MAS 04a TyreDynamics - University of...

Modelling of Automotive Systems 1

Tyre Dynamics


Wheels have been used for at least 5700 years. Near the northern side of the Caucasus several graves were found, in which since 3700 BC people had been buried on wagons or carts.


Tires or tyres are pneumatic enclosures used to protect and enhance the effect of wheels.

The earliest tires were bands of iron made by by skilledcraftsman, known as a wheelwright.

The first practical pneumatic tire was made by the Scot John Boyd Dunlop for his son's bicycle, in an effort to prevent the headaches his son had while riding on rough roads.

The pneumatic tire also has effect of vastly reducing rolling resistance compared to a solid tire on rough ground. It is able to "absorb" bumps in the road as it rolls over them without experiencing a reaction force opposite to the direction of travel, as is the case with a solid (or foam-filled) tire.

Pneumatic tires are made of a flexible elastomer material such as rubber with reinforcing materials such as fabric and wire.

Tire companies were first started in the early 20th century. Today over 1 billion tires are produced annually.


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,

)nin tractio when n faster tha isit (

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since hand,other On the

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Longitudinal tyre force is a function of slip ratio It is linear near slip ratio = 0

xrσrxr

xfσfxf

σCF

σCF

=

=


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stiffiness tyrecalled are ,

region,linear smallFor

eldriven wheon or mode brakingin on wheel for tyre

moden in tractio on wheel for tyre

as defined are ratio Slip

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on depends and force tyrealLongitudin

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σCF

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=

=

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−

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ωσ

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Longitudinal tyre force Brush model Net velocity at treads :

backwards ofdirection in 0s

bending iselement tread the wheel,drivingfor >

−= Vrs xweffω

The bending defection generate longitudinal force

- proportional to s - proportional to time duration for which the tread

element stays in the contact patch, or inverselyproportional to the velocity

Therefore,

r

sCFweff

σfxf ω=

For driven wheel

e).(resistanc force ground backwards subject to is Tyre backwards. ofdirection in

bending iselement tread theel,driven whefor

0<−= Vrs xweffω

effV


stronger force half forward causes Viscousity energy dissapates material tyrein the Damping

patch contact ain n deformatio tyrecauses load Normal resistance Rolling

•••


04.001.0

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raaerorf

zf

mglhxmhFll

F

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F

+++

=

+−−+

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&&

&&

MAS 04a TyreDynamics - University of...

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