# Physics Simulation Forum

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 Post subject: Tire model - slip computationPosted: Mon Jun 08, 2009 7:58 am

Joined: Sat May 02, 2009 9:38 am
Posts: 38
Hi,
I'm interested in vehicle simulation. I'm trying to put together some tire model. I discovered that almost every model (for example Pacejka) uses "slip". I have no idea how to compute it. The engine produces primarily torque, not slip. So what is the relation between these two things?
I think input variables for tire model may be: Tire load (Fz), engine torque, tire front direction, tire linear velocity (not speed) and coefficient of friction between tire and surface. Is it possible to compute actual Fx (longitudinal force), Fy (lateral force) and aligning torque from these (for one certain type of tire described by some constants as in Pacejka model)? Or am I missing some input variables?
Thanks

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 Post subject: Re: Tire model - slip computationPosted: Mon Jun 08, 2009 3:41 pm

Joined: Tue Feb 20, 2007 4:56 pm
Posts: 190
Most basic tire models use the following inputs at a bare minimum:

1) Slip angle (what you call the 'direction', the angle difference between where the tire is pointed and where it is actually going). Slip angle mostly results in lateral forces on the tire.
2) Slip ratio, which indicates the longitudinal slip; i.e. how fast the tire is currently rotating vs. how fast it would be rotating if there were no torques applied.
3) Tire load (because tire forces aren't directly proportional to the load, unlike Coulomb friction).
4) Camber angle (how much the tire is leaning, because tires can produce significantly more force in the direction that they are leaning).

To calculate these values correctly, I would recommend Googling the SAE definitions of each.

If you are driving on different surfaces, yes you'll probably need another scalar for the tire/surface grip, but it's usually already built into the coefficients for a model like Pajecka.

The relationship to the engine torque mostly comes from the slip ratio. The engine makes the tire rotate a little faster, which changes the slip ratio which leads to changes in longitudinal force. Similarly, braking causes the tire to rotate a little slower, eventually resulting a longitudinal force in the other direction.

Speed is really only used to calculate the slip angle and ratio (there is a small but often ignored negative correlation between speed and grip). Note that the equations for slip angle and slip ratio break down near zero speed. If accuracy near zero speed isn't critical, you can typically just use a minimum speed to calculate the slip values.

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 Post subject: Re: Tire model - slip computationPosted: Mon Jun 08, 2009 5:34 pm

Joined: Sat May 02, 2009 9:38 am
Posts: 38
bone wrote:
The engine makes the tire rotate a little faster... Similarly, braking causes the tire to rotate a little slower.

That's exactly what I have problems understanding. How exactly compute this "little faster/slower"? All I have is wheel axis torque, either positive when accelerating, or negative when braking. I still have no idea how to compute the "little faster/slower" value from it. Making up this value makes no sense to me as the slip value depends on it and the tire model depends on the slip value.
Thanks.

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 Post subject: Re: Tire model - slip computationPosted: Mon Jun 08, 2009 6:27 pm

Joined: Tue Feb 20, 2007 4:56 pm
Posts: 190
The wheel rotation speed is an important state variable that you have to keep track of. Just as one would use vehicle acceleration to integrate the vehicle velocity, you use rotational acceleration to integrate the rotational speed.

If you are simulating only 1 DOF for the wheel, then rotational acceleration simply equals torque divided by rotational inertia of the wheel (notice the similarity to acceleration = force/mass). If you don't know the rotational inertia of the wheel about its axle, a good guess for normal cars is somewhere between 1.0 and 2.0.

Hope this helps.

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