Calculating efficiency of a DC motor

Let's take a look at the efficiency of the DC motor we just discussed

Like almost anything in the real world, the motor won't be 100% efficient

The power generated by the motor will be less than the power we input, and the efficiency can be defined as
𝜂=P{useful}P{produced}
or
𝜂=PoutPin

We could also look at this like a circuit in series where the power in is our source power and the power lost and power generated are modeled as resistors.

In this case we'd have a circuit like this

And due to the conservation of power, the Power in would have to equal the combination of the Power out and the Power lost.

Another way you could look at this is the power generated, or output power, as the power in minus the power lost, or

𝜂=Pin−PlossPin

In the case of our motor we have several sources of loss.

Loss from the brush, which we can call
Pbrush

There is typically some electrical loss here with sparking as well as the frictional loss of the brush going against the commutator

There is a lot of current going through a lot of wire wrapped around the rotor, so there will be
I2R
losses, or
Pheat
as the current heats up the wire a little

There are some losses,
Pcore
, in the core of the magnet due to the electromagnetics involved

And lastly, there is some loss due to air resistance and the friction of the rotor turning, or
Pmech
, similar to the reasons your skateboard stops coasting even when you're not going up a hill.

Given that nomenclature, our efficiency of the motor could simply be found as:

𝜂=Pin−Pbrush−Pheat−Pcore−PmechPin

Typicall efficiency for a DC motor might be in the range of 70-85%, which Isn't too bad.

But that was just a brief overview of how one might go about calculating the efficiency of a DC motor based on it's various types of losses.