Electric motors and generators

DC motors

• * A number of different nmemonics are used to remember the direction of the force. Some use the right hand, some the left. For students who know vector multiplication, it is easy to use the Lorentz force directly: F = q v X B , whence F = i dL X B . That is the origin of the diagram shown here.

• Throughout, we use blue for the North pole and red for the South. This is just a convention to make the orientation clear: there is no difference in the material at either end of the magnet, and they are usually not painted a different colour.

Note the effect of the brushes on the split ring. When the plane of the rotating coil reaches horizontal, the brushes will break contact (not much is lost, because this is the point of zero torque anyway – the forces act inwards). The angular momentum of the coil carries it past this break point and the current then flows in the opposite direction, which reverses the magnetic dipole. So, after passing the break point, the rotor continues to turn anticlockwise and starts to align in the opposite direction. In the following text, I shall largely use the 'torque on a magnet' picture, but be aware that the use of brushes or of AC current can cause the poles of the electromagnet in question to swap position when the current changes direction.

The torque generated over a cycle varies with the vertical separation of the two forces. It therefore depends on the sine of the angle between the axis of the coil and field. However, because of the split ring, it is always in the same sense. The animation below shows its variation in time, and you can stop it at any stage and check the direction by applying the right hand rule.
 

Motors and generators

If you use mechanical energy to rotate the coil (N turns, area A) at uniform angular velocity ω in the magnetic field B, it will produce a sinusoidal emf in the coil. emf (an emf or electromotive force is almost the same thing as a voltage). Let θ be the angle between B and the normal to the coil, so the magnetic flux φ is NAB.cos θ. Faraday's law gives:

• emf = − dφ/dt = − (d/dt) (NBA cos θ)

  = NBA sin θ (dθ/dt) = NBAω sin ωt.

An alternator

In the next animation, the two brushes contact two continuous rings, so the two external terminals are always connected to the same ends of the coil. The result is the unrectified, sinusoidal emf given by NBAω sin ωt, which is shown in the next animation.

Back emf

So here is an interesting corollary. Every motor is a generator. This is true, in a sense, even when it functions as a motor. The emf that a motor generates is called the back emf. The back emf increases with the speed, because of Faraday's law. So, if the motor has no load, it turns very quickly and speeds up until the back emf, plus the voltage drop due to losses, equal the supply voltage. The back emf can be thought of as a 'regulator': it stops the motor turning infinitely quickly (thereby saving physicists some embarrassment). When the motor is loaded, then the phase of the voltage becomes closer to that of the current (it starts to look resistive) and this apparent resistance gives a voltage. So the back emf required is smaller, and the motor turns more slowly. (To add the back emf, which is inductive, to the resistive component, you need to add voltages that are out of phase. See AC circuits.)

Coils usually have cores

In practice, (and unlike the diagrams we have drawn), generators and DC motors often have a high permeability core inside the coil, so that large magnetic fields are produced by modest currents. This is shown at left in the figure below in which the stators (the magnets which are stat-ionary) are permanent magnets.

'Universal' motors

The stator magnets, too, could be made as electromagnets, as is shown above at right. The two stators are wound in the same direction so as to give a field in the same direction and the rotor has a field which reverses twice per cycle because it is connected to brushes, which are omitted here. One advantage of having wound stators in a motor is that one can make a motor that runs on AC or DC, a so called universal motor. When you drive such a motor with AC, the current in the coil changes twice in each cycle (in addition to changes from the brushes), but the polarity of the stators changes at the same time, so these changes cancel out. (Unfortunatly, however, there are still brushes, even though I've hidden them in this sketch.) For advantages and disadvantages of permanent magnet versus wound stators, see below. Also see more on universal motors.

Build a simple motor

Make the coil out of stiff copper wire, so it doesn't need any external support. Wind 5 to 20 turns in a circle about 20 mm in diameter, and have the two ends point radially outwards in opposite directions. These ends will be both the axle and the contacts. If the wire has lacquer or plastic insulation, strip it off at the ends.

AC motors

The first thing to do in an AC motor is to create a rotating field. 'Ordinary' AC from a 2 or 3 pin socket is single phase AC--it has a single sinusoidal potential difference generated between only two wires--the active and neutral. (Note that the Earth wire doesn't carry a current except in the event of electrical faults.) With single phase AC, one can produce a rotating field by generating two currents that are out of phase using for example a capacitor. In the example shown, the two currents are 90° out of phase, so the vertical component of the magnetic field is sinusoidal, while the horizontal is cosusoidal, as shown. This gives a field rotating counterclockwise.

(* I've been asked to explain this: from simple AC theory, neither coils nor capacitors have the voltage in phase with the current. In a capacitor, the voltage is a maximum when the charge has finished flowing onto the capacitor, and is about to start flowing off. Thus the voltage is behind the current. In a purely inductive coil, the voltage drop is greatest when the current is changing most rapidly, which is also when the current is zero. The voltage (drop) is ahead of the current. In motor coils, the phase angle is rather less than 90¡, because electrical energy is being converted to mechanical energy.)

In this animation, the graphs show the variation in time of the currents in the vertical and horizontal coils. The plot of the field components B_x and B_y shows that the vector sum of these two fields is a rotating field. The main picture shows the rotating field. It also shows the polarity of the magnets: as above, blue represents a North pole and red a South pole.

If we put a permanent magnet in this area of rotating field, or if we put in a coil whose current always runs in the same direction, then this becomes a synchronous motor. Under a wide range of conditions, the motor will turn at the speed of the magnetic field. If we have a lot of stators, instead of just the two pairs shown here, then we could consider it as a stepper motor: each pulse moves the rotor on to the next pair of actuated poles. Please remember my warning about the idealised geometry: real stepper motors have dozens of poles and quite complicated geometries!

Induction motors

The animation at right represents a squirrel cage motor. The squirrel cage has (in this simplified geometry, anyhow!) two circular conductors joined by several straight bars. Any two bars and the arcs that join them form a coil – as indicated by the blue dashes in the animation. (Only two of the many possible circuits have been shown, for simplicity.)

This schematic suggests why they might be called squirrel cage motors. The reality is different: for photos and more details, see Induction motors. The problem with the induction and squirrel cage motors shown in this animation is that capacitors of high value and high voltage rating are expensive. One solution is the 'shaded pole' motor, but its rotating field has some directions where the torque is small, and it has a tendency to run backwards under some conditions. The neatest way to avoid this is to use multiple phase motors.

Three phase AC induction motors

If one puts a permanent magnet in such a set of stators, it becomes a synchronous three phase motor. The animation shows a squirrel cage, in which for simplicity only one of the many induced current loops is shown. With no mechanical load, it is turning virtually in phase with the rotating field. The rotor need not be a squirrel cage: in fact any conductor that will carry eddy currents will rotate, tending to follow the rotating field. This arrangement can give an induction motor capable of high efficiency, high power and high torques over a range of rotation rates.

Linear motors