How an electric motor works

The type of electric motor we use in R/C racing is a DC permanent magnet 3 pole motor. You can familiarize yourself with its component parts by looking here.

Introduction

Whenever electrical current flows through an electrical conductor, it produces a magnetic field. Conversely, whenever an electrical conductor moves through a magnetic field, or when a magnetic field moves with respect to an electrical conductor, a voltage is induced in that conductor.

Since we enjoy following the laws of Thermodynamics in this world, we should look at some of the consequences of the above behaviors. If a wire is in a magnetic field, and we apply current to the wire, we will have a mechanical force exerted by the wire against the existing magnetic field. The direction of the force (whether it attracts or repels the magnet) depends on the direction of the current. This force exerted is directly proportional to the current which flows in the wire -- increase the current, and you increase the force, decrease the current and you decrease the force.

Remember that I said if a wire moves through a magnetic field, a voltage is induced in it? Well, if the wire carrying a current is free to move, then, according to our friend Newton, it will move in the direction the force is acting on the wire. This movement in turn will induce a current in the wire which opposes the current that is generating the force. This acts in a manner very similar to resistance.

This duality of magnetism and electricity can be seen in several examples; most notably the microphone/speaker and motor/generator pairings. A traditional permanent magnet/coil magnet speaker has a permanent magnet mounted to the base and a coil attached to a movable cone with the coil centered in the magnet. As a current is passed through the coil on the speaker, the resulting force pushes the cone against the air, causing sound waves. If instead you connect the speaker to an input, the sound waves in the air will push the speaker cone/coil through the magnetic field of the permanent magnet, inducing a potential into the coils of the speaker, which the amplifier would amplify into a sound.

Let's illustrate a small example with easy numbers to work with. We have a length of wire with a resistance of 1 Ohm. We put a potential of 1 volt across it. This causes 1 ampere of current to flow in the wire. This causes the wire to have a magnetic field (calculating how much of a magnetic field is much more involved and beyond the scope of this document), and this magnetic field will cause it to interact with the magnetic field the wire is in. Let's say the wire exerts a force of 1N against the existing magnetic field. This will cause the wire to accelerate through the magnetic field, following Newton's formula F = m * a. This movement in turn will induce a potential in the wire which opposes the original potential applied to the wire. If we live in a world with no friction and magnetic fields infinite in size, the wire would accelerate forever, but it's rate of acceleration would diminish as the time and speed increased, and the potential induced in the wire would approach that of the original potential applied to the wire. Let's get back to our example. Let's say we have 0.75 volts potential applied to our wire by its movement through the magnetic field. Therefore the wire only sees 1 - 0.75 = 0.25 volts across the resistance of 1 Ohm, meaning after the wire gets moving only 0.25 amperes of current flows. In this case, it is said the wire acts as though it has 1 * 0.25 = 4 Ohms of resistance.

Capiche?

Electric Motors

The electric motors we work with consist of permanent magnets in the can, and three coils mounted on the armature. The coils receive their power from the commutator through the brushes. As electric current flows through the wire making a coil, the resulting magnetic field will attract one permanent magnet and repel the other permanent magnet. The commutator determines the polarity of each coil, which makes it attract and repel the appropriate magnets at the appropriate time, as the armature rotates.

Let's look now at how all of this adds up. One pole of a stock motor, for instance, has 27 turns of 22 AWG wire, with a minimum length of 64 inches. At room temperature, 64 inches of 22 AWG copper wire has a resistance of 0.0880 Ohms (Pocket Ref, Thomas J. Glover). If you connect 7.2 Volts to this wire, you will have a current of 7.2 Volts / 0.0880 Ohms = 82 Amperes. On our armatures, one pole is always connected in parallel with two others wired in series. Therefore, if you were to connect 7.2 Volts to the armature, there would be 1 / (1 / 0.0880 + 1 / (0.0880 * 2)) = 0.0587 Ohms resistance, giving a current of 7.2 Volts / 0.0587 Ohms = 123 Amperes. When you run your motor, you do not get this kind of current draw -- free running, a stock motor will draw close to 5 Amps, depending on lots of variables.

Why is this?

When you connect power to the motor, a large current flows through the armature. This causes a magnetic field to form, which opposes the existing magnetic field in the can. This in turn makes the armature rotate. The rotating coils on the armature then start moving through the stationary field from the can, which in turn induces a potential in the coils which opposes the current flowing from the battery. Therefore, the maximum current a stock motor can pull is 123 Amperes, when it is stalled. Since the strength of a magnetic field is proportional to the current through the wire, the maximum torque will also be produced when the motor is stalled. As the armature accelerates, the potential induced in the coils increases. For example, if a stock motor is drawing 5 Amps at 7.2 Volts, the voltage induced in the armature coils is 7.2 - (0.0587 * 5) = 6.91 Volts. This leaves 0.293 volts potential from the battery to act through the 0.0587 Ohms armature resistance -- 0.293 Volts = 5 Amps * 0.0587 Ohms. If you increase the load on the armature, the back-EMF (the voltage induced in the armature due to its rotation) will be less, causing more current to be drawn and more torque to be produced, and if you decrease the load on the armature, the back-EMF will be higher, causing less current to be drawn and less torque being produced. When free-running, the only load on the armature comes from air resistance, bearing drag, and brush drag.

This relationship can be extrapolated. If there is negative drag on the armature (you are turning the armature fast, as though it is in a coasting car), the back-EMF (back Electro-Motive-Force) will be larger than the potential provided by the battery, and as such the current will flow backwards. Everything acts as though instead of the motor having a positive resistance, it has a negative resistance. The motor acts as a generator, and instead of being a current drain, it supplies current. If you put a load on the motor, the current in the coils on the armature will oppose the magnetic field in the can and cause the motor to slow down. This is where electric brakes come from. If you spin the motor backwards, the back-EMF will have a negative polarity, and if you apply positive power to the motor, you can pull more current through the motor than the armature resistance alone would allow.

Put another way, as the armature turns, the coils cut the magnetic flux lines from the can magnets, inducing a potential into them. When you put an electrical load on to the motor, the current flows from the coils to the terminals (the opposite direction from when current goes from the terminals to the coils), creating a magnetic field in the coils which opposes the can magnetic field, slowing the armature.

Of course, life is a little bit more complicated than this though. Copper, like any non-superconductor, heats up when current is passed through it. As the temperature of copper increases, so does its resistance. Therefore, all of the calculations done above give exacting numbers for a motor at room temperature. When the motor heats up, the resistance increases, which means that the current draw of the motor will lessen, causing a smaller magnetic field to form, making the motor run slower and less efficiently. You may notice that a cool motor performs better than a hot motor; this is one of the primary reasons.

Not only that, but brushes have a not-insignificant resistance. This is by design, to minimize damage to commutators due to arcing. Part of the reason silver brushes (a combination of carbon, copper and silver) are considered to wear out commutators more quickly than carbon/copper brushes is for this very reason; silver brushes have less resistance than their more benign cousins. This resistance (and the contact resistance between the brush face and the commutator surface) will reduce the stall current draw of a motor.

Windings

So a little bit more about the windings. The magnetic field in a wire is proportional to the current flowing through it, and the magnetic field of a coil is proportional to both the current in the wire and the number of turns in the coil. If, for example, you have two coils, both with 5 Amps flowing, one with 5 turns and the other with 10 turns, the one with 10 turns will have double the magnetic field than the 5 turn one. Even though a modified motor has a lower resistance armature than a stock motor, since the stock motor has lots of turns, it will have more torque. But since the stock motor has more torque, and therefore it would have more torque at all motor speeds, then why is the stock motor slower than the modified?

Quite simply, it is because of the back-EMF. Since a modified motor has fewer turns, it must move faster than a high turn motor in order to produce the same back-EMF. And the motor will continue to produce torque until the torque produced by the motor equals the drag on the armature. Therefore the motor is spinning fast enough so that the back-EMF is the appropriate amount below the terminal voltage so that the current through the armature is low enough to produce that torque. Therefore, a modified motor will have to spin faster than a stock motor to produce the same back-EMF.

Okay, well, why then can't we just gear up a stock motor, and make use of its increased torque, and go faster than a modified motor? Well, a modified motor produces more power than a stock. A stock motor produces more torque than a modified, but less power. Remember that Power = Torque * RPM. A modified motor produces more power since it has a lower armature resistance than a stock motor, due to both a shorter length of wire (fewer turns), and a larger wire diameter (since there are fewer turns).

Well, why does a single wind perform differently than a double or triple, etc.? A poly-strand armature will have a larger cross-sectional area than a single-strand armature (more strands will give more area), and therefore the armature will have less air in it (less resistance), making it more efficient. It should therefore produce more torque and also more RPM throughout its performance envelope.

Then why sometimes do we prefer single strand armatures? Quite simply, it's because of one of the things everyone raves about on their cars -- rotational inertia. The armature weighs a significant portion of the whole rotating mass of the drivetrain, and it also spins up damn fast -- in lots of cars around 10 times the speed of the wheels. A small change in mass on the armature can make a fairly big difference in the energy required to bring the drivetrain up to speed. Therefore, although a poly-strand armature produces more torque than a single, it also has more rotational inertia, causing the car to accelerate slower than if it were to use a single.

Timing

What about timing? Well, timing in our motors is sub-optimal. The ideal timing angle is always changing as the motor load changes, and as the motor speed changes. As the magnetic field in the armature increases, it interacts with the magnetic field in the can, and the resultant magnetic field is rotated. The timing angle of the brushes should be changed by the same amount as the field rotation, in order to compensate for this effect. This field rotation is, of course, directly proportional to the torque output of the motor, which again is directly proportional to the current draw of that particular motor. Also, since the windings of the armature also act as an inductor (an inductor is basically a coil of wire which "resists" changes in current in the same way a capacitor "resists" changes in voltage), higher armature speeds require the coils to be energized sooner so that they come up to full magnetic field strength in time to react with the field magnets. A side effect of the optimal timing angle is no arcing at the brush/commutator interface. This is why the brakes on an electric motor cause it to arc so much -- the timing angle is furthest off when the brakes/reverse is applied. This is partly why the optimal timing angle is always so elusive -- it depends on so many varying things (both motor speed and torque). Since increased timing should make the motor work better under both high torque and high speed situations, you'd think more timing is better, however it is very easy to give a motor too much timing.

Please email me with comments, corrections, aditions, questions, etc. about this article. You can contact me at tyounger@csc.uvic.ca.