Page 325 - Automotive Engineering Powertrain Chassis System and Vehicle Body

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

given to the phenomenon of oscillatory instability that V x
r e ¼ (11.1.1)
may show up with the car trailer combination. U o
When the wavelength of an oscillatory motion of the
Although the effective radius may be defined also for
vehicle that may arise from road unevenness, brake
a braked or driven wheel, we restrict the definition to the
torque fluctuations, wheel unbalance or instability
case of free rolling. When a torque is applied about the
(shimmy), is smaller than say 5 m, a non-steady-state or
wheel spin axis a longitudinal slip arises that is defined as
transient description of tyre response is needed to
properly analyse the phenomenon. Applications demon- follows:
strate the use of transient and oscillatory tyre models and V x r e U U o U
provide insight into the vehicle dynamics involved. k ¼ ¼ (11.1.2)
V x U o
The sign is taken such that for a positive k a positive
11.1.2 Tyre and axle characteristics longitudinal force F x arises, that is: a driving force. In that
case, the wheel angular velocity U is increased with
Tyre characteristics are of crucial importance for the respect to U o and consequently U > U o ¼ V x /r e . During
dynamic behaviour of the road vehicle. In this section an braking, the fore and aft slip becomes negative. At wheel
introduction is given to the basic aspects of the force lock, obviously, k ¼ 1. At driving on slippery roads,
and moment generating properties of the pneumatic k may attain very large values. To limit the slip to
tyre. Both the pure and combined slip characteristics of a maximum equal to one, in some texts the longitudinal
the tyre are discussed and typical features presented. slip is defined differently in the driving range of slip: in
Finally, the so-called effective axle characteristics are the denominator of (11.1.2) U o is replaced by U. This will
derived from the individual tyre characteristics and the not be done in the present text.
relevant properties of the suspension and steering Lateral wheel slip is defined as the ratio of the lateral
system. and the forward velocity of the wheel. This corresponds
to minus the tangent of the slip angle a (Fig. 11.1-1).
Again, the sign of a has been chosen such that the side
11.1.2.1 Introduction to tyre force becomes positive at positive slip angle:
characteristics
V y
tan a ¼ (11.1.3)
The upright wheel rolling freely, that is without applying V x
a driving torque, over a flat level road surface along
a straight line at zero side slip, may be defined as the The third and last slip quantity is the so-called spin
starting situation with all components of slip equal to zero. which is due to rotation of the wheel about an axis normal
A relatively small pulling force is needed to overcome the to the road. Both the yaw rate resulting in path curvature
tyre rolling resistance and a side force and (self) aligning when a remains zero, and the wheel camber or inclination
torque may occur as a result of the not completely sym- angle g of the wheel plane about the x axis contribute to
metric structure of the tyre. When the wheel motion the spin. The camber angle is defined positive when
deviates from this by definition zero-slip condition, wheel looking from behind the wheel is tilted to the right. The
slip occurs that is accompanied by a build-up of additional forces F x and F y and the aligning torque M z are results of
tyre deformation and possibly partial sliding in the contact the input slip. They are functions of the slip components
patch. As a result, (additional) horizontal forces and the and the wheel load. For steady-state rectilinear motions
aligning torque are generated. The mechanism responsible we have in general:
for this is treated in detail in the subsequent chapters. For
now, we will suffice with some important experimental F x ¼ F x ðk; a; g; F z Þ; F y ¼ F y ðk; a; g; F z Þ; (11.1.4)
observations and define the various slip quantities that M z ¼ M z ðk; a; g; F z Þ
serve as inputs into the tyre system and the moment and
forces that are the output quantities (positive directions The vertical load F z may be considered as a given
according to Fig. 11.1-1). Several alternative definitions quantity that results from the normal deflection of the
are in use as well. tyre. The functions can be obtained from measurements
for a given speed of travel and road and environmental
For the freely rolling wheel the forward speed V x
(longitudinal component of the total velocity vector V of conditions.
Fig. 11.1-1 shows the adopted system of axes (x, y, z)
the wheel centre) and the angular speed of revolution U o
can be taken from measurements. By dividing these two with associated positive directions of velocities and
quantities the so-called effective rolling radius r e is forces and moments. The exception is the vertical force
obtained: F z acting from road to tyre. For practical reasons, this

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