Handbook of Small Electric Motors MAZ Part 12 doc

A close observation of this structure shows FIGURE 5.7 Outer-rotor BLDC motor rotor and stator assembly.. When the rotor has moved 180°electrical, it is sary to reverse the current in th

CHAPTER 5 ELECTRONICALLY COMMUTATED MOTORS

Chapter Contributors

Duane C Hanselman Dan Jones Douglas W Jones William H Yeadon

com-Next, several configurations of the stepper motor are discussed This is followed

by the switched-reluctance motor, which is really a specialized configuration of thevariable-reluctance stepper motor

Brushless direct-current motors (BLDCs) are so named because they have astraight-line speed-torque curve like their mechanically commutated counterparts,permanent-magnet direct-current (PMDC) motors In PMDC motors, the magnetsare stationary and the current-carrying coils rotate Current direction is changedthrough the mechanical commutation process

In BLDC motors (Fig 5.1), the magnets rotate and the current-carrying coils arestationary Current direction is switched by transistors The timing of the switchingsequence is established by some type of rotor-position sensor A typical rotor assem-bly for an inner-rotor configuration with sensors and commutation magnet is shown

in Fig 5.2 The three white devices mounted on the printed-circuit board are effect switches They are positioned next to the larger-diameter magnet wheel, whichcauses them to switch high and low as the wheel changes from north to south as it

Hall-* Section contributed by William H Yeadon, Yeadon Engineering Services, PC, except as noted.

Another type of motor has a rotor with solid magnet arcs, as shown in Fig 5.5.

FIGURE 5.1 BLDC motor.

FIGURE 5.2 BLDC rotor assembly.

FIGURE 5.3 BLDC rotor showing magnetic pole transitions.

FIGURE 5.4 BLDC stator assembly.

5.1.1 Basic Configuration of BLDC Motors

Outer-Rotor Motors. These motors are generally used where relatively high rotorinertia is beneficial to system performance Common applications are computer diskdrives and cooling fans Construction is shown in Figs 5.6 and 5.7

The rotor assembly in Fig 5.6 consists of a flexible magnet with four poles netized on it It is enclosed by a magnetically soft steel cup or housing A shaft which

mag-FIGURE 5.5 BLDC rotor assembly with core segment magnets.

FIGURE 5.6 BLDC outer rotor assembly.

allows the rotor to turn with respect to the stator is attached to the center of the steelhousing.

The stator assembly (Figs 5.8 and 5.9) consists of a lamination stack with coils ofwire wrapped around the pole pieces This is supported by a mounting base whichalso contains a bearing support and a control circuit This motor’s poles are alter-nately magnetized N-S-N-S

As the rotor turns, the currents are turned off in one winding set and turned on inthe other set by the Hall switch This results in an S-N-S-N magnetization in whichthe S poles are induced at the interpoles and the poles where no current exists in thewindings This keeps the rotor turning A close observation of this structure shows

FIGURE 5.7 Outer-rotor BLDC motor rotor and stator assembly.

FIGURE 5.8 Outer-rotor BLDC stator diagram.

that it is in fact a single-phase motor and, as such, will have rotor positions wherethere is zero torque This could result in failure to start This is overcome by placinginterpoles between the wound poles, as shown in Fig 5.10 The magnet providessome position bias, which always results in rotation when the pole is energized.Some other methods used to start these single-phase motors are shown in Figs.5.11 and 5.12 In the case of Fig 5.11, the reluctance torque produced by the magnet

FIGURE 5.9 Outer-rotor BLDC wound stator assembly.

FIGURE 5.10 Outer-rotor motor diagram.

causes the rotor to line up over the pole When the coils are energized, the fieldresulting from the energized coil appears to move across the face of the pole in thedirection of the wider section of the pole that is closest to the gap This starts rota-tion, which may then be maintained by alternately reversing the winding currents.The structure shown in Fig 5.12 is another method of providing an unbalanced mag-netic circuit which causes the rotor to have a preferred resting position in the unen-ergized state that is different from that of the energized state.

All of the motors just discussed are single-phase motors Although this is bly the case for most outer-rotor motors, it is quite possible to build a multiphasemotor in this configuration, as shown in Fig 5.13

proba-FIGURE 5.11 Stator with reluctance notches.

FIGURE 5.12 Stator with reluctance holes.

Inner-Rotor Motors. If one simply inverts the outer-rotor motor diagrammed inFig 5.8, the device shown in Fig 5.14 is generated This is also a single-phase device,and it would operate in the same fashion as the outer-rotor motor.

Some observations need to be made about these motors The outer-rotor motorhas much more magnetic material than the inner-rotor device, which means it iscapable of more flux when the identical materials are used It would be necessary touse a higher-energy-product magnet to get the same performance from an inner-rotor motor

The inertia of the inner-rotor motor is lower because of its smaller rotor ter Therefore, it accelerates more rapidly than the outer-rotor motor

diame-FIGURE 5.13 Multiphase outer-rotor motor.

FIGURE 5.14 Single-phase inner-rotor motor.

Most inner-rotor motors have multiple phases in an effort to reduce the startingproblems associated with single-phase motors The stators may have salient poles ordistributed windings Figure 5.15 illustrates a three-phase four-pole salient-polemachine Here the rotor is a magnetically soft steel core with magnet arc segments

bonded to it As the phases are switched in sequence A-B-C, the rotor moves to line

up with the subsequent phase When the rotor has moved 180°electrical, it is sary to reverse the current in the windings, starting with phase A, in order to prop-erly polarize the stator poles with respect to the magnet poles

neces-FIGURE 5.15 Multiphase inner-rotor motor.

In order to properly switch the coil currents at the right time and in the rightorder, the control electronics must know the rotor position This is usually accom-plished by means of Hall-effect devices, encoders, or counter-emf sensing

Salient-pole machines have inherently high torque perturbation characteristicsbecause of the abrupt permeance changes as the rotor moves from pole to pole Thiscan be reduced by distributing the windings over several stator teeth per pole This

is illustrated in Fig 5.16

of the distributed-winding multiphase brushless motor is the slotless brushlessmotor As shown in Fig 5.17, the winding distribution is similar to that of the statorshown in Fig 5.16 However, the stator section has no teeth The advantage of thistype of motor is that there are no variations in permeance as the rotor moves Thus,there are no torque perturbations or cogging There is, however, a price to be paid.The lack of teeth increases the effective air gap, thereby lowering the available flux.Another variation is the axial airgap motor This motor is illustrated in Fig 5.18

It has a stator with triangular coils (Fig 5.19) and a disc rotor which is alternatelymagnetized NS-NS-NS-NS through its thickness The stator coils (Fig 5.20) aremounted to a nonmagnetic substrate, while the rotor disc is mounted to a magneti-cally soft steel The advantage of this motor is that, like the other slotless motor, it islow cogging, but it also has relatively high inertia

FIGURE 5.16 Inner rotor distributed-wound stator.

FIGURE 5.17 Inner rotor slotless stator.

5.1.2 Sizing and Shaping the Motor

assumptions Generally, there is a specification of some type which includes outputperformance, available power input, mechanical mounting method, and means ofconnecting the load First, look at the intended application and determine whether

an inner- or outer-rotor motor would be the first choice Some common indicatorsare charted in Table 5.2

magnetic-circuit design is an interactive process and that the following rules are justguidelines to establish a starting point At this point, the outside diameter of themotor and the shaft diameter have been selected The next task is to roughly pro-portion the magnetic-circuit components to establish a starting point for the design.First look at the outer-rotor motor (Fig 5.21) Then look at the inner-rotor motor(Fig 5.22)

The shaft and bearing space has already been established, so the space for activematerial that remains is the area between the shaft hole and the outside diameter.Next, decide on the air gap Gaps on the order of 0.020 to 0.040 in per side are verycommon The smaller the air gap, the more flux that is available, but the higher thevalue of cogging torque Manufacturing tolerances on stack diameter and magnetthickness generally dictate a gap somewhere in the range stated Start with thesmallest gap your factory can comfortably hold If in doubt, try 0.030 in to start

In order to set the rotor and stator magnetic circuit dimensions, you must makesome assumptions with respect to the level at which you will work the materials This

is accomplished by setting the flux densities in the magnetic circuit as outlined inTable 5.3

FIGURE 5.18 Axial air gap brushless dc motor.

FIGURE 5.19 Axial air gap rotor with magnets.

FIGURE 5.20 Axial air gap stator with windings.

TABLE 5.1 Comparison of Outer-Rotor and Inner-Rotor Motors

Single phase or multiphase Single phase or multiphase

Can be wound with dc armature-winding Requires ac stator-winding

Bifilar windings can be employed on single- Salient-pole machines utilize more copper.phase motors; 50% copper utilization

Available copper space on distributed- Distributed-winding motors providewinding motors is less than on inner-rotor smoother performance and better copper

Shorter end turns yield lower inductance Longer end turns yield higher inductance and

Less torque perturbation More torque perturbation

Lower-energy magnets can be used Higher-energy magnets required

TABLE 5.2 Inner-Rotor Versus Outer-Rotor Motor Applications

Use with speed reducers Good Poor to okay

Rotor Back Iron. In the outer-rotor motor, this is usually a steel cup of some kind

To determine its thickness, keep in mind that the flux has a long steel path thatrequires mmf to overcome Set the flux density equal to 75 kline/in2

Then:

But you don’t yet know how much flux will be needed You do know, however, that

it will be constant on a per-pole basis This allows you to proportion the steel ing and lamination sections based on the relative flux densities given in Table 5.3.Taking the nominal values and setting the stator teeth as 1.0, you can define ratiosfor the remaining parts There are still some problems to overcome before you canproceed You have not yet decided on the number of poles or teeth

hous-Poles and Teeth. Some general rules on selecting the number of poles, teeth, andphases are presented in Table 5.4

Number of Phases. Single-phase motors have poor conductor utilization, hightorque ripple, and null zones that may create starting problems, but they are easy towind and low cost and require only one or two power switches.

Two-phase motors also have poor conductor utilization, but the null zones areeliminated, the torque ripple is greatly reduced, and the cost is higher because a min-imum of four power switches are required

Three-phase motors have better conductor utilization, no starting problems, andgreatly reduced torque ripple; they can get by with as few as three power switches,but they generally cost more to wind

Increasing the number of phases to four or greater realizes small gains in copperutilization and torque ripple, but the costs of winding and power switches usuallyoutweigh the gains

FIGURE 5.22 Inner-rotor motor

FIGURE 5.21 Outer-rotor motor

As a starting point then, assuming that performance is as important as cost, thethree-phase motor is a good choice.

number of poles are the following:

1 As the total number of poles increases, the requirement for rotor and stator back

iron decreases because the total flux is spread over more poles reducing the sity

den-2 Since less back iron is needed, more space is available for windings, allowing for

a reduction in copper losses

3 More poles have more parts and cost more money.

Two-pole motors require substantial back iron and long winding spans, whichmeans more expensive winding equipment Four-pole motors require about half theback iron and have shorter coil spans Although the equipment required may be thesame as for two-pole motors, four-pole motors have shorter end turns—thereforeless mutual inductance, less copper loss, and an easier time in winding

TABLE 5.3 Preferred Flux Densities

Flux densityMagnetic path section kline/in2 T

Stator yoke section 80–100 1.24–1.55

TABLE 5.4 Effects of Changing Number of Poles, Teeth, and Phases

Effect on design factors

Activematerial

Number of

poles

Number of

teeth

Number of

phases

Number of Teeth. So far, you have picked three phases and four poles The nextmajor item is the number of teeth There are many combinations of teeth and polesthat will work for motors having two, three, four and more phases Common num-bers of teeth for two-phase motors are 8, 12, 16, 24, and 48 Common three-phasenumbers are 6, 9, 12, 15, 24, 36, and 48 There are obviously other numbers of teeththat will work for these motors These are just some of the common ones As thenumber of teeth selected increases, the number of slots available for winding alsoincreases, resulting in more coils per pole In general, one should choose the lowestnumber of teeth possible that will provide a reasonable winding pattern.

Some things to keep in mind as combinations of teeth, poles, and phases are sen are the following:

cho-● Cogging. A torque perturbation occurs every time a magnet pole tip passes a tor tooth Even numbers of teeth and poles cause a greater perturbation thanuneven numbers because at any given time there are more pole tips passing teeth.This can be addressed by using an uneven number of teeth versus poles, which givesfewer poles passing teeth at a given time, or by skewing the stator or the magnets

sta-● Manufacturability. Increasing the number of teeth to improve performance hasits limits As the number of teeth increases, the laminations may become difficult

to punch, or the teeth may bend easily as the slots are wound

For this example, choose 12 teeth Therefore, you have chosen 3 phases, 4 polesand 12 teeth

To estimate the size of the respective components, look at the motor section inFig 5.23 and note the flux paths

The flux from any one pole of this four-pole motor travels through the teeth tothe stator yoke, then splits through the yoke, goes back through the teeth under the

FIGURE 5.23 Outer-rotor motor flux path.

adjacent magnet pole across the air gap, goes through the magnet, splits through therotor yoke, and goes back to the originating magnet The magnet sets up the flux; allthe flux goes across the gap (except for leakage), into the tooth tips, and through theteeth When proportioning the sizes, refer to Table 5.5.

TABLE 5.5 Nominal Flux Densities

Magnetic-circuit Nominal flux density, kline/in2

outer-Since the flux density is inversely proportional to the area (B= φ/A), and the area

is proportioned to the width of the magnetic-circuit component times the length of

the stack Lstk, the widths may be ratioed directly according to the flux density inTable 5.5

Ratio all components to the teeth as follows:

Asy=Yws⋅Lstk

where Lstk=stack length

The density ratio is divided by 2 because of the flux split

Att=Ttw⋅Lstk

∴Ttw∝ ≈2

Ary=Ywr⋅L s

In the case of the outer-rotor motor, the length of the shell L sis usually longer

then the stator stack, so Ywris more in the range of 30 to 40 percent of total toothwidth

To estimate the width of the teeth, assume that the area available after ing magnet area, air gap area, and stator yoke is to be divided up so that the slot area

subtract-is approximately 2.5 times the tooth area In thsubtract-is case, tooth area subtract-is the tooth widthtimes its length in the radial direction Assume straight teeth with parallel sides Thentake the total tooth width and divide it by the number of teeth per pole you havechosen In this case, the number is 3 These dimensions may need to be modified tobalance mmf drops once the magnetic circuit is solved

115

75(2)

115

60115

(90)(2)

reduce the torque perturbations and audible noise.A radius should be added at tion 1 to allow for easy entry of the magnet wire and at position 2 to reduce magnetic

posi-saturation of this region The width of the slot opening Wsoshould be wide enough toallow the largest-diameter wire you intend to use to be easily wound in place It

FIGURE 5.24 Outer-rotor tooth shapes.

should be kept small enough so that the magnet wire will be easily retained after thewinding operation is complete

The inner-rotor motor (Fig 5.25) follows the same rules with respect to tip ness as the outer rotor design Some of the significant differences occur with thewidth of the slot opening and the shape of the slot If the stator is going to be wound

thick-with a needle or gun winder, Wsomust be sufficient to allow for the needle width andlateral motion If the stator coils are going to be wound on forms and then insertedinto the stator with ac-motor-type inserters, the following rules apply (Fig 5.26):

1 The slot depth D to the slot width Ws, D/Wsratio should be as great as possible,with 4 being a good value and 3 being the minimum value

2 The slot bottom shape is not critical Round or square will work, but round is

eas-ier to fill

3 The angle αshould be between 15 and 30 degrees

An important rule to remember when establishing part dimensions is that thewidth of any part should be 1.5 times the thickness of the material Failure to followthis rule results in part distortion and die wear The material should be selectedbased on cost, induction, and core loss requirements

Structural Magnetic Materials. There are some parts of the motor magnetic cuit that generally wind up being used for mechanical structural purposes as well.The outer-rotor motor in Fig 5.23 has a rotor yoke which is used to contain the mag-nets as well as serve as a flux path The inner-rotor motor in Fig 5.24 has a rotor core

cir-to which the magnets are bonded This core serves as the magnetic rocir-tor yoke as well

as the means of attaching the output shaft to the magnets These materials are ally a magnetically soft steel of the type ANSI CRS 1008 to 1026 It is not a require-ment that theses parts be laminated because the direction of the flux in them doesnot change; therefore, there are no core losses A typical magnetization curve of thismaterial is shown in Fig 5.27

usu-FIGURE 5.25 Inner-rotor tooth shapes.

FIGURE 5.26 Inner-rotor tooth proportions.

Rotor Inertia. The following method for calculating rotor inertia is based on theassumption that all parts of the rotor rotate around the center of the shaft.

For the outer-rotor motor in Fig 5.28, calculate the inertia of each part separately,then add the parts together for the total rotor inertia First, calculate the inertia ofthe shaft:

Jshaft=0.0184  4

Lshell

D s

2

FIGURE 5.27 Unannealed 1020 CRS housing material.

FIGURE 5.28 Outer-rotor inertia.

Then calculate the inertia of the disk:

Lmag(mag density)



772

Dri

2

Dri

2

Dro

2

D s

2

Dro

2

TABLE 5.6 Densities of Common Magnetic Materials

Jrotor=J s+J D+jshell+Jmag

Now, consider the rotor of the inner-rotor motor (Fig 5.29)

Drm

2

Lmag(mag density)



772

Drm

2

Lmag(mag density)

5.1.3 Stator Winding Design Considerations*

Brushless dc motors initially were designed in large numbers for spindle drives inWinchester disk drives The early designs were three-phase, later moving to two-phase and then one-phase, due to the very slow start-up requirements, very smallfriction loads, and the need to reduce unit cost at all levels The industrial andmachine tool markets started with and continue to use three-phase BLDC motors intheir variable-speed, variable-load, high-start-up applications The overwhelmingpopularity of three-phase BLDC motors focuses this subsection toward three-phasewindings Many of the initial design activities for various winding patterns can betraced back to the 1920s and earlier based on work done on three-phase ac windings.This subsection reviews the various winding line connections, the key windingpatterns and hookups, various winding constants, and winding selection and designtechniques

Basic Winding Configurations. There are other basic decisions that must be made

by the design engineer before a BLDC motor design can commence Previouslydefined is the number of phases, which is three here Next in importance is the num-ber of poles The use of two poles is waning, and the use of six or eight poles isincreasing Four-pole BLDC motors are among the most popular used today Two-and four-pole BLDC motor designs are used here, but the rules for two and fourpoles can be extended to higher pole counts The number of stator slots (and teeth)and the winding pattern are key design decisions This section is dedicated to review-ing the important parameters of these two design decisions

In a three-phase motor there are three windings or phases positioned 120°trical apart Figure 5.30 shows the location of 6 coils in a representative 12-slot sta-tor A two-pole rotor (not shown) will rotate as the three windings are energized in

elec-sequence A-B-C, as A-A′, B-B′, and then C-C′are energized sequentially The phase winding always develops positive starting torque, no matter where the rotorstarts its motion

three-FIGURE 5.29 Inner-rotor inertia

* Subsection contributed by Dan Jones, Incremotion Associates.

There are many winding line connections that can be used in three-phase drive

systems Figure 5.31 illustrates the various configurations The half-wave wye is the simplest three-phase line configuration (Fig 5.31a) It uses three power lines and

one return line (four leads) The excitation is shown adjacent to the schematic in Fig

5.31a Only 33 percent (one lead) of the half-wave wye windings are energized at any time in operation The second wye winding, the full-wave wye (Fig 5.31b) has

only three leads but 66 percent (two leads) of the windings are in operation neously The excitation scheme is shown to the right of the schematic

simulta-The third major winding connection pattern is the delta, shown in Fig 5.31c It

possesses the same excitation scheme as the full-wave wye The delta winding figuration has been used more extensively than the wye in fractional-horsepower(≤746 W) motor applications The wye is more popular with the larger-sized integral-

con-horsepower BLDC motor users The final winding to be reviewed is the independent winding line connection (Fig 5.31d) In this scheme, each winding is independent of

its neighbor The excitation scheme is more complicated, but each winding can beoperated in parallel, thereby distributing the total current The windings are still sit-uated 120°electrical away from each other This winding configuration has seen lim-ited use to date

The most popular winding line configurations are the full-wave wye and thedelta In a balanced wye configuration, the line and coil (phase) currents are equal,

FIGURE 5.30 Basic 3-phase winding layout.

the neutral current is zero, and the line-to-line voltage is 3 times the phase voltage.

In a balanced delta connection, the line-to-line and coil (phase) voltages are equal,but coil currents are 1/3 times the line-to-line currents

Key Winding Patterns. There are many types of winding patterns that can be lized Four major winding patterns are listed here:

uti-1 Constant integral pitch—lap winding (full)

2 Variable pitch—concentric winding

3 Constant fractional pitch—lap winding for even or odd stator slots

4 Half-pitch

Each of these winding patterns has two coils per stator slot There is one windingtype designated, a consequent pole winding where there is only a single coil per slot.Consequent pole windings are very popular in single-phase ac motors of fractional-horsepower size

Table 5.7 is revised from Veinott and Martin (1987) It displays the various tor slot and rotor pole combinations along with the maximum number of parallelcircuit combinations with a specific slot and pole combination For purposes of sim-plicity, either 12- or 24-slot stators are used here to illustrate the various windingpatterns In one case, a 15-slot stator is used to illustrate an odd-slot fractional-pitchlap winding

sta-FIGURE 5.31 Popular 3-phase BLDC motor winding line connections:

(a) wye (half wave), (b) wye (full wave), (c) delta, and (d) independent.

If one uses a 12-slot stator winding, there are two full-pitch integral lap windings

available, one for two poles and the other for four poles

If P=2, Ph =3, and S=12, then n=2, an integer Figure 5.30 shows the basic

winding-slot pattern for a 12-slot 2-pole 3-phase 2-coils-per-pole-per-phase (n=2)

configuration The coil pattern for this winding configuration is shown in Figs 5.32

and 5.33 as a series wye line configuration and as a parallel wye line configuration,

respectively There are really 12 coils used in this design, but only 6 are shown There

are two 1- to 7-throw coils—one inserted on the right side (CW direction), the

sec-ond inserted on the left side (CCW direction), and doubles on the other five coils

also, inserted as described previously Note the position of the teeth for the 12-slot

stator The slot pitch (adjacent slot to slot) is 360/12 or 30°mechanical or electrical

The angular location for the phase 2 winding (CW direction) is only 60° It is

sup-posed to be 120° Symmetry solves the problem if 180°(polarity change) is added to

the 60°to achieve 240°mechanical or electrical So the 1, 2, 3 winding phase hookups

displayed in Fig 5.32 will yield a CCW rotation

The series and parallel hookup options are very important from a practical aspect

of magnet wire size selection It is easier to pack smaller-sized magnet wires in a

TABLE 5.7 Slots Versus Poles Versus Parallel Hookups Versus Coils per Pole per Phase

coils Circuits pole Circuits pole Circuits pole Circuits pole

FIGURE 5.32 Series hookup for 2-pole wye-winding slot brushless dc motor.

12-FIGURE 5.33 Parallel hookup for 2-pole 3-phase wye-winding 12-slot brushless dc motor, constant-pitch lap winding pattern.

BLDC stator slot than larger ones Since total turns per phase are directly

propor-tional to torque, putting all the needed turns (N per phase) in a single coil with

smaller magnet wires and then paralleling the coils will yield extra space for moreturns This is a packing factor consideration

The disadvantage of using parallel coils is that both sets of coil leads must be used

to properly connect the coils (see Fig 5.33) Figure 5.34 shows a representation ofhow two coils would be inserted into adjacent stator slots Remember that there are

2 slots per coil per phase for this 2-pole 12-stator-slot winding pattern

FIGURE 5.34 12-slot lamination, 2 poles, 3-phase constant-pitch lap pattern.

Figure 5.35 shows the winding pattern for a constant-pitch 4-pole 12-slot BLDC

stator There is now only one coil per pole per phase (n=1) in this winding, as shown

in the following equation:

4 poles ×3 phase =12 slots

The four coils per phase can be connected as four coils in a series hookup or fourcoils in a parallel hookup It is also possible to connect two coils in series and two coils in parallel to achieve a series-parallel hookup Figure 5.36 displays twoadjacent coils inserted into the proper stator slots Note the shorter length of thesecoils because the end turns are shorter while the segments of the turns (conductors)within the appropriate stator slots remain the same length The shorter the end-turnlength (which doesn’t create any torque), the better the motor design

The variable-pitch winding was developed to reduce the stator end-turn heightcaused by the numerous adjacent coil crossovers by nesting the coils inside eachother, as shown in Fig 5.37 This pattern can be used only when coils per phase per

pole n is 2 or greater Figure 5.37 displays an n=3 condition The actual winding

pat-tern is shown in Fig 5.38 Since n=2, there will be two different winding lengths or

FIGURE 5.35 Winding pattern for a constant-pitch 4-pole 12-slot stator, 3-phase hookup, 30 °

mechanical, 60 ° electrical.

FIGURE 5.36 Constant-pitch 4-pole lap winding tern with adjacent coil layout.

pat-throws The following equation describes the method used to determine the twovariable winding pitches:

VSP1=7 and VSP2=5 The average of these two variable-pitch coils should equalthe integral winding pitch for a 3-phase 2-pole 12-slot design, which is 6 Figure 5.39displays the location of two adjacent coils placed in the proper stator slots Thiswinding pattern will reduce end-turn height and coil lengths by 10 to 15 percent Theconcentric winding with variable pitch has been used extensively in larger integral-horsepower units, particularly by the various electric winding repair houses

number of stator slots

concen-The third winding pattern is fractional-pitch winding, which is used in manyapplications, particularly odd stator slots where cogging torque must be reduced.Table 5.7 identifies the fractional pitch as 11⁄4for a 15-slot 4-pole configuration Thispattern is popular for resolver windings and some low-cog BLDC motors The fol-lowing equation yields the pitch:

15

4

number of slots



FIGURE 5.38 Variable-pitch concentric winding pattern, 2 poles, 3-phase series hookup.

FIGURE 5.39 2-pole 3-phase variable-pitch concentric pattern.

As with any winding, there are advantages counterbalanced by disadvantages.The following equation defines the tooth or slot pitch of the 15-slot stator.

SP =

Now, since this design is a four-pole BLDC design, there are two full electricalcycles for one full mechanical cycle The next equation defines the relationshipbetween electrical and mechanical degrees for any four-pole design

Degrees electrical =degrees mechanical ×number of pole pairs

A 48°electrical pitch does not equal the desired 60°pitch, so there must be torqueloss

Figure 5.41 illustrates the winding pattern for a 12-slot 2-pole fractional-pitchwinding A full winding pitch would possess a value of 6 with a throw of 1 to 7 Thiswinding pattern has a winding pitch of 5⁄6(fractional) or a throw of 1 to 6 This group

of fractional-pitch windings has a pitch less than 1 when an even stator slot count isemployed This winding pattern is used in larger three-phase ac motors to decreasethe harmonic content of both the voltage and mmf waveforms This technique is verysimilar to that of short-pitch lap windings used in brush dc motors

The final winding type is the half-pitch winding, which has the simplest windingpattern The coil is wound directly around the stator tooth with a winding pitch of 1

360

15

FIGURE 5.41 Constant fractional-pitch even-slot 2-pole

3-phase series hookup.

tance per coil It does suffer from reduced torque, as all fractional pitch windings do.The various winding factors that determine the reduced torque values are reviewed

in the next subsection

factors that adjust for the peak magnetomotive force (mmf) and the generated flux φwhich directly leads to adjustments to the winding back emf (Ke)and peak developed torque of the BLDC motor These factors can be identified asfollows:

winding-● Chord factor (pitch factor)

● Distribution factor (breadth factor)

● End-turn factor (coil-length factor)

The pitch factor K p and the distribution factor K dare the factors discussed in this

subsection The end-turn factor KETis discussed in a later subsection The pitch tor is defined by the following equation:

fac-K p=sin

which is the pitch factor for a 2-pole 12-slot integral-pitch winding

The distribution factor K dis delineated by Eq (5.9)

Table 5.9 contains the tabulated results for the K p and K dvalues for the six ing patterns presented plus a 24-slot 4-pole integral-pitch winding pattern illustrated

wind-in Fig 5.42

0.500

0.5176

Filling the Stator Slots. The first item in filling the stator slot is to compute thearea of the slot There are many types of stator slot shapes but the trapezoidal (constant-tooth-width) slot shown in Fig 5.30 and the round (variable-tooth-width)slot are the most popular slot shapes One can use basic trigonometry to determinethe slot area or obtain the actual slot area from the lamination vendor.

There are three methods used to compute slot area and the total volume of per magnet wire used They use the following units:

cop-● Square inches (in2)

● Square mils (mil2)

● Circular mils (cmil)

The circular mils method uses the nominal diameter of the insulated wire in mils orthousandths of an inch and takes the square of this diameter, which is the circularmil value

For 18 AWG (American Wire Gauge), the nominal insulated single-build wirediameter from the Phelps Dodge magnet wire chart (Table 2.76) is 41.8 mil The

TABLE 5.8 Summary of Distribution Factors

or coils per group 2 Phase Conventional Consequent pole

TABLE 5.9 Summary of K p and K dFactors

Slot Slots per Stator Winding Winding Winding pitch, pole per

slots Poles type pitch throw ° mechanical phase n K d K p K d K p

wire area is 1747 cmil per Eq (5.10) The square mils value is smaller and can becomputed by modifying Eq (5.10) to Eq (5.11) In many cases, the wire chartscompute the magnet wire’s nominal diameter without insulation coating (barewire diameter) It is strongly recommended that the insulated wire dimensions

be used

The Phelps Dodge magnet wire chart (Table 2.76) also shows wires per squareinch The more important parameter is turns (conductors) per square inch It yieldsthe value of total number of turns—or, more appropriately, conductors—that can beplaced in a slot, assuming 100 percent fill Now, the most copper fill in terms of a per-centage of actual turns per square inch versus 100 percent fill turns per square inchthat this author has actually done by hand-insertion methods is 73 percent with 37AWG and 63 percent with 21 AWG

The practical limit is somewhere between 40 and 50 percent of this theoreticalvalue depending on the type of winding machine, tooling used on the windingmachine, length of stator stack, size of stator slot, etc If one wanted to use 22 AWG,the turns (conductors) per linear inch would be 37.5 and the turns (conductors) persquare inch would be 1410

(nominal diameter, mils)2



1.27324

FIGURE 5.42 24 stator slots, 4 poles, 3-phase hookups 30 ° mechanical, 60 ° electrical.

Total conductors (theoretical) =(SA) (turn/in2)

where SA =slot area

The total conductors must be an even number because 2 conductors equal 1 turn.Here the maximum value is 308 conductors with 22 AWG magnet wire That would

be 308/2 or 154 turns, since two coils are represented in every stator slot Based on apractical slot fill of 45 percent, the maximum number of turns would probably be69.3, or 69 turns per coil The actual number of turns to achieve the desired perfor-mance has not yet been determined but for the AWG size selected, 69 turns or 138conductors is the maximum practical limit

The next important parameter to establish is the coil resistance First, one mustestablish the MLT in the stator coil

KET=end-turn coil factor,≤1.00

The value of KETis based on experience but a guide for its use is that the KET

value approaches unity as the design increases in pole count and decreases in ber of turns For example, an 8-pole design using 10 turn/coil of 22 AWG would have

num-a KETvalue of 0.97 A 2-pole design using 60 turn/coil of 22 AWG would have a KET

value of 0.88

The MLT for the example is 5.894 in/turn and the resistance per coil is 0.549 Ω,which can be computed using the formula in the following equation

The MLT value is converted into turns per feet to resolve the units and the value ofohms per foot for 22 AWG is 0.162 Ω

required to be computed in order to establish overall motor performance They are

the torque constant K t and the phase resistance Rphase From these two parameters,all motor performance can be essentially derived

The K tvalue is derived for the case of RMS torque based on a trapezoidal torqueversus position profile and near-perfect commutation There is an adjustment of 10percent to achieve a reasonable value for RMS torque This value can be adjustedbased on actual torque waveforms if required

The following equation computes the K tvalue per phase as described

ET

φg=gap flux, kmaxwell

Torque constant and resistance computations are as follows:

Fig 5.43

brushless PM motor As a result, it is necessary to fix some of them and then mine the remaining ones as part of the design Which parameters to fix is up to thedesigner Usually, one has some idea about the overall motor volume allowed, thedesired output power at some rated speed, and the voltage and current available todrive the motor Based on these assumptions, Table 5.10 shows the fixed parametersassumed here

deter-The parameters given in Table 5.10 are grouped according to function deter-Therequired power or torque at rated speed, the peak counter-emf, and the maximum

coil resistance

coils/phase

* Subsection contributed by Duane C Hanselman, University of Maine at Orono.

conductor current density are measures of the motor’s input and output Topologicalconstraints include the number of phases, magnet poles, and slots per phase The airgap length, magnet length, outside stator radius, outside rotor radius, motor axiallength, core loss, lamination stacking factor, back-iron mass density, conductor resis-tivity and associated temperature coefficient, conductor-packing factor, and magnetfraction are physical parameters Magnet remanence, magnet recoil permeability,and maximum steel flux density are magnetic parameters Shoe parameters includethe slot-opening width and shoe depth fraction Finally, the winding approach must

be specified

Of the parameters in the table, it is interesting to note that the stator outsideradius, motor axial length, and rotor outside radius are considered fixed The statoroutside radius and axial length are fixed because they specify the overall motor size.The rotor outside radius is fixed because one often wishes to either specify the rotor

inertia, which increases as R4

ro, or to maximize Rro, since torque increases as R2

ro

Clearly, as Rroincreases for a fixed Rso, the area available for conductors decreases,forcing one to accept a higher conductor current density to achieve the desiredtorque Secondarily, by specifying the rotor outside radius, the design equations fol-low in a straightforward fashion, and no iteration is required to find an overall solu-tion

dimen-sional description shown in Figs 5.43 and 5.44, it is possible to identify importantgeometric parameters The various radii are associated by

show-The pole pitch at the inside surface of the stator is related to the angular pole pitchby

Jmax Maximum slot current density, A/m2

Nsp Number of slots per phase; Nsp≥N m

Γ(B, f) Steel core loss density versus flux density and frequency

kst, pbi Lamination-stacking factor and steel mass density

ρ,β Conductor resistivity and temperature coefficients

αsd Shoe depth fraction (d1+d2)/wtb

Winding approach Lap or wave, single or double layer, or other

αs= (5.32)

As shown in Fig 5.44, the stator teeth have parallel sides and the slots do not.However, the situation where the slots have parallel sides and the teeth do not isequally valid A trapezoidal-shaped slot area maximizes the winding area availableand is commonly implemented when the windings are wound randomly, when theyare wound turn by turn without any predetermined orientation in a slot (Hender-shot, 1990) On the other hand, a parallel-sided slot with no shoes is more commonlyused when the windings are fully formed prior to insertion into a slot

The unknowns in the preceding equations are the back-iron widths of the rotor

and stator wbi Given these two dimensions, all other dimensions can be found Inparticular, the total slot depth is given by

greater than zero If either of these constraints is violated, then Rroor Rsomust bechanged

the solution of the magnetic circuit The air gap flux and flux density are given byEqs (5.34) and (5.35), respectively, and can be evaluated using the fixed and knowngeometric parameters given previously

φbi=

If the flux density allowed in the back iron is Bmaxfrom the table of fixed values, thenthe preceding equation dictates that the back-iron width must be

where kstis the lamination-stacking factor

Since there are Nsm=NsppNphslots and teeth per magnet pole, the air gap flux

from each magnet travels through Nsmteeth Therefore, each tooth must carry 1/Nsm