Influence of tire wear and asphalt temperature on vehicle stopping distance

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Universit`

a di Pisa

Dipartimento di Ingegneria Civile e Industriale Corso di Laurea Magistrale in Ingegneria dei Veicoli

Tesi di laurea magistrale

Influence of tire wear and asphalt temperature on

vehicle stopping distance

Candidato:

Yuri Gaspari

Relatori:

Prof. Massimo Guiggiani Ing. Stefano Murgia

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Abstract

During tire development process car maker shares with tire supplier some information about the performances that a tire must reach. One of these information is vehicle stopping distance. Tire suppliers and car makers are not the only ones to be interested on this parameter.

Antilock braking systems (worldwide known as ABS) providers work closely with car maker in order to find the right tuning that minimizes the stopping distance of the car.

It is enough, moreover, to read an automotive magazine to realize that also press is interested on it, since the braking performance of a car is measured in terms of stopping distance.

Stopping distance measurement is affected by many source of variability. Two of them in particular are tire wear resulting from braking and tarmac temperature during tests. The aim of this work is to evaluate the influence of tire wear and asphalt temperature on vehicle stopping distance, and to achieve a method with which it is possible to correlate stopping distance measurements performed for different conditions of the above mentioned factors using a simple instrumentation.

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Ringraziamenti

Giunto al termine del mio percorso universitario, con enorme piacere desidero ringraziare tutti coloro che, per un motivo o per un altro, in larga o piccola scala, hanno contribuito al raggiungimento di questo obiettivo.

Il ringraziamento più importante va alla mia famiglia. Mi avete sempre supportato e mi è stata data piena fiducia in ogni occasione, anche a spese di un vostro maggiore sacrificio. Questa tesi è dedicata a voi, piccolo Edoardo, Simone, Chiara, Manuel, Roberta, Stefano, Gina.

Ringrazio il Prof. Massimo Guiggiani, per il supporto dato nell’elaborazione di questa tesi e per gli insegnamenti ricevuti dai corsi di Meccanica Applicata e Dinamica dei Veicoli, riuscendo a stimolare in me grande curiosità e senso critico.

Ringrazio il mio tutor Ing. Stefano Murgia, l’Ing. Giovanni Alberto Bissoli e l’amico Ing. Lorenzo Ceccarini per avermi aiutato nella realizzazione della tesi e per avermi affiancato durante lo stage.

Ringrazio gli amici d’infanzia, tra tutti un ringraziamento particolare va a Alessandro, Emiliano e Jonathan. Spero d’ora in poi di poter passare un pò più tempo insieme a voi.

Ringrazio Luca, Roberto, Davide, e tutti gli amici per i quali “una brutta giornata di pesca è sempre meglio di una bella giornata di lavoro”, che hanno compreso la mia latitanza nei periodi più intensi di studio.

Ringrazio i molti amici che ho conosciuto durante il percorso universitario e con i quali ho condiviso esperienze stupende, che porterò per sempre con me: il Lau, il Tambe, Paolone, Eugenio, la Franz, Maria, Luana, Oleg, il Ferra, il Borto, il Loppa, il Cambri, Eggi.

Ringrazio gli amici della formula SAE, perchè l’E-Team squadra corse non si molla mai: Benvenuti, Corti, Francesca, Monica, Bandini, Gmaz, Sal, Ivan, Pelli, FDR, Stacchio, Carletto, Maurizio, Monda, Tommy, Vinny, FDR e tutti gli altri.

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Chapter 1 Introduction

The internship that led to the drafting of the following thesis was held at the headquarters of the experimental circuit of the FCA group, located in Balocco. After defining the goals to be achieved, the procedures that led to data acquisition and processing will be described. A Matlab software has been developed for this purpose, and will be described in the document.

1.1 Project Objectives

The objective of this work is to study the influence of tire wear and asphalt temperature on vehicle stopping distance, longitudinal acceleration and friction coefficient.

In order to achieve this objective, experimental tests were carried out on a FCA group vehicle, for different conditions of tire wear and asphalt tempera-ture, and after data processing it has been possible to evaluate the influence of the two factors, mentioned above, on vehicle stopping distance.

The result of the work will therefore remain available to the company, in order to improve the efficiency and effectiveness of tire development process and ABS system tuning.

1.2 Planning

In the first phase of the study the vehicle mathematical model has been devel-oped, which allowed to obtain typical tire behavior, longitudinal acceleration and friction coefficient directly from the available signals.

Then, four tests campaigns were carried out, which provided the basis for the implementation of the model. In order to process data, a Matlab software has been developed which allowed to upload data and to evaluate vehicle stopping distance, acceleration and friction coefficient in a systematic way.

The software has been subsequently improved, allowing to fit observed data. In the last phase of the stage the definitive model has been developed, and it allows to predict stopping distance, acceleration and friction coefficient for a certain brand of tire, asphalt temperature and tire wear.

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CHAPTER 1. INTRODUCTION 2

1.3 Balocco Proving Ground

The Balocco Proving Ground (more often referred to simply as the Circuit of Balocco) is a complex of motor racing circuits located in Balocco (VC), built by Alfa Romeo and currently owned by Fiat Chrysler Automobiles S.p.A.

Figure 1.1: Balocco Proving Ground. In red, the Iveco Track. The circuit is characterized by several tracks, the main one being:

• High Speed track, which allows speed over 300 km h−1_;

• Langhe track, a reproduction of a secondary street inspired by the homony-mous historical region located in Piemonte, and characterized by a lenght of more than 22 km;

• Alfa Romeo track, a real hi-speed circuit that allows to test the vehicles dynamics;

• Comfort track, that allows to test suspension for different pave condi-tions;

• Dynamic Platform, a 300 m large round.

The tests object of the study were performed in the Iveco Track, that is straight track, about one kilometer long, characterized by a good grip and perfectly flat tarmac surface.

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Chapter 2 The Tire

2.1 Description

The tire of a car is the interface between the vehicle and the road surface, and it make possible to control the vehicle. The factor that characterizes the quality of a tire in terms of performance is the coefficient of friction between the road surface and the tire itself. All other things being equal (the main ones being the pneumatic pressure, tire wear, ambient temperature, road surface temperature, road surface quality) a high friction coefficient will provide good acceleration to the vehicle (and, in a broad sense, also the decelerations) and then, in case of braking, low stopping distances.

For the formal definition of friction coefficient, please refer to Sect. 3.3.

2.2 Tire Slip

In the science of vehicle dynamics particular attention is given to the char-acterization of the tire, i.e. the determination of the longitudinal and lateral forces that can be exchanged between the tire and the ground under certain conditions of motion and vertical load. In the following sections the quantities of interest will be described.

2.2.1 Rolling Radius

According to Fig. 2.1, this document will refers to the following characteristic radii:

• Ru: unloaded tire radius;

• Rl: tire radius with a Fz load applied;

• Rr: rolling radius.

The rolling radius Rr is, among the three, the one of greatest interest, and

is the ratio between the translation speed of the rim and its angular velocity in pure rolling conditions

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CHAPTER 2. THE TIRE 4 Rr = Vc ωc _σ x=0 and, typically, is Ru > Rr> Rl.

F

z

F

z R R Rl r u

V

c ωc

Figure 2.1: Comparison between unloaded tire radius, tire radius with vertical load applied in rolling condition and tire radius with vertical load applied and in static condition.

2.2.2 Pure Longitudinal Slip

In this document and, in general, in vehicle dynamics, the longitudinal slip represents an index of how far the motion of the wheel is from the pure rolling condition.

Consider a vehicle travelling a straight road at a certain speed. When the driver act on the brake pedal, braking torque is applied to the wheels of the vehicle via the braking circuit. At that moment, the angular speed of the braked wheels decreases and the rolling speed of the tyre drops below the vehicle speed. To compensate for this difference, the tires begin to slip on the road at a certain slippage rate. There are many definitions to describe

the same concept but the most commonly used are the theoretical slip σx and

practical slip κx, defined as

σx = Vc− ωcRr ωcRr (2.1) κx = Vc− ωcRr Vc (2.2)

where Vc is the velocity of wheel centre, ωc is the angular velocity of the

wheel and Rr is the rolling radius defined as in Sect. 2.2.1.

In this document, for reasons of continuity with company conventions, with

the term slip we will refer to the practical slip. The slip κx can vary, under

pure braking conditions, between 0, that is pure rolling condition, and 1, wheel lock condition.

2.2.3 Grip Longitudinal Forces

In order to find the longitudinal force that a tire is able to exchange with the road when is subjected to a certain slip, bench tests are usually carried out,

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CHAPTER 2. THE TIRE 5 and the longitudinal load is measured varying vertical force and rotational velocity of the rim.

The result of this kind of tests leads to plots similar to those shown in the figure 2.2. FZ=208 N FZ=659 N FZ=1092 N FZ=1540 N - 0.10 - 0.05 0.00 0.05 0.10 0.15 0.20 - 2000 - 1000 0 1000 2000 σx FX

Figure 2.2: Experimental results for longitudinal force Fx vs theoretical slip

σx

Why is it so important to evaluate the trend of the braking force depending on the longitudinal slip?

According to Fig. 2.2, the longitudinal force Fx, which is the main responsible

of the stopping distance of the vehicle, has a maximum for a certain value of longitudinal slip and vertical force. In order to reduce the stopping distances, the control unit that controls the ABS system must be tuned so as to guarantee a slip value close to that for which the braking force peak is obtained.

If −κ_x is the slip value corresponding to the peak of the longitudinal force

Fx for a certain vertical load, the angular speed of the wheel must therefore

be maintained by the ABS system close to: −

ω= Vc(1 −

− κx)

Rr (2.3)

In this way, the stopping distances will be the least achievable for a given type of tire and vehicle. For further information on ABS system, please refer to 2.4.

2.3 Tire Wear

One of the factors that influence vehicle stopping distance is the tire wear. It is mandatory to distinguish two main different types of wear: abrasion wear and mileage wear. Let us consider a tread block, like the one shown in Fig. 2.3.

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CHAPTER 2. THE TIRE 6 Vehicle speed Tread block Pressure Braking force f hr

Figure 2.3: Tread block pressure distribution during a braking.

During a braking, the tread block will deflect as a consequence of the brak-ing force applied at the summit of the block itself. In general, the higher the force, the higher the deflection of the tread block in the longitudinal direction. As a first approximation, it is possible to assume that the pressure distribution assumes a trend like the one shown in figure 2.3: the forward edge of the block (in the direction of the vehicle speed), is subjected to a higher pressure than the rear edge, and this asymmetric distribution is more pronounced for soft rubber compound and high depth of the tread, main features for winter and all seasons tires. This difference in pressure distribution is the main responsible of an asymmetric wear of the tread blocks which, after high number of braking, will result to have an increased supporting surface during the braking itself,

caused by the different height of the forward and rear edges (hf and hr in Fig.

2.3). This could be one of the reasons why, in most cases and at the same testing conditions, an abraded tire results to be more efficient of a new tire in terms of maximum acceleration achievable and, hence, stopping distances.

Mileage wear is less affected by the above described phenomena, because the extent of braking is less pronounced, and, hence, the pressure distribution results to be more homogeneous in the longitudinal direction of the tread block. Throughout this document, with the term wear will be referred to as the one obtained by subsequently ABS braking performed and, hence, it will be intended as abrasion wear.

2.4 ABS System

One of the main scopes of the present work is to use the result of the model in order to improve the efficiency and effectiveness of tire development process and ABS system tuning. In this section a brief introduction to the Anti-Lock Braking System is given.

One of the most serious hazards of driving is the locking of wheels under heavy braking. The loss of braking efficiency will greatly increase the stopping distance and, coupled with this, will be loss of steering response if the front wheels lock and even worse a loss of directional stability if the rear wheels lock. Anti-lock brake systems (ABS), generally also referred to as anti-lock systems

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CHAPTER 2. THE TIRE 7

Figure 2.4: Brake system overview: 1 brake pedal, 2 brake booster, 3 master cylinder, 4 reservoir, 5 brake line, 6 brake hose, 7 wheel brake, 8 wheel speed sensors, 9 hydraulic modulator, 10 ABS control unit, 11 ABS warning lamp [6].

(ALS), are designed to prevent the vehicle wheels from locking as a result of the service brake being applied with too much force, especially on slippery road surfaces.

2.4.1 System Overview

The scheme of a braking system equipped with ABS system is shown in Fig. 2.4. The core of a braking system equipped with ABS is the hydraulic mod-ulator, which incorporates a series of solenoid valves that open or close the hydraulic circuits between the master cylinder and the brakes. The fixed sen-sor connected to the wheel continuously picks up the rotary movement of the wheel by means of the phonic wheels. The electrical pulses generated within the sensor are transmitted to the electronic control unit (ECU) which uses them to compute the wheel speed. At the same time, the ECU estimate a reference speed that is close to the vehicle speed, which is not measured. From all of this information the ECU continuously computes the wheel acceleration or deceleration and brake slip values.

2.4.2 Principle of Hydraulic Modulator

The hydraulic modulator incorporates two solenoid valves that can open or close the hydraulic circuits between the master cylinder and the brakes: the inlet valve (between the master cylinder and the brake) controls pressure ap-plication, while the outlet valve (between the brake and the return pump)

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CHAPTER 2. THE TIRE 8 3 6 1 2 4 9 7 8 5

Figure 2.5: Brake system: 1 master cylinder, 2 booster, 3 brake pedal, 4 wheel brake, 5 damping chamber, 6 return pump, 7 inlet valve (shown in open setting), 8 outlet valve (shown in closed setting), 9 brake fluid reservoir [6].

controls pressure release (Fig. 2.5). There are two solenoid valves for each brake.

Under normal conditions, the inlet valve is open. As a consequence, the brake pressure generated in the master cylinder when the brake pedal is applied is transmitted directly to the brakes at each wheel.

As the slip increases, due to braking on a slippery surface or heavy braking, the connection between the master cylinder and the brakes is shut off (inlet valve is closed) so that any increase of pressure in the master cylinder does not lead to a pressure increase at the brakes.

If the degree of slip of the wheel increases further despite this action, the pressure in the brake must be reduced. To achieve this, the inlet valve is still closed, and in addition, the outlet valve opens in order to allow the return pump to draw brake fluid from the brake concerned in a controlled way. The pressure in the brake is thus reduced so that wheel lock-up does not occur.

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Chapter 3 Braking Performance

3.1 Hypothesis

The study of the equilibrium equations that will be analyzed is greatly simpli-fied under the following hypothesis.

• Since it is difficult to find the right point of application of the aero-dynamic forces, and being the aeroaero-dynamic drag an order of magnitude lower than the braking force, the hypothesis of applying the aerodynamic drag D to the car’s center of gravity was considered realistic.

• Negligible downforce. The test vehicle is not characterized by strong aerodynamic qualities, so the downforce can be neglected. Also in this case, it is a realistic hypothesis limited to the study in exam.

• Negligible wheel inertia. The wheel assembly inertia appears in the

equi-librium equation at momentum, and has direct influence on the Z1 and

Z2 forces.

However, since the rate of change of the angular momentum of the tyre-and-wheel assembly is two orders of magnitude lower than the vertical

load Z1 and Z2 that we obtain neglecting this effect, the hypothesis is

very realistic.

• Negligible pitch oscillation and, consequently, negligible rate of change of sprung mass angular moment.

• Flat and straight road, with uniform grip.

3.2 Equilibrium Equations

3.2.1 Vehicle Equilibrium

According to Fig. 3.1, and with the hypothesis listed in Sect. 3.1, the vehicle equilibrium equations are

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CHAPTER 3. BRAKING PERFORMANCE 10

−X1− X2− D = m ˙u

Z1+ Z2− mg = 0

(X1+ X2)h + Z2a2− Z1a1 = 0

(3.1)

in which D represents the aerodynamic drag, that is, with obvious meaning of the symbols used

D = 1

2ρSCxu

2 _(3.2)

Figure 3.1: Vehicle free body diagram.

The system described in Eq. (3.1) has three algebraic equations and four

unknown functions (X1, X2, Z1 e Z2). Combining the equations and including

the drag formula it is however possible to obtain the vertical load

Z1 = mga2 l − h lm ˙u − h 2lρSCxu 2 Z2 = mg a1 l + h lm ˙u + h 2lρSCxu 2 (3.3)

Since it is possible to get by data acquisition the instantaneous value of longitudinal acceleration and longitudinal velocity, and since geometrical and aerodynamics characteristics are known, the instantaneous value of vertical

forces Z1 and Z2 are given by Eq. (3.3). In particular, the two forces are

characterized by having a constant term, a term dependent on acceleration and a term dependent on the longitudinal velocity of the vehicle.

For consistency with the terminology used in literature, the two constant terms are the so-called static load and it will be referred to as follows

Z₁0 = mga2 l Z₂0 = mga1

l

(3.4)

The static load represents the load we would have on the two axles imposing u = ˙u = 0 (standing vehicle).

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CHAPTER 3. BRAKING PERFORMANCE 11 The two terms acceleration depending are the so-called longitudinal load transfers ∆Z

∆Z = −h

lm ˙u (3.5)

From Eq. (3.5) if the car is decelerating ( ˙u < 0) the vertical load on the

front axle grows, while the one on the rear axle decreases, as expected.

Replacing in Eq. (3.3) the static load and the longitudinal load transfer

above mentioned, and imposing ξ = _2lhρSCx, it is possible to obtain

Z1 = Z10+ ∆Z − ξu

2

Z2 = Z20− ∆Z + ξu

2 (3.6)

with Zi ≥ 0.

Considering the longitudinal forces, the breaking force must not exceeed the grip limit

|X1| ≤ µ1Z1 |X2| ≤ µ2Z2

(3.7)

where the longitudinal friction coefficient µi is the ratio between the peak

longitudinal force and its corresponding vertical load

µi(Zi) = X max i Zi (3.8)

3.2.2 Wheel Equilibrium

In order to find the longitudinal forces Xi, and hence to solve the system described in Eq. (3.1), we have to solve the equilibrium at momentum of the wheel.

Xirr− Zis − Mfi = Jrω˙ri (3.9)

In Eq. (3.9) the subscript i refers the function to a generic axle, s is the

distance between the vertical load application point and the wheel center, Jr

is the inertia momentum of the wheel assembly and ωri is the wheel angular

velocity. In order to find X1 e X2 is, hence, necessary to know the braking

force acting on the wheel.

The alternative would be to evaluate X1 as a function of X2, but it would

presuppose to know the brake bias of the vehicle with which the tests were carried out. In the next section the solution of the problem will be discussed.

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Figure 3.2: Free body diagram of the wheel.

3.3 Vehicle Mathematical Model

For the test object of the study it was not possible to measure either the braking torque acting on the wheel assembly or the characteristic brake bias (the vehicle has electronic brake force distribution).

It has been therefore decided to remove rear brakes so that it was possible

to calculate, with the available data, the longitudinal ground force X1.

Figure 3.3: Free body diagram of the vehicle without rear braking system. The scheme is, hence, the one shown in Fig. 3.3 and the equations describing the vehicle dynamics are readily obtained from Eq. (3.1)

−X1− D = m ˙u

Z1+ Z2− mg = 0

X1h + Z2a2− Z1a1 = 0

(3.10)

The solution of the three algebraic equations in the three unknowns X1, Z1

and Z2 is X1 = −m ˙u − l hξu 2 Z1 = Z10+ ∆Z − ξu 2 Z2 = Z20− ∆Z + ξu2 (3.11)

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where ξ = _2lhρSCx. In the remainder of this work it will be made large use

of the coefficient µ, which is the ratio between longitudinal force and applied_e

vertical force

e

µ = X1

Z1 (3.12)

It must be borne in mind that µ is not the friction coefficient, since the_e

longitudinal force is not the maximum one achievable with respect to the ap-plied vertical load. However, since this ratio has no dimension and since it has been largely used in order to evaluate the performance of a tire for a cer-tain type of vehicle and asphalt, sometimes in the present document it will be

referred to µ simply as µ._e

Combining Eq. (3.11) and neglecting the aerodynamic forces, the adhesion

coefficient µ depends, as well as longitudinal acceleration, on both ζ and λ_e

e µ = − ˙u g(1 − ζ) − λ ˙u (3.13) where ζ = a1 l and λ = h

l. In Fig. 3.4 the adhesion coefficient trend vs

longitu-dinal acceleration is shown.

In this document the acceleration will always be considered a negative term (the vehicle is braking).

Let’s suppose to increase ζ (move the center of gravity backward). This

leads, with the same acceleration value, to have higher µ as a consequence of_e

the lower vertical force Z1.

On the other hand, increasing λ (move the center of gravity upward), with the

same longitudinal acceleration, leads to a decrease of µ, due to a greater Z_e 1.

But if we have the same acceleration, and therefore the same X1, and

different Z1 forces we will have different longitudinal slips, as can be seen from

Fig 2.2.

In order to have comparable results it is therefore important that the tests are carried out with the same vehicle and same mass distribution, with the same geometrical characteristics and therefore be able to have, for certain

deceleration (slip dependant), always the same value of adhesion coefficient µ._e

With the same vehicle, therefore, same accelerations correspond to the same adhesion coefficients, regardless of tire type, asphalt temperature, wear. This consideration results directly from the equilibrium equations and from the definition of adhesion coefficient (3.13).

In Fig. 3.5 the dependence between longitudinal acceleration and adhesion coefficient is shown.

It is of some interest to observe that both curves do not pass from the origin but, at zero acceleration, we have a negative value of the adhesion coefficient. This phenomena origins by the mathematical model, which takes

into account the aerodynamic drag: at a certain, constant speed ( ˙u = 0), in

order to overcome the aerodynamic drag, a longitudinal force X1 is required

in the opposite direction to that shown in Fig. 3.3, and hence, according to

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CHAPTER 3. BRAKING PERFORMANCE 14 0 2 4 6 8 10 Long. acceleration [m\s^2] 0 0.5 1 1.5 2 =0.15 =0.37 =0.6 0 2 4 6 8 10 Long. acceleration [m\s^2] 0 0.2 0.4 0.6 0.8 1 1.2 =0.15 =0.22 =0.5

Figure 3.4: Adhesion coefficient, ax-dependent, for various ζ (left) and λ (right)

coefficients. 0 1 2 3 4 5 6 7 8 9 Long. acceleration [m/s2_] 0 0.2 0.4 0.6 0.8 1 1.2

Figure 3.5: Adhesion coefficient versus longitudinal acceleration ax for the

tested vehicle.

3.4 Maximum Deceleration

The maximum deceleration achievable for a car braking with the only front tires can be obtained by assuming that the front axle is braking at its grip limit

X1 = µZ1 (3.14)

where µ is the longitudinal friction coefficient defined in (3.8). Since the aero-dynamic drag D is very small compared to the braking forces, it will not been included in the calculation of the limit deceleration. The maximum

deceler-ation ˙umax,2 for a car braking with the only front tires can be thus obtained

from (3.10)

| ˙umax,2| =

µga2

l − µh (3.15)

A car equipped with front and rear brakes has a maximum deceleration ˙umax,4

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CHAPTER 3. BRAKING PERFORMANCE 15 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Grip 0 2 4 6 8 10 12 14 16 18 20 Max. deceleration [m/s 2]

Front tire braking All tire braking Overturning limit

Figure 3.6: Comparison between the maximum deceleration achievable with car braking with two (blue) and four (red) wheels. The dot line represents the overturning limit.

| ˙umax,4| = µg (3.16)

It could be of some interest to compare the maximum deceleration achievable for the two considered configurations, shown in Fig. 3.6. Considering the geometrical features of the tested vehicle, and considering a µ = 1 (realistic value), there is a gap of about 0.2g between the maximum theoretical decel-eration achievable with a car braking with four wheels and the tested vehicle, in the case of grip limit. Moreover, it is possible to notice that the condition

of overturning deceleration, that is equal to | ˙uot| = a1g/h, is not met, since a

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Chapter 4 Data Acquisition

4.1 Vehicle

For the test session it has been used a Fiat Tipo Sedan. The vehicle was already in testing conditions, in particular rear brakes got off and measurement of the

longitudinal distances a1 and a2 of centre of gravity from the front and rear

axles, and centre of gravity height from the ground were done, according to the procedure described in [2].

Figure 4.1: Fiat Tipo Sedan [7]. In Tab. 4.1 the main data of interest are listed.

4.2 Signals of Interest

In order to find the longitudinal force and adhesion coefficient, for Eq. (3.11),

vehicle longitudinal acceleration ˙u and longitudinal speed u are needed.

Since the rear braking system of the vehicle has been deactivated (thus, the rear wheels can rotate freely), it has been made the hypothesis to consider as absolute longitudinal speed of the vehicle u the one calculated on the basis of the rear phonic wheels, without the need to install a GPS

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CHAPTER 4. DATA ACQUISITION 17 Vehicle Characteristics

Weight m 1460 kg

Wheelbase L 2.64 m

Dist. a1 from G to front axle 0.98 m

Dist. a2 from G to rear axle 1.66 m

Dist. h from G to ground 0.58 m

Drag coefficient Cx 0.312

Frontal surface S 2.2 m2

Table 4.1: Main vehicle characteristics.

0 1 2 3 4 5 6 7 8 9 10 11 Time [s] 0 20 40 60 80 100 120 V ehicle speed [m /s] GPS Phonic wheel

Figure 4.2: GPS (blue) and CAN (red) vehicle speed signals comparison. The speed signal acquired via CAN has been obtained by rear phonic wheels.

u(t) = Rrωr (4.1)

where ωr is the mean value of rear wheels angular speed

ωr =

ω21+ ω22

2 (4.2)

The maximum percentage error that is committed assuming as absolute speed the one calculated on the basis of the rear phonic wheels instead of the GPS signal is about 2%, so the hypothesis is quite realistic.

For the purposes of tire characterization, the data of interest are

accelera-tion and adhesion coefficient as a funcaccelera-tion of the practical slip κx. Since the

velocity value u is known (thanks to the above consideration) and since it is possible to obtain the angular velocity of the front wheels from CAN network, it has been possible to calculate the practical slip as follow

κx = ωr− ωf

ωr

(4.3)

where ωr and ωf are the angular velocity of the rear wheels and front wheels

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CHAPTER 4. DATA ACQUISITION 18 In order to have comparable results it is quite obvious that the vehicle must have the same wheel size on both axles.

0 1 2 3 4 5 6 7 8 9 10 Time[s] 10 20 30 40 50 60 70 80 90 100 110 V ehicle speed [km /h] 0 20 40 60 80 100 120

Brake system pressure

[bar]

Vehicle speed Brake system pressure

Figure 4.3: vehicle speed and master cylinder pressure trend during a progres-sive braking.

The other signal that is useful for data processing is the pressure of the braking system. Since we are interested on stopping distances, braking forces and friction coefficients, we assumed as trigger event of start/end of acquisition the overcoming of a certain level of pressure of the braking system (synonymous of braking). In Fig. 4.3 the dotted lines represent the instant of start/end of acquisition.

4.3 Instrumentation

The relevant data necessary to evaluate the performance of a given type of tire were acquired directly from the CAN network of the tested vehicle. It has been possible, through the sensors installed on the standard vehicle, to process the longitudinal, lateral acceleration, individual wheel speeds, yaw rate and brake system pressure.

The main sensors that allows data analysis are listed below.

• Phonic wheels on each wheel. The signal coming from these sensors al-lows to evaluate both longitudinal slips and vehicle speed. Vehicle speed is also necessary to evaluate stopping distances by integration method (Sect. 5.1.3).

• Two axes accelerometer. It allows to evaluate both longitudinal ation, necessary to study the braking tire behavior, and lateral acceler-ation, which allows to find out any incorrect manoeuvre during tests.

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CHAPTER 4. DATA ACQUISITION 19 • Pressure sensor on braking system circuit, which allows to set the start

and the end conditions for data processing.

During the first tests session the vehicle was also equipped with a Vbox R

Racelogic GPS sensor, which allowed to obtain information regarding vehicle speed, stopping distance and acceleration.

Figure 4.4: Vbox R _{Racelogic 3i.}

After evaluation of stopping distances with the vehicle speed integration (Sect. 5.1.3), it has been possible to remove the GPS sensor and obtain all the relevant data by processing the sole CAN network signals.

For data acquisition from CAN network it has been used a Vector R _GL1000

Compact Logger. The device allows to work in standalone mode, saving data in a SD card. Data can be subsequently downloaded and processed by interfacing the PC to the USB port of the device.

Figure 4.5: Vector R _GL1000.

The asphalt temperature was measured with a Raytek R _{MX2 infrared}

ther-mometer. The datasheet for each above described device is set out in annex 9.

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CHAPTER 4. DATA ACQUISITION 20

Figure 4.6: Raitek MX2 infrared thermometer.

4.4 Test Procedure

Each test consists of two steps: progressive braking and ABS braking, whose meanings are described in Sections 4.5 and 4.6. Broadly speaking, progres-sive braking gives information about tire characterization (maximum grip co-efficient, tire slip curve, tire stiffness), while ABS braking are necessary to evaluate stopping distance and mean fully developed deceleration.

A test session consists of several tests , typically 10-20 tests, executed with the same type of tire at different temperatures. In this way it is possible to test the tire in different conditions of asphalt temperature and tire wear (during test sessions, tire wears out). The number of tests executed in a test session depends on the wear of the tire: typically, after 40-50 safety braking the tire looks pretty worn and it has no sense to execute further tests.

Before any test, particular attention was paid to check the tire pressure of the vehicle (2.3 bar on the front and 2.1 bar on the rear) and the fuel level (full tank). With regard to the tarmac condition, tests were executed on dry track and on the same portion of the track.

4.5 Progressive Braking

This kind of manoeuvre is necessary to evaluate longitudinal acceleration and adhesion coefficient as a function of practical slip (tire slip curve).

In this manoeuvre, the vehicle is at first accelerated to 110 km h−1, keeping

the vehicle speed constant for a couple of seconds, than it is progressively decelerated, until the front wheels lock. The manoeuvre have to last about five seconds and, while braking, the vehicle shall be in neutral gear, in order to cut off minor effects due to engine inertia and to avoid vehicle engine stalling. The ABS system shall be deactivated by removing corresponding fuse. Data

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CHAPTER 4. DATA ACQUISITION 21 ends after wheels locking.

In this way, it is possible to evaluate longitudinal acceleration for different load transfer conditions, and, therefore, different longitudinal practical slips.

An example of progressive braking analysis is shown in Fig. 4.7, where data have been fitted with the Pacejka four parameters curve. The fit allows to obtain information on the maximum grip coefficient measured (which is related to longitudinal acceleration and geometrical characteristics of the vehicle) and its respective slip (function of front and rear angular velocity).

Since one of the main goals of this project is to evaluate how the asphalt temperature and tire wear affect the maximum grip coefficient, each test is composed by three progressive braking, in order to have a suitable number of data, which means to have the best estimation of the grip coefficient.

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Longitudinal slip 0 0.2 0.4 0.6 0.8 1 1.2 Observed data Pacejka fit max= 1.11 @ 19.3%

Figure 4.7: Progressive braking analysis. In black, Pacejka fit curve, which allows to obtain the maximum grip coefficient and its respective longitudinal slip value.

4.6 ABS Braking

This manoeuvre is necessary to evaluate the influence of tire wear and asphalt temperature on vehicle stopping distance.

With the term ABS braking will be referred to as the braking with en-gaged ABS system and in which the brake pedal force must be high enough to guarantee ABS control throughout the entire stop after ABS activation [4] (sometime known as emergency braking or safety braking).

For further informations on stopping distance calculation please refer to Sect. 5.1.

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Chapter 5 Data Processing

5.1 Stopping Distance Calculation

The stopping distance is the distance travelled from the point at which the driver first applies force to the actuation device (set onto the brake pedal) to the point at which the vehicle is at a standstill, during a braking performed at the grip limit with active ABS system. In order to evaluate the stopping distances two procedures were adopted, and will be described in Sect. 5.1.1 and 5.1.2. Both procedures share, however, the same test set-up and the same manoeuvre.

The evaluation of the stopping distance is carried out starting from 5

dif-ferent initial speeds, from 80 km h−1 to 120 km h−1, equally spaced.

Stopping distance shall be measured from the time brake pedal force rises through 60 N until the vehicle come to complete stop. Alternate brake pedal transducers such as pressure contact switches that typically activate in the range of 60 N brake pedal force may also be used [4]. For the purposes of this work, the last method described above will be used.

The complete stop is, instead, marked by a lower limit on the speed, limit that varies according to the procedure that is used to calculate the stopping distance.

In figure 5.1 the trend of longitudinal acceleration, vehicle speed and brake system pressure is shown. During braking, acceleration keeps quite constant and, consequently, vehicle speed decrease linearly. It is of some interest to note that acceleration and vehicle speed presents pitch oscillation around the complete stop, that’s the reason why in calculation of vehicle stopping distance

the complete stop is marked by a lower limit on the speed (Vf ≤ 2 km h−1

or Vf ≤ 0.1V0, depending on the method adopted in calculation). Looking

at brake pressure trend, it is notable that the mean value decreases during braking, and it is due to the higher pressure required in the first phase to overcome the inertia of the braking system fluid, to expand the pipeline and, more generally, it represents a transient behavior.

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CHAPTER 5. DATA PROCESSING 23 0 2 4 6 8 10 12 14 Time [s] -10 0 10 20 30 40 50 60 70 80

Acceleration & Speed

0 20 40 60 80 100 120 140 160 180 200 Brake pressure Long. acceleration [m/s2] Vehicle speed [ Brake pressure [bar]

km/h]

Figure 5.1: Typical acquisition during an ABS braking test.

V0 Vf

s

Figure 5.2: Trigger method for evaluating the stopping distance s.

5.1.1 Trigger Method

The stopping distance is evaluated as the space s travelled during braking from the start condition, marked by the trigger (pressure contact switch on brake

pedal), to the end condition, marked by Vf, as shown in Fig. 5.2, where V0 is

the initial vehicle speed at the trigger event, and Vf is the vehicle end-speed,

with Vf ≤ 2 km h−1.

Stopping distance is automatically obtained by the GPS software Vbox R

Racelogic which provides a report in txt format containing, as well as stopping

distance, also the trigger speed V0 and the Mean Fully Developed Deceleration

MFDD, which will be described in Sect. 5.1.2. An example of report is shown below.

Stopping distances obtained for different start condition V0 are plotted in

a diagram like that shown in Fig. 5.4.

In order to provide a result for a certain value of start condition speed

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CHAPTER 5. DATA PROCESSING 24

Trigger speed Dist(m) MFDD(m/s²) 119,60 77,26 7,33 108,79 63,13 7,66 98,73 51,55 7,55 88,60 39,91 8,09 80,20 38,96 6,12

Figure 5.3: Report of a test, automatically generated by the Vbox R _Racelogic

software. 70 80 90 100 110 120 130 Speed V₀[km/h] 30 40 50 60 70 80 90 100 Stopping distance [m] Data acquisition Parabola fit = 0.0055x2+-0.0077x Stopping distance = 53.81 @ 100km/h

Figure 5.4: Stopping distances for different start condition. In red, the poly-nomial curve used to fit the experimental datas.

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V

₀

V

_e

V

_b

s

b

s

e

Figure 5.5: MFDD method for evaluating the stopping distance s.

curve which form is

s = p1V02+ p2V0 (5.1)

In this way, we will have realistic values of stopping distances s even if the

initial speed V0 is slightly different from the standards.

5.1.2 Mean Fully Developed Deceleration Method

The Mean Fully Developed Deceleration (MFDD) represents the average decel-eration during the period in which deceldecel-eration is at its fully developed level.

According to current legislation ECE 13H, the mean fully developed

de-celeration dm shall be calculated as the deceleration averaged with respect to

distance over the interval Vb to Ve, according to the following formula

dm = V_b2− V2 e 25.92 (Se− Sb) (5.2) where:

• V0 is the initial vehicle speed, in km h−1;

• Vb is the vehicle speed at 0.8 V0, in km h−1;

• Ve is the vehicle speed at 0.1 V0, in km h−1;

• Sb is the distance travelled between V0 and Vb, in m;

• Se is the distance travelled between V0 and Ve, in m.

In the evaluation of the stopping distance during a safety braking (with ABS system enabled) the space travelled until vehicle standstill condition can

be obtained as, according to the hypothesis to have constant deceleration dm,

as

s = V

2 0

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CHAPTER 5. DATA PROCESSING 26 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Grip 30 40 50 60 70 80 90 100 110 120 Stoppin g distance MFDD [m] s_MFDD

Figure 5.6: MFDD stopping distance versus grip coefficient, for a starting

speed V0 = 100 km h−1.

and subsequently plotted in a diagram like the one shown in Fig. 5.4. Combining the above equation with Eq. (3.13), it is possible to obtain the stopping dis-tance as a function of the adhesion coefficient (in the calculation, it has been

assumed − ˙u = dm) s = 1 2V 2 0 l −µh_e e µga2 (5.4) which trend is shown in Fig. 5.6.

5.1.3 Integration Method

Both Trigger and MFDD methods decribed in Sect. 5.1.1 and 5.1.2 makes use of the GPS signal data acquisition and, hence, they need to carry on board additional instrumentation such as the Racelogic Vbox.

It is anyhow possible to evaluate the stopping distance by integrating the speed values taken by the rear phonic wheels. The space s travelled between

the trigger event t0 and the stanstill condition tf is

s = Z tf

t0

V (t)dt (5.5)

where, in order to evaluate the absolute speed V (t) of the vehicle, it has been used the signal coming from the rear (not braked) phonic wheels

V (t) = Rr

ω21+ ω22

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CHAPTER 5. DATA PROCESSING 27 Trigger Integration Method

According to the trigger method (Sect. 5.1.1) the goal is to evaluate the space

travelled from the trigger event (vehicle speed V0) to the standstill condition

(vehicle speed Vf ≤ 2 km h−1_).

Thanks to data acquisition by Vector GL1000, it has been possible to obtain information about vehicle speed and master cylinder pressure, which are the main signals of interest for data processing and subsequently evaluation of stopping distances: it has been set a master cylinder pressure of 2 bar as initial condition (trigger), and this value has been used in order to find the

starting speed V0. The end speed is, as well as in 5.1.1, Vf = 2 km h−1. It has

been used a for cycle applying the trapezoid method

s(k) = s(k−1)+ V(k)+ V(k−1)

2 (t(k)− t(k−1)) (5.7)

from k = 2 to k = length(V ), where V is the vehicle speed array and t is the

elapsed time. The stopping distance strigg is the last element of the array s

obtained as in Eq. (5.7).

MFDD Integration Method

According to the method of the mean fully developed deceleration explained

in Sect. 5.1.2, the goal is to evaluate the stopping distance smfdd as

smfdd=

V₀2

2dm

(5.8)

where dm is the mean fully developed deceleration

dm =

V2

b − Ve2

25.92 (Se− Sb)

(5.9)

In order to evaluate dm it is therefore necessary to calculate the distances Se

and Sb as Se = Z te t0 V (t)dt; Sb = Z tb t0 V (t)dt (5.10) where:

• t0 is the instant in which the speed of the vehicle V is equat to V0 (trigger

event);

• te is the instant in which the speed of the vehicle V is equat to Ve (Ve =

0.1V0);

• tb is the instant in which the speed of the vehicle V is equat to Vb (Vb =

0.8V0).

Applying the trapezoid method, it has been then possible to calculate Se and

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5.1.4 Results Comparison

In Fig. 5.7 the difference between the methods is shown. Although at a first sight the results are not matching, the percentage error that we commit using a method instead of another is quite negligible, as shown in Tab. 5.1.

It could be useful to use the integration method because with no need of GPS it is possible to analyse both stopping distances and the typical behavior of

the longitudinal force Fx as a function of the practical longitudinal slip κx.

75 80 85 90 95 100 105 110 115 120 Speed V₀[km/h] 30 35 40 45 50 55 60 65 70 Stopping distance [m] GPS Trigger Method Integral Trigger Method

(a) GPS vs Integral TRIGGER method.

75 80 85 90 95 100 105 110 115 120 Speed V₀[km/h] 25 30 35 40 45 50 55 60 65 Stopping distance [m] GPS MFDD Method Integral MFDD Method (b) GPS vs Integral MFDD method.

Figure 5.7: Comparison between the methods.

Method Stop. distance @ 100 km h−1 Percentage Error Difference

GPS Trigger Method 48.38 m

Integral Trigger Method 48.32 m 0.1% 0.06 m

GPS MFDD Method 45.78 m

Integral MFDD Method 46.69 m 2% 0.9 m

Table 5.1: Stopping distances evaluated at 100 km h−1 for each of the methods.

The robustness and reliability of the integration method has been verified for different test, and results confirm the goodness of the method.

It should be remembered that these values of stopping distances are quite high, but this is the result of braking with the only front tires, as reported in section 4.2.

5.1.5 Weighted Fit for Trigger Method

During the earliest moments of a braking there is a transient in which the longitudinal acceleration pass from zero (constant speed) to its mean fully developed value. This transient affect the stopping distances evaluated with

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CHAPTER 5. DATA PROCESSING 29 1 1.5 2 2.5 3 3.5 Time 0 50 100 150 200 250

Brake pressure [bar]

-12 -10 -8 -6 -4 -2 0 2 Longitudinal acceleration[m/s 2]

Longitudinal acceleration[m/s2_]

Shakedown

(a) Initial speed V0= 80 km h−1.

1 1.5 2 2.5 3 3.5 4 4.5 Time 0 50 100 150 200 250

-12 -10 -8 -6 -4 -2 0 2 Longitudinal acceleration[m/s 2]

Longitudinal acceleration[m/s2_]

Shakedown

(b) Initial speed V0= 120 km h−1.

Figure 5.8: Effect of initial transient for two different starting speed. For low value of starting speed the initial shakedown has a more relevant impact on stopping distance.

trigger method, and the effect is more relevant for low values of starting speed since the total braking time is lower.

In order to take into account this phenomena it has been improved the fit using the array of weights. In this way, the fitting curve is the one that minimize, with respect to the coefficients Xi, the function

F (X, k, r, w) = n X i=1 wi(y(X, ki) − ri)2 (5.11) where:

• w is the weight array;

• y is the chosen function (quadratic curve); • X is the array of the function coefficients;

• ki is the independent variable (vehicle speed);

• ri is the observation value (stopping distance);

• n is the number of observations.

It has been chosen to assign, with proportional relationship, more weight to the tests performed from higher starting speeds, in which the shakedown effect has a minor influence in terms of stopping distances. The result of the weighted fit is shown in Fig. 5.9.

Of course, these considerations are valid only in the case of stopping dis-tances evaluated with trigger method, in fact in the case of stopping distance evaluated with MFDD method the initial transient is not taken into account.

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CHAPTER 5. DATA PROCESSING 30 60 70 80 90 100 110 120 Speed V₀[km/h] 20 30 40 50 60 70 Stopping distance [m]

Stop. Distance Trigger Fit

Weighted Fit

Figure 5.9: Non weighted and weighted fit of stopping distances.

5.2 Multiple Linear Regression Model

The main difficulty encountered during the data analysis phase was to separate the effects of asphalt temperature and tire wear on vehicle stopping distance calculation. In fact, while it is quite easy to evaluate the effect of the solely tire wear, i.e. trying to conduct the test at the same asphalt temperature, it is not so simple to evaluate the effect of asphalt temperature keeping tire wear constant (the tire wears out during tests).

In this section the multiple linear regression model will be described, which is the model that was firstly developed in order to take into account the effect of both tire wear and asphalt temperature.

A data model explicitly describes a relationship between predictors (tire wear and asphalt temperature) and response variables (i.e. stopping dis-tance). Linear regression fits a data model that is linear in the model coeffi-cients. The most common type of linear regression is the least-squares fit, which can fit both lines and polynomials, among other linear models, and which will be used to achieve the goals. The best fit in the least-squares sense mini-mizes the sum of squared residuals (a residual being: the difference between an observed value, and the fitted value provided by a model).

The model will be thus able to predict the response on vehicle stopping dis-tance, maximum longitudinal acceleration and maximum adhesion coefficient for each value of asphalt temperature and tire wear.

Throughout this document, X1 will be referred to the number of ABS

brak-ing, X2 to the asphalt temperature and Y to the response (stopping distance,

maximum acceleration or maximum adhesion coefficient, as appropriate). Formally, the multiple linear regression mean function is

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where α is called intercept and the βj are called slopes or coefficients. Going

one step forward, we can describe how the response vary around their multiple linear regression function. Observed data will be therefore described by the following equation

Yi = α + β1Xi,1+ β2Xi,2+ i (5.13)

which is the same as Yi = E(Y |Xi) + i, where i is the residual. It will be

referred Xi,j to as the jth predictor variable (j = 1, 2 in our case) for the ith

observation (i = 1, ..., n ). Equation 5.13 can be rearranged using algebraic notation, in the form

Y = βX + (5.14)

where:

• Y = (Y1, Y2, ..., Yn) is the response vector ;

• = (1, 2, ..., n) is the residual vector ;

• β = (α, β1, β2) is the slope vector ;

• X is the design matrix given by

X =       1 X1,1 X1,2 1 X2,1 X2,2 ... ... 1 Xn,1 Xn,2       (5.15)

A more efficient model which describes the trend of the observed data has been obtained taking into account also the interaction between the predictors with

an additive term in the form γ12X1X2.

Eq. (5.12) can be thus modified in this way

E(Y |X) = α + β1X1+ β2X2+ γ12X1X2 (5.16)

and the slope of X1 thereby depends on X2 and vice versa. It is possible to

rearrange Eq. (5.16) in terms of intercept and slope, as in the following equation

E(Y |X) = (α + β2X2) + (β1+ γ12X2)X1 (5.17)

This highlights the fact that the intercept (first bracket term) and slope

(second bracketed term) for the regression of Y on X1 now vary as a function

of X2 [3].

It has been therefore developed a Matlab software in order to allow data analysis in a systematic way, and which will be described in Chapt. 7.

In Fig. 5.10 a comparison between the two models is shown. It is evident that although the simple multiple regression linear model fits data quite well, the model with interaction between predictors is more efficient in terms of fit goodness.

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CHAPTER 5. DATA PROCESSING 32 42 44 46 50 48 0 50 52 Stop distance R2= 0.90 54 56 40 10 30 Temperature Number stop 20 ₃₀ ₁₀ 20 0 40 Observed data

(a) Model without predictor interaction.

R2= 0.93 42 44 46 0 48 50 50 52 54 Stop distance 56 40 10 20 30

Number stop 30 400 10 20Temperature Observed data

(b) Model with predictor interaction.

Figure 5.10: Comparison between linear regression models.

5.3 Multiple Polynomial Regression Model

The plot of the response versus predictors may suggest a non linear relation-ship. Polynomial regression is a form of regression analysis in which the de-pendent response Y is modelled as a nth degree relation in the X indede-pendent variable.

In order to find the best fit for the observed data, the previous model has been subsequently modified using a quadratic polynomial surface, which formally is the described by

E(Y |X) = α + β1X1 + β2X2+ γ1X12+ γ2X22+ δX1X2 (5.18)

where:

• X1 and X2 are the predictors, respectively number of ABS braking and

asphalt temperature;

• Y is the response (stopping distance, maximum acceleration or maximum adhesion coefficient, as appropriate);

• β1 and β2 are the so called linear effect parameters;

• γ1 and γ2 are the so called quadratic effect parameters.

The equation described in Eq. (5.18) suggests that, keeping X1 constant,

Y is described by a parabolic curve in the variable X2, and vice versa.

Observed data Yi will be therefore described by the model

Yi = α + β1Xi,1+ β2Xi,2+ γ1X_i,12 + γ2X_i,22 + δXi,1Xi,2+ i (5.19)

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Yi = E(Y |Xi) + i (5.20)

The above equation suggests that observed data Yi will deviate from the

model for the quantities i, which are the residuals of the model. The smaller

are the residuals, the better is the fit.

The model described in this section is the one that will be used for data analysis in the present document.

The Matlab command that has been used for this purpose is the fit com-mand, which allows to fit both curves and surfaces, and whose syntax is the following

[f itresult, gof ] = f it([X1, X2], Y, f itT ype) (5.21)

where:

• fitresult returns the value of the polynomial equation coefficients de-scribed in Eq. (5.18) and, hence, is the most important output of the model;

• gof returns an array containing information on the goodness-of-fit statis-tics;

• X1 is the number of performed ABS braking, X2 is the asphalt

temper-ature and Y is the response;

• fitType creates a fit type for the model. For a quadratic polynomial surface it is ’poly22’.

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Chapter 6 Data Analysis

In this chapter the results obtained by data processing will be analysed. In particular four test session will be taken in consideration, comparing different type of tire and range of asphalt temperature, as follows:

• first test session, held from July 11, 2017 until July 19, 2017, in which all

season TIRE 1 was tested, in a range of asphalt temperature from 30◦C

to 58◦C;

• second test session, held from July 24, 2017 to July 28, 2017, in which all season TIRE 2 was tested, in a range of asphalt temperature from

29◦C to 58◦C;

• third test session, held from September 15, 2017 until March 21, 2018, in which all season TIRE 3 was tested, in a range of asphalt temperature

from 2◦C to 25◦C;

• fourth test session, held from March 27, 2018 until May 26, 2018, in which summer TIRE 4 was tested, in a range of asphalt temperature

from 9◦C to 50◦C.

6.1 Statistics Fundamentals

In this section the meaning of some coefficients that are largely used in statistics for interpreting and drawing conclusions from collected data will be called up. In particular, there will be made use of the following statistics:

• Mean Y is the sum of observed values in a data divided by the number−

of observations − Y = Pn i=1Yi n (6.1)

• SSR is the regression sum of squares and quantifies how far the estimated regression surface E(Y |X) is from the horizontal surface given by the

sample meanY− SSR = n X i=1 (E(Y |Xi)− − Y )2 (6.2) 34

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CHAPTER 6. DATA ANALYSIS 35 • SST is the total sum of squares and quantifies how much the observed

data Yi vary around their mean value

− Y SST = n X i=1 (Yi−Y )− 2 (6.3)

• R2 _{is the coefficient of determination and is given by the ratio between}

SSR and SST. It ranges from 0 to 1, and it is a statistic value that gives information about the goodness of the fit. For example, an R-square value of 0.85 means that the fit explains 85% of the total variation in the data about the average. The larger the R-squared is, the more variability is explained by the regression model.

R2 = SSR SST R 2 adj = 1 − n − 1 n − p SSE SST (6.4)

SSE is the sum of squared error, SSR is the sum of squared regression, SST is the sum of squared total, n is the number of observations, and p is the number of regression coefficients. Note that p includes the intercept, so for example, p is 2 for a linear fit. Because R-squared increases with added predictor variables in the regression model, the adjusted R-squared adjusts for the number of predictor variables in the model. This makes it more useful for comparing models with a different number of predictors.

• σr is the error standard deviation, also known as RM SE, root mean

squared error, and it is a useful parameter in order to evaluate the prob-ability density function of the distribution

σr =

s Pn

i=1i

n − p (6.5)

where is the array of residuals, n is the number of observations and p is the number of predictors (p = 2).

• DF E, error degree of freedom, is defined as the number of response values n minus the number of fitted coefficients p estimated from the response values

DF E = n − p (6.6)

DF E indicates the number of independent information involving the n data points that are required to calculate the sum of squares.

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CHAPTER 6. DATA ANALYSIS 36

6.2 First Test Session Analysis

In the first test session the vehicle was equipped with TIRE 1 all season tire, and nine tests were performed, alternating between morning and afternoon in order to have different asphalt temperature.

Date, Year 2017 N◦ of ABS stops Asphalt Temp. [◦C]

July 13 10 58 July 14 15 35 July 14 20 55 July 17 25 30 July 17 30 54 July 18 35 34 July 18 40 58 July 19 45 32 July 19 50 58

Table 6.1: Main data for the analysis of the first test session.

On each test both progressive braking and ABS braking were performed, respectively in number of three and five, in order to have both tire behav-ior data (typically acceleration and adhesion coefficient trends) and stopping distances values.

The session began with new TIRES A equipped on the vehicle and, at the end of the session, 9 × 5 = 45 ABS braking were performed.

The next step has been evaluating the trend of the observed data and the goodness of the developed fit.

6.2.1 Stopping Distance

In figures 6.1 and 6.2 stopping distance calculated at 100 km h−1 (evaluated

with the two methods of trigger and MFDD) and respective fits are shown. For both the methods applied, stopping distance value decreases with respect to the number of safety braking performed and it has a tendency to saturate for great number of braking, according to what expected. To notice that there is a gap of about 10 m in stopping distance between the best and the worst condition.

With respect to asphalt temperature, stopping distance increases in an almost linear way with the temperature for both method applied, and the trend is almost the same for all the levels of tire wear.

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CHAPTER 6. DATA ANALYSIS 37 50 52 54 10 56 58 60 Stop distance MF DD [m] 62 55 20 ₃₀ ₄₅ 50 Temperature Number stop 40 5030 35 40 Observed data, R2= 97% [°C]

(a) Global view.

10 15 20 25 30 35 40 45 50 Number stop 50 52 54 56 58 60 62 Stop distance MF DD[m ] Observed data, R2= 97% T=58°C T=30°C (b) Wear dependence. 30 35 40 45 50 55 Temperature [°C] 50 52 54 56 58 60 62 Stop distance MF DD [m] Observed data, R2= 97% N=10 N=50 (c) Temperature dependence.

Figure 6.1: Trend of stopping distance evaluated with MFDD method respect to tire wear and asphalt temperature, for the first test session.

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CHAPTER 6. DATA ANALYSIS 38 52 54 56 10 58 60 62 Stop distance t rigger [m] 64 55 20 ₃₀ ₄₅ 50 Temperature Number stop 40 5030 35 40 Observed data, R2= 98% [°C] (a) Global view.

10 15 20 25 30 35 40 45 50 Number stop 52 54 56 58 60 62 64 Stop distance t rigger [m] Observed data, R2= 98% T=58°C T=30°C (b) Wear dependence. 30 35 40 45 50 55 Temperature [°C] 52 54 56 58 60 62 64 Stop distance t rigger [m] Observed data, R2= 98% N=10 N=50 (c) Temperature dependence.

Figure 6.2: Trend of stopping distance evaluated with trigger method respect to tire wear and asphalt temperature, for the first test session.

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CHAPTER 6. DATA ANALYSIS 39 -0.6 -0.4 -0.2 10 0 0.2 0.4 0.6 Stop distance MFDD [m ] 0.8 20 ₃₀ 50 Temperature Number stop 40 5030 40 Residuals analysis 1 2 3 4 5 6 7 8 9 61.41 61.18 0.23 57.36 57.22 0.14 57.32 57.60 -0.28 53.46 53.93 -0.47 54.39 55.10 -0.70 53.03 52.09 0.94 54.89 54.14 0.75 50.31 50.66 -0.35 53.22 53.49 -0.26 Model output[m]

Observed data[m] Residuals[m]

[°C]

Figure 6.3: Residuals in the stopping distance model (with respect to MFDD stopping distances). Regression Statistics − Y 55.04 SSE 2.5 Rsquared 0.97 DF E 3 Rsquaredadj 0.92 RM SE 0.91 Observations 9

Table 6.2: Regression statistics for the first test session (with respect to MFDD stopping distances).

In Fig. 6.3 the residuals of the model are shown. The percentage error around the mean value is less than 2%, that is a fairly positive result.

6.2.2 Grip Coefficient

The grip coefficient is a fairly significant parameter for ABS tuning, and it is the reason why it is important to understand how asphalt temperature and tire

wear affect this parameter. The maximum grip coefficient µmax is the result

of the analysis on data obtained during progressive braking (see Sect. 4.5).

In Fig. 6.5 the values of µmax, obtained through Pacejka fit of the observed

data, for different conditions of tire wear and asphalt temperature are plotted. As well as stopping distance, the better condition is represented by low values in asphalt temperature and high number of ABS braking performed.

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CHAPTER 6. DATA ANALYSIS 40 grows quite significantly during the first ABS braking executed and it tend to saturate at the end-of-life of the tire.

With respect to the asphalt temperature, the µmax decreases in an almost

lin-ear way, and it means that the quadratic effect parameter γ2 of the model

described in 5.18 has an almost negligible contribution in the model.

In Fig. 6.6 the trend of the grip coefficient evaluated for an acceleration equal to the MFDD value is shown. In other words, it represents the local grip

coefficient value during an ABS braking, considering a deceleration ˙u =MFDD

(see also 3.12). The result of the fit is almost the same as the previous one, and, hence, the same considerations apply. The maximum percentage error around the mean value is about 1%, and it is an auspicious result.

-10 -5 10 0 5 10-3 MFDD 20 ₃₀ 50 Temperature Number stop 40 5030 40 Residuals analysis 1 2 3 4 5 6 7 8 9

Observed data Model output Residuals

0.83 0.84 -2.6660e-03 0.88 0.88 -1.5822e-03 0.88 0.88 2.8425e-03 0.93 0.93 5.5590e-03 0.92 0.91 8.8321e-03 0.94 0.95 -1.1518e-02 0.92 0.92 -8.7890e-03 0.98 0.97 4.3586e-03 0.94 0.93 2.9634e-03 [°C]

Figure 6.4: Residuals in the grip coefficient (with respect to µM F DD).

Regression Statistics − Y 0.91 SSE 3.64e-04 Rsquared 0.97 DF E 3 Rsquaredadj 0.93 RM SE 0.011 Observations 9

Table 6.3: Regression statistics for the first test session (with respect to µM F DD).

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CHAPTER 6. DATA ANALYSIS 41 0.95 1 10 1.05 1.1 max 1.15 55 20 ₃₀ ₄₅ 50 Temperature Number stop 40 5030 35 40 Observed data, R2= 99% [°C] (a) Global view.

10 15 20 25 30 35 40 45 50 Number stop 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 max Observed data, R2= 99% T=30 °C T=58° C (b) Wear dependence. 30 35 40 45 50 55 Temperature [°C] 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 max Observed data, R2= 99% N=10 N=50 (c) Temperature dependence.

Figure 6.5: Trend of maximum grip coefficient value, respect to tire wear and asphalt temperature, for the first test session.

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CHAPTER 6. DATA ANALYSIS 42 0.82 0.84 0.86 0.88 10 0.9 0.92 0.94 0.96 0.98 MFDD 1 55 20 ₃₀ ₄₅ 50 Temperature Number stop 40 5030 35 40 Observed data, R2= 97% [°C] (a) Global view.

10 15 20 25 30 35 40 45 50 Number stop 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 MFDD Observed data, R2= 97% (b) Wear dependence. 30 35 40 45 50 55 Temperature [°C] 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 MFDD Observed data, R2= 97% (c) Temperature dependence.

Figure 6.6: Trend of grip coefficient value obtained for an acceleration equal to MFDD, respect to tire wear and asphalt temperature, for the first test session.

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CHAPTER 6. DATA ANALYSIS 43

6.3 Second Test Session Analysis

The second test session was held from July 24, 2017 to July 28, 2017 and during the session ten test were performed. The procedure adopted is the same as the first session, with the difference that the vehicle was equipped with BRAND A (TIRE 2) all season tires.

In each test, five ABS braking were performed, so that at the end of the test session 5 × 10 = 50 emergency braking have been carried out. The test were executed alternating between morning and afternoon, so that the range of temperature was as wide as possible.

Date, Year 2017 N◦ of ABS stops Asphalt Temp. [◦C]

July 24 5 32 July 24 10 56 July 25 15 32 July 25 20 58 July 26 25 32 July 26 30 55 July 27 35 29 July 27 40 48 July 28 45 31 July 28 50 55

Table 6.4: Main data for the analysis of the second test session.

6.3.1 Stopping Distance

As well as for the first test session data fit, stopping distances seems to be well approximated with a polynomial (quadratic) regression model, and the same considerations apply: stopping distance grows with respect to the asphalt temperature and for new tires.

The best condition is represented by low asphalt temperature and high number of safety braking performed, confirming the results of the first test session analysis. Since there is no difference in the output of the model obtained for stopping distances evaluated with the two trigger/MFDD methods (there is only a constant term of difference between the two surfaces), in this section only the result of the analysis on trigger stopping distances will be reported.

According to Fig. 6.7, the model well fit observed data and the goodness of fit is confirmed by the coefficient of determination R-squared. The main difference with the previous test session is that the trend of stopping distance with respect to wear (6.7a) is more linear, which is due to a negligible effect

of the quadratic effect coefficient γ1 in the response of the model.

With regard to the asphalt temperature, the trend is very similar to the one of the first test session: stopping distances grows in an almost linear way with respect to the asphalt temperature.

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CHAPTER 6. DATA ANALYSIS 44 50 52 54 56 58 60 62 64 Stop distance t rigger [m] 66 55 10 ₂₀ ₄₅ ₅₀

Number stop Temperature [°C]

30 ₄₀ ₃₀ ₃₅ 40

50

Observed data, R2= 91%

(a) Global view.

5 10 15 20 25 30 35 40 45 50 Number stop 50 52 54 56 58 60 62 64 66 Stop distance t rigger [m] Observed data, R2_{= 91%} (b) Wear dependence. 30 35 40 45 50 55 Temperature [°C] 50 52 54 56 58 60 62 64 66 Stop distance t rigger [m] Observed data, R2_{= 91%} (c) Temperature dependence.

Figure 6.7: Trend of stopping distance evaluated with trigger method respect to tire wear and asphalt temperature, for the second test session.

Influence of tire wear and asphalt temperature on vehicle stopping distance

Universit`

a di Pisa

Influence of tire wear and asphalt temperature on

vehicle stopping distance

Abstract

Ringraziamenti

Contents

Chapter 1

Introduction

1.1

Project Objectives

1.2

Planning

1.3

Balocco Proving Ground

Chapter 2

The Tire

2.1

Description

2.2

Tire Slip

2.2.1

Rolling Radius

F

F

V

2.2.2

Pure Longitudinal Slip

2.2.3

Grip Longitudinal Forces

2.3

Tire Wear

2.4

ABS System

2.4.1

System Overview

2.4.2

Principle of Hydraulic Modulator

Chapter 3

Braking Performance

3.1

Hypothesis

3.2

Equilibrium Equations

3.2.1

Vehicle Equilibrium

3.2.2

Wheel Equilibrium

3.3

Vehicle Mathematical Model

3.4

Maximum Deceleration

Chapter 4

Data Acquisition

4.1

Vehicle

4.2

Signals of Interest

4.3

Instrumentation

4.4

Test Procedure

4.5

Progressive Braking

4.6

ABS Braking

Chapter 5

Data Processing

5.1

Stopping Distance Calculation

5.1.1

Trigger Method

V

V

V

s

s

5.1.2

Mean Fully Developed Deceleration Method