10 Permanent Magnet Motors I

Transcription

1 Lectures 10-13, Page1 10 Permanent Magnet Motors I Permanent magnets are found in motors of various types. Clearly magnets can be used on place of dc field windings in dc motors and synchronous motors. These motors share more than simply a magnetic field produced by permanent magnets Permanent-magnet dc Machine Dc Machine design The field in a modern dc machine is usually provided by a radially-magnetised permanent-magnet material, as shown in Fig Stator core, airgap, rotor core, magnet and rotor teeth are designed according to the process in Lectures 3-5. The resulting permanent magnet motor (p.m. motor) has a number of advantages over the historical field winding excited machine: No field current is required and there are no I 2 R losses in the field coils; the overall (outside) diameter is smaller. Although the air-gap specific magnetic loading is lower than in historical dc field current excited machines so that the rotor has to have a larger diameter for the same rating, the radial depth of the magnets is less than that of coil-carrying poles. Fig 10.1 Motors rated at up to 100 kw are available and these are usually called dc servo motors, as they will be used in a motor drive.

2 Lectures 10-13, Page2 In any permanent-magnet device it is important to consider the influence of the demagnetising current on the magnets and the possibility of demagnetisation (Lecture 5). In the case of PMDC motors, the demagnetising current is the armature current whose polarity and position is fixed by the action of the commutator, as shown in Fig Fig also shows a typical flux line set up by the armature current. A typical arrangement is to shape the stator magnets as shown in Figure 10.2 so that the airgap is greater under the pole edges than at the centre. This reduces the flux density produced by the armature at the pole edges and hence minimises the possibility of demagnetisation. Fig Speed control The main disadvantage is that field control is no longer possible, so that the flux per pole remains constant. The armature current creates a magnetic field, shown in a loop in Fig But it adds on one side and subtracts on the other, so the average flux in the machine remains constant. See the equivalent circuit and equations in Section 2.4, noting that kφ is fixed. In a servo application, the motor is often run in a closed loop, as a torque producing motor, according to equation 2.3: T = This requires feedback of the motor current and operation of the full or H bridge shown in Fig to control the current.

3 Lectures 10-13, Page3 Fig.10.3 H Bridge Speed control is in effect achieved by varying the armature voltage, Va. r = V a k R at (k) 2 (10.1) The H bridge converter shown allows reversing and braking Switching strategies for PWM H bridges Positive armature current (say) is accommodated by the switching of T 1, T 2 as a pair: T 1, T 2. on gives forward volts and T 1, T 2. off (D 3, D 4 on) gives reverse volts for forward current. Where ρ is the duty cycle of (T 1, T 2 ) V a = (10.2) Reverse armature voltage by switching T 3, T 4 as a pair instead of T 1, T 2. When regenerating, power is delivered to the dc supply (fully controlled by the duty ratio). 1

4 Lectures 10-13, Page4 Again, it is important to give consideration to the nature of power supply. If the supply is from the ac mains via a simple diode rectifier, a dynamic brake resistor is required across the dc supply capacitor (if its voltage rises too high). As these motors are found in servo applications the regenerative mode is likely to occur, so the dynamic braking resistor is often found. The dynamic braking resistor required may be found by considering the energies involved in the application. E.g. 2 Typical driver chip, with 4bit DAC on current to give torque control. 3A, 55V drive capability. 2

5 Lectures 10-13, Page Permanent magnet AC synchronous machines The adjustable field in synchronous machines may be replaced with permanent magnets, with similar advantages to those found in the PMDC motor. Unlike the PMDC there are many variations on this theme, and therefore some revision and development of the theory of synchronous machines is required before progress can be made Review of equations Equations derived for standard ac synchronous motors may be used here, noting: 1. The field generated excitation voltage E will always be proportional to the rotor speed and therefore the supply frequency. 2. The terminal voltage V is set by the resultant flux in the airgap (neglecting the effects of the stator leakage inductance and stator resistance). Therefore we really want V/ω to be constant as in an induction motor drive. Fig The equations can now be reworked with V and E proportional to ω E = k ω (10.3)

6 Lectures 10-13, Page6 Then, Hence, T = 3 s VE L s sin = 3V s k L s sin (10.4) T = k k sinδ (10.5) However, while instructive, this is no longer particularly convenient. The angle δ merely helps us know if it is motoring or generating. The torque is best expressed as T = 3 s IaE sin (10.5) since (Vcosφ=Esinβ). The torque angle β is the angle of the flux vector given by the stator current with respect to the rotor position and rotor flux vector. Compare with the dc motor Fig and induction motor Fig. 6.3, where the torque producing rotor flux is at right angles to the imposed field flux. In a rotating machine it is easier to think about fluxes at right angles rather than J X B, since J X B is at the airgap surface or in the windings just below. If the angle β is maintained at 90 o by applying the stator currents in the correct orientation to the rotor position, the synchronous machine has dc motor behaviour. Noting that E is proportional to ω and therefore ω S T = (10.6) This is just like a dc motor, and also allows the maximum torque per amp of stator current to be achieved, which enhances efficiency and performance (cost!). Note we have neglected the stator resistance, which is reasonable for a large machine, but the stator resistance losses remain important. For small motors the winding resistance should be included.

7 Lectures 10-13, Page Salient Pole AC synchronous machines In some synchronous machines, the radial length of the air-gap is variable, as shown in Figure The axis along the rotor poles is called the direct (d) axis, and the axis at right angles to the rotor poles is called the quadrature (q) axis. The variation in the shape of the rotor is known as saliency. Fig As a result, of the variation around the airgap, the magnetic reluctance is low along the d-axis and high along the q-axis. This will lead to a lower inductance for the stator current component vector in the q-axis. A lower inductance gives a lower component flux. The solution method lies in resolving the stator current vector into a d axis component, aligned with the rotor (and in quadrature with the rotor field induced voltage E) and a q axis component aligned with the rotor field induced voltage E and defining two stator inductances. Fig. 10.6

8 Lectures 10-13, Page8 The torque producing component of the stator current in Fig is the quadrature stator current, again reinforcing the necessary right angle Torque and power The output power of the machine is given by P o = 3 VI cos φ With reference to Figure 10.6, I cosφ = I d sin δ + I q cos δ And I d X ds = E -V cos δ I q X qs = V sin δ Substituting these equations into the power equation. Po = (10.7) The first term represents the torque due to the interaction of the rotor and stator magnetic fields, and is called excitation torque. The second term is due to the tendency of the d-axis of the salient-pole rotor to want to align with the stator magnetic field, and is independent of rotor excitation. This is simply a reluctance effect and the torque so produced is called alignment or reluctance torque. The combination of these effects is exploited in a number of synchronous motor types and drives. Most familiar is the stepper motor, but it also appears in variations of the PM synchronous motor. In some cases considerable effort is made to avoid the reluctance torque.

9 Lectures 10-13, Page9 The variation of T with δ is illustrated in Fig Fig Motors may be based on the reluctance effect alone. They offer cheap construction. However, their power factor and efficiency are not in the end as good as that of the similarly rated induction motor. In addition the reducing costs of magnet materials also mean that magnets will be incorporated in most motors, other than induction motors. Later we shall examine the switched reluctance motor, which does have some attractions.

10 Lectures 10-13, Page10 11 Permanent Magnet Motors II 11.1 Sinusoidal Brushless DC Drives In the PMDC machine, the commutator can be regarded as a mechanical rectifier and suffers from a variety of electrical and mechanical problems. If we were to replace the commutator with an electronic bridge to perform the switching we would need to know the position of the rotor. Clearly having the electronics rotating is inconvenient, so the motor is turned inside out. Then we have a brushless dc motor (BLDC). The name however is a little misleading as the motor is now strictly an ac synchronous motor! One manufacturer at least attempts to explain this to customers, listing the BLDC motor under ac motors. Most simply list it separately. With a fixed angular orientation of the inverter switching, the behaviour is essentially identical to that of the dc motor, so the name fits. Two forms of brushless dc drives exist Sinusoidal PM Brushless dc motor construction The description sinusoidal refers to the field generated emf (hence the flux pattern and winding) and the phase currents applied. The stator is like that of the classic three phase induction motor, with a standard three phase winding. Often, shaped magnets are glued to the surface of the rotor. Fig A natural consequence of this design is the large effective air-gap as the reluctance of the magnet material is high compared to the iron. So the synchronous reactance is small The saliency is small as the stator and rotor are effectively cylindrical.

11 Lectures 10-13, Page11 In this example, the magnets are simple blocks glued to a nearly cylindrical rotor (with small machined flats for the magnets). The winding is concentrated. There may be a significant cogging torque as the magnets want to align with the iron in the position shown. This may be small enough to be ignored, or the stator laminations may be skewed by one slot pitch down the length of the machine to eliminate the cogging. Some companies refer to this type of motor as a Permanent Magnet Synchronous Motor (PMSM). This is not especially helpful as they are run as the motor in a brushless dc drive. Nonetheless, the brushless dc regieme may be relaxed for higher speed running. To obtain the dc motor characteristics, the torque angle β maintained at 90 O by ensuring that the currents are applied to the stator windings with the correct timing to give the correct orientation with respect to the rotor position. Rotor position feedback is usually essential with sinusoidal brushless dc. This gives the following phasor diagram Fig With a permanent magnet field, the field mmf is constant and that E is proportional to ω (and therefore ω S ). Clearly, the total airgap flux does vary here, but not by much as Ls is small.

12 Lectures 10-13, Page12 Max speed with β =90 O is when E = Vrated and I a falls to zero. Voltage boosting is needed at low speeds Sinusoidal BLDC motor drive The question remains as to how the current is injected according to the rotor position. Noting that the motor is three phase, a three phase bridge is used. There must be knowledge of the rotor position. A shaft-mounted rotor position sensor (shaft encoder) is required to provide the necessary switching instants very accurately for the bridge inverter to ensure the stator supply is of the correct frequency and phase. A closed loop around the stator currents may be used, with a suitable PID controller, Fig Fig. 11.3

13 Lectures 10-13, Page13 With an up to date Digital Signal Processors (DSP) a model of the motor may be incorporated into the controller to work out the phasor diagram and the terminal voltages applied by the inverter as a voltage vector in the same was as for the induction motor. If a position encoder is used as in Fig. 11.3, the phasor diagram is the same as the vector diagram and the calculations are easy. Although 'brushless'd.c. motors are made in a wide range of sizes, Sinusoidal BLDC drives are most commonly found in the 1-10 kw range 3. These are the high quality devices, and produce very smooth torque. The torque is almost instantaneously available as the inductance of the winding is so low. They may be considered the Ferrari of motor drives, but the complexity of the sinusoidal current references is obvious, hence the move to calulating the required applied voltages. These drives are commonly found in high quality machine tools, where the encoder or resolver feedback is an acceptable proposition. Other names are AC Servo and Brushless Servo Applications considerations Brushless DC motors usually have a low stator resistance so that fan cooling is not needed (and there are no rotor losses). This, along with the small synchronous reactance means their electrical time constant is short. The motors are usually long and small in diameter to reduce the inertia to give a small electro-mechanical time constant. This also aids cooling, by having an increased surface area to volume. The combination gives the 'brushless PM dc drive'an unrivalled dynamic response to step changes in speed and torque. Regenerative braking is possible merely by changing the torque angle to -90 degrees (ie changing the sign of the currents with respect to the rotor position). For regenerative braking to be effective, there must be a means of recovering or dumping the recovered energy, so dynamic braking resistors are almost always found in BLDC drives. Reversing is achieved in the same way as regeneration, merely allowing the machine to reverse direction under negative torque. Hence, four quadrant control is easily effected. 3

14 Lectures 10-13, Page Permanent Magnet Synchronous Motor Drive The microcontroller scheme in Fig has a voltage controller, with sinusoids calculated in the DSP core. It is in a speed loop with a PID. Fig This is not BLDC, although the motor has the same construction usually as sinusoidal BLDC. For BLDC the phase advance of V should depend on the current according to the BLDC phasor diagram, Fig Here the phase advance is fixed, so the angle δ is fixed, not β. This is acceptable in that everything is sinusoidal, and it works, but it lacks the efficiency benefits of a true Sinusoidal BLDC. It is clearly much easier to program. This mode can be reverted to by BLDC drives to get higher than base speeds. At higher than base speed the motor becomes overexcited so runs with a leading power factor.

15 Lectures 10-13, Page Trapezoidal Brushless dc The distinguishing feature of trapezoidal pm brushless dc drives, is the use of square pulses of current in a current feedback set up. The term trapezoidal is adopted here to cover the whole range of non-sinusoidal drives, although we will cover the main form in some detail. The variety of such drives is only limited by the imagination of the engineers and the proliferation of patents. Applications range from disc drives to tens of kw industrial drives Basic principle of operation and motor construction Fig illustrates the design of a typical trapezoidal 'brushless'd.c. Motor. Fig.11.5 The stator now appears to have many poles. The rotor too has many poles, but a different number to avoid cogging. In fact the typical machine has three phases and a floating star connection. The ideal trapezoidal torque functions are generated when two of the three phases are excited by a constant current. Fig. 11.6

16 Lectures 10-13, Page16 At a first sight it appears to operate in steps. That is true for starting but once rotating it rotates quite smoothly: Consider a typical set of torque-theta profiles for the constant current excitation of the typical machine, Fig Fig By switching the currents AB, AC, BC, BA, CA, CB (noting the signs), a constant positive torque may be produced. It should be noted that the generated voltage waveforms will be trapezoidal also. The magnitude of these back emf waveforms will depend on the rotation speed as usual. Smooth torque depends on lovely squarewave currents with precise timing. Clearly at speed the inductance of the windings slows the edges of the currents and the torque gains some dips.

17 Lectures 10-13, Page17 Figure 11.8 illustrates the generated phase voltages with the appropriate phase currents applied. Fig.11.8 As in the case of sinusoidal BLDC, the current is clearly in phase with the generated voltage. Accurate timing of the current is important for efficient running. Sometimes for high speed running a phase advance is added to give the current time to rise before the volts appear and to allow for the di/dt due to the inductance of the winding. The winding voltage E A =

18 Lectures 10-13, Page18 There are several advantages of the trapezoidal scheme when compared to the sinusoidal scheme: Most importantly the motor performance and rating for a given motor size is greater as the specific magnetic loading is based on square wave flux. The inverter benefits in the same way. Also, depending on the application, the position feedback may be nothing more than three opto devices and a simple masked disc giving the commutation instants directly (three Hall effect devices 4 seems more common), Fig No sophisticated control is required. Fig Lastly current feedback is relatively easy, especially with special IC motor driver chips and only a constant level of current is required. This makes it simple to implement with a basic pwm (duty cycle control) method. The principle is the same from standstill through a wide speed range. Thus trapezoidal systems, are usually preferred on the basis of lower cost for drives below about 5kW. The disadvantage is that the current cannot maintain its nice shape at high speeds as the winding voltage is much higher so the current cannot rise as fast. Then the torque is low at the crossovers. This is a problem in high performance drives for machine tools where ripples can appear in the workpiece. However, Trapezoidal is good enough in laser copier drum drives and many such applications, where the inertia smooths the torque. Versions eliminating the hall effect sensors are also available. These use the voltage of the unused winding to give a position sense. It needs to be multiplexed around the phases, with the rotation

19 Lectures 10-13, Page Drive scheme The typical drive again uses a voltage fed inverter, with current feedback, as for the sinewave drives, Fig However, the modulation of the inverter bridge is simply to maintain the constant current magnitude for the required period determined by the position encoder. This requires no processing power. Fig Trapezoidal BLDC drive The basic output of the drive is torque so the demand current magnitude is a torque demand. A speed loop is usual and a position loop (shown) may be added. In the usual fashion, speed information may be obtained from the position feedback and a speed loop may be completed with a PID controller to stabilise the performance. The D term is usually necessary in the PID, as there is little friction.

20 Lectures 10-13, Page20 12 Permanent Magnet Motors III 12.1 Small Brushless dc drives For small motors, the windings are predominantly resistive. This means that the current changes quickly, from phase to phase, and also means that current control may not be necessary. A common additional feature with these small motors is the design for single direction phase currents, known as unipolar windings. The advantage is the simplicity of the power electronics. Such motor drives find application by the million disk drives, laser printers, and such like, where high performance and minimal cost are required. An example of a unipolar drive scheme is shown below. The current is limited by the resistive windings, and freewheel diodes are not shown. Fig. 12.1

21 Lectures 10-13, Page21 Other interesting things can be done to reduce cost. Fig Fig BLDC cooling fan It now only has two phases to reduce cost further and has a very cleverly magnetised rotor magnet which gives it a nice torque characteristic, with no zero torque regions. The stator also has interpoles with no windings, as part of the magnetic circuit Demonstrations Floppy drive with a three phase winding Hard drive with a concentrated three phase winding. Hard drive starting up

22 Lectures 10-13, Page Hybrid Stepper Motors Stepper motor drives are a common choice in small drives applications. The particular advantages are the open loop position control, high torque and the possibility of a genuine holding torque at standstill. Accurate position control is ensured by arranging the motor to have a large number of steps per revolution. The basic idea dates to 1919 and a Scottish engineer Stepper Motor Design There are two types of fundamental torque production in stepper motors, that due to reluctance variations and that due to an interaction of currents with a permanent magnet field mmf. (NI) Motor designs use varying mixtures of these principles, the classic stepper motor being described as hybrid or PM stepper. The stator and rotor are The stator has a number of poles and each pole has a large number of teeth or castellations. The rotor also has a large number of teeth (not the same number to avoid cogging). Fig The important feature is that alignment of the rotor with one pair of poles will cause miss-alignment with the others.

23 Lectures 10-13, Page23 The Hybrid stepper makes use of an axially-oriented permanent magnet between pairs of rotor wheels, as shown in Fig The permanent magnet produces a flux which travels radially outward through the North wheel, across the shortest airgap, axially along the stator core, and returning radially inwards to the South wheel, again through the shortest arigap. The standard motor has two stator phases, excited in turn. The important feature is that alignment of one set of teeth on each rotor wheel with one of the pair of poles will cause a half tooth pitch miss-alignment with the teeth of the other phase (poles 3 and 4 in Fig. 12.3) and completely misaligned with the other pole of the same phase (pole 2 in Fig. 14.3). Note that the two stator stacks are aligned with each other, so that a single simple set of stator coils can be used right through the motor. By having two identical but misaligned rotor wheels, the flux due to the stator current will travel axially along the rotor and through the magnet, completing a familiar magnetic circuit with both stator current ampere turns and a permanent magnet, along with reluctances, particularly those of the airgaps and magnet. A complete cycle of excitation gives four steps and a rotor movement of one rotor tooth pitch. If Nr is the number of rotor teeth, the step angle is given by step angle = (12.1) This is 200 steps per revolution, which has become a fairly standard design. If eight stator poles are employed, the rotor layers will be miss-aligned so that the flux will enter the rotor through a pair of poles, go along the magnet and then twist through 90 o to exit the rotor through the other pair of poles in the same phase. Consideration of the side on view in Fig shows that the polarity of the current in the poles needs to reverse so that the directly opposite position can be obtained, while retaining the same sense of flux through the axial permanent magnet. Half-stepping is also possible. Both phases are on and the rotor finds an intermediate position. 200 steps per cycle becomes 400 steps per cycle.

24 Lectures 10-13, Page Torque production The torque is produced when the rotor is misaligned from the step position, Fig Fig 12.4 If the rotor is displaced by more than about 1/4 of one tooth angle, A straight line (constant dt/dθ) is nice mechanically. In addition to having a high torque at standstill with full current, hybrid stepper motors also possess a detent torque. This is the small torque produced by the permanent magnet which holds the rotor at a particular step position if the stator excitation is removed. This can be a useful feature in applications where the rotor position must be preserved during a low power standby. Clearly the detent torque is only available in the full step positions. Note the torque function is not necessarily sinusoidal, and depends on the shape of the stator and rotor teeth. This can be examined by finite element analysis.

25 Lectures 10-13, Page Operation at speed When at high speed, the hybrid stepping motor may be considered as similar to a conventional sinusoidal PM synchronous motor. Since PM steppers are often small, the effects of the winding resistance should be considered and included in the phasor diagram if significant, see Fig Fig 12.5 It should be remembered that the 200 step hybrid motor has effectively 100 pole pairs! Excitation sequence The phases are excited in the following order: A, B, A*, B*, A,B, A*, B*, A,... Note the sequence is different in each direction, so the motor also can go forward or reverse quite simply by changing the excitation.

26 Lectures 10-13, Page Torque-Speed characteristic of stepper motors At speed the generated voltage due to the PM field or variable reluctance will be large (proportional to speed as in PM brushless dc). In conventional Hybrid Steppers the inverter output voltage will reach its dc supply voltage and will be unable to maintain the phase current at the design level for full torque. So the current reduces and the pull-out torque will roll off with increasing speed. Fig In open loop drives considerable care is required at commissioning to avoid demanding too much torque causing pull out or stepping out. This are dealt with by setting the acceleration and deceleration ramp rates. Fig Typically done at commisioning via a simple computer interface. The total number of steps is calculated for exact positioning.

27 Lectures 10-13, Page Mechanical Resonances The transient response of a stepper motor to a single step excitation is illustrated in Fig. 12.8, showing that an inertial overshoot takes place and the rotor oscillates about its new position Fig The restoring torque generated by the motor is approximately which for small values of θ can be linearised to T = T sin(nt) (12.2) T = TNt (12.3) 1For a lightly-damped system this torque balances the inertia load torque, T = J d2 dt 2 Equating these two torques, we arrive at the differential equation for simple harmonic motion, where ω is the natural frequency defined as TN t ω Ο = (12.4) J From what we know of resonance in general, it is important that pulse rates which may excite this resonance should be avoided, i.e. avoid the following switching rates f s (in steps per second): f s = ω Ο /2nπ However, this is idealistic! We must accelerate, so we must hit these frequencies sometime. Noting that we are accelerating or decelerating, we must not allow time for the oscillations to evolve.

28 Lectures 10-13, Page28 13 Stepper Motor Applications Bipolar drive circuit Large Hybrid motors require a full bridge per phase, Fig. 13.1a, (diodes across MOSFET switches not shown) and usually the motors have two phases. Since zero voltage free wheel paths can cause difficulties with the resonant behaviour of the system, it is common to use them in the bipolar switched mode (T 1 T 2 then T 3 T 4 ). For a 200 step hybrid motor at 3000rpm, the phases change at the rate of 5kHz. The current chopping frequency will be of the order of 20kHz, and the power device used in modern drives is the MOSFET. Fig 13.1 In small motors, the complexity of a full bridge is dispensed with by using bifilar phase windings, Fig. 13.1b. The cost is in reduced efficiency, but the gain in simplicity was attractive, particularly when IC stepping motor drivers were considered brought a significant number of new stepper chips onto the market, where a full bridge is integrated into the design. The complexity of the full bridge is no longer an issue as it is a single chip solution, with both motor phases.

29 Lectures 10-13, Page29 Example Current Waveforms 7 : Fig Example Circuit TI DRV8811 Fig Full Step 7

30 Lectures 10-13, Page Half step and Microstepping operation One way to avoid resonances is to vary the position smoothly. Both phases may be energised at the same time. In the Half step mode the current in each phase should be reduced to 70% of its rated value if operating at low speeds. The stable position will be exactly between steps exploiting the symmetry. 100% current in two phases can be used for a short period for extra torque - full step mode AB, A*B, A*B*, AB*, AB... This approach may be further developed by adding more in-between positions 8 : The standard seems to be operating in ¼ or 1/8 steps. Example waveforms for quarter step mode. Fig Quarter Step This requires accurate control of the phase currents and the chips designed to perform this will include D/A converters giving a variable demand to the inner current loop (one for each phase) Fig

31 Lectures 10-13, Page31 These microsteps cannot be expected to be accurate positions as they lack symmetry, and rely on the flux paths to be moderately linear, even when there is a lot of flux into the sides of the teeth. But their purpose is really to avoid resonances at the cost of much more sophisticated control Static position error With no load applied the rotor aligns its teeth so as to present the least reluctance to magnetic flux flow. However, eqn makes it clear that a non zero torque will give a deviation from this point. The maximum load that can be applied must he less than the peak torque or else the motor will not be able to hold the load at the demand position. An estimate of the static position error, θe, due to a load torque of T L can be obtained directly from eqn In many applications the stepper motor is further geared so the position error may be extremely small (as long as resonance did not lead to lost steps! An alternative and more useful mechanical approach to estimating the static position error involves the concept of stiffness. This is defined as the slope of the static torque versus rotor position characteristic [eqn. 12.3] at the equilibrium position. Some motors have a static torque versus rotor position characteristic that is shaped to give a high stiffness near the designed equilibrium position, thus keeping static position errors small..

32 Lectures 10-13, Page The Variable Reluctance stepper motor The basic principle of the single-stack variable reluctance (VR) stepper motor is illustrated in Fig Both the stator and rotor are of salient construction and with different numbers of poles or teeth. This difference, which is commonly 2, determines the step angle of the motor. The stator carries coils around each salient pole with opposite poles forming a pole pair. The rotor is has no current or magnets. With the low cost of magnets this type is largely extinct. Fig In Fig. 13.5, phase 1 is energised and the rotor teeth 1 and 3 are aligned with the phase 1 axis. When phase 1 is turned off and phase 2 turned on, the rotor turns so that teeth 2 and 4 align with the phase 2 axis and so on. The step angle can be seen to be the difference between the rotor tooth pitch and the stator tooth pitch. For the stepper motor shown, the step angle is 30. In general for a motor with N phases, excitation of all the phases in sequence produces N steps of rotor motion, after which the rotor will have turned by one rotor pole pitch. Originally, this type of motor was built in sizes ranging from 0.5 W to about I kw. Machines rated at more than 25 kw have been manufactured. The motivation for this is not position control, but Variable Speed through control of the stepping rate. The main advantage lies with the cost of the motor unit when compared to that of a conventional three-phase induction motor, but they tend to be noisy. Machines designed for variable speed drive applications are referred to as Switched-Reluctance (SR) motors. The most successful is rated at about 400W and is used in some US washing machines.

33 Lectures 10-13, Page Special Drives E.g. The analog watch, Fig 13.6 Fig 13.6 P.R. Palmer February 2010