3.1 ALTERNATING MAGNETIC FIELDS
It is shown in the manual
‘Fundamentals of Electricity 1’ how Oersted’s discovery that a magnetic field
surrounds every current-carrying conductor led to the construction of coils,
with or without an iron core, which concentrated the magnetic field surrounding
each single piece of wire in each turn of the coil to give a strong magnetic
field mainly along the axis of the coil.
FIGURE 3.1
MAGNETIC FIELD AROUND A
COILED CONDUCTOR
The word ‘mainly’ is used advisedly,
because there is also some return field outside
the coil, and not all the inside field is wholly concentrated in the
centre. When iron is present the
concentration is greater, but some of the field ‘gets away’, even with
iron. This is known as ‘leakage field’,
as distinct from the useful axial field which it is the coil’s purpose to
produce.
Taking Oersted’s Law literally, any
current in a wire gives rise to a field around it, and the strength of that
field is proportional to the strength of the current producing it. This applies to the direction of the
current also. A current flowing in one
direction will produce a certain field; the same magnitude of current flowing
in the opposite direction will produce a field of the same strength but in the
opposite direction.
Thus in Figure 3.1, with an
alternating current flowing, if the current direction in one half-cycle is as
shown, the field direction at the same time is also as shown. Half a cycle later the current will be
flowing in the opposite direction; so too the field will be in the opposite
direction.
Therefore an alternating current
will produce a corresponding alternating field, whose strength at any instant
is proportional to the magnitude of the current at that instant and which
varies ‘in phase’ with the current - that is, it rises, falls and reverses in
exact synchronism with it.
3.2 ROTATING MAGNETIC FIELD
A rotating magnetic field is an
essential part of all electrical machines. In an a.c. generator it is provided
by the rotor carrying d.c.-excited magnetic poles, whose effect is just as if a
large permanent magnet were rotating inside the machine.
A rotating field is also necessary
for the operation of an induction motor (see manual ‘Electric Motors’), where
it must be produced by the stator which, of course, is not moving. The problem then is: how to produce a moving,
rotating magnetic field from stationary windings.
Fortunately this is possible if the
supply is 3-phase. Three separate
windings are provided in the stator slots, and their axes are arranged to be
displaced in space by 120° as explained in Chapter 1. Also the three alternating line voltages of a
3-phase system are displaced 120° in time. It is this combination which makes possible a
rotating magnetic field. This can be
proved mathematically, but the following description explains it using first
principles.
FIGURE 3.2
ROTATING MAGNETIC FIELD
In the centre of Figure 3.2 are
shown the three stator windings of an induction motor, each drawn as a simple
coil. The winding which is connected to
each phase is distinguished by its colour - red, yellow or blue. The three windings are distributed 120° apart in space around the stator.
At the top is shown one cycle of
currents of the 3-phase supply, each current wave being coloured. The 120° displacement in time is clearly seen.
The current in each of the three
windings gives rise to a magnetic field along its axis; these are shown by
coloured arrows for each field near the centre of the figure. As the current alternates, so also does the
direction of the field along its axis.
The convention has been adopted that, when the current is positive
(above the line in the upper part of the figure), the arrow points towards the centre, and when it is
negative, it points away from the centre.
Looking at the left-hand centre
figure, taken at the instant where t = 0 (left-hand edge of the current
waves), R phase current is at its maximum positive, and Y and B phases are
negative and both equal in magnitude to half the maximum. Therefore the R phase flux is shown as ‘1’
with its arrow pointing towards the centre, and Y and B phase fluxes are both
shown as ‘½’ with their arrows pointing away from the centre.
These arrows can be regarded as flux
vectors, and in the bottom figure they are resolved. The R phase flux is at 12 o’clock and
pointing downwards, and the Y and B phase fluxes are respectively at 4 and 8
o’clock, half the length of R and pointing outwards in those directions. The latter two, by normal vector addition,
combine to give a single flux of length ½ at 6 o’clock in a downward direction.
The R phase (length 1) and the
combined Y and B phases (length ½) are both in the same direction and add
together to give a single resultant flux of length 1½ in a 6 o’clock direction.
If exactly the same procedure is
adopted for a time one-third of cycle (120°) later, Y phase is now at a maximum positive and B and R phases at
half that value negative. B and R now
combine to add to Y, giving a resultant flux of magnitude 1½ in the 10 o’clock
direction.
Similarly at a time one-third of a
cycle still later (240°), B phase is at a maximum positive and
R and Y phases at half that value negative.
R and Y now combine to add to B, giving a resultant flux of magnitude 1½
in the 2 o’clock direction.
One-third of a cycle still later
(360°) the conditions are the same as at 0° (t = 0), and the process
repeats with each cycle.
As time advances and the current
cycle changes from 0°, through 120° and 240°, back to 0° and then repeats, the resultant flux constantly changes direction
(but not magnitude, which remains constant at 1½) and swings from 6 o’clock,
through 10 and 2 o’clock, back to 6 o’clock and then starts again. Although only three different points in the
cycle have been described, the same treatment at intermediate points would show
the resultant flux in intermediate positions.
For example, if the currents were taken at 60° and the fluxes combined as before, the resultant flux would come
out at 8 o’clock.
This is therefore a continuous
process, and the resultant flux direction moves continuously round the stator,
remaining constant in magnitude and completing one revolution per cycle of
supply. A rotating magnetic field has
been produced from a set of stationary stator windings.
Note: the statement that the flux
completes one revolution per cycle of supply is only true when there is one winding
per phase as shown in Figure 3.2; this is a so-called ‘2-pole’ machine (by
analogy with d.c.), and with a 60Hz supply the field rotates at 60 rev/s or
3 600 rev/mm (with 50Hz at 50 rev/s or 3 000 rev/mm). If there were two windings per phase (‘4-pole’ machine), a similar treatment
would show that the field rotates only half a revolution per cycle, so that it
makes one revolution per two cycles; at 60Hz this is 30 rev/s or 1 800
rev/mm (at 50Hz, 25 rev/s or 1 500 rev/mm). Similarly a ‘6-pole’ machine (three windings
per phase) would at 60Hz have 1 200 rev/mm (50Hz, 1 000 rev/mm), and
so on.
3.3 ROTATING FIELD FROM SINGLE PHASE
What has been described (para. 3.2)
is the production of a rotating field from a 3-phase supply. It can however be done from a single-phase
supply, although it is seldom found except in the smallest motors which have
only a single-phase supply to run on.
FIGURE 3.3
ROTATING FIELD FROM
SINGLE-PHASE SUPPLY
(APPLIED TO A CAPACITOR
MOTOR)
It is achieved by giving the motor
two separate windings displaced in space by 90° One, the ‘running’ winding,
is fed direct from the single-phase supply, and the other, the ‘starting
winding’, is fed from the same supply but through a series capacitor. This causes the current in that winding to lead nearly 90° on the current in the other, so there is the situation where the
two windings are displaced 90° in space and are fed from supplies 90° displaced in time. By an
exactly similar treatment to that used for the 3-phase case, it will be found
that this too will produce a rotating field, enabling the motor to start and
run. Such a motor is referred to as a
‘Capacitor Motor’ or ‘Split Field Motor’.
It is further described in the manual ‘Electric Motors’.
On most such motors a centrifugal switch
cuts out the capacitor-fed starting winding when the motor is up to speed; it
will then continue to run with only its single-phase ‘running’ winding
connected. Very small motors often
dispense with the centrifugal switch and leave the capacitor in circuit all the
time.
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