# ECE 252 Introduction to Electrical Engineering

## Lesson 19. Motors

### Introduction

Motors and generators consist of two basic parts, as shown below. The stator is the stationary part of the motor or generator; the rotor is the rotational part. Both parts are usually made of iron so that they can contain the magnetic flux. Also, a motor or generator usually has:
Field Winding - Sets up a magnetic field for the machine.
Armature Winding - Current is developed here. For a motor, the current is proportional to the mechanical load.

The field winding may be on the stator or rotor, depending on the machine design. The same goes for the armature. Sometimes the field is provided by permanent magnets, but more often the field is produced by an externally-applied current.

### DC Motors

Most DC motors have the armature on the rotor; the stator has the field coil or else there is a permanent magnet to create the field. It is unusual to find a DC motor in an AC system because rectifiers are required, but DC motors are quite common in battery-operated DC systems, such as automobiles and toys.

Most DC motors have a commutator and brushes, as shown below. There are exactly two brushes, but there may be any number of commutator bars, from two to more than twenty. The brushes are typically made from carbon. One is connected to the positive supply, and the other to the negative supply. The commutator is connected to the shaft of the motor. It rotates with the motor, sliding under the brushes. In this way, the brushes connect electricity to a sequence of commutator bars. The number of motor windings is the same as the number of commutator bars. Each commutator bar is connected to two windings (not shown).  When current flows through an armature winding, it generates a magnetic field which interacts with the magnetic field from the field windings to cause motor torque. Brushes and commutators are prone to wear.

Permanent magnet motors are usually small - at most a few horsepower. They have the advantage that it is not necessary to power the field, but they suffer from lower torque and poor performance at low RPM. They are used in cars to operate fans and electric windows. Most small electric toys have permanent magnet motors.

Larger DC motors usually have wound field coils. These can be either in series or parallel (shunt) with the armature windings, as shown below. Both the field coil and the armature coil have resistance and inductance. The inductance is frequently ignored. In the series-wound motor, the same current goes through the field and the armature coils. In the parallel-wound (or shunt) motor, the currents are independent; in fact, the current in the field winding is constant, because its applied voltage is constant; thus the parallel-wound motor has a constant magnetic field, just like a permanent magnet.

For either motor, the current in the armature coil is more complicated. It depends on the applied field and the speed of the motor. Consider the following equation:

(1)  IA = (VA - EA)/RA

In this equation, IA is the armature current, RA is the armature resistance, VA is the voltage applied to the armature, and EA is the back EMF. This last term needs a bit of explanation. EMF stands for electromotive force. The back EMF is also called the counter EMF. This is a voltage that is developed by the armature as its coils move through the magnetic field set up by the field coil (or permanent magnet). The back EMF is proportional to the rotational speed of the motor and is in the opposite direction of the applied voltage:

(2)  EA = Kemfφnm

In this equation, Kemf is a constant, φ is the magnetic flux produced by the field, and nm is the rotational speed of the motor in revolutions per minute (rpm). As the speed of the motor increases, the back EMF increases. More information on the back EMF can be found at http://en.wikipedia.org/wiki/Counter-electromotive_force. As the back EMF increases, Equation (1) tells us that the armature current will decrease.

A third equation to be considered describes motor torque:

(3) T = KφIA

In this equation, T is motor torque (in lb-ft or N-m), K is a constant, φ is the magnetic flux produced by the field, and IA is the armature current.

Let's see how these equations are applied to analysis of series-wound and parallel-wound motors.

#### Parallel-Wound (Shunt) DC Motors

In a shunt motor, φ is constant, as has been described above. Therefore, by Equation (2), the back EMF is directly proportional to the rotational speed of the motor. If the motor starts from rest, Equation (1) gives the initial current as VA/RA. The initial torque is therefore, by Equation (3), KφVA/RA. This is called the stall torque. As the motor speeds up, Equation (2) tells us that EA will start to appear, and the current will decrease linearly with the motor speed. Torque will also decrease linearly with speed. The motor will reach its maximum speed when VA - EA = 0, approximating the motor as frictionless, and assuming there is no mechanical load on the motor. This is shown graphically below. Such motors are used for hoists and grinding tools.

The field current is usually much less than the armature current. A rheostat (variable resistor) in series with the field coil of a shunt-connected motor can be used as a speed control.

For shunt motors, it is important to keep the field intact. If the field current is lost, say, due to the field coils burning out, the magnetic field goes to zero, except for the residual magnetic field in the iron. This drastically reduces the back EMF, and the motor speed can increase to dangerous levels, perhaps destroying the machine.

#### Series-Wound DC Motors

In a series-wound motor, the magnetic flux φ varies with armature current, because the armature current also passes through the field coil. Equation (4) below shows how the field depends on the armature current.

(4)  φ = KφIA

Kφ is a constant. The magnetic flux varies linearly with armature current. Plugging this into Equation (3) we get:

(5)  T = KKφ(IA)2

As you can see, the torque is proportional to the square of the current. If the motor starts from rest, Equation (1) gives the initial current as VA/RA, ignoring the resistance of the field coil. The initial torque is therefore, by Equation (3), KφVA/RA. As the motor speeds up, Equation (2) tells us that EA will start to appear, and the current will decrease (but not linearly) with the motor speed. If the motor has no load and the motor is approximated as frictionless, the motor will never reach a terminal velocity. This happens because, as armature current goes to zero, so does φ. EA therefore drops off as speed increases. This is shown graphically below. Sometimes series-connected DC motors have a resistor in series with the armature to limit starting current. The resistor is removed once the motor comes up to speed.

Of course, real motors do have friction, so under no-load, the motor will eventually reach some high speed. Nevertheless, some series motors can be damaged by excessive speed, and precautions must be taken.

Series-wound motors have some useful characteristics. A series-wound motor has high starting torque. It can be operated at low speed. The power output is approximately constant over its entire speed range. It will change its speed to accommodate various loads. This type of motor can be used for winches and cranes where large loads can be moved slowly and light loads can be moved quickly.

#### Regenerative Braking

Most hybrid electric vehicles use regenerative braking. This means that, when the brakes are applied, the electric drive motors are used to brake the vehicle. The back EMF generated by the motors is used to recharge the batteries.

### AC Motors

AC motors may be either single-phase or three-phase. The fan motor in your oven is single-phase. Most industrial motors are three-phase. The most common type of motor is the induction motor. A special section in this lesson is devoted to the induction motor. Synchronous motors are also quite common. They have the property that they rotate at constant speed, dependent only on the number of stator windings and the power line frequency. They maintain this constant speed regardless of the load.

#### Losses in AC Motors

The electrical input power to a motor is always greater than the mechanical output power. There are five different kinds of power losses:

• Copper losses - Since the windings in a motor are made of copper, there will be i2R losses due to the resistance of the copper.
• Eddy current losses - The changing magnetic fields in an AC system cause currents to flow in the iron of the rotor and stator. These currents flow in small circles, like the eddies in a river. Most rotors and stators are made of laminated iron to reduce the loss due to eddy currents.
• Hysteresis loss - In a 60 Hz system, the current, and thus the magnetic field, reverses 120 times per second. Some power loss occurs with each reversal.
• Friction loss - Friction exists in all mechanical systems.
• Windage loss - This is loss due to the generation of air movement.

All of these losses manifest as heat generated in the motor.

#### Power in Motors

AC motors are either single-phase  or three-phase. For a single-phase motor, the electrical input power is given by Equation (6).

(6)  Pin = VIcosθ

V is the rms line voltage, I is the rms line current, and cosθ is the power factor.

As we learned in the lesson on three-phase,

(7)  Pin = √3 VIcosθ

The output mechanical power is:

(8)  Pout = Toutωm

Pout is the output mechanical power, Tout is the output torque, and ωm is the angular frequency of the shaft in radians/second.

(9)  Pin = Pout + Ploss

Ploss refers to the copper, eddy current, hysteresis, friction, and windage losses.

Pout is usually given in horsepower (746 W/HP).

The efficiency of a motor (η) is the ratio of the powers:

(10)  η = Pout/Pin

Typical efficiencies for industrial motors are between 85% and 95%. It should be understood that these efficiencies are for full load. Efficiency decreases significantly for light loads.

Since motor speeds are usually given in rpm rather than shaft angular frequency, conversion is frequently necessary:

(11)  ωm = nm(2π radians/revolution)/(60 seconds/minute)

nm is the motor shaft rotation in rpm. ωm is the angular frequency of the shaft in radians/second.

#### Universal motors

Universal motors are virtually the same as DC series-wound motors. They can operate on either DC or AC. They have the same speed-torque curve as given for the series-wound motor. They have all the advantages mentioned for series-wound motors. This type of motor is found in almost all hand-held electric tools such as drills, screwdrivers, saber saws, and kitchen mixers.

#### Induction motors

By far the most common motor in industrial use is the induction motor. It has both single-phase and three-phase versions. It has extremely simple architecture and few moving parts. It is rugged and efficient.

The most common form of the induction motor is the three-phase squirrel cage version. A cross-sectional view of such a motor is shown below. Notice that there are three sets of two stator windings, one set for each of the three phases. The three electrical phases are directly connected to the stator windings. No slip rings or brushes are involved. The electric current set up in the stator windings causes a rotating magnetic field in the stator. This rotating field is the secret behind the operation of all induction motors. In this two-pole motor, the field will make a complete rotation sixty times per second. A four-pole induction motor has a field that rotates at 30 rotations per second. The rotating magnetic field tends to pull the rotor along with it, causing the motor shaft to rotate.

Below is shown a simplified diagram of the squirrel cage rotor of a typical induction motor. The rotating stator field sets up currents in the aluminum or copper rotor bars. The resulting magnetic field causes the rotor and shaft to spin. Current flows through a rotor bar to the end cap and then back through the opposite rotor bar to the other end cap. There are no external electrical connections. The laminated iron bars (if they exist) are there to concentrate the magnetic field. Although not obvious in this diagram, the rotor bars are angled. This is clearer in the view in this link: http://en.wikipedia.org/wiki/File:Wirnik_by_Zureks.jpg

The rotor spins at a slower rate than the rotating magnetic field of the stator, depending on the load. If the motor is unloaded, the shaft speed will approach the synchronous speed. This is the speed of the rotating field. In a 60 Hz system, this synchronous speed will be 60 revolutions per second for a two-pole motor, or 377 radians/second, given by the following formula:

(12)  Synchronous speed = ωs = 2ω/P

ω is the line frequency (377 radians/second at 60 Hz) and P is the number of poles for each phase of the motor.

The speed-torque curve for a typical three-phase induction motor is shown below. The curve's shape may change radically dependent upon how the motor is designed. Unlike the universal motor, which has high starting torque, the induction motor has low starting torque, so it is best suited for applications in which the load increases with the speed, such as fans and pumps. The maximum torque the motor can develop is called the breakover torque or pull-out torque. Some induction motors are started at reduced voltage to avoid high starting current.

The normal operating range of an induction motor is near the synchronous speed. At no-load, the induction motor operates at just short of its synchronous speed. As the motor is loaded, slip occurs, given by Equation (13).

(13)  S = (ωs - ωm)/ωs or S = (ns - nm)/ns

ωs is the synchronous speed and ωm is the motor speed in radians per second. ns is the synchronous speed and nm is the motor speed in RPM. If the slip is small, the torque is proportional to the slip:

(14)  T = kS

Instead of using aluminum or copper bars in the rotor, some induction motors use coils of wire with electrical connections on slip rings on the motor shaft. These machines are more expensive and less rugged, but it makes it possible to adjust the speed-torque curve.

When specifying an induction motor for an application, the engineer must consider many trade-offs.

• Efficiency - The higher, the better.
• Starting torque - The starting torque must be high enough so that the motor will not stall.
• Starting current - This should be small, but its minimum value may be dictated by the requirement for starting torque.
• Pull-out torque - This should be high, or at least as high as necessary to handle the full-speed load.
• Power factor - A high power factor (90% or better) reduces the need for power factor correction.
• Reliability - The motor should have a long service life with minimum maintenance.
• Cost - This is probably the least important consideration. Going cheap can doom a project.

For any motor application, the engineer must consider the torque required. Torque is force times distance.

Single-phase induction motors are also quite common. For example, most home air conditioners have an outside compressor unit with a 240 V single-phase induction motor. A single-phase induction motor is somewhat more complicated than its three-phase cousin. When the rotor is stationary, the stator field does not rotate, and the motor has zero starting torque. The problem is in how to get the stator to create a rotating magnetic field. This is usually done by using a starting capacitor to create phase shift for an auxiliary coil. After the rotor begins to spin, the stator field begins to rotate on its own. A centrifugal switch disconnects the capacitor and the auxiliary coil when the rotor speed is about 75% of its maximum. Capacitors in these systems are a frequent point of failure.

Some single-phase induction motors have no starting capacitor. Instead, they a have a run capacitor, which is not disconnected by a centrifugal switch. Such motors have poor starting torque. Other single-phase induction motors have both starting capacitors and run capacitors.

#### Synchronous machines

Some motors and generators are intended to operate exactly at their synchronous speeds. Nearly all electrical energy all over the world is produced by synchronous generators. In the United States, these generators are made to rotate 60 times per second, producing 60 Hz three-phase power.

When used as motors, synchronous machines are usually used in higher power, lower speed applications than induction motors, or in applications where precise timing is critical. As with the induction motor, the synchronous speed is given by Equation (12). For such machines, the speed of the motor is constant, independent of the load, unless the load is so great that the machine slips phases. The speed-torque curve for a synchronous motor is nothing more than a vertical line at the synchronous speed.

The stator of a synchronous motor is just like the stator of an induction motor. In large motors, the rotor is an electromagnet operated by DC current. In very small motors, the rotor is a permanent magnet.

Synchronous motors can be tuned to give positive reactive power. For this reason, they are sometimes used instead of capacitors to correct power factor. Some engineers use synchronous motors with no load – their only function is to correct power factor.

Unlike induction motors, synchronous motors have near-zero starting torque. There are various ways to get such motors moving.

• Use a cycloconverter. Start the machine at a very low frequency (less than 1 Hz), and ramp up the frequency as the machine gets moving.
• Use another motor to bring the synchronous motor up to speed.
• Start the motor like an induction motor. When it nears synchronous speed, switch it to synchronous operation, and then connect the load.

#### Understanding Motor Nameplate Data

Shown below is a simplified version of an industrial induction motor nameplate. NEMA NOM. EFFICIENCY 96.2 - NEMA stands for National Electrical Manufacturers' Association. This organization specifies the minimum information that must be on a motor nameplate. The simplified diagram presented here does not show all the required NEMA information. The efficiency is the ratio of output mechanical power to input electrical power in percent. The efficiency numbers apply only when the motor is under full load. At lighter loads, the efficiency will probably be less.

POWER FACTOR 89.7 - This is the ratio of real power to apparent power in percent. Although not specified, the power factor is lagging. The power factor is specified at full load. At lighter (or heavier) loads, the power factor may be different.

MAX. CORR. KVAR. 20.0 - Maximum correction to power factor. This specifies that no more than 20 KVAR in power factor correction should be applied to this motor.

AMPS 163 - Under full load, this motor draws 163 A.

VOLTS 460 - You might have expected that the motor would be specified at 480 V, because 480 V is a typical supply voltage. The lowered specification is because line losses are assumed to lower the voltage before it gets to the machine.

PH 3 - Like virtually all other industrial motors, this motor operates on three-phase power.

HZ 60 - The standard for power distribution in America is a frequency of 60 Hz.

HP 150 - This is a 150 HP motor, when operated at full load.

RPM 1785 - At full load, this motor spins at 1785 RPM. Since this is an induction motor, you might guess that its no-load speed approaches its nearest synchronous speed, 1800 RPM.

S. F. 1.15 - SF is the service factor. With an SF of 1.15, this motor can be reliably operated at 15% over its rated load. Nevertheless, operating at increased load will shorten the life of the motor.

DUTY CONT - "Cont" is short for "continuous." This motor is rated for continuous operation at full load.

OTHER INFORMATION - A lot of other information is presented on a motor nameplate. Only basic information pertinent to electricity is shown here.

### Special Purpose Motors

#### Stepper motor

Sometimes it is desirable to rotate a shaft in precise increments. The stepper motor provides this capability. When the stepper motor receives a pulse, it rotates a specific number of degrees, based on the motor's design. For example, the shaft may rotate 5° with each pulse. The speed of rotation depends upon the pulse rate, but the maximum speed is limited. Stepper motors can be operated in forward or reverse. Such motors provide accurate, repeatable shaft positioning.

The head positioning motors in inkjet printers are stepper motors. So are the motors for hard disk drive heads. Some students use stepper motors for the drive wheels of small robots because analyzing the pulses delivered to the wheels can yield a precise location for the robot by "dead reckoning."

#### Selsyn synchro

The Selsyn, or synchro, is a motor-generator pair connected by wires. Rotating the generator cause the motor to rotate exactly the same number of degrees as the generator. Digital devices have largely replaced the Selsyn in modern systems.

#### Brushless DC motors

Instead of having brushes and a commutator, a brushless DC motor has an external electronic commutator. Typically, these small motors have a permanent magnet in the rotor and provide a rotating magnetic field by controlling current through the field coils on the stator. This design improves efficiency, avoids wear and tear on brushes and commutator bars, and avoids electronic noise from arcing. The down side is that brushless motors are much more expensive than brushed motors.

#### Reluctance Motors

The rotor of a reluctance motor is a ferromagnetic material (one that can store a magnetic field temporarily — not a permanent magnet). No wires are connected to the rotor, so no commutator or brushes are needed. Poles on the stator are energized in sequence to cause a rotating magnetic field that the rotor attempts to follow. These motors may suffer from "torque ripple;" as the motor turns, the torque of the motor may vary, which can cause noise and vibration.

### Motor Selection

Selecting a motor depends, first, on the environment in which the motor will be used. Is it going to be used in an automobile? Then the motor will probably be a 12 V DC motor. Is it going to be used in a residence? Then the motor may be a single-phase induction motor or a universal motor operating from a 120 V AC supply. If the application is industrial, the motor will probably be a three-phase induction motor or (more rarely) a three-phase synchronous motor.

Next one needs to consider the task the motor is intended to do. Is it for a hand-held tool? Then the motor will probably be a light-weight universal motor either powered by a rechargeable battery or connected with a power cord to 110 V AC. Is it for an application requiring precise timing? If so, a synchronous motor is probably the best selection. The table below lists some of the choices.

#### Motor Selection Table

 Application or Environment Typical Motor Choice Industrial Three-phase motors, usually induction motors with squirrel cage rotors Residential Single-phase AC motors (120 V) Automotive 12 V DC motors Toys Small DC motors, usually with a permanent magnet field Pumps Induction motors Hand-held tools Universal motors Timing Synchronous motors Positioning Stepper motors Power factor correction Synchronous motors

These are only some of the basic choices. Other factors to consider are operating speed, torque characteristics of the load, expected life, operating conditions (heat, cold, moisture, etc.), size, weight, forward/reverse operation, speed or positional accuracy, and cost.

At this time you should complete Tutorial 19 on motors.