o Under ‘In’
ur In
ur CoG
dP dP
ur CoG r

rP z
dt
dt
ur In dP
dt

r
ur
m(V&x Vyr)x m(V&y Vxr) y
uur In dH
• Tire model
Wheel slip ratio Wheel slip angle Camber angle Wheel speed
Tire Model
Longitudinal force Lateral force Normal force Overturning torque Rolling resist. torque Aligning torque
2 Slip Angle [rad]
Slip Angle [rad]
Tire Lateral TFoorrcqeu[eN[]Nm]
Longitudinal Force [N]
Merge Merge
Magic Func
Driving Wheel Slip Angle [rad] R*W
Slip Ratio if { } Vx
• Friction circle
Tire: 165SR13
Lateral force /N
Load: 4000N Tire pressure: 206kPa
µy
Slip angle/deg
Traction force/N
余志生，汽车理论，第五版，2008
Brake force/N
13/37
Vehicle Dynamics Model
3/37
Introduction
• Parking length and turning radius
o Smaller turning radius makes parking length smaller
L A'B' o1o' o1o22 o'o22
• Research direction (Rlouter Rrinner )2 (Rlinner Rrinner )2
arctan(Vx )
Vy
Direction of wheel travel
α
Lateral force
12/37
Vehicle Dynamics Model
• Combined longitudinal and lateral motion
o Composition of force is fixed µx
Driven Wheel
Tra cti on Jw*w' = T - Rw*Fx
s =(rw-V)/rw
1 Tire Longitudinal Force [N]
2 Tire Lateral Force [N]
3 RL Angular Speed [rad/s]
17/37
Vehicle Dynamics Model
x
lr
Fx 4
RL Tire
Inertial C.S.
Fy 4
B
r Vy
CoG C.S.
Fx3
y
Fy 3 RR Tire
y
Vehicle motion
o Under ‘CoG’
ur
r
ur
linear momentum: P mVx x mVy y ur r
angular momentum: H Jzr z
16/37
Vehicle Dynamics Model
• Simulink model
1 Torque [Nm]
Slip Ratio
Tire Longitudinal Force [N]
1/Jw
1
s
Rw
TIre Moment of InertiaIntegrator
Wheel Rolling Radius
Motion states
Vehicle Model
Force and moment
18/37
Vehicle Dynamics Model
x
lf

Fx 2
•

Fx1
FL Tire
Fy 2
V x
FR Tire
Wheel C.S.
Fy1
x
lr
Fx 4
RL Tire
Inertial C.S.
Fy 4
B
r Vy
to 2WRlinner 2rWeRdriunncereWpa2 rking space requirement. C
A D0
B0
2W (Rlinner Rrinner ) W 2
D
B
o2
Rrinner
4/37
Contents
• Introduction
o Parking space and turning radius
• Ongoing Research
o Additional moment and turning radius (qualitative analysis)
• Summary
2/37
Introduction • Background & motivation
o Skyrocketing increase of cars o Limited parking space o Alleviate parking space requirement
• Vehicle force and motion
Wheel slip ratio Wheel slip angle Camber angle Wheel speed
Tire Model
Longitudinal force Lateral force Normal force Overturning torque Rolling resist. torque Aligning torque
Long. Speed [m/s]
Lateral Force [N] Rw
Wheel Rolling Radius1 Angular Speed [rad/s]
if (u1 ~= 0) u1
else
If
else { }
Out1
RL Tire Mode
3 Tire Linear Long. Speed [m/s]
俯仰角
喻凡，林逸，汽车系统动力学，2000
侧倾角 横摆角
8/37
Vehicle Dynamics Model
• Control and vehicle dynamics
Research direction
Vehicle motion
Tire force
La. D. V. D.
Lateral motion Yaw motion Roll motion

R2 louter
2Rlouter Rrinner

R2 linner
2Rlinner Rrinner
Rlinner
o1
o'
( o Rlinner AWc)a2 dRel2minneric e2Rvrainnleur (aRtloiuoternoRnlinnetrh)e potentiaRlolunoterf in-wheel mC0otor EVA0
10/37
Vehicle Dynamics Model
• Wheel slip ratio (滑动率)
Vx

s




r v r
r v
v
traction brake
w
r
• Slip ratio
Longitudinal force
11/37
Vehicle Dynamics Model
• Vehicle Dynamics Model
o Background o Tire dynamics o Vehicle dynamics o Simulink model
• Ongoing Research
o Additional moment and turning radius (qualitative analysis)
O
Overturning moment 翻转力矩
X
Direction of
α
wheel travel
Slip angle 侧偏角
Spin axis
Z
Y
7/37
Vehicle Dynamics Model
• Vehicle coordinate system
o Three linear motions and three rotations
Vehicle Dynamics
Liu Lu February 25, 2012
Contents
• Introduction
o Parking space and turning radius
• Vehicle Dynamics Model
o Background o Tire dynamics o Vehicle dynamics o Simulink model
(Fy3 Fy4 )lr ((Fx2 Fx1) cos (Fy1 Fy2 ) sin Fy3 Fy4 )
B/2
y
20/37
Vehicle Dynamics Model
x
lf

Fx 2