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Electrical machines can be classified in many different ways, such as by:
No one classification is entirely satisfactory, not least because the marriage of machines and electronic control systems has produced variable speed drives which don’t fall easily into any of the main groups. In this sect. six main groups are identified which cover the most commonly found motors. These main groups, induction, synchronous, commutator, permanent magnet, switched reluctance machines and steppers. Together, these cover the vast majority of all motors driving equipment in domestic, commercial and industrial applications. Each is described briefly in turn in the following sections.
Invented in the 1880s, the induction machine is by far the most common motor in domestic, commercial and industrial use, driving fans, pumps, compressors, conveyors, machine tools and a wide range of other loads. Motors ranging from a few watts to several megawatts can be found, single-phase motors being commonly used up to around a kilowatt and three-phase machines for higher powers. Two main subdivisions are immediately apparent: the cage rotor induction motor and the wound rotor induction motor.
The simplest, commonest, most rugged and reliable type is the cage rotor induction motor, in which the rotor has a winding in the form of conducting bars embedded in slots and connected together at the ends of the rotor core by short-circuiting rings called endrings. In larger machines the cage is usually fabricated from copper bar and care has to be exercised to ensure the integrity of all the joints in the fabrication.
In smaller motors, the cage is usually formed by casting aluminum into the slots of the rotor core and around the ends to form the cage. In these machines, the cage is often referred to as a 'squirrel cage' because of its shape. Sometimes the endrings have cooling fins cast onto them to act as rudimentary fans when the rotor is rotating. There is virtually no insulation between the cage and the rotor core, unless (exceptionally) particular steps are taken to insulate the cage during fabrication.
Fig. 5--Main classes of motors.
The wound rotor type, as its name implies, has a conventional insulated winding in the slots of the rotor core. Almost invariably it will be a three-phase winding, with its ends brought to shaft-mounted sliprings to provide a sliding connection. The winding can be connected either to a resistance (usually variable) or to a supply to modify the performance during starting or running, as will be described below.
Regardless of the type of rotor used, the stator carries the principal winding which, with the exception of some very small motors, is embedded in the slots of the stator core. The coils of the winding are connected so that, when fed from a balanced supply system (normally three phase, although two phase, six phase and 12 phase are also found in specialized applications) they produce a magnetic field of constant magnitude which rotates around the bore of the stator. It can be shown that this rotates at a speed of N, given by N, = 120flp
…where N, is in rev/min, f is the supply frequency in Hz and p is an even integer describing the number of poles in the field pattern of the winding. For a 50 Hz supply and a 4-pole winding (the most commonly found type), the speed of the field is therefore 1500 rev/min.
This rotating field cuts the rotor conductors and induces (hence the name induction motor) voltages which drive currents around the cage. The magnetic field of the stator interacts with these currents to produce electromagnetic torque, as previously described. Note that the field only cuts the conductors if the speed of the rotating field is not equal to the rotor speed, so that when the rotor speed is synchronous with the magnetic field, the torque will be zero. The torque is therefore a function of the velocity of the rotor relative to the synchronous speed of the field.
This relative speed is referred to as the slip, defined as the ratio: s = (N, - N,)IN, where N, is the synchronous speed of the field and N, is the rotor speed. The ratio is often expressed as a percentage, and full-load slip ranges from 10 per cent in small motors to less than 0.5 per cent on large motors. Because the induction motor cannot run at synchronous speed, it’s sometimes (and particularly in continental Europe) called the asynchronous motor.
As the motor accelerates, the torque changes and a characteristic of the form shown results. This is the torque-speed curve which is obtained by supplying the motor from a fixed voltage. At standstill the motor is connected to the supply and allowed to run up to full speed, and this torque-speed curve is followed regardless of the applied load. If the load has a characteristic shown by the broken line then the difference between the motor torque and the load torque at any speed is the accelerating torque which is available to accelerate the load. If the torque-speed curve were to have dips in it which intercepted the load line, the motor would not accelerate through that point to reach full speed.
Fig. 6--Torque-speed characteristic of an induction motor
Fig. 7-- Star and delta connections
The shape of the torque-speed characteristic can be influenced considerably by, among other things, the depth and shape of the rotor conductors. To achieve high efficiency and power factor, the rotor resistance and reactance are minimized but unless the many design parameters are carefully chosen, the starting torque and current may be adversely affected. At starting, the slip is 100 percent and the frequency of current in the rotor is the main supply frequency; under these conditions skin effect forces current to the top of the rotor bars, increasing their effective resistance and limiting the starting current. Special designs of rotor slot such as the double cage design have been developed to maximize this effect. Even when these designs are used, the starting current is typically 6 to 7 times the full-load rated current. This can create difficulties when a motor is to be started from a 'weak' supply with high internal impedance, causing a dip in the supply voltage which may affect other equipment and result in an unacceptably long run-up time for the motor.
The most common means of overcoming this problem for three-phase motors is to use a star-delta start, in which the stator windings are connected in slur (sometimes called 'wye') for starting, and a timed contactor reconnects the windings to delta (sometimes called 'mesh') during run-up. The star and delta connections. The voltage appearing across each winding when in star is only 58 per cent of the full delta-connected voltage; the motor presents a higher impedance to the supply and the starting current (and, unfortunately, the torque) is limited to one-third of what it would have been in the delta connection. A second means of reducing starting current is a soft starter, which uses a simple device such as a triac or pairs of thyristors to delay the switching on of the voltage every cycle, and this reduces the effective voltage applied to the motor during starting. High- voltage motors, which are usually connected in star for normal running in order to reduce the voltage across each winding and the level of insulation required, are often started through an autotransformer to reduce the motor voltage at starting.
When the motor has run up to speed on no load, the slip is very small, the torque produced being only just enough to overcome friction and windage losses. As the load on the motor is increased, the slip increases, the rotor current is increased and the torque is greater, reaching a peak at the pull-out torque. The pull-out torque is important because it determines the maximum temporary overload that the motor can withstand. The torque of an induction motor varies approximately as the square of voltage, so if the voltage drops to 90 percent of its nominal value, the torque would be reduced to 81 percent. For this reason it’s important to ensure that the pull-out torque is adequate to cope with any short-term overloads even on lowest supply voltage.
The wound rotor variant was mentioned earlier, although it’s now becoming relatively rare. It can be operated simply as a cage rotor, but the presence of a winding accessible to the user can be exploited in two main ways. First, a resistance can be added in series with each phase of the rotor winding. This resistance can comprise a group of fan-cooled resistors or a liquid resistor in the form of a tank of electrolyte into which electrodes are lowered. By using the maximum added resistance at standstill, the starting current is reduced to a minimum, and by selecting a particular value of resistance, pull-out torque can be achieved at standstill, with a good value of torque per amp. As the motor runs up, the resistance can be gradually reduced to zero, giving high efficiency at full speed. Secondly, the winding can be connected to a second supply which is able to inject currents to alter the torque-speed curve.
Motors operated in this way are known as doubly fed motors and they were commonly used in speed-controlled drives. In recent times they have been supplanted by inverters feeding a standard cage rotor motor. It was noted above that the induction motor has to run at some level of slip even on no-load, since it has to supply losses to the rotor. If the rotor is driven faster, the slip will decrease to zero then become negative as the speed rises above synchronous speed and the machine will then naturally generate power back into the supply. This is a convenient way of braking an overhauling load, although the machine has a negative pull-out torque beyond which it cannot increase its braking torque and load control would then be lost.
Single-phase induction motors:
Single-phase induction motors are common in domestic appliances such as refrigerators, freezers, fans and air conditioners. While they are necessary in situations where a three-phase supply is not available, they are typically limited to around 1 kW because of supply current limits and because of their inherent low efficiency and high torque ripple.
In this section, reference was made to three-phase distributed windings in the stator and the way in which these windings produce a rotating field. In a single-phase motor the field pulsates, rather than rotates and it can be mathematically represented by two contra-rotating fields, each producing its own torque-speed curve, but in opposite directions. The resultant field gives no starting torque so special arrangements have to be made for starting, and the motor has a much higher full-load slip (and hence lower efficiency) than the three-phase version.
Fig. 8-- Torque-speed characteristic of a single-phase induction motor
Single-phase motors are normally started by adapting them to be an approximation to a two-phase motor, in which two windings 90-degrees apart in space around the bore of the machine have balanced emfs 90-degrees apart in time applied to them. The 90-degrees spacing between the windings is achieved by inserting the second winding (the starting or auxiliary winding) at the correct places in the stator, but providing balanced emfs 90-degrees apart in time generally involves a greater approximation. There are four common arrangements, each having varying degrees of effectiveness.
In the split-phase or resistance-split motor, the starting winding uses fewer turns of a finer wire and so has a higher resistance and a lower reactance than the main winding. This results in the starting winding current leading the main winding current.
The consequent phase difference is sufficient to provide reasonable starting torque.
The starting winding is rated only for short periods because of its high current density and it’s switched out when the motor reaches 60 to 70 percent of full speed.
Switching is usually done by a shaft-mounted centrifugal switch, although current- operated relays are sometimes used. The split-phase motor is best suited to infrequent starting with low-inertia loads, since its starting current is relatively high.
The capacitor start motor has a capacitor connected in series with the starting winding. The result is that the starting winding current leads the main winding current by a larger angle than in the split-phase case; this angle may approach 90-degrees if a sufficiently large capacitance is used. A short-time rated electrolytic capacitor is normally used, and this is switched out of circuit when the motor reaches about 75 percent of full speed, The capacitor start motor can deal with more frequent starting and higher inertia loads with higher starting torque such as pumps and compressors, and its starting current is lower.
In a capacitor start and run motor, a paper capacitor is connected permanently in series with the starting winding. The starting torque is low and this type is generally confined to fan drives, but running performance can approach that of a balanced two- phase motor if the capacitor is correctly chosen and it’s generally quieter than a split-phase or capacitor start motor, with higher efficiency and power factor. These are also known as Permanent Split Capacitor (PSC) motors.
In the capacitor start, capacitor run motor, a large electrolytic capacitor is used for starting, but this is switched out before the motor reaches full speed and a smaller paper capacitor is in circuit for normal operation. There are alternative switching methods in which the paper capacitor is either permanently connected or switched into circuit when the electrolytic starting capacitor is switched out. In this way the good starting performance achieved with the large short-time rated electrolytic capacitor is combined with the good running performance achieved with the smaller paper capacitor.
Another variant of the single-phase induction motor is the shaded pole motor.
These are to be found in sizes up to about 300 W output and comprise a standard cage rotor and a stator with a small number of salient poles, typically 2,4 or 6. The poles each carry a coil, with the coils connected together to form the single main winding.
At one side of each pole, near the air gap, a conducting ring is set into the lamination, the function of which is to distort the pulsating field and produce a crude approximation to a rotating field. Constructional variants abound, particularly in the so-called unicoil motors using a single bobbin-wound coil to excite the magnetic circuit. Although very low in efficiency, these motors are often used for driving fans and pumps where an ac supply is readily available.
The construction of synchronous machines has been described in relation to generators, so it’s sufficient to note here that wound field motors are typically only found in the larger sizes of synchronous motor. However, where the wound field is replaced by a permanent magnet, the machine is (somewhat confusingly!) often called a brushless dc machine (). These abound in sizes below about 20 kW, particularly in small sizes where they are used, for example, in audio equipment and computer fan drives. Synchronous motors have higher efficiency than induction motors and for this reason are particularly found in the MW sizes in petrochemical and other pumping applications where operation is almost continuous.
All of these motors, whatever their size, share the characteristic that the rotor locks or synchronizes to the speed of the rotating field in the motor, so there is no variation of speed with load, unlike the induction motor. Various methods are used for starting and many of them use induction motor action to bring the motor to near synchronous speed, allowing it to lock onto the field. The synchronous running is exploited in applications where precise, constant speed is required, for instance in paper or textile making equipment.
Fig. 9--Commutator on a dc machine
This category covers a variety of motors which share the feature of having a commutator mounted on the rotor shaft, to which the coils on the rotor are connected. ___ a typical commutator; it consists of copper bars (segments) set in insulation, with the ends of one or more coils connected to the riser portion. The surface of the commutator is accurately machined for concentricity and surface finish and carbon brushes provide sliding electrical connections. In all cases, the function of the commutator is to switch the polarity of one or more coils as the rotor rotates so that the direction of current in the coil is always correct with respect to the direction of the magnetic field, enabling electromagnetic torque to be produced in the desired direction.
AC commutator motors:
These are now seldom produced, generally being variants of three-phase induction motors with a third or tertiary winding on the rotor. They were used in speed- controlled applications, particularly lifts and hoists, but are now superseded by inverter drives.
The dc machine, shown schematically, is the classical commutator motor. The winding on the rotor is generally referred to as the armature and carries the main current. The magnetic field can be produced by a conventional winding, which can either be supplied from a separate source (separately excited), connected in parallel across the armature supply (shunt connected), or connected in series with the armature to carry the same current (series connected). Alternatively, the field can be produced by permanent magnets housed in the stator, in which case the magnetic field strength cannot be easily varied.
Field -- Armature -- L conductors -- Commutator
Fig. 10 DC motor in schematic form
The operation and control of the dc machine is, in principle, very simple. As explained, varying either the strength of the magnetic field or the magnitude of the armature current will directly vary the torque; varying the direction of either one will alter the direction of the torque. The ease of controlling the dc motor made it the obvious choice for controlled-speed drives before inverter-fed induction motors were available. It remains common in rail traction, steel rolling mills, winders, hoists and cranes, despite frequent forecasts of its demise.
The main disadvantage is the high cost of the machine and the life and reliability of the commutator and brushes, which also limit its operating speed. As the brushes wear, carbon debris is deposited on the winding insulation, potentially shortening its life. Overloads or fault currents can cause flashover on the commutator, often resulting in permanent damage to the surface of the commutator segments, necessitating a major overhaul.
Many of the developments in dc motors have concentrated on improving the commutation action, the best known being the introduction of interpoles. These are narrow poles situated between the main stator poles and carrying a winding with a few turns connected in series with the armature. The field of these interpoles is arranged to induce a motional emf in the coils undergoing commutation, thus enabling faster current reversal and preventing sparking.
Through-ventilated machines are the most common, with a fan driven either by the armature shaft or, more commonly, by a small auxiliary motor. Not only does this allow at least some of the carbon dust from brushes to be swept clear of the machine, it allows direct cooling of the armature winding and yields a higher output from a given motor size.
Before solid-state control became economic, series-connected dc motors were to be found in virtually every traction application. They exhibit high starting torque, with a falling torque which approaches zero at high speeds. By contrast, the shunt- connected machine operates substantially at constant speed, the speed being broadly set by armature voltage and its drop with load being relatively small. However, with the availability of modern controllers the separately excited machine is normally used; this can be programmed to give a range of torque-speed curves.
In small sizes, typically in automotive auxiliary drives for radiator fans and windshield wipers, the wound field is replaced by a cheaper permanent magnet, often using simple ferrite magnets. The dc supply is connected directly to the brushes, and reversal of direction is simply achieved by reversing this connection. Speed control is achieved by reducing the armature voltage by a variety of means.
These motors are so called because they will operate on either dc or single-phase ac supplies. This is because they are series connected, so the ac current reverses direction in the field and armature at the same time, leaving the direction of torque unchanged.
Typically they are rated under 1.5 kW at several thousand rev/min. The highest speeds are normally found in vacuum cleaners (up to 25 000 rev/min is common) and the highest torques are in washing machines (up to 5 N m in horizontal axis models). They are normally of frameless construction to reduce cost. Being high-speed machines, the life of the carbon brushes is a major limitation (it may be only a few hundred hours in some cases) and commutator noise is often obtrusive.
Because of the high speeds, the specific power output of these machines is much higher than, say, induction motors running at 1500 or 3000 rev/min, so they are often used where space and/or weight is at a premium, with the final drive geared down from the motor shaft.
Permanent magnet motors
Motors with permanent magnets have been mentioned in two of the previous sections, illustrating the difficulty of using a simple classification method. Nevertheless it’s worth summarizing here the types of motors with permanent magnets that are likely to be encountered.
Great care must always be exercised in working near or dismantling any permanent magnet machine. If the magnets are allowed to adhere to a surface suddenly there is a risk of the brittle magnet material chipping and firing out debris; the speed with which articles are attracted together often catches the user unaware and traps ends of fingers. In some cases removing the rotor from a machine can partially demagnetize the magnets. During manufacture or maintenance, metallic swarf tends to stick to the magnets, often causing a hazard.
The last two decades have seen huge strides in the quality and performance of magnetic materials. The energy product of magnets now varies by an order of magnitude from the cheaper ferrites (typically used on cheap domestic appliance motors), through Alnico (traditionally used on loudspeakers) and samarium- cobalt to neodymium-iron-boron (see Table 2 for a general comparison of properties). The range of materials now available to motor designers has enabled the performance boundaries of permanent magnet motors to be considerably extended.
Permanent magnets on the stator:
It was noted that small dc motors sometimes use a permanent magnet instead of a winding to produce the field. These are usually referred to as brushed permanent magnet motors since the armature current is supplied through the carbon brushes as before. The motivation for adopting this construction is cost; in the smaller sizes it’s more economical to use a magnet than a wound field. The stator normally comprises a steel shell, into which the blocks of magnet material (usually unmagnetized) are assembled. The blocks may be held in place mechanically or they may be bonded in place with a suitable adhesive. The armature and end frames are assembled and the motor is placed in a magnetizing fixture, where a very high pulse of magnetic field is applied to the motor to 'charge' the magnets. This system is amenable to volume production, but it can produce variable results in the motor performance due to differences in the field strength of the magnets.
Since the magnet field strength is approximately constant, the performance of these motors is similar to that of a separately excited motor supplied with constant field current and the speed regulation with load is relatively small. The speed is varied by controlling the armature voltage: this is done using external resistor(s) or by using a pair of brushes not diametrically opposite each other, or more commonly now by electronic control.
Permanent magnets on the rotor:
In this section it’s noted that a synchronous motor may have the wound field on the rotor replaced by a permanent magnet system. This gives rise to two groups of motors, although in principle there is little difference between them.
The first group has a distributed stator winding embedded in a large number of slots, like an induction motor, and often has the rotor magnets embedded in the rotor core. When the stator is supplied with balanced polyphase voltages, the rotor field locks onto the resultant rotating field and synchronous running is achieved. Sometimes a rudimentary cage winding is also provided for starting the motor, or the frequency of the supply voltages can be linked to shaft position by providing rotor position feedback to the controller. These motors have a very low rotor loss and an overall efficiency which is significantly higher than induction motors. They have attracted much academic interest over the past few years but, in spite of their apparent promise, usage is limited and shows little sign of growth.
The second group is much more significant. Here the magnets are usually bonded to the surface of the rotor core and, particularly in smaller sizes, the stator has only a few slots. This is an inverted form of the brushed dc commutator motor, since we now have stationary windings and a rotating magnet. Instead of the mechanical commutator, the currents are electronically switched (commutated) at the correct moments by using position feedback from the rotor (often from the rotor magnets themselves). This class of motor is almost always described as the brushless dc motor. It’s to be found in small sizes in medical and computer equipment and in larger sizes (typically up to 10 kw) in servo drives where absolute shaft position and shaft speed are of interest, for instance in weaving machines where many shafts have to move in precise relationship to each other.
Switched reluctance motors
These were known in primitive form from around the 1830s. However, since there was no convenient method of switching the currents in the inductive windings, they were overtaken by the advent of good quality commutators for dc motors and by the invention of the induction motor. In the 1970s the maturing capability of the power semiconductor rekindled interest in this separate class of machine which produces torque purely by reluctance action (). After intensive development at the academic level, products have been developed commercially and drives based on these motors are considered by many commentators to be at least the equal of drives based on motors producing electromagnetic torque.
The motors are characterized by having clearly visible poles on both stator and rotor (hence they are often described as doubly salient), but they only have windings on the stator. They are supplied not from a sinusoidal supply but from a dc voltage which is electronically switched to the appropriate winding, giving an essentially triangular phase flux. While it’s possible to operate without rotor position feedback (so-called open loop), operation with simple position feedback (rotor position switched) is normal, and it’s not possible to operate without an electronic drive system. Since the motor is supplied from a dc source, the number of independent phase circuits is a choice of the designer; systems with one to four phases are common and five phases or more have been seen in specialist applications. Similarly, the number of stator poles is flexible; 2 poles per phase gives a 2-pole field pattern and 4 poles per phase gives a 4-pole pattern. The number of rotor poles is also variable. Using a number of rotor poles two different from the stator poles gives vernier action; two less makes the rotor move against the rotation of the field and two more makes it move with it. A common choice is the machine with 6 stator poles and 4 rotor poles. Torque is developed by the tendency for the magnetic circuit to adopt a configuration of minimum reluctance, that is for a pair of rotor poles to be pulled into alignment with an excited pair of stator poles, maximizing the inductance of the exciting coils.
Continuous rotation in either direction is assured by switching the phases in the appropriate sequence, so that torque is developed continuously. In simple terms, the larger the current supplied to the coils, the greater the torque, although the design and analysis of these machines is complex because the magnetic circuit is generally operated above its linear region. The torque is independent of the direction of current flow, so unidirectional currents can be used. This permits a simplification of the electronic switching circuits compared with those required for most other forms of motor.
Fig. 11--2-pole and 4-pole field patterns in a switched reluctance motor
(a) 2-pole field pattern (b) 4-pole field pattern
Fig. 12--Power converter for a switched reluctance motor
The motors are generally operated in chopping mode or in single-pulse mode. For the motor with each phase supplied by a switching circuit, current is established in a phase winding by connecting it to the dc supply by closing the switches S1 and S2 when the rotor poles are not aligned with that phase. The current rises rapidly to the desired level. S1 and S2 are now opened and the stored energy in the magnetic field ensures that the current continues to flow through D1 and D2. The voltage now impressed on the winding is negative, driving the current down. During this time some magnetic energy is being returned to the supply and, while the inductance continues to rise, some is being converted into mechanical output. When a lower specified current level is reached, SI and S2 are closed and the current rises again. At the end of the required phase conduction period when the rotor poles are aligned with the stator poles, both switches are turned off and the current falls to zero. Torque is controlled by varying the level at which the current is chopped. This is only one of a number of methods of chopping control.
At higher speeds, the rise and fall times for the current will be such that the current is switched on and off only once in each conduction period and is never chopped. This is the single-pulse mode of operation in which torque is controlled through the switching angles.
Because of the flexibility of control of switched reluctance machines, their performance characteristics can be tailored to suit a wide range of applications.
Fig. shows motors developed for automatic door openers, rotary screw compressors and mining conveyors. Their operation is characterized by an ability to operate over very wide speed ranges, developing high efficiency over a wide range of both torque and speed. They can also be arranged to give extremely high overload torques in both motoring and braking.
The switched reluctance motor and controller are extremely robust. The motor has simple coils, with small end windings and no overlapping of phase windings, and the rotor has no coils or magnets. The power converter has to supply only unidirectional currents and the maximum rate of rise of switch current is limited by the stator coils, thus avoiding the possibility of 'shoot-through' faults. More details on the design and control of these machines can be found in the Reference.
Fig 13--Typical chopping and single-pulse currents in a switched reluctance motor
Fig. 14-- Selection of SR Drives
Fig. 15--Stepper motor system
Stepper motors are often considered as a separate class of machines because of the way in which they are operated, although construction-wise they are similar to the other types discussed above and they produce torque by reluctance action. However, they are supplied from a source of discrete pulses, in response to which they move or 'step' to a new angular position which is retained until the next pulse is sent. They are positioning devices rather than variable speed motors, although they are sometimes run in variable speed mode by simply increasing the pulse frequency so that they appear to move continuously. They are entirely dependent on the driving electronics, so they must be considered as part of a system.
Two types are commonly encountered:
Fig. shows a variable reluctance stepper produces torque purely by reluctance action and normally is constructed with a relatively small number of poles giving relatively large step angles. For instance a 6-stator, 4-rotor pole machine will have a step angle of 30 deg., giving 12 steps per rev. Switched reluctance machines are sometimes thought of as large variable reluctance steppers because the construction is the same. These are normally found in the power range 0.1 kW to 2 kW. a hybrid stepper has on the rotor an axially magnetized permanent magnet, and it normally has a large number of rotor teeth. The stator poles are divided at the air gap to have several teeth per pole. These machines have relatively small step angles. A typical small hybrid stepper might have 8 stator poles each with 5 teeth, and a rotor with 50 teeth, giving a step angle of 1.8" or 200 steps/rev. The permanent magnet gives a detent or holding torque in the absence of any excitation on the stator poles. Hybrid steppers are found in disc drives, processing machinery and handling equipment.
There are many ways of operating steppers. The simplest is the single-step mode where a pulse is sent to a phase winding and the machine takes one step to the new detent position. By equally exciting two adjacent phases, half-stepping can be achieved, where the rotor takes up a position midway between the single step positions of the two phases. For very fine resolution such as for driving a print head in a printer, the currents in the phases are carefully controlled to be unequal, giving a mode known as step division, mini stepping or micro stepping. More complex schemes exist where a position transducer is used to give feedback, rather than relying on the motor to move to the correct position on demand. The transient behavior of the rotor is of great importance during stepping and further details on this can be found in Section 8 covers the entire subject in some detail.
Fig. 16 Quadrants of operation
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