Chapter 6 Brushless Motors and Controllers

8/2/2019 Chapter 6 Brushless Motors and Controllers

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Chapter 6Brushless motors and controllersThe Application of brushless motors, of all types, is becoming of considerable im-port^ ce to the designers of machine tools and robotic systems. This is largelydue to the benefits that these types of motor bring to a system, particularly in improvements in the reUability. If the term is used in its broadest sense, this classification will include permanent-magnet motors, stepper motors, and alternatingcurrant (a.c.) induction motors. This chapter is concerned with permanent-magnetbrushless motors and their associated controllers; a.c. asynchronous induction motors and stepper motors will be considered in Chapters 7 and 8, respectively.Within the market place, there appears to be a degree of confusion in the naming df motors, with given constructions. To prevent confusion, the following motors ^ d their associated controllers are considered in this chapter.

Permanent-magnet synchronous motors with a trapezoidal winding distribution, commonly known as d.c. brushless motors. The associated controllerconsists of a conventional three-phase bridge, whose switching pattern isdetermined by a low-resolution rotor-position sensor. Sinewave-wound permanent-magnet synchronous motors incorporate wind

ings with an approximately sinusoidal distribution which are supplied withsinusoidal currents. These motors are normally controlled by a version ofvector control, which has considerable similarities with the method used tocontrol the asynchronous induction motors discussed in Chapter 7. In order to achieve the required control resolution, these motors are fitted with aresolver or a similar high-resolution position transducer. Linear brushless motors are making significant inroads to the drives market;based on conventional brushless technology, they made an ideal replacementfor high performance applications that would have been previously based onleadscrews and ballscrews.As will be discussed, the operation of these permanent-magnet brushless motors is totally dependent on their associated electronics; so as the reliability and

169


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170

Commutationdevices Stator with windingspre-installed - ^

Rear earthmagnets

Rotor

Figure 6.1. Key features of a frameless bnishless dc motor.

availability of power electronic devices and specialist integrated circuits has improved over the last twenty years the number of applications has also increased.Due to these motors' high reliability and low-maintenance requirements, they areideally suited to a wide range of applications including computer cooling fans androbotic drives.As with brushed motors, the bnishless motor can be obtained in a number of

versions, not only in is electromagnetic characteristics as summarised above, butalso in its mechanical construction. The motors can be supplied either as a conventional framed or a frameless motor. The general arrangements of frameless brush-less motors is shown in Figure 6.1. A three-phase stator winding is constructed in asimilar fashion to that of an a.c. induction motor; it is wound to give a trapezoidalair-gap flux in the case of a d.c. bnishless motor, or with a sinusoidal distribution in the case of a sinewave-wound, permanent-magnet, synchronous motor. Therotor consists of a number of high-performance permanent magnetsrigidlyfixedto the rotor's core structure; the arrangement, shapes, and location of the magnetscan be modified to give a range of motor characteristics. One of the problems ofthe construction of a permanent magnet rotor is the possibility of the failure of themagnet-rotor bond at high rotational speeds and accelerations. The preferred solutions to this problem include encasing the rotor in a thin stainless-steel jacket, orbinding the outer surface with a glass-fibre or similar non-metallic yam. In addition, a suitable adhesive should be used; and, to prevent problems, the compoundwhich is selected should be thermally stable and it should have a linear-expansion


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CHAPTER 6, BRUSHLESS MOTORS AND CONTROLLERS 171coefiScient which is close to that of the magnets and the rotor material.

The magnetic material selected for a motor is largely determined by the required output specifications; in high-performance motors neodymiumiron-boron,N d F i B , usually has the highest energy product of commercially available magnets, typically 20 kJm~^, whereas ferrite has an energy product of 200 Jm~^ . Toobtain a high flux density in the air gap, the magnet's flux density and the poleface area need to be considered in considerable detail during the electromagneticdesign pro cess for the motor. In practice, the limiting factors are the volume of themagiietic material required for ferrite m agne ts, or the high cost of the material forNdF^B; hence careful optimisation of the design is necessary. The net result is asmall permanent-magnet motor, when compared with brushed d.c. or a.c. inductionmotors with a similar power output.

When compared with the brushed d.c. motors, the advantages of the brushlessdesign are readily apparent:

Th e construction of the motor, with the heat-gen erating stator windings onthe outside of the motor frame, allows direct heat dissipation to the environment, without heat flowing through bearings and across the air gap.

Any possibility of sparking is eliminated by the removal brushe s; this allowsthe motors to be used in hazardous environments, and there is a considerablereduction in the radio-frequency interference (RFI) which is generated.

M aintenan ce costs are reduced , both for brush replacem ent and for problem sresulting from the dust which is generated by brush wear.

The speed -torque restrictions caused by the conm iutation limit, as found ind.c. brushed motors, are eliminated.

However, these advantages do not come without a corresponding set of disadvantages. In a d.c brushed motor, the commutation of rotor currents is undertakenby th0 mec hanical arrange men t of the comm utator and brush gear. In brushless motors fiis mechanical system is replaced by an electronic commutator comprising athree-phase power bridge, a rotor-position encoder with a suitable resolution, andcomitiutation logic to switch the bridge's devices in the correct pattern to producea motoring torque (see Figure 6.2).

As part of any selection procedure, it is necessary to compare brushless motors against their main competitors. Compared with brushed d.c. motors they aremore expensive, but they are also smaller, easier to maintain, and more reliable,and there is the additional complexity of the three-phase drive. Co mpa red w ithindu(^tion motors they are again smaller and more expensive, but the power electronic design is identical. For the majority of motor types, the speed and torq ueperformance are almost identical when complemented by high-performance controllers. Hen ce perm anent-m agnet brush less mo tors are widely used for pow eroutputs of up to 20 kW; above this pow er level, vector-controlled ind uction mo tors


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172 6.1. THE D.C. BRUSHLESS M OTOR

M 3-PhasePowerBridge7 Y

SwitchingController

d.c supply

SpeedController

Speeddemand

Figure 6.2. A block diagram showing the key features of a brushless motor-drivesystem.

are predominating for specialist applications. As with all design problems, the final selection of the system is left to the system designer, wh o is able to balanc e therelative advantages and disadvantages on an objective basis.

6.1 The d.c. brushless motorThe basic torque and voltage equations of d.c. brushless motors closely resemblethose of d.c. brushed mo tors. This section presents a simple analysis for determining a motor's characteristics; this also allows an appreciation of its limitations.In this analysis, a simple two-pole motor is considered (see Figure 6.3); the keyfeatures of this design are the rotor's magnetic pole arc of 180, and a three-phasestator winding w ith two slots per phase and A turns per slot, (Miller, 1989). Th eair-gap flux, neglecting any fringing, can be considered to be a square wave (seeFigure 6.4(a)). As the rotor is rotated, a voltage is induced within the stator windings, and the flux linkage varies linearly as a function of the rotor position, with themaximum positive linkage for the winding occurring at ^ = 0 and the maximumnegative flux linkage occurring at ^ = 180 .

If a single phase is considered, the total flux linkage can be determined byintegrating the contribution of individual turns, to give a maxim um flux linkage of

^n = NBgTvrl (6.1)where Bg is the air-gap flux density and / and r are the length and radius, respectively, of the stator. If the roto r's position is now considered , the flux linkage isgiven as a function of position by

^e) = 1 - 7r/2 V'n (6.2)


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CHjmrER6. BRUSHLESS MO TORS AND CONTRO LLERS 173

Figufe 6.3. Cross section of idealised brushless motor, showing two coils for asingle phase, 0 = 30.if{9) is shown in Figure 6.4(b) for both coils. From the flux linkage, the instantaneous e.m.f. induced in the coil can be determined in the conventional manneras

_ dip _ dip d6 _ dip^^~~dt^ ~~dd'di " ~'^'^'dB (6.3)

=NBgT:rlu)mwhere Um is the mechanical rotational speed in rad s~^ To obtain the total backelectnomotive force (e.m.f.) for the individual windings, the contribution from bothcoils needs to be considered; this gives

ep = NpBgTrrlum (6.4)where Np is the number of turns per phase; it is equal to 2N for this particular motor. Tihe phase e.m.f. is shown as a function of the rotor position in Figure 6.4(c);it is the sum of the voltages for the two windings, which are displaced by 30,Figure 6.4(d). In the case of the motor under consideration; the length of constantportion of the e.m.f. waveform is theoretically 150, but due to the construction ofthe niotor and magnetic fringing, it is in practice closer to 120.

To control the power to a brushless d.c. motor, a three-phase bridge. Figure 6*5(a), is used. With the motor star connected, only two phases can carry acurrent at any one time, and hence only two devices need to conduct in any oneswitching period. The idealised phase currents are shown in Figure 6.5(c); they are120 Wide, with a peak magnitude of /. The switching pattern is arranged to give acurrent flow against the e.m.f.; a positive current is defined as a motoring current.The device switching sequence in Figure 6.5(d) is arranged to produce a balancedthree-phase motor supply.


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174 6.L THED.C.BRUSHLESSMOTOR

8(9)

180 360

(a) The m agnetic flux density in the airgap, B(6)A (ff)1 ^*Vs^ ^

1^ ^ ^ ^ ^ 180 ^ ^ .' ' ^360

(b) The magnetic flux linkage in the airgap, tp(6)4e^

1$0 3600

180

(c) The e.m.f. of the individual co ils.4 e^

36 00

p\ 1$0 /M 150

(d) The e.m.f. of a phase.Figure 6.4. The waveforms for an idealised brushless motor, adapted from Miller(1989).


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CHAPTER 6. BRUSHLESSMOTORS AND CONTROLLERS 175

i i' i(a) The relationship between the power bridge and motor windings.|e^

f6

(b) The e.m.f. for phase A as a function of poition.

(c) Ideal current for the A phase.

2.6 2,4 3,4 3.5 1,5 1,6 2.6(d) The switching pattern for the three phase bridge.

Figuiie 6.5. The switching requirements for an ideal brushless motor, adapted fromMillet (1989).


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176 6.1. THE D.C.BRUSHLESS MOTO RThe torque and the speed constants can be determined by considering the bal

ance between the motor's mechanical output power and its electrical input powerover each conduction period; that is

P = LJmTe - 2epl (6.5)Th e factor of tw o in this equation is the result of the current simultaneou sly flowingthrough two motor phases. The electromagnetic torque can be determined fromequations (6.4) and (6.5)

Te = mpBglrl (6.6)Rewriting the voltage and torque equations with E 2ep, to represent the e.m.f.of any two phases in series, equations (6.4) and (6.6) can be rewritten as

E = kipLJm = K'^^rn (6.7a)Te = k^I = K'TI (6.7b)

where the armature constant, k = ANp, and the flux, ip = BgixrU are determinedby the construction of the motor. The form of these twoequations is very similarto the corresponding equations for brushed d.c. motors (see equation (5.1)); thisexplains, to a large extent, why these m otors are called brushless d.c. mo tors withinthe drives industry, when they are more correctly described as permanent-magnetsynchronous m otors with a trapezoidal flux distribution. In practice, the equationsabove w ill only hold good if the switching between the phases is instantaneous, andif the flux density is uniform with no fringing; while this does not hold true for realmotors, these equations can be safely used during the normal selection procedurefor a motor and its associated controller.

6.1.1 Torque-speed characteristicsUsing the relationships above, the torque-speed characteristics of an ideal d.c.brushless motor can be determined; it is assumed that the commutation and backe.m.f. voltage waveforms are perfect, as shown in Figure 6.5(b) and Figure6.5(c).If the star-connected motor configuration is considered, the instantaneous voltageequation can be written as

Vs--E IR (6.8)where R is the sum of the individual phase resistances, Vs is the motor's terminalvoltage (neglecting semiconductor and other voltage drops), and E is the sum oftwo phase e.m.f.'s. Using the voltage, torque , and speed equations discussed above,the motor's torque-speed characteristics can be determined. The torque-speed relationship is given by


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CHAPTER 6. BRUSHLESS MOTORS AND CONTROLLERS 111

Torque

\ Intermittent\ Operation\\. V V V \\ \ \ \ \\ \ \ \ \\ \ \ \ \\ \ \ \ \\ \ \ \ \\ \ \ \ \^ \ ^Incre asing ^\ ^ Voltage \\ \ \ ^ \\ \ \ \ \\ \ \ \ \\ \ \ \ \

ContinuousOperation

SpeedFigure 6.6. The torque speed characteristics of an ideal brushless d.c. motor.


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178 6.L THE aa BRUSHLESS MOTORsubject to any power-dissipation restrictions. The characteristics will be degradedin real motors by the effects of winding inductance, armature reactance and nonuniform f lux distribution. In order to undertake a full analysis of the characteristicsof a d.c. brushless motor, a full electromagnetic analysis must be undertaken usinga computer-aided design (CAD) package.6.1.2 Bru shless d.c. m otor controllersAs discussed above, a brushless d.c. motor controller is based on a standard three-phase, six-device power bridge, while high-powered systems will use bridges constructed from discrete components; advances in power-electronics integration techniques have resulted in a range of smart power controllers for small-drive applications. In all cases the control of brushless d.c. motors depends on an ability tocontrol the winding currents relative to the rotor's position, to obtain the switchingpattern shown in Figure 6.5(d). The block diagram of a suitable controller is shownin Figure 6.7; the controller consists of the following elements:

A low-resolution, rotor-position measurement system. Commutation logic to determine the main power device's switching pattern. Speed controller incorporating the pulse-width-modulator. A three-phase power bridge.

Rotor-position measurementSince a motor's output performance largely depends on the accuracy of a powerbridge's switching, relative to the phase voltages, a reliable and accurate rotor-position-measurement system is required. This can be achieved by the use of Hall-effect devices, by terminal voltage measurement for a limited range of applications,and by resolvers and encoders for specialist high-performance applications. Inpractice. Hall-effect devices are the most widely used.

Hall-effect devices are low-cost magnetic sensors, whose principle of operation is shown in Figure 6.8(a). When a magnetic field is applied to a piece of acurrent-carrying semiconductor, a voltage which is proportional to the magneticfield applied is generated, as long as the current is held constant. The directionsof the applied magnetic field, the current, and the Hall voltage are mutually perpendicular. The digital devices used in brushless d.c. motors consist of Hall-effectdevices enhanced by the addition of a Schmitt-trigger to give a known switchingpoint (see Figure 6.8(a)); the resultant hysteresis ensures a positive switching characteristic (see Figure 6.8(b)). The resultant digital output is suitable for use withthe commutation logic with a minimal interface. Hall-effect devices have a number of advantages, including the capability of operating at frequencies in excess of100 kHz, high reUability, and low cost. In most applications. Hall-effect devices


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CHAPTER 6. BRUSHLESS M(jrORS AND CONTROLLERS 179

1 fDirection Enable

Figiire 6.7. Block diagram of a controller for a brushless d.c. motor. The speedconttroller has been omitted for clarity, the circuit used can be based on that shownin Figure 5.17.


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180 6.1 . THE D.C. BRUSHLESS MOTO R

Hall voltageCurrentSource

(a) The Hall-effect, when a magnetic flux is applied to a pieceof semiconductor carrying a current, a voltage results. The Hallvoltage is proportional to the applied flux.+V x.

JTOV B

(b) A digital Hall-effect devise, a Schmitt trigger is applied tothe output of the Hall device to give a clean waveform.Figure 6.8. The operation of Hall-effect devices.

normally directly sense the rotors's field; however, in certain applications (normally asso ciated w^ith high-tem peratures ), a separate magn et assem bly is attachedto the rotor shaft. While it is possible to obtain military-specification devices thatare capable of operating at 150C, in general Hall-effect devices have tem perature-sensitivity problem, due to their physical characteristics.

As noted earlier, Hall-effect devices are used in combination with the commutation logic to provide the required drive signals for the power bridge . Satisfactoryoperation requires the mechanical separation of the three sensors to be given by:

360 (6.13)Num ber of phases x Num ber of pole pairsIn the case of a two-pole, three-phase, d.c, brushless motor, a mechanical displacement of 120 between individual Hall-effect devices is required. In practiceHall-effect devices are normally mounted on a small printed circuit board that isfactory fitted to the moto r; wh ile this is a robust construction , the relative positionbetween the sensors and the magnets is fixed and it cannot be optimised at a laterdate.

While d.c. brushless commutation logic normally only requires the determina-


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CHAPTER 6. BRUSHLESS MOTORS AND CONTROLLERS 181

Tablje 6.1. Typical commutation sequence which should be used in conjunctionwith Figure 6.7, for device identificationHall deviceA B0 01 01 01 10 10 1

C110001

Active power deviceForward221133

466554

Reverse1 53 53 42 42 61 6

tion of three points within 360 electrical degrees, resolvers or encoders are usedin hijgh-performance d.c. brushless-motor applications. With the use of high reso-lutiob position measurement, it is possible to correct for any inaccuracies resultingfroni the manufacture of the motor, and therefore to maximise the output. Theopemtion of resolvers and absolute optical position encoders was considered inChapi&T 4. The use of this approach, while beneficial in certain applications, doesnegate the relative simplicity of d.c. brushless motors. If a very-high performanceappnoach is required then a sinewave-wound machine should be considered.Coiilimutation logicConimutation logic is used to determine the switching sequence of the power circuit. The pattern is developed from the design of the motor, from the requireddirection of motion, and from the positional information obtained from the rotor-posikion-measurement system. An example of a suitable truth table is given inTable 6.1. In this example, the Hall-effect devices are separated by 120 electricaldegifees, for a two-pole motor.

The logic to decode the sensor output can either be implemented as discretelogi(:, or more commonly as a customised logic-gate array. In a commercial device, a number of additional features are normally provided, particularly the ability lo operate with d.c. brushless motors of different construction, for example,three-phase motors with the Hall-effect devices separated by either 30, 60, or 240elecltrical degrees, and four-phase motors with a separation of 90 electrical degrees.In addition, most commutation-logic devices provide a facility for totally disablingthe |)ower bridge, and are capable of directly driving power-bridge devices with aminimum of additional circuitry.Speled controllerTha speed control of a d.c. brushless motor is undertaken by the control of themotlor's terminal voltage; this is normally achieved by PWM of the supply voltage.


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182 6.2. SINEWAVE-WOUND BRUSHLESS MOTO RSIf a d.c.-brushless-motor-commutator integrated circuit is used, the PWM switching waveform can be directly gated with the commutation switching pattern; but,in practice, only the lower devices need to be controlled. As with d.c.-brushed-motor servo amplifiers, PWM can be undertaken by either subharmonic or current-controlled hysteresis techniques, as discussed in Section 5.3.3. As discussed ear-Uer, the characteristics of brushless d.c. motors are very similar to those of brushedmotors; hence it is possible to control these motors over a wide speed and torquerange using a conventional analogue control loop.Power-bridge circuitsThe power circuit for a d.c brushless drive consists of a conventional six-device,three-pha se, power bridg e, as shown in Figure 6.7, the devices used will depend onthe rating of the drive, but for small applications M OS FE Ts (metal-oxide semicon ductor field-effect transistors) predominate. As with the PWM bridge discussed inSection 5.3.5 the bridge is provided with a number of auxiliary circuits to ensureprotection against over-voltages, under-voltages, fault currents, and excessive device temperatures. When the motor regenerates, the energy which is returned willcause the bus voltage to rise; this excess energy can be dissipated by the use of aconventional bus-voltage regulator, as discussed in Section 5.4.

6.2 Sinewave-wound brushless motorsSinewave-wound permanent-magnet brushless motors have a number of significantdifferences w hen compared with the trapezoidally woun d d.c. brushless mo torswhich affect their detailed construction and analysis. These motors' main characteristics are (Miller, 1989):

The air gap flux is sinusoidal, generated by a num ber of specially shapedrotor magnets. The windings have a sinusoidal distribution. The motor is supplied with three-phase sinusoidal current.While the analysis is more complex than for d.c. brushless motors, it must be

considered in some detail if the operation of these mo tor is to be fully unde rstood.The cross section of an idealised sinewave-wound brushless motor is shown inFigure 6.9. If the number of turns per pole, Np, is given by

Np = - (6.14)Vyand given an ideal winding distribution, the number of conductors within the angled6 of a/7-pole-pair motor, at a position 9, is given by


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CHAPTER 6.BRUSHLESS MOTO RS AND CONTROLLERS 183

Figilire 6.9. Cross section of an ideal sinewave-wound permanent magnet machine.

N sin pOde (6.15)The sinusoidal flux distribution within the air gap is provided by specially shapedrotor magnets. The rotor-flux distribution is centred on the north axis, which canbe considered to be displaced by a radians from the axis of the stator winding ; andis given by

B{e) = Bcos{pe-a) (6.16)Usittg the above relationships, it is possible to determine the torque and speedcharacteristics of a sinusoidally wound perm anent-m agnet motor by the applicationof conventional electromagnetic theory.6.2 i l Torque char acter is t icsThe force on a group of stator conductors of length L, within the angle d6 of thestator, is determined by the product of the flux and the stator current, i;

F = Bil N smp9cos{p6 a)d6 (6.17)The resultant torque on a rotor of radius r, including the contribution of the opposite winding element, is

T = -2Fr (6.18)


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184 6.2 SINEWAVE-WOUND BRUSHLESS MOTORSThe total output torque of the motor can therefore be determined by integration ofthe elemental contribution over the whole air gap; giving for a/7-pole pair motor

-i ""/^ _ ,^ nrBUN sin a ,^ . ^ .2Frde = (6.19)The peak torque will be generated when the rotor's north axis lags the axes of thestator's ampere-conductor distribution by 90.

The case where the rotor is stationary relative to the stator was considered inthe analysis above. In order to produce a constant torque with the rotor rotatingat a constant speed, the stator's ampere-conductor distribution must rotate in synchronism with the rotor. This is achieved by using a three-phase winding suppliedwith a three-phase balance current. If the r.m.s. phase current is /, then for a m otorwhere the winding are 120 apart, the rotating ampere conductor distribution canbe shown to be

zcoso;^- s m p ^ -f/ 27 r\ TV . / 27 r\

zcos I ut - j sm I pO - j -\- (6.20). ^ . / ^ 27r\ / 2 ^ \ 3V2I^ . , ^I sm I p6' + - 1 cos \ujt-\ j = N sm[pU Lut)

The rotating m agnetic-flux distribution is given byB{e) = B cos{pe -Lut-a) (6.21)

If this is combined with equation (6.19), the output torque can be calculated to be

T = ^ V 2 / ^ s i n / ? (6.22)The ang le /?, which equals - a , is termed the torque ang le, and it is held positivefor motoring; any variation in (3 will require adjustment of the phase current tohold a constant torque . This equation shows that the peak torque, and hence am oto r's efficiency, is optimal w hen /3 = 7r/2. To ensure that the amp ere-cond uctordistribution remains in synchronism with the rotor's magnetic field, the stator'ssupply frequency, / , is made equ al to the roto r's rotational frequency, Ug, hence

Us = 27r/ (6.23)which is related to the motor's mechanical angular velocity, tUm, by

P (6.24)


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CHAPTER 6. BRUSHLESS MOTORS AND CONTROLLERS 185In order for the torque angle to be kept constant (and hence for the stator's

ampere distribution to be kept in synchronism with the rotor), use is made of avector or field oriented app roach to the contro l; this requires a resolver or a similarhigh-performance position-measurement system to be fitted to the motor.6.2 .2 Voltage cha racter is t icsThe e.m.f. of a sinusoidally wound brushless motor can be determined in a manner which is similar to that used for the determination of the torque relationships.For the same elemental group of conductors in a machine with /7-pole pairs, thecontribution to the back e.m.f. of an elemental portion of the winding is given by

^^ ^ B{9)lumN sin p06e ^^ ^^^

Using the flux relationship given in (6.21) and integrating, the r.m.s. phase e.m.f.is given by

^ NrBlumn ^^^^^^ 2y/2p

and the line-to-line voltage by \ / 3 ^ .6 . 2 .3 Torqu e- speed character i s t i c sIdeal motors were considered in the analysis above; inpractice, the construction ofthe stator w indings, and p articularly the effect of the stator's slots, has a significanteffect on the mo tor's performance and characteristics. In addition, the location ofthe itiagnets, either mounted on the surface or within the body of the rotor, has tobe considered in detail. It is normal to undertake a detailed modelling of this typeof motor using electromagnetic CA D packages (Hendershot and Miller, 1994).

If the analytic method considered above is extended to include the effects ofthe construction of the windings, it can be shown that the r.m.s. phase e.m.f. isgiven by

Epu^s^ (6.27)v/2and the output torque is given by

^ 3TrplV2tpm sin /?8

The flux hnkage provided by the rotor-mounted magnets is given byxPm = kNpBm (6.29)


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186 6.2. SINEWAVE-WOUND BRUSHLESS MOTO RS

f Torque

Constantpower curve

Speed

Figure 6.10. The torque speed characteristics of a sinewave wound machine.Above base speed P can be adjust to increase motor speed, however a constantpower Umit as defined by equation (6.31) will apply.

where /c is a constant which is introduced to accommodate the physical construction of the stator w indings, and Bm is the air-gap flux density. T he torque equationcan also be expressed in the form;

pEpI sin (3LJ s

(6.30)

and hence,

LUmT = SEpI sin (3 (6.31)

This verifies that the product of the back e.m.f. and the phase current is equal to theinput pow er at /? = 7r/2; therefore, the ability to control this angle is considered tobe critical to the satisfactory performance of the motor.The overall torque-speed characteristics of the motor derived from this equation is shown in Figure 6.10. The peak torqu e can be maintained up to the basespeed. Above this speed, by modifying /?, the motor will effectively enter a field-weakening mode, allowing an increase in the speed at the expense of the peaktorque . The m oto r's efficiency is reduced in this region be cause the mo tor is beingsupplied with the peak current.


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CHAPTER 6. BRUSHLESS MOTO RS AND CONTROLLERS 187

Demand- Control Loop

P demand

Revolver toDigitalconverter

PROM DAC

PROM DAC

-(A+B)

Figure 6.11. The block diagrams of a sinewave wound machine controller, usinga resolver as the position transducer. The control loop provides two signal, ananalogue input to the multiplying DACs and (3 as digital word to the PROMs toallow ope ration above base speed. Th e three outputs (A ,B and C) are fed via asuitable power am plifier to the motor.

6.2.4 Control of sinewave-wound brushless motorsThe block diagram for a simple hardware-based controller for a sinewave-woundmotor is shown in Figure 6.11; it can be seen to be superficially similar to that fora d.c. brushless mo tor. The major difference is in the type of position en coderwhich is employed and in the interpretation of its data. To synchronise the winding currents w ith the rotor's position and to hold /3 constant at the required v alue,a number of different techniques can be used; Figure 6.11 shows one approach.The digital output of the motor's shaft encoder or resolver is used to address apro9*anmiable read-only memory (PROM) which holds a number of synthesisedsinewaves. Due to the symmetry of a three-phase supply, only two sinewaves arestored; the third sinewave can be computed. As the position of the motor changes,the Sinewaves are read out sequentially, ensuring that the motor's current remainsin synch ronism w ith the moto r's position. By digital addition, it is possible tomove the supply waveform away from the optim um value, effectively adjusting thevalue of /?. The analogue current demand determined by the servo amplifier modulates the sinewave which is generated by using a multiplying digital-to-analogueconverter. The winding current can be produced either by direct amplification ofthe analogue demand using a linear amplifier, or by PWM within a conventionalthree-phase pow er bridge. Th e use of a linear-amplification current waveform withminim al harmon ics results in exceptional pe rformance, but this requires more com -


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188 6.3. LINEAR MOTORSMagnet embeddedin the substrate

V , IHall effect

device Windings

y ! Linear bearingarrangementLinear opticalencoder

Figure 6.12. The construction of a linear brushless motor. The upper figure showsthe plan of the substrate, the lower shows a cross section through the substrate andthe carriage that contains the windings.

plex electronics and a highly dissipative linear amplifier. In practice, this approachis restricted to critical applications, for example, in the manufacture and testing ofmagnetic media.An additional approach to the control of sinusoidally wound machines is to usevector control in an identical fashion to that used with a.c. induction motors, theimplementation of which is discussed in Section 7.3.2.

6.3 Linear motorsA linear motor operates with a conventional d.c. brushless motor amplifier operating in the force, instead of torque mode as used in rotary machines. As with aconventional brushless motor the operation requires the use of a position feedbackto control position, velocity and acceleration. In principle the operation of the motor is identical to that of its rotary equivalent. The magnets are mounted on thestationary track, with the coil and sensors fitted to a moving assembly. Figure 6.12.In the figure the encoder track for the linear encoder is glued to the side of thestationary substrate, (see Section 4.3.5). As with the rotary machine the windingsare 120 electrical degrees apart. For a trapezoidal winding. Hall-effect devices


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CHAPTER 6. BRUSHLESS MOTORS AND CONTROLLERS 189are mounted adjacent to the coils to control the comm utation pattern. If sinewavecommutation is used, the linear encoder used for the position feedback is also tocontnol the commutation of the motor. A phase finding strategy based on Hall-effect encoders is required on power-up, then the motor phases are incrementallyadvanced on each encoder pulse.

6.4 SummaryThis chapter has discussed the rotary d.c. brushless motors and sinewave-woundmotors. While the application requirements will normally dictate which is the bestoption, a number of comparisons can be drawn:

If the torque per r.m.s. ampere is compared using equations (6.6) and (6.22),for identical peak motor fluxes, the torques of square-wave-wound motorsexceed those of sinewave-wound motors by a factor of 1.47. This effectivelydetermines the relative sizes between two motors with comparable characteristics. The control systems for square-wave-wound d.c. brushless motors are considerably simpler than those required for sinusoidally wound motors. Direct-

current brushless motors only require low-cost position encoders, whereassinewave-wound motors require high-precision systems.While both types of motor give performances in excess of those of brushedmotors, they do so at a cost premium, which needs to be considerable. Brushlessmotors are being more widely used as the cost of motors, and their essential electronics, continues to fall as the technology matures. With the present technology,the performance is exceptional; this has led to the introduction of electric drives inapplications which have been the preserve of hydraulics. However, as with all decisions of drive-system selection, the additional complexity of these types of driveshas to be balanced against their high reliability and performance. The final pointneeds to be considered in some detail when a Unear motor is being used to replacea ball screw driven by conventional rotary machine.

Chapter 6 Brushless Motors and Controllers

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Transcript of Chapter 6 Brushless Motors and Controllers