238252169-2011-PhDCourse-SpecialElectricalMachines.pdf

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Scuola di Dottorato in Ingegneria Industriale

Attività didattica 2011 in Ingegneria Elettrotecnica

Dr. A.Dr. A. TortellaTortella

Laboratory of Electric MachinesLaboratory of Electric Machines

Dipartimento di Ingegneria ElettricaDipartimento di Ingegneria Elettrica



2

SummarySummary

• Introduction (motor classification and characteristics)• Magnetic materials (permanent magnets, SMC)

• Small electric motors

oLine-start single-phase induction and synchronous motorsoSingle-phase PM brushless motors

oC ser!omotors

• Single-phase self-e"cited alternators (lo# rate)

• Step motors (reluctance, PM and hybrid types)

• S#itched reluctance motors• Linear machines

oifferences #ith rotating electrical machines

o Induction and synchronous machineso Industry and transport applications



3

Medium and high rated motorsMedium and high rated motors• Conventional motors (I st row)

o $ormal operation if supplied directly by

the mains

o Self-starting #ithout adopting au"iliary

de!ices

o Constant steady-state tor%ue

T.J.E. Miller : “Brushless

Permanent-Magnet and

elu!tan!e Motor "rives#

"C !ommutator

(!onventional e!itation)

-'hase s*n!hronous

(!onventional e!itation)

-'hase indu!tion • Motors &or ele!tri! drives (II nd e III rd rows)

o $ormally operated using a po#er

con!erter #ith a suitable control

o &a!orable operating and manufacturing

features #ith respect to the con!entionalmotors

o Possibility of high speed operation

(reluctance type machines)PM "C !ommutator - hase h %rid-PM

drives

o 'nergy sa!ing (ma"imum process

efficiency, lo#er po#er for cooling)

o Positionspeed control

o

Impro!ement of transient phenomena(limitation of electric and mechanical

stresses, suitability for startstop

processes)

s*n!hronous

"C or sinusoidal %rushless

(PM e!itation)

+wit!hed relu!tan!e



4

Small electric motorsSmall electric motors

• Single-phase or C supply generally re%uested for both industrial and

home appliances (*+C, portable tools, #ashing machines, )

• ated po#er ranging from some W to several hundreds of W

• e%uested performances often different from the high rated machines

o Reduced weight and volume

o Reliability (application and #or.ing cycles not defined in ad!ance)

o Reduced costs and maintenance

o

Low EMC and acoustic noise emissions• esign and manufacturing issues to obtain self-starting capability (+C)

o 2-phase stator winding (main and au"iliary) #ith cage-type rotors

o o e a r-gap s ap ng mac nes

• Commutation concerns because of the low number of slots, in!ol!ing

current and tor%ue ripple (C)

• Pulsating component (bac.#ard field) and harmonics in the main field (+C)

o Efficiency and power factor lower than 3-phase machines

o ignificant tor!ue ripple (especially /nd harmonic)



5

Permanent magnetsPermanent magnets

• eplacement of the conventional e"citation in C and +C synchronous

machines

Efficiency impro!ement and volume reduction

Problems #ith flu" control and operating temperature

• igh range of applications ⇒ from some tens of 0 (ferrites) to M0machines (rare earths)

• ard magnetic materials (1rinell hardness !alues as high as 234)

Wide hysteresis cycle (high amount of magneti5ing anddemagneti5ing energy)

#igh coercivity #ith respect to the soft magnetic materials (operation

n e %ua ran o - cur!e

Low permeability at the normal operating point

• Main materials (solid often sintered form, bonded or molded)

Ceramics (strontium and barium ferrites)

$lnico (alloy of aluminum, nic.el and cobalt)

Rare earths (samarium-cobalt, neodymium-iron)



6

Examples of PM machinesExamples of PM machines

Small DC motorsSmall DC motors High speed rotor High speed rotor

Traction motor (IPM)Traction motor (IPM)Small and high rated generators for windSmall and high rated generators for wind

turbines (axial and radial flux)turbines (axial and radial flux)



!!""# characteristics# characteristics• % 6 µ4# 7 8 ⇒ $ormal hysteresis loop

• 8- cur!e ⇒ Intrinsic loop (domainorientation)

• '"perimental determination

o Increasin field in the !ir in

,eadon: and%oo/ o& small ele!tri! motors0

816µ478

Intrinsic (8, i)

material

o omain orientation (868s)

o 5ero setting (161r ≈8s)

o

in!ersion ⇒ demagneti5ingcur!e

o Cancellation of 1 (6c)

•

Magneti5ation cur!es

position (%uadrant II or III)o 99 reduction abo!e the .nee ⇒

1 → 1r

o 99 reduction belo# the .nee ⇒

1 → 1:r ; 1r

o ecoil line based on µrec



$

PM typical propertiesPM typical properties• emanen!e r < defines the PM section needed to obtain a gi!en magnetic flu"

• 1'erating remanen!e %d< 1 !alue after remo!ing the magnetic load

o Linear cur!e ⇒ 1d≡1r

o $on-linear cur!e ⇒ 1d depends on µrec related to the linear part

• oer! v * c< e nes e ma" mum a o#a e e ec r c oa # ou e ma er ademagneti5ation

• Maimum s'e!i&i! energ* or grade %#ma"< defines the minimum PM !olume to

obtain a gi!en (air-gap) energy

o =ptimal operating point to minimi5e costs (important for design purpose)

o Constraint on the tor%ue density (1m → φ+m , m → $Ilm)

• Tem erature !oe&&i!ients 'C % 'C # < define the 1 cur!e modification #hen

the operating temperature changeso >C(1r )6(d1r d>)1r ?@44 A >C(c)6(dcd>)c?@44

o e!ersible during cooling only if the cur!e remains linear (condition fi"ed by

the ma"imum temperature 'ma"), other#ise a ne# magneti5ation is needed

• Curie tem'erature 'C< defines the temperature limit after #hich the magnetic

domains lose their orientation ⇒ complete and irre!ersible demagneti5ation

%



%

&lnico&lnico

• igh temperature stability (operation up to **+ ) and relati!ely high remanence

• ,on- linear %-# curve #ith lo# c (long and thin shapes, use of magnetic shunts)

• Production #ith casting processes (for comple" shapes) or by sintering

• >roublesome machinin because of the hardness and brittleness of the material

"eter Magnet Te!hnolog*: “Permanent Magnet Catalog#

• sotropic (un-oriented particles #hich can be magneti5ed #ith any pattern) or

anisotropic (particles oriented according to the magneti5ation direction) property

'(



'(

)errites)errites

• #igh coercivity (demagneti5ation robustness), resistance to o"idation and low

electric conductivity

• Cheap material #idespread for lo# rated PM machines (no#adays considered also

for medium si5ed machines because of the cost)

•

brittleness of the material (cut effecti!ely only #ith diamond tools)

• .le"ible ferrites (combined #ith rubber ) to obtain comple" shapes or direct

incorporation #ith shaft

Brade @< anisotropic (not oriented)

Brade < readily a!ailable and !ery ine"pensi!e

Brade D< 1- cur!e .nee belo# the a"is (high le!el of resistance

to demagneti5ation)Brade E (and !arious subgrades)< more po#erful, useful for ne#design of ferrite permanent-magnet motors and actuators

Magnetic .nee

''



''

*eodymium*eodymium""+ron+ron""!oron!oron

• #ighest magnetic performances (remanence and grade)

• Low temperature and o"idation resistance (protection coating made of 5inc,

nic.el or polymers), electric conductivity (shielding re%uires), troublesome

production and machining (brittleness, to"ic materials, dangerous to handle,

amage o e! ces sens !e o g magne c e s• Production by direct particle sintering (sintered magnets) or co!ering them by

polymers as nylon or epo"y resins (bonded magnets → lo#er performances,

easier production and shaping, lo# conducti!ity)efine operating temperature

'2



'2

Samarium cobaltSamarium cobalt

• Common compositions Sm@Co and Sm/Co@D

• Less po#erful and more e"pensi!e than neodymium-iron, !ery brittle (small pieces),

very good temperature (/4 C), linear curve and corrosion resistance

• Production by sintering or by bonding #ith polymer binders (needed also in case

o arge assem es, o#er opera ng empera ure

+m2Co3 +m4Co25

'3

d dd d



'3

!onded magnets!onded magnets• Pre!ision< superior mechanical tolerances because of the elimination of the

sintering operation, finish machining not re%uired (more cost-effecti!e)• Isotro'i! %ehavior < multiple magneti5ation patterns including a"ial, diametric, radial

and multi-pole are possible

• 6orm< com acted to the net sha e throu h a die elimination of subse uent

machining, greater consistency)

• 7egligi%le edd* !urrents< insulation due to the polymer bonding

Tem'erature de'enden!eMagneti! 'ro'erties (rare earth)

'4

i ii i ff di ldi l flfl hihi



'4

Magneti,ationMagneti,ation forfor radialradial fluxflux machinesmachines

• >hree basic orientations #ith bonded magnets

2) +traight: &lu" lines are parallel and unconstrained by magnet geometry

4) adial: &lu" enters and e"its the ring along a radial !ector

) al%a!h: &lu" orientation is continuously rotating #ith respect to the magnet

http://www.mitechnolog!.com

(only one side is magneti5ed)

Im'li!ations regarding the &lu

densit* 'ro&ile and the %a!/-

iron design

+inusoidal"C %rushless

ma!hine

'5

M i iM i i - i- i



'5

Magneti,ationMagneti,ation s-e.ings-e.ing http://www.mitechnolog!.com

• +dopted to reduce cogging or noise in a motor without s&ewing armature

laminations (too comple" and e"pensi!e)

• eduction of the magnetic flu" harmonic content according to the #ell-.no#ns&ewing coefficient

( ) ( ) ( )22sin k k k hk hphp f ξξ=ξ• h< harmonic order • p< pole pairs

Eam'le o& &ituress.

o >otal amplitude reductiono Shape modification (important #hen

cogging is used for the motor

starting)

o Proper choice to a!oid e"cessi!e

decrease of the output tor%ue+teel 'lates

s ew ng

'6

/ i l b d d t/ i l b d d t



/ommercial bonded magnets/ommercial bonded magnetsare earths

TTopop ((°°C) =110C) =110--150150

µµrecrec= 1.10= 1.10--1.201.20

6errites

°° == -- 4F@

4F@

4F/ 1 G>Hinterpolation InterpF (I-III harmF) Measured

ing PM aial al%a!h magnetiation

opop

µµrecrec= 1.3= 1.3

-4F/

-4F@

-4F@

-4F4

4

4F4

4 /4 4 24 E4 @44 @/4 @4 @24 @E4

GJH

C C

'

P ffi i t l l ti lP ffi i t l l ti l



Permeance coefficient0 calculation examplePermeance coefficient0 calculation example

+ φm

ℜtφt

φt/ φt/

rushless motor with surface magnets

( ) mmm Lht r A ⋅−−⋅= 232 1π PM se!tion:

-

PM &lu

!on!entration

&a!tor t

m

A

AC =φ

r @

+mhm t

φr ℘m4r4/

r4/

mt 1 ⋅−⋅

( )000 1 r mr mm p+⋅℘=℘+℘=℘

t

ct

A

t k

0µ

⋅=ℜ

m

mrecm

h

Aµ µ 00 =℘

$ir-ga' relu!tan!e:

PM 'ermean!e:

otor 'ermean!e: 'r; < (;.;3 ÷ ;.4)otor lea/age

!oe&&i!ient

'$

P ffi i t l l ti lP ffi i t l l ti l



Permeance coefficient0 calculation examplePermeance coefficient0 calculation example

$ir-ga' &lu densit*: r t m

t B

C

B ℜ℘+= 1

φ

r t m

t φ φ

ℜ℘+=1

1

PM &lu densit*: r t r

m B Bℜ+

ℜ℘+=1

1 Magneti! !ir!uit

!hara!teristi! mt φ φ ℜ+

=1

1

=⋅ℜ℘

ℜ℘+=

⋅= rec

t m

t r

m

m

H

Bµ

µ 00

1 PC

t k C

L

Lt k C

Lt k C p

c

m

mc

mcrecr

⋅≅

+=

φ φ

φ µ 01

1

1r

Permean!e !oe&&i!ient:

PM !hara!teristi!

rec

mr m

B B H

µ µ ⋅

−−=

0

recr

m

PC

PC

B

B

µ +

=

• 1y substituting PC in the magnetic circuit

characteristic

85.0≅

r

m

B

B

PC ≈ ≈≈ ≈ (! ÷ ÷÷ ÷ ")cm

1m

P

'%

Parametric 1ariationsParametric 1ariations



Parametric 1ariationsParametric 1ariations

#ir$gap %ariation

(linear motors=

e!!entri!it*

'ro%lems)

&xternal m'm'f'

(no-load to load

!ondition short-

!ir!uit= >)

2(

Summary of PM characteristicsSummary of PM characteristics



Summary of PM characteristicsSummary of PM characteristics

• /istance point 0

* mm

• .lu" density %01++ m'

eference sies

is !on!erned *d+e

SmCo

2'

*eodymium*eodymium magnetmagnet costcost 2('(2('( http://www ndmagnets com



*eodymium*eodymium magnetmagnet costcost 2('(2('( http://www.ndmagnets.com

• Price determined by three categories

o manufacturing processo supply of its ra# materials

o re%uired performance

• Sintered $eo< anisotropic material #hose

alignment is imposed during the pressingoperation

• Isotropic bonded $eo magnets< made

from isotropic po#der magneti5ed after

molding ⇒ simpler and more economic

process, though methods #hich de!elop

greater densification conse%uently

produce higher magnetic remanence and1ther &a!tors a&&e!ting the 'ri!e

Prices of certain rare earth elements such as

• +nisotropic bonded $eo magnets< highestK.g because their fine po#der is %uite

unstable and has to be handled in a batch

process, #hich must also incorporate the

magnetic aligning field but this orientation

produces far superior magnetic properties

compared to isotropic bonded magnetsF

dysprosium or terbium) employed to enhance

the magnet ability to #ithstand more e"treme

operating or en!ironmental conditions

(a!ailability only in some regions)

Impro!ement in densification of the magnet

material andor #ith better orientation of themagnetic po#der (anisotropic sintered $eo is

!ery fa!orable)

22

Soft magnetic composites SM/Soft magnetic composites SM/



Soft magnetic composites SM/Soft magnetic composites SM/

• Inno!ati!e material adopted to produce magnetic cores of C and +Celectric machines #ith isotropic magnetic properties

• Iron particle po#der co!ered by an insulating material (organic resin,

polymers) thermally and mechanically processed to obtainuncon!entional shapes

• Main features

o

eali5ation of comple" magnetic geometries #ith 3/ flu" patterns(a"ial or trans!erse flu" machines, ) using suitable mouldso Low eddy current losses ⇒ high fre%uency (speed) applicationso Manufacturing automation (final form obtained by combining t#o

or three moulds, easy mounting of the #inding coils)o Easy to recycle (crumbling and separation from the #inding)o 'emperature stability of the magnetic properties

23

/omparison .ith laminations/omparison .ith laminations




adial &lu ma!hines

Poles &or aial &lu ma!hines

Ainear tu%ular

ma!hines

(statorassem%lies)

24





W/kgf = 50 Hz f = 100 Hz f = 200 Hz f = 400 Hz

* &ncor7 Lam735 * &ncor7 Lam735 * &ncor7 Lam735 * &ncor7 Lam735

!8(75 9 '7$5 (755 37$' '76 $7( 27% '74 7(

!8'7( 9 67($ '76 '275 47( 2675 '(7( 5$7 247(

• Moreo!er<o Lo#er mechanical resistance and thermal conductivity

o Nnsuited for reluctance machines (too high magnetiing current)

o igh production costs

o /ifficult efficiency prediction from prototypes obtained from

sample machining (loss of particle electrical insulation)

more than uadrati! more than dou%le

1SingleSingle--phase induction motorsphase induction motors



SingleSingle phase induction motorsphase induction motors

• Main winding directly supplied by the mains ⇒ presence of

a pulsating field which can be decomposed in two rotating

fields F+ and F-, with forward (+) and backward direction (-)

F F

F

M −=⋅=22

,1

F+F− ω ω/p /p

F−F+

• Induced e.m.f. E+ and E- related to the rotatin field

components which represents the rotor reaction due to theeddy current in the cae bars

R1 X 1Electromagnetic torque

Absence of a starting

X

R 12

X

I1

I12−

m

2

X m2

E +

E −

s2

R

s12

2 2 −

12

2

X 12

2V

-

!

-".#" ".# !

n/n"

$+

$−

$

torque due to the balanced

field action (s%!)

&ull tor'ue for s" (nn")

Reduced steady torque

with respect to a *symmetric

motor (neatie tor'ue due

to the backward fields)

resence of a pulsating

torque (kpθ, k%!,,)

2Starting methodsStarting methods



Starting methodsStarting methods

• 0doption of an auxiliary circuit with 90 spatial displacement

with respect to the main one and supplied by a current hain a

pase sifting possibly near to 90 (-phase windin system)

o 1fficiency, power factor and tor'ue improement (both mean

and pulsatin alues) because of the backward field reduction

!) 2plit phase

Main starting arrangementsPreliminary torque comparison

apac or s ar

3) ermanent-split capacitor

4) $apacitor start and run (two

capacitors)

#) 2haded pole

3Split phaseSplit phase



Split phaseSplit phase

Auxiliary winding having different reactance/resistance ratio

• 5ated power ! "00 #

• 6ih resistance, low inductance ⇒ open slots, small wire gauge

• 17cluded at $%& of the rated speed by a centrifual switch to limit losses

• 8wo application cateories

o '(tandard)9 startin tor'ue comparable to the rated one, low startin

current because of the fre'uent startin and lon operatin cycles

(fans, burners)

o '(pecial)9 hih startin tor'ue and currents with intermittent operation

(washin machines)

4Capacitor startCapacitor start



pp

Capacitor connected to the auxiliary winding excluded before

reaching the operating speed

Lower phase

displacement

• 5ated power ! $%0 #, hih startin tor'ue ⇒suitable for ig inertia loads

• *iger torque for a ien line current wit

respect to a split-pase motor

• apacitor ,oltage increasin with speed (as

faster as hiher is $ alue) ⇒ e7clusion at about

:"; of the synchronous speed

• Electrolytic-type capacitor more suitable mainly

for cost reason and intermittent operation

I

I a I mI’ m

I’ a

|! a | " | a |

5PermanentPermanent--split capacitorsplit capacitor



p pp p

Capacitor permanently connected to the auxiliary winding

• $ondition nearest to the pure -pase supply ⇒ better efficiency and

power factor, smoother tor'ue• .mpregnated paper capacitor suitable for continuous operation ⇒ low

,alue of because of the cost and ma7imum oltae re'uirements,

#plit capacitor

proidin startin tor'ue lower than the rated one

• Increase of the starting performance in combination with9

o 2plit-phase windin9 capacitor connected at a proper speed to aoid

an oeroltae condition (efficiency problem at the rated condition)

o $apacitor-start and run (two alue capacitors)9 startin capacitor

e7cluded at a ien speed ($start%!""<#"" µF = $perm%!<!" µF)

CapacitorCapacitor--t!pe motors "commercial data#t!pe motors "commercial data#



pp !p " #!p " #

>?@

n

>rpm@

I

>0@

(at " A)

cosϕ$

>µF@

?eiht

>k@rated

s

I

I

rated

s

8

8

rated

ma7

8

8

Capacitor start

. . . . . .

#" :"" .B ".C 3 .D # B.:

C#" :#" D.: ".CD 4 .# . #" !C

Permanent split capacitor

$Re%ersing rotation "PSC#Re%ersing rotation "PSC#



gg

#inding

A

iA i

t! t t1 ON

A +

+

#inding

)1 ON 2 ON

A

t! t t

2 ON

A)

A

φφφφA ≡≡≡≡φφφφR

t $ t %

φφφφA φφφφR

φφφφ1

t $ t &

φφφφ ≡≡≡≡φφφφR

φφφφA φφφφR

φφφφ1

t $ t % t $ t &

&'ultiple speed operation'ultiple speed operation



• Insertion of one or more

intermediate windings betweenthe line and the main windin

(same spatial position)

• Reduction of te air- a flux for

$ E3

'perating speed

a ien oltae) because of theincreased number of turns when

the intermediate windin is inserted

29 low speed

*9 hih speed

*

M

n2

E!

E

dependant on the load

characteristic L(n)

(nstable operation with

high loads and selector

switched on low speed)problem with voltage

variations*

(Shaded pole induction motorShaded pole induction motor



φφφφ(1

19 main windin

(9 shadin coil

φφφφs9 flu7 due to the coil

current

φφφφ )9 main flu7 in theφp

φp - φs

( φφφφ(

φφφφp) φφφφp3ββββ

shaded partφφφφp39 main flu7 in the

open part

ββββ9 spatial displacement

between open and

shaded parts (4#G→D"Gelectr.)

φs

- s

1s

Is

φp

α

φp + φs

Phasor diagram

Rotating direction

φpF-φs

β φp+φs

t%"

φpF-φs

β φp+φs

t%α/ω

+otating direction from

the open to the shaded part

ntroduction of two

shaded coils to

modify the rotating

direction

1)'otor characteristics'otor characteristics



Design solutions +ound,frame design )- poles*

.C! ,frame design)&,poles*

lux bridges and

notched poles0

increase lea1age

then flux in

shading coil

Tpical applications

• 8in openers

• 6ood aspirators• 2mall fans

• Hicrowae oens

• Aideo-proectors• Aideo-recorders

• 2mall pumps

• 8imers

!eneral c"aracteristics

A

• Po#er rating 9 fraction of ? to 3"=4" ?• $%%icienc 0 ".! = ".

• Po#er %actor 0 ".4 = ".D

• &peed 0 !#"" = 3""" rpm

• &i'es0 related to power (see table)

0

>cm@".B# !.C !.#B !.B! . .#4

>?@

3.4" #.44 C.CC !3.D !#.! !B.4



12Instantaneous tor+ue and currentInstantaneous tor+ue and current



D

:

".!

".!#

".

2 $ &34 2 5 loc1ed rotor

4 > m & m @ tor'ue mean alue

-".!

-"."#

"

"."#

$urrent

> 0 @

"" # !" !# " #

>G@-".

- .8or'ue

#econd harmonic components in the torque profile )often odd harmonics

because of air,gap asymmetries → 4637 mm*

8igh harmonic content in the current waveform because of the magnetic

saturation

13,ine,ine--start single phase s!nchronous motorsstart single phase s!nchronous motors



• 2trictly constant operatin speed (n % D"⋅f/p)

• ower ratins ranin from fractional # to a few 5# and speed ranin

from / rpm (with reduction ears) to 0000 rpm

• 8 ical a liances re uirin re-defined and re etiti,e wor5in c cles

$locks and timers for relay

rinters, recorders, instrumentation

?indin systems for te7tile industry,

• 5e'uirements (elf-starting with sinle-phase supply and load synchroniJation

double- hase stator rotor ca es low inertia loads

Absence of 6 excitation (small rated motors)

• Hain types different as concerns the rotor confiuration9 reluctance,

ysteresis and permanent magnet

14S!nchronous reluctance motorS!nchronous reluctance motor



θ

bb

Po#er alance (linear condition)

pe9 input electric power pem9 conerted power

pec 9 power related to the manetic fieldeceme p p p +=

didl d d

2

2

1i

d

dl cem ⋅

θ⋅=

e6m6 torque

dt d dt dt pe ⋅⋅+⋅⋅

θ=⋅⋅=⋅=

dt

diil i

d

dl il

dt

d

dt

dW p ec

ec ⋅⋅+⋅Ω⋅θ

⋅=

⋅⋅== 22

2

1

2

1

Ω⋅=⋅Ω⋅θ

⋅=−= emeceem cid

dl p p p 2

2

1

( ) ( )[ ]δ θ θ δ θ 24sin22sin22sin2

2

2, +⋅−⋅−⋅⋅= p p I L p

c bbem

9ean value C em:4 C em:& ) θ * C em:- ) θ *

( ) ( ) ( ) θ⋅+=θ⋅Λ+Λ⋅=θΛ⋅=θ p L L p N mm N

mml bbbbb

p

sbb

p

sb 2cos2cos

2,0,2,0,

22

e

( )θ⋅⋅−=θ

p L pd

dl b

b 2sin2 2,

( ) ( ) ( )δ+θ⋅=δ+ω⋅= p I t I t i bebb cos2cos2 ( ) ( )[ ]δ+θ+⋅= 22cos122 p I t i bb

Parallel connected coils

#eries connected coils

2

2

2,

0,

qd

b

qd

b

Λ−Λ=Λ

Λ+Λ=Λ

15or+ue pro.ileor+ue pro.ile



".4

".D

".:

!

inductance

Eb," Eb,

δ%"Gδ%π/4

".3

-!

-".#

"

".#

!

coil

current

"

.

Electrical angle

δ%π/4

δ%em,"

e6m6 torque

-".

-".!

"

".!

".

piCpi/43pi/#pi/4pi3pi/4pi/pi/4"

;orque production only on half a cycle

122--phase /indingsphase /indings



!

θ

!

( ) θ θ 2cos2,110,1111 ⋅+= L Ll

( ) ( ) θ π θ θ 2cos22cos 2,110,112,220,2222 ⋅−=+⋅+= L L L Ll

( ) ( ) θ π θ θ 2sin42cos 2,120,122,120,1212 ⋅+=−⋅+= L L L Ll

dentical windings

Po#er alance (linear condition)

( ) ( )

++++

++=

=+++⋅=⋅+⋅=

dii

diil

diil

diil ii

dl i

dl i

dl

il il dt

d iil il dt

d idt

d idt

d i p

m

e

12

2112

2222

111121

122

2222

111

222112221211112

21

1

2ω

ϕ ϕ

( ) ( )δ ω +⋅= t I t i m cos1

( ) ( )2cos2 π δ ω −+⋅= t I t i m

If the windins are

identical and are

supplied by a

++++

+

++=

++=

dt

dii

dt

diil

dt

diil

dt

diil

iid

dl i

d

dl i

d

dl iil il il

dt

d p m

ec

12

2112

2222

1111

21122

2222

111

2112

2

111

2

111 222

1

2

1

θ θ θ

ω

21122

1222

111

2

1

2

1ii

d

dl i

d

dl i

d

dl cem

θ θ θ ++=

memeceem c p p p ω ⋅=−=

balanced current set

(-phase balancedsymmetrical system),

the tor'ue is constant

1$Rotor con.igurationsRotor con.igurations



• (alient rotor obtained by a cae

rotor lamination, cuttin some teeth

to enerate the saliencies

d

q

• ae s ep or s ar ng an

syncroni7ation purpose

• Asymmetric teet cutting to

weaken the dependence of

starting torque on rotor position

and to limit cogging effects due todd

qFlu7 barriers

s o n poss y nu resu an

alinment tor'ue actin on the

poles)

• Increase of the reluctance effects

by insertin suitable flux barriers

q

1&Starting and stead!Starting and stead!--state operationstate operation



• 2tartin usin asynchronous tor'ue (-phase

stator windin K rotor cae)

/

• 0t the startin phase ⇒ s + A8 m + i

o 9 ulsatin s nchronous tor ue ω ω /

o A9 asynchronous tor'ue actie durin the

whole startin (edi cure / and )

o m9 load tor'ue

o i9 inertial tor'ue ⇒ LMdωm/dt

sm

• 2ynchroniJation durin the half cycle when

8

• +equirements to ease synchroni<ation9 low cae resistance ($ 0! when

speed!), low inertial loads ($i")

• 2teady-state operation with lower efficiency and power factor than an

induction motor with the same power ratin (larer mean air-ap, absenceof N$ e7citation)

sm m

1(0!steresis s!nchronous motor0!steresis s!nchronous motor



#haft

=on magnetic cylinder

with low mass brass

#tator having a &,phase

winding generating the main

field

(

• 2tator flu7 (() crossin the

rotor in two points the rotorsurface ( poles) which rotates

at the synchronous speed

8ard magnetic material )iron,

cobalt alloys: Alnico*

• u sa n e across e ro or

which enerates hysteresis

losses

R

O

µ"6

δ

O

P

(

6L

δδδδ

+otor field lagging by δ with

respect to the stator fieldbecause of the hysteresis effect

2)Electromechanical characteristicsElectromechanical characteristics



• 8or'ue almost independant from speed durin startin phase

⇒ Hain dependence on the hysteresis loop area (not on fre'uency)

⇒ Outpresence of eddy current losses

• 5otor and stator field synchronous at steady state

⇒ Qperation like a conentiona H synchronous machine⇒ 2teady-state load anle same as in transient condition

⇒ ossibility to accelerate the loads that can be drien at steady state

• $haracteristics with tor'ue on

abscissa

• u pu power ≈

• Ha7imum current and tor'ue at

startin (!. 0 e B &m)

• Ha7 efficiency 4#; at steady

state

• 2tartin/rated tor'ue ≈ !.3

21'ain'ain +uantities+uantities .rom.rom datadata--sheetssheets



Rated starting tor*ue9 tor'ue deeloped after switchin on the motor supply systemR it is not

uaranteed the reachin of synchronous speed

Running tor*ue9 tor'ue deeloped before reachin the synchronous speed (it can be related to

the ma7imum).

&nc"ronous tor*ue9 rated synchronous tor'ue

Hodel / 4 " %2tartin >&cm@ !!.3 :.3 !4.! 3!.C C".D

2ynchronous >&cm@ D.! D.! !4.! 4.C !B.C

5unnin >&cm@ 4C.3 #C. !4.! C." !"#.B

8emperature rise >G$@ 4" #" #" #" !""Input power >?@ .# 4." 4." #." :."

2peed >rpm@ !:"" (D" 6J) = !#"" (#" 6J)

!. Snidirectional, low enery consumption (.# ? = 4 A0), use for hih temperature or sealin enironments

. Snidirectional, 4 ? = #.C# A0, hih tor'ue, use for continuous operation

3. Snidirectional, 4 ? = #.C# A0, presence of anothe ear to obtain till ! round eery 3! days, low tor'ue.

4. Oi-directional, # ? = D A0, capacitor start

#. Oi-directional, : ? = !! A0, capacitor start , hih tor'ue, intermittent operation with ade'uate coolin deice

;orque values at >4 8< 5 % rpm

22E*ample /ith /ound statorE*ample /ith /ound stator



rame with cooling

holes

?eadon0 .8andboo1 of small electric motors!

@inding with concentric coils

)capacitor start*

+otor with surface Alnico ring

23Small P' motorsSmall P' motors



• 2tator with sinle-phase windin (concentrated coil) with

manetic circuit hain some asymmetries to enable thestartin

• Hs on the rotor with hih coerciity (enerally ferrites)

mounted on a manetic cylinder

• &on null Hean tor'ue only at synchronous speed

o (incroni7ation only durin alf cycle of te supply

,oltage because of the pulsatin rotor tor'ue

o 0pplication only to low inertial loads

&-,poles rotor

% • ndetermined rotating direction at startin as it depends on

%6 Cam with teeth

&6 8oo1ing system

36 +eturn spring

&

3

the initial position

o adoption of a mechanical deice (monodirectional) or

electrical one with au7iliary capacitor (bidirectional)

• &umber of *linkin positions dependant on the number of poles,

displacement between stator and rotor poles defined by theload tor'ue

24Cloc motorsCloc motors



#upply cable

+eduction gear

#tator teeth

Asymmetric distribution of

the stator teeth to limit

bearing

?eadon0 .8andboo1 of small electric motors!

cogging effect

+otor with surface P9 ring

)ferrite*

25SingleSingle--phasephase rushlessrushless motorsmotors



• Hotors enerally supplied by a square wa,e

,oltage controlled by an electronic conerter

• 2tator poles suitably saped to enable the

motor startin

• ?indin made by series-connected

concentrated coils

• 5otor H rin (ferrite or bonded rare earts)

cast on the shaft or mounted in a plastic support

to be coupled to the shaft

• Aery hih speed achieable accordin to the

ma7imum su l olta e and the load

mechanical parameters (from 4000 to 0000

rpm)

• Hain applications in small home appliances

(fans, acuum cleaner, small washin machines)

replacin uniersal or shaded pole motors to

improe reliability, noise and efficiency

2Con%entionalCon%entional startingstarting tecni+uestecni+ues



• 1ole soe saping to loc5 te rotor in a position wit respect to te winding

axis (asymmetric air-ap profile)

Cogging torque profile more regular tapered air,gap )only two opposite pea1s per period: one stable point*

2$Suppl!Suppl! !! 00--ridgeridge con%ertercon%erter

• (ingle pase rectifier wit ,oltage



• (ingle pase rectifier wit ,oltage

le,eling capacitor Adc

• 2witch commutation to obtain a 'uadrature

condition between the m.m.f. and the H

and induced bac5-emf )

• Adoption of *all sensor to detect the H

position and control accordinly the switch

commutations (a current control is alsopossible at low speed)

• 1roblematic ositionin :acti,ation of te

*all sensors because of the phase la

caused by the coil inductance at hih speed

or by manetic saturation (neatie tor'ue

must be aoided)

!) hase adancin tecni'ue

) ulse width control

;echnique % ;echnique &

2&a%e.ormsa%e.orms o. o. aa %acuum%acuum cleanercleaner motormotor

; h i % )34 d * ; i & )%&4 d ti *C ti l



;echnique % )34 advance* ;ecnique & )%&4 conduction*Conventional

+ dc

,- + . n,--- rpm

+ dc //- + . n2---- rpmN00 Noticeale tor*ue ripple ecause no current control is implemented

2(0al. 0al.--ridgeridge con%ertercon%erter suppl!suppl!



• eap solution re'uirin only two switches

• 2tator bifilar winding (subdiision in two

separate strictly coupled coils wound in

opposite direction supplied by only one

switch)• 8he double of te supplied ,oltage

applied to the windin terminals ⇒ choice of

a suitable wire insulation (double

insulated wire)

• 1ery semi-coil is supplied by the whole

current for half of the period ⇒ the double

of te turns:pole are needed to obtain te

same torque of a conentional windin

(small wire aues ⇒ difficult wirin,

resistance increase)

'vervoltage due to the non,

perfect coil coupling

3)ComparisonComparison /ith/ith anan uni%ersaluni%ersal motormotor

# ff



=mB =mB

;orque,speed 3ni4ersal Motor rus"less

8igh variation

#tiff characteristics

Efficiency,speed 3ni4ersal motor rus"less

with speed

8igher efficiency

8igh variation

with speed

31SensorlessSensorless suppl!suppl!

• 6all sensors are costly sensiti,e to



• 6all sensors are costly; sensiti,e to

temperature canges and ysteresiserrors and troublesome to place ⇒

adoption of alternatie tecni'ue which

• 0doption for small fans (room and cost

problems)

• Hain problem9 reent ariation of the

rotatin direction because of the possiblealinment positions ((/, ()

& 1 & 2

axis: force current to <ero and then supply the motor accordingthe pre,defined control technique

%* Long duration pulse with very slow current decrease )absence of oscillations

around the standstill position* ⇒ Met"od 1

&* #hort duration pulse with fast current decrease ⇒ Met"od 2

32StartingStarting processprocess ""methodmethod 1#1#

inal position



Standstill position 1

Rotor speed

p

Standstill position 2

• oc w se an coun er-c oc w se ro a on accor n o e curren pu se s gn

(possibility to modify the standstill position by !:"°)

• 2low current decrese to aoid oscillations and ibrations, which can lead to an

incorrect direction at start if the motor is supplied too soon

• Interals (t/; t< and =t; t4< suited accordin to the motor and load characteristics(friction; inertia, )

33StartingStarting processprocess ""methodmethod 2#2#



lignment due to the

cogging tor+ue

ree motion determined !

the initial energ!

• r e pu se ura on ns an # → ! ⇒ ro or a gnmen ecause o e cogg ng

torque enerated by the air-ap shapin

• $ounter-clockwise rotation indipendently from the current pulse ⇒ clockwise

direction achieable only by mirroring te air-gap sape

• Faster alignment, but some oscillations could arise around the standstill position

34SensorlessSensorless suppl!suppl! schemescheme



• ac5-emf measured at the windin teminals by an auxiliary circuit which forces

the current to Jero (interal (4-(") ⇒ 2witchin is made with hih back-emf alues,

measure with low back-emf alues (low tor'ue)

• 6etection of te 7ero e>m>f>9 all switches at QFF, use of two au7ialiary resistances

(5!, 5) much reater than the phase one, A" measure when the current is Jero

• Heasure of the delay after which the current becomes Jero with respect to the Jero

of the back-emf to decide the increase or decrease of te switc conduction

inter,al in the ne7t supply interal (interal (%)

35SingleSingle--phasephase 6C6C rushlessrushless motormotor

• P' designed to pro%ide a trape7oidal ac em. /a%e.orm



• P' designed to pro%ide a trape7oidal ac-em. /a%e.orm

• 0-ridge con%erter controlled ! a 0all sensor signal• Current regulated according to a dead eat control strateg!dead eat control strateg!

θ" θ!

θθ"+π/p

θ!+π/p

-Ima7

Ima7

"

Maximum backMaximum back e.m.f e.m.f. zone. zone

Voltage chopped at constant

frequency and varying the switch

duty cycle to limit the current

value (constantconstant ± ± IImax max )

8

Current transition determined by thevoltage equation

L

Rid

d U

L

RieU

d

di dcdc

Ω

−Ω−#=

Ω

−−#= θ

ϕ

θ

0

0

integration "ac-em. ee00

and inductance LL

pre-calculated ! 26 E' code#

8 Choice o. the leading angleleading angle θθθθθθθθ00 /ith respect to

the null-.lu* position ⇒ ma*imi7ation o. the

mean electromagnetic tor+ue

39rushless9rushless motormotor .or.or smallsmall .an s!stem.an s!stem



• 5aplacement of an e7istin ery low efficient shaded-pole motor

• 2elf-startin thanks to the H misaliment because of the presence of the shaded

coil slot (asymmetric air-ap not applied as the laminations must be unchaned)

• 0doption of a H ferrite (Or

%". 8 and 6c

%-!#! k0/m)

• 0ssumption to supply by both 6 bride (series-connected coils) or by half-bride

conerter (bifilar windin) commutated accordin a 6all sensor sinal

3$6!namic model6!namic model



( ) ( ) ( ) ( ) ( )[ ]

( ) ( ) ( ) ( ) ( )[ ]$$=

θ⋅%&&+θ⋅%&=θ

θ⋅Λ&&+θ⋅Λ&=θ'1

1

,,

0

,,

sincos,

sincos,

n

sk s sk s sem

n

k

sk s sk s s s

k ik iiT

k ik ii

lux and torque as functions of

the position and currentdetermined by interpolating the

results of magnetostatic 5$M=1k 2D analses

s s s i Lk ⋅+'⋅=' ' 0

*Correction formulas to include /D e%%ects )P9 longer

than the lamination stac1: end,winding lea1age:

lea1age fluxes from the laminations* using a set of 3D

analyses emT em T k T ⋅=*

ynam c equa ons

=umerical solution by a#imulin1 model

Analisys for the optimal

choice of the 8all sensor

position and of the winding

parameters

3&E' modelsE' models

2D model/D model ( d l t l t th ti ti fl



2D model

(nchanged mesh because of the rotationof the magneti<ation axis

(sed also to evaluate the activation flux

density

"."B

".!

J6%-C mm

-".!-"."B

-"."D

-"."3

"

"."3

"."D

-!#" -!"" -#" " #" !"" !#"

O n

> 8 @

2tator anular coordinate >G@

J6%-: mm

3('odel at stead!'odel at stead!--state speedstate speed

&c"eme %or parametric analsis



'utputcharacteristics

'ptimal sensor positioning

;emperature

changes

@inding parameters P9 characteristic

DC lin1 voltage variations

4)'agnetic .lu* model'agnetic .lu* model;otal flux ac1,emf



96m6f6θ

ncremental voltage

41Electromagnetic tor+ue modelElectromagnetic tor+ue modelourier series expansion



θ

3D correction

coefficient

96m6f6

Current dependant

coefficients

42'ain results'ain results

C"ec6 o% t"e /D correction %ormulas

( i id l t )

/D e%%ects e4aluation

( i id l t )



(sinusoidal currents) (sinusoidal currents)

!"

!# 8em >m&m@ F1H 3N2tatic measurements

-!#

-!"

-#

"

#

" D" !" !:" 4" 3"" 3D"

Interpolatin cures

• constant current supply

• Limited torque and flux increase

• +elevant end,winding lea1age

• ood areement with the measurements,

but sliht uncertainties near ma7imumtor'ue position

o appro7imated measurement set-up

o difficult improin the 3N air-ap mesh

o presence of mechanical tolerances

o uncertainties of the H and lamination

characteristics


7all sensor positioning (stead.state)



$urrent and back-emf displacement → " when

θH → -3"

30

35

40

45

25

30

]

[ m A ]

[

Ω*Tem,0

Is

Tem,0/Is2

2tartin tor'ue

re'uirements may also be

concerned (ma7imum

alue for θH → "G)

5

10

15

2025

-60 -50 -40 -30 -20 -10 0 105

10

15

[ r p m ] · 1 0 - 2 [ m N m

/ A2 ]

θH [°]

Optimal range

""

#" D"θ6 % "°

θ6 % -3"°

es 6iher current and lower

-#"

-""

-!#"

-!""

-#"

"

#"

!""

!#"

.3 .3"# .3! .3!# .3 .3# .33 .33# .34-D"

-4"

-"

"

"

> A @

> m 0 @

>s@

i s

37>4 rpm

& @ &F&4 rpm%6F @

speed and output power

in case of inaccurate 6allposition

6ih harmonic content in

both back-emf and

current waeform


Per%ormances #it" di%%erent #indings



1DC servomotorsDC servomotors



DC supply(battery)

+

- Vω

i

commutator

2NoNo--load magnetic networkload magnetic network

ℜsℜs ( )r

r r

c

ccc

+

−+=

12

21

2

1

1

2

1 β Slot effect evaluation



+ℜ0

Mm=Hc⋅hm

φ0

( )

wwr

t r w

cc

c

cc

c

++=

=′

1

2

2

1

β 1 wc

!"c

ℜt

ℜ#

ℜr ℜr

( )t w

t wr

t t

c

cc

+=5

2

2

0 $#

1-%βc

wc

d

ccc

P

wk

′−=′ β 1

Carter factor: k c =1/k’ c

Air-gap reluctance:mm

c

t w L

t k

0µ

=ℜ w m, Lm, hm: larghezza, profondità, altezza magnete

t: ampiezza traferro - k s:fattore di stipamento

PM reluctance: mmm

m

w L

h

µ =ℜ

0

eeth reluctance:d d r sd

d d

nw Lk

h

′=ℜµ

Stator !oke reluctance

: s s

s s

h L R

02µ π =ℜ "otor !oke reluctance:

r r sr

r r

h Lk R

µ π

2=ℜ

# , r ,

hs, hr : altezza statore, rotore

" s, " r : raggio medio statore, rotore

µ s, µ r , µ m : permea$ilità statore, rotore, magnete

w d , hd , µ d : larghezza, altezza, permea$ilità dente

n% d : n& medio denti sotto un magnete

3NoNo--load operationload operation

Motor driven at the speed ω ωω ω ∗ ∗∗ ∗ and with no mechanical load



( ) t sd t

m M ℜ+ℜ+ℜ+ℜ+ℜ⋅

=0

0

2

2φ **

0

*

002

ω ω φ ω φ π

⋅=⋅⋅=⋅⋅= ee K k N E

F.e.m. indotta alle spazzole

& a u a' one n se e proge o e a ens one a e spa''o e a a e oc nom na e

& Valuta'ione in se#e sperimentale #el *lusso φ0 e #ella somma #elle per#ite

meccaniche $m(ω) e nel *erro $*e(ω) #alla poten'a siluppata #al motore primo

No-load test: voltae ! applied and no mechanical load

,0 a sp

& Misura olt-amperometrica #i a. sp(,) con

ω=0 (o a+sp(,))

V /0 ω

& Misura #i ,0 con V ariabile (a #ierse elocit)

( ) ( ) ( )2

00 I R R I V P P spa fem ⋅+−⋅=+

ω ω

00 I R RV E spa ⋅+−=

ω φ

⋅=

ek

E 0

0

4

Motor operatin mode: voltae ! applied and ωωωω = cost.

Load operationLoad operation



& Corrente assorbita alle spa''ole ariabile nel tempo. a causa #el transitorio #outoalle matasse in commuta'ione ⇒ si consi#era un alore me#io , = cost

& ,potesi φ ≈ φ0 ⇒ / ≈ /0 (a parit #i ω) e ∆Vsp ≈ sp2, velocità a vuoto

Caratteristica elettromeccanica della velocit"e

spa

e

spa

K

I R R

k

I R RV +

−=

+−

= 0ω φ ω

Caratteristica elettromeccanica della coppia I K I k I N

C t t === φ φ π 2

costante

di coppia

Caratteristica meccanica ( )ω ω −+

=0

spa

et

R R

K K C

#eenerative $rakin

& Motore *atto ruotare #a un carico esterno a# una elocit ωωωω > ωωωω0 a V=cost oppure

abbassamento #i V con ω=cost

& $oten'a $ = /2, erogata erso l"alimenta'ione ⇒ ricarica batterie

%rake operatin mode

3pplica'ione #i una coppia #i carico in opposi'ione ⇒ I = (V + | E|)/(Ra+Rsp)

'orrente circa doppia di (uella allo spunto

5

& Riduzione campo nei pressi dell’asse neutro

Solutions to improve current commutationSolutions to improve current commutation



o

4celta opportuna #ella larghe''a #el magneteo 4agomatura #el tra*erro ai bor#i #el magnete

& Riduzione dell’induttanza #ell"aol imento #i armatura

o Cae meno pro*on#e

o 4celta opportuna #ella larghe''a #ell"apertura #i caa

o i#u'ione #el numero #i spire

& Spostamento del piano di commutazione in anticipo rispetto alla posi'ionenaturale

o 4 a''ole arretrate ris etto al senso #el moto er *em che aiutano

& 5so #i spazzole in elettrograite

o 3lta ca#uta #i tensione che compensa la *em in#otta nella matassa in

commuta'ione

l"inersione #ella corrente

o Vali#o per carichi praticamente costanti (, poco ariabile)

6

3mpere

!ample!ample



#ated power 1&' (

)nal*sis at n = +''' rpm,

1%6

r r e n t

76

s

C -

160

(/-8) 9m

1

%

8

(/-8) :eber

oad Fl

100

1%6

0008 000; 0006 000< 0007 000=

s

0 o r 1

- e

-8

-%

-1

0

%6/-8 0006 76/-8

s

"

2peed characteristic 'alcolo α e α dalla

C#aracteri$ation %rom measurementsC#aracteri$ation %rom measurements



φ ω

⋅⋅+−=

K

I R RV a sp

21 α α ω +⋅= I

'alcolo α )

e α *

dalla

caratteristica

elettromeccanica della

velocità

2haft tore characteristic

φ φ

φ

ω φ

K

V b I

K

R Rb K

b I K C

spa

L

−

++=

−=

43 α α +⋅= I C L

'alcolo α + e α dalla caratteristica

elettromeccanica

della coppia

all%asse

3erived antities

V

K

b R K R K

V a sp

φ α

φ α α φ 4

1

2−=−−==

100333

⋅

+−−=∆ α

φ

φ α α

K

R Rb K

spa tilizzata per verifica

&

ω0=α%

!perimental data interpolation!perimental data interpolation



21 α α ω +⋅= I

ω0 α%

3 n g u

l a r s p e e # ω

4 h a * t t o r > u e C ?

43 α α +⋅= I C L

4upplie# current ,

C0=α;

'

& Determina'ione sperimentale #elle caratteristiche elettromeccaniche ω ωω ω 45, e C 45,

(otor general per%ormances(otor general per%ormances



& @ran#e''e #eriate #alle caratteristiche elettromeccaniche

o Alusso φ φφ φ

o esisten'a e uialente #elle s a''ole #

o Coe**iciente #i attrito $

& 3ltre gran#e''e #eriate

o $oten'a assorbita 6 a = !75

o $oten'a resa 6 = C 7ω ωω ω

o $er#ite ohmiche 6 8 = 4# a 9 # sp , 75

&

o Coppia elettromagnetica C = ;7φ φφ φ 75 o $oten'a conertita 6 = C7ω ωω ω

o $er#ite meccaniche 6 m= $7ω ωω ω 2 22 2

o $er#ite nel *erro(+a##i'ionali) 6 Fe=6 a- 6 m - 6 8 - 6

1)

& 5so per motori DC a# alte prestazioni

polopoloinolucro

Con%iguration wit# *lnico +(sCon%iguration wit# *lnico +(s



5so pe oto C a# a te p esta o

& Con*igura'ioni generalmente con ! o "

poli (minor *lusso per polo)

lunghe''a per resistere agli eettidella reazione d’indotto

& 4trutture che si #i**eren'iano in base

alla *un'ione #ell"inolucro esterno

(a)# materiale non magnetico con

*un'ione #i solo contenimento

(a) (b)nuclei

c # ma er a e magne co acc a o

#olce) per ottenere la richiusura#el *lusso

& 5so anche #i magneti #i tipo

anisotropo per micromotori (e)

(c) (#)

(e)

11

B$ 'ona #el magnete

Demagneti$ation due to t#e armature m,m,%,Demagneti$ation due to t#e armature m,m,%,



B

g

pi sensibile allasmagneti''a'ione

3 uoto 4olo armatura 3 carico

$$

r

r

soracorrente

$E

$"r"

$E

& 3 causa #i una soracorrente (es inersione

#ella V per #ecelerare il motore) ⇒ % →→→→ %&

& Aorte riduzione del lusso e >uin#i #ella coppia

per l"abbassamento #ella retta #i recupero

(eri*ica #alla misura #ella elocit a uoto)

H$Hc H$E

poli

Magnete

& Contromisure

⇒ 5so #i espansioni polari (miglioramento

#istribu'ione #i *lusso. incremento costante

tempo elettrica) che sono soli#e solo se il

rotore F prio #i cae

⇒ 'raerro incrementato ai bor#i #el magnete

12

nucleomagnete

nucleo & Magneti con eleato campo coercitio

Con%iguration wit#Con%iguration wit# errite +(serrite +(s



polo ⇒ spessore ri#otto con ampia area perincrementare il *lusso

& $ossibilit #i utili''o #i espansioni

nucleo

polari () per ri#urre ancora lo

spessore #el magnete e migliorare la

concentrazione del lusso

& ucleo con unzioni magnetic*e

coinci#ente con l"inolucro #el motore

(d) (spessore #el nucleo e >uin#i peso

(a) (b)

& agnete sempre pi, lungo del paccorotorico per aumentare il *lusso e >uin#i

la coppia

& 5so anche #i magneti #i tipo anisotropo

per micromotori (c)

(c) (#)

13

polomagnete

polo magnete & 5so per motori ad alte

Comparison wit# rareComparison wit# rare--eart# +(seart# +(s



prestazioni (alto campocoercitio e in#u'ione resi#ua)

& inore spessore rispetto a#

4amario-cobalto 3lnico

3lnico con pi ampie espansioni

polari (*lusso meglio #istribuito)

& 3 parit #i area e #i lunghe''a.

lusso doppio rispetto a >uello

pro#otto #a una *errite

Comparison for a iven motor size

(3) 4mCo

() Aerrite

Gor>ueC 3 C

MaI power $maI.3 $maI.

Mechanical time

constant

Gm.3 Gm.

/lectrical time

constant

Ge.3 Ge.

16 %0 06 07

14

& Con#uttori in *ilo smaltato inseriti in

cae #i tipo semic*iuso

.otor slots and winding.otor slots and winding



cae #i tipo semic*iuso

& Cae inclinate e possibilmente in

numero eleato per ri#urre il cogging" e

>u n a rumoros

& 9umero #i ca-e dispari per ri#urre il

cogging". ma pi diicile da costruire

⇒ in genere si sceglie un numero pari

& 3 parit #i coppia ⇒ 9,a↑.φ↓ copper

motor (a) oppure 9,a↓.φ↑ iron motor ()

(a) uso con *erriti per il basso alore #i

(c)

*lusso (#enti sottili. molti con#uttori)

()uso con 3lnico (#enti larghi per non

portarli in satura'ione)

& 4istema'ione #ei con#uttori sul ondo

ca-a per applica'ioni a# alta dinamica

(basso s*ruttamento #el motore)

15*lternative structures*lternative structures& otore con con#uttori *issati al nucleo in

*erro sen'a usare le cae (slotless motor")nucleo

Motori slotless



& .assa inerzia e assenza di cogging’

& Aissaggio con#uttori problematico anche a

"

*or'a elettromagnetica& 5tili''o #i magneti a terre rare o lnico

per aere un *lusso accettabile

Aibra #i etro& otore *ormato #a un cilindro ca-o in

ira di -etro su cui sono *issati i con#uttori

Motori movin-coil

& .assissima inerzia. -elocit1 edaccelerazioni molto ele-ate e assenza di

cogging’

& Costru'ione complessa. tra*erro eleato

(uso #i 3lnico). problemi #i ra**re##amento9ucleo interno

16

Motori con cave

(otor comparison(otor comparison



Motori slotless

2 2

1SingleSingle--phasephase self self--excitedexcited alternatoralternator

Stator windings



θd• Main winding (1) connected tothe load

q

b1

33

33

b2b6

b5

b

1

2

2

1

1

1

11

1

1

1

1

11

to a capacitor (huge backwardfield component to enable self-

excitation)

Rotor windings

• Field winding (3) connected to

a diode (rectifying the induced

4 b3b72

2 2 2

1

1

emfs)

• !eparate damping cages (b1-

b2-b3-b4 e b5-b6-b7-b8 ) to

reduce "oltage harmonic

distortion without weakening

the backward field

2Self Self--excitationexcitation processprocess

• Residual magnetism ⇒ emf induced in the stator windings



• #ackward rotating field due to the stator currents ⇒ emfs induced in thefield winding (II harmonic order components)

• Non!ero mean "lu# in the field windin due to the rectified emfs ⇒ flux

and current increase in the stator winding• Final working point dependent on the magnetic saturation and on the

terminal impedances

%

&

'$

i 3 [A] λ λλ λ 3 [Wb]

*

'

+

$

$ * *$ ' '$ $

$

*

*$

'

$ * *$ ' '$ $

t [s]

3II22 growthgrowth duringduring self self--excitationexcitation ((nono--loadload))

$ (I2) $



$c

$m(I2) $σσσσ

I2Equiva!nt "ir"uit o# t$!

S!ri!s o# instants at "onstant !%"itation #u% ' ϕ ϕϕ ϕ 3("ost)*

%2&1($m&1'$σσσσ'$c)I2

%2&3ϕϕϕϕ3&3 ϕϕϕϕ3&2%2&2

($m&2'$σσσσ'$c)I2

2au%iiar& winding

I2I2&1

ϕϕϕϕ3&1

I2I2&3

m&3 σσσσ c 2

I2I2&2

ϕϕϕϕ3&2 ϕϕϕϕ3&1

I 2 increases ⇒ ϕ 3 increases⇒ both E 2 and magnetic saturation

increase (X m ↓ ) ⇒ I 2 increases further

4SteadySteady--statestate operationoperation

• Auxiliary current ,' leading the emf .' phasor

/h i l d ( t ,* i h ith th f .*)

Main current



• /hmic load (current ,* in phase with the emf .*)• .* leading the emf .' phasor (windings

displaced b *+ ) Auxiliary

current

Low phase displacement between I 1 and I 2

⇒ High backward field component

⇒ agnetic a!es of the main field rotated of

less than "# ° with respect to the d a!is

Linee di Flusso

+oad #u% in!s

Mappa Magnitudine Induzione

+oad #u% d!nsit& ,a

5OutputOutput characteristiccharacteristic

'+

'0 • 4n5'' k2A6 2n5'+ 2

,agneti ing e""ect d e to the



*%

'

'+

3

2

• ,agneti!ing e""ect due to thecombined action of ,* and ,' at light

loads

+

0

*'

* ' +

1

1A3

,cc,n

because of "oltage drop6 saturationeffects (lower flux) and machine

heating

• Icc ≈≈≈≈ 4 In to guarantee adequate

"oltage stability

• n5 6 n5 6 w ou amp ng cages

• I2 increase /ith 0 leading to higher 2

• 7hoice of 7 in order to ha"e 2*≈ cost

• 0 smaller ⇒ 1(I1) increase because of the series

magneti8ation produced by the load current and the

lower saturation with reduced ,' "alues,* 1A3

2*

,' 1A3,' 2 * 1 2 3

!ffects of the da"ping cages!ffects of the da"ping cages

$elf%e!citation process'uoa $accardo otori documentation



agnetic saturation

&eduction of the harmonic distortion100

22

6

2

5

2

4

2

3

2

2 ⋅++++++

= E E E E E E

THD nL

Wit$ da,ing "ag!s Wit$out da,ing "ag!s

.ar,oni" ord!r 1 3 5 7

.ar,oni" s!"tru,

.ar,oni" ord!r

.ar,oni" s!"tru,

#$achine$achine "odel"odel

• igh harmonic content in the air gap m m f

/ain rob!,s



• igh harmonic content in the air-gap mmf

• 0omple# rotor con"iguration

• ,agnetic saturation in the polar shoes (cross-coupling between d and

axes)

'ew method (E

magnetostatic module)E transient *nal+tical methods

o

9efinition of a generald model

o ,ntegration procedure

to sol"e the dynamical

equations

o

Multiple solutions foreach configuration

o :igh number of

simulations

o .laboration time

o

9ifficult to obtain ageneral formulation

o Approach limited to

analy8e the steady

state conditions

%

!lectric!lectric e&uationse&uations

/ain winding di

cage euialent

/inding



dt

di Li Rv cc

111 += 2

24

4+

5+

Au%iiar& winding

0i!d winding

C

i

dt

dv 22 =

13

03 −= t V ve I i η

d

q

3

1θ

5

cage euialent

/inding

i2

1

i1 3i3

i6

6

ψ

+

vk =0 k=4, 5, 6

a, ng "ag!s

Soution o# t$!

,atri% !quation

[ ] [ ] [ ] [ ]

[ ] [ ] [ ]i L

i Rv p

app ⋅=

⋅+=−

λ

λ 'on%linear set of e,uations ( +a

dependent on θ θθ θ and [i] ) to sole

numericall+

'

u"ericalu"erical solutionsolution

dt

id Li Ri Rvi R

dt

d

L L

1

111111

1 ++=+=− ϕ

L

L

RRR

i L

+′

+=′

11

111 ϕ ϕ

11

1 ''

i Rdt

d =−

ϕ 1



dt dt L R R R +=′ 1111dt

2d =−

ϕ ⋅= 22

2 1id d ϕ 2 222

dt 22 222 C dt dt

−

3333333 ir i Rvi R

dt

d d +=+=−

ϕ 03 /

1 I i

f r

f d e

R R Rr

+

−+= 33

3 ' i Rdt

d =−

ϕ 3

1,1,11,1,1 −− +′=

′−′− k k k k iiϕ ϕ

St!-b&-st! int!gration 'st! ∆∆∆∆t ( t - t -1 * ⇒ ⇒⇒ ⇒ ag!brai" !quations• ;on-linear system of equations

( ) t C iiii R

t

k k

k k

k k k ∆++−′=∆

′+′−′− −−

−−

22 1,2,2

1,2,22

2,21,2,2 ϕ ϕ ϕ

2∆t

( )6,...,3

2

1,,1,, =+

′=

∆

′−′− −−

jii

R

t

k jk j

j

k jk j ϕ ϕ

trape!oidal rule

• !olution by an iteratie

method adopting an adequate

rela#ation parameter to a"oid

numerical instability

1

Se"plifiedSe"plified approachapproach

Saturation ,od!

• 9efinition of two equi"alent m m f distributions ha"ing amplitudes ,d along



• 9efinition of two equi"alent mmf distributions ha"ing amplitudes ,d alongd axis and , along q axis6 dependant on the position6 on the winding

currents and on the eometric confi urations b suitable sha e "actors

(harmonic analysis of the air-gap mmf wa"eform)• 7alculation of the d and q permeances ΛΛΛΛd and ΛΛΛΛq 6 using the characteristics

ϕϕϕϕd(,d) and ϕϕϕϕ(,) obtained by %, analses

/utua !r,!an"! ΛΛΛΛi b!tw!!n i-t$ and -t$ windings

iqi jid iiij

( )iiiiiii ! L 0

2

)( Λ+Λ= θ

S!#-indu"tan"!

),( jiij jiij ! ! L θ θ Λ=

/utua indu"tan"!

11

Si"plifiedSi"plified approachapproach

0u% aong d and q a%!s 'no "ross-"ouing*

2alues in linear condition



( ) ( ) d d "d d d d d d # # # # ⋅Λ=⋅Λ= 0ϕ qq "qqqqqq # # # # ⋅Λ=⋅Λ= 0ϕ 2alues in linear condition

• sd6 s< reduction factorsbecause of the magnetic

saturation ("alues ≤*)

• ,nterpolation of the F.M

"alues by analytical+

$

%

&

0 1m=b>m3

functions

• ,n linear condition

Λd≈*$ Λq

• !aturation effect similar

for the two axes

*

'

$ * *$ ' '$ $ + +$ $

1A3

ϕd

F.M

ϕq

12

Si"plifiedSi"plified approachapproach

*'

*+

*%i 1A3

*

*$i* 1A3



0

* $

'+

%

' + % 0 * *' *+

1s3

-*$

-*

-$

+

% i' 1A3

!imulated

.xperimental

!imulated

.xperimental

'

'$ i 1A3

t t?* t?' t? t?+-%

-+

-'

1ms3

$

*

*$

t t?* 1ms3t?'

!imulated

.xperimental

13

Self Self andand "utual"utual inductanceinductance

( ) ( ) ( )( )k ,h

n

2jLl ∑ ξ+θθ iii

R!r!s!ntation b& ana&ti"a #un"tions



( ) ( ) ( )( )0 j

k ,h, j

k ,h

k ,h, jk ,hT2 jcosL,l ∑

=

ξ+θ=θ iii

6,..,1k ,h =

!t!r,ination o# + $ and ξ ξξ ξ $

* @eproduction of the magnetic saturation by '9 F.M magnetostatic

analyses (air-gap current sheet ⇒ total air-gap fmm)

' 7alculation of the indu"tan"! ,atri% [+a ] 6 ind!!nd!nt& #ro, θ θθ θ

related to suitable elementary circuits deri"ed from the machine windings

9efinition of a connection matrix [] for [+a ] "a"uation so that

9app: 0:t ⋅⋅⋅⋅ 9app;: ⋅⋅⋅⋅ 0:

+ ,nterpolation of the inductance "alues calculated for di""erent positions by

a Fourier series expansion

14

*ependance on*ependance on currentcurrent

-efinition of an e,uialent air%gap current distribution !(ψ) which

reproduces the resultant m.m.f. distribution



Ampereturns /%th m.m.f harmonic

$ j$ j$ j% " −= cos

2,,

=inding coefficient4osition of

magnetic axis

(h%th winding)

( ) ( )( )$

$

j$ j$ j

#

j θ ψ " ψ ! −−= sin2,,Mean airgap radius

/%th current harmonic

(h%th winding)

( ) ∑∑ == +=

qd n

&dd j j

jq

n

&dd j j

jd jr jr 1

,

1

, sincos ψ ψ ψ ! !d (ψ) !q (ψ)

&esultant d%,

current distribution(b+ elaborating the

preious e,uation)

r d e r q new state ariables (nd 03n,01 and h3 ensuresgood accurac+ and acceptable computational time)

15

!le"entary circuits!le"entary circuits

d 1

d 2 d 3

d 4

4



0u it"$ "oi

5

6

!,!n ar& ro or "o s

• 7onnection matrix 0: to transform the elementar circuits (independenton position # same model also for meshing) to the actual /indings

• <lot pitch rotation simulated b sliding the 0: coe""icients6 for a gi"en

saturation condition• 7age bars connection reproduced by three euialent /indings

!,!n ar& s a or "o qu va !n "ag! "o s

1

+o"plete circuit "odel+o"plete circuit "odel

&&&λ i02R'R

ag! windings "ir"uit

,

12 * 2 ,23 * 2 ,34 * 2



$$ &

'' ⋅$

$ &

''

−−−

−=$

$ &

''

λλλ

− 5

4

3 b52 b

2 b4

5

4

i

i

i

'R 2R 0

2R 'R 2R

02R R

dt

d

, , ,,

[ ] $$

%

&''

⋅$$

%

&''

=$$$

%

&'''

$$

%

&''

λλλ⋅!−=$

$

%

&''

λ′λ′λ′− −

6

5

4

6

5

4

6

5

41

6

5

4

i

ii

'R 00

0'R 000'R

dt

d

dt

d

9iagonali8ation matrix

onn!"tion ,atri%

*

42]0[][ "C

nn &

]0[1

13

i 4 i 5 i 6

,12 * 2 ,23 * 2 ,34 * 2

2 2 22

appapp ⋅⋅=

=

4525

][]0[r

C $

%

'

=

][]0[41 d

r

C

$

$

%

&

'

'

−−=

110000000011

001111111100][ "C

osition θ 0 45

$$

$$

%

&

''

''

−

−

=

1111

1100

0011

][ t

d C Indepen%

dant

from θ

1#

.rocedure for the inductance calculation.rocedure for the inductance calculation

=osition θθθθ

0urrents i9

St! 1

?irgap current sheet

parameters



,atri# o" the

elementar>atabase o" the

St! 1

inductanceselementar

inductances(2> %, analses)

St! 2 :r!i,inar&

st!

<et o" inductance

matri#es "or one slot

pitch rotations

St! 3

0oe""icients o" the

ourier series

e#pansion

?ctual sel" and mutual

inductances

i i θ (

) , i ( ) ( ∑ ) ) (

k , h

k , h T

2

cos L j,h,kl

+ θ

= ξ j,h,k

j!0

nh k

h,k!1,..,6

1%

/erification on co""ercial "achines/erification on co""ercial "achines

.022 / /023 / f05 n 3 rp" , 24 4 - + 13 5 "7

/ain ratings and !!"tri"a ara,!t!rsurr!nt sour"! 'wit$out "ag!s*



n03 rp" ,60244 - +0135 "7

,102# - ,20'24 - ,3053 -

,40#% "- ,501 "- ,0#% "-

,r0 - I0333 " ,f 01 "-

;uova Sa""ardo /otori sr

1'

Si"ulation at steadySi"ulation at steady--state (rated load)state (rated load)

'

+"* 123

.xperimental

!imulated

$

&$

*"' 123

.xperimental

!imulated



*

'$

-+

-

-'

-*

2*6rms 5 ''*% 2

:9 5 ++ B

2*6rms

5 '*&* 2

:9 5 +% B

$% $%$ $& $&$ $0

t 1s3

$% $%$ $& $&$ $0

t 1s3-*

-&$

-$

-'$

2'6rms 5 +%%0 2

2'6fund 5 %'+$ 2

2'6rms 5 +& 22'6fund 5 %++ 2

&

0 i 1A3 .xperimental!imulated

• 6er+ good

concordance as

*

'

+

$

%

$% $%$ $& $&$ $0

t 1s3

Mean "alue

regard load oltage

6 2rms and .i 3/• &educed 7H- for 1

• roblems8 saturation

probabl+

underestimatedau!iliar+ modeli9ation

2

8est ench8est ench

Alternator ratings

4*5$ k2A 25' 2



*

f5$ :8 n5 rpm

7apacitor 75 0F

21

Output characteristicOutput characteristic

'$

0

1

:ompound effect due to the

main winding



&

*

*$

'

+

$

%

2 * 1 2 3

4

* 1 k = 3=1

Measured

d-q model

$

$ * *$ ' '$

*

'

,* 1A3

F.M transient

-oubled calculation times than d%, model

22

$agnetic saturation reduction$agnetic saturation reduction2.8

2.4

2.0

1 6

B [T]



1.6

1.2

0.8

0.4

0.0

Initial configuration Rotor modified configuration

+onf

+

9"7:

∆/1

9/:

∆;<

9<:

8*

9<:

I1

9:

I2

9:

I3

9:

13"

9"=:

.d

9=:

Initial 32% 1%4 '' 45 23 #'3 5 ## 141'

$odified 2'2 13.6 %2 43 231 7.13 5#2 #% 1314

*iff 9<: -11 -25 - - -23 -11 11 22 -#3

: ad/usted during the parametric anal+sis toobtain the same rated no%load oltage 6 4

23

$odification of the ar connections$odification of the ar connections

C

d

C

d

C

B

Cob4

4

4

4"

2

2f 43

321 2+2+

∆∆2+

∆∆2= 3

:omparison of different connections

using an ob/ectie function to be

minimi9ed

weighted aerage of the performance inde!es



ddB 44"2 31 ∆∆enalties introduced if constraints are

;ptimi9ed connection

3 4 5 67

8

21

*$

'

'$

5

%

&

0

1 2 3

3

,nitial configuration

/ptimi8ed configuration

4

2*

not fulfilled (7H- current densities<)

Initial connection

3@4@5@6@7@

8@2@

1@

$

*

$ * *$ ' '$

*

'

+ 2 *

4 * 1 k

,* 1A3

1

StepperStepper motorsmotorsElectromechanical converters operated to obtain an incremental (not

continuous) motion ⇒ a current pulse produces a fixed rotation depending

on the stator/rotor poles



Benefits

Drawbacks

• Low efficiency• Fixed (discrete) angular step (problematic for fine rotations)

• Open control loop operation (no sensors are needed)

• Suitable for digital control (no current modulation• Economic manufacturing (simple magnetic configurations)

• Positioning errors with high frictional loads

Motor types (based on rotor configuration)

• ariable reluctance (!)

• Permanent magnet (P") → polarity#dependant tor$ue• %ybrid P"#reluctance

2

ApplicationsApplications



3

Variable reluctance stepper motors (VR)Variable reluctance stepper motors (VR)&# phase '

'

S

*

*

'

*+

+

• Salient stator and rotor

magnetic circuits (low rotor

cost and inertia → high



' ' acceleration)

'

S

*

*

*

'+

( )∂θ

∂

∂θ

θ ∂ Λ=

′= 2

2

1,F FF F

F FF F ecW C

• or$ue re ate on y to t e

reluctance -ariation

(12/8 motor 12/8 motor )

step angle ty pical operation • Unipolar current ⇒ simplification of supply

12/8 (m=3 phases) /2 (m=3 phases)

linear condition

. /0 1. 20 3.

phase ' phase * phase

• Step angle ⇒ εεεε= 2ππππ /(m⋅⋅⋅⋅Nr )

o m4 number of phase

o r 4 rotor teeth (high to reduce ε)

o np5m r 4 n6steps7re-

o displacement between the single#phasetor$ues

4

Configuration for very low step anglesConfiguration for very low step angles

/ / 82

• High number of steps without increasing

too much the number of phases (m9:)• Each stator poles subdi-ided in multiple



82p p

teeth ha-in the same itch of the rotor

/ /

1

1

1

1

8

8

2

2

ones (lower stator pole saturation )

• ondition to enable a regular motion4

stator poles

ππππ r ππππ s

2ππππq/Nr

εεεε

• Example

• Verification

maximum n!teeth for each stator pole

!ultiple!ultiple""stac#stac# VRVR stepperstepper motormotorphases ,eeth of each stator

module (;stac<=)

displaced by a stepangle with respect to the



ad>acent one (in the

?

rotor step angle)

Same effect by

displacing the rotor

teeth instead of the

stator ones

flux lines paths

benefits4 high number of steps? simple winding structure

ra!bac"s4 high inertia (1 rotors)? use of uncon-entionallaminations (see flux lines placed in the trans-erse plane)

$

StepperStepper motorsmotors wit%wit% &!&! rotorrotor '& • ,or$ue due to the interaction between the

supplie !ining fiel an #$s (r

coincident with the rotor poles)• %ipolar current operation complicating



• %ipolar current operation complicating

' @

&* @

o Aa-e dri-e (con-entional)

o Full step (higher tor$ue and current)

o %alf step dri-e (higher number of steps)

• Presence of a etent torque with no

supply which holds the rotor in position

• Benerally lo!er number of steps (higherC '

step angle) than V& motors because of

the more complicated manufacturingVR PM

'reuency 12 imp*s 4 imp*s

Step angle 1+,- . 1- 1- . /-

*

C '

C*

C '

C*

0

orueorue prouction (singleprouction (single p%asep%ase supplysupply))

( )

∑∑ == ∂∂

+∂∂

+∂∂

=∂∂

=

m

i

mii

mm

m

i

ii

miec

θ

Ψ F θ

Λ F θ

Λ F θ

,θ ,F F W' C

1

2

1

2

2

1

2

1

'i i4 m6m6f6 and permeance related to

the i#th phase self#inductance

(i5/?8?666?m)

'm m4 m6m6f6 and permeance related

to the P" flux

Linear condition



*im4 flux generated by the P" and"otor reluctance #tator reluctance $ lindricallin<ed with i#th phase

• i independent on D (magnet isotropic beha-ior

and r /)⇒ +i/+,-. (null rotor reluctance tor$ue)

• *im fundamental -aries according the function

cos(½N r (θ-2π(i-)!N s ))• m fundamental -aries according to the function

tor%ue

tor%ue

tor%ueθ

cylindrical tor%ueresu#tant

full&step supply

r

positioned in the same way with respect to the

stator teeth (m' r is the number of steps7re-)

• 'm costant and +m /+, has null mean -alue ⇒

stator reluctance tor$ue with null mean alue? but

generates a significant torque ripple worsening

the dynamic beha-ior

IB IA

&

'

@

'

&

*

@

*

reluctance tor%ue

.G H.G /10G /:.G 880G 8I.G 1/0G 13.G20G

,

ipolar supply circuitsipolar supply circuits

S/

S8S1

phas

e

Bifi#ar windings

(2 switc$es!p$ase)%nifi#ar windings (& switc$es !p$ase)



S1S2

S/ S8

tightly coupled

coils

Free#wheeling to a-oid o-er#-oltage on the turning off switch

urrent fall dependent on the

circuit time constant J 5L7!

'urrent suppression tecniues

%alf unipolar switches → cheap

supply con-erter

Aound on the same pole todecrease inductance during the

simultaneous conduction

*ul<y and expensi-e windings?

utiliKed only for a half of the

conducting period1 2 3

12

3

*ranches in parallel to the

winding4 see solutions 0?2?1



1

ComparisonComparison betweenbetween stepperstepper motormotor configurationsconfigurations

V& #$ Hbri

,or$ue7mass Low %igh %igh



$ g g

Steps7re- %igh Low high

nG switch7phase / 2 (8 if bifilar) 2 (8 if bifilar)

Efficiency Low %igh %igh

ynamicperformance

tor ue7inertia

Low %igh %igh

"anufacturing

complexity7costLow "edium#high (/) %igh

(1) depending on the , poles

11

orueorue c%aracteristicc%aracteristic• ,or$ue which can be produced without losing the step as a function of fre$uency

o Performance ecrease !ith increasing frequenc (less time to dri-e the load)

o ifferent cur-es according to the namic operation (pull#in and pull#out)



coppia di agganciamento

pull&in tor%ue

coppia di sganciamento

pull&out tor%ue

m coppia di trattenuta

holding tor%ue

campo di risposta

start&stop region campo difun4ionamento continuo

sle- range

f (n6steps7s)

12

orueorue c%aracteristicc%aracteristic pu##-in torue

• upper bound of the start#stop region (dynamic operation)

• tor$ue#fre$uency -alues that can be applied in namic conition without losing

the step (for instance? typical se$uence of starting? stopping and re-ersing rotation)



p ( ? yp $ g? pp g g )

coppia di agganciamento

pull&in tor%ue

Cmcoppia di trattenimento

holding tor%ue

f

-

• upper bound of the slew range (continuous operation)• "aximum tor$ue#fre$uency -alues that can be applied at constant frequenc

operation (without accelerating)

campo di

fun4ionamento continuo

sle- range

copp a sganc amen o

pull&out tor%ue

campo di risposta

start&stop region

f (n°passi/s)

f

t

t

13

orueorue c%aracteristicc%aracteristico#ding torue

• "aximum tor$ue with loc"e rotor which can be produced by supplying the phase

with constant current

• Aith no supply ⇒ etent torque4 maximum tor$ue due to the interaction between



pp y q $

detent tor%ue&' @'&* @*

holding tor%ue

?

a tor$ue ripple at load)

#table standstill

points (-ithout

supply)

14

orue profile in ynamic conitionorue profile in ynamic conition

2d θJ C C C

.yp! constant tor%ue as 5 varies (mean value)6 initial speed=0

*orue euation electromagnetic tor$uefrictional tor$ue

load tor$ue (effecti-e -alue)



d θJ = C - C - C load tor$ue (effecti-e -alue)

t

3namic conition ⇒ constant acceleration

⇒ ⇒2

em m 2fr

2em mfr

C - C - Cd θ 1 2∆θ 2J ∆θα = = α ∆t = ∆θ ∆t = =

J 2 α C - C - Cdt

•

#tep angle

⇒em m 2fr

m em fr

C - C - C1f < = C < C - C -2J ∆θ f

∆t 2J ∆θ

waiting time before supplying the next phase

• ,he supplying fre$uency f must be therefore lower than /7Mt4

start#stop region

1

orue profile at steayorue profile at steay""statestate

Stea4state (pull4out torque) ⇒ f5const6 ⇒ 5.2

2

d θ

d t

*orue euation



em m m emfr fr- - -

or a given $ em (same fre%uency and supply current)6$ m is higher than in dynamiccondition because of the lac+ of the inertial component

2m em frC < C - C -2J ∆θ f

Ahen fre$uency increases4

• increase of the frictional tor$ue fr N

• em decreases because of the current is decreasing as stated by the -oltage

ϕ

ϕ ∂ϕ

∂ϕ ∂ϕ ∂⇒∂ ∂

d div - ω - ×

d di dθ i dtv = Ri + = Ri + ω + × i =dt θ i dt R

• f6c6e6m6 increase with (f) ⇒ current decrease for a gi-en -oltage ⇒ em

decrease

e$uation

1$

Switc%eSwitc%e reluctancereluctance motorsmotors (SR!)(SR!)& • 3oubl salient motor with number of rotor

teeth r different form the stator one s

• ,or$ue generated only by the rotor tendency

to assume a minimum reluctance positionS



to assume a minimum reluctance positionS

1/ 8.

• Supply by unipolar s!itches with fre$uency

in-ersely proportional to the step angle• uite ifferent from the stepper V&$ (speed

control? presence of the position sensor ?

possibly continuous and smooth tor$ue?

efficiency)

ββs

r

372 :73 827/:

10

!ain!ain c%aracteristicsc%aracteristics

• Simple rotor configuration with low inertia

• Stator windings ease to manufacture• Losses mainly located in the stator? easier to

Benefits

&



• ,or$ue independent on the current polarity

(simple con-erter topology)

• Benerator operation -ery simple to obtain

• %igher operating temperature than P" motors

• ery high starting tor$ue and maximum speed• !otating direction re-ersed only modifying the

1 / 8 .

• %igh tor$ue ripple and radial forces (source of the motor noise)

• ery low air#gap length to maximiKe the tor$ue production

• %igh current ripple (need of a capaciti-e filter)

• %igh supply fre$uency for a gi-en winding utiliKation with respect to 1#phase motorsbecause of the pulsed supply (-ernier effect)

Drawbacks

1,

ApplicationsApplications (1)(1)



http//---!srdrives!co!u+/

1/


Electric motorbi+e (ectra 27)



2




21

5perating5perating principleprinciple ((linearlinear conitionconition))

L

R2 R1 R2 R2R3 R2R3

1 1 1 1

• ,rapeKoidal inductance profile

• Qseful Kone to produce tor$ue

restricted to βs (dL7dθR.4 motor @

dL7dθR.4 generator)



θβs βr #βs βs 8π7r #βr #βs

L8 L1L/

• Fa-orable conditions4 βr ≈ βs and

low unaligned inductance

• urrent wa-eform affected by both

the inductance and the bac<#emf

-ariation (especially at high speed)

obtain a constant tor%ue

operation

C8 C1

θ

C/

θ

22

ConsierationConsieration on t%eon t%e toruetorue prouctionprouction• Sign determined by the inductance deri-ati-e (position sensor is neee)

• "otor design must emphasiKe the ratio 5max /5min

• Significant tor$ue ripple because4

5/θθθθ≠≠≠≠const (magnetic saturation pole shapes)



5/θθθθ≠≠≠≠const6 (magnetic saturation ? pole shapes)

i≠≠≠≠const6 (chopping at low speed? presence of a bac<#emf at high speed)

• Phase supply r times per re-olution to ha-e continuous tor$ue ⇒ s!itching

frequenc higher than a conentional 67 machine (increased core losses? lower

flux per pulse)

∆ 22 π π θ r 6060

0

nn

p f ≡⋅=#ynchronous (p=1)

#-itching fre%uency

• Step angle4 rotation angle for each tor$ue pulse

N t r

s∆ 60 s ⋅=60

0 f N f r s ⋅=#", /7

r

N m ⋅π

=ε2

hase number

• m r pulses/rev!

• ε must be lo-er than β s to have continuous tor%ue

23

ActualActual apparentapparent inuctanceinuctance (,6$)(,6$)

H.

/..

/.'

:'

2'

i

Lapp m%T



/.'

2.

0.

3.

I.

:.

/:'

/3'

/2'

/8'

/.

8.

1.

#1.#80#8.#/0#/.#0.

θ [ ° ] Qn#aligned position 'ligned position

24

ActualActual e+m+e+m+ toruetorue ((78const78const+9 ,6$)+9 ,6$)

1.

10

em mT

/:'iSteep decrease with

high saturation

de-iation fron the



de-iation fron the

/.

/0

8.

80

/.'

/8'

/2'

/3'

rectangular profile)

.

0

. #0 #/. #/0 #8. #80 #1.

2'

:'

θ [ ° ]Qn#aligned position 'ligned position

2

':!':! simulationssimulations (,6$)(,6$)

3

2

11

"ated po-er/speed 7 +:/1;00 rpm

ength 1;3!; mm



Flux lines

Flux density map20.2°

21.7°

/$+,

0

2,

2$

SingleSingle p%asep%ase supplysupply

• Low speed operation (current

modulation)

• Supply of the next phase which

produces the maximum tor$ue

* a+

resultant tor$ue *( θ θθ θ )

single#phase tor$ue



ϕ

.G

Um

+

(step angle inter-al)

• Energy balance examination onthe ϕ @ i characteristic

, "? , "4 con-erted mechanical

energy between (#1.≤θ≤.°) and

(θ=≤θ≤θU) respecti-ely

, f 4 stored magnetic energy

/0 .

θU5#αααα

θ GT

θ=5#(αααα&ε)

#/0 #1.

A+f

O iin

AUm θ=−1.G

ϕ=

(θ5θU)

• , c 5, "&, f 4 supplied energy by

the con-erter

• ./0η ηη η 5, "7, c 4 con-ersion

efficiency

20

;esign;esign consierationconsieration

• 04 stator poles width lower than the

rotor slot width to a-oid a magnetic

short#circuit between two ad>acent

β s

β s + β r = 2 π ___

r

β s = β r

l i h li d i i



rotor poles in the unaligned position

• 24 stator poles narrower than the rotorones because the winding mounting

• 14 angle βs higher than the step angle

to a-oid null tor$ue Kones

%

7 6

β r

β s = ε

1

• Vertex 64 higher room for the winding? but remar<able effect of the flux fringing at

the pole edges (increase of the minimum inductance)• Vertex %4 high minimum inductance -alue and smaller -olume a-ailable for the

winding

• Vertex 74 higher efficiency and power density? but significant increase of the tor$ue

ripple

2,

C%oiceC%oice of of t%e polet%e pole numbernumber• "ost common combinations 372? :73? /87/. (8 poles7phase) @ /87:?/37/8 (2

poles7phase)

• High rotor poles

o %igh commutation fre$uency (core and switching losses)



o %igh importance of the current rise and fall inter-als (higher ohmic losses?

conduction o-erlap)

o Lower tor$ue ripple with high harmonic order

• 'doption of man poles/phase s 2 poles/phase

o %igher cost and winding manufacturing

o Lower filling factor (insulation? spacers) ⇒ lower power density

o Lower pole amperturns and then lower iron flux density for a gi-en air#gap

length (poor utiliKation of the magnetic material)o !educed flux lines length and unidirectional stator flux (limited core losses?

higher efficiency)

• 'doption of slotted stator poles (see ! stepper motor) in case of high number of

phases

2/

7nfluence7nfluence of of t%et%e geometricgeometric parametersparameters

r % u e < ( m =

• "ost con-enient pole arc7pitch ratio 2.#

20V with βr 5βs (higher -alues lead to

room and weight problems)t



, e a n t

=

• Stator pole arc7pole pitch more sensiti-e

as regards the mean tor$ue

ole arc >>>>> ( β s= β r )ole pitch

< . =

, e a n t o

r % u e < (

β s / β r ole arc >>>>> (stator)ole pitch

>>>>> (rotor)ole pitch

? l i g n e d i n

d u c t a n c

>>>>> (rotor)ole pitch



31

;ynamic;ynamic analysisanalysis3o#tage euation

( ) ( ) ω θ θ ∂θ

∂! ω ∂

∂! ! ω

θ ⋅+⋅=+⋅+==

==+ ,,

costcost

ik dt

diil dt

di

ii Rdt d i Rv inc

i

9ncremental *ac+&emf

* ti ind ctance coefficient



*orue euation

( )dt d C

dt d J C iC f mem

, θ=ωω=θ ++

11111 −−−− #% ω+ω

⋅−+

⋅−+

⋅− k k k k k k k k iiV V ii

Nu"erica# integration

inductance coefficient

( )

( )[ ]

2

,1

2,

22,

11

1

−−

−

ω

ω+ω=

∆θ−θ

−θ=∆ω−ω

&'θ∆

−k k k k

f mk k emk k

k k

k k inc

t

i J t

il t

C C C

4#gebraic non-#inear syste" of euations to be so#+ed

iterati+e#y for eac$ k-t$ step

32

'lu<'lu< lin#agelin#age

#/.

.

SGTθ



#1.

#8.

.63

.6:

.63

.6:

.

0

/.

/0

.

.68

6

.

.68

6

i S'T

33

StaticStatic toruetorue



.

/0

.

/.

8.

1.

..

/.

8.

1.

S(mT)em

#1.

#8.

#/.

.

0

/.

#1.

#8.

#/.

i S'T SGTθ

34

7ncremental7ncremental inuctanceinuctance

#/.

.

SGTθ

8.



#1.

#8.

2.

3.

:.

2.

3.

:.

/..

Sm%Tl inc

0

/.

/0

.

8.

.

8.

i S'T

3

ac#ac#""emf emf coefficientcoefficient

/0

8

/0

8i '

/./ /./

ra<ω



0

/.

.

/

0

/.

.

/ra<ω

#1.

#8.

#/.

.

#1.

#8.

#/.

.

SGTθ

3$

CurrentCurrent anan toruetorue waveformwaveform (1(1 p%asep%ase supplysupply))'T mT

Qseful inter-al

as concerns

the tor$ue

Low speed

(a)

(a)

production



production

ig$ speed (b)

(b)mT'T

'd-anced and

longer conduction

angle

30

ypicalypical toruetorue speespee c%aracteristicc%aracteristic

onductionangle

"ean tor$ue

%ysteresis

control

o-er conduction time



Operation with

increased -oltage

rofile suitable for

transport application

(electric vehicles)

ωb (8W1) ωb ω 'ngular speed

Switching fre$uency

limitation

3,

CommentsComments

• ery low bac<#emf ⇒ current controlled by chopping the supply -oltage

• Possibility to operate with increased -oltage ⇒ current increase ⇒ saturation

increase ⇒ higher con-erted energy ⇒ reduction of the conducting inter-al

Low speed

F li it ti f th it h t d ti t li it th it hi l



• Fre$uency limitation for the switch ⇒ current reduction to limit th switching losses

• *ase speed ωb4 highest speed -alue for which i 9 imax only by -oltage commutation

(the conduction angle θ and the maximum -oltage "'X are fixed)

ig$ speed

• Cncrease of θ by ad-ancing the phase turn on to enable a faster current rising

inc ω

• 'd-anced turn off to a-oid the operation in generator mode (dL7dθY.)

• "aximum limit on θ to a-oid mean -oltage components on an inducti-e circuit

(unlimite flux increase causing high saturation)

• ,or$ue ≈ /7ω8 with θ5cost6? because the conduction time as well as the flux are

decreased

3/

SupplySupply circuitscircuits (3(3""p%ase)p%ase) 4sy""etric bridge con+erter • Separate phase supply by two

transistors in series to the winding

(protection during faults)

• Free#wheeling for the energy

' * rigeneration during the turn#off



' * rigeneration during the turn off

• urrent control by modulating oneswitch only to reduce commutation

losses and current ripple

• ,hree le-el -oltage possible

• Switches rated according to the*?iZ *?

.ysteresis control :, control

max mum -o age -a ue

• %igh number of de-ices (high cost)

⇒ used mainly for high power and

number of phases

• urrent or -oltage reference -alue

generated by the speed loop

' '

-Z"onostable

4

VoltageVoltage anan currentcurrent waveformwaveform



40

alf alf brigebrige converterconverter

"amo 1



• omponenti per fase dimeKKati

• ,ensione di fase met[ di $uella del bus

• QtiliKKo solo con un numero pari di fasi

• omponenti dimensionati in base alla

massima tensione del bus

• ontrollo del bilanciamento del partitore

capaciti-o

Scuola di Dottorato in Ingegneria Industriale

Attività didattica 2011 in Ingegneria Elettrotecnica



Dr. A.Dr. A. TortellaTortella

Laboratory of Electric MachinesLaboratory of Electric Machines

Dipartimento di Ingegneria ElettricaDipartimento di Ingegneria Elettrica

2

ReferencesReferences

• William H. Yeadon, Alan W. Yeadon, ‘Handbook of Small Electric Motors’, McGraw-

Hill

• H.. St!ltin", E. #allenbac$, W. Amr$ein, ‘Handbook of %ractional-Horse&ower

ri'es’, S rin er

BooksBooks

• ( Ste&ina ‘Sin"le-&$ase ind)ction motors * constr)ction t$eor+ and calc)lation’



(. Ste&ina, Sin"le &$ase ind)ction motors * constr)ction, t$eor+ and calc)lation ,

$io Ma"na $+sics )blis$in"• ( Gieras, ‘ermanent ma"net motor tec$nolo"+ * desin" and a&&lications’, ew

York ekker

• /. #en0o and S. a"amori , ‘ermanent-ma"net and br)s$less dc motors’,

1ford 2larendon ress

• . Acarnle ‘Ste in motors * a )ide to t$eor and ractice’ 3EE Ste'ena e

• /. (. E. Miller, ‘4r)s$less ermanent-Ma"net and 5el)ctance Motor ri'es’ ,

1ford 2larendon ress• 5. #ris$nan, ‘Switc$ed 5el)ctance Motor ri'es 6 Modelin", Sim)lation, Anal+sis,

esi"n, and A&&lications’, 252 ress

• 3. 4oldea, S+ed A. asar, ‘7inear Act)ators and Generators’, 2ambrid"e 8ni'ersit+

ress

3

ReferencesReferencesPapersPapers

• S.#. Hon", H.#. #im, H.S. #im, and H.#. ()n", ‘/or9)e 2alc)lation of H+steresis Motor 8sin" :ector

H+steresis Model’, 3EEE /rans. on Ma"netics, :ol. ;<, o. =, ()l+ >???, && @;>-@;B

• S. 4ento)ati, C. D. C$), and . Howe, ermanent Ma"net 4r)s$less 2 Motors for 2ons)mer

rod)ctsF, t$ 3nt. 2onf. on Electric Mac$ines and ri'es, &&. @@-@>>, @-; Se&t. @, 2anterb)r+,

• C D C$) S 4ento)ati and Howe 2ontrol of Sin"le $ase &ermanent Ma"net 4r)s$less 2



• C. D. C$), S. 4ento)ati, and . Howe, 2ontrol of Sin"le-$ase &ermanent Ma"net 4r)s$less 2

ri'es for Hi"$-S&eed A&&licationsF, t$ 3EE 3nt. 2onf. on ower Electronics and :ariable S&eedri'es, &&. ;>-;;>, @-@ Se&t. >???, 7ondon, 8#

• W. Wan", C. W), W. (in and (. Yin", Startin" Met$ods for Hall-less Sin"le $ase 472 MotorF,

3E2 >??B, 5alei"$, ort$ 2arolina, 8SA, <-@? o'ember >??B

• W. Wan", C. W), W. (in and (. Yin", Sensorless 2ontrol /ec$nolo"+ for Sin"le $ase 472M4ased on t$e Windin" /ime-s$arin" Met$odF, 3E2 >??B, 5alei"$, ort$ 2arolina, 8SA, <-@?

• S. onaka and #. #esamar), ‘Anal+sis of ew 4r)s$less Self-E1cited Sin"le-&$ase S+nc$rono)s

Generator b+ %inite Element Met$od’, 3nd)str+ A&&lications Societ+ Ann)al Meetin", @>

• Andriollo, M., Martinelli G., Morini A., /ortella A., Cerbetto M., ‘erformance im&ro'ement of low-rate

sin"le-&$ase alternators’, 3EM2 >??;

• Andriollo M., e 4ortoli M., Martinelli G., Morini A., /ortella, A., ‘esi"n 3m&ro'ement of a Sin"le-

$ase 4r)s$less ermanent Ma"net Motor for Small %an A&&liances ‘, 3EEE /rans. on 3nd)strial

Electronics, :ol.B, &&. -B

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