Basic Motor Theory

It has been said that if the Ancient Romans, with their advanced civilization and knowledge of the sciences, had been able to develop a steam motor, the course of history would have been much different. The development of the electric motor in modern times has indicated the truth in this theory. The development of the electric motor has given us the most efficient and effective means to do work known to man. Because of the electric motor we have been able to greatly reduce the painstaking toil of man's survival and have been able to build a civilization which is now reaching to the stars. The electric motor is a simple device in principle. It converts electric energy into mechanical energy. Over the years, electric motors have changed substantially in design, however the basic principles have remained the same. In this section of the Action Guide we will discuss these basic motor principles. We will discuss the phenomena of magnetism, AC current and basic motor operation.

Now, before we discuss basic motor operation a short review of magnetism might be helpful to many of us. We all know that a permanent magnet will attract and hold metal objects when the object is near or in contact with the magnet. The permanent magnet is able to do this because of its inherent magnetic force which is referred to as a "magnetic field". In Figure 1 , the magnetic field of two permanent magnets are represented by "lines of flux". These lines of flux help us to visualize the magnetic field of any magnet even though they only represent an invisible phenomena. The number of lines of flux vary from one magnetic field to another. The stronger the magnetic field, the greater the number of lines of flux which are drawn to represent the magnetic field. The lines of flux are drawn with a direction indicated since we should visualize these lines and the magnetic field they represent as having a distinct movement from a N-pole to a S-pole as shown in Figure 1. Another but similar type of magnetic field is produced around an electrical conductor when an electric current is passed through the conductor as shown in Figure 2-a. These lines of flux define the magnetic field and are in the form of concentric circles around the wire. Some of you may remember the old "Left Hand Rule" as shown in Figure 2-b. The rule states that if you point the thumb of your left hand in the direction of the current, your fingers will point in the direction of the magnetic field.

Figure 1 - The lines of flux of a magnetic field travel from the N-pole to the S-pole.

Figure 2 - The flow of electrical current in a conductor sets up concentric lines of magnetic flux around the conductor.

When the wire is shaped into a coil as shown in Figure 3, all the individual flux lines produced by each section of wire join together to form one large magnetic field around the total coil. As with the permanent magnet, these flux lines leave the north of the coil and re-enter the coil at its south pole. The magnetic field of a wire coil is much greater and more localized than the magnetic field around the plain conductor before being formed into a coil. This magnetic field around the coil can be strengthened even more by placing a core of iron or similar metal in the center of the core. The metal core presents less resistance to the lines of flux than the air, thereby causing the field strength to increase. (This is exactly how a stator coil is made; a coil of wire with a steel core.) The advantage of a magnetic field which is produced by a current carrying coil of wire is that when the current is reversed in direction the poles of the magnetic field will switch positions since the lines of flux have changed direction. This phenomenon is illustrated in Figure 4. Without this magnetic phenomenon existing, the AC motor as we know it today would not exist.

Figure 4 - The poles of an electro-magnetic coil change when the direction of current flow changes.

The basic principle of all motors can easily be shown using two electromagnets and a permanent magnet. Current is passed through coil no. 1 in such a direction that a north pole is established and through coil no. 2 in such a direction that a south pole is established. A permanent magnet with a north and south pole is the moving part of this simple motor. In Figure 5-a the north pole of the permanent magnet is opposite the north pole of the electromagnet. Similarly, the south poles are opposite each other. Like magnetic poles repel each other, causing the movable permanent magnet to begin to turn. After it turns part way around, the force of attraction between the unlike poles becomes strong enough to keep the permanent magnet rotating. The rotating magnet continues to turn until the unlike poles are lined up. At this point the rotor would normally stop because of the attraction between the unlike poles. (Figure 5-b)

Figure 5

If, however, the direction of currents in the electromagnetic coils was suddenly reversed, thereby reversing the polarity of the two coils, then the poles would again be opposites and repel each other. (Figure 5-c). The movable permanent magnet would then continue to rotate. If the current direction in the electromagnetic coils was changed every time the magnet turned 180 degrees or halfway around,then the magnet would continue to rotate. This simple device is a motor in its simplest form. An actual motor is more complex than the simple device shown above, but the principle is the same.

How is the current reversed in the coil so as to change the coils polarity, you ask. Well, as you probably know, the difference between DC and AC is that with DC the current flows in only one direction while with AC the direction of current flow changes periodically. In the case of common AC that is used throughout most of the United States, the current flow changes direction 120 times every second. This current is referred to as "60 cycle AC" or "60 Hertz AC" in honor of Mr. Hertz who first conceived the AC current concept. Another characteristic of current flow is that it can vary in quantity. We can have a 5 amp, 10 amp or 100 amp flow for instance. With pure DC, this means that the current flow is actually 5,10, or 100 amps on a continuous basis. We can visualize this on a simple time-current graph by a straight line as shown in Figure 6.

Figure 6 - Visualization of DC

But with AC it is different. As you can well imagine, it would be rather difficult for the current to be flowing at say 100 amps in a positive direction one moment and then at the next moment be flowing at an equal intensity in the negative direction. Instead, as the current is getting ready to change directions, it first tapers off until it reaches zero flow and then gradually builds up in the other direction. See Figure 7. Note that the maximum current flow (the peaks of the line) in each direction is more than the specified value (100 amps in this case). Therefore, the specified value is given as an average. It is actually called a "root mean square" value, but don't worry about remembering this because it is of no importance to us at this time. What is important in our study of motors, is to realize that the strength of the magnetic field produced by an AC electro-magnetic coil increases and decreases with the increase and decrease of this alternating current flow.

Figure 7 - Visualization of AC.

An AC motor has two basic electrical parts: a "stator" and a "rotor" as shown in Figure 8. The stator is in the stationary electrical component. It consists of a group of individual electro-magnets arranged in such a way that they form a hollow cylinder, with one pole of each magnet facing toward the center of the group. The term, "stator" is derived from the word stationary. The stator then is the stationary part of the motor. The rotor is the rotating electrical component. It also consists of a group of electro-magnets arranged around a cylinder, with the poles facing toward the stator poles. The rotor, obviously, is located inside the stator and is mounted on the motor's shaft. The term "rotor" is derived from the word rotating. The rotor then is the rotating part of the motor. The objective of these motor components is to make the rotor rotate which in turn will rotate the motor shaft. This rotation will occur because of the previously discussed magnetic phenomenon that unlike magnetic poles attract each other and like poles repel. If we progressively change the polarity of the stator poles in such a way that their combined magnetic field rotates, then the rotor will follow and rotate with the magnetic field of the stator.

Figure 8 - Basic electrical components of an AC motor.

This "rotating magnetic fields of the stator can be better understood by examining Figure 9. As shown, the stator has six magnetic poles and the rotor has two poles. At time 1, stator poles A-1 and C-2 are north poles and the opposite poles, A-2 and C-1, are south poles. The S-pole of the rotor is attracted by the two N-poles of the stator and the N-pole of the rotor is attracted by the two south poles of the stator. At time 2, the polarity of the stator poles is changed so that now C-2 and B-1 and N-poles and C-1 and B-2 are S-poles. The rotor then is forced to rotate 60 degrees to line up with the stator poles as shown. At time 3, B-1 and A-2 are N. At time 4, A-2 and C-1 are N. As each change is made, the poles of the rotor are attracted by the opposite poles on the stator. Thus, as the magnetic field of the stator rotates, the rotor is forced to rotate with it.

Figure 9 - The rotating magnetic field of an AC motor.

One way to produce a rotating magnetic field in the stator of an AC motor is to use a three-phase power supply for the stator coils. What, you may ask, is three-phase power? The answer to that question can be better understood if we first examine single-phase power. Figure 7 is the visualization of single-phase power. The associated AC generator is producing just one flow of electrical current whose direction and intensity varies as indicated by the single solid line on the graph. From time 0 to time 3, current is flowing in the conductor in the positive direction. From time 3 to time 6, current is flowing in the negative. At any one time, the current is only flowing in one direction. But some generators produce three separate current flows (phases) all superimposed on the same circuit. This is referred to as three-phase power. At any one instant, however, the direction and intensity of each separate current flow are not the same as the other phases. This is illustrated in Figure 10. The three separate phases (current flows) are labeled A, B and C. At time 1, phase A is at zero amps, phase B is near its maximum amperage and flowing in the positive direction, and phase C is near to its maximum amperage but flowing in the negative direction. At time 2, the amperage of phase A is increasing and flow is positive, the amperage of phase B is decreasing and its flow is still negative, and phase C has dropped to zero amps. A complete cycle (from zero to maximum in one direction, to zero and to maximum in the other direction, and back to zero) takes one complete revolution of the generator. Therefore, a complete cycle, is said to have 360 electrical degrees. In examining Figure 10, we see that each phase is displaced 120 degrees from the other two phases. Therefore, we say they are 120 degrees out of phase.

Figure 10 - The pattern of the separate phases of three-phase power.

To produce a rotating magnetic field in the stator of a three-phase AC motor, all that needs to be done is wind the stator coils properly and connect the power supply leads correctly. The connection for a 6 pole stator is shown in Figure 11. Each phase of the three-phase power supply is connected to opposite poles and the associated coils are wound in the same direction. As you will recall from Figure 4, the polarity of the poles of an electro-magnet are determined by the direction of the current flow through the coil. Therefore, if two opposite stator electro-magnets are wound in the same direction, the polarity of the facing poles must be opposite. Therefore, when pole A1 is N, pole A2 is S. When pole B1 is N, B2 is S and so forth.

Figure 11 - Method of connecting three-phase power to a six-pole stator.

Figure 12 shows how the rotating magnetic field is produced. At time1, the current flow in the phase "A" poles is positive and pole A-1 is N. The current flow in the phase "C" poles is negative, making C-2 a N-pole and C-1 is S. There is no current flow in phase "B", so these poles are not magnetized. At time 2, the phases have shifted 60 degrees, making poles C-2 and B-1 both N and C-1 and B-2 both S. Thus, as the phases shift their current flow, the resultant N and S poles move clockwise around the stator, producing a rotating magnetic field. The rotor acts like a bar magnet, being pulled along by the rotating magnetic field.

Figure 12 - How three-phase power produces a rotating magnetic field.

Up to this point not much has been said about the rotor. In the previous examples, it has been assumed the rotor poles were wound with coils, just as the stator poles, and supplied with DC to create fixed polarity poles. This, by the way, is exactly how a synchronous AC motor works. However, most AC motors being used today are not synchronous motors. Instead, so-called "induction" motors are the workhorses of industry. So how is an induction motor different? The big difference is the manner in which current is supplied to the rotor. This is no external power supply. As you might imagine from the motor's name, an induction technique is used instead. Induction is another characteristic of magnetism. It is a natural phenomena which occurs when a conductor (aluminum bars in the case of a rotor, see Figure 13) is moved through an existing magnetic field or when a magnetic field is moved past a conductor. In either case, the relative motion of the two causes an electric current to flow in the conductor. This is referred to as "induced" current flow. In other words, in an induction motor the current flow in the rotor is not caused by any direct connection of the conductors to a voltage source, but rather by the influence of the rotor conductors cutting across the lines of flux produced by the stator magnetic fields. The induced current which is produced in the rotor results in a magnetic field around the rotor conductors as shown in Figure 14. This magnetic field around each rotor conductor will cause each rotor conductor to act like the permanent magnet in the Figure 9 example. As the magnetic field of the stator rotates, due to the effect of the three-phase AC power supply, the induced magnetic field of the rotor will be attracted and will follow the rotation. The rotor is connected to the motor shaft, so the shaft will rotate and drive the connection load. That's how a motor works! Simple, was it not?

Figure 13 - Construction of an AC induction motor's rotor.

Figure 14 - How voltage is induced in the rotor, resulting in current flow in the rotor conductors.

Preface

The intent of this paper is to provide one with an understanding of DC Motors in order that they can be applied with confidence. This paper contains basic information and specific information that applies to Reliance Medium HP and Large HP DC Motors. Due to the nature of Rockwell Systems business, emphasis has been placed on the Large DC motor product line.

The first generators and motors were called dynamos or dynamoelertric machines. Dynamo is from the Greek word dynamis which means power. Webster defines dynamoelectric as "relating to the conversion of mechanical energy into electrical energy or vice versa". The word motor is from the Latin word motus which means one that imparts motion or prime mover. The dynamo was the result of the efforts of several people, in different countries, in the mid-nineteenth century, to make electricity work for them.

Definitions

Landmarks Of Electric Motor Development

The first practical dynamo, about 1867

Section 2: Electric Motor And Generator Basics

Faraday's Law
In order that current can be obtained from an electric circuit, an electromotive force (voltage) must be established and maintained between the two ends of the circuit. This electromotive force may be established in several ways, one of which is by means of an electromagnetic generator.

Michael Faraday discovered that an electric potential can be established between the ends of a conductor in the following three ways:

Faraday's law states that, "the EMF (electromotive force) induced between the ends of a loop or coil is proportional to the rate of change of magnetic flux enclosed by the coil; or the EMF induced between the ends of a bar conductor is proportional to the time rate at which magnetic flux is cut by the conductor."

This law emphasizes rate of change or rate or flux cutting rather than density or extent of magnetic field.

Lenz's Law
Lenz's Law states that, "A change in the magnetic flux passing through or linking with, a loop or coil causes EMF to be induced in a direction to oppose any change in circuit conditions, this opposition being produced magnetically when current flows in response to the induced EMF."

Whenever there is a change in current in a magnetizing coil, which works to change the flux in the coil, a voltage is induced which tends to prevent the change. Thus, if we attempt to diminish the current flowing in a magnetizing coil, a voltage will be developed that will tend to keep the current unchanged. Likewise, if we attempt to establish a current in a magnetizing coil, a voltage will be developed that will tend to keep the current from increasing.

Energy Conversion
To produce voltage, it is necessary to move a conductor through a magnetic field as stated above. Mechanical energy is required to provide motion to this conductor. With the field energy remaining constant, the conductor is changing mechanical energy into electrical energy.

Voltage Generation
There is a definite relationship between the direction of the magnetic flux, the direction of motion of the conductor and the direction of the induced EMF. Figure 1 shows the motion of the conductor perpendicular to the magnetic field. The voltage and current output are perpendicular to both the motion of the conductor and the magnetic field.

To illustrate this with Fleming's right hand rule, the thumb and first two fingers of the right hand are extended at right angles to one another, the thumb will indicate the direction of motion of the conductor, the forefinger will indicate the direction of the magnetic field, and the middle finger will indicate the direction of voltage or current.

Applying this rule, one can see that the current will reverse if the motion of the conductor changes from down to up. This is true even though the magnetic field does not change position. Therefore, the rotating coil in Figure 2 will produce a voltage which is continually changing direction.

The coil in position AB, in figure 2, encloses the maximum amount of flux. The flux decreases as the coil moves toward position CD and becomes zero at CD, since the plane of the coil is parallel to the magnetic field. Then the flux increases in the opposite direction, reaching a negative maximum at BA and diminishing again to zero at DC. The flux reverses and increases again in the original direction to reach a maximum at AB.

Although the flux is maximum at positions AB and BA and zero at positions CD and DC, the induced EMF will be maximum at positions CD and DC and zero at positions AB and BA. This is true because the EMF depends upon the rate of change of flux or rate of cutting flux lines and not upon the quantity enclosed.

If the coil in Figure 2 were rotated at a constant speed in a uniform magnetic field, a sine wave of voltage would be obtained. This is shown in Figure 3 where both the amount of flux enclosed and the EMF induced are plotted against time.

Value of Generated Voltage
The EMF at any instant of time is proportional to the number of turns in the coil times rate of change of flux. The C.G.S. (centimeter gram second) unit of EMF known as the abvolt is defined as that value induced, in a coil of one turn, when the flux linking with the coil is changing at the rate of one line or Maxwell per second; or as that value induced when magnetic flux is being cut by the conductor at the rate of one line per second. A volt is equal to 108 abvolts or an abvolt is equal to 10^-8 volts. Therefore, the instantaneous value of voltage is expressed as:

where:

This equation can be further developed to obtain the voltage for movement of a conductor at constant velocity through a uniform magnetic field:

where:

If the conductor moves directly across the field at right angles to it, then = 90° and sin = 1. The equation then becomes:

It should be noted that this equation is a special form of the original equation and is not applicable in all cases.

Energy Conversion
As stated above, mechanical energy is changed into electrical energy by movement of conductor through a magnetic field. The converse of this is also true. If electrical energy is supplied to a conductor lying normal to a magnetic field, resulting in current flow in the conductor, a mechanical force and thus mechanical energy will be produced.

Producing Mechanical Force
As in the generator, the motor has a definite relationship between the direction of the magnetic flux, the direction of motion of the conductor or force, and the direction of the applied voltage or current.

Since the motor is the reverse of the generator, Fleming's left hand rule can be used. If the thumb and first two fingers of the left hand are extended at right angles to one another, the thumb will indicate the direction of motion, the forefinger will indicate the direction of the magnetic field, and the middle finger will indicate the direction of current. In either the motor or generator, if the directions of any two factors are known, the third can be easily determined.

Value of Mechanical Force
The force exerted upon a current carrying conductor is dependent upon the density of the magnetic field, the length of conductor, and the value of current flowing in the conductor. Assuming that the conductor is located at right angles to the magnetic field, the force developed can be expressed as follows:

where:

At the same time torque is being produced, the conductors are moving in a magnetic field and generating a voltage. This voltage is in opposition to the voltage that causes current flow through the conductor and is referred to as a countervoltage or back EMF. The value of current flowing through the armature is dependent upon the difference between the applied voltage and the countervoltage.

Sample Calculations

Generator

Given:

Find:

Motor

Given:

Find:

Generator

In a generator, moving a conductor through a stationary magnetic field generates voltage. If a coil is rotated through a magnetic field as shown in Figure 4, an alternating voltage will be produced. To make this voltage available to a stationary external circuit, two slip rings and brushes must be provided. For the external circuit to produce DC voltage, it is necessary to reverse the polarity of the external leads at the same time the voltage in the coil is reversed. This is accomplished by segmenting a slip ring to form what is called a commutator. An elementary two segment commutator is illustrated in Figure 5. This single coil, two piece commutator will yield an unidirectional but pulsating voltage as shown in Figure 6. However, when a large number of commutator segments or bars is used, the resulting voltage will be more uniform as shown in Figure 7.

Figure 6.
Unidirectional, Pulsating Voltage

Figure 7.
Uniform DC Voltage

As stated above, the generated voltage in a single conductor is:

where:

This equation can be developed to the following equation for DC machines:

where:

This equation represents the average voltage. For a given machine, it can be reduced to:

where:

Motor

As stated previously, if current is supplied to a conductor in a magnetic field, a force will be produced. The force developed in a single conductor is:

where:

This equation can be developed to the following for DC motors:

where:

For a given machine, this can be reduced to:

where:

K₂ is not the same as the K₁ for voltage. The above torque is not the output torque of the shaft, but rather the total torque developed by the armature. Part of this total torque is needed to overcome the inertia of the armature itself.

The horsepower output of any motor can be expressed as:

where:

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