Guideline for Vehicle Simulation using MATLAB

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A supplementary document for vehicle dynamics course taught at the Mechanical Engineering, Mahidol University.

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• Page | 1

Supplementary Document for Longitudinal Dynamics

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

1) Simulation Model Simulink Model 1. Engine Map Torque

RPM 2. 3.

i. ii.

iii. iv.

2) Simulation Model

Vehicle: CG height (inch): 20 Wheelbase(inch): 109 Fore/Aft (CG) (inch): 39/70 Mass (lb): 2500 Engine: Inertia (in-lb-sec2): 0.8 RPM/Torque (ft-lb): 800 120 2400 175 4000 200 1200 132 2800 181 4400 201 1600 145 3200 190 4800 198 2000 160 3600 198 2500 180 Transmission Data Gear 1 2 3 4 5 Inertia (in-lb-sec2) 1.3 0.9 0.7 0.5 0.3 Ratio 4.28 2.79 1.83 1.36 1.00 Efficiency 0.966 0.967 0.972 0.973 0.970 Final Drive Data Inertia (in-lb-sec2): 1.2 Ratio: 2.92 Efficiency: 0.99 Wheel Data

Inertia(in-lb-sec2): 11.0 (Drive and Non-Drive) Size (radius-in): 12.59

2.1) Simulation Model

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

2.1)1. (1 ) 2.1)2. (1 ) 2.1)3. (1 )

2.2) 2.1)3. 2- 5 (4 ) Max Tractive Force max Note: Simulate 10 Max Tractive Force

2.3) (1 ) 2.4) (1 ) 2.5) m-file

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle Guideline to construct Simulink simulation model to describe the longitudinal dynamic

of a vehicle

1.

( )( ) aINNINIrg

WWRRRTrNN

etfsfwharetf

t

+++=

22

2

1sin (1)

(1) aMWRRRF eharx = sin (2)

etftx TrNN

F

=

WKR rr = 2

21 VACR da =

( )( ) +++= etfsfwe INNINIrgWM 2221 Block Diagram 2. Simulink Simulation Diagram ( EGME 309: Lab3)

Block Diagram (1) Simulink simulation diagram Simulink simulation diagram 2 1. EGME 309

Mechanical Engineering Laboratory III Tutorials Website

eM1 x Fx

Rr

Ra

v a

Wsin -

--

+

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

3. Simulink Simulation Diagram Click Icon New Diagram

Open New Diagram

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

4. Block diagram (1) Simulation diagram Sum (Drag Sum Math Operation Drop Blank Diagram) Sum (2) (Double Click Sum (2) 4 )

5. (2) Output Sum 1/M Gain Diagram (Drag Gain Math Operation Drop Blank Diagram) 1/M (Double Click Gain )

Double Clicks Sum + - - -

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

6. Integrator Diagram (Drag Integrator Continuous Drop Blank Diagram) Integrator

Double Clicks Gain 1/M

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

7. Input ( (2))

1) Engine Map

Engine Map (2) Engine: RPM/Torque (ft-lb):

800 120 2400 175 4000 200 1200 132 2800 181 4400 201 1600 145 3200 190 4800 198 2000 160 3600 198 2500 180

?

Final Drive

( ) WheeltfEnginewheeltire

CarCar NNr

VV == (3) VCar Integrate (2)

(RPM)

Engine Map (Torque vs. RPM)

etf

t TrNN

Fx ( (2))

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

- Lookup Table Diagram (Drag Lookup Table Lookup Tables Drop Blank Diagram) Double Click () Vector of input values: () 1: [800 1200 1600 2000 2400 2800 3200 3600 4000 4400 4800 5200] 2: [800:400:5200] Vector of output values: [120 132 145 160 175 181 190 198 200 201 198 180]

- Gain Math Operation 2 Fx o )*2*/()60**( pirNN tf

o rNNEff tf /***12

- Diagram

Double Clicks

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

Lookup Table

1s

Integrator1

1s

Integrator

12*Eff*Nf*Nt/r

Gain4

Nf*Nt*60/(r*2*pi)

Gain3

1/M

Gain

Note: Diagram MSWord Edit Click Copy Model to Clipboard Paste MSWord Document

8. Input ( (2))

(2) Curb Weight () ( Class Notes)

: fsrrf WKR = (4) : rsrrr WKR = (5)

- Constant 2 (1 ) Sources Wfs Wrs

- Gain Math Operation 2 Gain Kr

- Sum Math Operation Sum 2 (2)

- Diagram

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

Lookup Table

1s

Integrator1

1s

Integrator

12*Eff*Nf*Nt/r

Gain4

Nf*Nt*60/(r*2*pi)

Gain3

Kr

Gain2

Kr

Gain1

1/M

Gain

Wrs

Constant1

Wfs

Constant

9. Input ( (2)) (2)

2

21 VACR da =

Fcn Function User-Defined Functions Diagram (Double Click Fcn )

- input u - Sin(X) X input sin(u) - u input V

( rho = ) 0.5*rho*A*Cd*u*u

Double Clicks Default 0.5*rho*A*Cd*u*u

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

- Diagram

Lookup Table

1s

Integrator1

1s

Integrator

12*Eff*Nf*Nt/r

Gain4

Nf*Nt*60/(r*2*pi)

Gain3

Kr

Gain2

Kr

Gain1

1/M

Gain

0.5*rho*A*Cd*u*u

Fcn

Wrs

Constant1

Wfs

Constant

10. Input ( (2))

Rh Constant 1 Sources Rh Diagram

Lookup Table

1s

Integrator1

1s

Integrator

Eff*Nf*Nt/r

Gain4

Nf*Nt/r

Gain3

Kr

Gain2

Kr

Gain1

1/M

Gain

0.5*rho*A*Cd*u*u

Fcn

Rh

Constant2

Wrs

Constant1

Wfs

Constant

11. Integrate Diagram

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

Lookup Table

1s

Integrator1

1s

Integrator

Eff*Nf*Nt/r

Gain4

Nf*Nt/r

Gain3

Kr

Gain2

Kr

Gain1

1/M

Gain

0.5*rho*A*Cd*u*u

Fcn

Rh

Constant2

Wrs

Constant1

Wfs

Constant

12. Clock Step (Drag Clock Step Source Drop Blank Diagram)

13. To Workspace (Drag To Workspace Sink Drop Blank Diagram) x v Fx time : To Workspace Structure () Structure Array (Double Click To Workspace Save Format)

14. (2) 15.

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

Fx

To Workspace3

time

To Workspace2

v

To Workspace1

x

To Workspace

Lookup Table

1s

Integrator1

1s

Integrator

12*Eff*Nf*Nt/r

Gain4

Nf*Nt*60/(r*2*pi)

Gain3

Kr

Gain2

Kr

Gain1

1/M

Gain

0.5*rho*A*Cd*u*u

Fcn

Rh

Constant2

Wrs

Constant1

Wfs

Constant

Clock

16. Save ! XXX.mdl Simulink Simulation Model

17. m-file Simulate : mfile %

%Vehicle: G = 386 %Gravity (in/sec2) CGh = 20; %CG Hight (inch) Wbase = 109; %Wheel Base (inch) FCG = 39; %Position of CG measured from the front axle (inch) ACG = 70; %Position of CG measured from the rear axle (inch) Mv = 2500; %Vehicle Mass (lb) Wfs = M*ACG/Wbase; % Front Axle Curb Weight (lb) Wrs = M*FCG/Wbase; % Rear Axle Curb Weight (lb)

% Engine Ie = 0.8; %Engine Inertia (in-lb-sec2)

% Transmission It = 1.3; %Inertia (in-lb-sec2)

Nt = 4.28; %1st Gear Ratio EffG = 0.966; %Gear Efficiency

% Final Drive EffF = 0.99; %Efficiency of the Final Drive

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

Nf = 2.92; %Final Drive Gear Ration Is = 1.2; %Inertia (in-lb-sec2) Eff = EffF*EffG; %Overall Efficiency

% Wheel Data

Iw = 11.0; %Inertia (in-lb-sec2) r = 12.59 %Tire Radius (inch) Kr = 0; %Coefficient of Rolling Resistant

% Other Resistant

Rh = 0;

% Effective Mass M = (Mv/G) + (Ie+It)*(Nt*Nf)^2 + Is*Nf^2 + Iw;

18. Save ! XXX.m

m-file Model 19. load parameters m-file Command Window MATLAB (

.m) F5 m-file 20. Play Simulation Diagram 21. plot MATLAB Command Window

>>plot(time,v),grid - (grid ) - MSWord Edit

Click Copy Figure Paste MSWord Document

0 1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

600

700

800

900

1000

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

- (....)

>> title('Simulation Response showing Vehicle Velocity in inch/sec') >> ylabel('Velocity (inch/sec)') >> xlabel('Time (second)')

0 1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

600

700

800

900

1000Simulation Response showing Vehicle Velocity in inch/sec

Vel

ocity

(inc

h/se

c)

Time (second)

22. plot plot MATLAB Command Window >>plot(time,v,k:,time,Fx,r),grid

0 1 2 3 4 5 6 7 8 9 100

500

1000

1500

2000

2500

• Supplementary Notes I Computer Simulation EGME 353 Mechanics of Vehicle

- plot >> help plot plot plot time v ( k) ( : ) time Fx ( r) ( -- ) help plot

- () >> plot(time,v,'k:',time,Fx,'r--'),grid >> title('Simulation Response showing Velocity and Tractive Force') >> xlabel('Time (second)') >> legend('Velocity','Tractive Force')

0 1 2 3 4 5 6 7 8 9 100

500

1000

1500

2000

2500Simulation Response showing Velocity and Tractive Force

Time (second)

VelocityTractive Force