The time necessary for current in an inductor to reach its full Ohm’s law value - RL time constant is given by formula:
τ=L/R
• τ - time for one time constant (sec.)
• R - resistance (ohms)
• L - inductance (henrys)
Motor principle
Fleming's Hand Rules
Whenever we use conventional current flow, Fleming’s Left-Hand Rule is used for ‘motor action’, while Fleming’s Right-Hand Rule is used for ‘generator action’. Depending on whether such a machine functions as a generator or a motor, the moving part that is attached to a mechanical system receives mechanical input or provides mechanical output. Each of these two above rules relates the relationships between the direction of a magnetic field, the direction of motion of a conductor within that field and the conventional direction of the current (and corresponding voltage).
1. When a current-carrying conductor is placed in a magnetic field, the conductor is subject to a force that acts to move the conductor out of the field. The direction of the magnetic field (north to south) is represented by the first finger. The direction of the conventional current is represented by the second finger. The direction of the motion, caused by the resulting force, is then represented by the thumb.
2. When a conductor is moved through a magnetic field, a voltage is induced into the conductor. If this conductor forms part of a closed loop, then a current will flow in the same direction as the induced voltage. The direction of the magnetic field (north to south) is represented by the first finger. The direction of the motion of the conductor through the field is then represented by the thumb. The direction of the induced e.m.f. (and any resulting current) is represented by the second finger.
Motor action
We learnt earlier that a current-carrying conductor placed between the poles of a magnet will experience a force at right-angles to the field’s magnetic flux. This force, which is known as the ‘Lorentz Force’, acts to push the conductor out of the magnetic field.
F=BIl
· F - force [N]
· B - flux density [N]
· I - current [A]
· l - length of conductor in field [m]
Last equation only applies to the condition when the conductor is perpendicular to the main flux.
If it lies at some angle less than 90°, then the force exerted on it will be reduced, so in general: F=BIlsinθ [N]
The principle of a force exerted on a current carrying conductor forms the basis of operation of a linear motor. However, since most electric motors are rotating machines, the above system must be modified.
Let us consider the conductor formed into the shape of a rectangular loop, placed between two poles, and current passed through it. A cross-sectional view of this arrangement, together with the flux patterns produced is shown on the next figure.
The flux patterns for the two sides of the loop will be in opposite directions because of the direction of current flow through it. The result is that the main flux from the poles is twisted as shown on the second figure. This produces forces on the two sides of the loop in opposite directions. Thus there will be a turning moment exerted on the loop, in a counterclockwise direction.
So the torque exerted on each side of the loop is given by T=Fr [Nm].
F=BIlsinθ [N], sinθ=1
The total torque exerted on the loop will be:
T=2BIlr [Nm]
It would have been seen that a single-turn loop produces a very small amount of torque, even if the coil dimensions and current were increased by some factor in specific cases. Using multi-turn coil can solve this problem in practice. Then, for N turns we would have the total torque T=2NBIlr [Nm].
The term 2lr in the above expression is equal to the area ‘enclosed’ by the coil dimensions, so this is the effective csa A, of the field affecting the coil.
T=BANI [Nm]
The principle of using a multi-turn current-carrying coil in a magnetic field is therefore used for rotary electric motors. The same principles apply to the operation of analogue instruments known as moving coil meters.
Generator action
The English physicist Michael Faraday (1791–1867) showed that the opposite of ‘motor action’ also occurs. That is, moving a conductor through a magnetic field (or moving the magnetic field relative to the conductor) will induce a voltage into the conductor. The direction in which this voltage acts can be determined by applying Fleming’s Right-Hand Rule. If the conductor forms part of a closed circuit, then this induced voltage will cause a current to flow in the same direction. The magnitude of this induced voltage, when the conductor is moved perpendicularly through a magnetic field, is given by the following equation:
U=Blv
· U - induced voltage [V]
· B - flux density [N]
· l - length of conductor in field [m]
· v - velocity of conductor [m/s]
Comparing ‘generator action’ with ‘motor action’, we will notice that the voltage (U) induced into the conductor by ‘generator action’ acts in the opposite direction to the voltage (E) that drives the current that causes ‘motor action’. For this reason, we call the voltage induced into the conductor by generator action a ‘back-e.m.f.’.
So, whenever there is ‘motor action’, there is always ‘generator action’ too, and the generated voltage (the back-e.m.f.) always opposes the voltage that causes the motor action to take place in the first place.
The stator comprises all the stationary components of the motor, including: the yoke (the cylindrical housing), the pole pieces and their field windings, bearings and the brushes.
The rotor comprises all the rotating parts of the motor, including: the drive shaft, armature, armature windings, commutator and impeller fan.
A single loop of conductor is placed between the poles of a permanent magnet, and is pivoted at its near and far ends in such a way that it is free to rotate.
With the current flowing around the loop in the direction shown, if we apply Fleming’s Left-Hand Rule to the left-hand side of the loop, we would find that it is subject to a downward-acting force; and applying the same rule to the right-hand side of the loop would confirm that it is subject to an upward-acting force. These forces couple to create a rotating force, or torque, which will act to rotate the loop in a counterclockwise direction.
The total torque acting on this single loop will be twice the torque acting on either side of the loop: T=2BIlr [Nm].
· r - perpendicular distance from centre of rotation (radius of the loop)
At the same time, a back-e.m.f. will be induced into the loop, the value of which will be: E=2Bl(ω·r)
A single-loop motor will produce very little torque so, in practice, a coil, called an armature winding, is used instead. If the armature winding has z loops, then the torque (and corresponding back-e.m.f.) will be increased by z.
So, whenever the armature winding is rotating, it behaves both as a motor and as a generator simultaneously! Passing a current through the winding causes it to move through the magnetic field (‘motor action’), but the movement of that winding through the field causes it to generate a voltage (‘generator action’) which always opposes the applied voltage that produces the current in the first place!
Ia=(E-U)/Ra
· Ia - current in loop [A]
· E - supply voltage [V]
· U - back e.m.f. [V]
· Ra - resistance of armature loop [Ω]
The ‘action’ and ‘reaction’ effect, described above, plays a very important role in causing d.c. machines (both motors and generators) to automatically react to changes in load.
For example, in the case of a d.c. motor, if its mechanical load should increase, then the armature winding will tend to slow down. As it slows down, the back-e.m.f. decreases, allowing the current through the armature winding to increase, creating more torque to match the increasing mechanical load. Similarly, if the motor’s mechanical load should decrease, then the armature winding’s speed will increase. As its speed increases, its back-e.m.f. also increases, reducing the load current and reducing the torque to match the reduced load.
Once the armature winding has rotated through 90° counterclockwise, and is in the vertical plane, the two perpendicular forces then exactly oppose each other, so the torque completely disappears, and the armature winding will immediately stop rotating. Even if the momentum of the armature winding is such as to cause it to rotate a little way past the vertical, there would be an immediate reversal of the two forces, resulting in a corresponding reversal in torque which would quickly return the loop back to the perpendicular position. Of course, this is an undesired effect and the armature winding should continue rotating in the same direction.
So, we can reverse the direction of the current every time the coil passes its vertical position by supplying current via a simple rotary switch, called a ‘commutator’ or, more accurately, a ‘split-ring commutator’.
One end of the armature winding is soldered or brazed to one half of the ‘split ring’, and its other end is soldered to the opposite half of the ‘split ring’. The commutator and the armature winding share the same shaft, and rotate together.
Current is fed on to, and away from, the commutator by means of a stationary pair of spring-loaded carbon brushes, which press against opposite sides of the commutator and ‘ride’ its surface as it rotates between them. As well as being a good conductor, carbon is self-lubricating – making it an ideal material from which to manufacture brushes.
We can say that the function of the split-ring commutator is to ensure that, as the armature winding of motor rotates, current always flows away from us in whichever side of the winding happens to be left of vertical, and the current always flows towards us in whichever side of the winding happens to the right of vertical. This ensures that, immediately the armature winding passes its vertical position, the current around the winding reverses direction and the armature winding will be subject to a continuous counterclockwise torque, causing it to continue to rotate in a counterclockwise direction as it passes through its vertical position. The combination of split-ring commutator and its carbon brushes is known as the motor’s ‘commutation system’. The split-ring commutator also conveniently solves the problem of how to continuously supply current to and from the coil while it is rotating.
In order to provide enough torque to drive larger mechanical loads, we need to use electromagnets, which will provide a greater flux density than permanent magnets. These are provided by field windings which are wound around the pole pieces, and form the motor’s ‘excitation system’.
At the same time, and in order to establish maximum flux density within the airgaps in which the armature rotates, those airgaps need to be as narrow as possible. This is achieved by using shaped pole pieces, which partially enclose the armature.
And finally, we need a low-reluctance magnetic circuit whose function is to guide the flux created by the excitation system to the airgaps, similar as an electric circuit, in which we use low-resistance copper wires to guide the current to some load. Because the resistance of the wire is so low, practically all the electromotive force applied to the circuit will appear across the load. Similarly, due to the low-reluctance of the magnetic circuit, practically all the magnetomotive force (m.m.f.) created by the field windings will appear across the airgaps.
Most practical d.c. motors have four or more poles, rather than just two, the armature windings are numerous, far more complex and occupy longitudinal slots that are distributed around the entire circumference of the armature and the commutator has numerous segments, not just two. These features ensure a constant torque is applied throughout the complete 360° rotation of the armature.
A motor’s starting current is always very much higher than its normal operating load current, because the armature is simply not yet rotating fast enough to generate sufficient back-e.m.f. to oppose that starting current. For larger motors, high starting currents will result in excessively high temperatures which may break down the insulation. So larger d.c. motors usually require some means of reducing their high starting currents. One method of achieving this is by inserting a variable resistor in series with the motor, and gradually lower the value of that resistance as the motor picks up speed. Such a device is called a ‘motor starter’.