DC Motor Analysis



AndyMark Motor Analysis Blog Post


Act 1: Set-up

Hello World! We’re Shaun and Kelly and we want to know how things work. Whether it’s our rebuilt espresso robot (George Clooney) or our little satellites (Doves), we’re constantly inquiring into how things are designed and function. Lately we’ve both been particularly interested in motion – that little bit of wonder when the machine comes alive right before your eyes. That wonder is carefully designed by engineers and inventors like ourselves with particular constraints and requirements in mind. We found ourselves itching to better understand those design decisions that go into making things move!


Many people understand how to use an electric motor in their design yet few understand the trade space of motor design itself. As a pair of electrical and mechanical engineers, the electric motor covers the perfect combination of concepts based in both of our fields. We wanted to start at first principles and work our way through estimating datasheet torque values, allowing us to bridge the gap between the theoretical and the applied. Join us as we break something to find out how it really works.


Physics Introduction: Calculating motor torque

There are two ways for calculating motor torque. The first is laid out in this paper[hyperlink] from Rice.

The force on a conductor in a magnetic field is dependent upon the magnetic field strength (B), the current flowing through the conductor (I), and the conductor length (l).

[F=BIl equation and Image]

If we fix our conductor around a rotating axis at a distance [r] from the center of rotation we can generate a torque due to the magnetic field.


[T=rBIlcos(theta) equation and Image]

For calculating maximum torque of the motor we assume that we’re generating a field that’s perpendicular to the magnetic field so theta is set to zero.


[T=rBIlcos(0) equation and Image]


The second approach is to use specific magnetic and electrical loading which is described in the book [link to book]. These specific loadings are intrinsic to the design of the physical motor and allow us calculate torque from motor size.


The specific electrical loading (abar) is the axial current per meter of rotor under each pole.


[Abar equation and image]


Bbar is the specific magnetic loading, the rotor flux averaged over the rotor surface area.


[Bbar equation and image]


Using these two terms we can then calculate the motor torque by using the following equation, which multiples the specific loading values with the surface area of the rotor.


[T = pi/2*AbarBbar*D^2*L equation and image]


This means that we have two ways of reach our expected torque using measurements we can take from any motor which should be equivalent. We then decided to find a motor to tear down  and calculate the expected torque.

Motor Introduction: AndyMark AM-0255 Motor


We wanted to find a powerful motor in the intersection of low cost and thoroughly documented. This lead us to the AndyMark AM-0255 2.5” CIM Motor – a mass production motor used heavily in the FIRST robotics competitions.


[Picture of the AndyMark Motor – Caption: AndyMark 2.5” CIM Motor]

This little motor runs about $30 and has, comparatively to other motors in that price range, extensive test documentation. So what’s the first thing we look at with a motor datasheet? The motor torque curve! It’s an interesting thing.


DC Motor on Cardboard


Dodo DC Motor