车辆动力学建模与分析
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(Fy3 Fy4 )lr ((Fx2 Fx1) cos (Fy1 Fy2 ) sin Fy3 Fy4 )
B/2
y
20/37
Vehicle Dynamics Model
x
lf
Fx 2
•
Fx1
FL Tire
Fy 2
V x
FR Tire
Wheel C.S.
Fy1
• 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
Vertical motion
Lateral force Normal force
Chassis control
Target
Steering control
DYC VSC 4WS
Suspension control
Handling Ride
Long. D.
Pitch motion Longitudinal motion
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
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
Longitudinal Dynamics
6/37
Vehicle Dynamics Model
• Tire coordinate system
o Three forces and three moments
Camber angle 外倾角
γ
Aligning moment 回正力矩
Rolling resistance moment 滚动阻力矩
• 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
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
CoG C.S.
Fx3
y•
Fy 3 RR Tire
y
Three coordinate systems (C.S.)
o CoG – vehicle center of gravity C.S.
o ‘W’ – wheel C.S. o ‘In’ – fixed inertial C.S.
Newton’s Law can only applied on fixed C.S.
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
Fra Baidu bibliotek
Tire Model
Longitudinal force Lateral force Normal force Overturning torque Rolling resist. torque Aligning torque
Motion states
Vehicle Model
Force and moment
Motion states
Vehicle Model
Force and moment
14/37
Tire Dynamics
Hans B. Pacejka, “Tyre and Vehicle Dynamics”, 2005
15/37
Vehicle Dynamics Model
V
T r
Fx
J& T rFx
• Summary
5/37
Vehicle Dynamics Model
• Vehicle Dynamics
o Force
motion
− Force: tire
− Motion: vehicle
o Three sub-subjects
Vertical Dynamics
Lateral Dynamics
R2 louter
2Rlouter Rrinner
R2 linner
2Rlinner Rrinner
Rlinner
o1
o'
( o Rlinner AWc)a2 dRel2minneric e2Rvrainnleur (aRtloiuoternoRnlinnetrh)e potentiaRlolunoterf in-wheel mC0otor EVA0
• 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
喻凡，林逸，汽车系统动力学，2000
Longitudinal force
Traction/brake control
ABS TCS
Acc/dcc 9/37
Vehicle Dynamics Model
Wheel slip ratio Wheel slip angle Camber angle Wheel speed
19/37
Vehicle Dynamics Model
• Force under vehicle
x
Fx 2
Fx1
C.S.
F
Wheel C.S.
y2
F
lf
FL Tire
y1
V
FR Tire
x
x
lr
Fx 4
RL Tire
Inertial C.S.
Fy 4
B
r Vy
CoG C.S.
Fx3
y
Fy 3 RR Tire
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
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
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
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
• 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
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
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]
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
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
• 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
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
Fx (Fx1 Fx2 ) cos
(Fy1 Fy2 ) sin Fx3 Fx4
Fy (Fy1 Fy2 ) cos
+(Fx1 Fx2 ) sin Fy3 Fy4
M z ((Fx1 Fx2 ) sin (Fy1 Fy2 ) cos )l f
B/2
y
20/37
Vehicle Dynamics Model
x
lf
Fx 2
•
Fx1
FL Tire
Fy 2
V x
FR Tire
Wheel C.S.
Fy1
• 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
Vertical motion
Lateral force Normal force
Chassis control
Target
Steering control
DYC VSC 4WS
Suspension control
Handling Ride
Long. D.
Pitch motion Longitudinal motion
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
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
Longitudinal Dynamics
6/37
Vehicle Dynamics Model
• Tire coordinate system
o Three forces and three moments
Camber angle 外倾角
γ
Aligning moment 回正力矩
Rolling resistance moment 滚动阻力矩
• 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
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
CoG C.S.
Fx3
y•
Fy 3 RR Tire
y
Three coordinate systems (C.S.)
o CoG – vehicle center of gravity C.S.
o ‘W’ – wheel C.S. o ‘In’ – fixed inertial C.S.
Newton’s Law can only applied on fixed C.S.
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
Fra Baidu bibliotek
Tire Model
Longitudinal force Lateral force Normal force Overturning torque Rolling resist. torque Aligning torque
Motion states
Vehicle Model
Force and moment
Motion states
Vehicle Model
Force and moment
14/37
Tire Dynamics
Hans B. Pacejka, “Tyre and Vehicle Dynamics”, 2005
15/37
Vehicle Dynamics Model
V
T r
Fx
J& T rFx
• Summary
5/37
Vehicle Dynamics Model
• Vehicle Dynamics
o Force
motion
− Force: tire
− Motion: vehicle
o Three sub-subjects
Vertical Dynamics
Lateral Dynamics
R2 louter
2Rlouter Rrinner
R2 linner
2Rlinner Rrinner
Rlinner
o1
o'
( o Rlinner AWc)a2 dRel2minneric e2Rvrainnleur (aRtloiuoternoRnlinnetrh)e potentiaRlolunoterf in-wheel mC0otor EVA0
• 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
喻凡，林逸，汽车系统动力学，2000
Longitudinal force
Traction/brake control
ABS TCS
Acc/dcc 9/37
Vehicle Dynamics Model
Wheel slip ratio Wheel slip angle Camber angle Wheel speed
19/37
Vehicle Dynamics Model
• Force under vehicle
x
Fx 2
Fx1
C.S.
F
Wheel C.S.
y2
F
lf
FL Tire
y1
V
FR Tire
x
x
lr
Fx 4
RL Tire
Inertial C.S.
Fy 4
B
r Vy
CoG C.S.
Fx3
y
Fy 3 RR Tire
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
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
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
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
• 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
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
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]
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
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
• 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
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
Fx (Fx1 Fx2 ) cos
(Fy1 Fy2 ) sin Fx3 Fx4
Fy (Fy1 Fy2 ) cos
+(Fx1 Fx2 ) sin Fy3 Fy4
M z ((Fx1 Fx2 ) sin (Fy1 Fy2 ) cos )l f