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In order to create linear motion, rotational motion is often converted by means of rack and pinion systems or chain driven linear sliders. Rotational motion is also desirable for robot actuators or fluid systems. The most widely used method of generating rotational motion in machinery is through electric motors. It is therefore important that student understand enough about the types of motors available, how they work, and how they are used. Electric motors and generators are included in the formal engineering education of some disciplines, but not all. This module is aimed at linking tier 1 streams such as electricity and magnetism to tier 3 projects. The student will need a familiarity with simple magnetism and AC circuits.
Tier 2: Technology Module
The following is a list of electrical and magnetic laws and how they relate to a loop of wire rotating in a changing magnetic field.
The general and complete forms of these laws are given in the .
Poly Phase Induction
Single Phase Induction
Motors can be generally divided as shown below. This module will investigated each of these in turn.
In general, DC motors are most desirable in two situations. The first is when the only power available is DC, which occurs in automobiles and small battery powered devices. The other is when a torque-speed curve needs to be carefully doctored. As technology and manipulation advances in AC motors this becomes a less important aspect, but historically the DC motor has been easy to configure making it good for servo and traction application. With high current and low voltage relative to the power supplied these motors provide high torque at low speed. The variations of the standard DC motor are the universal motor, which has been slightly modified to run on AC power, and the brushless DC motor, which is a highly complex device compared to the standard motor. DC motors are used in applications requiring velocity or position control and when a high starting torque is needed as AC motors have difficulty in this area.
Figure 1.1: DC Motor Cut Away
Source: San Diego State University
Brushed motors are the simplest form of DC motors. When a DC motor gives no indication on whether it uses brushes or not, it does. From the Lorentz force law, a force is known to be exerted proportional and perpendicular to both magnetic field and the relative velocity of a moving charge. This applies directly to DC motors. When current is run through a loop of wire in the motor’s rotor, the permanent magnetic field from the stator exerts a force. This creates a torque about the spindle and turns the motor 90 degrees from the picture below. At this point the force is acting through the axis of rotation. When the spindle rotates past this point the force creates a torque in the other direction and brings it back to this point. If the current flow is stopped for a very short period of rotation while the momentum carries loop past this stable point and then re-established and reversed, the motor will continue to rotate in the same direction toward the opposite stable point. Reversals are constantly repeated so that the motor never settles. This process is carried out by a mechanical device called a commutator.
Figure 1.2: DC Motor
The commutator works by connecting the wire ends to the input power through brushes. Brushes used to be literally copper brushes, but are now replaced with carbon pads. These brushes slide over rotating rings called slip rings that are attached to the rotor and divided into two parts. When one part is in contact with the positive brush, the current flows into one end of the copper wire. The other end is in contact with the negative end of the brush to complete the circuit. As the loop reaches alignment, the gap in the ring reaches both brushes and the current is short circuited. After the loop moves past the aligned position, the gap has past the brushes and the other side of the slip ring is in contact causing the current to flow in the other direction. Increasing the number of coils in the rotor is a good way to improve the performance of a DC motor giving more constant torque as the rotor rotates. For each loop added the commutator must be upgraded and additional brushes are required. Additional poles can also be added to the stator.
There are alternate ways to build DC motors that offer different performance characteristics. Another way to construct rotors is to use armature coils. Instead of loops, small electro-magnets are attached to the rotor. These coils produce magnetic fields attracting the poles on the permanent magnet causing the coils to rotate. The force exerted on the current in the loops has equal torque in both directions and so the only unbalanced force is the magnetic pull of the permanent magnet. A commutator is still needed to allow the rotor to pass freely across the magnet poles and to reverse the polarity if the current.
Figure 1.3: Armature Coil DC Motor
A wound field DC motor is made by replacing the permanent magnets of the DC motor stator with electro magnets and has the added benefit of reducing electrical noise. The torque on the motor can be controlled directly by varying the current to the coils, but the torque/speed ratios can also be edited this way. This model can be built using either coils or loops, but is more commonly seen with coils. If the electro-magnet coils are in a parallel circuit with the rotor magnet coils, a high speed low torque motor is produced and conversely in series a low speed high torque motor is created. Any combination of series or parallel can be used to calibrate the motor. Brushless motors use a wound field design with virtual commutators.
Brushless DC motors use multiple stator coils and a virtual commutator. The rotor is a permanent magnet this time and the stator consists of electro-magnetic coils (usually six poles). The commutator circuit measures back emf directly, or uses a Hall Effect sensor to find the position. From this information, each of the stator coils is activated at the correct time causing the rotor to align its self with the field. As the field rotates around the stator, the rotor is dragged with it causing the spindle to turn. The virtual commutator is already monitoring the position of the rotor and so to operate as a servo device the motor needs to share this information and no additional sensors are needed. The voltage graph for each pole follows a trapezoidal pattern unlike the sinusoidal slope of AC induction motors. Commutation of a brushless DC motor is a closed loop process, but the application for the motors vary widely and include both open and closed control loop applications. Brushless motors are usually chosen over conventional DC motors because brushes will inevitably wear and have capacity to cause sparks. This makes the brush motors dangerous in certain applications. Brushless motors also run at much lower temperatures than AC shaded pole motors increasing the lifetime of components such as bearings. They also have a longer life time than standard DC motors since they do not have brushes, slip rings, or mechanical commutators that can wear out. The penalty for these benefits is higher cost due to more components and a more complex commutating system. Below is an over simplified depiction of a brushless DC motor in operation. In real motors, all three sets of poles would have a voltage at any given time that would vary in magnitude and direction.
Figure 1.4: Poles of a DC Brushless Motor
Stepper motors also run on DC electricity. The rotor has a gear shaped cross section and the teeth of the gear are all magnetic poles. The electro-magnets on the stator, when activated, attract the tips of the nearest gear teeth and align them with the magnetic field. The next magnet in the sequence then activates and the teeth move through a slight rotation to the next alignment. The process is repeated and the motor continues to rotate. With as many as 50,000 micro steps per revolution, these high accuracy motors are ideal for positioning devices giving a rotational accuracy up to 0.0072o ignoring repeatability issues. Common stepper motors have four phase stators and 3.6o increments corresponding to 100 steps per revolution. Stepper motors have low torque rating, but have the advantage of very accurate built in position control.
Figure 1.5: Stepper Motor
Somewhere between DC and AC motors is the Universal motor. Based on wound field DC motor design, these motors can operate with either type of current and are usually used with AC to achieve similar performance as brushed DC motors. AC powered universal motors maintain several desirable traits of DC motors such as high starting torque, compact high speed designs and good power efficiency. Due to the requirements for commutator though, these motors are not as reliable as other AC or brushless DC motors preventing them from being used in industrial settings. They are optimal however for domestic applications such as vacuum cleaners and kitchen appliances.
Figure 2.1: Universal Motor
Source: Popular Woodworking
AC motors can be loosely divided into synchronous and induction or single phase and poly phase. Synchronous motors are build similarly to DC motors and can have a permanent magnet in the rotor or stator. They run at the synchronous speed defined by the number of poles and the input power frequency. Induction motors have conducting rotors and use a changing magnetic field to induce a current and then create a torque. The phase refers to the power supplied to the motor. Single meaning a single phase and poly meaning three phase power.
Figure 2.1: Squirrel Cage AC Induction Motor
Source: The IEEE
The simplest for of AC motor is the brushed synchronous motor. This motor work the same way as a DC motor except that instead of having a commutator the slip rings are always attached to the same brush. This way the commutation is automatic when the polarity of the current is reversed. This style of motor would use a wound coil rotor.
Figure 2.2: Synchronous AC Motor
Synchronous motors are usually powered by a rotating magnetic field that acts on a permanent magnet in the rotor. The field is created by the sinusoidal current signals flowing through stator coils. The signals are offset by a 120o phase angle. These motors run at the frequency of the sinusoids that power them; 60Hz in North America. These motors offer accurate speed control, but little in terms of position control. They are used usually for low speed applications. Since synchronous motors are almost exclusively three phase motors, they are ideal for industrial settings where uniform torque is required over varying speeds. For very high horsepower applications, synchronous motors are often chosen above induction motors for their efficiency. The leading power factor that comes from a synchronous motor is often desirable in heavy industrial settings to improve the overall power factor of the plant. The synchronous speed of an AC motor at which synchronous motors run is given by the formula below, where N is the speed in RPM, f is the frequency in Hertz, and p is the number of poles.
Figure 2.2a: Magnetic Field of a Synchronous Motor
Increasing Magnetic Field
Reaction Magnetic Field
Single Phase induction motors do not use permanent magnets or slip ring. Instead they require a current to be induced in the rotor coils before a force can be exerted corresponding to the Lorentz force law. In order to induce a current, the magnetic flux must change relative to the rotor coils. This is achieved by the AC current through an electromagnet changing in a sinusoidal pattern causing the magnetic field amplitude to change with it. The rotor must also be offset so that a torque is created. Once the rotor is moving at a reasonable speed, the current doesn’t react fast enough to the field and so a torque is created. Single phase motors are seldom available in more than five horsepower and usually are used for fractional horsepower applications.
Applying Lenz’s law and the Biot-Savart law to the stationary coil shown below, the induced current must flow into the top part of the loop and out of the bottom part in order to create a magnetic field opposing the increasing field. According to the Lorentz force law, there are forces pulling the moving particles toward the centre of the coil, but since this gives no torque it doesn’t create motion.
The force produced is proportional to the current and the field strength as shown in the Lorentz force law. The current in turn is proportional to the change in field as discussed in the last slide. This means that the force applied can be described as below where K is a constant incorporating the number of coils and various amplitudes and B is magnetic field.
Let the AC supply current generating the field be a sine curve. The change in field must be its derivative, a cosine curve. The inherent inductance of the rotor causes the responsive field to lag behind the stator field by an angle . Now force can be represented as below with as the AC power frequency and t as time.
Integrating over a single period gives a total impulse of . The desirable impedance of the rotor is therefore 90o to give the highest positive impulse. In this case, the field and the induced current switch directions at the same time.
If the coil was already rotating at speed, a moment is created about the centre of the rotor while the current is still 90o behind. The moment created causes the rotor to rotate further. The machine is then self sustaining until the dynamic field is removed or the required torque is higher than the motor stall torque.
The problem in motor design now is getting the motor started. If the coils won’t rotate in the field, the solution is to make the field rotate around the coils. With more than one set of poles as in the synchronous motor, a rotating field is created. In single phase induction motors there are several approaches to this including shaded pole, resistance split, permanent split capacitor, and split phase motors. The common concept to these motors is that the imaginary part of impedance can be used to shift the phase of the pole. Stated another way, impedance is a phasor and the phase angle can be controlled by inductors and capacitors.
Shaded Pole motors use thick copper rings as inductors to change the phase angles of the magnetic field generated by the main stator coil on one set of poles. A current is induced in the coils creating a magnetic field to oppose the magnetic field changes caused by the AC current in the stator winding. This responsive current cannot keep up with the AC current and so there is always a difference in the field strength giving the phase lag. As with all induction motors, shaded pole motors are not limited to two poles; six pole motors are also common. Shaded pole motors are for low torque applications as they have very low starting torque, but are cheap and reliable as they have fewer parts. As with all AC induction motors, they do not use brushes or slip rings and so are safer and easier to maintain. The diagram below shows how the poles are offset by inductors.
Figure 3.3: Shaded Pole Diagram
Split phase motors are very similar to shaded pole resistors at start up, but they then return to the generic motor type described earlier. The stator is a two part electro-magnet creating a field across the rotor. At start up, a second two part electro-magnet acts at 90o to the first. The magnetic field is not given a phase lag directly, but the current through the coil is given a phase lag, again by inductive element. This creates a rotating magnetic field and starts the motor moving. Once a certain speed is reached, a centrifugal switch is activated and the start up windings are disengaged. The motor then continues to run on two poles.
Capacitor start motors are essentially a variation of split phase motors. Capacitors increase the phase angle that can be reasonably expected from around 30o to almost 90o. The increased phase shift offers a much greater start up torque than shaded pole motors. The capacitor and other material considerations add parts to these motors making the more expensive and slightly less durable.
Permanent Split Capacitors are a slight variation of capacitor start motors in that the phase shift circuits are never disengaged. The high phase shift gives good starting torque and the capacitors lend themselves well to speed control.
Poly phase or three phase motors are a little simpler. This type of induction motor usually has three stator coils that create and maintain a rotating magnetic field in the same way as synchronous motors. The main difference is that these motors do not run at the synchronous speed. The difference between the actual speed and the synchronous speed is known as the slip speed. The rotating field induces a current in the rotor loop as the flux perpendicular to the field changes. The field then exerts a force on the loop as it rotates. In this way the rotor is dragged behind the field at a slightly slower speed. The advantage of three phase motors is that they are capable of producing hundreds of horsepower. This higher horsepower allows domestic applications that single phase motors are in capable of such as washing machines and air conditioning units. The strength of all induction motors is that they are simple, rugged and cheap. There require little maintenance and have few parts. This is especially true of three phase motors which contain no centrifugal switches. Like synchronous three phase motors, the induction versions are used for applications where torque is expected to be fairly constant regardless of speed. By choosing one of each set of poles as the positive end and the other as negative, it is easy to see how the sum of the fields will rotate.
Figure 3.5: Rotating Magnetic Field
Stators are built from laminated steel and have slots in them for the coils to run through. In three phase machines, each phase uses several coils and takes up multiple sets of slots. If three were used, this would give a total of nine coils between each pole and is done to minimize the effect of the signal harmonics. The coils are expected to cover nine stator slots for each pole. If only eight were covered, then the motor would be described as 8/9 pitch. A common motor type is a three phase four pole motor. This would need to have thirty six stator slots (four poles times three phases times three slots). In single phase motors, the poles for the main coils take up a large portion of the stator slots and the start up coils use the remaining portion. Regardless of the motor phase, the stator teeth are shaped to allow magnetic flux to cross the air to the rotor as efficiently as possible.
Figure 3.6: Induction Motor Stator
Source: University of Manchester
In actual motors the coils of wire in the above explanations are replaced with squirrel cage rotors or wound rotors. The latter uses slip rings and brushes and has the same number of windings as stator coils. Due to the mechanical components required, this reduces the reliability of the motor. Squirrel cage rotors are named for their appearance, which resembles a hamster wheel. Thick conducting bars transfer current along the length of a laminated iron core at a slight angle. These conducting bars are in turn enclosed within a steel casing to improve the flux transfer from the stator. Instead of loops, the current runs along lengths and through the end rings, reacting with the rotating field and creating the torque to spin the rotor.
Figure 3.7a: Wound Field RotorFigure 3.7b: Squirrel cage Rotor
Source: Teco WestinghouseSource: Energy Manager Training
The magnetic field caused by a current carrying wire can be found from the equation below. In the equation below, B is the magnetic field, r is the raduis to the point of interest, mu-zero is the permeability of free space, I is the current in the wire, L is the length of the wire, d is the derivative operator, x denotes a cross product, and ‘hat’ denotes a unit vector.
Electro Motive Force is measured in volts. The term force is a historical error which has none-the-less been universally adapted by physicists.
Faraday’s Law of Induction
The emf induced in a circuit is proportional to the time rate of change of the magnetic flux linking that circuit. In the equation below e is the emf, phi is the magnetic flux, t is time, and d is the derivative operator.
The emf induced in an electric circuit always acts in such a direction that the current it drives around a closed circuit produces a magnetic field which opposes the change in magnetic flux which produces the emf. In the equation below e is the emf, phi is the magnetic flux, t is time, and d is the derivative operator.
Lorentz Force Law
The force acting on a charged particle is given by the equation below where q is the charge of the particle, E is the magnetic field, v is the particles velocity, B is the magnetic field, and x denotes a cross product.
Magnetic flux is given by the following equation where B is magnetic field, A is the area through which the field is acting, and the dot represents a dot product.
Rotors are the inner part of the motor that turns to spin the shaft. Rotors are normally permanent magnet, wound rotor, or squirrel cage designs.
Slip Speed (induction motors only)
Slip speed is the difference between operating speed and synchronous speed. Slip increases with load generally from 2%-3%, but can go as high as 7% or even 100% for torque motors. This means that the motor is not moving
Stators are the outer part of the motor that creates the magnetic field for the rotor to react with. They are normally permanent magnets or electro-magnets.
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