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To further improve this work the inclusion of other vehicle’s components is the task at hand.

Several other suspension parts could be implemented with the use of FEA, be it via an interface between Matlab and a FEA software, as ANSYS for example, or even by previously performing the simulations and by mapping the displacements that arise from several load cases. The use of a previously built map of displacements could be the best choice but only if the superposition of results was validated via a combined load condition. If this superposition of results was valid, relevant savings in simulation time could be achieved. The other way would involve a FEA software setup for each added component and the inclusion of a bridge between the vehicle model simulation and the FEA analysis.

The chassis behavior could also be included in a simpler way. By having the stiffness of every suspension pickup point and with the loads in the suspension links, the compliance of the chassis could be directly introduced in the three-point method described in this work.

The methods used for the calculation of suspension links compliance could also be revised and the work done in (Ferreira 2013) to model the bonded joint with finite elements could be used.

If opportunity exists for K & C testing of the FST 05e, validation of the modeled compliant components could be achieved. This testing, as stated earlier is very expensive and other ways to validate the models may be investigated.

The instrumentation of the FST 05e with strain gauges in the suspension links, could give an insight to the forces present and also the compliance of each link.

Finally the tire model may be revised to introduce more parameters with the first target being the influence of the inclination angle in the longitudinal force to check the difference in the acceleration times. The equations for this model were used in (Neves 2012) but not in this work.

81

8 REFERENCES

Adams, R. D., J. Comyn and W. C. Wake (1996). Structural Adhesive Joints in Engineering.

Antona, J. F. d. Development of a full vehicle dynamic model of a passenger car using ADAMS/Car, Oxford Brookes University.

Beer, F. P., E. R. Johnston and W. E. Clausen (2006). Mecânica Vectorial para Engenheiros:

Dinâmica.

Beer, F. P., E. R. J. Jr., J. DeWolf and D. Mazurek (2011). Mechanics of Materials.

Blundel, M. and D. Harty (2004). Multibody Systems Approach to Vehicle Dynamics.

Ferreira, R. N. C. (2013). Analysis of Different Types of Chassis for Formula Student.

Fischer, E. (2001). ADAMS/Car-AT in The Chassis Development at BMW.

Holdmann, P., P. Köhn, B. Möller and R. Willems (1998). Suspension Kinematics and Compliance - Measuring and Simulation. S. t. papers.

Jazar, R. N. (2008). Vehicle Dynamics: Theory and Applications.

Kasprzak, J. Understanding your Dampers: A guide from Jim Kasprzak. Kaz Technologies website:

25.

McGuan, S. P. and S. Pintar (1994). Flexible Vehicle Simulation or Modeling Vehicle Suspension Compliance at Ford Motor Co. Using a Copuling of ADAMS and MSC/NASTRAN.

Milliken, W. F. and D. L. Milliken (1995). Race Car Vehicle Dynamics.

Morse, P. (2004). Using K&C Measurements for Practical Suspension Tuning and Development. S. T.

Papers.

Neves, T. V. (2012). Numerical Model for Dynamic Handling of Competition Vehicles. Masters in Mechanical Engineering, Universidade Técnica de Lisboa.

Pacejka, H. B. (2005). Tyre and Vehicle Dynamics.

Reddy, J. N. (1997). Mechanics of laminated composite plates and shell - Theory and Analysis.

SAE (2008). Vehicle Dynamics Terminology - J670: 73.

Valverde, N. M. P. d. A. (2007). Aplicabilildade de materiais compósitos em transmissões de protótipos FSAE/Formula Student.

Wale, D. V. (2009). Modelling and Simulation of Full Vehicle for Analysing Kinematics and Compliance Characteristics of Independent (Macpherson strut) and Semi Independent (Twist Beam ) suspension system. Second International Conference on Emerging Trends in Engineering (SICETE).

82

APPENDIX A – MAGIC FORMULA EQUATIONS

The equations used in this work to fit the tire experimental data were adapted from (Pacejka 2005) and the final set of implemented equations will also be presented next.

The equations have some minor simplifications and the majority of the scaling factors are set equal to one. The only factor used that has a value different from one is λµx,y and this is only for purposes of vehicle simulations. For tire modelling, one is used.

First, the lateral slip is defined to account for the case of large slip angles:

* tan(SA)

 (A.1)

For the spin due to camber angle the following is also introduced:

* sin( )

IAIA (A.2)

The normalized change in vertical load is presented next:

z zo

z

zo

F F

df F

  (A.3)

Longitudinal Force (pure longitudinal slip):

1 2

( )

Vx z Vx Vx z

SFppdf (A.4)

1 2

( )

Hx Hx Hx z

Sppdf (A.5)

1 2 3

( ) exp( )

x z Kx Kx z Kx z

KFppdfpdf (A.6)

 

1 2

( ) 0

x pDx pDx dfz x

   

 (A.7)

  0

x x z

D

F  (A.8)

 

1

0

x cx

Cp  (A.9)

x x

x x

B K

C D

(A.10)

x SL SHx

  (A.11)

1 2 3 2

1 4 sgn( )

 

1

x Ex Ex z Ex z Ex x

Eppdfpdf  p    (A.12)

 

 

sin arctan arctan( )

xo x x x x x x x x x Vx

FD C B E B  B S (A.13)

Lateral Force (pure side slip):

( 1 2 ) ( 3 4 ) *

Vy z Vy Vy z Vy Vy z

SFppdfppdfIA (A.14)

*

1 2 3

( )

Hy Hy Hy z Hy

SppdfpIA (A.15)

83

1

2

sin 2 arctan

z

y o Ky zo

Ky zo

K p F F

p F

  

       (A.16)

1

3 *2

y y o Ky

K K  pIA (A.17)

*2

 

1 2 3

( ) 1 0

y pDy pDy dfz pDy IA y

      

 (A.18)

y y z

D  F (A.19)

 

1

0

y cy

Cp  (A.20)

y y

y y

B K

C D

(A.21)

*

y SHy

 (A.22)

1 2

  1

3 2 *

sgn( )  1

y Ey Ey z Ey Ey y

Eppdf   ppIA

 (A.23)

 

 

sin arctan arctan( )

yo y y y y y y y y y Vy

FD C B

E B

B

S (A.24)

Longitudinal Force (Combined Slip):

1

Hx Hx

S r (A.25)

 

1 2

1

x Ex Ex z

Errdf  (A.26)

1

x Cx

Cr (A.27)

   

1cos arctan 2 0

x Bx Bx

Br  r    (A.28)

*

S SHx

   (A.29)

 

 

cos arctan arctan( )

x o x x Hx x x Hx x Hx

G  C B S E B S B S  (A.30)

 

 

cos arctan arctan( )

x x S x x S x S ( 0)

x

x o

C B E B B

G G

  

   

 

  (A.31)

x x xo

FGF (A.32)

Lateral Force (Combined Slip):

1 1

Hy Hy Hy z

S rrdf (A.33)

* *

1 2 3 3

( ) cos arctan( )

Vy y z Vy Vy z Vy Vy

D  Frr dfr IA   r   (A.34)

5 6

sin arctan( )

Vy Vy Vy Vy

S D r r   (A.35)

 

1 2

1

y Ey Ey z

Errdf  (A.36)

84

1

y Cy

C r (A.37)

*

 

1

cos arctan

2

(

3

) 0

y By By By

Br r

r   (A.38)

S SL SHy

   (A.39)

 

 

cos arctan arctan( )

y o y y Hy y y Hy y Hy

G  C B S E B S B S  (A.40)

 

 

cos arctan arctan( )

( 0)

y y S y y S y S

y

y o

C B E B B

G G

  

   

 

  (A.41)

y y yo Vy

FGFS (A.42)

Aligning Torque (pure side slip):

Vy

Hf Hy

y

S S S

K

  (A.43)

*

t SHt

   (A.44)

10

r Bz y y

Bq B C (A.45)

r

1

C  (A.46)

6 7

 

8 9

*

r z wheel Dz Dz z Dz Dz z y

DF R  qq dfqq dfIA  (A.47)

 

cos arctan[ ]

zro r r r r

MD C B

(A.48)

*

1 2 ( 3 4 )

Ht Hz Hz z Hz Hz z

Sqq dfqq dfIA (A.49)

*

r SHf

 (A.50)

Bz1 Bz2 z Bz2 z2

  1

Bz4 * Bz2 *

t

y

q q df q df q IA q IA

B

    

 (A.51)

1

( 0)

t Cz

Cq  (A.52)

1 2

( )

wheel

to z Dz Dz z

zo

D F R q q df

F

 

    (A.53)

1

3 * 3 *2

t to Dz Dz

DD  qIAqIA (A.54)

1 2 3 2

1

4 5 *

2 arctan

( 1)

t Ez Ez z Ez z Ez Ez t t t

E q q df q df q q IA B C

 

          (A.55)

 

 

cos arctan arctan( )

o t t t t t t t t t

tD C B E B  B  (A.56)

'z0 o yo

M   t F (A.57)

zo 'zo zro

MMM (A.58)

85

APPENDIX B – EQUIVALENT LAMINATE PROPERTIES

The carbon fiber tubes used in the FST 05e are purchased from Easy Composites. The fiber layup and the properties of the fiber and matrix used are known.

Besides being known as a CFRP tube, it also uses glass fiber together with carbon fiber. The tubes in this category are roll-wrapped pre-preg made.

The layup of the tube is as follows:

[ 0 90 0 90 0]

The fibers at 0 degrees are oriented parallel to the longitudinal axis of the tube and the 90 degrees fibers are oriented parallel to the radial direction of the tube.

At 0 degrees, carbon fiber from Toray is used: 300 gsm Toray T700. At 90 degrees, the reinforcement of glass fibers is used: 300 gsm E-glass.

The carbon fiber pre-preg is unidirectional and the glass fiber pre-preg can also be considered unidirectional.

To calculate the equivalent modulus of elasticity in the longitudinal direction, micro- mechanics and classic laminate theory are used.

To start one can approximate the thickness of each fiber layer by dividing the total thickness of the tube by the number of layers:

tube layer

layers

h h

n (B.1)

To calculate the fiber and matrix volume fraction in the layer the following equation is used, where g symbolizes the weight per area of the fiber and the density is represented as ρfiber.

1

f

fiber layer

m f

V g

h

V V

 



  

(B.2)

These volume fractions will be used to compute the rule of mixtures and obtain the elastic properties of the layer by knowing the properties of the matrix and fiber in the following way:

L m m f f

EE VE V (B.3)

LT Vm m Vf f

(B.4)

1 m f

T m f

V V

EEE (B.5)

86

1 m f

LT m f

V V

GGG (B.6)

LT TL

L T

E E

(B.7)

The elasticity matrix in the fiber coordinate system is then computed as:

   

   

1 1 0

1 1 0

0 0

L LT T

LT TL LT TL

L L

TL L T

T T

LT TL LT TL

LT LT

LT

E E

E E

G

   

 

  

   

 

 

   

 

   

 

   

      

    

    

 

 

(B.8)

In a laminate, every layer is not usually with the same orientation, so a transformation to the above properties must be made to obtain the said properties in the laminate coordinate system. In the following, ξ, symbolizes the angle at which the layer is oriented with respect to the laminate coordinate system.

2 2

2 2

2 2

2 2

c s cs

R s c cs

cs cs c s

  

 

  

   

 

(B.9)

cos sin

c

s

 

  (B.10)

The equations (B.9) and(B.8) are combined in the following way:

   

   

1

1 1 0

1 0 0

0 0 1 0

1 1

0 0 2

0 0

L LT T

LT TL LT TL

X X

TL L T

Y Y

LT TL LT TL

XY XY

LT

E E

E E

R R

G

   

 

  

   

 

 

   

 

     

 

     

         

       

      

 

 

(B.11)

This results in the following matrix:

87

   

   

1

1 1 0

1 0 0

0 0 1 0

1 1

0 0 2

0 0

L LT T

LT TL LT TL

TL L T

LT TL LT TL

LT

E E

E E

K R R

G

   

   

 

   

   

   

       

 

 

(B.12)

To compute the final stiffness matrix of the laminate one needs to assemble the several stiffness matrixes from the several layers present. This is done by writing the constitutive equations of the laminate. Since the only objective is to obtain the extensional properties of the laminate and since the laminate is symmetric one only needs to write the constitutive relations for a tensile force:

0

11 12 13

0

21 22 23

0

31 32 33

X X

Y Y

XY XY

N A A A

N A A A

N A A A

 

   

 

   

    

    

     

(B.13)

The A matrix is obtained with the knowledge of the components of matrix K:

1

layers

n

ij ij layer ji

t

A K h A

(B.14)

To obtain the final stiffness matrix the following is done:

tube

A A

h (B.15)

The stiffness variable that is used in this work is then obtained:

CFRP axial 11

E A (B.16)

88

APPENDIX C – FORMULA STUDENT RESULTS

Figure C.1 – Acceleration Results from Formula Student Electric 2012

Figure C.2 – Skid Pad results from Formula Student 2013 competition in the UK

89

APPENDIX D – MATLAB / SIMULINK DIAGRAMS

Signal 1 Group 1

Throttle Pedal

Signal 1Group 1 Steering Wheel Steering_wheel

Steering Displacements

Twist Angle Steer

Steering Mechanism vy

vx w Steer Slip angle

vi

Vehicle and Wheel Angles

Steer Vertical Displacements L_rods IA

IA calculator Throttle

Brake w vx

Torque available

Torque to wheels

Motor / Brake System

SA Torque to wheels vi Torque f rom Fx FZ

SL_raw

Wheels Angular Velocity

Wheel Rotational Dynamics

FZ SL_raw Torque to Wheels SA IA

Fx Fy Mz

Tire Dynamics

Steer

Mz

Fy

Fx

Vertical Displacements w vy vx v Torque f rom Fx FZ FX FY MZ Vehicle Dynamics Signal 1

Group 1

Brake Pedal

FZ

FX

FY

MZ

F_rods_FR

F_rods_FL

F_rods_RR

F_rods_RL

F_steering_rods Force Calculator

F_rods_FR

F_rods_FL

F_rods_RR

F_rods_RL

F_steering_rods

L_rods

Steering Displacements

Twist angle

Compliance Calculator Memory

Memory1

Memory2

Memory3 1

Zero 2 1

Zero 1

Memory4 0

Zero 2 Signal 1 Group 1

Throttle Pedal1

FY

w

FX

vy

DOWNFORCE

DRAG

vx ay

dvy

FZ

dvx

z

9DOF

steer

Fy

Fx FY

FX fcn

Fy/Fx -> FY/FX [a;a;-b;-b]

Gain

Sum of Elements 1/76

Gain1 1

s Integrator3 Yaw Velocity

Yaw Acceleration

1 s Integrator4 Yaw Position

yaw.mat To File1

[tf/2;-tf/2;tr/2;-tr/2]

Gain2 1

s Integrator Lateral Velocity

1/9.81 Gravity3 Lateral Acceleration

dvy

1 Steer

3 Fy

4 Fx

7 FZ

1 Vertical Displacements Linear Acceleration

1/9.81 Gravity

1 s Integrator1

u2 Velocity squared

0.91 Drag Coefficient

-2.12

Lift Coefficient Linear Velocity

3.6 m/s -> km/h

2 3 w

vy

4 vx

r Wheel radius

Torque from FX 6

Torque from Fx

yaw vx vy

VX fcn VY Visual Preparation

1 s Integrator6

1 s Integrator7

X.mat To File5

Y.mat To File6 u2

vx squared u2

vy squared

sqrt(u) Fcn

5 v

Yaw moment from FX Yaw moment from FY

Yaw moment

8 FX 9 FY

2 Mz Yaw moment from Mz

10 MZ Ay.mat

Lateral Acceleration to file - Ay

vy.mat Lateral Velocity to file - vy

vx.mat Longitudinal Velocity to file - vx

Ax.mat Longitudinal Acceleration to file - Ax

Yaw_m.mat Yaw Moment to file - Yaw_m Yaw_a.mat

YawAcc to file - Yaw_a Yaw_v.mat

Yaw vel to file - Yaw_v

FZ.mat FZ to file - FZ

Velocity

XY Graph X position

Product7

1/9.81 Gravity1 Radial Acceleration

u2 vx squared1 Divide1

Path Radius

v.mat Tangential Velocity to file - v ar.mat

Radial Acceleration to file - ar

R.mat Path Radius to file - R

Vehicle Dynamics Block

Vertical Force on tire Applied Forces

Matrix Multiply Product2

Matrix Multiply Product3

Matrix Multiply Product4

Product5

-K- Gain2 -1

Constant1

-Kt/1000 Constant2 C

Damping Ax

FX Az Ay FY

FORCES fcn

MATLAB Function

Minv Mass - Inverse

K Stiffness

Displacements Velocity Plot

Add

1 s Position 1

s Velocity

-502.3 -241.4 -591.4 -24.48 -466.6 -306.8 -602.8 -25.66 993.3 Display

-44.53 -6.85 -24.3 -1.224 -36.63 -7.141 -16.26 -1.187 1.021

Display1

1153 206.1 1202 199.9 Display2 3

FX

Sum of

Elements m

Mass

Divide

4 dvx

3 FZ 6

DRAG

5 DOWNFORCE

Divide1 m*9.81

Mass1

1 FY

Sum of Elements1 Divide2

m Mass2

2 dvy

7 vx 2

w

Product6

1 ay 4

vy

Product7

5 z

z_nom.mat To File 1

Gain

1/9.81 Gain3

1/9.81 Gain1

Vibrational Model Block

Iy_roda Wheel Inertia

Divide

Divide1 Subtract

Total Torque

Subtract1 1

Constant ~= 0

Switch2

[0;0;0;0]

SR for v = 0 T

Angular Acc - raw

v

FZ

w

Angular Acceleration and Velocity Product1

2 Torque to wheels 4 Torque from Fx

5 FZ

1

SA 1

SL_raw

3 vi

f(u) COS(SA)

2 Wheels Angular Velocity Wheels Velocity - angular

Velocity of wheels in the body CS x-y

SL raw plot

~= 0 Switch1 r

Wheel radius 1

Product2

wi.mat

Wheel Angular Velocity to file - wi

1/r Wheel radius 2

SL raw plot1

Wheel Dynamics Block

Product

Torque from the motors to the wheels

w

E_T_W E_T_M w_M fcn

MOTOR 21

Gear Ratio Motor Torque

Motor Speed

> 0

Switch Brake/Throttle >= 0

Switch1 [0 0 0 0]

Brakes if v = 0 4

vx

1 Throttle

3 w

2 Torque to wheels

1 Torque available Throttle Pedal

T_to_wheels.mat Torque to wheels to file - T_to_wheel Pedal_in.mat

Pedal input to file - Pedal_input

Memory1 2

Brake

F_Brake_Pedal T

fcn Brake System

Motor/Brake System

Steering Input Steering Displacements - Right Steering Displacements - Lef t Steering Right

Steering Lef t

Steering Mechanism

Steering_wheel Twist_angle Rack_d

fcn Rack Displacement

0 Rear Right Steering

0 Rear Left Steering ROT_FR

ROT_FL

ROT_RR

ROT_RL steer

fcn

Rotation matrix to steering angle

Steering wheel input

1 Steering_wheel

1 Steer

Wheels Steering

2 Steering Displacements 1

1 Gain Gain1 delta.mat

Steer to file - delta

delta_in.mat Steering input to file - delta_in

3 Twist Angle

~= 0

Switch1

[0 0 0 0]

Steering if steering wheel = 0

Steering Model

vy vx w xi yi

B

Bi

vi fcn

Sideslip angle calculation [a;a;-b;-b]

x Positions

[-tf/2;tf/2;-tr/2;tr/2]

y Positions x_positions.mat

To File3

y_positions.mat To File4

Subtract2 1

vy

2 vx

3 w

4 Steer

1 Slip angle Sideslip angle

2 vi

Slip angles B.mat

Sideslip to file - B SA.mat

Slip angles to file - SA

> 0

Switch1

[0 0 0 0]

SA if v = 0

Wheel Angles

Steer z L_rods up_f

Camber_nom KPI_nom Caster_nom z_NOM up_r

IA

fcn

IA calculation

up_f

Front Upright

Camber_nom

Camber_nom

z_NOM

Nominal Positions

KPI_nom

KPI_nom

Caster_nom

Caster_nom

up_r

Rear Upright

1

Steer

2

Vertical Displacements

1

IA IA plot

3

L_rods

IA.mat

IA to file - IA Inclination Angle Block

T SL_raw FZ SA IA COEFSXX COEFSXY COEFSYY COEFSYX COEFSMZY

Fx

Fy

Mz

SL fcn

P2002XY COEFSX

COEFSX COEFSXY

COEFSXY

Longitudinal Slip

T FX SL

FX_ef fcn Limit FX

Longitudinal Force - Raw

COEFSYY

COEFSYY COEFSYX

COEFSYY 3

Torque to Wheels 2

SL_raw 1

FZ 4

SA

1 Fx

2 5 Fy

IA

Lateral Force

Longitudinal Force

Self-Aligning Torque

COEFSMZY COEFSMZY

3 Mz

Fx.mat Fx to file - Fx Fy.mat

Fy to file - Fy

Mz.mat Mz to file - Mz

SL.mat SL to file - SL

Tire Model

2 FX

3 FY

1 FZ

[1;1;1]

Gain

[1;1;1]

Gain1

[1;1;1]

Gain2

[1;1;1]

Gain3

CG

CS4

CS6

CS9 CS1

CS7

CS2

CS8

CS3

CS5

Front Left Upright Ground

Env Machine Environment

B F

Spherical Ground1

Ground2

B F

Spherical3

Ground3

Ground4

Ground5

CS1 CS2

Tie-Rod

B F

Spherical7

B F Spherical1

B F Spherical4 Body Actuator

FLUF Sensor

CS1 CS2

Pullrod

B F

Spherical6 Ground6

B F

Six-DoF

CS1CS2

FL Upper A-Arm Front

B F

Spherical2

CS1CS2

FL Upper A-Arm Rear B

F Spherical5

CS1CS2

FL Bottom A-Arm Rear

CS1CS2

FL Bottom A-Arm Front

B F

Spherical8

B F

Spherical9

B F Spherical10

B F

Spherical11

FLUR Sensor

FLBF Sensor

FLBR Sensor

CG

CS4

CS6

CS9 CS1

CS7

CS2

CS8

CS3

CS5

Front Right Upright

Ground7 Env Machine Environment1

Body Actuator1 B

F Spherical12 Ground8

Ground9

B F

Spherical17 Ground10

Ground11

Ground12

CS1 CS2

Tie-Rod1

B F

Spherical21 B

F Spherical13

B F Spherical18 FRUF Sensor

CS1 CS2

Pullrod1 B F

Spherical20 Ground13

CS1 CS2 FR Upper A-Arm Front

B F Spherical16 CS1 CS2 FR Upper A-Arm Rear B

F

Spherical19

CS1 CS2 FR Bottom A-Arm Rear

CS1 CS2 FR Bottom A-Arm Front

B F

Spherical22

B F

Spherical23

B F Spherical14

B F

Spherical15 FRUR Sensor

FRBF Sensor

FRBR Sensor

B F

Six-DoF1

CG

CS4

CS6

CS9 CS1

CS7

CS2

CS8

CS3

CS5

Rear Left Upright Ground14

Env Machine Environment2

B F

Spherical24 Ground15

Ground16

B F

Spherical29

Ground17

Ground18

Ground19

CS1 CS2

Tie-Rod2

B F

Spherical33

B F Spherical25

B F

Spherical30

RLUF Sensor

CS1 CS2

Pullrod2

B F

Spherical32

Ground20

B F

Six-DoF2

CS1CS2

RL Upper A-Arm Front

B F

Spherical28

CS1CS2

RL Upper A-Arm Rear B

F Spherical31

CS1CS2

RL Bottom A-Arm Rear

CS1CS2

RL Bottom A-Arm Front

B F Spherical34

B F

Spherical35

B F Spherical26

B F

Spherical27

RLUR Sensor

RLBF Sensor

RLBR Sensor

CG

CS4

CS6

CS9 CS1

CS7

CS2

CS8

CS3

CS5

Rear Right Upright

Ground25 Env Machine Environment3 B

F

Spherical36 Ground26

Ground27

B F

Spherical41 Ground21

Ground22

Ground23

CS1 CS2

Tie-Rod3

B F

Spherical45 B

F

Spherical37

B F Spherical42 RRUF Sensor

CS1 CS2

Pullrod3 B F Spherical44

Ground24

CS1 CS2 RR Upper A-Arm Front

B F

Spherical40 CS1 CS2 RR Upper A-Arm Rear B

F

Spherical43

CS1 CS2 RR Bottom A-Arm Rear

CS1 CS2

RR Bottom A-Arm Front

B F Spherical46

B F

Spherical47

B F Spherical38

B F

Spherical39 RRUR Sensor

RRBF Sensor

RRBR Sensor

B F Six-DoF3

F_rods_raw up_f

up_f _s up_r up_r_t ch_f ch_r

F_rods_FR F_rods_FL F_rods_RR F_rods_RL F_rods_toe_tie

verif ica fcn

MATLAB Function up_f

UP Front

up_r UP Rear

ch_f Chassis Frontch_r

Chassis Rear

2 Matrix

Concatenate

-1158 -295.9 -1002 -2356

Display -477.2 -207.2 485 167.3

Display1

669.7 742.4 -1195 -735.1

Display2 -178 -178.7 72.35 722.2

Display3 Body Actuator4

>= 0

Switch [0;0;0]

Constant [1;0;0]

Gain4 >= 0

Switch1 [0;1;1]

Gain5

[1;0;0]

Gain6 >= 0

Switch2 Body Actuator5

[0;0;0]

Constant1 >= 0 Switch3

[0;1;1]

Gain7

Body Actuator6

[1;0;0]

Gain8 >= 0 Switch4 Body Actuator7

[0;0;0]

Constant2 >= 0 Switch5

[0;1;1]

Gain9

Body Actuator3

Body Actuator8

>= 0

Switch6 [0;0;0]

Constant3 [1;0;0]

Gain10 >= 0

Switch7 [0;1;1]

Gain11

1 F_rods_FR

2 F_rods_FL

3 F_rods_RR

4 F_rods_RL 4

MZ

Body Actuator2

Body Actuator9

Body Actuator10

Body Actuator11 [0;0;1]

Gain12

[0;0;1]

Gain14

[0;0;1]

Gain15 [0;0;1]

Gain13

Tie-L Sensor

Tie-R Sensor

Toe-R Sensor Toe-L Sensor

up_r_t UP Rear1 up_f_s UP Front2

660.3 -0.5335 -389.2 30.46

Display4 5.292e-14

660 -21.18

Display5

5.69e-16 1.485e-15 4.927e-16 2.429e-16 6.661e-16 4.441e-16 1.665e-16 2.394e-16 8.327e-17 9.992e-16 1.409e-17 3.574e-15 6.939e-16 3.331e-16 2.312e-15 -1.54e-17 1.912e-16 -7.914e-14 5.077e-15 8.571e-15

Display6

5 F_steering_rods F_rods_FR plot

F_rods_FL plot

F_rods_RR plot

F_rods_RL plot

F_rods_toe_tie plot F_FR.mat F_FR to file - F_FR

Wishbones Loads Block

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