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Also, I suggest to someone who has a little inspiration in that regard than I do that we need a fanfic that involves Tesla in steampunk.
AU steampunk London with Sir Arthur Conan Doyle as a main character and Helen as a redhead. Trail of Blood and Animus are coming up for me - tonight's ep is Kali Part 3, so ToB should be on Friday and Animus next Tuesday. High efficiency enables significant savings in energy costs during the motor's normal endurance. Three-phase single speed motors can normally be connected for two different voltage levels.
The winding is delta connected at 230 V and if the main voltage is 400 V, the Y-connection is used. This speed is the synchronous speed and a squirrel-cage or a slip-ring motor can never reach it. After the introduction of the DC electrical distribution system by Edison in the United States, a gradual transition to the more economical AC system commenced. Modern solid state electronic circuits drive brushless DC motors with AC waveforms generated from a DC source. Cruise ships and other large vessels replace reduction geared drive shafts with large multi-megawatt generators and motors.
At the system level, (Figure above) a motor takes in electrical energy in terms of a potential difference and a current flow, converting it to mechanical work. Early designers of AC motors encountered problems traced to losses unique to alternating current magnetics.
If the laminations are made of silicon alloy grain oriented steel, hysteresis losses are minimized. Once Steinmetz's Laws of hysteresis could predict iron core losses, it was possible to design AC motors which performed as designed.
Single phase synchronous motors are available in small sizes for applications requiring precise timing such as time keeping, (clocks) and tape players. Above 10 Horsepower (10 kW) the higher efficiency and leading powerfactor make large synchronous motors useful in industry. Since motors and generators are similar in construction, it should be possible to use a generator as a motor, conversely, use a motor as a generator. If more torque in the direction of rotation is applied to the rotor of one of the above rotating alternators, the angle of the rotor will advance (opposite of (3)) with respect to the magnetic field in the stator coils while still synchronized and the rotor will deliver energy to the AC line like an alternator. In the case of a small synchronous motor in place of the alternator Figure above right, it is not necessary to go through the elaborate synchronization procedure for alternators. Assuming that the motor is up to synchronous speed, as the sine wave changes to positive in Figure above (1), the lower north coil pushes the north rotor pole, while the upper south coil attracts that rotor north pole. As the sine wave changes to negative between (3&4), the lower south coil pushes the south rotor pole, while attracting rotor north rotor pole. The current in the coils of a single phase synchronous motor pulsates while alternating polarity. A 2-pole (pair of N-S poles) alternator will generate a 60 Hz sine wave when rotated at 3600 rpm (revolutions per minute).
Rather than wind 12-coils for a 12-pole motor, wind a single coil with twelve interdigitated steel poles pieces as shown in Figure above.
If the Westclox motor were to run at 600 rpm from a 50 Hz power source, how many poles would be required?
The rotor (Figure above) consists of a permanent magnet bar and a steel induction motor cup. A 3-phase synchronous motor as shown in Figure below generates an electrically rotating field in the stator. The 3-phase 4-pole (per phase) synchronous motor (Figure below) will rotate at 1800 rpm with 60 Hz power or 1500 rpm with 50 Hz power.
Small multi-phase synchronous motors (Figure above) may be started by ramping the drive frequency from zero to the final running frequency.
The block diagram (Figure above) shows the drive electronics associated with a low voltage (12 VDC) synchronous motor. If constant and accurate speed of rotation is required, (as for a disk drive) a tachometer and phase locked loop may be included. A motor driven by square waves of current, as provided by simple hall effect sensors, is known as a brushless DC motor. Ripple torque, or cogging is caused by magnetic attraction of the rotor poles to the stator pole pieces. If a motor is driven by sinewaves of current synchronous with the motor back emf, it is classified as a synchronous AC motor, regardless of whether the drive waveforms are generated by electronic means. The generation and synchronization of the drive waveform requires a more precise rotor position indication than provided by the hall effect sensors used in brushless DC motors. The variable speed drive must also reduce the drive voltage at low speed due to decreased inductive reactance at lower frequency. If the rotor and stator of a conventional rotary synchronous motor are unrolled, a synchronous linear motor results. This leading power factor can be exaggerated by removing the mechanical load and over exciting the field of the synchronous motor. Since a synchronous condenser does not supply a torque, the output shaft may be dispensed with and the unit easily enclosed in a gas tight shell. The efficiency of long power transmission lines may be increased by placing synchronous condensers along the line to compensate lagging currents caused by line inductance. The ability of synchronous condensers to absorb or produce reactive power on a transient basis stabilizes the power grid against short circuits and other transient fault conditions. The capacity of a synchronous condenser can be increased by replacing the copper wound iron field rotor with an ironless rotor of high temperature superconducting wire, which must be cooled to the liquid nitrogen boiling point of 77oK (-196oC). The variable reluctance motor is based on the principle that an unrestrained piece of iron will move to complete a magnetic flux path with minimum reluctance, the magnetic analog of electrical resistance. If the rotating field of a large synchronous motor with salient poles is de-energized, it will still develop 10 or 15% of synchronous torque.
If slots are cut into the conductorless rotor of an induction motor, corresponding to the stator slots, a synchronous reluctance motor results. If an iron rotor with poles, but without any conductors, is fitted to a multi-phase stator, a switched reluctance motor, capable of synchronizing with the stator field results. Sequential switching (Figure below) of the stator phases moves the rotor from one position to the next. If one end of each 3-phase winding of the switched reluctance motor is brought out via a common lead wire, we can explain operation as if it were a stepper motor. Variable reluctance motor drive waveforms: (a) unipolar wave drive, (b) bipolar full step (c) sinewave (d) bipolar 6-step. An electronic driven variable reluctance motor (Figure below) resembles a brushless DC motor without a permanent magnet rotor. While the variable reluctance motor is simple, even more so than an induction motor, it is difficult to control. Simple construction- no brushes, commutator, or permanent magnets, no Cu or Al in the rotor.
The servo amplifier is a linear amplifier with some difficult to integrate discrete components. Slo-syn synchronous motors can run from AC line voltage like a single-phase permanent-capacitor induction motor. Unipolar drive of center tapped coil at (b),   emulates AC current in single coil at (a). Stepper motors are rugged and inexpensive because the rotor contains no winding slip rings, or commutator.
Since stepper motors do not necessarily rotate continuously, there is no horsepower rating. Stepper motors move one step at a time, the step angle, when the drive waveforms are changed.
There are three types of stepper motors in order of increasing complexity: variable reluctance, permanent magnet, and hybrid.
A variable reluctance stepper motor relies upon magnetic flux seeking the lowest reluctance path through a magnetic circuit. Variable reluctance stepper motors are applied when only a moderate level of torque is required and a coarse step angle is adequate. The only type stepper with no detent torque in hand rotation of a de-energized motor shaft. Permanent magnet stepper motors require phased alternating currents applied to the two (or more) windings. The waveforms (Figure above) are bipolar because both polarities , (+) and (-) drive the stepper.
A bifilar winding is produced by winding the coils with two wires in parallel, often a red and green enamelled wire. Full step drive provides more torque than wave drive because both coils are energized at the same time. Half step drive is a combination of wave drive and full step drive with one winding energized, followed by both windings energized, yielding twice as many steps. The contruction of a permanent magnet stepper motor is considerably different from the drawings above.
The permanent magnet stepper (Figure above) only has two windings, yet has 24-poles in each of two phases. Note that the rotor is a gray ferrite ceramic cylinder magnetized in the 24-pole pattern shown. Can-stack construction provides numerous poles from a single coil with interleaved fingers of soft iron.
The hybrid stepper motor combines features of both the variable reluctance stepper and the permanent magnet stepper to produce a smaller step angle. The stator teeth on the 8-poles correspond to the 48-rotor teeth, except for missing teeth in the space between the poles. Enough torque applied to the shaft to overcome the hold-in torque would move the rotor by one tooth.
If the polarity of φ-1 were reversed, the rotor would move by one-half tooth, direction unknown. An un-powered stepper motor with detent torque is either a permanent magnet stepper or a hybrid stepper. The poles of one stator windings are offset by a quarter tooth for an even smaller step angle. Brushless DC motors were developed from conventional brushed DC motors with the availability of solid state power semiconductors. High torque pancake motors may have stator coils on both sides of the rotor (Figure above-b).
Lower torque applications like floppy disk drive motors suffice with a stator coil on one side of the rotor, (Figure above-a).
The commutation function may be performed by various shaft position sensors: optical encoder, magnetic encoder (resolver, synchro, etc), or Hall effect magnetic sensors.
The simple cylindrical 3-φ motor Figure above is commutated by a Hall effect device for each of the three stator phases.
The above cylindrical motor could drive a harddrive if it were equipped with a phased locked loop (PLL) to maintain constant speed.
If the three stator phases were successively energized, a rotating magnetic field would be generated. You may recall that conventional DC motors cannot have an even number of armature poles (2,4, etc) if they are to be self-starting, 3,5,7 being common.
Nikola Tesla conceived the basic principals of the polyphase induction motor in 1883, and had a half horsepower (400 watt) model by 1888. An induction motor is composed of a rotor, known as an armature, and a stator containing windings connected to a poly-phase energy source as shown in Figure below. The stator in Figure above is wound with pairs of coils corresponding to the phases of electrical energy available.
The stator in Figure above has salient, obvious protruding poles, as used on Tesla's early induction motor. However, for larger motors less torque pulsation and higher efficiency results if the coils are embedded into slots cut into the stator laminations. The stator laminations are thin insulated rings with slots punched from sheets of electrical grade steel. In Figure above, the windings for both a two-phase motor and a three-phase motor have been installed in the stator slots. Actual stator windings are more complex than the single windings per pole in Figure above. The key to the popularity of the AC induction motor is simplicity as evidenced by the simple rotor (Figure below).
A short explanation of operation is that the stator creates a rotating magnetic field which drags the rotor around. The torque developed by the disk is proportional to the number of flux lines cutting the disk and the rate at which it cuts the disk.
A rotating magnetic field is created by two coils placed at right angles to each other, driven by currents which are 90o out of phase.
In Figure above, a circular Lissajous is produced by driving the horizontal and vertical oscilloscope inputs with 90o out of phase sine waves. Figure above shows the two 90o phase shifted sine waves applied to oscilloscope deflection plates which are at right angles in space.
For reference, Figure belowshows why in-phase sine waves will not produce a circular pattern. If a pair of 90o out of phase sine waves produces a circular Lissajous, a similar pair of currents should be able to produce a circular rotating magnetic field. The rotation rate of a stator rotating magnetic field is related to the number of pole pairs per stator phase. The short explanation of the induction motor is that the rotating magnetic field produced by the stator drags the rotor around with it. The longer more correct explanation is that the stator's magnetic field induces an alternating current into the rotor squirrel cage conductors which constitutes a transformer secondary. When power is first applied to the motor, the rotor is at rest, while the stator magnetic field rotates at the synchronous speed Ns.


The frequency of the current induced into the rotor conductors is only as high as the line frequency at motor start, decreasing as the rotor approaches synchronous speed. The Figure above graph shows that starting torque known as locked rotor torque (LRT) is higher than 100% of the full load torque (FLT), the safe continuous torque rating. There are several basic induction motor designs (Figure below) showing consideable variation from the torque curve above.
Various standard classes (or designs) for motors, corresponding to the torque curves (Figure below) have been developed to better drive various type loads. Steinmetz contributed to solving these problems with his investigation of hysteresis losses in iron armatures. The brushless DC motor, actually an AC motor, is replacing the conventional brushed DC motor in many applications.
Though few AC motors today bear any resemblance to DC motors, these problems had to be solved before AC motors of any type could be properly designed before they were built. The laminations are coated with insulating varnish before stacking and bolting into the final form. Magnetic hysteresis is a lagging behind of magnetic field strength as compared to magnetizing force. This was akin to being able to design a bridge ahead of time that would not collapse once it was actually built. Though battery powered quartz regulated clocks are widely available, the AC line operated variety has better long term accuracy-- over a period of months. Large synchronous motors are a few percent more efficient than the more common induction motors. However, the synchronous motor is not self starting and must still be brought up to the approximate alternator electrical speed before it will lock (synchronize) to the generator rotational rate. In a similar manner the rotor south pole is repelled by the upper south coil and attracted to the lower north coil. In actual practice, loading the rotor will cause the rotor to lag the positions shown by angle α. If the permanent magnet rotor speed is close to the frequency of this alternation, it synchronizes to this alternation. Though the polarity of the coil alternates due to the appplied AC, assume that the top is temporarily north, the bottom south. Such motors are not self starting if started from a fixed frequency power source such as 50 or 60 Hz as found in an industrial setting.
These motors have a position sensor integrated within the motor, which provides a low level signal with a frequency proportional to the speed of rotation of the motor. This type of motor has higher ripple torque torque variation through a shaft revolution than a sine wave driven motor. A resolver, or optical or magnetic encoder provides resolution of hundreds to thousands of parts (pulses) per revolution.
The synchronous motor can also be smaller, especially if high energy permanent magnets are used in the rotor. As a result the industrial grade electronic speed control used with induction motors is also applicable to large industrial synchronous motors.
This is often usefull in cancelling out the more commonly encountered lagging power factor caused by induction motors and other inductive loads. The synchronous condenser may then be filled with hydrogen to aid cooling and reduce windage losses. More real power may be transmitted through a fixed size line if the power factor is brought closer to unity by synchronous condensers absorbing reactive power.
The superconducting wire carries 160 times the current of comparable copper wire, while producing a flux density of 3 Teslas or higher. When a stator coil pole pair is energized, the rotor will move to the lowest magnetic reluctance path. The mangetic flux seeks the path of least reluctance, the magnetic analog of electric resistance. However, microprocessors and solid state power drive makes this motor an economical high performance solution in some high volume applications. Sequential switching of the field coils creates a rotating magnetic field which drags the irregularly shaped rotor around with it as it seeks out the lowest magnetic reluctance path. Electronic control solves this problem and makes it practical to drive the motor well above and below the power line frequency.
Rather than a stepper, a variable reluctance motor is optimized for continuous high speed rotation with minimum ripple torque. The rotor moves in discrete steps as commanded, rather than rotating continuously like a conventional motor. A considerable design effort is required to optimize the servo amplifier gain vs phase response to the mechanical components.
If they do rotate continuously, they do not even approach a sub-fractional hp rated capability. The step angle is related to motor construction details: number of coils, number of poles, number of teeth. The maximum start frequency is the highest rate at which a stopped and unloaded stepper can be started. This torque load on the stepper is due to frictional (brake) and inertial (flywheel) loads on the motor shaft.
This means that an irregularly shaped soft magnetic rotor will move to complete a magnetic circuit, minimizing the length of any high reluctance air gap. With 3-pulses per stator tooth, and 8-stator teeth, 24-pulses or steps move the rotor through 360o. The direction, step rate, and number of steps are controlled by a stepper motor controller feeding a driver or amplifier.
Otherwise, we show the internal construction of a variable reluctance stepper motor in Figure above.
In practice, this is almost always square waves generated from DC by solid state electronics. The 6-wire motor, the most common arrangement, is intended for unipolar drive because of the center taps. Unipolar drive (not shown) would require a pair of unipolar waveforms for each of the above bipolar waveforms applied to the ends of a center tapped winding.
By varying the currents to the windings sinusoidally many microsteps can be interpolated between the normal positions. It is desirable to increase the number of poles beyond that illustrated to produce a smaller step angle. The rotor is a cylindrical permanent magnet, magnetized along the axis with radial soft iron teeth (Figure below). Thus, one pole of the rotor, say the south pole, may align with the stator in 48 distinct positions. However, we provide a simplified pictorial and schematic representation (Figure below) to illustrate details not obvious above.
The alignment would be south stator top to north rotor bottom, north stator bottom to south rotor.
The hybrid stepper will have a small step angle, much less than the 7.5o of permanent magnet steppers. True synchronous motors are considered to be single speed, a submultiple of the powerline frequency. The changing position of the permanent magnet rotor is sensed by the Hall device as the polarity of the passing rotor pole changes.
The rotor is a flat ferrite ring magnetized with eight axially magnetized alternating poles. Thus, it is possible for a hypothetical 4-pole motor to come to rest at a torque minima, where it cannot be started from rest. The sensors are spaced 90o electrical apart, which is 90o physical for a single pole rotor.
By poly-phase, we mean that the stator contains multiple distinct windings per motor pole, driven by corresponding time shifted sine waves. The 2-phase induction motor stator above has 2-pairs of coils, one pair for each of the two phases of AC. The rotor consists of a shaft, a steel laminated rotor, and an embedded copper or aluminum squirrel cage, shown at (b) removed from the rotor. The laminations are coated with insulating oxide or varnish to minimize eddy current losses. One means of creating a rotating magnetic field is to rotate a permanent magnet as shown in Figure below. If the disk were to spin at the same rate as the permanent magnet, there would be no flux cutting the disk, no induced current flow, no electromagnet field, no torque. With the disk restrained by a spring, disk and needle deflection is proportional to magnet rotation rate. The National Electrical Manufacturers Association (NEMA) has specified motor classes A, B, C, and D to meet these drive requirements. Transmission of electrical energy covered longer distances at lower loss with alternating current.
Nikola Tesla envisioned an entirely new type of motor when he visualized a spinning turbine, not spun by water or steam, but by a rotating magnetic field. And, the stepper motor, a digital version of motor, is driven by alternating current square waves, again, generated by solid state circuitry Figure above shows the family tree of the AC motors described in this chapter. Some of the electric energy is lost to heat, another form of energy, due to I2R losses in the motor windings. Eddy currents are minimized by breaking the potential conductive loop into smaller less lossy segments.
If a soft iron nail is temporarily magnetized by a solenoid, one would expect the nail to lose the magnetic field once the solenoid is de-energized. This knowledge of eddy current and hysteresis was first applied to building AC commutator motors similar to their DC counterparts. This is due to power plant operators purposely maintaining the long term accuracy of the frequency of the AC distribution system. If a load such as a brake is applied to one of the above units, the angle of the rotor will lag the stator field as at (3), extracting energy from the AC line, like a motor.
Once up to speed, the synchronous motor will maintain synchronism with the AC power source and develop torque. By the time that the sine wave reaches a peak at (2), the torque holding the north pole of the rotor up is at a maximum.
This angle increases with loading until the maximum motor torque is reached at α=90o electrical. Since the coil field pulsates and does not rotate, it is necessary to bring the permanent magnet rotor up to speed with an auxiliary motor. The induction motor cup outside of the bar magnet fits outside and over the tabs for self starting.
Furthermore, the rotor is not a permanent magnet as shown below for the multi-horsepower (multi-kilowatt) motors used in industry, but an electromagnet. Since the sine waves actually overlap, the resultant field will rotate, not in steps, but smoothly. The PM rotor may be rotated by hand but will encounter attraction to the pole pieces when near them.
A resolver provides analog angular position signals in the form of signals proportional to the sine and cosine of shaft angle.
The advent of modern solid state electronics makes it possible to drive these motors at variable speed.
Originally, large industrial synchronous motors came into wide use because of this ability to correct the lagging power factor of induction motors.
Since the density of hydrogen is 7% of that of air, the windage loss for a hydrogen filled unit is 7% of that encountered in air.
This supplements longer response times of quick acting voltage regulation and excitation of generating equipment. The synchronous torque is due to changes in reluctance of the magnetic path from the stator through the rotor as the slots align. The relationship between torque and stator current is highly nonlinear– difficult to control.
However, this is offset by the cost of the electronic control, which is not nearly as simple as that for a brushless DC motor. A variable reluctance motor driven by a servo, an electronic feedback system, controls torque and speed, minimizing ripple torque. It is necessary to measure the rotor position with a rotary position sensor like an optical or magnetic encoder, or derive this from monitoring the stator back EMF. When stopped but energized, a stepper (short for stepper motor) holds its load steady with a holding torque.
The expense and complexity of a servomotor is due to the additional system components: position sensor and error amplifier. Once the motor is up to speed, pull-out torque is the maximum sustainable torque without losing steps. The stator typically has three windings distributed between pole pairs , the rotor four salient poles, yielding a 30o step angle.(Figure below) A de-energized stepper with no detent torque when hand rotated is identifiable as a variable reluctance type stepper. Sequentially switching the stator phases produces a rotating magnetic field which the rotor follows.
The rotor has protruding poles so that they may be attracted to the rotating stator field as it is switched. The windings could be center tapped to allow for a unipolar driver circuit where the polarity of the magnetic field is changed by switching a voltage from one end to the other of the winding.
There are twice as many waveforms because a pair of (+) waves is required to produce an alternating magnetic field by application to opposite ends of a center tapped coil. The rotor aligns with the field poles as for wave drive and between the poles as for full step drive. It is also desirable to reduce the number of windings, or at least not increase the number of windings for ease of manufacture.
Brushless DC motors tend to be small– a few watts to tens of watts, with permanent magnet rotors.
We do not show that the rotor is capped by a mild steel plate for mounting to the bearing in the middle of the stator.


The addition of the four small salient poles with no windings superimposes a ripple torque upon the torque vs position curve.
Since we have a 4-pole permanent magnet rotor, the sensors must be placed 45o physical to achieve the 90o electrical spacing.
Since the Hall sensor has two complementary outputs, one sensor provides commutation for two opposing windings. The individual coils of a pair are connected in series and correspond to the opposite poles of an electromagnet. If the moving magnetic lines of flux cut a conductive disk, it will follow the motion of the magnet.
Thus, the disk speed will always fall behind that of the rotating permanent magnet, so that lines of flux cut the disk induce a current, create an electromagnetic field in the disk, which follows the permanent magnet.
The combination of 90o phased sine waves and right angle deflection, results in a two dimensional pattern– a circle.
By analogy three windings placed 120o apart in space, and fed with corresponding 120o phased currents will also produce a rotating magnetic field. The current induced in the rotor shorted turns is maximum, as is the frequency of the current, the line frequency.
If it falls behind by a few cycles, they will make up the lost cycles of AC so that clocks lose no time.
This figure below could either be two paralleled and synchronized alternators driven by a mechanical energy sources, or an alternator driving a synchronous motor. This torque decreases as the sine wave decreases to 0 VDC at (3) with the torque at a minimum.
These 6-souths are interleaved with 6-north tabs bent up from the top of the steel pole piece of the coil. Encoders provide a digital angular position indication in either serial or parallel format. This makes it possible to nearly cancel an arbitrary lagging power factor to unity by paralleling the lagging load with a synchronous motor. The synchronous condenser aids voltage regulation by drawing leading current when the line voltage sags, which increases generator excitation thereby restoring line voltage. A microprocessor performs complex calculations for switching the windings at the proper time with solid state devices.
Wide spread acceptance of the stepper motor within the last two decades was driven by the ascendancy of digital electronics. Determine that the rotor is a permanent magnet by unpowered hand rotation showing detent torque, torque pulsations.
They have torque ratings to a thousand in-oz (inch-ounces) or ten n-m (newton-meters) for a 4 kg size unit. In practice, the step rate is ramped up during starting from well below the maximum start frequency.
The hybrid stepper has soft steel teeth added to the permanent magnet rotor for a smaller step angle.
However, due to the lesser number of rotor poles, the rotor moves less than the stator angle for each step.
A bipolar drive of alternating polarity is required to power windings without the center tap. The 5-wire motor can only be driven by unipolar waves, as the common center tap interferes if both windings are energized simultaneously. For example, half stepping the motor moving the print head across the paper of an inkjet printer would double the dot density. The result is that the rotor moves in steps of a quarter of a tooth when the phases are alternately energized. In the next two figures, we attempt to illustrate the quarter tooth rotation produced by the two stator phases offset by a quarter tooth, and the rotor half tooth offset. The major difference is that synchronous motors develop a sinusoidal back EMF, as compared to a rectangular, or trapezoidal, back EMF for brushless DC motors. The speed of a brushless DC motor is not fixed unless driven by a phased locked loop slaved to a reference frequency.
When this ripple torque is added to normal energized-torque curve, the result is that torque minima are partially removed.
That is, one coil corresponds to a N-pole, the other to a S-pole until the phase of AC changes polarity. This eliminates the brushes, arcing, sparking, graphite dust, brush adjustment and replacement, and re-machining of the commutator. The lines of flux cutting the conductor will induce a voltage, and consequent current flow, in the conductive disk.
If a load is applied to the disk, slowing it, more torque will be developed as more lines of flux cut the disk.
As the rotor speeds up, the rate at which stator flux cuts the rotor is the difference between synchronous speed Ns and actual rotor speed N, or (Ns - N). Its ruggedness and simplicity (Figure above) make for long life, high reliability, and low maintenance. As the sine wave changes from negative to 0 VDC to positive, The process repeats for a new cycle of sine wave. Thus, a permanent magnet rotor bar will encounter 6-pole pairs corresponding to 6-cycles of AC in one physical rotation of the bar magnet. The sine wave drive may actually be from a PWM, Pulse Width Modulator, a high efficiency method of approximating a sinewave with a digital waveform. However, a small synchronous motor, which mounts inside a drive wheel, makes it attractive for such applications. A synchronous condenser is operated in a borderline condition between a motor and a generator with no mechanical load to fulfill this function. Such a machine is said to have considerable additional transient ability to supply reactive power to troublesome loads like metal melting arc furnaces. Low power factor, low pull-out torque, and low efficiency are characteristics of the direct power line driven variable reluctance motor. Stepper motor coils are wound within a laminated stator, except for can stack construction. Instead, the φ2 stator field attracts a different tooth in moving the rotor CCW, which is a smaller angle (15o) than the stator angle of 30o. The driver is not a linear amplifier, but a simple on-off switch capable of high enough current to energize the stepper. Each side wraps around to the center of the doughnut with twelve interdigitated fingers for a total of 24 poles. In other words, the rotor moves in 2×96=192 steps per revolution for the above stepper.
The quarter tooth stator offset in conjunction with drive current timing also defines direction of rotation.
The stator poles are also mounted atop a steel plate, helping to close the magnetic circuit.
The majority of the torque is due to the interaction of the inside stator 2-φ coils with the 4-pole section of the rotor. While we include numerous illustrations of two-phase motors for simplicity, we must emphasize that nearly all poly-phase motors are three-phase. This current flow creates an electromagnet whose polarity opposes the motion of the permanent magnet– Lenz's Law.
Torque is proportional to slip, the degree to which the disk falls behind the rotating magnet. In the case of 60 Hz power, the field rotates at 60 times per second or 3600 revolutions per minute (rpm). Numerous problems were encountered due to changing magnetic fields, as compared to the static fields in DC motor motor field coils. Yet small brushed AC motors, similar to the DC variety, persist in small appliances along with small Tesla induction motors. Also, the silicon (a semiconductor) added to the alloy used in the laminations increases electrical resistance which decreases the magnitude of eddy currents. The point is that in either case the rotors must run at the same nominal frequency, and be in phase with each other.
The rotor with multiple magnet poles (below right) is used in any efficient motor driving a substantial load. Yes, we do not want the motor to alternately speed and slow as it moves audio tape past a tape playback head. The high temperature superconducting version of this motor is one fifth to one third the weight of a copper wound motor.[1] The largest experimental superconducting synchronous motor is capable of driving a naval destroyer class ship. And the position of the rotor with respect to the stator field needs to be calculated, and controlled. It can compensate either a leading or lagging power factor, by absorbing or supplying reactive power to the line. As a result, a hydrogen filled synchronous condenser can be driven harder than an air cooled unit, or it may be physically smaller for a given capacity. Such was the status of the variable reluctance motor for a century before the development of semiconductor power control. Waveforms (a & b) are applicable to the stepper motor version of the variable reluctance motor.
The bipolar magnetic fields may also be generated from unipolar (one polarity) voltages applied to alternate ends of a center tapped winding.
As long as the load torque does not exceed the motor torque, the controller will know the carriage position.
The center tap is achieved by a bifilar winding, a pair of wires wound physically in parallel, but wired in series. The flat stator coils are trapezoidal to more closely fit the coils, and approximate the rotor poles.
The addition of eight permanant magnet poles to the normal 4-pole permanent magnet rotor superimposes a small second harmonic ripple torque upon the normal 4-pole ripple torque. Moreover, the 4-pole section of the rotor must be on the bottom so that the Hall sensors will sense the proper commutation signals. If there were no mechanical motor torque load, no bearing, windage, or other losses, the rotor would rotate at the synchronous speed. Higher efficiency higher torque multi-pole stator synchronous motors actually have multiple poles in the rotor. There is no explosion hazard as long as the hydrogen concentration is maintained above 70%, typically above 91%.
Such a synchronous condenser has a higher power density (smaller physically) than a switched capacitor bank. For smooth vibration free operation the 6-step approximation of a sine wave (c) is desirable and easy to generate. The strict drive requirements make this motor only practical for high volume applications like energy efficient vacuum cleaner motors, fan motors, or pump motors. The torque available is a function of motor speed, load inertia, load torque, and drive electronics as illustrated on the speed vs torque curve. If the detent angle is large, say 7.5o to 90o, it is likely a permanent magnet stepper rather than a hybrid stepper (next subsection). A pair of coils may be connected in series for high voltage bipolar low current drive, or in parallel for low voltage high current drive. The Hall output may drive a comparator to provide for more stable drive to the power device.
However, the slip between the rotor and the synchronous speed stator field develops torque. Large industrial synchronous motors are self started by embedded squirrel cage conductors in the armature, acting like an induction motor. It is implemented with a fast microprocessor driving a pulse width modulator for the stator phases.
The ability to absorb or produce reactive power on a transient basis stabilizes the overall power grid against fault conditions. Sine wave drive (d) may be generated by a pulse width modulator (PWM), or drawn from the power line. One such vacuum cleaner uses a compact high efficiency electronic driven 100,000 rpm fan motor. As the windings are energized in sequence, the rotor synchronizes with the consequent stator magnetic field. Thus, a 4-pole stepper motor may have two phases composed of in-line pairs of poles spaced 90o apart. Both driver and controller may be combined into a single integrated circuit accepting a direction command and step pulse. If the rotor spins a little faster, at the synchronous speed, no flux will cut the rotor at all, fr = 0. Silicon grain oriented steel, 4% silicon, rolled to preferentially orient the grain or crystalline structure, has still lower losses. The electromagnetic armature is only energized after the rotor is brought up to near synchronous speed. More modern Hall effect sensors may contain an integrated amplifier, and digital circuitry. No brushes, no commutator, no rotor windings, no permanent magnets, simplifies motor manufacture.
This speed is frequently not attainable due to mechanical resonance of the motor load combination. If the rotor were to run at synchronous speed, there would be no stator flux cutting the rotor, no current induced in the rotor, no torque. But, it requires considerable optimization, using specialized design techniques, which is only justified for large manufacturing volumes.



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