The Complete Model of the Vehicle Bicycle Approach For The Driving Simulator Machine

(1)

The Complete Model of the Vehicle Bicycle Approach

For The Driving Simulator Machine

Supervisor:

PhD. Joop Pauwelussen

Student Name:

Ali Sahir Hassan (484092)

(2)

ii | P a g e

Special Thanks:

S

pecial thanks to (

Mr. Menno Merts

) for his help among the project period.

His advices and comments were so positive and clear to me.

He transferred his experience and knowledge to the project in perfect way.

I really appreciate his help and hope I can work more under his advice..

Ali

(3)

iii | P a g e

Summary:

This project is focused on the modeling of vehicle in a simplified approach. This simplified approach consists of the lateral and longitudinal behavior as bicycle model. The complete model is integrated in the Greendino Driving simulator after code generation. The main goal of this project is to enable the Greendino simulator to use the HAN Simulink vehicle model.

The project was carried out by summarizing and listing all the equations and simplified equations of main vehicle components. All equations of the lateral and longitudinal behavior of the vehicle have been treated. These equations were linked in a sequence. Finally, a complete model was created using the Matlab-Simulink platform.

The model consisted of a set of inputs and the model produces a set of statuses as outputs. Those inputs and outputs were designed based on the GreenDino driving simulation machine.

Most of the simplified approach components are modeled based on the HAN test vehicle (BMW E90i) components parameters. Each system and subsystem in this model contains many designed parameters. The values of those parameters are taken from Appendix E.2 of The Automotive Chassis study book [5]. The complete model is tested by assuming simple driving condition and the output status has been discussed and compared with some real test data which are described in study book.

Based on several test methods, the model was able to generate and deliver all main output status based on the input signals.

(6)

II | P a g e

List of Symbols:

Symbol Parameter name units

ICE Internal Combustion Engine none

Teng Engine output torque N.m

Ωeng Engine angular speed rpm

Wheel angular speed rpm

Clutch output torque N.m

k Geometrical gear ratio factor none

Specific gear ratio none

Inverse gear ratio none

Gearbox output torque N.m

Angular speed of the transmission rpm

Transmission efficiency %

Wheel torque N.m

Wheel dynamic radius m

Longitudinal tyre force N

zaer y x

F

_, _, Aerodynamic air resistance N

 _{The air density.} _kg/m3

z y x

C

,

The drag coefficient in x-y-z-direction. -

S The front area of the vehicle. m2

rolling x

F

_, Rolling Resistance Force N

f The rolling resistance coefficient. -

K The rolling resistance factor. -

Fz Tyre normal force. N

grade x

F

_, Grade resistance N

m Vehicle mass kg

g Vertical gravity acceleration m/s2

αg Road level grade °

R Total motion resistance N

Tyre brake force N

: Brake disc friction coefficient. -

Wheel dynamic load. N

L Wheels base distance m

a Front wheel distance from the cog m b Rear wheel distance from the cog m

ax Longitudinal acceleration m/s2

G Mass center gravity m/s2

hg Mass center height m

Handbrake friction coefficient -

Front tyre brake force N

Rear tyre brake force N

(7)

III | P a g e

α2 Rear tyre slip angle °

β Body slip angle °

r Yaw rate °/s

δ Steering angle °

Fy1 Front tyre lateral force N

Fy2 Rear tyre later force N

Mz Aligning Torque (Bicycle model) N.m

Jz The polar moment of inertia Kg.m2

(8)

1 | P a g e

Introduction:

This project is part of B.Sc. in Automotive Engineer program at HAN University. This Project is done in cooperation with the company GreenDino1. The main goal of the project is to use the GreenDino driving simulator after integrating HAN vehicle model in it.

In this report, studying and modeling of vehicle bicycle model is carried out. In addition, the report also covers several output statuses as a result of applying simple drive test.

The Project report contains three chapters. The first chapter explains the theoretical background of the bicycle model approach. The bicycle model is a simplified approach of the main vehicle component as longitudinal system and the lateral behavior as the lateral system of the vehicle. Figure (1-10) shows the main parameters and status of the bicycle model.

Chapter Two explains the modeling process of all vehicle components. Longitudinal and lateral system modeling are explained carefully too. The input and output parameters as well as the status is listed within the limits of GreenDino simulator machine.

Chapter three treats several tests based on simple driving situations. Each test is discussed with different output parameter or status. Moreover, this chapter treats extra validation process. Those validation processes are:

a. Zero velocity problem. b. Acceleration correction. c. Inverse gear ratio.

The report is supported by some references that are mentioned in it. The result and recommendations of the project are explained in the conclusions.

Finally, the complete model of this project is delivered with this report as a softcopy.

(9)

2 | P a g e

Chapter One: Theoretical Background (Simplified approach longitudinal

and lateral Model)

In this chapter, the theoretical background of the simplified vehicle approach will be explained. The explaining process will go through the longitudinal behavior of the vehicle which includes the internal combustion engine and the power train. Also, the lateral behavior will be treated as lateral model. Also the integration process of the separate parts in one model is included..

1.1 Definition of the simplified approach:

From the title of this chapter, it is clearly mentioned that this project will be done based on a simple approach of the vehicle model (bicycle Model). The simplified approach is a simple model of a complete vehicle, which uses the main vehicle parameters as inputs and then provides the calculated and estimated parameters as outputs. The calculation will be done by simplified standard equations.

As mentioned earlier, the goal of this project is to get the GreenDino driving machine is working with HAN model. This integration process will go through code generation method, which is coding the vehicle model to C-language and then integrating it inside the GreenDino system. Because of using this coding method, the complex model may have some mistakes (error) or a duplicate parameter, and then the coding process may generate unrecognized code error. Therefore, simplified model is preferred an d it may have less and recognized error.

The simplified model will be divided into: a. Longitudinal Model.

b. Lateral Model.

(10)

3 | P a g e

1.2 Vehicle Model: (longitudinal Model)

The simplified vehicle model consists of two main models (Longitudinal and Lateral model). Those two models contain many subsystems. All theoretical background of those systems is going to be explained in this chapter.

The longitudinal model is a simple model of the vehicle component that can generate a power to reach the longitudinal behavior of the vehicle. This generated power will flow in a specific path, starting from Internal Combustion Engine (ICE) to the wheels as longitudinal velocity (Vx).

Figure (1-2) illustrates the complete power train components.

Figure 1- 2 Power train illustrate [1]

1.2.1 Internal combustion Engine (ICE):

The internal combustion Engine is the power generating part of the vehicle, which is the torque generator part of the simplified ICE subsystem. The output torque (Teng) is a function of the engine

(11)

4 | P a g e

Figure 1- 3 ICE Torque Curve.

Figure (1-32) shows the relationship between the engine inputs (which is the wheel angular speed (ωwh)

in the simplified ICE) and the engine outputs. This relationship is based on real data from the test vehicle in HAN Lab. Figure (1-4) shows the three dimensional plot of the real test data of this engine related to the throttle pedal position. The red dotted are:

a. Idle Speed line: the engine speed where the engine is not delivering any torque (or the start point of the torque curve). The engine should have no use under this idle speed. But in this project, the model will use a linear relationship below this speed to deliver the torque Descending. The purpose of this assumption is to use the wheel speed as input parameter to the internal combustion engine (ICE).

b. Speed at Maximum Engine Output: The speed where the engine can deliver the maximum output torque. (Or the top point of the curve).

c. Final Speed: The maximum speed of the engine. (Or the end point of the curve)

0 1000 2000 3000 4000 5000 6000 7000 8000 80 100 120 140 160 180 200 220 1 O u tp u t T o rq u e ( N .m )

Engine Angular Speed (rpm) ICE Torque Curve

Final Speed Idle speed line

Engine Max. Output

(12)

5 | P a g e

Figure 1- 4 3D plot of real engine data

1.2.2 Clutch Model:

The Clutch model is a simple linear model between the engine torque and clutch torque This function is related to the clutch pedal signal. In other meaning, the torque output from the clutch will be 0 when the clutch pedal fully pushed and torque values will same as engine torque when the clutch pedal is free. See equation (1-1):

Equation (1-1)

1.2.3 Transmission box (Gearbox):

The vehicle gear box is a simplified manual gear box model; this model is designed according to the BMW E90 320i gear box parameters. These parameters are changeable parameters according to the needs. The transmission (gearbox) model has 6-speeds (gear steps). Each gear step has its own gear ratio, the model will calculate each gear ratio according to the transmission box specifications, and the gear box

0 50 100 2000 4000 6000 -50 0 50 100 150 200 Throttle Paddel (%) BMW ( Engine Torque vs. Engine Speed related to the Throttle Paddel position)

Engine Speed (RPM) E n g in e T o rq u e ( N .m ) 0 50 100 150

(13)

6 | P a g e calculation is based on geometrical gear ratio calculation method. The actual output gear ratio depends on the gear shift stick position as an input to the subsystem. The geometrical calculation method will be used to calculate each gear ratio.

Equation (1-2)

Equation (1-3)

Equation (1-4) Where;

(n) ; number of gear steps.

(

);

the final gear ratio.

(k) ; the geometrical factor.

For example:

The , , which is the gear

box has 6 steps. (n=6).

= 1.4

= 0.85

= 1.4 x 0.85 = 1.19

= 1.4 x 1.19 = 1.666

= 1.4 x 1.666 = 2.3324

= 1.4 x 2.3324 = 3.26536

= 1.4 x 3.26535 = 4.571504

(14)

7 | P a g e The transmission has one inverse step (

i

inv), which is assumed as:

Equation (1-5)

Then the final output torque and speed from the Gearbox will be calculated according to equation (1-6) and (1-7) below. The transmission has specific efficiency (

which can reduce the final output of the transmission; this output can be called an actual output.

Equation (1-6)

Equation (1-7)

Equation (1-8)

(15)

8 | P a g e

1.2.4 Final drive transmission: (Differential)

The final drive is a component which can increase the amount of actual transmission torque and reduce the angular speed before transfer them to the driving wheel.

Figure 1- 6 Differential drawing. [1]

Equation (1-9)

Equation (1-10)

Equations (1-9) and (1-10) are referring to the final drive transmission equations, which is an increasing factor to the wheel torque ( ) and a decreasing factor for the wheel speed ( ). The final step

in longitudinal model is to calculate the longitudinal wheel force, which is as result of dividing the torque of driven wheel by the dynamic tyre radius (

)

of it.

(16)

9 | P a g e

1.2.5 Total driving resistance:

While driving, there are many motion resistances which affect the longitudinal drive line. Figure (1-6) shows the most of the vehicle parameters.

Figure 1- 7 Longitudinal Vehicle Parameters [7].

Figure (1-7) shows the most of the longitudinal parameters, those parameters are involved into resistance equations. There are three main resistance types:

Aerodynamic forces:

These are three directional air resistances which affects the vehicle motion. See equations (1-12), (1-13) and (1-14): x x aer x V SC F . . . . 2 1 2 , 



Equation (1-12) z x aer z V SC F . . . . 2 1 2 , 



Equation (1-13) My x aer y V SLC M . . . . . 2 1 2 , 



Equation (1-14) Where:

; The air density (kg/m3). V ; Vehicle speed (m/s)

z y x

C

,

; The drag coefficient in x-y-z-direction. S; is the front area of the vehicle (m2)

(17)

10 | P a g e Rolling Resistance:

This is the tyre rolling resistance which is generated due to lateral and longitudinal tyre forces.

f

F

x,rolling



z

.

Equation (1-15)

Where;

f ; is the rolling resistance coefficient. f (f₀ K.V_x2)

Grade Resistance:

This is the level road angle ( ) resistance, which completely depends on the road profile level, where (α) is the main effective parameter. See figure (1-6) above.



sin

.

,

m

g

F

_x_grade



Equation (1-16)

Combine force resistance:

In general, the combined equations of the motion resistances are explained below:







.

sin

2

1 .

.

2

1 cos

.

).

.

(

f

₀

K

V

2

m

g

V

2

S

C

V

2

S

C

m

g

R

_air _z



_x











_





Equation (1-17) To simplify equation (1-17): 4 2 . .V CV B A R   Equation (1-18) Where;



.cos



sin





. .



tan





. . 0   0 mg f mg f A Equation (1-19)



0



. . .



. 0



2 1 . . . . . . 2 1 cos . . .gK S C C f mgK S C C f m B







x z  



x z Equation (1-20) z C K S C . . . . 2 1

_

  Equation (1-21)

Finally, the longitudinal acceleration will be calculated from equation (1-22) below:

Equation (1-22)

Where;

(18)

11 | P a g e

1.2.6 Braking System:

Braking system can be classified into:  Normal brake system

 Handbrake system 1.2.6.1 Normal brake system:

The braking system is a system which produces a resistance force to reduce the tyre traction force and then reduce the vehicle speed. This force called a brake force (Fb), which is supplied by a hydraulic system to brake pads at each wheel (see figure 1-7) below. The brake forces can be calculated by:

Equation (1-23)

Where;

: brake disc pad friction coefficient.

: Wheel dynamic load force [N].

Figure 1- 8 Brake pad [1]

Fdynamic is calculated by applying the equilibrium equation on the whole vehicle twice. Figure (1-8) below shows the vehicle forces direction and cog location related to the wheels:

(19)

12 | P a g e

Figure 1- 9 Forces generate by the vehicle. [3]

The two equations below are the result of applying the equilibrium equation:





L

h

a

m

L

a

L

g

m

F

_front_dynamic



.









x



g



_{Equation (1-24)}

 

L

h

a

m

L

a

g

m

F

_rear_dynamic



.







x



g



Equation (1-25)

Where;

L; the vehicle wheel base (m).

a; the distance from the front tyre to the mass center (m). ax; the longitudinal acceleration (m/s2).

hg; the height of the mass center from the ground (m).

The brake disc/pad friction coefficient can be estimated by three methods:

 Ideal Method: the method in which it can be assumed that there is ideal relationship between the front and rear brake disc friction coefficients.

 Linear Method: The method in which it can be assumed that there is linear relationship between the front and rear brake disc friction coefficients.

 Manual Method: the method which is applied in this project and in this method all values of the friction coefficient will be manually added to the model.

(20)

13 | P a g e 1.2.6.2 Handbrake system:

The handbrake system is a simple brake system which supplies a hard brake force on the rear tyre only. This brake force can be calculated by:

Equation (1-26)

Where;

; Handbrake friction coefficient.

Finally, all brake forces will be added to the total motion resistance equation:

2 4 . .V CV B A  Equation (1-27) Where;

; Front tyre brake force. [N] ; Rear tyre brake force. [N]

(21)

14 | P a g e

1.3 Bicycle Model: Lateral Model

In this part, the complete vehicle will be assumed as bicycle model. The bicycle model is a one-track model which is the front tyres will be one front tyre and the rear as well. Figure (1-10) shows the vehicle bicycle model:

Figure 1- 10 Bicycle Model [4]

Where;

(αf) and (αr): are slip angles of front and rear tyre,respectively (°). (δf): Steering angle (°).

(a) and (b): are the distances between front and rear to the vehicle mass center, respectively. (r): vehicle yaw rate (°/s)

Figure (1-10) illustrates the vehicle bicycle model. It clearly shows that each wheel has its own slip angle; this slip angle value is depending on the value of the steering angle. (See equation 1-28) below:

Equation (1-28)

b

a

(22)

15 | P a g e

Equation (1-29)

For non-linear tyre model, the Magic formula approach will be applied in this project to calculate the lateral tyre forces. Equation (1-30) expresses the Magic formula:

Equation (1-30)

Where;

ί=1, 2 are the tyre number.

As shown in equation (1-30) it has many unknown factors, each factor has specific value which is depending on the tyre Characteristic, in this project, all those parameters got contact value.

The bicycle aligning torque (Mz) will be calculated as moment result of:

Equation (1-31)

Lateral velocity (Vy) and yaw rate (r) are two parameters that will be treated in the bicycle model as equation on motion (1-32):

Equation (1-32)

And;

Equation (1-33)

Where;

(Jz); Is the polar moment of inertia in z-direction.

As a result, the complete vehicle behavior is explained, the longitudinal behavior is treated carefully and the lateral behavior is converted into bicycle model to make it simpler. All these equations above are going to be modeled and explained in the next chapter.

(23)

16 | P a g e

1.4 Velocity Estimation:

As a result of the completed model layout, the list of the model output should be finished. Velocity vector of the center of gravity is the main output of this model. The vector consists of (V_x, Vy and Vz).

Each parameter of this vector is estimated by integrating the acceleration parameter according to equation of motion:

Equation (1-34)

Equation (1-35)

Where; (ί); is the axis.

(J); is a tyre number for example: (1) for front tyre and (2) for rear tyre

Finally, the model can provide as many parameters as possible. Therefore, an agreement has been reached with GreenDino Company about the main input and output parameters. This list will be discussed carefully in next chapters.

(24)

17 | P a g e

Chapter Two: Modeling

In this chapter, the model flow process will be explained. The model process has been done according to the simplified approach which is already explained in chapter one. Matlab Simulink software is used as modeling software. The modeling process was carried out according to a modeling Flowchart. This flowchart has been generated to make the project clear and indicate step by step procedure. The model has a list of the input and output parameters. Those parameters are based on the GreenDino Simulator Machine. In the next section, modeling flowchart will be explained.

2.1 Flowchart:

Before starting with the modeling process, a flowchart should be placed on the first step. The modeling flowchart will start and end by the input and output parameters, then the longitudinal and lateral model. The modeling flowchart is given below:

Figure 2- 1 Modeling Flowchart

Figure (2-1) shows the simple modeling flowchart (Flow process). According to this flow process, the complete model will be treated.

(25)

18 | P a g e

2.2 Model Top View:

As explained above, the model has four main parts, which are: 1. Input and Output parameters.

2. Longitudinal part. 3. Lateral part.

4. Velocity estimation part.

The complete top view layout of the model is shown below. In this layout, the main input and output parameter are shown.

Figure 2- 2 Model Top View

Figure (2-2) shows the model top view. The model top view has low details because of all system will be treated individually, later. The top view consists of four main systems. Input and output systems are system interfacing system between HAN model and GreenDino Simulator machine. The longitudinal and lateral systems are the modeling system according to the HAN bicycle approach.

Each black line or arrow refers to specific input and output signal to the system. The white block refers to specific subsystem. All those systems, subsystems and the signals are going to be explained individually.

(26)

19 | P a g e

2.3 Inputs Parameters:

Input signals are group of signals which refers to specific parameter. This group is the input connection from the GreenDino to the HAN model. Below, list of the input signal with its named parameters:

Signal No. Parameter Name Signal Type and range

1 Contact Key 0,1

2 Rest Bottom 0,1

3 Steering wheel angle -1:1

4 Brake Pedal 0:1

5 Throttle Pedal 0:1

6 Gear type switch 0,1

7 Automatic Gear -1:6

8 Manual Gear Stick -1:6

9 Clutch Pedal 0:1

10 Hand Brake Pedal 0:1

11 Front Right tyre (z-axis) inf (m) 12 Front Left tyre (z-axis) inf (m) 13 Rear Right tyre (z-axis) inf (m) 14 Rear Left tyre (z-axis) inf (m)

Table 2- 1 Input Parameters table

Table (2-1) listed all input signals to the project model. For example, the signal number (5) refers to the throttle pedal position signal. This signal has range from (0) to (1), which is equal to (0) when the throttle pedal are released and (1) when the throttle pedal is fully pushed. Each input signal has its own range and this range is assumed by GreenDino according to the simulator data interface.

2.4 Longitudinal System Model:

The longitudinal model is a system which contains several subsystems as shown in figure (2-2), those subsystems are the modeling of main vehicle components:

Internal Combustion Engine (ICE) subsystem. Clutch subsystem.

Transmission Box subsystem.

Vehicle Longitudinal Behavior system.

(27)

20 | P a g e

Figure 2-2a longitudinal system charts

Figure (2-2a) shows all longitudinal subsystem with all main input and output signals. Those subsystems will be carefully below:

Pedals signal + steering angle

ICE:

Applying engine torque curve Brake Pedal Clutch System Cl u tc h Ped al T_eng Transmission T_clutch G ea r S tic k

Final Drive and Trans. eff.

i_ratio

Actual wheel torque

Estimation Traction force Wheel radius

F_trac for driven tyre

Total Losses Equations

Total resistance

ax (cog)

Dynamic load for both wheels Brake system

Fdy1 and Fdy2 Fbf and Fbr Throttle Pedal Acceleration Correction Speed i_ratio Vx (cog) Wheel Speed New ax

Vx (cog) to the lateral model

Longitudinal acc.

(28)

21 | P a g e

2.4.1 Internal Combustion Engine subsystem:

As explained earlier in part (1.2.1) in chapter one, this simplified engine torque curve is model as the core of this subsystem (see figure (1-3)). The system has two inputs (Throttle pedal position and vehicle wheel speed) and the engine torque as the only output parameter signal form this subsystem. (Check figure (2-3) above).

Figure 2- 3 ICE subsystem

Figure (2-3) shows the ICE subsystem model, which is clear that the two input signals on left and the main output signal on right hand of this figure. The output of this subsystem is related to the throttle pedal signal. The throttle pedal is a factor over the maximum available amount of the deliver engine torque for a certain engine speed. Moreover, the subsystem delivers extra wheel speed signal in (rpm) to the output system.

2.4.2 Clutch Subsystem:

This subsystem is modeled according to a very simple approach of the clutch system function. The approach ignores the coupling mechanism in the clutch system (see part 1.2.2) in chapter one. From the figure (2-2a) and part (1.2.2), it is clearly shown that the engine torque and the clutch pedal position are the two inputs to the subsystem, and only the clutch torque is the main output.

Internal Combustion Engine (ICE) subsystem

2 Engine Speed 1 Engine Torque Product 1-D T(u) Engine torque 2 W_wheel 1 Throttle Padel Throttle pedal T_eng Vw

(29)

22 | P a g e

Figure 2- 4 Clutch subsystem

The system will reduce the amount of the engine torque related to the clutch pedal position. For example, if the clutch pedal is completely pushed, the clutch pedal will have value (1). According to equation (1-1) in chapter one, the clutch torque will be (0 N.m). (Check figure (2-4) above).

2.4.3 Transmission Subsystem:

The function of this subsystem is to calculate and provide the gear ratio; this calculation can be in two methods:

a. Automatic Ration calculator method: This method is clearly explained in part 1.2.3 in chapter one.

b. Manual Ratio editor: In this method, each gear ratio should be added by the model user.

According to figure (2-2a), the gear stick signal is the only input signal to the subsystem. The gear step ratio and the rotation direction signal are the outputs from this subsystem. The user should choose on which method the model will operate.

Figure (2-5) below shows the top view of this system:

2 Clutch Speed 1 Clutch Tourqe 1 3 Engine Speed 2 Engine Torque 1 Clutch Padel Engine torque

(30)

23 | P a g e

Figure 2- 5 Transmission subsystem (Top View)

By activating or deactivating the main parameter, the model will be switch between those two methods. As shown in figure (2-5), the output signals on the right hand of the model. Deeply, figures (2-6) and (2-7) will show the simple way in which those methods are modeled.

Figure 2- 6 Automatic Gear ratio subsystem

Figure (2-6) shows the (Automatic Method model), which clearly shows the gearbox specific parameters on left side of the figure; and the calculation process is in the middle. The input and output signals are on right. The calculation process is based on the list of equations from (1-2) to (1-5).

On the other hand, the manual edit method is already modeled by adding each gear step ratio manually in the M-file. The Simulink model callbacks those ratios from the M-file. Figure (2-7) shows the manual subsystem:

GearBox Properties of BMW E90 320i

2 Trans_sign 1 i_ratio Sign Product 0 *, 1 Multiport Switch

Gear Joy stic i_out

Manual Ratio man

Constant

Gear Joy stick i_out

Automatic Ratio Calculator 1 Gear stick 1 i_out n_t_max n@t_max n_p_max n@p_max final_ratio final gear ration

iout To Workspace Product -1 0 1 2 3 4 5 6 * Multiport Switch 0 -1 1 Gear Joystick k i_6 i_5 i_4 i_3 i_2 i_1

(31)

24 | P a g e

Figure 2- 7 Manual editor subsystem

2.4.4 Torque Flow and Final Drive (Differential) Subsystem:

The function of this subsystem is to transfer the engine torque (Teng) to the wheels (TWheel), then

generate the traction forces (longitudinal wheel force).

First of all, the gear step ratios (in) are already calculated via the transmission subsystem, the instant

transmission torque (TTrans) can be calculated according to equations (1-6) and (1-7), the actual torque

(Tact) is also calculated by multiplying the transmission torque (TTrans) with transmission efficiency ratio

(ɳ) (equation 1-8). Wheel torque (TWheel) is a result of multiplying the differential gear ratio with the

actual torque. See equation (1-9).

Finally, the total traction force of the wheel can be found according to equation (1-11) in chapter one.

Figure 2- 8 Complete Transmission Subsystem

1 i_out -1 0 1 2 3 4 5 6 * Multiport Switch inv i6 i5 i4 i3 i2 i1 0 1 Gear Joystic 2 Fx_total 1 V_wheel T_wheel To Workspace3 T_Act To Workspace2 T_Tran To Workspace1 T_clutch To Workspace fd eff_PT r_dyn Constant 3 Clutch Torque 2 Gear Ratio 1 Engine Speed re Gear RPM Actual RPM

Gear Torque Acatual torque

Wheel RPM

Wheel Torque

(32)

25 | P a g e

2.4.5 Total Driving Resistance Subsystem:

As explained in part 1.2.5 in chapter one, the driving resistances are summarized in main equation (equation 1-18), this main equation consist of three equations (1-19, 20 and 21). Those sub-equations are based on many constant variables. All these variables should be added in an M-file. Figure (2-9) shows the modeling of the total resistances subsystem.

This subsystem has two inputs (αg) and the total brake force (Fbrake). The total brake force subsystem will

be treated carefully in the next part. The resistance subsystem has only one output (Rtot).

Figure 2- 9 Total Resistances Subsystem

2.4.6 Total Brake Subsystem:

The complete brake subsystem consists of two main models: a. The Normal brake system: see part 1.2.6.1 in chapter one. b. Handbrake system: see part 1.2.6.2 in chapter one too.

For modeling of the first part, dynamic wheel forces need to be calculated, those two equations are (1-24 and 1-25) in chapter one. Those two equations contain many dimensional variables; all those variables should be added in M-file. The longitudinal acceleration is the only changeable variable in those two equations. See figure (2-10) below:

2 m 1 R_tot Product1 Product u^4 Fcn2 u^2 Fcn1 tan(u) Fcn Cz m fo -(0.5*roh*S*K*u) C u*9.81*K+(0.5*roh*S*(Cx-(Cz*fo))) B u*9.81*m A 3 Vx 2 alpha_grade_radian 1 F_brake Total resistance

(33)

26 | P a g e

Figure 2- 10 Dynamic force subsystem

Figure (2-10) clearly shows the dynamic force subsystem, the longitudinal acceleration is pasted in right side as input. The subsystem has five outputs. Only the outputs (1 and 3) are going to be used in normal brake force calculations.

To complete the brake force modeling, Normal brake subsystem has to be modeled; the modeling is based on equation (1-23).The complete normal brake system model shown in figure (2-11) below:

Figure 2- 11 Complete Brake model

Figure (2-11) can be explained by dividing it in three parts. Upper part shows the modeling of the front tyre braking force calculation. The lower part shows the modeling of the rear tyre brake force. The middle part is related to the handbrake force calculation.

The subsystem has four inputs; the first two inputs are the wheel dynamics forces. The third and fourth inputs are the brake pedal and the handbrake signals. The total brake force output is the summation of

5 G 4 Fb2 3 Fdy2 2 Fb1 1 Fdy1 Scope2 9.81 mu_b hg m a L m 1 ax G L a (L-a) m.ax Fdy 1 Fdy 2 Fb2 Fb1 1 Fbrake Manual Fbr To Workspace1 Fbf To Workspace Saturation1 Saturation mu_hb mu_r mu_f 4 Hand brake 3 Brake Pedal 2 Fdy2 1 Fdy1 Result

(34)

27 | P a g e all those forces related to the brake and handbrake signals. Finally the total brake force is a resistance signal which should be added to the total resistance according to equation (1-27) in chapter one.

2.4.7 Longitudinal Velocity and Acceleration:

The Final process in the longitudinal system is to estimate the longitudinal velocity (Vx) and the

acceleration (ax). The longitudinal acceleration will be estimated according to equation (1-22) or (1-34).

The longitudinal velocity will be calculated according to equation (1-35) in chapter one.

Checking up the figure (2-2a), the model is able to calculate the wheel velocity (Vw) in (rpm) unit and

send this signal back to the internal combustion engine as system input (Weng).

2.5 Lateral System Model:

The vehicle lateral behavior is simplified as bicycle model approach. The complete modeling of the lateral approach is illustrated in figure (2-12) below.

(35)

28 | P a g e The longitudinal velocity and the steering angle are the only input signals to the lateral model. The lateral model (as shown in figure 2-22) consists of four sub models. Each subsystem will be explained further.

2.5.1 Nonlinear Tyre Force Subsystem:

The function of this subsystem is to calculate the lateral tyre forces (Fy) based on the Magic Formula (see equation (1-30). The Magic Formula as function of the tyre slide slip angle (α1,2). The tyre side slip angles can be calculated by equation (1-28 and 1-29) from chapter one.

Note:

The lateral velocity will be mentioned as (v) instead of (Vy) in this part (2.5).

The Longitudinal velocity will be mentioned as (u) instead of (Vx) in this part (2.5).

Figure 2- 13 Nonlinear Tyre Force Subsystem

Figure (2-13) shows the nonlinear subsystem, the four main inputs on the left side. The slip angle calculation block is in middle. The Magic formula blocks function with the subsystem outputs are on right side. This subsystem is using the integration’s feedback signals (the lateral velocity and the yaw rate) and feedback input to this system. (See figure 2-12)

2.5.2 Force and Moment Subsystem:

The function of this subsystem is to calculate the aligning torque ( ) of the bicycle model round the center of mass. Moreover, the front tyre aligning torque is modeled too in this subsystem. This subsystem is modeled based on equation (1-31).

2 Fy2 1 Fy1 delta v r u alf a1 alf a2 slip angles f(u) function rear f(u) function front 4 u 3 r 2 v 1 delta

(36)

29 | P a g e

Figure 2- 14 Force and Moment subsystem

Figure (2-14) shows the force and moment subsystem. According to figure (2-12), the subsystem has two inputs (Fy1 and Fy1) and (Mz) as main output.

2.5.3 Integration Subsystem:

The goal of this subsystem is to estimate the value of the lateral velocity , acceleration (v and ay) and the yaw rate (r).The subsystem are modeled based on the equations (1-32) and (1-33).

Figure 2- 15 Integration Subsystem

Figure (2-15) shows the integration subsystem. The subsystem has three inputs (Mz, Ftotal and u). The

outputs of this subsystem are the yaw rate (r), the lateral speed (v) and the lateral speed changing (dv/dt). 3 Alt_f 2 -F total 1 Mz total b Gain18 a Gain17 tr Gain1 2 Fy2 1 Fy1 F- total Mz total 3 dv/dt 2 r 1 v Product 1 s 1 s 1/J 1/m 3 u 2 F total 1 Mz total dr/dt v dv /dt

(37)

30 | P a g e

2.5.4 Position Estimation:

The function of this subsystem is to estimate the position of the vehicle related to the global coordinates. This subsystem is not so important to the GreenDino project. However, it is important to the test and validation part of this project.

The subsystem is treating these set of equations:

Equation (2-1)

Equation (2-2)

And

Equation (2-4)

Where, (Ψ) is the yaw rate angle.

However, the ( ) are vehicle velocities in x and y direction. So, integration of these two parameters is required (equations 10 and 11) to get the vehicle position on global plane:

Equation (2-5)

Equation (2-6)

Figure 2- 16 Position Estimation Subsystem

Figure (2-16) shows the subsystem model which is modeled based on equations (2-1 to 2-6) above. cos sin x To Workspace1 y To Workspace Scope1 Scope Product3 Product2 Product1 Product 1 s 1 s 1 s 3 u 2 r 1 v

(38)

31 | P a g e

2.6 Output Parameters:

The output signals are group of signals which are the results of the estimation and calculation processes. All those estimation and calculation processes are done via the complete model. The naming of those parameters is done according to GreenDino simulator machine need. Table (2-2) lists all model output parameters:

Signal

No. Parameter Name Signal unit

1 Wheel angle degree (degree)

2 Velocity 3D vector (m/s)

3 Acceleration 3D Vector (m/sec2)

4 Angular Speed (degree/sec)

5 Angular Acceleration (degree/sec2₎

6 Wheel Speed rpm

7 Engine Speed rpm

8 Engine Torque N.m

9 Current Brake force N

10 Wheel Aligning torque N.m

11 Roll-out distance m

12 Front tyre aligning torque N.m

Table 2- 2 Output Parameters Table

(39)

32 | P a g e

Chapter Three: Model test and validation:

In this chapter, three types of model test scenarios are applied. The results of those tests are shown in graphs. Moreover, this chapter will carry on the many model corrections and validations. The idea of making those three tests is to check whether the model is delivering the correct status within the expected range.

3.1 Model Test:

In this section, the model inputs are used as the changeable parameters and the model outputs are used as the result states. It means, three driving scenarios will be applied in this process by changing the input parameter values. Then, all output states form the model outputs will be plotted to discuss them. The three driving three scenarios are:

1. Accelerating till three gear steps and then braking hard with step steering input (2°).

2. Accelerating till third gear step and then releasing the throttle pedal with sine wave steering input (5°).

3. Lane change scenario with certain speed. All those test scenarios will be treated in next parts.

3.1.1 Test 1:

In this test, accelerating till third gear step and then a hard brake will be applied with (2°) of a step steering input.

`

Figure 3- 1 Test 1: Input signals 0

0.2 0.4 0.6

0.8 _{Brake Pedal}

controller/Signal Builder : Group 1

0 0.5 1 Throttle Pedal 0 0.5 1 Gear Stick 0 0.5 1 Clutch Pedal 0 10 20 30 40 50 60 70 80 90 100 -1 0 1 HandBrake Time (sec)

(40)

33 | P a g e Figure (3-1) shows the driving input scenarios for all of brake, throttle, clutch pedal, gear and handbrake stick signals. In this figure, it is observed that the test starts after 10 sec. Then, the clutch pedal will be applied one time in sync with the gear stick changing. The gear stick will be shifted one level. The throttle pedal will be released within a time period of 20 sec. Finally, the brake pedal will be pushed linear for from tome of 60 till 70 sec. The step input signal of (2°) will be the tyre steering angle. See figure (3-2) below:

Figure 3- 2 Test 1: Tyre steering Input

According to GreenDino, the model provides (11) output states and parameters (see table 2-2). In this part, only the important output states will be treated. Velocity vector is the main output state of the model. The vector consists of 3D velocity components (Vx, Vy and Vz). Figure (3-3) shows the longitudinal velocity of test 1:

Figure 3- 3 Test 1: Longitudinal Velocity

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 -0.5 0 0.5 1 1.5 2 2.5 Time (1:100) sec T y re s te e ri n g a n g le ( d e g re e )

Test 1 : Tyre Steering Input

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 0 2 4 6 8 10 12 14 16 18 Time (100:1) sec V e lo c it y ( m /s )

(41)

34 | P a g e As shown in figure (3-3), the longitudinal velocity rises from time of 12 till 20 sec. This is a result of throttle pedal and gear step. The longitudinal velocity rises from (0 m/s) to (18 m/s = 64.8 km/h), that means the model reached a velocity of 18 m/s within 8 sec. As no throttle pedal is applied; the longitudinal velocity is dropped down linearly form 20 till 60 sec due to which the vehicle rolls out. Finally, the longitudinal velocity is dropped sharply from (8.73 till 0 m/s) within the interval of (60 to 64.9 sec) as a result of application of hard brake. , figure (3-4) shows those two states:

Figure 3- 4 Test 1: Lateral and Normal Velocity

Figure (3-4) shows the lateral velocity component related to the fix origin point (start point). As the vehicle is turning to left, the velocity has positive value. The tyre steering angle is very small (see figure (3-2) which leads to small amount of the lateral speed. In figure (3-4), the value of the lateral velocity is zero (from t=0 till t=30 sec). After steering angle is applied, the value of the lateral velocity is jumped to (0.09 m/s) and then it reduced to (0.05 m/s). The lateral velocity rises till the brake force is applied from (t=60 till t=64.9 sec). The braking force is affected in the lateral velocity, within the time during which the braking has been applied. Finally, the lateral velocity is kept constant till the end of simulating time. The acceleration vector is one of the important model output states. Figure (3-5) shows this state’s behavior:

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 0.02 0.04 0.06 0.08 0.1 0.12 Time (100:1) sec V e lo c it y ( m /s )

(42)

35 | P a g e

Figure 3- 5 Test 1: Longitudinal Acceleration

In figure (3-5), it is observed that the longitudinal acceleration is increased while the throttle pedal is pushed (t=12 to t=20 sec). As the throttle pedal is released at (t=20 sec), the longitudinal acceleration is dropped to the negative part. The negative value of the longitudinal acceleration is the result of rolling resistance and aerodynamic effect. Finally, the brake is applied at (t=60 sec), which gives hard deceleration with amount of (ay=3.5 m/s2).The behaviour of the lateral acceleration is clearly observed in this figure (3-6) below. The lateral acceleration value is jumped to less than (2.5 m/s2) at time of tyre steering angle has been applied (t=30 sec). Then, this value is decreased (decelerating linearly) at time when the throttle pedal is released (rolling out). Finally, the lateral acceleration is dropped hard at time of brake force has been applied till the vehicle is stopped.

Figure 3- 6 Test 1: Lateral Acceleration.

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 -4 -3 -2 -1 0 1 2 3 4 5 Time (100:1) sec A c c e le ra ti o n ( m /s 2)

Test 1 : Longitudinal Acceleration

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 -0.5 0 0.5 1 1.5 2 2.5 Time (100:1) sec A c c e le ra ti o n ( m /s 2)

(43)

36 | P a g e In addition, the model provides the yaw rate (r) at the vehicle center of gravity which is treated in figures (3-7) below:

Figure 3- 7 Test1: Yaw Rate

Yaw rate of the vehicle center of gravity is following the lateral acceleration behavior. That seems to be correct according to the lateral velocity and tyre steering input (see equation 1-32 and 1-33).

Figure 3- 8 Test 1: Tyre Aligning Torque.

Figure (3-8) shows the curve of front tyre aligning torque. The value of the torque is following the lateral acceleration curve behaviour (see figure 3-6) which is a result of equations (1-30 to 1-33). The tyre aligning torque is a result of linear approximation:

0 2000 4000 6000 8000 10000 12000 0 1 2 3 4 5 6 7 8 Time (100:1) sec Y a w ra te ( d e g re e /s ) Test 1 : Yawrate 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 0 5 10 15 20 25 Time (100:1) sec A lig n in g T o rq u e ( N .m )

(44)

37 | P a g e

where, tyre trails is assumed to be between (0 - 0.075) m. (This value is changeable by M-file) To examine this part, the value of aligning tyre torque is compared with figure (3-8a) below:

Figure 3- 8a Aligning Torque vs. Tyre Slip Angle [6]

By comparing this figure, HAN model has value of normal tyre force (Fzo = 8000 N) which is equal to (1798.5 Lbs), and the test is applied with (0.5°) of front tyre slip angle. This leads to the red circle in figure (2-8a) above. The result of applying the test situation to the model parameters is that, the value of aligning torque is less than (30 Lb-Ft) which is equal to (40.67 N.m). Figure (3-8) shows that the value of the aligning torque is about (22 N.m). That gives close value to the value of figure (3-8a).

As mentioned in the beginning of this part, the model can provide many output states and parameters. Therefore, only the important states will be discussed. Finally, Figure (3-9) shows the vehicle path according to test 1 inputs:

(45)

38 | P a g e

Figure 3- 9 Test 1: Vehicle Path

As shown in figure (3-9), the vehicle model traveled on the observed path, where the point of (0,0) refer to the start running point.

3.1.2 Test 2:

After test 1 has been discussed, test 2 will be treated. The test will have the same pedal situation as test one (see figure 3-1). However, Sine wave with (5°) amplitude will be the tyre steering input. Figure (3-10) shows the tyre steering input signal:

Figure 3- 10 Test 2: Tyre steering input signal.

In this part, only lateral behavior of the vehicle, tyre slip angles, lateral forces, lateral acceleration and aligning torque will be discussed. Firstly, lateral acceleration and tyre forces will refer to the lateral behavior of this test. Figures (3-11 and 3-12) shown below:

0 100 200 300 400 500 600 0 50 100 150 X-Coordinate (m) Y -C o o rd in a te ( m )

Test 1: Vehicle Path ( test time =100 sec)

0 10 20 30 40 50 60 70 80 90 100 -6 -4 -2 0 2 4 6 Tyre Steering Time (sec)

(46)

39 | P a g e

Figure 3- 11 Test 2: Lateral acceleration.

Figure 3- 12 Test2: Lateral forces.

As shown in figures (3-11 and 3-12) above, the lateral acceleration and tyre forces are plotted. The lateral acceleration behavior is following the tyre steering angle with low value. The lateral value is between (±0.7 m/sec2). This value is small because of the small steering angle. It is calculated according to Magic Formula equation (See equation (1-30) in chapter one).

The value of the lateral force depends on tyre slip angle. The slip angle angles is plotted in figure (3-14) below: 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Time (100:1) sec L a te ra l a c c e le ra ti o n ( m /s e c 2)

Test 2: Lateral acceleration

1000 2000 3000 4000 5000 6000 7000 -800 -600 -400 -200 0 200 400 600 800 Time (100:1) sec L a te ra l F o rc e ( N )

Test 2: Tyre Lateral Forces

Front Tyre (Fy1) Rear Tyre (Fy2)

(47)

40 | P a g e

Figure 3- 13 Test 2: Tyre slips angles.

Figure (3-14) shows the value of the tyre slip angles. As the front tyre is the steering wheel tyre, the value of the slip angle in front tyre is bigger than the value of the slip angle of the rear tyre. Moreover, the value of front tyre aligning torque in plotted in figure (3-15):

Figure 3- 14 Test 2: Front Tyre Aligning Torque.

Figure (3-16) shows real test data of the longitudinal tyre force curve related to the tyre slip angle of experiment and it has been already done by Prof. Genta.

1000 2000 3000 4000 5000 6000 7000 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Time (100:1) sec T y re s lip a n g le ( d e g re e )

Test 2: Tyre Slip Angles

alfa1 alfa2 1000 2000 3000 4000 5000 6000 7000 -50 -40 -30 -20 -10 0 10 20 30 40 50 Time (100:1) sec A lig n in g T o rq u e ( N .m )

(48)

41 | P a g e

Figure 3- 15 Lateral Force vs. Slip angle [5]

Figure (3-15) shows the range of the lateral force value related to the tyre slip angles, as a result of Test2, the front tyre slip angle is less than (1°) and the front tyre lateral force is between (±600 N). Comparing these values with figure (3-15) above, it gives a good result within the maximum range of lateral force. Figure (3-16) plots the relationship between lateral forces vs. slip angle of the front tyre.

Figure 3- 16 Lateral Force vs. Tyre Slip Angle (front Tyre)

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 -800 -600 -400 -200 0 200 400 600 800

Test 2: Lateral Force vs. Slip Angle

Slip angle (degree)

L a te ra l F o rc e ( N )

(49)

42 | P a g e Now, comparing the aligning torque result of the test2, figure (3-17) shows the range of the tyre aligning torque range related to the axle normal load and tyre slip angle.

Figure 3- 17 aligning torque vs. slip angle [5].

It is observed that the value of the aligning torque should not go over (50 N.m) after applying slip angle less than (1°). Figure (3-14) shows the maximum value of the aligning torque in test2 less than (50 N.m). Figure (3-18) plots the test2 aligning torque vs. tyre slip angle of the front tyre.

Figure 3- 18 aligning torque vs. slip angle

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 -50 -40 -30 -20 -10 0 10 20 30 40 50

Slip angle (degree)

A lig n in g T o rq u e ( N .m )

(50)

43 | P a g e

3.1.3 Test 3:

In this section, test three will be treated. Test tree will use the same as test one pedal situation (see figure 3-1). The tyre steering input will be standard double lane change. The vehicle path, lateral and longitudinal tyre forces will be discussed.

Figure (3-19) shows the tyre steering input signal (double lane change).

Figure 3- 19 Test 3: Tyre steering input signal.

The vehicle path is the first output state that will be plotted in this test. Figure(3-20) shows the vehicle path under this test situation.

Figure 3- 20 Test 3: Vehicle Path.

As shown in figure above, the vehicle follows a double lane change path. As the velocity is reduced and hard brake is applied, the vehicle could not come back to the same start path.

Next, figure (3-21) shows the tyres lateral forces under test three driving situation:

30 31 32 33 34 35 36 37 38

-20 -10 0 10

20 Double lane change

Time (sec)

controller/lane change1 : Group 1

0 100 200 300 400 500 600 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 X-Coordinate (m) Y -C o o rd in a te ( m )

(51)

44 | P a g e

Figure 3- 21 Test 3: Tyres Lateral Forces.

As shown in figure (2-21), the front tyre has higher lateral force (±800 N). This is because the front tyre is the steerable tyre where the steering signal is applied. The rear tyre has less lateral force (<±500 N) and more homogenous shape.

As the rear tyre is only the driven tyre in this model, the rear tyre generates all traction forces while driving. However, the front tyre freely rotates. Figure (3-22) shows the tyre longitudinal force:

Figure 3- 22 Test 3: Rear Tyre Longitudinal Force.

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 -800 -600 -400 -200 0 200 400 600 800 Time (100:1) sec T y re L a te ra l F o rc e ( N )

Test 3: Lateral Forces

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 Time (100:1) sec L o n g it u d in a l F o rc e ( N )

(52)

45 | P a g e Figure (3-22) shows the rear tyre longitudinal force. This value depends on the throttle position and push interval of the throttle pedal and depends also on the instant gear ratio. The longitudinal force in test3 has value of (-10<Fx<7 KN) which is traction force in positive value and braking force in negative value. Comparing this result with the testing data from Prof. Genta, figure (3-23) shows the different values of the traction forces related to normal load:

Figure 3- 23 Longitudinal Force vs. kappa (longitudinal slip). [5]

According to figure (3-23), the maximum value of longitudinal force under traction condition with normal force of (8000 N) is less than (10 KN) in traction side and less than (-8 KN) in braking side. As a result, test3 has longitudinal force with value of (6725 N) in traction side which is actually less than (10 KN), and test3 has (-9681 N) in braking side which is actually more than limit. This extreme braking value gives the rear tyre hard braking.

3.2 Validation and correction processes:

Many validation and correction processes were treated under this project, but only the important processes will be explained in this section. The most important correction process is the zero speed situations. Then, the acceleration correction, and finally the inverse gear ratio signal.

3.2.1 Zero Speed Correction:

While working on this project, the main problem is discovered in the lateral part. This problem means when the longitudinal velocity reaches zero value, the division process on this value will give an infinite number. This infinite value affects the model calculations and then gives illogical output status.

(53)

46 | P a g e The problem is shown in the tyre slip angle calculations (see figure (3-24) below), the model divides the lateral calculation on the longitudinal velocity:

Figure 3- 24 Tyre slip old model.

Figure (3-24) shows that the two product blocks are using the longitudinal velocity as dividing number. Therefore, simple solution is used to avoid this problem. The solution is assumed to be an exponential equation within a small range when the velocity reaches zero. Equation (3-1) shows the solution equation:

Equation (3-1)

That means the solution equation will be valid within the certain velocity value. In this model, the interval has value of (0-4) m/s. See the flow process below:

2 alfa2 1 alfa1 In2 Out1 Zero Problem1 Product1 Product b Gain1 a Gain 4 u 3 r 2 v 1 delta

(54)

47 | P a g e

Figure 3- 25 Velocity correction flow chart

As shown in figure (3-25), the process will be valid if only the longitudinal velocity have value between (0-4) m/s. Otherwise; the velocity will keep the original value. According to equation (3-1), the lowest output value will be about (2.2 m/s) and the maximum value is (4 m/s). Those two limits values can be modified by changing them in equation (3-1).

The result of the solution equation is shown in figure (3-26) below and the final model after correction shown in figure (3-27) below:

Figure 3- 26 Solution Equation.

0 0.5 1 1.5 2 2.5 3 3.5 4 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

Input Logitudinal Velocity (V_x0)

O u tp u t L o g it u d in a l V e lo c it y ( Vx )

(55)

48 | P a g e

Figure 3- 27 Corrected tyre slip calculation model

3.2.2 Acceleration Correction:

This correction process is applied on the longitudinal velocity estimation process. The longitudinal velocity is estimated by integrating the value of the longitudinal acceleration. The longitudinal acceleration is a calculated value which depends on the longitudinal force and the summation of the losses. The longitudinal acceleration has a positive value when the longitudinal force is positive and has negative value when the losses are great. The brake system generates an extreme value of the longitudinal resistance which is generating a negative longitudinal acceleration, and then negative velocity.

For instance, when throttle pedal is applied (pushed) after hard brake is applied (which means the driver wants to move after stop), the vehicle will start to accelerate from the last value of the deceleration. The vehicle will start to generate a positive acceleration from the last negative value of the longitudinal acceleration (-ax), which means the model will integrate the negative velocity and ascend till the positive velocity is reached. That gives a growing velocity from negative region to zero and then to the positive part. See figure (3-28):

2 alfa2 1 alfa1 In2 Out1 Zero Problem1 Product1 Product b Gain1 a Gain 4 u 3 r 2 v 1 delta

(56)

49 | P a g e

Figure 3- 28 illustrating of the velocity growing.

Figure (3-28) illustrates the longitudinal velocity growing from the negative part to the positive part. That means the vehicle does not move when the velocity is in negative part. Then the vehicle has to wait till its velocity becomes positive. This leads to a delay time in the throttle pedal to the vehicle reaction (the vehicle will move after some second of throttle pedal is pushed). To avoid this delay, simple model is created to shift the longitudinal acceleration to zero when the velocity is negative, which makes the vehicle ready to generate the positive velocity after throttle pedal is pushed. Figure (3-27) shows the throttle and brake pedals together.

-6 -4 -2 0 2 4 6 1 2 3 4 5 6 7 8 9 10 11 Positive Velocity Negative Velocity 0 10 20 30 40 50 60 70 80 90 100 0 0.2 0.4 0.6 0.8 1 Throttle Pedal Time (sec) controller/Gear Shift3 : Group 1

(57)

50 | P a g e

Figure 3- 29 Throttle and Brake pedals

Figure (3-29) shows both throttle and brake pedals which are related to the time. The throttle pedal is pushed from (0-30 sec) and then the brake is applied till it is reached the (80%) at (55 sec). After (2 sec) delay, the throttle pedal is increased smoothly till it is completely pushed at (70 sec). Figure (3-30) shows the small model that is designed to avoid the delay in the velocity related to the throttle pedal action.

Figure 3- 30 Acceleration Correction Subsystem.

The result of this subsystem is observed in figure (3-31). The value of the longitudinal acceleration jumps to zero (less than zero if it is air resistance) when the vehicle velocity reaches zero.

Figure (3-31) below, shows the longitudinal acceleration and velocity related to time. It is shown that the acceleration is moving from (-7 m/s2) to almost zero at time of (55 sec). Then after 2 seconds, the throttle pedal is pushed (as shown in figure 2-27), where the positive acceleration is generated and velocity is integrated. As a result, the delay behavior of pushing the throttle pedal to the velocity integrated is decreased. 0 10 20 30 40 50 60 70 80 90 100 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Brake Pedal Time (sec) controller/Gear Shift2 : Group 1

1 New_ax Merge Merge else { } In1 Out1 if { } Out1 u1 if (u1 ==0) else If 2 ax 1 Vx_gps

(58)

51 | P a g e

Figure 3- 31 longitudinal velocity and acceleration after the correction.

3.2.3 Reverse Gear Correction:

In this section, the inverse gear ratio model will be discussed. The design of gearbox system is based on BMW E90 320i gearbox properties. The gear box has six gear steps with one reverse step. The reverse step is assumed to have a gear ratio equal to the first gear ratio in opposite direction (see equation 1-5). According to Matlab, the magnitude of longitudinal velocity has a range, designed from (0) to (inf) value. This designed value refers to the velocity magnitude only. In reverse gear

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 0 50 100 150 200 250

Sample Time Ts (100:1 sec)

L o n g it u d in a l V e lo c it y ( k m /h ) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 -8 -6 -4 -2 0 2 4 6

Sample Time Ts (100:1 sec)

L o n g it u d in a l a c c e le ra ti o n ( m /s e c 2) mu=0.9

(59)

52 | P a g e ratio, the velocity has same value of the normal first gear ratio but in different direction. To solve this, sign block is added to the transmission system. This sign block will sense the velocity direction and transfer it to the output system.

Figure 3- 32 Inverse Gear Sign

Figure (3-32) shows the sign block is pasted on gearbox output signal. By applying following test signals:

Figure 3- 33 Input signals (Inverse gear test)

Figure (3-34) shows the magnitude of longitudinal velocity of this test, where the next figure (3-35) shows the magnitude and direction of this status after applying the transmission sign block:

GearBox Properties of BMW E90 320i

2 Trans_sign 1 i_ratio Sign Product 0 *, 1 Multiport Switch

Gear Joy stic i_out

Manual Ratio man

Constant

Gear Joy stick i_out

Automatic Ratio Calculator 1 Gear stick -1 0 1 Brake Pedal

controller/Signal Builder : Group 1

0 0.5 1 Throttle Pedal -1 -0.5 0 Gear Stick 0 0.5 1 Clutch Pedal 0 5 10 15 20 25 -1 0 1 HandBrake Time (sec)

(60)

53 | P a g e

Figure 3- 34 Longitudinal Velocity Magnitude

Figure 3- 35 Longitudinal Velocity (Magnitude and Direction)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (100:1) sec V e lo c it y ( m /s )

Longitudinal Velocity Magnitude

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 -5 -4 -3 -2 -1 0 1 Time (100:1) sec V e lo c it y ( m /s )

(61)

54 | P a g e

Result and Recommendations:

Firstly, the complete bicycle model has been modeled. The model of the longitudinal system is modeled based on simplified equations of the components. The lateral system and longitudinal system have been linked via tyre part. The velocity and acceleration status have been estimated based on equation of motion.

The inputs and outputs of the model are designed based on the GreenDino driving simulator machine interface, for which the model has been built using Matlab-Simulink platform.

Several test processes are done on individual systems. These individual test processes are done after the systems or subsystems have been modeled. The complete model system is tested by assuming simple driving situation. The test inputs were based on the GreenDino driving simulator interface. The test results data were compared with the real vehicle test data from the study book [5]. According to the study book data, the test results were realistic and close to the real data.

The project faced several challenges. Those challenges have been treated carefully, and some of the treating processes are explained in chapter three.

As a result and according to the project goal, the GreenDino driving simulator machine could run under HAN bicycle model.

Secondly, as mentioned in this report, the model has been made based on bicycle model approach. The longitudinal system has many vehicle components which are simplified. Because of the simplified components, the model is missing some real behavior. Therefore, the recommendations are:

1. Validate the complete model under GreenDino driving simulator machine. The validation process should done by running (driving) the simulator machine based on HAN bicycle model.

2. Modify the model based on the validation result.

The Complete Model of the Vehicle Bicycle Approach For The Driving Simulator Machine