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ON THE STEERING BEHAVIOUR OF MOTORCYCLES
A. DORIA, M. DA LIO, R. LOT
European Automotive Congress 1999 - Barcelona 30 june - 2 july
ABSTRACT
This paper deals with the effect of steering system design and
tyre properties on the behaviour of a motorcycle. First the kinematic
analysis of the system is carried out using a 3D model, the displacement
of the front tyre contact point (caused by the roll and steering
angles) is analysed and its influence on the steering torque is
discussed. Then the steady turning behaviour is studied by means
of a dynamic model, which is based on Newton-Euler equations and
takes into account suspension deflections. Results are presented
in terms of steering torque, which is an index of vehicle handling,
and a steering ratio, which shows the understeering or oversteering
behaviour of the vehicle and is related to safety.
PAPER OVERWIEW
MATHEMATICAL MODEL
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The schematization of motorcycle takes the following into account:
sprung and unsprung steering components, rear frame (with rider
rigidly attached), rear swing arm, front and rear wheels, front
and rear suspension, tyre forces, aerodynamic forces. |
Tyre forces and torques are calculated with non-linar expressions,
accordind to experimental results
Tyre forces act at the contact ponts of toroidal tyres. |
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The steady turning matematical model consists of 8 simultaneous
non-linear equations with 8 variables, which are solved numerically
for each value of the speed of travel and the turning radius.The
model makes it possible to calculate roll and steering angles,
tyre sideslip angles and longitudinal slips, tyre forces and steering
torque. |
EFFECTIVE TRAIL
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The trail is the distance between the contact point of the front
wheel and the steering axis.
When roll and steering angles increase, trail decreases markedely.
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The head tyre radius is also important: trail increases with head
tyre radius (at a constant value of roll and steering angles).
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STEERING TORQUE
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Steering torque strongly depends on tyre geometry and properties
and on steady turning conditions.
The steering torque is negative when the velocity is low and reaches
the larger positive values when the speed is high and the steady
turning radius significant |
With an increased tyre head radius, the steering torque values
are larger.
This effect is only due to the geometric variation in the trail.
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STEERING BEHAVIOUR
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When the cornering and roll stiffness of front and rear tyres
are equal, the motorcycle has a neutral steering behaviour at
a low speed. If the speed increases, there is oversteering. |
When the motorcycle is equipped with a rear tyre having greater
cornering stiffness, there continues to be oversteering; but the
steering ratio is smaller than the previous case. |
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When the rear tyre has increased roll stiffness, there is understeering
at a high speed for a wide range of values of the turning radius.
There is oversteering at a low speed and a low turning radius. |
When the rear tyre has both increased cornering and increased
roll stiffness, there is understeering for a wide range of speeds
and turning radii.
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