Ⅳ- 92Copyright ⓒ 2002 by Kumho Tire
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Vehicle Handling
Simulation
•Many Degrees of
Freedom
•Detailed Information
•Needed on Vehicle Parts
Mathematical
Model
Multibody S/W
Package
•A Few Degrees of
Freedom
•Measured Characteristics
of Suspension Needed
2). Vehicle Handling Simulation
Ⅳ- 93Copyright ⓒ 2002 by Kumho Tire
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Handling
Simulation
F&M Calculation On
ABAQUS
• Version 6. 2.
• Steady State Cornering
Vehicle Dynamics On
ADAMS
• Version 12. 0.
• 10 Vehicle Models
3). Handling Simulation in KH
Ⅳ- 94Copyright ⓒ 2002 by Kumho Tire
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Hardware
ADAMS Full Simulation Package
ADAMS/Car Suspension Design
ADAMS/Tire Handling
SGI Indigo2 Extreme
IBM Intellisation Xeon Z-Pro
Software ADAMS
Vehicle
Model
现 量产车辆 : 3 种
现 开发车辆 : 1 种
(1) Vehicle Handling on ADAMS
Ⅳ- 95Copyright ⓒ 2002 by Kumho Tire
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Automobile Handling Study
Course Keeping - Tracking a straight road under
wind and/or road disturbances
Vehicle Pull
Course
Keeping
Intentional Maneuvering - Turning or Cornering
Handling
Stability
Steady State
Test
Transient
Response
Test
Intentional
Maneuvering
-. Vehicle Handling in KUMHO Tire
Ⅳ- 96Copyright ⓒ 2002 by Kumho Tire
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-. Simulation Related to Vehicle Handling
Vehicle Straight Ahead
Motion Test
Vehicle Pull Test Vehicle Stability Test
Steady State Test
Constant Steer Angle
Test Constant Speed Test
Constant Radius Test
Understeer Gradient : Steer angle vs. Lateral
Acc.
Roll Angle Gradient : Roll angle vs. Lateral
Acc.
Steering Sensitivity
Ⅳ- 97Copyright ⓒ 2002 by Kumho Tire
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Slalom
Braking in
a Turn
Single Lane
Change
Double
Lane
Change
Transient Response Test
ISO7401
J-Turn Test
Sine Input
Test
Random
Input Test
Pulse Input
Test
ISO3888 ISO 7975 ISO9816
Powering
Off in a
Turn
Analysis Method
Time Domain Analysis Frequency Domain Analysis
Ⅳ- 98Copyright ⓒ 2002 by Kumho Tire
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① J-Turn Test Simulation
② Lane Change Test Simulation
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③ Simulation Input/Output
Input Output
Steering
Input
Sinusoidal
Step
Random
Pulse
Path Follow
Vehicle
Speed
Constant
Speed
Acceleration
Deceleration
Lateral
Acceleration
Response Time
Peak Value
Steady State
Gain
Overshoot
Yaw Rate
Response Time
Peak Value
Steady State
Gain
Overshoot
Roll angle
System
Ⅳ- 100Copyright ⓒ 2002 by Kumho Tire
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2) F&M Calculation On ABAQUS
Lateral Force Characteristics
-6000
-4000
-2000
0
2000
4000
6000
-15 -10 -5 0 5 10 15
Slip Angle (deg)
La
er
al
Fo
rc
e
(N
)
Aligning Torque Characterisitcs
-150
-100
-50
0
50
100
150
-15 -10 -5 0 5 10 15
Slip Angle (deg)
Ali
gn
ing
T
oru
qe
(N
m)
Cornering Stiffness
Cornering Coefficient
Cornering Power
Aligning Stiffness
Aligning Coefficient
Pneumatic Trail
Ⅳ- 101Copyright ⓒ 2002 by Kumho Tire
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Lateral Force (N)
-1000
-500
0
500
1000
-5 -3 -1 1 3 5
Slip Angle (deg)
La
te
ra
l F
or
ce
(N
)
Camber Stiffness
Camber Coefficient
Load Transfer
Sensitivity
Load Sensitivity
Ⅳ- 102Copyright ⓒ 2002 by Kumho Tire
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车辆 : KIA Sephia
轮胎 : P185/65R14 716 PTN, 760 PTN, 757 PTN
① 轮胎单品F&M 试验结果
项 目 716 757 760
CC(1)
CC(4)
ATC(1)
ATC(4)
G-F(4)
H-F(1)
0.288
0.736
8.490
11.317
0.229
0.188
0.256
0.694
9.449
13.949
0.298
0.126
0.245
0.697
9.649
15.871
0.291
0.136
1) Application
② Feeling Test
Tire 716 716 716
Driving effort
On center feel
Steering response
Linearity
Roll control
Yaw stability
Lateral grip
Lateral stiffness
Throttle lift-off
7.5
7.5
7.5
7.5
7.0
7.0
7.0
7.0
7.0
7.0
7.0
7.0
6.5
6.5
6.5
7.0
6.3
6.8
7.0
6.8
7.0
7.0
7.0
7.0
7.0
7.0
6.7
Overall handling 7.3 6.5 7.0
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③ Steering Input
Left Turn Right Turn
Step
Input
Sinusoidal
Input
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④ Responses from Step Input
Left Turn Right Turn
Yaw
Rate
Lateral
Acceleration
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⑤ Responses from Sinusoidal Input
Left Turn Right Turn
Yaw
Rate
Lateral
Acceleration
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插入
轮胎称号变更
1. 36*4(BFG, 1986), 900*65(MC,1989).36*6(MC,1920)
- ~ 到1920年
- 轮胎外径 * 轮胎宽
- 高压轮胎 (50~70psi)
- 10,12,14Ply
2. 4.40-21 4PLY(宽*内径,inch,最初的量产车,ford)
12*45 (宽*内径.cm,MC,1927)
- 1920年代: Balloon轮胎, 低压使用(30psi)
- 扁平率 100%
- 背景 : 汽车公司的要求
Hard Tire容易损伤。
타이어 Section Height增大, Thin Sidewall
Deflection 增大, 障碍物自然 roll over
Bursting 下坠, 但是 Load Capacity增大
High Speed 可能
3. 6.50-13 4PR(宽*内径,inch)
- 1930年代
- Super Balloon轮胎, 低压使用(30psi)
- 扁平率95%
- 背景 : 单面形象 扁平, 胎面宽 加宽.
运行稳定性,高速耐久性,耐磨损性改善
4. 6.00-13 4PR
- 1940-1960年代
- Medium Low Profile轮胎
- 扁平率 86%
- Rayon,Nylon 使用 Ply Rating 概念使用
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5. 165-330, 165-13, 6.45-13
- 在法国 metric system创建
- 82 Series
6. F70-14
- 1967年出现在TRA。
- 负荷范围,扁平率,轮辋直径
- 背景 : 单面形象 扁平, 胎面宽 加宽.
运行稳定性,高速耐久性,耐磨损性改善
7. 185/70HR13
- 在欧洲使用
- 宽,扁平率,速度范围,Radial,轮辋直径
- 背景 : Low Profile(82 Series),
Ultra Low Profile(77 Series)
70 Series (?)
8. P155/80R13
- 1977年在TRA显示。
- 把复杂的统一。
- P(轿车),宽,扁平率,Radial,轮辋直径
9. 205/70R14 93H
- 1978年 ETRTO
- 宽,扁平率,Radial,轮辋直径, 负荷范围,速度范围
Ⅳ- 108Copyright ⓒ 2002 by Kumho Tire
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3. Handling Characteristics
1). Handling Characteristics 概要
SAE Tire Axis System
Force in
x : Traction/Braking
y : Handling
z : Vehicle Load
Moment in
x :(Handling)
y : Rolling Resistance
z : Handling
Ⅳ- 109Copyright ⓒ 2002 by Kumho Tire
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2). Basic Properties In Vehicle/Tire
v + ar
u
r
u
u
v - br
v
f
r
a
b
Bicycle Model
1) No body rolling motion
2) No lateral load transfer
3) No pitch, bounce or hop motion
4) Constant Forward velocity
5) Small angle assumption
6) Position control
Equations of Motion
Steering Kinematics (1)
M
dv
dt
ru F Fyf yr( )+ = +
I
dr
dt
a F b F M Myf yr zf zr= - + +
f
v
u
ar
u
v
u
ar
u
= + - = + --1tan ( )
r
v
u
br
u
v
u
br
u
= - = --1tan ( )
= - + +r f a b ru
( )
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(1) Steady State Cornering
u
r
u
f
r
R
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Equations of Motion
Steering Kinematics
Tire F&M properties governs the Basic Dynamic
Characteristics of a Vehicle
(2) Equations of
Motion
( )
{( ) ( )( )}
a b
R
W
C
Wr
C
W
a b
K K
C C
uf
f r
f r
f r gR
2
Mru F Fyf yr
MMFbFa zrzfyryf 0
yf f fF C , yr r rF C
zf f fM K , zr r rM K
r f a bR
( )
f
f
r
f r
b
a b C
K
a b C C
M
u
R ( ( ) ( ) )
2
f
r
f
f r
a
a b C
K
a b C C
M
u
R
( ( ) ( ) )
2
Ⅳ- 112Copyright ⓒ 2002 by Kumho Tire
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(3) Lateral Load Transfer
( ) { ( ) ( )}a b
R
W
c
W
c
W
c
b F
c
W
c
b F
c
u
g R
f
f
r
r
f
f
z f
f
r
r
z r
r
2 22 2 2
Ⅳ- 113Copyright ⓒ 2002 by Kumho Tire
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3). Free Rolling Characteristics
Lateral Force Characteristics
-6000
-4000
-2000
0
2000
4000
6000
-15 -10 -5 0 5 10 15
Slip Angle (deg)
La
era
l F
orc
e (
N)
IA=-5
IA=0
IA=5
Aligning Torque Characterisitcs
-150
-100
-50
0
50
100
150
-15 -10 -5 0 5 10 15
Slip Angle (deg)
Ali
gn
ing
T
oru
qe
(N
m)
IA=-5
IA=0
IA=5
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(1) Load Transfer Effect
Ⅳ- 115Copyright ⓒ 2002 by Kumho Tire
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(2) F&M Characteristics
Lateral Force Characteristics
-6000
-4000
-2000
0
2000
4000
6000
-15 -10 -5 0 5 10 15
Slip Angle (deg)
La
er
al
Fo
rc
e
(N
)
Aligning Torque Characterisitcs
-150
-100
-50
0
50
100
150
-15 -10 -5 0 5 10 15
Slip Angle (deg)
Ali
gn
ing
T
oru
qe
(N
m)
Cornering Stiffness
Cornering Coefficient
Cornering Power
Aligning Stiffness
Aligning Coefficient
Pneumatic Trail
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Lateral Force (N)
-1000
-500
0
500
1000
-5 -3 -1 1 3 5
Slip Angle (deg)
La
te
ra
l F
or
ce
(N
)
Camber Stiffness
Camber Coefficient
Load Transfer
Sensitivity
Load Sensitivity
Ⅳ- 117Copyright ⓒ 2002 by Kumho Tire
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4). GM Tire Performance Criteria
Vertical Load
Lateral Force
1 Slip Angle
P
F
y
Cornering Coefficient = Fy/P
Aligning Torque
1 Slip Angle
P
A
T
Vertical Load
Aligning Coefficient =
AT/P
Vertical Load
Lateral Force
1 Slip Angle
P
F
y
0.8P
Load Sensitivity (H) = D
Fy/(P-0.8P)
Lateral Force
4 Slip Angle
P
F
y
0.6P
Vertical Load
Load Transfer Sensitivity
(H) =D Fy P/(D P)2
Ⅳ- 118Copyright ⓒ 2002 by Kumho Tire
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4. Vehicle Pull
1). Vehicle Pull 概要
(1) Vehicle Pull
Pull
(Drift)
车辆集中
Steering Pull, Vehicle Pull, Vehicle Drift
Pull : Steering effort to make a car go straight.
Drift : Deviation from the straight ahead line.
* Brake Pull
Ⅳ- 119Copyright ⓒ 2002 by Kumho Tire
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(2) 对车辆集中有影响的因素
车辆集中
车辆特性
外部因素
路面倾斜
风
Tire
Chassis
悬空装置
转向装置
Power Train
Ⅳ- 120Copyright ⓒ 2002 by Kumho Tire
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2). Conicity和车辆集中
1) 作用在轮胎的横向力 (Slip Angle = 0)
作用在轮胎的横向力 (Lateral Froce) 成分中 Conicity Force
是发生车辆集中的 主要因素。
• Plysteer Force = (|L.F. c.w.| + |L.F. c.c.w.|) / 2
• Conicity Force = (|L.F. c.w.| - |L.F. c.c.w.|) / 2
c.w.c.c.w.
L.F.
0 kgf
Frequency
Conicity
Plysteer
横向力
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偏左集中 直线运行 偏右集中
(2) 前轮的Conicity和车辆集中
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(3) 前轮的Conicity和车辆集中
Ⅳ- 123Copyright ⓒ 2002 by Kumho Tire
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3). 残留复原PRAT和车辆集中
1) PRAT 相关Vehicle Pull
Fixed Control Free Control
Fixed Control : 前轮没作用横向力。
Free Control : 转向系不作用Moment。
2) 轮胎坐标轴
Ⅳ- 124Copyright ⓒ 2002 by Kumho Tire
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(3) 轮胎F&M试验 Data
• RAT (Residual Aligning Torque) =
Aligning Torque at slip angle where L.F. = 0
• RCF (Residual Cornering Force) =
Lateral Force at slip angle where A.T. = 0
21
RCFRAT
• Aligning Torque Static Phase : a1 - a2
Slip Angle的范围(deg) : -1 ~ +1
Ⅳ- 125Copyright ⓒ 2002 by Kumho Tire
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轮胎 C.C.W.回转时
轮胎 C.W. 回转时
PRAT =(RAT c.w + RAT c.c.w)/2 :
因素
CRAT= (RAT c.w - RAT c.c.w)/2 :
偏差
Slip Angle
Aligning Torque
Lateral
Force
RAT c.w.
RAT c. c.w.
4) 轮胎RAT
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y = 0. 7272x - 3. 1155
R2 = 0. 9626
-20
-10
0
10
20
-20 -10 0 10 20
C o n ic ity (kg f)
RA
T
(N
-m
)
-. Conicity 和 RAT
Ⅳ- 127Copyright ⓒ 2002 by Kumho Tire
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T ire - A
y = 4.4399x + 12.14
R 2 = 0.6603
-100
-50
0
50
100
-10 -5 0 5 10
F ro n t A xle C o n ic ity. [kg f]
La
te
ra
l
Dr
if
t
[c
m] D rift + : R ig h t, - : L e ft
T ire - B
y = 7.7358x - 12.2
R 2 = 0.6971-100
-50
0
50
100
-10 -5 0 5 10
F ro n t A xle C o n ic ity [kg f]
La
te
ra
l
Dr
if
t
[c
m]
D rift + : R ig h t, - : L e ft
5) PRAT和Vehicle Pull
Tire P185/ A PTN Tire P185/ B PTN Tire
PRAT [N-m] 3.02 N-m 1.21 N-m
(1) 타이어 PRAT
Ⅳ- 128Copyright ⓒ 2002 by Kumho Tire
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试验车辆 : 相同model的车辆2台
D Car Pull Test
y = 8.0475x - 23.333
R2 = 0.8031
y = 20.163x - 37.333
R2 = 0.9435
-250
-200
-150
-100
-50
0
50
100
150
200
-8 -6 -4 -2 0 2 4 6 8
FRONT TOTAL CON. [kgf]
集
中
量
[c
m
]
(2) 车辆间偏差
Ⅳ- 129Copyright ⓒ 2002 by Kumho Tire
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直线运行范围
车辆/Tire System 散步范围
直线
7点
7—点
6+点
左侧集中车辆
直线
7点
7—点
6+点
良好车辆
直线
7点
7—点
6+点
右侧集中车辆
(3) 轮胎别/车辆别
Ⅳ- 130Copyright ⓒ 2002 by Kumho Tire
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5. Tire Ride
1) Run Out
(1) Tire Run-Out
-. Radial Run-Out : Harmonic Analysis
-. Lateral Run-Out : Harmonic Analysis
-. Tire/Wheel Matching Properties : Interaction
Ⅳ- 131Copyright ⓒ 2002 by Kumho Tire
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0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0
- 1
- 0 . 8
- 0 . 6
- 0 . 4
- 0 . 2
0
0 . 2
0 . 4
0 . 6
0 . 8
1
P 1 7 5 / 7 0 R 1 3 L A T E R A L R U N - O U T _ F R O N T R IG H T
¿ ø Á Ö ¹ æÇ â À § Ä ¡ ( d e g )
R
un
-O
ut
(m
m
)
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In-Phase Run-Out
-1.5
-1
-0.5
0
0.5
1
1.5
0 90 180 270 360
位置 (deg)
Ru
n-
Ou
t(m
m
)
LRO_in
LRO_out
LRO_tilt
Ⅳ- 133Copyright ⓒ 2002 by Kumho Tire
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Out-Phase Run-Out
-1.5
-1
-0.5
0
0.5
1
1.5
0 90 180 270 360
位置 (deg)
Ru
n-
Ou
t(m
m
)
LRO_in
LRO_out
LRO_tilt
Ⅳ- 134Copyright ⓒ 2002 by Kumho Tire
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2. Static & Dynamic Balance
车辆上的影响
-) Tramping现象发生 : 轮胎内部重的部位接触到地面
时发生振动。
-) 根据以Unbalance Mass的回转运动的圆心力妨碍回
转轴的直线运动。
-) 发生上下方向振动。
Static
Balance
轮胎在静止状态时,在轮胎内部找出相对重的地
方。
(1) Static Balance
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(2) Dynamic Balance
Dynamic
Balance
因回转中轮胎的内部Unbalanced Mass 及Run-
Out, 发生轮胎不均匀的回转运动的现象。
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Static Balance 와 Dynamic Balance와의 Correlation
(3) Static & Dynamic Balance
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3. Run Out & Dynamic Balance
Radial Run-Out 问题时
根据回转半径r的差异圆心力差异发生 。
Lateral Run-Out 问题时
根据 Moment的原因距离 d 发生差异,通过
惯性力增大,发生回转轴的变化