10 permanent magnet motors i - university of cambridgeprp/3b4/3b4lec10-13.pdf · 10 permanent...

10 Permanent Magnet Motors IPermanent magnets are found in motors of various types. Clearly magnets canbe used on place of dc field windings in dc motors and synchronous motors.These motors share more than simply a magnetic field produced by permanentmagnets.

10.1 Permanent-magnet dc Machine

10.1.1 Dc Machine design

The field in a modern dc machine is usually provided by a radially-magnetisedpermanent-magnet material, as shown in Fig. 10.1. Stator core, airgap, rotorcore, magnet and rotor teeth are designed according to the process in Lectures3-5. The resulting permanent magnet motor (p.m. motor) has a number ofadvantages over the historical field winding excited machine:

� No field current is required and there are no I2R losses in thefield coils;

� the overall (outside) diameter is smaller.

Although the air-gap specific magnetic loading is lower than in historical dcfield current excited machines so that the rotor has to have a larger diameter forthe same rating, the radial depth of the magnets is less than that of coil-carryingpoles.

Fig 10.1

Motors rated at up to 100 kW are available and these are usually called dcservo motors, as they will be used in a motor drive.

Lectures 10-13, Page1 Engineering IIA, 3B4 Machines and Drives

In any permanent-magnet device it is important to consider the influence of thedemagnetising current on the magnets and the possibility of demagnetisation(Lecture 5). In the case of PMDC motors, the demagnetising current is thearmature current whose polarity and position is fixed by the action of thecommutator, as shown in Fig. 10.1. Fig. 10.1 also shows a typical flux line setup by the armature current.

A typical arrangement is to shape the stator magnets as shown in Figure 10.2 sothat the airgap is greater under the pole edges than at the centre. This reducesthe flux density produced by the armature at the pole edges and henceminimises the possibility of demagnetisation.

Fig. 10.2

10.1.2 Speed control

The main disadvantage is that field control is no longer possible, so that the fluxper pole remains constant. The armature current creates a magnetic field, shownin a loop in Fig. 10.1. But it adds on one side and subtracts on the other, so theaverage flux in the machine remains constant. See the equivalent circuit andequations in Section 2.4, noting that kφ is fixed.

In a servo application, the motor is often run in a closed loop, as a torqueproducing 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. 10.2 to control the current.


Fig.10.3 H Bridge

Speed control is in effect achieved by varying the armature voltage, Va.

(10.1)�r = Vak� − RaT

(k�)2

The H bridge converter shown allows reversing and braking1.

10.1.3 Switching strategies for PWM H bridges

Positive armature current (say) is accommodated by the switching of T1, T2 as apair: T1, T2. on gives forward volts and T1, T2. off (D3, D4 on) gives reversevolts for forward current.

Va = (10.2)

Where ρ is the duty cycle of (T1, T2)

Reverse armature voltage by switching T3, T4 as a pair instead of T1, T2 .

When regenerating, power is delivered to the dc supply (fully controlled by theduty ratio).


1 http://www.onsemi.com/pub/Collateral/MC33030-D.PDF

Again, it is important to give consideration to the nature of power supply. Ifthe supply is from the ac mains via a simple diode rectifier, a dynamic brakeresistor is required across the dc supply capacitor (if its voltage rises toohigh). As these motors are found in servo applications the regenerativemode is likely to occur, so the dynamic braking resistor is often found. Thedynamic braking resistor required may be found by considering the energiesinvolved in the application.

E.g.2 Typical driver chip, with 4bit DAC on current to give torque control.

3A, 55V drive capability.


2 http://www.national.com/ds/LM/LMD18245.pdf

10.2 Permanent magnet AC synchronous machinesThe adjustable field in synchronous machines may be replaced with permanentmagnets, with similar advantages to those found in the PMDC motor. Unlikethe PMDC there are many variations on this theme, and therefore some revisionand development of the theory of synchronous machines is required beforeprogress can be made.

10.2.1 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 tothe 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 statorresistance). Therefore we really want V/ω to be constant as in aninduction motor drive.

Fig. 10.4

The equations can now be reworked with V and E proportional to ω

E = k ω (10.3)


Then,

(10.4) T = 3�s

VE�Ls

sin � = 3V�s

k��Ls

sin �

Hence,

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

(10.5) T = 3�s IaE sin�

since (Vcosφ=Esinβ). The torque angle β is the angle of the flux vector givenby the stator current with respect to the rotor position and rotor flux vector.

Compare with the dc motor Fig. 10.1 and induction motor Fig. 6.3, wherethe 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 ratherthan J X B , since J X B is at the airgap surface or in the windings justbelow.

If the angle β is maintained at 90o by applying the stator currents in the correctorientation to the rotor position, the synchronous machine has dc motorbehaviour. Noting that E is proportional to ω and therefore ωS

T = (10.6)

This is just like a dc motor, and also allows the maximum torque per amp ofstator current to be achieved, which enhances efficiency and performance(cost!).

Note we have neglected the stator resistance, which is reasonable for a largemachine, but the stator resistance losses remain important. For small motorsthe winding resistance should be included.


10.2.2 Salient Pole AC synchronous machines

In some synchronous machines, the radial length of the air-gap is variable, asshown in Figure 10.5. 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. 10.5

As a result, of the variation around the airgap, the magnetic reluctance is lowalong the d-axis and high along the q-axis. This will lead to a lower inductancefor the stator current component vector in the q-axis. A lower inductance givesa lower component flux. The solution method lies in resolving the stator currentvector into a d axis component, aligned with the rotor (and in quadrature withthe rotor field induced voltage E) and a q axis component aligned with the rotorfield induced voltage E and defining two stator inductances.

Fig. 10.6


The torque producing component of the stator current in Fig. 10.6 is thequadrature stator current, again reinforcing the necessary right angle.

10.2.3 Torque and power

The output power of the machine is given by

Po = 3 VI cos φ

With reference to Figure 10.6,

I cosφ = Id sin δ + Iq cos δ

And

Id Xds = E -V cos δ

Iq Xqs = 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 statormagnetic fields, and is called excitation torque. The second term is due to thetendency of the d-axis of the salient-pole rotor to want to align with the statormagnetic field, and is independent of rotor excitation. This is simply areluctance effect and the torque so produced is called alignment or reluctancetorque.

The combination of these effects is exploited in a number of synchronousmotor types and drives. Most familiar is the stepper motor, but it alsoappears in variations of the PM synchronous motor. In some casesconsiderable effort is made to avoid the reluctance torque.


The variation of T with δ is illustrated in Fig. 13.9.

Fig. 10.7

Motors may be based on the reluctance effect alone. They offer cheapconstruction. However, their power factor and efficiency are not in the endas good as that of the similarly rated induction motor. In addition thereducing costs of magnet materials also mean that magnets will beincorporated in most motors, other than induction motors. Later we shallexamine the switched reluctance motor, which does have some attractions.


11 Permanent Magnet Motors II

11.1 Sinusoidal Brushless DC DrivesIn the PMDC machine, the commutator can be regarded as a mechanicalrectifier and suffers from a variety of electrical and mechanical problems. If wewere to replace the commutator with an electronic bridge to perform theswitching we would need to know the position of the rotor. Clearly having theelectronics rotating is inconvenient, so the motor is turned inside out. Thenwe have a brushless dc motor (BLDC). The name however is a littlemisleading as the motor is now strictly an ac synchronous motor! Onemanufacturer at least attempts to explain this to customers, listing the BLDCmotor under ac motors. Most simply list it separately. With a fixed angularorientation of the inverter switching, the behaviour is essentially identical tothat of the dc motor, so the name fits. Two forms of brushless dc drives exist.

11.1.1 Sinusoidal PM Brushless dc motor construction

The description sinusoidal refers to the field generated emf (hence the fluxpattern and winding) and the phase currents applied. The stator is like that ofthe classic three phase induction motor, with a standard three phase winding.Often, shaped magnets are glued to the surface of the rotor.

Fig. 11.1

A natural consequence of this design is the large effective air-gap as thereluctance of the magnet material is high compared to the iron. So thesynchronous reactance is small The saliency is small as the stator and rotor areeffectively cylindrical.


In this example, the magnets are simple blocks glued to a nearly cylindricalrotor (with small machined flats for the magnets). The winding isconcentrated. There may be a significant cogging torque as the magnetswant to align with the iron in the position shown. This may be small enoughto be ignored, or the stator laminations may be skewed by one slot pitchdown the length of the machine to eliminate the cogging.

Some companies refer to this type of motor as a Permanent MagnetSynchronous Motor (PMSM). This is not especially helpful as they are runas the motor in a brushless dc drive. Nonetheless, the brushless dc regiememay be relaxed for higher speed running.

To obtain the dc motor characteristics, the torque angle β maintained at 90O byensuring that the currents are applied to the stator windings with the correcttiming to give the correct orientation with respect to the rotor position. Rotorposition feedback is usually essential with sinusoidal brushless dc.

This gives the following phasor diagram

Fig. 11.2

With a permanent magnet field, the field mmf is constant and that E isproportional to ω (and therefore ωS).

Clearly, the total airgap flux does vary here, but not by much as Ls is small.


Max speed with β =90O is when E = Vrated and Ia falls to zero.

Voltage boosting is needed at low speeds.

11.1.2 Sinusoidal BLDC motor drive

The question remains as to how the current is injected according to the rotorposition. 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 positionsensor (shaft encoder) is required to provide the necessary switching instantsvery accurately for the bridge inverter to ensure the stator supply is of thecorrect frequency and phase. A closed loop around the stator currents may beused, with a suitable PID controller, Fig. 11.3.

Fig. 11.3


With an up to date Digital Signal Processors (DSP) a model of the motor maybe incorporated into the controller to work out the phasor diagram and theterminal voltages applied by the inverter as a voltage vector in the same was asfor the induction motor. If a position encoder is used as in Fig. 11.3, the phasordiagram 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 range3.These are the high quality devices, and produce very smooth torque. Thetorque is almost instantaneously available as the inductance of the windingis so low. They may be considered the Ferrari of motor drives, but thecomplexity of the sinusoidal current references is obvious, hence the moveto calulating the required applied voltages. These drives are commonlyfound in high quality machine tools, where the encoder or resolverfeedback is an acceptable proposition. Other names are AC Servo andBrushless Servo.

11.1.3 Applications considerations

Brushless DC motors usually have a low stator resistance so that fan cooling isnot needed (and there are no rotor losses). This, along with the smallsynchronous reactance means their electrical time constant is short. The motorsare usually long and small in diameter to reduce the inertia to give a smallelectro-mechanical time constant. This also aids cooling, by having an increasedsurface area to volume. The combination gives the 'brushless PM dc drive' anunrivalled dynamic response to step changes in speed and torque.

Regenerative braking is possible merely by changing the torque angle to -90degrees (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 ordumping the recovered energy, so dynamic braking resistors are almost alwaysfound 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 http://ww1.microchip.com/downloads/en/devicedoc/92003a.pdf

11.2 Permanent Magnet Synchronous Motor DriveThe microcontroller scheme in Fig. 11.4 has a voltage controller, with sinusoidscalculated in the DSP core. It is in a speed loop with a PID.

Fig. 11.4

This is not BLDC, although the motor has the same construction usually assinusoidal BLDC. For BLDC the phase advance of V should depend on thecurrent according to the BLDC phasor diagram, Fig.11.2. Here the phaseadvance is fixed, so the angle δ is fixed, not β . This is acceptable in thateverything is sinusoidal, and it works, but it lacks the efficiency benefits of atrue Sinusoidal BLDC.

It is clearly much easier to program. This mode can be reverted to by BLDCdrives to get higher than base speeds. At higher than base speed the motorbecomes overexcited so runs with a leading power factor.


11.3 Trapezoidal Brushless dcThe distinguishing feature of trapezoidal pm brushless dc drives, is the use ofsquare pulses of current in a current feedback set up. The term trapezoidal isadopted here to cover the whole range of non-sinusoidal drives, although wewill cover the main form in some detail. The variety of such drives is onlylimited by the imagination of the engineers and the proliferation of patents.Applications range from disc drives to tens of kW industrial drives.

11.3.1 Basic principle of operation and motor construction

Fig. 11.5 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 adifferent number to avoid cogging. In fact the typical machine has three phasesand a floating star connection. The ideal trapezoidal torque functions aregenerated when two of the three phases are excited by a constant current.

Fig. 11.6


At a first sight it appears to operate in steps. That is true for starting but oncerotating it rotates quite smoothly: Consider a typical set of torque-theta profilesfor the constant current excitation of the typical machine, Fig. 11.7.

Fig. 11.7

By switching the currents AB, AC, BC, BA, CA, CB (noting the signs), aconstant positive torque may be produced. It should be noted that the generatedvoltage waveforms will be trapezoidal also. The magnitude of these back emfwaveforms 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 thecurrents and the torque gains some dips.


Figure 11.8 illustrates the generated phase voltages with the appropriate phasecurrents applied.

Fig.11.8

As in the case of sinusoidal BLDC, the current is clearly in phase with thegenerated voltage. Accurate timing of the current is important for efficientrunning. Sometimes for high speed running a phase advance is added togive the current time to rise before the volts appear and to allow for the di/dtdue to the inductance of the winding.

The winding voltage EA =


There are several advantages of the trapezoidal scheme when compared to thesinusoidal scheme: Most importantly the motor performance and rating for agiven motor size is greater as the specific magnetic loading is based on squarewave flux. The inverter benefits in the same way.

Also, depending on the application, the position feedback may be nothing morethan three opto devices and a simple masked disc giving the commutationinstants directly (three Hall effect devices4 seems more common), Fig. 11.7. Nosophisticated control is required.

Fig. 11.7

Lastly current feedback is relatively easy, especially with special IC motordriver chips and only a constant level of current is required. This makes itsimple to implement with a basic pwm (duty cycle control) method. Theprinciple is the same from standstill through a wide speed range.

Thus trapezoidal systems, are usually preferred on the basis of lower costfor drives below about 5kW. The disadvantage is that the current cannotmaintain its nice shape at high speeds as the winding voltage is much higherso 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 whereripples can appear in the workpiece. However, Trapezoidal is good enoughin laser copier drum drives and many such applications, where the inertiasmooths the torque. Versions eliminating the hall effect sensors are alsoavailable. These use the voltage of the unused winding to give a positionsense. It needs to be multiplexed around the phases, with the rotation5.


5 http://www.allegromicro.com/sf/8904/

4 http://www.allegromicro.com/sf/3936/

11.3.2 Drive scheme

The typical drive again uses a voltage fed inverter, with current feedback, as forthe sinewave drives, Fig. 11.8. However, the modulation of the inverter bridgeis simply to maintain the constant current magnitude for the required perioddetermined by the position encoder. This requires no processing power.

Fig. 11.8 Trapezoidal BLDC drive

The basic output of the drive is torque so the demand current magnitude is atorque demand. A speed loop is usual and a position loop (shown) may beadded.

In the usual fashion, speed information may be obtained from the positionfeedback and a speed loop may be completed with a PID controller tostabilise the performance. The D term is usually necessary in the PID, asthere is little friction.


12 Permanent Magnet Motors III

12.1 Small Brushless dc drivesFor small motors, the windings are predominantly resistive. This means thatthe current changes quickly, from phase to phase, and also means that currentcontrol may not be necessary. A common additional feature with these smallmotors is the design for single direction phase currents, known as unipolarwindings. The advantage is the simplicity of the power electronics. Such motordrives 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 limitedby the resistive windings, and freewheel diodes are not shown.

Fig. 12.1


Other interesting things can be done to reduce cost. Fig. 12.2

Fig. 12.2 BLDC cooling fan

It now only has two phases to reduce cost further and has a very cleverlymagnetised rotor magnet which gives it a nice torque characteristic, with nozero torque regions. The stator also has interpoles with no windings, as part ofthe magnetic circuit.

12.1.1 Demonstrations

Floppy drive with a three phase winding

Hard drive with a concentrated three phase winding.

Hard drive starting up


12.2 Hybrid Stepper MotorsStepper motor drives are a common choice in small drives applications. Theparticular advantages are the open loop position control, high torque and thepossibility of a genuine holding torque at standstill. Accurate position control isensured by arranging the motor to have a large number of steps per revolution.The basic idea dates to 1919 and a Scottish engineer.

12.2.1 Stepper Motor Design

There are two types of fundamental torque production in stepper motors, thatdue to reluctance variations and that due to an interaction of currents with apermanent magnet field mmf. (NI) Motor designs use varying mixtures of theseprinciples, the classic ‘stepper motor’ being described as hybrid or PMstepper.

The stator and rotor are The stator has a number of poles and each pole has alarge number of teeth or castellations. The rotor also has a large number ofteeth (not the same number to avoid cogging).

Fig. 12.3

The important feature is that alignment of the rotor with one pair of poles willcause miss-alignment with the others.


The Hybrid stepper makes use of an axially-oriented permanent magnet betweenpairs of rotor wheels, as shown in Fig. 12.3. The permanent magnet produces aflux which travels radially outward through the ‘North’ wheel, across theshortest airgap, axially along the stator core, and returning radially inwards tothe ‘South’ wheel, again through the shortest arigap.

The standard motor has two stator phases, excited in turn. The importantfeature is that alignment of one set of teeth on each rotor wheel with one of thepair of poles will cause a half tooth pitch miss-alignment with the teeth of theother phase (poles 3 and 4 in Fig. 12.3) and completely misaligned with theother pole of the same phase (pole 2 in Fig. 14.3). Note that the two statorstacks are aligned with each other, so that a single simple set of stator coils canbe used right through the motor.

By having two identical but misaligned rotor wheels, the flux due to thestator current will travel axially along the rotor and through the magnet,completing a familiar magnetic circuit with both stator current ampere turnsand a permanent magnet, along with reluctances, particularly those of theairgaps and magnet.

A complete cycle of excitation gives four steps and a rotor movement of onerotor 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 sothat the flux will enter the rotor through a pair of poles, go along the magnetand then twist through 90o to exit the rotor through the other pair of poles inthe same phase.

Consideration of the side on view in Fig. 12.3 shows that the polarity of thecurrent in the poles needs to reverse so that the directly opposite position can beobtained, while retaining the same sense of flux through the axial permanentmagnet.

Half-stepping is also possible. Both phases are on and the rotor finds anintermediate position. 200 steps per cycle becomes 400 steps per cycle.


12.2.2 Torque production

The torque is produced when the rotor is misaligned from the step position, Fig.12.4

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 ahigh torque at standstill with full current, hybrid stepper motors also possess adetent torque. This is the small torque produced by the permanent magnet whichholds 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 bepreserved during a low power standby. Clearly the detent torque is onlyavailable in the full step positions.

Note the torque function is not necessarily sinusoidal, and depends on theshape of the stator and rotor teeth. This can be examined by finite elementanalysis.


12.2.3 Operation at speed

When at high speed, the hybrid stepping motor may be considered as similar toa conventional sinusoidal PM synchronous motor.

Since PM steppers are often small, the effects of the winding resistance shouldbe considered and included in the phasor diagram if significant, see Fig 12.5.

Fig 12.5

It should be remembered that the 200 step hybrid motor has effectively 100 polepairs!

12.2.4 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 goforward or reverse quite simply by changing the excitation.


12.2.5 Torque-Speed characteristic of stepper motors

At speed the generated voltage due to the PM field or variable reluctance will belarge (proportional to speed as in PM brushless dc). In conventional HybridSteppers the inverter output voltage will reach its dc supply voltage and will beunable to maintain the phase current at the design level for full torque. So thecurrent reduces and the pull-out torque will roll off with increasing speed.

Fig. 12.6

In open loop drives considerable care is required at commissioning to avoiddemanding too much torque causing ‘pull out’ or ‘stepping out’. This aredealt with by setting the acceleration and deceleration ramp rates.

Fig. 12.7

Typically done at commisioning via a simple computer interface. The totalnumber of steps is calculated for exact positioning.


��

��

12.2.6 Mechanical Resonances

The transient response of a stepper motor to a single step excitation is illustratedin Fig. 12.8, showing that an inertial overshoot takes place and the rotoroscillates about its new position

Fig. 12.8

The restoring torque generated by the motor is approximately

T = (12.2)−T sin(Nt�)

which for small values of θ can be linearised to

T = (12.3)−TNt�

1For a lightly-damped system this torque balances the inertia load torque,

T = J d2�dt2

Equating these two torques, we arrive at the differential equation for simpleharmonic motion, where ω is the natural frequency defined as

ωΟ = (12.4)TN t

J

From what we know of resonance in general, it is important that pulse rateswhich may excite this resonance should be avoided, i.e. avoid the followingswitching rates fs (in steps per second):

fs = ωΟ/2nπ

However, this is idealistic! We must accelerate, so we must hit thesefrequencies sometime. Noting that we are accelerating or decelerating, we mustnot allow time for the oscillations to evolve.


13 Stepper Motor Applications

13.1.1 Bipolar drive circuit

Large Hybrid motors require a full bridge per phase, Fig. 13.1a, (diodes acrossMOSFET switches not shown) and usually the motors have two phases. Sincezero voltage free wheel paths can cause difficulties with the resonant behaviourof the system, it is common to use them in the bipolar switched mode (T1T2 thenT3T4).

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 powerdevice used in modern drives is the MOSFET.

Fig 13.1

In small motors, the complexity of a full bridge is dispensed with by usingbifilar phase windings, Fig. 13.1b. The cost is in reduced efficiency, but thegain in simplicity was attractive, particularly when IC stepping motor driverswere considered. .

2008 brought a significant number of new stepper chips onto the market,where a full bridge is integrated into the design. The complexity of the fullbridge is no longer an issue as it is a single chip solution, with both motorphases.


Fig. 13.2 Example Circuit TI DRV8811

Example Current Waveforms 7:

Fig. 13.3 Full Step


7 http://www.national.com/ds/LM/LMD18245.pdfhttp://focus.ti.com/lit/ds/symlink/drv8811.pdf

13.1.1 Half step and Microstepping operation

One way to avoid resonances is to vary the position smoothly. Both phases maybe energised at the same time.

In the Half step mode the current in each phase should be reduced to 70% ofits rated value if operating at low speeds. The stable position will be exactlybetween steps exploiting the symmetry. 100% current in two phases can beused 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 positions8: The standard seems to be operating in ¼ or 1/8 steps.

Example waveforms for quarter step mode.

Fig. 13.4 Quarter Step

This requires accurate control of the phase currents and the chips designedto perform this will include D/A converters giving a variable demand to theinner current loop (one for each phase) Fig. 13.2.


8 http://focus.ti.com/lit/ds/symlink/drv8811.pdf

These microsteps cannot be expected to be accurate positions as they lacksymmetry, and rely on the flux paths to be moderately linear, even whenthere is a lot of flux into the sides of the teeth. But their purpose is really toavoid resonances at the cost of much more sophisticated control.

13.1.1 Static position error

With no load applied the rotor aligns its teeth so as to present the leastreluctance to magnetic flux flow. However, eqn. 12.2 makes it clear that a nonzero torque will give a deviation from this point. The maximum load that canbe applied must he less than the peak torque or else the motor will not be able tohold the load at the demand position. An estimate of the static position error,θe, due to a load torque of TL can be obtained directly from eqn. 12.2.

In many applications the stepper motor is further geared so the position errormay be extremely small (as long as resonance did not lead to lost steps!

An alternative and more useful mechanical approach to estimating the staticposition error involves the concept of stiffness. This is defined as the slopeof the static torque versus rotor position characteristic [eqn. 12.3] at theequilibrium position. Some motors have a static torque versus rotor positioncharacteristic that is shaped to give a high stiffness near the designedequilibrium position, thus keeping static position errors small.

.


13.1.2 The Variable Reluctance stepper motor

The basic principle of the single-stack variable reluctance (VR) stepper motor isillustrated in Fig. 13.5. Both the stator and rotor are of salient construction andwith different numbers of poles or teeth. This difference, which is commonly 2,determines the step angle of the motor. The stator carries coils around eachsalient pole with opposite poles forming a pole pair. The rotor is has no currentor magnets. With the low cost of magnets this type is largely extinct.

Fig. 13.5

In Fig. 13.5, phase 1 is energised and the rotor teeth 1 and 3 are aligned with thephase 1 axis. When phase 1 is turned off and phase 2 turned on, the rotor turnsso that teeth 2 and 4 align with the phase 2 axis and so on. The step angle can beseen 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 withN phases, excitation of all the phases in sequence produces N steps of rotormotion, 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 aboutI kW. Machines rated at more than 25 kW have been manufactured. Themotivation for this is not position control, but Variable Speed throughcontrol of the stepping rate. The main advantage lies with the cost of themotor unit when compared to that of a conventional three-phase inductionmotor, but they tend to be noisy. Machines designed for variable speed driveapplications are referred to as Switched-Reluctance (SR) motors. The mostsuccessful is rated at about 400W and is used in some US washingmachines.


13.1.3 Special Drives

E.g. The analog watch, Fig 13.6

Fig 13.6

P.R. PalmerFebruary 2010


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