Page 329 - Automotive Engineering Powertrain Chassis System and Vehicle Body

CHAP TER 1 1. 1 Tyre characteristics and vehicle handling and stability

ma y h 0 about the king-pins with the steering wheel held fixed, the
4 ¼ (11.1.8)
c 41 þ c 42 mgh 0 additional steer angle becomes when for simplicity
the influence of camber on the pneumatic trail is
The total moment about the roll axis is distributed disregarded:
over the front and rear axles in proportion to the
front and rear roll stiffnesses. The load transfer DF zi
from the inner to the outer wheels that occurs at j ¼ F y1 ðe þ t 1 Þ (11.1.14)
axle i (¼1 or 2) in a steady-state cornering motion c1 CJ
with centripetal acceleration a y follows from the
formula:
In addition, the side force (but also the fore and aft
DF zi ¼ s i ma y (11.1.9) force) may induce a steer angle due to suspension com-
pliance. The so-called side force steer reads:
with the load transfer coefficient of axle i

j ¼ c F yi (11.1.15)
1 c 4i 0 l a i sfi sfi
s i ¼ h þ h i (11.1.10)
2s i c 41 þ c 42 mgh 0 l For the front axle, we should separate the influences
of moment steer and side force steer. For this reason,
The attitude angle of the roll axis with respect to the side force steer at the front is defined to occur as
horizontal is considered small. In the formula, s i denotes a result of the side force acting in a point on the king-
0
half the track width, h is the distance from the centre of pin axis.
gravity to the roll axis and a 1 ¼ a and a 2 ¼ b. The Beside the wheel angles indicated above, the wheels
resulting vertical loads at axle i for the left (L) and right
may have been given initial angles that already exist at
(R) wheels become after considering the left and right
straight ahead running. These are the toe angle j o (pos-
increments in load:
itive pointing outwards) and the initial camber angle g o
(positive: leaning outwards). For the left and right wheels
DF ziL ¼ DF zi ; DF ziR ¼ DF zi
we have the initial angles:
F ziL ¼ ½F zi þ DF zi ; F ziR ¼ ½F zi DF zi
(11.1.11)
j iLo ¼ j ; j iRo ¼ j io (11.1.16)
io
The wheels at the front axle are steered about the g iLo ¼ g ; g iRo ¼ g io
io
king-pins with the angle d. This angle relates directly to Adding all relevant contributions (11.1.12)to
the imposed steering wheel angle d stw through the (11.1.16) together yields the total steer angle for each of
steering ratio n st , that is:
the wheels.
The effective cornering stiffness of an axle C eff,i is
d stw
d ¼ (11.1.12) now defined as the ratio of the axle side force and the
n st virtual slip angle. This angle is defined as the angle be-
tween the direction of motion of the centre of the axle
In addition to this imposed steer angle the wheels may
i (actually at road level) when the vehicle velocity would
show a steer angle and a camber angle induced by body be very low and approaches zero (then also F yi / 0) and
roll through suspension kinematics. The functional re- the direction of motion at the actual speed considered.
lationships with the roll angle may be linearised. For axle The virtual slip angle of the front axle has been indicated
i we define:
in Fig. 11.1-4 and is designated as a a1 . We have in
general:
j ri ¼ 3 i 4 (11.1.13)
g ri ¼ s i 4
F yi
Steer compliance gives rise to an additional steer angle C eff;i ¼ (11.1.17)
a ai
due to the external torque that acts about the king-pin
(steering axis). For the pair of front wheels this torque The axle side forces in the steady-state turn can be
results from the side force (of course also from the here derived by considering the lateral force and moment
not considered driving or braking forces) that exerts equilibrium of the vehicle:
a moment about the king-pin through the moment arm
which is composed of the caster length e and the pneu- l a i
matic trail t 1 . With the total steering stiffness c j1 felt F yi ¼ l ma y (11.1.18)

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