An Introduction to Motors

As an introduction to motors, this article explains the basic principles of electric motors. The basic information presented here should be acquired first before learning about motor driving and motor control technology. The reader should also be aware that some knowledge of physics will be necessary to understand this explanation of motor fundamentals.

We begin with a basic explanation of motors.

What are Motors?

Motors are devices that create and output motive power. They may use various kinds of energy to generate motive power, but in this article, the motors being discussed are electric motors. These motors convert electrical energy into mechanical energy.

The electrical energy in question is a voltage and current that are applied to a motor. The electrical power is found by multiplying the voltage and the current. A motor uses this electrical energy to create an electromagnet. Here, “creating an electromagnet” means applying a voltage to the two ends of a coil (windings) and passing an electrical current, to create a magnet.

The mechanical energy is the rotational (turning) force of a motor. This rotational force is called torque. By generating this torque, a motor moves an object that is attached to the motor.

From the above, a “device that converts electrical energy into mechanical energy” is in fact a “device that uses electrical power to move things.”

How, then, does a motor change electrical power into motive power? In order to understand this principle of the motor, it is first necessary to understand electromagnets and torques.

The Basics of Electromagnets

An electromagnet consists of an electric conductor wound around a magnetic material; by passing a current through the conductor, the magnetic material functions as an electromagnet. The electromagnet part of a motor is referred to as the windings or the coil.

What are commonly called magnets are typically rod-shaped or U-shaped items painted red or blue, or sometimes black sheet-shaped items. Items used in this form are called permanent magnets. A permanent magnet can maintain its magnetic force even when no electric power or other energy is provided. However, its magnetic force (polarity and magnitude) cannot easily be changed. In contrast, an electromagnet requires electric power (an electric current), but its magnetic force can be adjusted by changing the direction and size of the current. This characteristic can be regarded as the reason for the use of electromagnets in motors.

Let us now take a look at the specific features of electromagnets. To begin with, an electromagnet does not have magnetic force unless a current is passed through a conductor. This is an important characteristic. By passing a current, it can be imparted with magnetic force, and by changing the direction of the current, the polarity (N pole, S pole) can be changed. This characteristic is described using what is called the right-hand rule (right-hand screw rule). And, by changing the size of the current, the strength of the magnetic force can be adjusted.

In other words, an electromagnet has a number of characteristics that are important for motors: it is possible to reduce the magnetic force to zero, to change the polarity of the magnet, and to adjust the strength of the magnet.

The following is a more detailed explanation of the strength of an electromagnet.

The strength of an electromagnet is essentially proportional to the number of windings of the wound conductor wire and the size of the electric current that flows in the windings. The diagram below shows how the magnetic force changes if the number of windings or the diameter of the wire is changed. If the conductor wire is made thick, the magnetic force is increased. This is because when a conductor wire is made thick its electrical resistance decreases, so that the current value increases. If the wire thickness is unchanged but the number of windings is increased, there is no large change in the magnetic force. This is because increasing the number of windings means the wire is longer, so that the resistance value rises and the current value decreases. However, if the number of windings is increased, and in addition the wire is made narrower, the wire resistance value rises and the current value falls. The increase in the number of windings cannot by itself compensate for the decrease in the current value, and so the magnetic force is weakened.

Strength of electromagnet = number of windings × current

In actual motors also, the number of windings and the wire diameter are adjusted as described above. This is because the current that can be used and the required magnetic force may change, depending on the motor. Of the above graphics, that described as the reference has the same magnetic force as the one with the increased number of windings, and so the intended change may not be obvious. As a matter of fact, however, the power consumption for the two is different. This fact is related to the motor efficiency and energy savings.

Here we explain the relationship between the power consumption of the windings (electromagnet part) and the magnetic force which is the output.

Suppose that the values for the reference electromagnet are each 100, excepting the current, which as reference is set to 1 (when the voltage, of value 100, is divided by the resistance, of value 100, the resulting value for the current is 1).

To consider cases in which the conductor wire is thick, suppose it to be thicker by 1.41 times. This means that the cross-sectional area of the wire is 2 times greater, and so the resistance value is half as great. As a result, the current consumption and the magnetic force are both twice as large. In order to compare this with the reference case, suppose we adjust the voltage such that the magnetic force is 100. Then the power consumption becomes 50, and we see that the power consumption is lower than for the reference case.

In the cases in which there is a greater number of windings, suppose that the number of windings is twice as great. Then the power consumption is half, and a magnetic force of 100 is obtained.

In the case in which the number of windings is greater and the wire is narrower, suppose that the number of windings is twice as great, and the wire diameter is equal to 0.71 times that of the reference case. The wire length is twice as great and the wire cross-sectional area is half as large, so that the resistance value is four times greater. As a result, the power consumption is 1/4 as great, and the magnetic force is half as great. Adjusting the voltage such that the magnetic force is 100, the power consumption becomes 100, which is the same as for the reference case.

In this way, taking the magnetic force as reference, the performance resulting from the other cases can be inferred. Among these cases, the power consumption is lower with respect to the magnetic force for the cases in which the wire conductor volume is greater (when the volume is 200 in the figure below). Here the conductor volume, calculated as the product of the number of windings (length) and the square of the wire diameter (cross-sectional area), can be described as the quantity of the conductor. Thus the quantity of the conductor wire used in a motor is closely related to the power consumption of the motor. The efficiency of power consumption is also an important design item, and so the number of windings and the wire diameter (called the coil specifications) must be examined with this in mind as well.

It was explained above that the power consumption can be reduced by winding many coils of wire (“wind many coils” means not just the simple number of coils, but also that the amount of the conductor wire is large). Here we mention limits to the amount of windings in a motor.

In order to improve motor efficiency, more coils of wire should be wound; but in actuality, there are various limits imposed. To begin with, the windings of a motor have shapes such as those shown in the diagrams below. The magnetic material (primarily iron) part around which the coils are wound is called the core; some cores have shapes that are opened on the inside, and others have shapes opened on the outside. If the dimensions of these shapes are not changed, then there are of course limits to the space in which the wires are wound. Wires cannot be wound more times than is allowed by the space available. Moreover, there are also design limits when taking magnetic saturation into account. Above it was explained that if the number of windings and the current are increased, the magnetic force increases in proportion; but in actuality, the magnetic flux (magnetic force) cannot increase beyond the saturation flux density of the magnetic material. Whether the number of windings is large or small, if the current increases too much, magnetic saturation occurs (see the diagram below). Should magnetic saturation occur, the magnetic force will not increase even if the current is increasing, and this extra current is wasted. Hence windings must be designed such that magnetic saturation does not occur. Apart from this, there are limits to the cost of the conductor wire and the method of winding the coils.

The above summarizes the fundamentals of electromagnets in motors.

Fundamentals of Torque

Torque is a force that causes rotation. A rotation-causing force of a motor is an indicator of the ability to move an object in rotation, and is a numerical value used when calculating the output power of a motor, and is also a characteristic relating to vibrations of the motor. Because the output power and vibrations of a motor relate to efficiency and noise, which are principal performance aspects of the motor, the concept of torque must be understood when learning about motors.

While this is the gist of torque, its definition is a bit complicated. For example, forces pushing objects are measured in Newtons (N), with 1 N defined as the force that pushes a 1 kg object to cause an acceleration of 1 m/s2. A force pushing an object is the same however it is applied, and so such a definition is used. However, in the case of a force causing rotation, a definition indicating from what position the force is applied is necessary. For example, there are reasons why the handle of a screwdriver that rotates a screw might be thick, or why a tool used to tighten a bolt might be long.

This is because such tools utilize the fact that the force causing rotation changes in proportion to the distance from the rotation axis to the position at which the force is applied. Expressed as an equation, torque is calculated as the product of the distance from the axis (radius r) and the force F, expressed in units of Newton-meters (N∙m). When the same force is applied, the torque increases as the distance from the rotation axis is increased.

Up until now, torque has been explained from the standpoint of force application, but torque is what a motor outputs. When torque is considered in terms of its output rather than its application, a torque of 1 N∙m can be said to be the rotational force that produces a force of 1 N at a distance of 1 m from the motor shaft center. When considering torque output, as the distance increases, the force decreases by the same amount.

Next we explain the relationship between the load rotated by the motor (the object that the motor moves) and torque.

The concept of torque also applies to what is being moved by a motor. For example, as indicated in the figure on the left below, if a weight of m kg is suspended by a rope, and a disc of radius r is used to move the weight, then the torque required is r×m×g N・m. (Here g is gravitational acceleration, 9.8 m/s2.) The magnitude of this torque does not depend on the motor rotation rate (the speed at which the weight moves). However, if the speed is changed (if the acceleration is not zero), a torque corresponding to the acceleration is necessary (the torque is increased when accelerating, decreased when decelerating). On the other hand, when a fan is being rotated as in the figure on the lower right, the required torque will depend on the characteristics of the fan. For characteristics of typical fans, as the rotation rate increases, the required torque is greater.

In this way, loads rotated by motors have all kinds of torque characteristics. When a motor rotates such loads, the torque needed for the load must be output. This is why the torque of a motor is the indicator of the force moving an object (the indicator of whether or not the object can be moved).

Here we explain the relationship of the output torque (force causing rotation) of a motor, mentioned at the outset, to the output electric power and to vibrations.

In general, output power is calculated as the product of the force and the movement distance per unit time (one second) (see the equation below). In the case of a rotating body, the movement distance is calculated using the circumference and the rotation rate (rotation speed). If the radius is r (m) and the number of rotations of the motor in one minute is N (r/min), then converting to unit time by dividing by 60, the movement distance is 2πrN/60. Multiplying this movement distance by the force F, substituting the torque T（N・m）for rF in the equation, and using a constant α for 2π/60, we obtain as the output power the constant times the torque times the rotation rate (αTN), as an equation relating torque to the output. This equation is used when calculating the output power of a motor.

Next we consider vibrations. In the above discussion we have explained the output torque of a motor as though it were of constant magnitude, as in the figure below. However, the actual output torque is not necessarily constant. The figure below indicates changes in the output torque, with time as the horizontal axis. Ideally, the output torque would be constant, but depending on the motor, there may be periodic pulses, as shown in the figure. The main cause of such pulsation lies with the method used when the motor converts electric power into torque; the pulses occur within one rotation of the motor. Of course, torque conversion may occur over longer periods than a single rotation, but torque pulses such as those shown in the figure are closely related to fine vibrations in the motor.

It should be noted that load rotation indicators and torque values used when calculating output power are average values.

Method of Conversion into Torque

We have covered the basics of electromagnets and torque; next, we will explain how motors change electric power into a force that can move things.

A motor uses electric power to create (activate) an electromagnet, generating a magnetic field. In order to use this magnetic field to obtain a force, the attractive and repulsive forces of the magnet are made to interact with electromagnetic forces. The attractive force of a magnet is a force of the magnet that pulls a magnetic material. If the magnetic material is a magnet, depending on the magnet polarity, a repulsive force (force that pushes away) may occur. An electromagnetic force is a force that occurs when an electric current is passed in a conductor that is in a magnetic field. A force acts in the direction indicated by Fleming’s left-hand rule.

A motor converts this force into a rotational force. Specifically, a shaft is affixed to an object to which a force is to be applied, as shown below, so that the force acts in a direction of rotation.

On the basis of this method of conversion into a rotational force, combinations such as those shown below are used in actual motors.

• ・Combination of an electromagnet and a permanent magnet
  The forces of attraction/repulsion between magnets are used. There are motors in which the permanent magnet rotates, and those in which the electromagnet rotates.
  The motors in the figure are a brushless motor, and a brushed motor with a permanent magnet magnetic field.
• ・Combination of an electromagnet and an electromagnet
  The forces of attraction/repulsion between magnets are used.
  The motor in the figure is a brushed motor with an electromagnet magnetic field.
• ・Combination of an electromagnet and a magnetic material
  The attractive force between the magnet and the magnetic material is used. In general, the magnetic material rotates.
  The motor in the figure is a stepping motor.
• ・Combination of an electromagnet and a conductor
  Electromagnetic force is used.
  The motor in the figure is a squirrel cage induction motor.
  An induction motor is a motor that obtains electromagnetic force by passing an induced current in a conductor.

Below are explained the abovementioned induced current, electromagnetic force, and induction motor.

When an electrical conductor moves in a magnetic field (or when the magnetic field moves), a current flows in the conductor. This current is called an induced current. The direction in which the current flows, relative to the direction of motion, is indicated by Fleming’s left-hand rule. For example, if a magnetic field has moved from the position in figure 1 below to that in figure 2, a current flows outward from the figure toward the reader. Due to the occurrence of this current, an electromagnetic force appears, as in figure 3.

To sum up, in an induction motor, a magnetic field (magnet) is moved, causing current to flow in a conductor, and the force that acts on this conductor is utilized.

Up to this point, we have explained how a motor obtains rotational power. However, based on the explanation thus far, it might be imagined that once the rotational power has been obtained, rotation would then stop at a position such as that shown below (the example of the figure is for the case of an electromagnet and a permanent magnet). Of course, in an actual motor nothing like this happens. Moreover, in our explanation of an induction motor we indicated that the magnetic field moves, but did not explain the method by which it is moved.

Hence we begin by explaining the method by which rotation of a motor is continued using the attractive force of a magnet. Specifically, we describe changes in rotational force and switching of the electromagnet (induction motors, which use electromagnetic forces, will be explained afterwards).

Before explaining changes in rotational power, we must first modify the schematic diagram of our motor as indicated below. The side that rotates will be called a rotor, and the side that applies rotational power or force to the rotor is called the stator.

The rotational force of a motor changes with the relative angle made by two magnets or with the relative angle made by a magnet and magnetic material. The change in rotational force varies as shown in the figure below.

The figure below shows the change in rotational force (torque) when the rotor is a permanent magnet and the stator is an electromagnet, and the magnetic force of the electromagnet is made constant. The position at which the same poles oppose each other is taken to be relative angle 0°; at this angle the torque is zero. At the position at which the relative angle is 90°, the torque for counterclockwise rotation is maximum. At the 180° position the torque is again zero, and at the 270° position the clockwise torque is maximum.

Next, a case of a magnetic material rotor not having a magnetic force is described. Here the relative angle between the magnet and the magnetic material is defined as in the figure below. When the relative angle is 0°, the torque is zero. At position 45°, the counterclockwise rotation torque is maximum. At 90° the torque is zero, and at 135° the clockwise rotation torque is maximum. From 180° to 360°, the relation is the same as for angles from 0 to 180°. This is because the magnetic material does not have a magnetic force, and so the changes over the same angular range are repeated.

From these results, in order for the motor to continue turning, the relative angle between the rotor and the stator must be kept within a fixed range. The figure below is for a case in which the rotor is rotated counterclockwise.

• ・Magnet and magnet, counterclockwise: a position is maintained such that the relative angle is between 0° and 180°.

  

• ・Magnet and magnetic material, counterclockwise: A position is maintained such that the relative angle is between 0° and 90° (angles beyond 180° omitted).

  

Here, in order for the magnet of the stator to maintain the above relative position with respect to the rotating rotor, the magnet must be moved. Of course the stator cannot itself be moved, and so in actuality what the motor does is switch the electromagnet. If the stator electromagnet is switched in the following way, the rotor can continue to rotate.

First of all, in the case of an electromagnet and a permanent magnet, a counterclockwise rotation torque can always be obtained by switching the polarity of the stator electromagnet as in the figure below.

There are also motors in which the placement of the electromagnet and the permanent magnet are changed, using the electromagnet in the rotor and the permanent magnet in the stator. In the case of such a configuration as well, the electromagnet polarity is switched according to the position of the rotor.

In the case of a magnet and a magnetic material, some minor innovation is required. In order to change angles in the previous figure from angles for clockwise torque to angles for counterclockwise torque, an electromagnet that is shifted 90° is needed. Hence the construction shown below is adopted, and by switching each of the electromagnets, a counterclockwise torque can always be obtained.

To summarize the explanation thus far of methods for conversion into torque:

• ・Rotational force can be obtained using the attractive force of magnets and electromagnets.
• ・In a motor that uses the attractive force of magnets, the magnitude of the rotational force changes with the relative angle between the stator and the rotor.
• ・In order to make continuous rotation possible, the poles of an electromagnet are switched.

We have explained the simplest example of switching the polarity of an electromagnet. In actuality, however, there are a number of more complicated methods for operating a motor, and these are used in a wide variety of motors.

The main objective of more complicated operations is to expand the options for the direction of the magnetic field created by an electromagnet. In the main configuration explained above for the coil (of an electromagnet), there is effectively a single coil, and the magnetic field can be directed in either of two directions (as in the figure below) simply by changing the direction in which current flows in the coil. Even with such a configuration, a motor can be rotated; but the torque will pulsate considerably, affecting motor vibrations. Moreover, the torque is sometimes small even though the same current is being passed, so that motor operation is not efficient. In order to resolve these issues, it must be possible to adjust the direction of the electromagnet magnetic field precisely according to the rotation position of the rotor. For example, if the number of coils is increased eight-fold, torque pulsations can be reduced as in the figure below, and the motor can continue to use large torques. However, in the case of such a configuration each of the electromagnets becomes smaller, and there are numerous coils that, for most positions of the rotor rotation, are not activated to act as electromagnets. Thus in reality there are these and many other problems with this configuration (the reader may have seen motors with numerous electromagnets like these, but such motors are probably different from the motors described here).

In fact, there is a method for precisely adjusting the direction of the magnetic field without increasing the number of coils in keeping with the number of magnetic field directions desired. This can be achieved by combining magnetic fields and adjusting the magnitudes of the magnetic fields.

When magnetic fields are combined, magnetic fields in two or more directions are thought of as vectors, resulting in one direction. For example, as indicated in the figures below, magnetic fields with an angle difference of 90°, and magnetic fields formed by coils at 120° intervals, can be combined and thought of as a magnetic field in one direction. Upon combining cases in which a current is passed in a coil and cases in which no current is passed and a magnetic field is not formed, magnetic fields can be formed in eight directions and in six directions respectively (with currents, when passed, having a constant value).

By further adjusting the magnitudes of the magnetic fields (the sizes of the currents), the direction of the resulting magnetic field can be freely adjusted. The figure below shows an example of the polarities and magnitudes of each of the magnetic fields generated when the direction of the composite (combined) magnetic field is adjusted. The direction of the composite magnetic field is indicated by the right-pointing arrow at 0° (the 3:00 direction on the face of a clock), and rotates counterclockwise from there. The example waveforms in the figures are all sinusoidal waveforms. By using sinusoidal waveforms, the magnitude of the composite magnetic field can be made constant.

In a motor with electromagnets in two directions, there are coils A and B. If for example one electromagnet A is the S pole, the opposing electromagnet A ̅ is the N pole, and the magnetic field direction is upward. Hence when an electromagnet magnetic field like that in “1” in the figure is generated, the composite magnetic field is directed as indicated in the figure (in the 1:00 direction on a clock face). The figure may be a bit difficult to understand, but by recalling the relationships of sine (sin) and cosine (cos), it should be easy to see that a composite magnetic field can be generated in this way over the entire range from 0° to 360°.

In a motor with electromagnets in three directions, there are coils a, b, and c. When this placement is used, there are no mutually opposing coils, and so for example when a is the S pole, the magnetic field is directed upwards. The basic approach is the same as when there are electromagnets in two directions, the only difference being that there are three vectors forming the composite magnetic field.

As explained above, various composite magnetic fields can be created in a motor by designing electromagnets with different directions and by adjusting the magnitudes of the magnetic force.

Here induction motors are explained. As mentioned above, in an induction motor an induced current is caused to flow in a conductor by moving a magnetic field, and the magnetic force acting on the conductor is utilized. The conductor follows the movement of the magnetic field; hence the magnetic field must always be moving continuously relative to the following conductor. It is possible to continuously move the magnetic field using the rotating magnetic field (rotational magnetic field) described above.

However, in an actual motor there is still an issue to resolve. Because the magnetic field is rotating, the direction of the magnetic field and the direction in which the conductor rotates are not kept perpendicular. If the two are not perpendicular, the effective current magnitude is only the magnitude of the movement component that is in the direction perpendicular to the magnetic field (think here in terms of vector analysis). Also, the component of the electromagnetic force contributing to rotation also changes according to the angle.

This issue is resolved by providing multiple conductors. The figure below shows an example with two conductors; as the conductors move, induced currents flow in order, and an electromagnetic force (rotational force) is maintained.

Due to these facts, a stator that creates a rotating magnetic field and a rotor using conductors with constructions like those shown below are used. The shape of the rotor resembles a squirrel cage, and so such a motor is called a squirrel cage induction motor (the stator in the figure has a simple construction).

The above has been an explanation of methods used for conversion into torque.

Control of Electromagnets

Up to this point, we have explained what it is that motors do. In order for a motor to continue to rotate, electromagnets must be switched (magnetic forces must be adjusted). From here we explain this control of the electromagnets.

There are two major aspects to control of electromagnets. One is the methods used for magnetic force switching and adjustment; the other is the timing of that switching and adjustment. There are multiple approaches to each of these, and differences between them are also differences between different types of motors.

First of all, there are the methods of switching and adjustment shown below.

• ・AC power supplies
  The single-phase AC 100 V power supplied to household outlets, and the three-phase AC power used in plants and the like, are used essentially without modification to activate electromagnets. Rotating magnetic fields synchronized to the frequency of the AC power (sinusoidal) are generated.
• ・Mechanical switches
  DC or AC power voltages are connected to two brushes, and the voltage applied to a coil is switched by contact between the brushes and a commutator. The coil is connected to the commutator (which rotates). When using this method, the switching timing is determined by the timing of contact of the commutator with the brushes.
• ・Electrical switches
  DC or AC power voltages (when supported by the circuit) are divided among coils by electronic components. Transistors are used as the electronic components serving as switches. Transistors are semiconductor devices that function to turn a voltage (current) on or off; this turn-on/off operation instruction can be received by an electrical signal.

The timing of electromagnet switching and adjustment is determined by the principles of torque conversion in a motor, and by the performance desired. More specifically, methods such as the following are available. However, an explanation as to whether the rotor position has been determined explains the operation of the motor when it is driven. When enhancing motor control or performing advanced control such as speed or position control, it may be necessary to determine the rotor position for this purpose.

• ・Determine the rotor position, generate a magnetic field (figure: Rotor position determined)
  While determining the rotor position, create an electromagnet magnetic field in the direction in which the required torque will appear.
  By activating the electromagnet such that the magnetic field rotates ahead of where the rotor is completely attracted to the electromagnet, the rotor can be driven efficiently.
  Motors that use such a switching method include brushless motors and brushed motors.
• ・Generate a magnetic field such that the rotor follows while being aware of the rotor position (figure: Rotor position semi-determined)
  Create an electromagnet magnetic field in the required direction, without directly detecting the rotor position.
  The rotor position is not determined, but the magnetic field is moved on the assumption that the rotor is attracted by the electromagnet and follows the electromagnet. The rotor is moved to the magnetic field position, so position control is easy.
  Motors that use this switching method include stepping motors.
• ・Generate a magnetic field without paying attention to the rotor position (figure: Rotor position not determined)
  A rotating magnetic field is created without determining the rotor position.
  Used in motors in which there is no need to determine the rotor position.
  Motors that use such a switching method include induction motors.

The above is an explanation of electromagnet control.

Next, motor drivers, which are necessary for such electromagnet control and motor control, are explained.

The Role of Motor Drivers

In order to operate a motor, generally an electric circuit called a motor driver is combined with the motor. Of course, the above-described motors running only on AC power and the motors of mechanical switches may not necessarily require motor drivers. However, when there is a need to control the rotation rate or rotation direction, the motors are also combined with a motor driver for use.

We first explain the role of motor drivers.

One reason for using a motor driver is that motors require a wide variety of functions and performance levels. Shown below are the main performance parameters and functions sought from motors. The rotation operation shown in the figure may be achieved by mechanical switches or AC power, as explained above, but there are also motors that require electronic components (motor drivers) to provide such operation. In addition, motor drivers are essential for output adjustment and for improved basic performance, as well as for sophisticated motor control.

The roles of motor drivers used to achieve such performance and provide such functions are indicated below. A motor driver can freely adjust the output voltage value. In addition to adjusting the motor output, motor drivers are also utilized to reduce operation noise by suppressing torque pulsation, to execute control so as to limit losses, and to execute control using motor torque information and the like in order to freely manipulate the motor.

Motor drivers performing the above roles are mainly configured from the electronic components shown below. Electronic components known as power transistors or the like supply electric power to coils (sometimes via mechanical switches). “Power transistors” can handle large amounts of power; by turning such transistors on or off, coils and power sources are connected or disconnected. This on/off control of these transistors is performed by ICs (here meaning devices that do not use software) and microcontrollers (meaning devices that do use software). These components, which are all driving controllers, perform signal processing and calculations in order to realize the above-described functions and performance. Because the performance and functions demanded of a motor will differ depending on the motor application, the processing performance required of a driving controller will likewise differ for different motors.

Here we explain the differences in circuits when mechanical switches are and are not present. The figure below shows the circuits for a three-phase brushless motor and a three-phase brushed motor.

When there is no mechanical switch, power is supplied to the three coils directly from power transistors. In this case, the motor driver controls the magnitude, direction and timing of the power supplied to the coils. Hence the basic circuit configuration consists of six power transistors and one controller that turns the power transistors on and off.

When there are mechanical switches, the timing of power supply to the three coils is determined by the mechanical switches. In this case, the motor driver controls the magnitude and direction of power supplied to the mechanical switches. Hence the basic circuit configuration consists of four power transistors and one controller that turns the power transistors on and off.

This concludes our explanation of the role of motor drivers.

A Necessary Discussion of Induced Voltages in Motors Using Permanent Magnets

Up to this point, motors have been described as devices in which electromagnets create and rotate magnetic fields, with voltages applied to coils in the electromagnets causing currents to flow to create the fields, with the sizes of the currents corresponding to the magnitudes of the magnetic fields created by the electromagnets, and adjustment of the magnetic field sizes being important for rotating the motor. However, there has not yet been a discussion of a factor affecting the size of the currents that flow. This factor is the induced voltages of the heading of this section.

In a motor that uses permanent magnets, induced voltages is an unavoidable topic. An induced voltage is a voltage that appears in a coil due to rotation of the rotor, and is a so-called generated voltage. When speaking of voltage generation, it may sound as though electric power is generated by using an external force to rotate a motor; but voltage generation occurs even when a motor is being rotated by electric power (when it is rotating by itself). In other words, when a voltage is applied in order to cause current to flow in a coil, the motor rotates and an induced voltage (a generated voltage) that tends to cancel the applied voltage appears, so that the current is reduced. In order to understand these phenomena, we first explain the principle of occurrence of an induced voltage.

An induced voltage is a potential difference appearing across the two ends of a coil due to the phenomenon of electromagnetic induction. Here “electromagnetic induction” means the phenomenon in which, when the amount of magnetic flux passing through a coil changes, a voltage appears in the coil in the direction causing the appearance of a magnetic field in opposition to the change (to maintain the original amount of magnetic flux). For example, when the N pole of a magnet is brought near a coil as in the figure below (center), the rightward magnetic flux within the coil increases. The coil then tries to generate a leftward magnetic field so as to oppose the increase. The direction of the current that generates the leftward magnetic field is as shown in the figure, in accordance with the right-hand rule, and so a voltage of polarity in accordance with this direction appears across the ends of the coil. Conversely, if the magnet is moved away from the coil, the magnetic flux passing through the coil decreases, and so a current and voltage appear in the direction that causes an increase in the magnetic flux (see the figure on the right).

The magnitude of the voltage appearing across the ends of the coil is proportional to the change in magnetic flux. Moreover, the voltage is also proportional to the number of coil windings, and so is expressed by the following equation. In the equation, bemf stands for “back electromotive force”, and means an induced voltage or reverse voltage.

The figure of a motor below helps explain this phenomenon. The figure shows changes in the magnetic flux passing through the motor stator when the rotor, which uses a permanent magnet, is rotating inside the stator.

Magnetic flux that has left the N pole of the permanent magnet is shown on a path to enter the S pole. At the rotor position in 1 in the figure, the teeth (the part of the magnetic material around which the conductor is wound) of coil A are opposing the S pole, and magnetic flux passes into the S pole. As the motor rotates counterclockwise (2 in the figure), some of the tips of the teeth of A begin to be opposed to the N pole, and the area opposed to the S pole is reduced, so that the magnetic flux passing through the coil is reduced. As the rotor rotates further, the magnetic flux passing through the coil becomes zero, as in 3 in the figure (though not shown, upon further rotation the amount of magnetic flux leaving the N pole increases).

As a permanent magnet in a motor approaches or recedes, the polarity or flux density of the magnet opposing the coil (teeth) changes with the rotation.

This is the principle of generation of induced voltages in a motor using permanent magnets. Here, we will discuss in some detail the waveform of an induced voltage in a motor. The graph below displays, in order from the top, the distribution of magnetic flux density of the permanent magnet, the amount of magnetic flux passing through the teeth part labeled A in the figure, and the induced voltage that occurs in the coil A (changes in the amount of magnetic flux passing through the teeth become the induced voltage waveform, and so it is necessary to include the magnetic flux density distribution of the permanent magnet).

From the permanent magnet magnetic flux density and the width of the opposing teeth, we obtain the amount of magnetic flux passing through the teeth. The left end of the next graph represents the amount of magnetic flux when the rotor is at the position shown in the figure. Roughly the same surface areas of the N pole and the S pole are in opposition, so that the magnetic flux amount is zero. When the rotor then rotates counterclockwise by 90°, only the N pole is opposing the teeth, and the magnetic flux amount (in the N pole direction) is maximum. When the rotor further rotates counterclockwise, again zero is reached, and thereafter the S pole area increases; after one full rotation, the amount returns to zero.

The induced voltage is the differential of this magnetic flux amount. Hence the waveform of the induced voltage is a waveform that repeatedly becomes positive and negative, as in the figure.

In the figure above, the induced voltage has a sinusoidal shape, but this is not the induced voltage waveform in all motors. The waveform of the induced voltage is determined by various factors, but is influenced in particular by the waveform of the magnetic flux density distribution of the permanent magnet, called the magnetization waveform. More specifically, a waveform like that shown above occurs when the magnetization is a sine wave. If the magnetization waveform is trapezoidal, like that shown below, the magnetic flux passing through the teeth differs from the case of a sine wave, and the induced voltage, which is the differential, will be as shown below (theoretically, it will be the waveform of the solid line, but in actuality it is often a waveform like that of the broken line).

Up to this point, the principle of generation of induced voltages and induced voltage waveforms in actual motors have been explained. Next, we will consider the effect of such induced voltages on motor characteristics.

First, we look at the effect on coil currents, mentioned at the beginning of the explanation of induced voltages. When there is no induced voltage, the coil current is determined by the applied voltage and the coil impedance (resistance R and inductance L), as indicated by the equation in the figure below. Upon considering that an induced voltage then appears, the negative-signed induced voltage is added to the left side of the equation. The polarity of the induced voltage is a concern here: when a motor is operating normally, the relation between the applied voltage and the induced voltage is as indicated in the figure (details are here omitted, but upon considering the rotor position, the waveform of the induced voltage that appears, the direction of the current that flows as a result (related to the torque) explained earlier, and other matters, we find the two are related as in the figure). In the relationship of the figure, the induced voltage is subtracted from the voltage that is applied, so that the current is smaller than it would be if the induced voltage were not taken into consideration. Moreover, the induced voltage has an almost sinusoidal shape, as stated above, so that if a constant voltage is applied, the voltage actually appearing across the coil is not a constant value, and the current undulates (see the figure below).

As an addendum regarding the magnitude of an induced voltage, as explained above, an induced voltage is the differential of the magnetic flux passing through teeth (a coil). Hence when the rotation rate of a motor changes, the induced voltage magnitude changes. For example, when the rotation rate increases from 100 (arbitrary units) to 200, the speed of magnetic flux change is doubled, and so the induced voltage is also doubled. If the rotation rate becomes 400, the induced voltage is again doubled. Conversely, if the motor is not rotating, the induced voltage is zero. Thus the induced voltage increases in proportion to the motor rotation rate.

Up to this point, we have explained that an induced voltage occurs due to a change in the magnetic flux passing through a coil; that the induced voltage waveform affects the current waveform; and, that the magnitude of the induced voltage changes in proportion to the rotation rate of the motor. These phenomena are related to the following motor characteristics.

• ・The induced voltage waveform affects the current waveform, and therefore is also related to torque pulsations, vibrations, and noise.
• ・When a certain voltage is applied and a motor begins to rotate, the induced voltage becomes larger, the current decreases, and the torque also declines.
• ・The maximum value of the rotation rate of a motor to which a certain voltage has been applied is the rotation rate at which the applied voltage and the induced voltage are in equilibrium (and the torque is zero).
• ・When the applied voltage is zero (coils are short-circuited), if the motor rotates, the induced voltage causes a current to flow; the direction of the current (torque) at this time is in the direction that brakes the motor rotation.
• ・A change in magnetic flux appears in the induced voltage, and so the position of a permanent magnet rotor (the position relative to the coil) can be inferred from the induced voltage.

Thus in a motor that uses a permanent magnet, induced voltages are related to the motor performance and output range, the method of motor control, and other motor aspects.

The above concludes our explanation of induced voltages.

Torque Constant and Induced Voltage Constant

Up to here we have discussed the basics of motors and explained motor torques and induced voltages. It is now necessary to understand the relationship between the two.

Torque is proportional to the current, and induced voltage is proportional to the rotation rate. These facts are expressed by the following equations; and it is known that in these equations, the torque constant and the induced voltage constant have the same value.

torque = torque constant × current

induced voltage = induced voltage constant × rotation rate

The quantities multiplied by the constants and the quantities being calculated are completely different, but the constants are the same. This fact is explained below.

First, consider the torque constant. Here the torque can be thought of as the force that is brought to bear when a current flows in a conductor in a magnetic field. A conductor of length L such as shown below is placed in a magnetic field (magnetic flux density B), and when a current I flows, a force F acts. At this time, the force F is calculated as the product of the magnetic flux density B, the length L, and the current I (this is for a case in which the directions are perpendicular, as in the figure; when the angle is not a right angle, the force differs from this). Based on this, we consider the torque for a rotating body such as that in the figure. This rotating body is formed from a single loop (one winding) of a conductor so as to have a radius R. The force F acts at positions at the radius R, and because there are two such parts on which the force acts, the torque T is calculated as two times the product of the radius R and the force F.

Here, the coils in a motor are not just a single winding, but may have multiple windings, so that when considering the torque constant, the number of windings N is a further factor in the above equation. From this equation, the factors other than the current I become the torque constant, Kt(＝2RNBL).

Next we consider the induced voltage constant. In the above discussion of induced voltages, it was explained that an induced voltage occurs upon a change in the magnetic flux quantity passing through a coil; let us consider this using Fleming’s right-hand rule. When a conductor of length L as in the figures below moves through a magnetic field (magnetic flux density B) at a velocity v, an induced voltage e appears across the ends of the conductor. The induced voltage e at this time is calculated as the product of the magnetic flux density B, the length L, and the velocity v (similarly to the case of torque, we assume that the quantities are mutually perpendicular). When the conductor is considered as a rotating body, the velocity is the product of the angular velocity ω and the radius R, and because the total length of the conductor parts in which the induced voltage appears is twice as great, the equation for the induced voltage shown below is obtained.

Similarly to the case of the torque constant, when the number of windings N is included in the equation, the equation below is obtained. If the factors other than the velocity (angular velocity) ω are together taken to be the induced voltage constant Ke, then we have Ke=2RNBL, and we see that the induced voltage constant and the torque constant have the same value.

An induced voltage can also be explained in terms of “something that occurs when the magnetic flux amount passing through a coil changes”, as mentioned above. In this case, the conductor in question is thought of as part of a closed conductor loop. When the loop is placed in a magnetic field, magnetic flux passes through the loop (light gray in the figure). Suppose that the conductor of interest in the loop moves at velocity v as shown below (the loop expands); then the magnetic flux within the loop increases by the amount of the gray part. If the movement distance per unit time of the conductor is x, and the conductor length is L, then the amount by which the magnetic flux has increased is obtained by multiplying by the magnetic flux density, to obtain BLx. The induced voltage is the change amount (differential) of the magnetic flux, and so differentiating the movement distance x we obtain the velocity v, to derive the aforementioned relation e=BLv.

The torque of a motor is a mechanical output, and an induced voltage is an electrical output. In the previous section, the effect of induced voltages on motor characteristics were explained, but it is also necessary to understand that when the induced voltage constant is changed the torque constant also changes, and that conversely if the torque constant is changed the induced voltage constant changes.

The torque constant explained here is a constant that indicates the magnitude of the torque at the position indicated in the lower-left figure. If the angle changes, the torque changes (center, right figures), even if the electromagnetic force is the same. A similar matter is explained in the section “Method of Conversion into Torque”. It should be kept in mind that if the positional relationship changes, the output torque changes, even if the torque constant and current remain the same. Similarly, it should be recalled from the previous section that if the equation is used to calculate the induced voltage from the rotation rate, it may appear that a constant (direct current value) is involved, but this is not the case.

In Conclusion

Motors in widely diverse forms, drawing on a number of basic principles explained above, have been proposed. These can be said to be designs that emphasize different performance parameters such as efficiency, quietness, reliability, ease of use, and cost. Moreover, through the evolution of circuit technology to control motor operation, configurations to realize desired performance have changed and grown more complex. In order to understand these developments, a firm grasp of basic motor technology is required.

Hopefully this article will prove helpful for understanding motor technology.