Electric motor on the wheels of an RC-car

[Runei]

Hello

Im doing a physics project and I am trying to come up with an idea for calculating the torque done by an electric motor on the wheels of an RC-car, and the resulting acceleration of the car.

We have modified the car with some stronger batteries, and now we are in a dilemma.

Each rear wheel is driven by its own motor and when we set the car to go forwards the motors turn fully on (there's no gradual rise in the current).
This means that the wheels at first begin to slide.

All we need to to is make some measurements, and we need to find out how torque has something to do with the cars translational motion.

---- WHEELS SPINNING ----

I have deduced so far, that when the motors turn on, and the wheels begin to spin, the force exerted on the road by the wheels must be greater than the force the static friction is capable of exerting on the wheels. And thus, the wheels begin to spin, and the force exerted on the wheels is now the kinetic friction.

F_{k,fric}=\mu_{k}\cdot m_{car}\cdot g (Because the normal force is equal to the gravitational force.

The force due to kinetic friction exerts a force on the wheels and thus applying a torque on the wheels, slowing the angular velocity. Also the friction force accelerations the center of mass of the wheels (the axle) and thus the car accelerates, with an acceleration given by

\frac{F_{k,fric}}{m_{car}}

I know that at some point when the car has picked up some speed, the wheels "grip" the road and then it is the static friction that accelerates the car.
If that is correct the force exerted on the road by the wheels must decrease with increasing velocity of the car, and at some point the force must come below a given point, and the static friction kicks in.

How can I calculate how the force exerted on the road? (I did it with torque, since force is torque dividid by the distance to the place where the contact is)
How can I calculate when the velocity of the car is high enough for the static frictio to kick in?

 

[log0]

The force exerted on the road is equal to torque divided by radius for the no slip case (|T / r| < us * Fn). If you've got slip the force will be equal to kinetic friction. You would have to reduce the torque to get rid of the slip. There is no velocity dependency in this friction model.

There are more complex tire friction models where the friction coefficient depends on tire slip. Starting at 100% slip(car standing still) the friction coefficient will increase until its maximum as the car is accelerating.

 

[jack action]

How can I calculate how the force exerted on the road? (I did it with torque, since force is torque dividid by the distance to the place where the contact is)
How can I calculate when the velocity of the car is high enough for the static frictio to kick in?

The only thing that stay constant throughout the process is the power.

the power (P) of the motor is (in SI units):

P=T\omega

T is the torque and \omega is the angular velocity. The same equation holds for the power at the wheel (if there is a gear ratio between the two) with its respective torque and ang. vel. (the power is the same).

And for the car:

P=Fv

F is the friction force at the wheel and v is the car velocity. The power is still the same as the one from the wheel or the engine.

Since the power is determine by the motor, as the car velocity increases, the friction force needed goes down.

 

[K^2]

Don't know exactly what you're looking for, but these equations might help.

For an ideal motor, the torque is proportional to current flowing through the coil. The later is determined by the net voltage across coil via Ohm's law.

\tau = k I = k \frac{V - V_i}{R}

Here, R is resistance of the coil, V_i is induced voltage, V is applied voltage, and k is a constant to be determined experimentally.

Induced voltage is proportional to angular velocity, and knowing maximum angular velocity of the motor with no load, it's easy to estimate.

V_i = \frac{\omega}{\omega_{max}} V

Where ω is angular velocity and ω_max is maximum angular velocity achieved under no load and applied voltage V.

Using all of this, you should be able to estimate at what speed the torque is no longer sufficient for slipping.