One thing that happens in the real world is moving stuff. Eliminating moving parts is a commonly sought-after goal in the world of electronics. However, I suspect that sometime in your career you will need to make things move and you will be thrust into the world of electromechanical devices. Considering that what I knew about motors when I left school could be written on the thin edge of a postage stamp, 9 I felt a need to cover some of the basics behind
motors and a few other electromechanical devices here.
DC Motors
My eldest son was elated when he got a Lego Mindstorms kit for Christmas a few years back. For those who don’t know, this is a ready-made robot kit based on—you guessed it—Legos. My wife claims I was much more excited than our son was. I beg to differ, but we won’t go into that now. The whole point of a robot is that it moves. The Lego kit uses little DC permanent magnet motors with gears and such to get along. Since this type of motor is so popular, a lit- tle discussion about DC permanent magnet motors and how to control them seems prudent.
The DC permanent magnet (PM) brush motor is probably the easiest motor to understand. It consists of just a few parts: an armature, some magnets, a case, wires, and brushes. I remember as a kid making a motor out of a couple of nails, a dowel, and some wire. It looked something like what’s in Figure 4.7 .
You can make a motor by winding the wire onto the armature in a loop. The ends of the wire terminate on segments that the brushes rub on, as shown in
Figure 4.8 .
Permanent magnets are attached to the case in such a way as to surround the armature. The armature is supported in the case by bearings or bushings so that it can rotate freely. At its most basic, the coil of wire on the armature is nothing more than an inductor. As we learned earlier, an inductor develops a magnetic fi eld when you pass current through it. This magnetic fi eld is just like the one present around the permanent magnet. By controlling when the magnetic fi eld is present around the armature, you cause the fi eld around the
9 My father was fond of this saying, so as a boy I spent more than a little bit of time looking at a stamp on edge and wondering just what you could fi t there …
CHAPTER 4 The Real World
152wires to push or pull against the fi eld around the magnet. The current to the armature is switched on and off (which turns the magnetic fi eld on and off) in a sequence that causes the armature to turn. This is calledcommutation. In the DC PM brush motor, the brushes are the method of commutation. They switch the current through various sections of the armature as it turns.
FIGURE 4.7
A home-built motor.
FIGURE 4.8
A DC PM motor has two inputs and two outputs. You put voltage and current in and get speed and torque out. One nice thing is that the speed is proportional to the voltage and the torque is proportional to the current. Motors are devices in which the physical equivalents of electric components are not only similar in nature but are actually linked in performance. Think of it this way: Voltage and current together equal power. Speed and torque together also equal power. So in a motoryou put electrical power in and get mechanical power out. That actually makes sense, doesn’t it? The equivalent circuit looks like the one shown in Figure 4.9 . What do you think the resistor is doing in this circuit? Have you ever noticed a motor getting warm when it operates? This heating comes from the resistive component in the motor. Any wire short of a superconductor has resistance. The armature, being made out of wire, also has resistance. Current fl owing through a resistor will create a voltage drop across said resistor, and power across that resistor turns into heat. Ohm’s Law still works.
The inductor creates the magnetic fi eld that turns the armature. The battery rep- resents what is called the back EMF, or electromotive force. If you were to spin the shaft of the motor with nothing but a voltmeter hooked up to it, you would see a voltage appear on this meter that is proportional to the speed at which you spin the shaft. When you apply a voltage to the motor, the shaft will spin at a speed in the same proportion. However, not all the voltage you apply to the leads makes it to this point in the motor. Some of it is lost across the resistor. All this leads to some characteristic equations of this type of motor.
R
L
V F(KV)
FIGURE 4.9
Inside a DC PM motor.
CHAPTER 4 The Real World
154The relationship between voltage and speed is known as the voltage constant , with units of volts per Krpm. It is referred to as Ke or Kv :
K V IR
Krpm
ν Eq. 4.1
V the amount of voltage applied at the leads
I the current fl owing through the motor
R the equivalent resistance of the motor 10
Krpm the speed of the shaft in thousands of revolutions per minute The IR term in this equation accounts for the loss of heat in the motor. As current approaches zero, this effect disappears. This is what happened earlier when we hooked it up to a voltmeter and spun the shaft, reading the voltage generated. Do you see how that minimizes the error, giving you an accurate idea of the voltage constant?
The relationship between current and torque is known as the torque constant , usually referred to asKi, which has the units inch-ounces per amp (in-oz/amp):
K V IR Krpm ν Eq. 4.2 T torque in inch-ounces
I the current in amps
These two constants are linked; changing one changes the other. In fact, if you know one, you can calculate the other with this equation:
K T I t Eq. 4.3 Kt Kv [Nm/A; V/rad/s] Kt 9.5493 10 3 Kv [Nm/A; V/Krpm] Kt 1.3524 Kv [oz-in/A; V/Krpm]
As you can see, it turns out that we are really only dealing with one constant in the motor. This constant is controlled by the number of windings on the
10 Note that you can get a fairly close idea of this with a simple ohmmeter turning the arma- ture very, very slowly. (Too fast and the voltage generated will mess up the reading.) To be more precise, you need to take the resistance of the brushes and the way they contact the armature into account, a discussion that we will save for another book.
armature and the strength of the magnets. More windings increase the voltage/ torque constant, fewer decrease it. The size of the armature and the strength of the magnets also affect this constant.
We now know that the main electrical components of a motor are resistance, inductance, and a voltage source. Can you extrapolate the mechanical proper- ties? They are friction and inertia. 11 The fi rst thing you should note is that the load, or whatever is hooked to the motor shaft, will likely be the largest con- tributor to these two characteristic factors, masking the effects of the armature inertia and brush or bearing friction.
Inertia will tend to make the motor take time spinning up to speed, increasing the load and current draw as you accelerate. Once at speed, inertia will tend to keep the motor spinning, so during deceleration you will notice a lessening of the current the motor needs.
Friction will create a constant load on the motor that will appear as an increase in current in our “ sparky ” universe. To gain further light and knowledge on all things motor, I refer the reader to the “ pink book. ” 12
“ But what about the Lego Mindstorms? ” you ask. Well, my boys and I have built quite a few projects, but my oldest son lost interest since we couldn’t seem to build a robot that would clean his room. I told him that I sincerely hope he can someday solve that particular problem, but till then it is up to him to get the job done.