Modeling torque on a half car model

[mattia]

Imagine an half car model with the two suspension and two wheels. There is a torque applied to the rear wheels, that torque create the force between tire/asphalt that pull the car.
How that torque react in the main body? I have two hypotesis:
1) It's only internal force that tend to bend the suspension. If we consider a rigid model, it has no effect
2) it divide between wheel and body, compared to the relative inertia respect to the rear wheel hub. For example, if the inertia of the rear wheel is 1 Nm^2 that of the body is 999 Nm^2 and the torque is 1000 Nm, the results is 999 Nm on the rear wheel, and 1 Nm that tend to lift the front wheel.

Is one of these two hypotesis correct?
If the second one is correct, how the 1Nm of the torque affect the body? A rotation, with compression of the rear suspension and extension of the front one?

Thank you

 

[BvU]

Half a car is comparable to a motorcycle -- when they accelerate heavily, a wheelie can result. So I'd vote for #2 . Make an FBD of the extended object.

 

[mattia]

I'm sorry but I'm not good on english acronym, what is an FBD?

 

[A.T.]

It's only internal force that tend to bend the suspension. If we consider a rigid model, it has no effect

If you model the whole car as one body, then you have to look at the external forces acting on it.

it divide between wheel and body, compared to the relative inertia respect to the rear wheel hub. For example, if the inertia of the rear wheel is 1 Nm^2 that of the body is 999 Nm^2 and the torque is 1000 Nm, the results is 999 Nm on the rear wheel, and 1 Nm that tend to lift the front wheel.

Why are you looking at the inertia of the wheel only. Is your car floating in space, or does it have ground contact?

 

[BvU]

A diagram with the acting forces (free body diagram) -- google is your friend

 

[mattia]

That's the diagram.
The two torque create the forces Fr and Ff, but my doubt is, it has influence on the main body?
To better say, I know that the torque (Fr+Fr)*h is correct, but I have to add also Mr and Mf like in the point 2 in the beginning of this thread?

Thank you

 

[BvU]

We had a thread on that:

How to use Moments of Inertia to find acceleration

but that was for a rear-wheel drive. Your FBD suggests an all-wheel drive. Is mg the center of mass of the whole thing ? It is off-axis from the accelerating force, so there is a torque to be compensated for (if not, you get rotation of the whole thing - the wheelie I referred to).

Google is your friend

 

[mattia]

I read it but it not help me.
I google it for one month, I can't find the solution and that's why I open this topic. The only paper that I found, similar to what I want to do, is a work of the prof. Vittore Cossalter, "Optimum suspension design for motorcycle braking".
Sadly, in that work there is the equation of motion of the motorcycle, but without explanation of how to find it.
My problem is that when I think a lot, I start to have doubt also on the most simple things.

Then, I try to summarize more clearly my doubt:

If I consider the half car model as a whole, with only external forces, no problem. I found the load transfer and the acceleration of the center of gravity.
If I consider the suspension and the tire stiffness, again no problem.
The problem is when I consider the torque on the wheels!
That torque generate the forces Fr and Ff on rear and front wheel, that I calculate with the pacejka magic formula.
There is torque on both wheels because in my model I consider also the braking, then in different part of the simulation I can have acceleration on the rear wheel or braking on both.
Now, my sistem is composed by three body: two wheels, and the main body attached together with the rear and front suspension.
The rotational equilibrium of the rear wheel (the front is the same) give me:

$$M_r + F_r R_r = I_r \ddot \theta$$

And that's ok.
The rotational equilibrium of the main body consider the forces of the suspension multiplied for the distance from the center of gravity, the forces Fr and Ff multiplied for the height of the center of gravity... and the two torque?
It's a big problem, because with the geometrical data that I'm considering, the maximum torque before reach the wheelie condition is about 930 Nm without considering that torque, and 580 Nm if I consider it.
It's obvious that one of the two is wrong.
Or are both wrong, and I must consider only the torque and not the forces Fr and Ff?

Help me go back to sleep!