Page 512 - Automotive Engineering Powertrain Chassis System and Vehicle Body

FRONT RIGHT TYRE – 100 km/LANE CHANGE
10000.0
9000.0 Roll stiffness model _ _ _ _ _ _ _
8000.0 Linkage model __________
7000.0
Vertical force (N) 6000.0

5000.0
4000.0
3000.0
2000.0
1000.0
0.0
1.0 3.0 5.0
0.0 2.0 4.0
Time (s)
Fig. 15.1-57 Vertical tyre force comparison – linkage and roll stiffness models.

differential equations for acceleration, torque and yaw w ¼ G (15.1.31)
€
rate can be derived: J z
1
_ v x ¼ ðF xfl cos d F yfl sin d þ F xfr cos d where the additional parameters are defined as:
m
_
F yfr sin d þ F xrl þ F xrr Þþ v y w F xij ¼ longitudinal forces on tyre ij (N)
(15.1.28) F yij ¼ lateral forces on tyre ij (N)
0
F xij ¼ longitudinal forces on tyre ij in the vehicle’s
1
_ v y ¼ ðF yfl cos d þ F xfl sin d þ F yfr cos d co-ordinate system (N)
m F yij ¼ lateral forces on tyre ij in the vehicle’s co-
0
_
þ F xfr sin d þ F yrl þ F yrr Þ v x w ordinate system (N)
(15.1.29) M zij ¼ self-aligning moment on tyre ij (N m)
t f 0 t f 0 t r t r m ¼ mass of vehicle (kg)
2
G ¼ F F þ F xrl F xrr J z ¼ moment of inertia around vertical axis (N m )
2 xfl 2 xfr 2 2
0 0 t f ,t r ¼ front and rear track width (m)
þ bF þ bF cF cF yrr þ M
yfl yfr yrl zfl b, c ¼ position of centre of gravity between
þ M zfr þ M zrl þ M zrr (15.1.30) wheels (m)
FRONT LEFT TYRE – 100 km/h LANE CHANGE
10000.0
9000.0 _ _ _ _ _ _ _
Roll stiffness model
8000.0 Linkage model __________
7000.0
Vertical force (N) 6000.0

5000.0
4000.0
3000.0
2000.0
1000.0
0.0
1.0 3.0 5.0
0.0 2.0 4.0
Time (s)
Fig. 15.1-58 Vertical tyre force comparison – linkage and roll stiffness models.

520