Vehicle model for tyre-ground contact force evaluation

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KTH Teknikringen 8 +46 8 790 6000 +46 8 790 6500 www.kth.se

Vehicle Dynamics Stockholm

SE-100 44 Stockholm, Sweden

Vehicle model for tyre-ground

contact force evaluation

Lejia Jiao

Master Thesis in Vehicle Engineering

Department of Aeronautical and Vehicle Engineering

KTH Royal Institute of Technology

TRITA-AVE 2013:40

ISSN 1651-7660

i

Acknowledgment

I owe gratitude to many people for supporting me during my thesis work. Especially, I would

like to express my deepest appreciation to my supervisor, Associate professor Jenny Jerrelind,

for her enthusiasm and infinite passion for this project. Without her patient guidance and

persistent help, this thesis would not have been possible.

I am particularly indebted to my parents for inspiring me to this work.

I would like to thank Associate professor Lars Drugge, who introduced me to vehicle-road

interaction and gave me enlightening instruction.

In addition, I would like to give my sincere thanks to Nicole Kringos and Parisa Khavassefat,

for helping me to understand the pavement and sharing model and data with me; to Ines

Lopez Arteaga, for giving me feedbacks from tyre expert’s point of view. The great

interdisciplinary cooperation and teamwork helped me to have a good understanding of the

whole vehicle-tyre-pavement system, and get rational tyre and pavement parts included in my

models.

Last but not least, I would like to thank all my friends, for their understanding,

encouragement and support.

Stockholm June 26, 2013

Lejia Jiao

iii

Abstract

Economic development and growing integration process of world trade increases the

demand for road transport. In 2008, the freight transportation by road in Sweden reached 42

million tonne-kilometers. Sweden has a tradition of long and heavy trucks combinations.

Lots of larger vehicles, with a maximum length of 25.25 meters and weight of 60 tonnes, are

used in national traffic. Heavier road transport and widely use of large vehicles contribute to

the damages of pavement. According to a recent research by the VTI, total cost of road wear

by freight transport in Sweden in 2005 was about 676 million SEK. If the weights of all

vehicles were limited to 40 tonnes, according to the new EU rules, the cost of wear in 2005

would have been 140 million SEK less.

Lots of studies about road damage caused by vehicle have been done since the last decades.

It has been found that the dynamic tyre force plays an important role in the damages of

pavement. However, the influence of vehicle-pavement interaction on pavement damage has

not been investigated to any large extent yet. The aim of this study is to provide suitable

computational truck models, study the influence of vehicle-pavement interaction and

parameters of vehicle on pavement damage.

To fulfil the aims, this study presents vehicle models, including quarter, half, full vehicle

models and quarter vehicle model coupled with pavement, used to compute the dynamic tyre

force. The different models are then compared. Two actual road profiles measured by laser, a

smooth one and an uneven one, are used for evaluation. The models are analysed to find out

the vehicle parameters that influence the road damage most and to learn about how detailed

models are needed.

It’s found that difference does exist between more detailed models and less detailed ones,

and it’s non-negligible. It will increase with the increase of road unevenness. The dynamic

tyre force will not be affected much by coupling the pavement, unless the road surface is very

uneven or wheel hop exists. On uneven roads, energy mainly dissipates in vehicle suspension.

However, on even roads, vibration can be well damped in tyre before it reaches suspension,

so most of energy dissipates in tyre. Different components influence the tyre force differently.

The influence varies with different frequency range of input signal (road profile) as well. The

effects of sprung parts are mainly in low frequency range, while the effects of unsprung parts

are mainly in high frequency range. Parameters of vehicle body influence the dynamic tyre

force most. The effect of cabin is much smaller compared to vehicle body and unsprung part.

Changes in parameters of pavement will not influence the road load, but its resonant

frequency. Therefore, the best way to reduce dynamic tyre load is to design a more

lightweight vehicle body, softer and better damped suspension.

v

Contents 1 Introduction ............................................................................................................. 1

1.1 Background ............................................................................................................................. 1

1.2 Problem description ............................................................................................................... 1

1.3 Aim ........................................................................................................................................... 3

2 Methodology ........................................................................................................... 4

3 Vehicle models ........................................................................................................ 5

3.1 Introduction ............................................................................................................................ 5

3.2 Model establishment .............................................................................................................. 6

3.2.1 Quarter vehicle model .................................................................................................... 6

3.2.2 Quarter vehicle model coupled with pavement ......................................................... 8

3.2.3 Half vehicle model ........................................................................................................ 10

3.2.4 Full vehicle model ......................................................................................................... 13

4 Model comparison .................................................................................................. 16

4.1 Parameters used in simulation ............................................................................................ 16

4.1.1 Vehicle parameters ........................................................................................................ 16

4.1.2 Pavement parameters ................................................................................................... 17

4.2 Quarter, half and full vehicle .............................................................................................. 18

4.3 Influence of coupled pavement ......................................................................................... 24

4.4 Energy dissipation ................................................................................................................ 27

5 Parametric study .................................................................................................... 29

5.1 Typical response and frequency distribution ................................................................... 29

5.2 Effect of mass ....................................................................................................................... 32

5.3 Effect of stiffness ................................................................................................................. 35

5.4 Effect of damping ................................................................................................................ 38

6 Conclusions ............................................................................................................ 41

7 Future work ............................................................................................................ 44

8 References .............................................................................................................. 45

1

1 Introduction This chapter gives a brief review of history and background, a short introduction to the subject and the

goals of this study.

1.1 Background With the growing and deepening of the integration process of world trade, the demand for

freight transport, especially by road, continues to increase. According to the Swedish Road

Administration, the freight transport by road is continuously increasing, and arrived around

45 billion tonne-kilometres in 2008, which has exceeded train and marine transport [1].

Sweden has a tradition of long and heavy trucks combinations. Lots of larger vehicles, with a

maximum length of 25.25 metres and weight of 60 tonnes, are used in national traffic [2].

Heavier road transport and widely use of larger vehicles will contribute to the damages of

pavement, such a fatigue cracking, permanent deformation etc. The maintenances of road

call for huge amount of investment. According to research performed by the Swedish

national Road and Transport Research Institute (VTI), in Sweden, total cost of road wear by

freight transport in 2005 was about 676 million SEK. If all the freight transportation carried

out with vehicles weighing more than 40 tonnes is redistributed to vehicles that weigh a

maximum of 40 tonnes, according to the new EU rules, the cost of wear in 2005 would have

been 140 million SEK less [2].

However, limiting the maximum weight of vehicles isn’t the only and best measurement to

reduce the pavement wear and thereby reduce the associated cost. If the mechanisms, which

lead to the road surface damage, and the factors that affect them, could be figured out, it

would be possible for vehicle industry, especially heavy vehicle manufacturers, to find out a

way to optimize and improve their trucks in order to minimize the damage. It would also be

good news for the road administration and the construction sector, since they can enhance

roads with explicit target to minimize the damage from vehicle factors.

1.2 Problem description To accurately describe how the vehicle dynamics will interact with and influence the

pavement, a large amount of work has been carried out from both vehicle dynamic and

pavement point of views. Sun and Deng’s work [3] proved that pavement loads are moving

stochastic loads whose power spectral density (PSD) is in proportion to the PSD of

pavement roughness. Then Sun and Greenberg [4], [5] presented the theory to solve the

dynamic response of pavement structure under moving stochastic loads.

A large amount of work has been performed by researchers in order to reveal how the

vehicle parameters affect the pavement load, and then affect the pavement performance [6–

2

12]. The importance of dynamic loads’ frequency and velocity was identified. Markov et al [8]

found that the characteristics most important for dynamic loading include vehicle suspension

type and characteristics, speed, height of pavement faults and joint spacing. Other factors

(such as tyre pressure) contribute to a smaller extent. It was also found that under certain

conditions dynamic loads are 40 % higher than static loads. Hudson et al [9] studied the

impact of truck characteristics on pavements with truck load equivalency factors, and it was

found that the frequency and speed of dynamic loads affects the pavement performance.

Hardy and Cebon [10] studied the validated dynamic road response model and found out

that the base strain and soil strain of flexible pavement are sensitive to vehicle speed, but not

sensitive to the frequency of applied dynamic loads except for some resonance points. Collop

and Cebon [13] used a simple road damage analysis based on the ‘fourth power law’. The

result showed that road-friendly suspension (which is air-suspended in this study) does not

have significant e ect on thick pavement damage. However, it does reduce thin pavement

damage. Cebon [14] studied the dynamic axle effects on road damage with a

six-degrees-of-freedom, two dimensional vehicle model, which is similar to a walking beam

model. Four road-damage-related wheel load criteria were developed, namely aggregate force

criterion, fatigue weighted stress criterion, tensile strain fatigue criterion and permanent

deformation criterion. He also proved that the dynamic component of wheel forces may

reduce significantly the service lives of road surfaces which are prone to fatigue failure. Sun

and Kennedy [12] investigated the effects of vehicle parameters, speed, and surface

roughness on the PSD of stochastic pavement loads with quarter-vehicle model. They found

that all these factors will influence the PSD loads. Their influence on the PSD loads were

then given out based on frequencies. It was also found that passenger vehicles produce more

high-frequency PSD loads than heavy vehicles do, and the frequency distribution of

stochastic loads are quite different for these two kinds of vehicles. Sun [15] analysed the

relation between suspension properties and tyre loads based on a walking beam suspension

model. He used the probability that the peak value of the tyre load exceeds a certain given

value to evaluate the road damage, which was based on the fourth power law. It was found

that tyres with high air pressure and suspension systems with small damping will lead to large

tyre loads and thus greater pavement damage. Elseifi et al [16] and Khavassefat et al [17]

established finite element (FE) pavement model to analysis its behaviour under moving

stochastic loads.

Although the vehicle-pavement interaction has been studied for several decades, the principle

of interaction between vehicle and pavement and its influence on road wear haven’t been

fully revealed yet. The study is still in a primary stage. It is noticed that, most of the studies

use an existing moving load profile, or a stochastic one. A few recent studies used dynamic

tyre loads from vehicle models, in which walking beam model or quarter vehicle model were

used. Quarter vehicle model is a simple yet powerful model for most of vehicle dynamic

3

analysis, which concentrate their attention only on the most important characteristics of

dynamic tyre forces. It provides details about vehicle suspension, but ignores the influence of

yaw and pitch motion. Walking beam model represents the minority of suspensions which

generate large dynamic tyre forces due to unsprung mass pitching motion as well as low

frequency sprung mass motion. However none of them contain the detailed suspension

nonlinearities and complexities of sprung mass motion that are typical of heavy vehicles [18].

To the best knowledge of author, the study of the vehicle related road damage using a more

complex model than the quarter vehicle model has not been found in the literature. None

includes a coupled vehicle-pavement model to study their interaction as well.

1.3 Aim The aim of this study is to solve the two problems mentioned in previous section: excluding

the influence of yaw and pitch motion and ignoring the interaction between vehicle, tyre and

pavement. It will provide more detailed vehicle models for moving load, which includes pitch

and roll motion, and a vehicle model coupled with pavement mass to include the movement

and force feedback from the pavement. It aims at building a more detailed yet simple model

and more suitable model for further research regarding vehicle, tyre and pavement as a whole

system.

There are three main aims in this study:

1. Build computational truck models, including quarter vehicle, half vehicle and full vehicle

models, as a part of vehicle-tyre-pavement system to estimate road damage;

2. Build a vehicle model coupled with pavement to evaluate the characteristics of

vehicle-tyre-pavement motion as a whole system;

3. Preliminary parameter analysis with the built models to find effects of different

parameters and possible ways to reduce road damage caused by heavy vehicles and the

huge associated cost.

4

2 Methodology This chapter explains the methods used in this study to reach the aims.

The work is divided into two major parts:

Building and validating the computational model of vehicle is one of the major parts of this

study. In the first part, vehicle models suitable for vertical vehicle dynamics are studied.

Differential equations for the systems are formulated. Computational models based on the

equations of motion are constructed in Simulink. They are then compared to each other to

evaluate advantages and disadvantages. In the second part, a parametric study is done with

the selected model. Main parameters of the vehicle and the pavement, including mass,

stiffness and damping, are variated to reveal the influence. Then regular patterns are summed

up according to the results.

5

3 Vehicle models This chapter introduces the suitable vehicle models and their differential equations.

3.1 Introduction Dealing with vehicle dynamic problems, there are several models to choose from: from the

simplest quarter vehicle model to the more complicated three-dimensional vehicle model.

Each of them has its own scope of application and degree of precision.

In order to choose the suitable models, properties of concern should be reviewed from view

of pavement engineering first. There are several types of pavements, including flexible,

composite and rigid, used in modern road. Depending on type of pavement, different

materials are used. No matter what type the pavement is, the most important types of road

damage due to heavy vehicles are fatigue cracking and permanent deformation (or rutting)

[19]. Examples are shown in Figures 1-2.

Figure 1 – Fatigue cracking [20]

Figure 2 - Permanent deformation-rutting [20]

6

Both kinds of failure mechanism are affected by several factors, such as construction method,

material properties, environment and traffic load. In this study, only the vehicle load factor is

investigated. Road vehicles interact with the pavement via the tyres that are in direct contact

with the pavement. Tyre force, especially vertical force, and its distribution affect road wear

to a large extent. While fatigue cracking is related to non-uniform contact traction

distribution [21], rutting has a closer link with the vertical forces. Densification (compaction)

and shear plastic deformation induced by vertical tyre force are two major mechanisms

within the pavement materials contributing to permanent deformation [22]. So the vehicle

model used to study pavement failure problems should at least reflect its vertical dynamics.

Other properties, like horizontal motion and vehicle or wheel slip, are not that important.

The quarter vehicle model is the simplest one among models suitable for studying vertical

dynamics of vehicle. It provides vertical dynamics only. The half vehicle model adds pitch

characteristics compared to the quarter vehicle model, and the full vehicle (or four wheels)

model adds the roll motion compared to the half vehicle model. The calculation amount will

increase with the complexity of model. Even the full vehicle model is still a kind of very

simplified model of a vehicle. With the help of a MBS-program like ADAMS, one can model

the vehicle in more detail. However, as the complexity increases, so do the computation time

and the complexity to analyse the results. In this study, the focus is on the three more simple

models: the quarter vehicle, the half vehicle and the full vehicle, since those models are

believed to provide sufficient results.

3.2 Model establishment In this section, the three vehicle models: the quarter vehicle, the half vehicle and the full

vehicle models are presented. First, the equations of motion are derived under the

assumption that springs and dampers are linear. Then the differential equations are

implemented in Simulink models in order to simulate the models dynamic behaviour.

Dampers and springs in the Simulink model can easily be replaced by nonlinear components

to reveal vehicle’s nonlinear properties.

3.2.1 Quarter vehicle model

The quarter vehicle model is often used in simple vehicle dynamics calculation when one is

only interested in the vertical motion of the vehicle. It is the simplest vehicle model used to

study vertical motion.

Figure 3 shows the quarter vehicle model, in which dynamics are simplified to vertical

motion of sprung mass and unsprung mass. Sprung mass is the mass of the vehicle part

which is supported above the vehicle suspension. In complex vehicles, like heavy truck in

this study, it can be subdivided into cabin mass and vehicle body mass. Unsprung mass is a

mass representing a part of the suspension, the wheels, the wheel axle and other components

7

connected to them. Sprung mass is coupled to unsprung mass via a spring and a damper,

which represent the vehicle suspension. Likewise unsprung mass is coupled to the pavement

via a spring and a damper, representing the tyre. [23] gives the typical quarter vehicle model,

with and without damper, and methods to decouple and analyse. The quarter vehicle model

can often provide acceptable predictions of vertical motion.

Figure 3 – 2-DOF Quarter vehicle model [12]

In this study, the object is to model a heavy truck, which is a little different. Considering

comfort of driver, the cabin of modern truck usually isn’t rigidly connected to chassis, but via

cabin suspension. The mass of the cabin generally is close to the unsprung mass. The motion

of cabin will influence the whole vertical dynamics of vehicle to some extent, and should be

taken into consideration. It can easily be solved by connecting a mass-spring-damper system

serially to the sprung mass (which represents the vehicle body mass now in the new truck

model), as shown in Figure 4. Figure 5 shows the Simulink model of the 3-DOF quarter

vehicle.

Figure 4 – 3-DOF quarter vehicle model representing a truck

8

The motion of the quarter vehicle model of a truck that includes the cabin dynamics can be

described by the following equations of motion:

� � ��

� � � � � � � � �

� � ��

Where is mass, is spring stiffness, c is damping coefficient, is vertical displacement

(positive direction is upward and measured from loaded position), is road unevenness as

input, F is external force acting on each mass. Subscript c indicates cabin, subscript t indicates

tyre/unsprung part, subscript s or no subscript indicates sprung part.

Figure 5 – Simulink model of the 3-DOF quarter vehicle model representing a truck

3.2.2 Quarter vehicle model coupled with pavement

By including a coupled pavement part, the influence of movement and force from pavement

vibration (although small) can be included, and pavement movement can be roughly

estimated. The integration will give a better understanding of pavement-vehicle interaction

and evaluate the strategy of separating vehicle and pavement model. The pavement could be

represented by a spring and mass combination as a basic assumption, as in Figure 6.

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9

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10

Figure 7 - Simulink model of the 4-DOF quarter vehicle model representing a truck, coupled with simplified pavement

3.2.3 Half vehicle model

A quarter vehicle model can provide vertical motion behaviour for a vehicle. However, it

doesn’t take lateral and longitudinal dynamics as well as pitch and roll motion into account,

as well as pitch, which may also be important. Figure 8 a) shows the 4-DOF half vehicle

model without cabin dynamics. Figure 8 b) shows the 5-DOF half vehicle model with cabin

dynamics. The structure of the front part and rear part of the half vehicles models are similar

to the quarter vehicle model. Pitch motion is included in both models. Figures 9-10 show the

Simulink models of the 4-DOF half vehicle model and 5-DOF half vehicle model

respectively.

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11

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12

For both models, the pitch angles are assumed to be small, thereby small angle

approximations have been used in the equations of motion.

By assuming that the front and rear axle will be exposed to the same road profile but with a

time delay, the road profile for the rear axle, �, can be expressed as a function of �, the

road profile of the front axle, as follows:

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Where is wheel base and is vehicle speed, which is assumed as a constant.

Figure 9 – Simulink model of half vehicle model without cabin dynamics (4-DOF)

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13

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3.2.4 Full vehicle model

The half vehicle model can be easily extended to a full vehicle model shown in Figure 11.

Here the cabin dynamics is neglected. Similar to the half vehicle models, the pitch angle

and the roll angle are assumed to be small, thereby small angle approximations have been

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15

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Fz

z

z'

z

z

z'

phi

phi'

zt11

zt11'

zt12

zt12'

zt21

zt21'

zt22

zt22'

theta

theta'

theta

theta

theta'

z

z'

zt11

zt11'

zt12

zt12'

zt21

zt21'

zt22

zt22'

phi

phi'

phi

FullCar

To Workspace

Fzt11

Fzt12

Fzt21

Fzt22

Road input1

w11

w11'

w12

w12'

w21

w21'

w22

w22'

Road input

-K-

Gain

Fz

Constant1

16

4 Model comparison This chapter compares the different models presented in the previous chapter, in order to choose a

suitable model for further studies.

The higher model complexity doesn’t necessarily lead to matching improvement between

measurements and simulated results. By comparing the models’ response when exposed to

the same input, the use of a simpler model can be justified if the difference is small enough.

The use of simpler model is often wanted since they reduce the amount of calculation and

thereby reduces the calculation time. This chapter compares the outputs of different models

to the same sinusoidal input and real road profile, and investigates their advantages and

disadvantages.

4.1 Parameters used in simulation

4.1.1 Vehicle parameters

Typical heavy truck parameters specified for the different models are shown in Tables 1-4.

To make different models comparable, the parameters are estimated from the same truck.

They are calculated for each model so that it will represent the front axle dynamics of a truck.

Table 1 – 2-dof quarter vehicle model parameters

Parameters Value Parameters Value

3400 kg 350 kg

300000 N/m 1000000 N/m

2000 Ns/m 500 Ns/m

20000 Ns/m

Table 2 – 3-dof quarter vehicle model parameters


650 kg 2000 Ns/m

75000 N/m 20000 Ns/m

7500 Ns/m 350 kg

2750 kg 1000000 N/m

300000 N/m 500 Ns/m

17

Table 3 - Half vehicle model parameters


650 kg 400000 N/m

75000 N/m * 4000 Ns/m

7500 Ns/m * 40000 Ns/m

8800 kg 450 kg

300000 N/m 1800000 N/m

* 2000 Ns/m 1000 Ns/m

* 20000 Ns/m 50000

350 kg 2.54 m

1000000 N/m 1.16 m

500 Ns/m

* com denotes compression; ext denotes expansion.

Table 4 - Full vehicle model parameters


18900 kg , * 40000 Ns/m

, 300000 N/m , 450 kg

, * 2000 Ns/m , 1800000 N/m

, * 20000 Ns/m , 1000 Ns/m

, 350 kg 100000

, 1000000 N/m 20000

, 500 Ns/m 2.37 m

, 400000 N/m 1.33 m

, * 4000 Ns/m 1.1 m

* com denotes compression; ext denotes expansion.

4.1.2 Pavement parameters

By adding a mass-spring-damper part to the system, the movement and force of pavement

can be included as well. However, the equivalent damping is hard to estimate, and is not

available during this study. Therefore pavement is simplified to a mass-spring system in this

study, which can provide approximation of pavement movement but lacks damping

properties.

The equivalent pavement mass and stiffness can be estimated by the Finite Element Method

(FEM) [17]. The mass cannot be the mass of the model used in FE analysis, but it can be

estimated by obtaining a ratio between the maximum displacement and average displacement

in depth and using this coefficient as multiplier of vehicle mass. In this case:

18

��

Therefore the estimated pavement mass in the dynamic system would be:

�

To estimate the pavement stiffness, a selected pavement structure is analysed in order to

obtain the displacement field caused by a uniform pressure on the surface. Figure 13 shows

the vertical displacement of pavement and the corresponding radial distance. The load is

applied with a 30 centimetres radius circular contact patch. Therefore the equivalent mean

stiffness is about 160 MN/m.

Figure 13 – Pavement vertical displacement vs. radial distance

4.2 Quarter, half and full vehicle When the model is improved from quarter vehicle without cabin to half one without cabin,

or from half vehicle without cabin to full one, its complexity increases, so does its

computational amount. How about the improvement on estimation? Two actual road

profiles, E4 Grimsmark longitudinal profile (E4) and 265 East longitudinal profile (265), are

selected to test their responses. The first set of data E4 belongs to a highway 600 km north

of Stockholm. It has high level of unevenness (International Roughness Index: IRI= 2.30

m/km). In Sweden the standard increment for longitudinal direction is 0.1 meter and

thereafter the data is averaged for every 20 meters in order to obtain the IRI value. The

second set of data 265 is the longitudinal roughness of a highway north of Stockholm. The

highway is fairly new and also fairly even (IRI =0.99 m/km), which has lower level of

unevenness compared to E4. It has however some short bridges which are visible on the

19

profile measurements with relatively higher roughness magnitude. The data for these

measurements are from Laser 13 (a laser measuring device) which follows the right rut.

As mentioned in Chapter 1, force (or load) applied on the road from the tyre is commonly

used as a measure of road damage. The force applied on the road from the tyre is

chosen as output. The dynamic contribution of it can be derived by:

�

in model without pavement, or by:

�

in model with pavement. Where is stiffness of tyre, is damping coefficient of tyre,

is vertical displacement of unsprung mass, is vertical displacement of pavement, and

are both measured from loaded position, is position of road surface. According to the

circumstances, may also include both static and dynamic contributions, which will be

specified. The static part given in Equation 31, which equals to the gravity of the whole

vehicle, should be added to the dynamic part.

where is mass of various parts of vehicle, is the acceleration of gravity.

There is only one set of data for each profile. If all wheels in all models use the same set of

data as input, the output from different models will be exactly the same. To reveal the effect

of roll and pitch motion in half or full vehicle models, the road profile data should be

processed first for each wheel. The road profile data is used directly in quarter vehicle model.

For half vehicle model, front wheel uses it directly, rear wheel uses data computed from it

and vehicle speed according to Equation 17. The vehicle speed used in the simulation is

selected as 20 m/s (~72 km/h). For full vehicle model, left wheels use the same data as half

vehicle data. In order to make the input to right wheels different from left wheels, right

wheels use the data shifted by time t. The forces applied on the road from each model are

then compared. To make them comparable, the front wheel of the half vehicle model and the

front left wheel of the full vehicle model are chosen and plotted.

The responses from the different models due to E4 road profile are shown in Figure 14, in

which t=0.1 s. Subfigure b) is the partial enlarged drawings of Subfigure a). The root mean

square (RMS) value of dynamic portion of force applied on the road from quarter, half and

full vehicle model are 1.3617 kN, 2.0396 kN and 2.2537 kN respectively.

20

Figure 15 shows tyre force of the models due to the 265 road profile. The RMS value of the

dynamic portion of force applied on the road from quarter, half and full vehicle model are

0.6516 kN, 0.9780 kN, and 0.9811 kN respectively.

The differences between models are caused by their differences in including the pitch and

roll dynamic. Similarities can be observed in both amplitude and frequency of tyre force. It is

seen that the differences greatly depend on the unevenness of road. The increased

unevenness will generate larger dynamic tyre force, and bigger roll, pitch and bounce motion,

which will increase output differences between the models. Profile 265 is evener compared to

profile E4, so its RMS values are smaller than those of E4. The RMS difference between half

vehicle model and quarter vehicle model of profile 265 is much smaller compared to E4 as

well.

21

Figure 14 – The dynamic portion of the force applied on the road when the vehicle models are simulated with the E4 Grimsmark longitudinal road profile.

0 2 4 6 8 10 12-8

-6

-4

-2

0

2

4

6

8

10

12

a)

Force applied on the road

Fw

(kN

)

Time (s)

Quarter vehicle

Half vehicle

Full vehicle

4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6

-6

-4

-2

0

2

4

6

8

10

12

b)


Fw

(kN

)

Time (s)

Quarter vehicle

Half vehicle

Full vehicle

22

Figure 15 - The dynamic portion of the force applied on the road when the vehicle models are simulated with the 265 East longitudinal road profile.

0 2 4 6 8 10 12-4

-3

-2

-1

0

1

2

3

4

a)


Fw

(kN

)

Time (s)

Quarter vehicle

Half vehicle

Full vehicle

7.4 7.6 7.8 8 8.2 8.4 8.6 8.8

-3

-2

-1

0

1

2

3

4

b)


Fw

(kN

)

Time (s)

Quarter vehicle

Half vehicle

Full vehicle

23

Figure 16 shows the tyre force due to the E4 road profile. Inputs and outputs of the quarter

vehicle model and the half vehicle model are exactly the same as in Figure 14. Here equals

to 1 s instead of 0.1 s, which increases the unevenness level between left and right sides. The

RMS values of the dynamic portion of force applied on the road are equal to 1.3617 kN,

2.0396 kN, and 6.5414 kN respectively. Larger difference can now be observed between

models due to the increase in unevenness. For uneven road, the usage of simulation results

from the quarter vehicle model or the half vehicle model may introduce large error when

evaluating the dynamic tyre force. The quarter vehicle model can well represent the real

dynamics only when the road is relatively even.

Figure 16 - The dynamic portion of the force applied on the road when the vehicle models are simulated with the E4 road profile.

To the author’s knowledge, there isn’t any clear boundary for large tyre force with respect of

road damage proposed in literatures. In [15], Sun used , the possibility of peak value of

wheel load exceeds a certain value , to estimate the road damage from vehicle. is related

to vehicle gravity:

where is mass of various parts of vehicle, is the acceleration of gravity, is the

percentage of the static vehicle load for a given level of .

0 2 4 6 8 10 12-15

-10

-5

0

5

10

15

20Force applied on the road

Fw

(kN

)

Time (s)

Quarter vehicle

Half vehicle

Full vehicle

24

In this study, when . It’s in the same order of magnitude compared

with the tyre force difference between models shown in Figures 14-16. The difference in

amplitude isn’t negligible, especially when the road is relatively uneven. It can also be

observed that the difference between the half vehicle model and the full vehicle model is

smaller than the difference between the quarter vehicle model and the half vehicle model.

That is because the inertia � and track width are much less than and wheelbase. There is

no obvious change in frequency.

4.3 Influence of coupled pavement The quarter vehicle model is the most common model used when evaluating road damage. A

quarter vehicle coupled with pavement is introduced in Section 3.2.2. How large difference is

there in response between the models when evaluating tyre-road contact force? In this

section, quarter vehicle models with and without pavement are compared to see the effect of

coupled pavement.

Figures 17-18 show responses from model with and without coupled pavement to sinusoidal

road profile and E4 road profile. They include both the static and dynamic contribution of

the tyre contact force. The difference is small enough to be neglected. Figure 19 shows the

amplitude of tyre and pavement motion in response to E4. To make the motion of tyre and

pavement comparable, only dynamic contribution is shown in the figure. Pavement

displacement is a high-frequency vibration. The amplitude of the displacement is so small,

that it is enlarged by 50 times in the figure to be seen clearly. It is much smaller compared to

the motion of the unsprung mass, even after being enlarged by 50 times. The pavement

dynamics’ influence on the vehicle dynamics is rather small, so it is possible to use only the

quarter vehicle model to compute the contact force. However, with the help of the coupled

model, one can get a rough estimation for pavement dynamics.

25

Figure 17 – The force applied on the road when the vehicle model is excited with 1 Hz sinusoidal input.

Figure 18 - The force applied on the road when the vehicle models are excited with the E4 road profile.

0 1 2 3 4 5 6 7 8 9-41

-40

-39

-38

-37

-36

-35

-34

-33Force applied on road

Fw

(kN

)

Time (s)

Without pavement

With pavement

0 1 2 3 4 5 6 7 8 9 10-42

-40

-38

-36

-34

-32

-30


Fw

(kN

)

Time (s)

Without pavement

With pavement

26

Figure 19 – The vertical movement of tyre and pavement when the vehicle models are excited with the E4 road profile.

Wheel hop is a special condition which needs to be considered in all vehicle models. Large

displacement of the road will induce large dynamic tyre forces. When the induced upward

dynamics tyre force is greater than the downward vehicle gravity, the tyres will lose contact

with road surface, and wheel hop will occur. For vehicle models without pavement dynamics,

wheel hop can easily be handled by setting zero as the upper limit of tyre force (combination

of both dynamic and static tyre force). For vehicle models including pavement dynamics,

pavement should be decoupled from vehicle when wheel hop happens. The decoupling

algorithm is implemented in the Simulink model. An extreme condition is designed to reveal

it. It is assumed that the vehicle is running on a very uneven road, the height difference is

about 1 meter. Vehicle speed is still 20 m/s. The vertical dynamics of the vehicle is so large

that it’s possible for tyre to loose contact with the pavement. As shown in Figure 20, the

model is decoupled when ( is the tyre force acting on the pavement, whose

positive direction is upward), which means tyre has lost contact with the pavement, and is

kept to be 0 until the tyre get in contact with road surface again. The pavement part will

freely oscillate during the wheel hop. Compared to the model excluding pavement but with

wheel hop taken into account, difference exists after wheel hops, which is introduced by the

free oscillation of pavement mass during wheel hop. The model including pavement but

without wheel hop taken into account will result in positive , which is impossible for a

real vehicle.

0 1 2 3 4 5 6 7 8 9 10-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04Vetical motion

Z (

m)

Time (s)

Unsprung mass(without pavement)

Unsprung mass(with pavement)

Pavement*50

27

Figure 20 - The force applied on the road when the vehicle models are simulated with high-level unevenness, to activate wheel hop.

4.4 Energy dissipation The 4-DOF quarter vehicle model with simplified pavement is used in this section to study

the energy dissipation in the vehicle. Figure 21 shows the power dissipation in each damper

of the quarter vehicle model simulated with the road profile E4. The Root Mean Square

(RMS) value of the power dissipation is 9.7 W in cabin suspension damper, 91.1 W in vehicle

suspension damper, and 5.8 W due to the tyre damping. Figure 22 shows the power

dissipation in each damper in the quarter vehicle model simulated with the road profile 265.

The RMS value of power dissipation is 1.0 W in cabin suspension damper, 5.7 W in vehicle

suspension damper, and 6.9 W due to the tyre damping. The dissipation in pavement is not

included since its damping is not included in the model. With relatively uneven road profile,

like E4 in Figure 21, loss in vehicle suspension is dominant, because most of the vehicle

vertical dynamics are damped in main suspension. However, with relatively even road profile,

0 1 2 3 4 5 6 7 8 9 10-0.5

0

0.5

1

1.5Road profile

w (

m)

0 1 2 3 4 5 6 7 8 9 10-200

-100

0

100Force applied on road

Fw

(kN

)

Time (s)

28

like 265 in Figure 22, loss in the tyre may be higher than in vehicle suspension, because the

vertical dynamics are light enough to be well damped in tyre.

Figure 21 – Power dissipation in each damper in the quarter vehicle model simulated with Profile E4

Figure 22 – Power dissipation in each damper in the quarter vehicle model simulated with Profile 265

0 2 4 6 8 10 12 14 16 18 20-200

0

200

400

600

800

1000

1200

1400

1600

1800Power dissipation in each damper

Pow

er

(W)

Time (s)

Cabin suspension

Vehicle suspension

Tire

0 2 4 6 8 10 12 14 16 18 20-50

0

50

100

150

200

250Power dissipation in each damper

Pow

er

(W)

Time (s)

Cabin suspension

Vehicle suspension

Tire

29

5 Parametric study In this chapter, the 4-DOF quarter vehicle model with simplified pavement is analysed to find the

parameters that influence the road damage most.

5.1 Typical response and frequency distribution Road damage is the general term for deterioration of road conditions. It is caused by the

combination of various factors including pavement material, construction, tyre force,

temperature etc. Fatigue cracking and rutting are two major mechanisms causing road

damage by heavy vehicles. Besides them, each kind of road damage has its unique

mechanisms. There isn’t a widely-agreed unified standard to evaluate the combined effect of

different kinds of road damage.

The ‘fourth power law’ is usually used in pavement design to aggregate the estimated traffic

during the service life into the number of equivalent standard axle loads (ESALs)[25], [26]. It

can be used to give out a rough estimation of road damage by static axle load. The number of

ESALs N attributed to static load P is

��

where is generally taken to be 80 kN. It aggregates the traffic into a simple number of

ESLAs, and uses ESLAs to indicate the road damage caused by the traffic loads. However,

its validity is questionable. Current vehicle and pavement conditions, traffic volumes are

figured out to be significantly different from the conditions of the AASHO road test, which

is the basis and source of the ‘fourth power law’ [27], [28]. The results from most recent

researches show that the damage exponent in Equation 33 may take a wide range of values

[25].

There isn’t any widely recognized method to estimate the overall damage to road based on

dynamic tyre force. According to Sun et al [5], Hardy et al [10] and Cebon [14], road damage

is directly related to tyre force and its frequency, especially the tyre force. Cebon [26] gave

out the common fatigue models developed from laboratory experiments:

� ��

where is the number of cycles to failure at strain level , is a constant that usually

depends on the stiffness of the material, is a constant that depends on the material and

the mode of distress. The strain can be calculated from dynamic tyre force by FEM

model of pavement. As mentioned in previous chapter, Sun [15] took the times that is

higher than a selected limit as an indicator of possible road damage. is quite important in

analysis of road damage caused by vehicle, so how vehicle parameters and pavement

30

characteristics affects it will be studied in this chapter. The quarter car model with coupled

pavement is chosen for this investigation.

Although there is inaccuracy because of the absence of roll, pitch motion in quarter vehicle

model, the parameter study with quarter vehicle model can reveal the effects of major vehicle

parameters investigated in this study.

Figures 23-25 show the model response to different road profiles. Tyre force is summation

of the static force (the normal load is 36.75 kN) and the dynamic force. The amplitude of

dynamic part is of concern and should be as small as possible to reduce the road damage.

Pavement motion is high frequency resonance around its equilibrium position. The

amplitude is quite small due to its high stiffness.

Figure 23 - The force applied on the road and the pavement motion when the vehicle models are simulated with the 0.5 Hz / 10 mm sinusoidal input.

0 1 2 3 4 5 6 7 8 9 10-0.01

0

0.01Road profile

w (

m)

0 1 2 3 4 5 6 7 8 9 10-38

-37


Fw

(kN

)

0 1 2 3 4 5 6 7 8 9 10-5

0

5x 10

-6 Pavement motion

Zp (

m)

Time (s)

31

Figure 24 - The force applied on the road and the pavement motion when the vehicle models are simulated with the E4 road profile.

Figure 25 - The force applied on the road and the pavement motion when the vehicle models are simulated with the 265 road profile.

0 5 10 15 20 25 30 35 40 45 50-0.1

0

0.1Road profile

w (

m)

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

-40

-20


Fw

(kN

)

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

-5

0

5x 10

-4 Pavement motion

Zp (

m)

Time (s)

0 5 10 15 20 25 30 35 40 45 50-0.1

0

0.1Road profile

w (

m)

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

-40

-30


Fw

(kN

)

0 5 10 15 20 25 30 35 40 45 50-2

0

2x 10

-4 Pavement motion

Zp (

m)

Time (s)

32

Figure 26 shows the Bode diagram of the quarter vehicle model with the parameters in

Chapter 4.1.1. Table 5 presents the systems’ natural frequencies and damping. There are four

eigenvalues and their corresponding eigen-frequency. The eigen-frequency of vehicle body

suspension and cabin suspension is too close that they locate at the same peak in lower

frequency range.

Figure 26 – Bode diagram of quarter vehicle model

Table 5 - Natural frequency and damping of the quarter vehicle model

Part Eigenvalue Damping Freq. (Hz) Suspension -1.18e+000 ± 7.73e+000i 1.51e-001 1.2446

Cabin -7.15e+000 ± 1.05e+001i 5.64e-001 2.0213 Tyre -1.72e+001 ±5.80e+001i 2.85e-001 9.6289

5.2 Effect of mass By changing the parameters of the model, the effect of different parameters can be revealed.

Mass, spring stiffness and damping coefficient are investigated separately in the following

sections to study their effects. Tyre force is chosen as the indicator of their effects, because it

affects pavement damage directly. Its dynamic part is influenced more by changes in

parameters mentioned above and of more interests than the static part. In addition, in the

investigation of effect of mass, tyre forces will be not comparable if static part is included. So

only dynamic force is presented and discussed in following sections.

60

80

100

120

140

160M

agnitu

de (

dB

)

10-1

100

101

102

103

104

0

45

90

135

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

33

In this section, mass of different part of the 4-DOF quarter vehicle model is changed to

investigate its effect. Figures 27-29 a) show the tyre force in response to E4 road profile. The

original mass is compared to the mass altered based on it. For instance, the original sprung

mass, , is compared with 50 % of it, , and 200 % of it, . It can be seen from the

simulation results that with greater mass, the amplitude of tyre force tends to be higher. The

effects of cabin, vehicle body and unsprung mass are different. Vehicle body mass has the

biggest effect, while unsprung mass has the smallest. Figures 27-29 b) show the Bode

diagram of the vehicle with different masses. It’s clear that, for sprung mass (vehicle body

and cabin), increasing mass will lead to increasing gain in low frequency range (0-2 Hz), and

decreasing gain in medium frequency range (2-10 Hz). Sprung mass won’t influence high

frequency behaviour. On the contrary, unsprung mass only affect high frequency part.

Greater unsprung mass will lead to larger gain in high frequency range (>10 Hz). The road

profile input is usually in the low frequency range (<2 Hz), where the effect of vehicle body

mass is prior to cabin. So the difference in tyre force is most obvious in Figure 27 a), and

nearly indiscernible in Figure 29 a).

a) b)

Figure 27 - Effect of vehicle body mass a) The dynamic portion of the force applied on the road when the vehicle model is simulated with different body mass, b) Bode diagram of models with different body mass.

0 2 4 6 8 10 12 14 16 18 20-10

-5

0

5

10


Fw

(kN

)

Time (s)

0.5m

m

2m

50

100

150

Magnitu

de (

dB

)

10-1

100

101

102

103

104

0

45

90

135

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

0.5m

m

2m

34

a) b)

Figure 28 – Effect of cabin mass a) The dynamic portion of the force applied on the road when the vehicle model is simulated with different cabin mass, b) Bode diagram of models with different cabin mass.

a) b)

Figure 29 – Effect of unsprung mass a) The dynamic portion of the force applied on the road when the vehicle model is simulated with different unsprung mass, b) Bode diagram of models with different unsprung mass.

Pavement mass will not influence tyre force at all, except on its natural frequency. As

discussed in Section 4.1.2, the original pavement mass is 1.4 times of the total vehicle mass.

0 2 4 6 8 10 12 14 16 18 20-10

-8

-6

-4

-2

0

2

4

6

8


Fw

(kN

)

Time (s)

0.5mc

mc

2mc

60

80

100

120

140

160

Magnitu

de (

dB

)

10-1

100

101

102

103

104

0

45

90

135

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

0.5mc

mc

2mc

0 2 4 6 8 10 12 14 16 18 20-10

-8

-6

-4

-2

0

2

4

6


Fw

(kN

)

Time (s)

0.5mt

mt

2mt

60

80

100

120

140

160

Magnitu

de (

dB

)

10-1

100

101

102

103

104

0

45

90

135

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

0.5mt

mt

2mt

35

In Figure 30, where � !��" is the total vehicle mass, it is compared with pavement mass

which is 0.6 times and 5 times of � !��" . Figure 30 b) shows the Bode diagram of models

with different pavement mass. The gain is almost the same, and the natural frequency of

pavement is high (>12 Hz). So for normal road-vehicle interaction studies, changes of

pavement mass will not influence the tyre force. It is confirmed by the response to road

profile in Figure 30 a).

a) b)

Figure 30 - Effect of pavement mass a) The dynamic portion of the force applied the on road when the vehicle model is simulated with different pavement mass, b) Bode diagram of models with different pavement mass.

5.3 Effect of stiffness Figure 31-33 show the responses and Bode diagrams of vehicles with different spring

stiffness. Spring stiffness mainly influences the medium and high frequency behaviour. Effect

of suspension spring is significant. Higher spring stiffness implies higher gain in 1-5 Hz

frequency range, which means stiffer suspension spring will introduce higher damage. Cabin

spring doesn’t have much effect. So change of cabin spring will not influence the road

damage much. Tyre stiffness has similar effect as the suspension spring. Stiffer tyre gives

higher road damage, but in high frequency range (>9 Hz).

0 2 4 6 8 10 12 14 16 18 20-10

-8

-6

-4

-2

0

2

4

6


Fw

(kN

)

Time (s)

mp=0.6m

vehicle

mp=1.4m

vehicle

mp=5m

vehicle

20

40

60

80

100

120

140

160

Magnitu

de (

dB

)

10-1

100

101

102

103

104

180

225

270

315

360

Phase (

deg)

Bode Diagram

Frequency (Hz)

mp=0.6m

vehicle

mp=1.4m

vehicle

mp=5m

vehicle

36

a) b)

Figure 31 – Effect of suspension spring stiffness a) The dynamic portion of the force applied on the road when the vehicle model is simulated with different suspension spring stiffness, b) Bode diagram of models with

different suspension spring stiffness.

a) b)

Figure 32 – Effect of cabin spring stiffness a) The dynamic portion of the force applied on the road when the vehicle model is simulated with different cabin spring stiffness, b) Bode diagram of models with different

cabin spring stiffness.

0 2 4 6 8 10 12 14 16 18 20-10

-8

-6

-4

-2

0

2

4

6

8


Time (s)

0.5ks

ks

2ks

60

80

100

120

140

160

Magnitu

de (

dB

)

10-1

100

101

102

103

104

0

45

90

135

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

0.5ks

ks

2ks

0 2 4 6 8 10 12 14 16 18 20-10

-8

-6

-4

-2

0

2

4

6


Fw

(kN

)

Time (s)

0.5kc

kc

2kc

60

80

100

120

140

160

Magnitu

de (

dB

)

10-1

100

101

102

103

104

0

45

90

135

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

0.5kc

kc

2kc

37

a) b)

Figure 33 – Effect of tyre stiffness a) The dynamic portion of the force applied on the road when the vehicle model is simulated with different tyre stiffness, b) Bode diagram of models with different tyre stiffness.

As show in Figure 34, pavement stiffness will only influence on its natural frequency, which

is similar to the effect of pavement mass. It does not change the tyre force. That is because

compared to the suspension or the tyre stiffness of the vehicle, the pavement is much stiffer

and not comparable to them. The pavement can thereby be considered as rigid here.

0 2 4 6 8 10 12 14 16 18 20-15

-10

-5

0

5

10


Fw

(kN

)

Time (s)

0.5kt

kt

2kt

60

80

100

120

140

160

180

Magnitu

de (

dB

)

10-1

100

101

102

103

104

105

0

45

90

135

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

0.5kt

kt

2kt

38

a) b)

Figure 34 - Effect of pavement stiffness a) The dynamic portion of the force applied on the road when the vehicle model is simulated with different pavement stiffness, b) Bode diagram of models with different

pavement stiffness.

5.4 Effect of damping Changes in damping will affect the tyre force as well, but in a different way compared with

changes in mass or spring stiffness. With smaller suspension damping, the resonance peaks at

the resonance frequencies of the sprung mass and the tyre tend to be higher, and the valley

between them tend to be lower (Figure 35 b). With increasing suspension damping, the gain

between sprung mass and tyre resonant frequency will increase as well. However, when the

damping is increased to its saturation, it will stop increasing and keep to be a gradual slope.

I.e. a better damped road will result in smaller tyre force as shown in Figure 35 a). In Figure

36, it can be seen that changes in the cabin damping don’t affect the tyre force much, and the

difference is small for the real road response as well. Figure 37 shows that the tyre damping

only effect the gain in the high frequency range (>40 Hz), and has no effect on the lower

part. Increasing the tyre damping will increase the gain in the high frequency range, but for

the low or medium frequency range, the gain will remain the same. So the tyre forces in

Figure 37 a) are almost the same. Compared to mass and stiffness, damping does not affect

the tyre force significantly.

0 2 4 6 8 10 12 14 16 18 20-10

-8

-6

-4

-2

0

2

4

6


Fw

(kN

)

Time (s)

0.5kp

kp

2kp

0

50

100

150

Magnitu

de (

dB

)

10-1

100

101

102

103

104

180

225

270

315

360

Phase (

deg)

Bode Diagram

Frequency (Hz)

0.5kp

kp

2kp

39

a) b)

Figure 35 – Effect of suspension damping a) The dynamic portion of the force applied on the road when the vehicle model is simulated with different suspension damping, b) Bode diagram of models with different

suspension damping.

a) b)

Figure 36 – Effect of cabin damping a) The dynamic portion of the force applied on the road when the vehicle model is simulated with different cabin damping, b) Bode diagram of models with different cabin damping.

0 2 4 6 8 10 12 14 16 18 20-10

-8

-6

-4

-2

0

2

4

6


Fw

(kN

)

Time (s)

0.5cs

cs

2cs

60

80

100

120

140

160

Magnitu

de (

dB

)

10-1

100

101

102

103

104

0

45

90

135

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

0.5cs

cs

2cs

0 2 4 6 8 10 12 14 16 18 20-10

-8

-6

-4

-2

0

2

4

6


Fw

(kN

)

Time (s)

0.5cc

cc

2cc

60

80

100

120

140

160

Magnitu

de (

dB

)

10-1

100

101

102

103

104

0

45

90

135

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

0.5cc

cc

2cc

40

a) b)

Figure 37 - Effect of tyre damping a) The dynamic portion of the force applied on the road when the vehicle model is simulated with different tyre damping, b) Bode diagram of models with different tyre damping.

0 2 4 6 8 10 12 14 16 18 20-10

-8

-6

-4

-2

0

2

4

6


Fw

(kN

)

Time (s)

0.5ct

ct

2ct

60

80

100

120

140

160

Magnitu

de (

dB

)

10-1

100

101

102

103

104

0

45

90

135

180

Phase (

deg)

Bode Diagram

Frequency (Hz)

0.5ct

ct

2ct

41

6 Conclusions This chapter concludes the work done in this study, discusses the results and their implication to road

damage caused by heavy vehicle.

In this study, vehicle models used in vehicle-road interaction are investigated. The quarter

vehicle model, the half vehicle model and the full vehicle model are selected. The equations

of motion are derived for each of them, which are then implemented into Simulink models in

order to simulate the vehicle motions for different road inputs. To study the interaction

between pavement and vehicle, a simplified pavement model is added to the quarter vehicle

model.

All models are then compared. From quarter vehicle to half vehicle and then to full vehicle,

the complexity increases. In section 4.2, it is showed that how detailed the model is does

affect its estimation results. The difference in response between the models is non-negligible,

and it will increase with the increase of road unevenness. For simple road damage analysis,

the quarter vehicle model is sufficient. However, for more complicated road damage analysis,

especially with uneven road profile, more complex model should be used to get better results.

Adding the pavement part won’t change the dynamic behaviour of vehicle part much. The

difference between models coupled with and without pavement is negligible. However, with

the help of the coupled pavement part, the movement of pavement mass can be estimated.

The coupled pavement will also influence the tyre force, when the road surface is greatly

uneven and wheel hop exists.

The performed parametric study reveals the relation between pavement loads and

vehicle/pavement parameters, which can help to understand the dynamic pavement loads

explicitly. A summary of the results are shown in Table 6 below.

42

Table 6 – Effects of different parameters on tyre force

Parameters ↑ Gain

Around Around Cabin mass

↗ ↓ －－－

Vehicle body mass ↑ ↑ ↘ －－

Unsprung mass －－ ↑ ↑

－ Pavement mass

－－－－－ Cabin spring

－ ↗ －－－ Suspension spring

－ ↑ ↑ ↘ －

Tyre stiffness －－－ ↑ ↑

Pavement stiffness －－－－－

Cabin damping －－－－－

Suspension damping － ↓ ↑ ↓

－ Tyre damping

－－－－ ↑

↑↓: Significantly increase or decrease; ↗↘: Slightly increase or decrease; －: No change.

: Natural frequency of sprung mass; : Natural frequency of unsprung mass.

From the results in Table 6 it can be concluded:

1. The tyre force will change with change of vehicle parameters. Vehicle body and

suspension part have the greatest effect, while cabin and its suspension have the least

effect;

2. The effects of vehicle body and suspension are mainly in low frequency range (<2 Hz).

Cabin and its suspension’s effects are mainly in medium frequency range (2-10 Hz).

Unsprung mass and tyre’s effects are mainly in high frequency range (>10 Hz). Normal

road profile is mainly in low frequency range, so the effect of changes in cabin and tyre is

not obvious compared to vehicle body and suspension part;

3. Different components influence the tyre force differently. Increasing the mass or the

spring stiffness will increase the gain from road input to tyre force. Increasing the

damping will lower the peak on its corresponding natural frequency and level up the

valley between them, until the system is well damped. After it’s well damped, the gain

between peaks should be a gradual slope, and will not change according to increasing of

damping anymore;

43

4. Changes of pavement parameters will not influence the dynamic road load. It will only

change its resonant frequency, which is quite high and hard to be reached during normal

road transport.

From vehicle point of view, the best way to reduce dynamic tyre force and road damage is to

decrease the mass, especially vehicle body mass, and the suspension stiffness, especially main

suspension. Having vehicle well damped helps to reduce road damage as well. More

lightweight vehicle body design and restricting vehicle load can help to reduce vehicle mass.

Using softer suspension can lower dynamic tyre load, but will degrade roll stiffness and

hence reduce static roll-over performance at the same time. It also increases static suspension

deflection, and therefore increases the sensitivity of ride height to static load, which is

undesirable in a truck [29]. However these problems can be solved by using anti-roll bars,

independent suspension, active or semi-active suspensions. Compared with mass and spring

stiffness, it’s more complicated to optimize dynamic tyre force by changing damping, because

changing damping will increase gain in some frequency and decrease it in other frequency.

Active damper provides a good solution for the problem. By using an actuator instead of a

passive damper, active damper can provide different damping to difference force which can

be controlled and optimized by designer. Thus it can be adjusted to minimize the dynamic

tyre force.

44

7 Future work This chapter gives some suggestion for future work.

In this study, different models suitable for analysis of vehicle road dynamic and road damage

caused by it are developed and analysed. Although the quarter vehicle model is used because

of its simplicity and acceptable accuracy when performing the parameter analysis, half- and

full vehicle can still be used to handle more complex problems or problems needing higher

accuracy, especially for uneven road. The pavement model used in this study contains only

mass and spring. The damping part should also be added in further studies to improve the

accuracy of model. However, it’s tricky to find out a value for pavement damping.

If available, the tyre model can replaced by more advanced tyre model, which can compute

force distribution. And then pavement model can be replaced by an FE model to give out

detailed damage estimation.

45

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