# How to get stall current from DC motor model

I'm studying the model of a dc motor from this link :

http://ctms.engin.umich.edu/CTMS/index.php?example=MotorSpeed&section=SystemModeling

The equations are:

$$\\ s(Js+b)\theta(s)=K I(s)\$$

$$\\ (Ls+R)I(s)=V(s)-Ks\theta(s)\$$

To calculate the Stall current I set the angular velocity to zero(since theta is the angle, the derivative is the angular velocity):

$$\\ s \theta (s)=0 \$$

but I get:

$$\\ 0=K I(s)\$$

$$\\ (Ls+R)I(s)=V(s)\$$

and then

$$\\ I(s)=0\$$

$$\ I(s)=\frac{V(s)}{Ls+R}\$$

The two results are different.To be equal, V(s)=0 but it is strange.How is possible that the stall current is zero?

• Your last equation of $I(s)$ contains the answer to your question. I'm not sure why you say that $I(s)=0$ before that, perhaps you meant $s=0$?. – Harry Svensson Nov 11 '18 at 12:21

An electrical machine is basically an electrical energy to mechanical energy converter which utilises magnetic fields.

As a result these domains need to be considered when dealing with electrical machines.

Electrical domain

This is represented by a voltage source, the resistance and the inductance which will produce a current flow

Magnetic domain

For simplicity this is treated as a current-torque conversion (kt) from the electrical to the mechanical and a velocity-voltage conversion (ke) from the mechanical to the electrical

Mechanical domain

This is represented by inertia and drag. when subjected to torque greater than the mechanical loading the rotor will accelerate. This inertia governs how quickly.

Under a stall condition it can be seen that there is no rotation and thus the impact of the rotational mechanical drive chain is out of scope.

In this situation the electrical characteristics are key.

$$\(Ls + R)I(s) = V(s) - Ks\theta(s) \$$

Since the rotor isn't rotating the backEMF, the $$\Ks\theta(s) \$$ is zero

$$\(Ls + R)I(s) = V(s) \$$ and we have a simple RL load across a voltage source.
This the stall current is related to the impedance of the stator.

$$\ I(s) = \frac{V}{Ls+R} \$$

There will be a transient aspect to this 1st order equation related to the inductor, but for the purpose of stall current this isn't of use as typically the periods of time of interest are longer than the RL constant.

The equation can be reduced to.
$$\R\cdot I = V \$$

Therefore the stall current can be expressed as:

$$\ I = \frac{V}{R} \$$

Thus the stall current is governed by the resistance of the stator.

I don't know where you got your second equation from.

$$L \frac{di}{dt} + Ri = V - K\dot{\theta}$$
Setting $$K\dot{\theta} = 0$$ and $$\frac{di}{dt} =0$$
since the rotor is locked and not turning, and the current has reached steady-state gives $$Ri = V$$ and
$$i = \frac{V}{R}$$