I always thought I knew a lot
about motors. Last week I realized there was a very basic question that I
couldn’t answer. Does a motor work by magnetic attraction or by repulsion? It’s
a funny question.
I know we all built little motors
in grade six. There were two magnets; the idea was that you switch the
polarity on the rotating magnet every time the pole passes under the stationary
magnetic. So it’s always attracting. Actually, if you think about it, it’s
repelling just as much as it’s attracting. But that’s not the case I want to
talk about.
Ninety percent of all motors in
the world are AC induction motors. Maybe 98%. I’ve always thought of the
induction motor as one of the most ingenious inventions of all time: because even
after you’ve seen it work, it’s really hard to explain exactly what’s
happening. (By the way, I think Tesla gets credit for the invention; I don’t
know if it was an evolutionary thing that came about naturally, or if he just
pulled it out of his ass one day. But that’s another story.)
There is a small complication
with understanding induction motors, and that is the issue of rotation of the
field, which is problematic on small household motors running on single-phase
power. The problem goes away when we consider three-phase motors, which are the
workhorse of heavy industry. With three-phase power, you easily get a rotating
magnetic field set up in the stationary part of the motor (the “stator”). My
purpose today is not to explain how that works; I’m just going to take note of
the fact that the magnetic field rotates in sync with the AC power frequency.
The rotor gets dragged along by this rotating field: the question is, how
exactly does this happen?
There are of course no wires
connected to the rotor. Current flows in the rotor, but it flows via inductive
pickup. The rotating magnetic field in the stator induces currents in the
rotor: the interaction between those two systems of currents creates a torque,
and the motor turns. Simple? I don’t think so. If you think it’s simple, I’m
going to aks a question that goes to the very core of how the motor works, and
I guarantee you won’t be able to answer it. Bear with me...
I read something many years ago
that I thought gave me a tremendous insight into how motors work. I don’t
remember where I read it but this is what it said: At the speed when a motor
develops its maximum torque, the resistance of the rotor is equal to its
inductive reactance. That’s it: that’s the key to understanding induction
motors.
An induction motor is a kind of
rotating transformer. The stator is the primary winding, and the rotor is the
secondary winding. The alternating current in the primary winding (the stator)
sets up an alternating magnetic field. The alternating magnetic field sets up
an alternating voltage in the secondary winding (the rotor). The alternating
volatage drives the rotor current. The catch is, that the rotor is rotating,
which means that the frequency of the AC voltage in the rotor is different from
the frequency in the stator. If the rotor is stationary, it sees the same
frequency as the primary, or 60 Hz. But if it winds up to sychronous speed,
there is zero frequency in the second winding. With no frequency, there is no
induced voltage, and no current. If there is no current, there is no torque,
and the motor doesn’t turn. That’s why an induction motor can never run at
synchronous speed.
In practice, an induction motor
almost always runs just a little slower than the line frequency, so that from
the point of view of the rotor, there is always an alternating voltage to drive
the current, even if that voltage only reverses once or twice a second. The
smaller this driving frequency, the less voltage is available. That’s because
it is the field which is constant, and the amount of voltage is proportional to
the frequency of the alternating field. So as the motor approaches synchronous
speed, the voltage in the rotor approaches zero.
Doesn’t that mean that the
current also approaches zero; that the maximum flows when you have maximum
voltage, which occurs at maximum frequency, which from the rotor’s point of
view is when the rotor is stationary? Here’s where it gets interesting.
The amount of current is not the
only thing that determines the torque. You also have to consider the relative
displacement between the rotor currents and the stator currents. There is no torque
unless there is some relative displacement. There is force, but the force is
all in the radial direction, so it has no effect. Ideally, the magnetic fields
of the rotor and stator should be at ninety degrees to each other, just like in
the little toy DC motor you wound in Grade Six. But just what is it that allows
you to control the relative angle of the fields in an induction motor?
In Electrical Engineering we
learn abous something called leading and lagging current. In AC power, when the
voltage is a sine wave, the current also flows in a sine wave. For a simple
resistive device like a toaster, the current flows in sync with the voltage.
The two sine waves track each other. But for other types of devices, this doesn’t
always hold. For devices with magnetic windings, the current tends to lag
behind the voltage, to a maximum of ninety degrees. For other types of devices,
known as capacitors, the current can even flow ahead of the voltage; it’s
called a leading power factor and we don’t need to worry about that for now.
The nature of a motor winding is
that is is partially resistive, like a toaster, and partially inductive. If the
rotor winding were made of superconducting copper, it would be pure inductance,
but that’s not how is is. There is always some resistance, and we will see that
the resistance becomes significant.
It is the nature of inductance
that as the driving frequency increases, the inductive resistance also
increases; wheras the pure, “toaster-style” resistance doesn’t change. The
combination of ordinary and inductive resistance is called the impedance, and
it depends on the driving frequency. In the rotor of an induction motor, it
turns out that in starting conditions, when the rotor sees the full 60-Hz of
the line frequency, the rotor impedance is mostly inductive; so the current
lags the voltage by almost 90 degrees. On the other hand, as the motor comes up
to speed, the inductance impedance gets lower and lower until finally, at some
point, it is less than the ordinary resistance. Even though the copper may be
very good copper, it still has resistance, and in the absence of inductance
that is the only thing to limit the current. That’s why you don’t need a lot of
voltage to drive the rotor currents near synchronous speed: although the
available voltage has become very low, there is at the same time very little
resistance.
The important thing to note is
that as the rotor goes from zero 100% of synchronous speed, the impedance
changes from inductive to resistive; and therefore, the relative phase of the two magnetic fields changes by ninety
degrees. To be clear, when we talk about relative phase we usually mean the
time lag between the driving voltage and the driven current; but in the case of
motors, this time lag translates directly into a physical angle of displacement
between the two fields.
And that’s where the optimization
comes in. As you go from zero to 100%, the rotor voltage is decreasing. So the
current is going down. But at the same time, the phase angle is advancing through
ninety degrees, as the impedance of the rotor changes from a pure inductance to
a pure resistance. It turns out that at the same time the current is become “less
favorable” to the development of torque, the phase angle is becoming…more favorable. Somewhere there is an
optimum.
And I already told you where it
occurs. It’s something I read in a book and it always stuck in my mind: the
maximum torque of a motor occurs at that speed where the inductive impedance of
the rotor becomes equal to its resistive impedance. At that speed, the torque
is a maxium and the physical angle between the stator field and the rotor field
is 45 degrees.
This is a tremendously useful
insight, and we will have more to say about it. But there is one more nagging
question that is still not answered. What is the polarity of the relative
phase? If we identify the north pole of the stator field, then where is the
rotor field? Because there are two possibilities. We might have a south pole in
the rotor, trailing behind the rotor by 45 degrees, and getting dragged along
because north attracts south. Or we might just as well have a north pole, 45
degrees ahead of the stator field,
getting pushed along because north repels north!
Which one is it? It can’t be
both; it has to be one or the other. Does the induction motor work by
attraction or repulsion?
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