 0 0 −5th wheel Fy 0 0 −5th wheel Fz −114671 −11689 −

Table D.1: static axle loads and coupling forces, laden LZV D


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV D (laden)

steer axledrive axle1drive axle2dolly axle1dolly axle2semitrailer axle1semitrailer axle2semitrailer axle3Z = Klegal borders

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV D (unladen)

steer axledrive axle1drive axle2dolly axle1dolly axle2semitrailer axle1semitrailer axle2semitrailer axle3Z = Klegal borders

Figure D.2: braking performance and legal demands, laden/unladen LZV D

4. load transfer

truck 1 truck 2 truck 3 dolly 1 dolly 2 semi 1 semi 2 semi 30

20

40

60

80

100

120

140

160

180

axle [−]

Fz

[kN

]

axle loads of LZV D (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

[kN

]

Fx pin−180

−120

−60

0

60

120

180coupling forces of LZV D (laden)

Fy pin

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz pin

−180

−120

−60

0

60

120

180

[kN

]

Fx 5th−180

−120

−60

0

60

120

180

Fy 5th−180

−120

−60

0

60

120

180

Fz 5th

Figure D.3: axle (un)loading and coupling forces when braking, laden LZV D

LZV conguration D D3

5. ABS performance

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV D (laden)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6


late

ral p

ath

[m]

dolly1 axle1 no ABSdolly1 axle2 no ABSdolly1 axle1 ABSdolly1 axle2 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl2 no ABScpl2 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV D (unladen)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6


late

ral p

ath

[m]

dolly1 axle1 no ABSdolly1 axle2 no ABSdolly1 axle1 ABSdolly1 axle2 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl2 no ABScpl2 ABS

Figure D.4: path and articulation angles during µ-split braking, laden/unladen LZV D


50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV D (laden)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −1.5 m/s2

50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV D (unladen)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −1.5 m/s2

Figure D.5: ax, ay, ψ and articulation angles during braking at a circle, laden/unladen LZV D


20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), LZV D (laden)

0 m/s2

−1.5 m/s2

reference

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), LZV D (unladen)

0 m/s2

−1.5 m/s2

reference

Figure D.6: path deviation of steer axle when braking at a circle, laden/unladen LZV D


0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

Vx

[km

/h]

signals during highway exit, LZV D

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ax [m

/s2 ]

0 m/s2

−3 m/s2

input

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ay [m

/s2 ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50

−8−6−4−2

02

yaw

vel

[o /s]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−80−60−40−20

020

δ s

[o ]

0 m/s2

3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −3 m/s2

Figure D.7: signals during braking at a highway exit, laden LZV D


8. roll-over: sinusoidal steering input

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]Dynamic Load Transfer Ratio, LZV D

DLTR 1DLTR 2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.5

1

1.5

2

2.5

3

3.5

freq [Hz]

RA

[−]

Rearward Amplification axles, LZV D

steerdrive1drive2dolly axle1dolly axle2semitrailer axle1semitrailer axle2semitrailer axle3

Figure D.8: DLTR and RA against frequency of single lane change, laden LZV D


0 5 10 15 20 25 30−50

−25

0

25

50

δs [o ]

double lane change signals, LZV D

δs

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2

0 5 10 15 20 25 30−4

−2

0

2

4

ay [m

/s2 ]


0 5 10 15 20 25 30−6

−3

0

3

6

art.

angl

e [o ]

cpl 1cpl 2

0 5 10 15 20 25 30−6

−3

0

3

6

time [sec]

φ [o ]

front truckrear truckdollyfront semitrailerrear semitrailer

Figure D.9: signals during a double lane change, laden LZV D



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of LZV D, Vx= 80km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 50km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 10km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

d= 10%

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Croll= 50%

DLTR1DLTR2

Figure D.10: dynamic load transfer ratio for various velocities, damping ratios and roll stiness,LZV D


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]rearward amplification of LZV D, Vx= 80km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

freq [Hz]

RA

[−]

Croll= 50%


Figure D.11: rearward amplication for various velocities, damping ratios and roll stiness, LZVD


Appendix E

LZV conguration E

1. dimensions of LZV E

Figure E.1: dimensions of LZV E

LZV E consist of a 6x4 truck and two 2 axle db-trailers. The first truck axle is steered while thesecond and third truck axle are driven. The first db-trailer is connected to the truck by a pincoupling and the connection between the 2 db-trailers is also a pin coupling. Both pin couplingsallow a rotation around a vertical, a lateral and a longitudinal axis.

E1

E2 LZV conguration E


axle load [N ] load [ton] limit [ton]steer axle 72514 7.39 7.50drive axle 1 92699 9.45 9.50drive axle 2 92724 9.45 9.50db-trailer1 axle 1 84396 8.60 10.00db-trailer1 axle 2 84388 8.60 10.00db-trailer2 axle 1 80945 8.25 10.00db-trailer2 axle 2 80944 8.25 10.00total 588610 60.00 60.00

coupling load [N ] load [kg] limit [kg]pin1 Fx 0 0 −pin1 Fy 0 0 −pin1 Fz −2867 −292 −1000pin2 Fx 0 0 −pin2 Fy 0 0 −pin2 Fz −4881 −498 −1000

Table E.1: static axle loads and coupling forces, laden LZV E


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV E (laden)

steer axledrive axle1drive axle2dbtrailer1 axle1dbtrailer1 axle2dbtrailer2 axle1dbtrailer2 axle2Z = Klegal borders

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV E (unladen)

steer axledrive axle1drive axle2dbtrailer1 axle1dbtrailer1 axle2dbtrailer2 axle1dbtrailer2 axle2Z = Klegal borders

Figure E.2: braking performance and legal demands, laden/unladen LZV E

4. load transfer

truck 1 truck 2 truck 3 dbtrailer1 1 dbtrailer1 2 dbtrailer2 1 dbtrailer2 20

20

40

60

80

100

120

140

160

180

axle [−]

Fz

[kN

]

axle loads of LZV E (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

[kN

]

Fx pin1−180

−120

−60

0

60

120

180

Fy pin1

coupling forces of LZV E (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz pin1

−180

−120

−60

0

60

120

180

[kN

]

Fx pin2−180

−120

−60

0

60

120

180

Fy pin2−180

−120

−60

0

60

120

180

Fz pin2

Figure E.3: axle (un)loading and coupling forces when braking, laden LZV E

LZV conguration E E3

5. ABS performance

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV E (laden)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200

−150

−100

−50

0

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl2 no ABScpl2 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV E (unladen)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200

−150

−100

−50

0

art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl2 no ABScpl2 ABS

Figure E.4: path and articulation angles during µ-split braking, laden/unladen LZV E


50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV E (laden)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −1.5 m/s2

50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV E (unladen)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −1.5 m/s2

Figure E.5: ax, ay, ψ and articulation angles during braking at a circle, laden/unladen LZV E


20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), LZV E (laden)

0 m/s2

−1.5 m/s2

reference

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), LZV E (unladen)

0 m/s2

−1.5 m/s2

reference

Figure E.6: path deviation of steer axle when braking at a circle, laden/unladen LZV E


0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

Vx

[km

/h]

signals during highway exit, LZV E

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ax [m

/s2 ]

0 m/s2

−3 m/s2

input

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ay [m

/s2 ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50

−8−6−4−2

02

yaw

vel

[o /s]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−80−60−40−20

020

δ s

[o ]

0 m/s2

3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

time [sec]

art.

angl

e [o ]

cpl2 0 m/s2

cpl2 −3 m/s2

Figure E.7: signals during braking at a highway exit, laden LZV E



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]Dynamic Load Transfer Ratio, LZV E

DLTR 1DLTR 2DLTR 3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.5

1

1.5

2

2.5

3

3.5

freq [Hz]

RA

[−]

Rearward Amplification axles, LZV E

steerdrive1drive2dbtrailer1 axle1dbtrailer1 axle 2dbtrailer2 axle1dbtrailer2 axle2

Figure E.8: DLTR and RA against frequency of single lane change, laden LZV E


0 5 10 15 20 25 30−50

−25

0

25

50

δs [o ]

double lane change signals, LZV E

δs

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2DLTR 3

0 5 10 15 20 25 30−4

−2

0

2

4

ay [m

/s2 ]


0 5 10 15 20 25 30−6

−3

0

3

6

art.

angl

e [o ]

cpl 1cpl 2

0 5 10 15 20 25 30−6

−3

0

3

6

time [sec]

φ [o ]


Figure E.9: signals during a double lane change, laden LZV E



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of LZV E, Vx= 80km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 50km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 10km/h

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

d= 10%

DLTR1DLTR2DLTR3

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Croll= 50%

DLTR1DLTR2DLTR3

Figure E.10: dynamic load transfer ratio for various velocities, damping ratios and roll stiness,LZV E


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]rearward amplifications of LZV E, Vx= 80km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

freq [Hz]

RA

[−]

Croll= 50%


Figure E.11: rearward amplication for various velocities, damping ratios and roll stiness, LZVE


Appendix F

LZV conguration F

1. dimensions of LZV F

Figure F.1: dimensions of LZV F

LZV F consists of a 8x4 truck and a 3 axle semitrailer. The first and fourth axle of the truck aresteered, while the second and third truck axle are driven. The semitrailer is connected to thetruck by a fifth coupling which only allows a rotational DOF around a vertical axis.

F1

F2 LZV conguration F


axle load [N ] load [ton] limit [ton]steer axle 1 70243 7.16 7.50drive axle 1 100338 10.23 9.50drive axle 2 101974 10.40 9.50steer axle 2 78285 7.98 7.50semitrailer axle 1 73116 7.45 8.00semitrailer axle 2 72721 7.41 8.00semitrailer axle 3 72326 7.37 8.00total 569004 58.00 58.00

coupling load [N ] load [kg] limit [kg]5th wheel Fx 0 0 −5th wheel Fy 0 0 −5th wheel Fz −125186 −12761 −

Table F.1: static axle loads and coupling forces, laden LZV F


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV F (laden)

steer axle1steer axle2drive axle1drive axle2semitrailer axle1semitrailer axle3semitrailer axle3Z = Klegal borders

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV F (unladen)

steer axle1steer axle2drive axle1drive axle2semitrailer axle1semitrailer axle3semitrailer axle3Z = Klegal borders

Figure F.2: braking performance and legal demands, laden/unladen LZV F

4. load transfer

truck 1 truck 2 truck 3 truck 4 semi 1 semi 2 semi 30

20

40

60

80

100

120

140

160

180

axle [−]

Fz

[kN

]

axle loads of LZV F (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

[kN

]

Fx 5th−180

−120

−60

0

60

120

180

Fy 5th

coupling forces of LZV F (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz 5th

Figure F.3: axle (un)loading and coupling forces when braking, laden LZV F

LZV conguration F F3

5. ABS performance

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV F (laden)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV F (unladen)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl1 no ABScpl1 ABS

Figure F.4: path and articulation angles during µ-split braking, laden/unladen LZV F


50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV F (laden)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

time [sec]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV F (unladen)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

time [sec]

cpl1 0 m/s2

cpl1 −1.5 m/s2

Figure F.5: ax, ay, ψ and articulation angles during braking at a circle, laden/unladen LZV F


20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle 1 (zoom), LZV F (laden)

0 m/s2

−1.5 m/s2

reference

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle 1 (zoom), LZV F (unladen)

0 m/s2

−1.5 m/s2

reference

Figure F.6: path deviation of steer axle when braking at a circle, laden/unladen LZV F


0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

Vx

[km

/h]

signals during highway exit, LZV F

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ax [m

/s2 ]

0 m/s2

−3 m/s2

input

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ay [m

/s2 ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50

−8

−6

−4

−2

0

2

yaw

vel

[o /s]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−80

−60

−40

−20

0

20

δ s

[o ]

0 m/s2

3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

4

6

art.

angl

e [o ]

time [sec]

cpl1 0 m/s2

cpl1 −3 m/s2

Figure F.7: signals during braking at a highway exit, laden LZV F



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]Dynamic Load Transfer Ratio, LZV F

DLTR 1DLTR 2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.5

1

1.5

2

2.5

3

3.5

freq [Hz]

RA

[−]

Rearward Amplification axles, LZV F

steer1steer2drive1drive2semitrailer axle1semitrailer axle2semitrailer axle3

Figure F.8: DLTR and RA against frequency of single lane change, laden LZV F


0 5 10 15 20 25 30−50

−25

0

25

50

δs [o ]

double lane change signals, LZV F

δs

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2

0 5 10 15 20 25 30−4

−2

0

2

4

ay [m

/s2 ]


0 5 10 15 20 25 30−6

−3

0

3

6

art.

angl

e [o ]

cpl 1

0 5 10 15 20 25 30−6

−3

0

3

6

time [sec]

φ [o ]

front truckrear truckfront semitrailerrear semitrailer

Figure F.9: signals during a double lane change, laden LZV F



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of LZV F, Vx= 80km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 50km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 10km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

d= 10%

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Croll= 50%

DLTR1DLTR2

Figure F.10: dynamic load transfer ratio for various velocities, damping ratios and roll stiness,LZV F


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]rearward amplification of LZV F, Vx= 80km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

freq [Hz]

RA

[−]

Croll= 50%


Figure F.11: rearward amplication for various velocities, damping ratios and roll stiness, LZVF


Appendix G

LZV conguration G

1. dimensions of LZV G

Figure G.1: dimensions of LZV G

LZV G consists of a 8x4 truck and a 3axle db-trailer. The first and second truck axle are steered,while the third and fourth axle are driven. The db-trailer is coupled to the truck by a pin coupling,allowing 3 rotational DOF’s namely around a vertical, a lateral and a longitudinal axis.

G1

G2 LZV conguration G


axle load [N ] load [ton] limit [ton]steer axle 1 706960 7.21 7.50steer axle 2 72590 7.40 7.50drive axle 1 87912 8.96 9.50drive axle 2 88520 9.02 9.50db-trailer axle 1 90081 9.18 10.00db-trailer axle 2 89632 9.14 10.00db-trailer axle 2 89182 9.09 10.00total 588614 60.00 60.00

coupling load [N ] load [kg] limit [kg]pin Fx 0 0 −pin Fy 0 0 −pin Fz −5784 −589 −1000

Table G.1: static axle loads and coupling forces, laden LZV G

3. brake performance w.r.t legal demands

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV G (laden)

steer axle1steer axle2drive axle1drive axle2dbtrailer axle1dbtrailer axle2dbtrailer axle3Z = Klegal borders

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

LZV G (unladen)

steer axle1steer axle2drive axle1drive axle2dbtrailer axle1dbtrailer axle2dbtrailer axle3Z = Klegal borders

Figure G.2: brake performance and legal demands, laden/unladen LZV G

4. load transfer

truck 1 truck 2 truck 3 truck 4 dbtrailer 1 dbtrailer 2 dbtrailer 30

20

40

60

80

100

120

140

160

180

axle [−]

Fz

[kN

]

axle loads of LZV G (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

[kN

]

Fx pin−180

−120

−60

0

60

120

180coupling forces of LZV G (laden)

Fy pin

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz pin

Figure G.3: axle (un)loading and coupling forces when braking, laden LZV G

LZV conguration G G3

5. ABS performance

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV G (laden)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, LZV G (unladen)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl1 no ABScpl1 ABS

Figure G.4: path and articulation angles during µ-split braking, laden/unladen LZV G


50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV G (laden)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

time [sec]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, LZV G (unladen)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

time [sec]

cpl1 0 m/s2

cpl1 −1.5 m/s2

Figure G.5: ax, ay, ψ and articulation angles during braking at a circle, laden/unladen LZV G


20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle 1 (zoom), LZV G (laden)

0 m/s2

−1.5 m/s2

reference

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle 1 (zoom), LZV G (unladen)

0 m/s2

2 m/s2

reference

Figure G.6: path deviation of steer axle when braking at a circle, laden/unladen LZV G


0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

Vx

[km

/h]

signals during highway exit, LZV G

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ax [m

/s2 ]

0 m/s2

−3 m/s2

input

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ay [m

/s2 ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50

−8

−6

−4

−2

0

2

yaw

vel

[o /s]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−80

−60

−40

−20

0

20

δ s

[o ]

0 m/s2

3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

4

6

art.

angl

e [o ]

time [sec]

cpl1 0 m/s2

cpl1 −3 m/s2

Figure G.7: signals during braking at a highway exit, laden LZV G



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]Dynamic Load Transfer Ratio, LZV G

DLTR 1DLTR 2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.5

1

1.5

2

2.5

3

3.5

freq [Hz]

RA

[−]

Rearward Amplification axles, LZV G

steer1steer2drive1drive2dbtrailer axle1dbtrailer axle2dbtrailer axle3

Figure G.8: DLTR and RA against frequency of single lane change, laden LZV G


0 5 10 15 20 25 30−50

−25

0

25

50

δs [o ]

double lane change signals, LZV G

δs

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2

0 5 10 15 20 25 30−4

−2

0

2

4

ay [m

/s2 ]


0 5 10 15 20 25 30−6

−3

0

3

6

art.

angl

e [o ]

cpl 1

0 5 10 15 20 25 30−6

−3

0

3

6

time [sec]

φ [o ]

front truckrear trucktrailer

Figure G.9: signals during a double lane change, laden LZV G



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of LZV G, Vx= 80km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 50km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 10km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

d= 10%

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Croll= 50%

DLTR1DLTR2

Figure G.10: dynamic load transfer ratio for various velocities, damping ratios and roll stiness,LZV G


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]rearward amplification of LZV G, Vx= 80km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

freq [Hz]

RA

[−]

Croll= 50%


Figure G.11: rearward amplication for various velocities, damping ratios and roll stiness, LZVG


Appendix H

Tractor semitrailer

1. dimensions of tractor semitrailer

Figure H.1: dimensions of tractor semitrailer

A tractor semitrailer configuration consists of a 4x2 tractor and a 3 axle semitrailer. The frontaxle of the tractor is steered, while the rear axle is driven. The two units are coupled by a fifthwheel coupling which only allows a rotational degree of freedom around a vertical axis.

H1

H2 Tractor semitrailer


axle load [N ] load [ton] limit [ton]steer axle 73576 7.50 7.50drive axle 112804 11.50 11.50semitrailer axle 1 68672 7.00 8.00semitrailer axle 2 68674 7.00 8.00semitrailer axle 3 68676 7.00 8.00total 392402 40.00 40.00

coupling load [N ] load [kg] limit [kg]5th wheel Fx 0 0 −5th wheel Fy 0 0 −5th wheel Fz −117708 −11999 −

Table H.1: static axle loads and coupling forces, laden tractor semitrailer


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

tractor semitrailer (laden)


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

tractor semitrailer (unladen)


Figure H.2: braking performance and legal demands, laden/unladen tractor semitrailer

4. load transfer

tractor 1 tractor 2 semi 1 semi 2 semi 30

20

40

60

80

100

120

140

160

180

axle [−]

Fz

[kN

]

axle loads of tractor semitrailer (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

[kN

]

Fx 5th−180

−120

−60

0

60

120

180

Fy 5th

coupling forces of tractor semitrailer (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz 5th

Figure H.3: axle (un)loading and coupling forces when braking, laden tractor semitrailer

Tractor semitrailer H3

5. ABS performance

100 110 120 130 140 150 160 170 180 190 200−2

−1

0

1

2

3

4

5

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, tractor semitrailer (laden)


100 110 120 130 140 150 160 170 180 190 200−2

−1

0

1

2

3

4

5

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−2

−1

0

1

2

3

4

5

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, tractor semitrailer (unladen)


100 110 120 130 140 150 160 170 180 190 200−2

−1

0

1

2

3

4

5

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]

cpl1 no ABScpl1 ABS

Figure H.4: path and articulation angles during µ-split braking, laden/unladen tractor semitrailer


50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, tractor semitrailer (laden)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0.5

2

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

3

8

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, tractor semitrailer (unladen)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

time [sec]

cpl1 0 m/s2

cpl1 −1.5 m/s2

Figure H.5: ax, ay, ψ and articulation angles during braking at a circle, tractor semitrailer


20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), tractor semitrailer (laden)

0 m/s2

−1.5 m/s2

reference

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), tractor semitrailer (unladen)

0 m/s2

−1.5 m/s2

reference

Figure H.6: path deviation of steer axle when braking at a circle, laden/unladen tractor semitrailer


0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

Vx

[km

/h]

signals during highway exit, tractor semitrailer

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ax [m

/s2 ]

0 m/s2

−3 m/s2

input

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ay [m

/s2 ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50

−8

−6

−4

−2

0

2

yaw

vel

[o /s]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−80

−60

−40

−20

0

20

δ s

[o ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

4

6

time [sec]

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −3 m/s2

Figure H.7: signals during braking on a highway exit, laden tractor semitrailer



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]Dynamic Load Transfer Ratio, tractor semitrailer

DLTR 1DLTR 2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.5

1

1.5

2

2.5

3

3.5

freq [Hz]

RA

[−]

Rearward Amplification axles, tractor semitrailer

steerdrivesemitrailer axle1semitrailer axle2semitrailer axle3

Figure H.8: DLTR and RA against frequency of single lane change, laden tractor semitrailer


0 5 10 15 20 25 30−50

−25

0

25

50

δs [o ]

double lane change signals, tractor semitrialer

δs

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2

0 5 10 15 20 25 30−4

−2

0

2

4

ay [m

/s2 ]


0 5 10 15 20 25 30−6

−3

0

3

6

art.

angl

e [o ]

cpl 1

0 5 10 15 20 25 30−6

−3

0

3

6

time [sec]

φ [o ]

front tractorrear tractorfront semitrailerrear semitrailer

Figure H.9: signals during a double lane change, laden tractor semitrailer



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of tractor semitrailer, Vx= 80km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 50km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 10km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

d= 10%

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Croll= 50%

DLTR1DLTR2

Figure H.10: dynamic load transfer ratio for various velocities, damping ratios and roll stiness,tractor semitrailer


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]rearward amplification of tractor semitrailer, Vx= 80km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

freq [Hz]

RA

[−]

Croll= 50%


Figure H.11: rearward amplication for various velocities, damping ratios and roll stiness, tractorsemitrailer


Appendix I

Truck trailer

1. dimensions of truck trailer

Figure I.1: dimensions of truck trailer

The truck trailer configuration consists of a 4x2 truck and a 2 axle full trailer. The front axleof the truck is steered while the rear axle is driven. The truck and trailer are coupled by a pincoupling and the trailer can rotate freely with respect to the truck.

I1

I2 Truck trailer


axle load [N ] load [ton] limit [ton]steer axle 73141 7.46 7.50drive axle 113251 11.54 11.50trailer axle 1 83385 8.50 9.00trailer axle 2 83385 8.50 9.00total 353162 36.00 36.00

coupling load [N ] load [kg] limit [kg]pin Fx 0 0 −pin Fy 0 0 −pin Fz 0 0 −

Table I.1: static axle loads and coupling forces, laden truck trailer


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

truck trailer (laden)

steer axledrive axletrailer axle1trailer axle2Z = Klegal borders

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

truck trailer (unladen)

steer axledrive axletrailer axle1trailer axle2Z = Klegal borders

Figure I.2: braking performance and legal demands, laden/unladen truck trailer

4. load transfer

truck 1 truck 2 trailer 1 trailer 20

20

40

60

80

100

120

140

160

180

axle [−]

Fz

[kN

]

axle loads of truck trailer (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

[kN

]

Fx pin−180

−120

−60

0

60

120

180coupling forces of truck trailer (laden)

Fy pin

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz pin

Figure I.3: axle (un)loading and coupling forces when braking, laden truck trailer

Truck trailer I3

5. ABS performance

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, truck trailer (laden)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

trailer axle1 no ABStrailer axle2 no ABStrailer axle1 ABStrailer axle2 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45

art.

angl

e [o ]

cpl1 no ABScpl2 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, truck trailer (unladen)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

trailer axle1 no ABStrailer axle2 no ABStrailer axle1 ABStrailer axle2 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45

art.

angl

e [o ]

cpl1 no ABScpl2 ABS

100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art.

angl

e [o ]


Figure I.4: path and articulation angles during µ-split braking, laden/unladen truck trailer


50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, truck trailer (laden)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

turntable 0 m/s2


50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, truck trailer (unladen)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

time [sec]

art.

angl

e [o ]

turntable 0 m/s2


Figure I.5: ax, ay, ψ and articulation angles during braking at a circle, laden/unladen truck trailer

I4 Truck trailer

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), truck trailer (laden)

0 m/s2

−1.5 m/s2

reference

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), truck trailer (unladen)

0 m/s2

−1.5 m/s2

reference

Figure I.6: path deviation of steer axle when braking at a circle, laden/unladen truck trailer


0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

Vx

[km

/h]

signals during highway exit, truck trailer

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ax [m

/s2 ]

0 m/s2

−3 m/s2

input

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ay [m

/s2 ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50

−8−6−4−2

02

yaw

vel

[o /s]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−80−60−40−20

020

δ s

[o ]

0 m/s2

3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

art.

angl

e [o ]

cpl1 0 m/s2

cpl1 −3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4−2

0246

time [sec]

art.

angl

e [o ]

turntable 0 m/s2

turntable −3 m/s2

Figure I.7: signals during braking on a highway exit, laden truck trailer

Truck trailer I5


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]Dynamic Load Transfer Ratio, truck trailer

DLTR 1DLTR 2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.5

1

1.5

2

2.5

3

3.5

freq [Hz]

RA

[−]

Rearward Amplification axles, truck trailer

steerdrivetrailer axle1trailer axle2

Figure I.8: DLTR and RA against frequency of single lane change, laden truck trailer


0 5 10 15 20 25 30−50

−25

0

25

50

δs [o ]

double lane change signals, truck trailer

δs

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2

0 5 10 15 20 25 30−4

−2

0

2

4

ay [m

/s2 ]


0 5 10 15 20 25 30−6

−3

0

3

6

art.

angl

e [o ]

cpl 1

0 5 10 15 20 25 30−6

−3

0

3

6

time [sec]

φ [o ]

front truckrear truckfront trailerrear trailer

Figure I.9: signals during a double lane change, laden truck trailer

I6 Truck trailer


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of truck trailer, Vx= 80km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 50km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 10km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

d= 10%

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Croll= 50%

DLTR1DLTR2

Figure I.10: dynamic load transfer ratio for various velocities, damping ratios and roll stiness,truck trailer

Truck trailer I7

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]rearward amplification of truck trailer, Vx= 80km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

freq [Hz]

RA

[−]

Croll= 50%


Figure I.11: rearward amplication for various velocities, damping ratios and roll stiness, trucktrailer

I8 Truck trailer

Appendix J

Truck drawbar-trailer

1. dimensions of truck drawbar-trailer

Figure J.1: dimensions of truck db-trailer

A truck drawbar-trailer configuration consists of a 6x2 truck and a 2 axle drawbar-trailer. Thefront axle of the truck is steered while the second and last axle of the truck are driven. The truckand drawbar-trailer ar connected via a pin coupling and all rotational DOF’s are allowed whileall translational DOF’s are restricted.

J1

J2 Truck drawbar-trailer


axle load [N ] load [ton] limit [ton]steer axle 71961 7.34 7.50drive axle 1 93539 9.54 9.50drive axle 2 93980 9.58 9.50db-trailer axle 1 66793 6.81 10.00db-trailer axle 2 66137 6.74 10.00total 392410 40.00 40.00

coupling load [N ] load [kg] limit [kg]pin Fx 0 0 −pin Fy 0 0 −pin Fz −4410 −450 −1000

Table J.1: static axle loads and coupling forces, laden truck db-trailer


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

truck dbtrailer (laden)

steer axledrive axle1drive axle2trailer axle1trailer axle2Z = Klegal borders

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ax / g [−]

Fb

/ Fz

[−]

truck dbtrailer (unladen)

steer axledrive axle1drive axle2trailer axle1trailer axle2Z = Klegal borders

Figure J.2: braking performance and legal demands, laden/unladen truck db-trailer

4. load transfer

truck 1 truck 2 truck 3 dbtrailer 1 dbtrailer 20

20

40

60

80

100

120

140

160

180

axle [−]

Fz

[kN

]

axle loads of truck dbtrailer (laden)

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

[kN

]

Fx pin−180

−120

−60

0

60

120

180coupling forces of truck dbtrailer (laden)

Fy pin

ax= 0 m/s2

ax= −6 m/s2

−180

−120

−60

0

60

120

180

Fz pin

Figure J.3: axle (un)loading and coupling forces when braking, laden truck db-trailer

Truck drawbar-trailer J3

5. ABS performance

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, truck dbtrailer (laden)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art .

angl

e [o ]

cpl1 no ABScpl1 ABS

100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]

µ−split, path of axles and articulation angles, truck dbtrailer (unladen)


100 110 120 130 140 150 160 170 180 190 200−2

0

2

4

6

late

ral p

ath

[m]


100 110 120 130 140 150 160 170 180 190 200−180

−135

−90

−45

0

45


art .

angl

e [o ]

cpl1 no ABScpl1 ABS

Figure J.4: path and articulation angles during µ-split braking, laden/unladen truck db-trailer


50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, truck dbtrailer (laden)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

time [sec]

cpl1 0 m/s2

cpl1 −1.5 m/s2

50 55 60 65 70 75 80

0

20

40

60

Vx

[km

/h]

braking in a turn, truck dbtrailer (unladen)

0 m/s2

−1.5 m/s2

50 55 60 65 70 75 80−2

−1

0

1

2

ax [m

/s2 ]

0 m/s2

−1.5 m/s2

input

50 55 60 65 70 75 80−1

0

1

2

3

ay [m

/s2 ]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−2

1

4

7

10

yaw

vel

[o /s]

0 m/s2

−1.5 m/s2

reference

50 55 60 65 70 75 80−8

−6.5

−5

−3.5

−2

art.

angl

e [o ]

time [sec]

cpl1 0 m/s2

cpl1 −1.5 m/s2

Figure J.5: ax, ay, ψ and articulation angles during braking at a circle, truck db-trailer


20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), truck dbtrailer (laden)

0 m/s2

−1.5 m/s2

reference

20 25 30 35 40 45 50 55 60 65 7060

65

70

75

80

85

90

95

100

105

110

lateral path [m]

long

itudi

nal p

ath

[m]

path of steer axle (zoom), truck dbtrailer (unladen)

0 m/s2

−1.5 m/s2

reference

Figure J.6: path deviation of steer axle when braking at a circle, laden/unladen truck db-trailer


0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

Vx

[km

/h]

signals during highway exit, truck dbtrailer

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ax [m

/s2 ]

0 m/s2

−3 m/s2

input

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

ay [m

/s2 ]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50

−8

−6

−4

−2

0

2

yaw

vel

[o /s]

0 m/s2

−3 m/s2

0 5 10 15 20 25 30 35 40 45 50−80

−60

−40

−20

0

20

δ s

[o ]

0 m/s2

3 m/s2

0 5 10 15 20 25 30 35 40 45 50−4

−2

0

2

4

6

art.

angl

e [o ]

time [sec]

cpl1 0 m/s2

cpl1 −3 m/s2

Figure J.7: signals during braking at a highway exit, laden truck db-trailer



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]Dynamic Load Transfer Ratio, truck dbtrailer

DLTR 1DLTR 2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.5

1

1.5

2

2.5

3

3.5

freq [Hz]

RA

[−]

Rearward Amplification axles, truck dbtrailer

steerdrive1drive2dbtrailer axle1dbtrailer axle2

Figure J.8: DLTR and RA against frequency of single lane change, laden truck db-trailer


0 5 10 15 20 25 30−50

−25

0

25

50

δs [o ]

double lane change signals, truck dbtrailer

δs

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

DLT

R [−

]

DLTR 1DLTR 2

0 5 10 15 20 25 30−4

−2

0

2

4

ay [m

/s2 ]


0 5 10 15 20 25 30−6

−3

0

3

6

art.

angl

e [o ]

cpl 1

0 5 10 15 20 25 30−6

−3

0

3

6

time [sec]

φ [o ]

front truckrear trucktrailer

Figure J.9: signals during a double lane change, laden truck db-trailer



0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

dynamic load transfer ratio of truck dbtrailer, Vx= 80km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 50km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

Vx= 10km/h

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

DLT

R [−

]

d= 10%

DLTR1DLTR2

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.2

0.4

0.6

0.8

1

freq [Hz]

DLT

R [−

]

Croll= 50%

DLTR1DLTR2

Figure J.10: dynamic load transfer ratio for various velocities, damping ratios and roll stiness,truck db-trailer


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4R

A [−

]rearward amplification of truck dbtrailer, Vx= 80km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 50km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

Vx= 10km/h


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

RA

[−]

d= 10%


0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

1

2

3

4

freq [Hz]

RA

[−]

Croll= 50%


Figure J.11: rearward amplication for various velocities, damping ratios and roll stiness, truckdb-trailer


Appendix K

Tyre characteristics

steer axle tyres, "truck2b2.tpf"

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−50

−40

−30

−20

−10

0

10

20

30

40

50pure braking, steer axle tyre

κ [−]

Fx

[kN

]

Fz = 18.5 kNFz = 37 kNFz = 55.5 kN

K1.1

−20 −15 −10 −5 0 5 10 15 20−40

−30

−20

−10

0

10

20

30

40pure cornering, steer axle tyre

α [deg.]

Fy

[kN

]

Fz = 18.5 kNFz = 37 kNFz = 55.5 kN

K1.2

−20 −15 −10 −5 0 5 10 15 20−1500

−1000

−500

0

500

1000

1500pure cornering, steer axle tyre

α [deg.]

Mz

[Nm

]

Fz = 18.5 kNFz = 37 kNFz = 55.5 kN

K1.3

−30 −20 −10 0 10 20 30−10

−5

0

5

10

15

20

25

Fx [kN]

Fy

[kN

]

combined slip, Fz=37 kN, steer axle tyre)

α= −8 degα= −5 degα= −2 degα= −1 degα= 1 degα= 2 deg

K1.4

K1

K2 Tyre characteristics

−20 −15 −10 −5 0 5 10 15 20−30

−20

−10

0

10

20

30

α [deg]

Fy

[kN

]camber influence on Fy, Fz=37 kN, steer axle tyre

γ= −2 degγ= 0 degγ= 4 deg

K2.5

−20 −15 −10 −5 0 5 10 15 20−800

−600

−400

−200

0

200

400

600

800

α [deg.]

Mz

[Nm

]

camber influence on Mz, Fz=37 kN, steer axle tyre


K2.6

0 20 40 60 80 100 120 1400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fz [kN]

µ [−

]

adhesion coefficients , steer axle tyre

µx maxµy maxµx lock

K2.7

0 20 40 60 80 100 120 140−2000

2000

4000

6000

8000

10000

12000

14000

16000

Fz [kN]

stiff

nes

[N/%

N/d

eg]

stiffness , steer axle tyre

longitudinalcorneringcamber

K2.8

0 20 40 60 80 100 120 1400

100

200

300

400

500

600

Fz [kN]

Mz

stiff

[Nm

/deg

]

aligning torque stiffness, steer axle tyre

corneringcamber

K2.9

Tyre characteristics K3

drive axle tyres, "truck1.tpf"

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−40

−30

−20

−10

0

10

20

30

40pure braking, drive axle tyre

κ [−]

Fx

[kN

]

Fz = 14 kNFz = 28 kNFz = 42 kN

K3.10

−20 −15 −10 −5 0 5 10 15 20−40

−30

−20

−10

0

10

20

30

40pure cornering, drive axle tyre

α [deg.]

Fy

[kN

]


K3.11

−20 −15 −10 −5 0 5 10 15 20−800

−600

−400

−200

0

200

400

600

800pure cornering, drive axle tyre

α [deg.]

Mz

[Nm

]


K3.12

−25 −20 −15 −10 −5 0 5 10 15 20 25−10

−5

0

5

10

15

20

Fx [kN]

Fy

[kN

]combined slip, Fz=28 kN, drive axle tyre)


K3.13

−20 −15 −10 −5 0 5 10 15 20−30

−20

−10

0

10

20

30

α [deg]

Fy

[kN

]

camber influence on Fy, Fz=28 kN, drive axle tyre


K3.14

−20 −15 −10 −5 0 5 10 15 20−800

−600

−400

−200

0

200

400

600

800

α [deg.]

Mz

[Nm

]

camber influence on Mz, Fz=28 kN, drive axle tyre


K3.15


0 20 40 60 80 100 120 1400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fz [kN]

µ [−

]

adhesion coefficients , drive axle tyre


K4.16

0 20 40 60 80 100 120 140−2000

2000

4000

6000

8000

10000

12000

14000

16000

Fz [kN]

stiff

nes

[N/%

N/d

eg]

stiffness , drive axle tyre


K4.17

0 20 40 60 80 100 120 1400

50

100

150

200

250

300

350

400

450

Fz [kN]

Mz

stiff

[Nm

/deg

]

aligning torque stiffness, drive axle tyre

corneringcamber

K4.18

Tyre characteristics K5

trailer axle tyres, "truck3.tpf"

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−60

−40

−20

0

20

40

60pure braking, trailer axle tyre

κ [−]

Fx

[kN

]


K5.19

−20 −15 −10 −5 0 5 10 15 20−50

−40

−30

−20

−10

0

10

20

30

40

50pure cornering, trailer axle tyre

α [deg.]

Fy

[kN

]


K5.20

−20 −15 −10 −5 0 5 10 15 20−1500

−1000

−500

0

500

1000

1500pure cornering, trailer axle tyre

α [deg.]

Mz

[Nm

]


K5.21

−25 −20 −15 −10 −5 0 5 10 15 20 25−10

−5

0

5

10

15

20

Fx [kN]

Fy

[kN

]combined slip, Fz=50 kN, trailer axle tyre)


K5.22

−20 −15 −10 −5 0 5 10 15 20−30

−20

−10

0

10

20

30

α [deg]

Fy

[kN

]

camber influence on Fy, Fz=50 kN, trailer axle tyre)


K5.23

−20 −15 −10 −5 0 5 10 15 20−800

−600

−400

−200

0

200

400

600

800

α [deg.]

Mz

[Nm

]

camber influence on Mz, Fz=50 kN, trailer axle tyre


K5.24


0 20 40 60 80 100 120 1400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fz [kN]

µ [−

]

adhesion coefficients , trailer axle tyre


K6.25

0 20 40 60 80 100 120 140−2000

2000

4000

6000

8000

10000

12000

14000

16000

Fz [kN]

stiff

nes

[N/%

N/d

eg]

stiffness , trailer axle tyre


K6.26

0 20 40 60 80 100 120 1400

50

100

150

200

250

300

350

400

450

500

Fz [kN]

Mz

stiff

[Nm

/deg

]

aligning torque stiffness, trailer axle tyre

corneringcamber

K6.27