2011_PhDCourse_SpecialElectricalMachines

(1)

Special electric machines

Scuola di Dottorato in Ingegneria Industriale

Attività didattica 2011 in Ingegneria Elettrotecnica

Special electric machines

Dr. A.

Dr. A. Tortella

Tortella

Laboratory of Electric Machines

Dipartimento di Ingegneria Elettrica

(2)

Summary

• Introduction (motor classification and characteristics)

• Magnetic materials (permanent magnets, SMC)

• Small electric motors

o

_{Line-start single-phase induction and synchronous motors}

o

_{Single-phase PM brushless motors}

o

_{DC servomotors}

• Single-phase self-excited alternators (low rate)

• Step motors (reluctance, PM and hybrid types)

• Switched reluctance motors

• Linear machines

o

_{Differences with rotating electrical machines}

o

_{Induction and synchronous machines}

(3)

3

Medium and high rated motors

• Conventional motors (Ist _row)

o Normal operation if supplied directly by the mains

o Self-starting without adopting auxiliary devices

o Constant steady-state torque

Permanent-Magnet and Reluctance Motor Drives”

• All the motors suitable for variable speed DC commutator

(conventional excitation)

3-phase synchronous (conventional excitation)

3-phase induction • Motors for electric drives (IInd_{e III}rd _rows)

o Normally operated using a power converter with a suitable control

o Favorable operating and manufacturing features with respect to the conventional motors

o Possibility of high speed operation (reluctance type machines)

PM DC commutator 3-phase hybrid-PM _{• All the motors suitable for variable speed}

drives

o Energy saving (maximum process efficiency, lower power for cooling) o Position/speed control

o Improvement of transient phenomena (limitation of electric and mechanical stresses, suitability for start/stop processes)

PM DC commutator 3-phase hybrid-PM synchronous

DC or sinusoidal brushless (PM excitation)

(4)

Small electric motors

• Single-phase or DC supply generally requested for both industrial and

home appliances (HVAC, portable tools, washing machines, …)

• Rated power ranging from some W to several hundreds of W

• Requested performances often different from the high rated machines

o

Reduced weight and volume

o

Reliability (application and working cycles not defined in advance)

o

Reduced costs and maintenance

o

Low EMC and acoustic noise emissions

• Design and manufacturing issues to obtain self-starting capability (AC)

o

2-phase stator winding (main and auxiliary) with cage-type rotors

o

Pole air-gap shaping (PM machines)

o

Pole air-gap shaping (PM machines)

• Commutation concerns because of the low number of slots, involving

current and torque ripple (DC)

• Pulsating component (backward field) and harmonics in the main field (AC)

o

Efficiency and power factor lower than 3-phase machines

(5)

Permanent magnets

• Replacement of the conventional excitation in DC and AC synchronous

machines

Efficiency improvement and volume reduction

Problems with flux control and operating temperature

⇒

• High range of applications ⇒ from some tens of W (ferrites) to MW

machines (rare earths)

• Hard magnetic materials (Brinell hardness values as high as 690)

Wide hysteresis cycle (high amount of magnetizing and

demagnetizing energy)

High coercivity with respect to the soft magnetic materials (operation

in the II° quadrant of B-H curve)

Low permeability at the normal operating point

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

Ceramics (strontium and barium ferrites)

Alnico (alloy of aluminum, nickel and cobalt)

(6)

Examples of PM machines

Small DC motors

Small DC motors High speed rotorHigh speed rotor

Traction motor (IPM)

(7)

B

B--H characteristics

H characteristics

• B = µ₀H + J ⇒ Normal hysteresis loop

• J-H curve ⇒ Intrinsic loop (domain orientation)

• Experimental determination

o Increasing H field in the virgin

Yeadon: ‘Handbook of small electric motors’

J B=µ0H+J Intrinsic (J, H_i)

o Increasing H field in the virgin material o Domain orientation (J=J s) o H zero setting (B=B r≈Js) o H inversion ⇒ demagnetizing curve o Cancellation of B (H=H c)

• Influence of the magnetic knee

Magnetization curves

• Influence of the magnetic knee

position (quadrant II or III)

o |H| reduction above the knee ⇒ B → B_r

o |H| reduction below the knee ⇒ B → B’_r< B_r

o Recoil line based on µ

(8)

PM typical properties

• Remanence B_r: defines the PM section needed to obtain a given magnetic flux • Operating remanence B_d: B value after removing the magnetic load

o Linear curve ⇒ B

d≡Br

o Non-linear curve ⇒ B

d depends on µrec related to the linear part

• Coercivity H : defines the maximum allowable electric load without the material • Coercivity H_c: defines the maximum allowable electric load without the material

demagnetization

• Maximum specific energy or grade BH_max: defines the minimum PM volume to obtain a given (air-gap) energy

o Optimal operating point to minimize costs (important for design purpose) o Constraint on the torque density (B

m → φ/Am , Hm → NI/lm)

• Temperature coefficients TC(B_r), TC(H_c): define the BH curve modification when

the operating temperature changes o TC(B

r)=(dBr/dT)/Br·100 – TC(Hc)=(dHc/dT)/Hc·100

o Reversible during cooling only if the curve remains linear (condition fixed by the maximum temperature T_max), otherwise a new magnetization is needed • Curie temperature T_C: defines the temperature limit after which the magnetic

(9)

Alnico

• High temperature stability (operation up to 550 ) and relatively high remanence • Non- linear B-H curve with low H_c (long and thin shapes, use of magnetic shunts) • Production with casting processes (for complex shapes) or by sintering

• Troublesome machining because of the hardness and brittleness of the material

Dexter Magnet Technology: “Permanent Magnet Catalog”

• Troublesome machining because of the hardness and brittleness of the material • Isotropic (un-oriented particles which can be magnetized with any pattern) or

(10)

Ferrites

• High coercivity (demagnetization robustness), resistance to oxidation and low

electric conductivity

• Cheap material widespread for low rated PM machines (nowadays considered also for medium sized machines because of the cost)

• Ceramics ferrites troublesome to machine because of the hardness and • Ceramics ferrites troublesome to machine because of the hardness and

brittleness of the material (cut effectively only with diamond tools)

• Flexible ferrites (combined with rubber) to obtain complex shapes or direct incorporation with shaft

Grade 1: anisotropic (not oriented)

Grade 5: readily available and very inexpensive

Grade 7: B-H curve knee below the H axis (high level of resistance to demagnetization)

Grade 8 (and various subgrades): more powerful, useful for new design of ferrite permanent-magnet motors and actuators

(11)

Neodymium

Neodymium--Iron

Iron--Boron

Boron

• Highest magnetic performances (remanence and grade)

• Low temperature and oxidation resistance (protection coating made of zinc, nickel or polymers), electric conductivity (shielding requires), troublesome production and machining (brittleness, toxic materials, dangerous to handle, damage of devices sensitive to high magnetic fields)

damage of devices sensitive to high magnetic fields)

• Production by direct particle sintering (sintered magnets) or covering them by polymers as nylon or epoxy resins (bonded magnets → lower performances, easier production and shaping, low conductivity)

(12)

Samarium cobalt

• Common compositions Sm₁Co₅ and Sm₂Co₁₇

• Less powerful and more expensive than neodymium-iron, very brittle (small pieces),

very good temperature (250 C), linear curve and corrosion resistance

• Production by sintering or by bonding with polymer binders (needed also in case of large assemblies, lower operating temperature)

of large assemblies, lower operating temperature)

(13)

Bonded magnets

• Precision: superior mechanical tolerances because of the elimination of the sintering operation, finish machining not required (more cost-effective)

• Isotropic behavior: multiple magnetization patterns including axial, diametric, radial and multi-pole are possible

• Form: compacted to the net shape through a die (elimination of subsequent • Form: compacted to the net shape through a die (elimination of subsequent

machining, greater consistency)

• Negligible eddy currents: insulation due to the polymer bonding

Temperature dependence

(14)

Magnetization

Magnetization for

for radial

radial flux

flux machines

machines

• Three basic orientations with bonded magnets

1) Straight: Flux lines are parallel and unconstrained by magnet geometry 2) Radial: Flux enters and exits the ring along a radial vector

3) Halbach: Flux orientation is continuously rotating with respect to the magnet

http://www.mqitechnology.com

(only one side is magnetized)

Implications regarding the flux density profile and the back-iron design Sinusoidal machine DC brushless machine machine

(15)

Magnetization

Magnetization skewing

skewing

http://www.mqitechnology.com

• Adopted to reduce cogging or noise in a motor without skewing armature laminations (too complex and expensive)

• Reduction of the magnetic flux harmonic content according to the well-known

skewing coefficient

(

)

sin

(

2 ) (

2 )

,h sk sk sk sk

hp

f

ξ

=

ξ

• h: harmonic order • p: pole pairs • ξ : skewing angle Example of fixtures 18° skewing

(

)

(

) (

)

,h sk sk sk sk _• _ξ sk: skewing angle o Total amplitude reduction

o Shape modification (important when cogging is used for the motor

starting)

o Proper choice to avoid excessive decrease of the output torque

Steel plates

(16)

Commercial bonded magnets

Rare earths T T_op_op ((°°C) =110C) =110--150 150 µ µ_rec_rec= 1.10= 1.10--1.201.20 Ferrites T T_op_op ((°°C) =80C) =80--120 120 0.1 0.15 0.2 B [T]

interpolation Interp. (I-III harm.) Measured Ring PM axial Halbach magnetization

T T_op_op ((°°C) =80C) =80--120 120 µ µ_rec_rec= 1.3= 1.3 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0 20 40 60 80 100 120 140 160 180 [°] C C

(17)

Permeance coefficient: calculation example

A_t φm

ℜ_t φ_t

φ_t/2 φ_t/2

℘ ℘

Brushless motor with surface magnets

(

_m

)

_m m

r

t

h

L

A

=

2 π

3 ⋅

₁

−

2 ⋅

(

)

[

r

t

]

(

L

t

)

A

=

2 π

3 ⋅

−

2 +

2 ⋅

+

2

PM section: Air-gap section: PM flux concentration factor t m

A

C =

_φ r₁ A_m A_t h_m _t φ_r ℘m0 ℘_r0 2 ℘_r0 2

(

)

[

r

t

]

(

L

t

)

A

_t

=

2 π

3 ⋅

₁

−

2 +

2 ⋅

_m

+

2

Air-gap section: t factor

(

₀

)

0 0 r m

1

r m m

=

℘

+

℘

=

℘

⋅

+

p

℘

t c t

A

t

k

0

µ

⋅

=

ℜ

m m rec m

h

A

µ

₀ 0

=

℘

Air-gap reluctance: PM permeance: Rotor permeance: pr0 = (0.05÷0.2) Rotor leakage coefficient

(18)

Permeance coefficient: calculation example

Air-gap flux density: r

t m t B C B ℜ ℘ + = 1 φ r t m t

φ

ℜ ℘ + = 1 1 PM flux density: r t m t r m B B ℜ ℘ + ℜ ℘ + = 1 1 Magnetic circuit characteristic m t r t

φ

ℜ

℘

+

=

1

1 =

⋅

ℜ

℘

ℜ

℘

+

=

⋅

=

_rec t m t r m m

H

B

µ

₀ ₀

1 PC

t

k

C

L

t

k

C

L

t

k

C

p

c m m c m c rec r

⋅

≅

+

=

φ φ φ

µ

0

1

• By substituting PC in the magnetic circuit B B_r PC t mℜ ℘ + 1 t r

ℜ

℘

+

1

Permeance coefficient: PM characteristic rec m r m

B

H

µ

⋅

−

=

0 rec r m

PC

B

µ

+

=

• By substituting PC in the magnetic circuit characteristic

85 .

0 ≅

r m

B

PC

≈

(5

÷

6)

H_c H PC H_m B_m

P

(19)

Parametric variations

Air-gap variation

(linear motors,

eccentricity

problems)

External m.m.f.

(no-load to load

condition,

short-circuit, …)

(20)

Summary of PM characteristics

Very interesting as far as cost/energy ratio

• Distance point P

5 mm

• Flux density B_P

100 mT

Reference sizes

Very interesting as far as cost/energy ratio is concerned

NdFe

(21)

Neodymium

Neodymium magnet

magnet cost

cost (2010)

(2010)

http://www.ndmagnets.com

• Price determined by three categories

o manufacturing process

o supply of its raw materials

o required performance

• Sintered Neo: anisotropic material whose • Sintered Neo: anisotropic material whose alignment is imposed during the pressing operation

• Isotropic bonded Neo magnets: made from isotropic powder magnetized after molding ⇒ simpler and more economic process, though methods which develop greater densification consequently

produce higher magnetic remanence and hence better price performance

Other factors affecting the price

Prices of certain rare earth elements (such as _{hence better price performance}

• Anisotropic bonded Neo magnets: highest $/kg because their fine powder is quite unstable and has to be handled in a batch process, which must also incorporate the magnetic aligning field; but this orientation produces far superior magnetic properties compared to isotropic bonded magnets. Prices of certain rare earth elements (such as

dysprosium or terbium) employed to enhance the magnet ability to withstand more extreme operating or environmental conditions

(availability only in some regions)

Improvement in densification of the magnet material and/or with better orientation of the magnetic powder (anisotropic sintered Neo is very favorable)

(22)

Soft magnetic composites (SMC)

• Innovative material adopted to produce magnetic cores of DC and AC

electric machines with isotropic magnetic properties

• Iron particle powder covered by an insulating material (organic resin,

polymers) thermally and mechanically processed to obtain

unconventional 3D shapes

• Main features

o

Realization of complex magnetic geometries with 3D flux patterns

(axial or transverse flux machines, …) using suitable moulds

o

Low eddy current losses ⇒ high frequency (speed) applications

o

Manufacturing automation (final form obtained by combining two

or three moulds, easy mounting of the winding coils)

o

Easy to recycle (crumbling and separation from the winding)

o

Temperature stability of the magnetic properties

(23)

Comparison with laminations

Radial flux machines

Poles for axial flux machines

Linear tubular machines

(stator

(24)

Comparison with laminations

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

GKN – Ancor. Lam.35 GKN – Ancor. Lam.35 GKN – Ancor. Lam.35 GKN – Ancor. Lam.35

B=0.5 T 1.85 0.55 3.81 1.6 8.0 2.9 17.4 7.0

B=1.0 T 6.08 1.6 12.5 4.0 26.5 10.0 58.7 24.0

more than quadratic

• Moreover:

o

Lower mechanical resistance and thermal conductivity

o

Unsuited for reluctance machines (too high magnetizing current)

o

High production costs

o

Difficult efficiency prediction from prototypes obtained from

sample machining (loss of particle electrical insulation)

(25)

Single

Single--phase induction motors

phase 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 (-)

( )

t F t p F

(

p t

)

F

(

p t

)

F

θ

_, = _cos

ω

⋅_cos

θ

= M _cos

θ

−

ω

+ M _cos

θ

+

ω

F

( )

t F t p

(

p t

)

(

p t

)

F M M M

ω

θ

ω

θ

ω

θ

= ⋅ = − + cos + 2 cos 2 cos cos , 1

F

₊

F

−

ω ω

/p /p

F

₋

F

₊

• Induced e.m.f. E

₊

and E

_-

related to the rotating field

components which represents the rotor reaction due to the

eddy current in the cage bars

R R I 1 X1 I₁₂₊ Electromagnetic torque Absence of a starting X R₁₂ X I₁ I12+ I₁₂₋ m 2 X_m 2 E₊ E₋ s 2 R s 12 2 2 − 12 2 X₁₂ 2 V -1 -0.5 0 0.5 1 n/n₀ C+ C− C Absence of a starting torque due to the balanced

field action (s=1)

Null torque for s>0 (n<n₀)

Reduced steady torque

with respect to a ‘symmetric’ motor (negative torque due to the backward fields)

Presence of a pulsating

(26)

Starting methods

• Adoption of an auxiliary circuit with 90 spatial displacement

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

phase shifting possibly near to 90 (2-phase winding system)

o

Presence of a starting torque

o

Presence of a starting torque

o

Efficiency, power factor and torque improvement (both mean

and pulsating values) because of the backward field reduction

1) Split phase

2) Capacitor start

Main starting arrangements

Preliminary torque comparison

2) Capacitor start

3) Permanent-split capacitor

4) Capacitor start and run (two

capacitors)

5) Shaded pole

(27)

Split phase

Auxiliary winding having different reactance/resistance ratio

• Rated power < 400 W

• High resistance, low inductance ⇒ open slots, small wire gauge

• Excluded at 75% of the rated speed by a centrifugal switch to limit losses

• Two application categories

o

‘Standard’: starting torque comparable to the rated one, low starting

current because of the frequent starting and long operating cycles

(fans, burners)

o

‘Special’: high starting torque and currents with intermittent operation

(washing machines)

(28)

Capacitor start

Capacitor connected to the auxiliary winding excluded before

reaching the operating speed

Lower phase displacement

• Rated power < 750 W, high starting torque ⇒

suitable for high inertia loads

• Higher torque for a given line current with

respect to a split-phase motor

• Capacitor voltage increasing with speed (as

faster as higher is C value) ⇒ exclusion at about

80% of the synchronous speed

• Electrolytic-type capacitor more suitable mainly

for cost reason and intermittent operation

I

I_a Im

I’_m

I’_a

(29)

Permanent

Permanent--split capacitor

split capacitor

Capacitor permanently connected to the auxiliary winding

• Condition nearest to the pure 2-phase supply ⇒ better efficiency and

power factor, smoother torque

• Impregnated paper capacitor suitable for continuous operation ⇒ low

value of C because of the cost and maximum voltage requirements,

providing starting torque lower than the rated one

Split capacitor

providing starting torque lower than the rated one

• Increase of the starting performance in combination with:

o

Split-phase winding: capacitor connected at a proper speed to avoid

an overvoltage condition (efficiency problem at the rated condition)

o

Capacitor-start and run (two value capacitors): starting capacitor

(30)

Capacitor

Capacitor--type motors (commercial data)

type motors (commercial data)

P [W] n [rpm] I [A] (at 220 V) cosϕ C [µF] Weight [kg] 92 2700 1.75 0.7 2.33 2.5 1.8 20 6.1 rated s I I rated s T T rated max T T

Capacitor start

92 2700 1.75 0.7 2.33 2.5 1.8 20 6.1 250 2800 2.9 0.72 3 2.6 2 25 9.8 750 2850 6.8 0.76 4 2.5 2.2 50 17

(31)

Reversing rotation (PSC)

Winding A

C

1

2 i

_A

i

_B t₁ t₂ t 1 ON A + C

i

B + C Winding B

1 B’

1 ON _{2 ON}

i

_B

i

_A t₁ t₂ t 2 ON

B

A’

A

φφφφ

_A

≡≡≡≡

φφφφ

_R t = t₁

φφφφ

_A

φφφφ

R

φφφφ

_P t = t₂

φφφφ

_B

≡≡≡≡

φφφφ

_R

φφφφ

_A

φφφφ

R

φφφφ

_P t = t₁ t = t₂

(32)

Multiple speed operation

• Insertion of one or more

intermediate windings between

the line and the main winding (same spatial position)

• Reduction of the air-gap flux (for

C

_L

3

Operating speed

dependant on the load

• Reduction of the air-gap flux (for a given voltage) because of the increased number of turns when the intermediate winding is inserted

L: low speed H: high speed

H

M

n

L

₁

L

₂

dependant on the load

_{characteristic L(n)}

Unstable operation with

high loads and selector

switched on low speed

(problem with voltage

variations)

(33)

Shaded pole induction motor

φφφφ_S

P

P: main winding S: shading coil

φφφφ_s: flux due to the coil current

φφφφ_p’: main flux in the

-φs φ ’ φp”

φ

_p

” -

φ

_s S φφφφS φφφφ_p’ _ββββ φφφφ_p” p shaded part

φφφφ_p”: main flux in the

open part

ββββ: spatial displacement between open and shaded parts (45°→60° electr.) φs -φs Es I_s φp’

α

φ

_p

’ + φ

_s Phasor diagram

φ

r

φ

r

Rotating direction

φ

r

φ

p

”-φ

s β

φ

p

’+φ

s t=0

φ

p

”-φ

s β

φ

_p

’+φ

_s t=α/ω

φ

r

Rotating direction from the open to the shaded part

Introduction of two shaded coils to modify the rotating direction

(34)

Motor characteristics

Design solutions

_{Round-frame design (4 poles)}

‘C’ -frame design (2-poles)

Flux bridges and notched poles: increase leakage then flux in shading coil

Typical applications

• Tin openers • Hood aspirators • Small fans • Microwave ovens • Video-projectors • Video-recorders • Small pumps • Timers

General characteristics

A

General characteristics

• Power rating: fraction of W to 30–40 W • Efficiency: 0.1 – 0.2

• Power factor: 0.4 – 0.6 • Speed: 1500 – 3000 rpm

• Sizes: related to power (see table)

A

[cm] 0.95 1.27 1.59 1.91 2.22 2.54 P

(35)

Example motor

Shaded coil Main winding Saturable bridge ₅ 10 15 20 20 40 60 80 100 120 [mNm] [%] [W] [mA] torque efficiency input power current Hole for bearing support Aluminium bars 0 0 5 20 0 2 4 6 8 10 0 500 1000 1500 2000 2500 3000 [rpm]

torque (ball bearings) efficiency (ball bearings) torque (standard bearings) efficiency (standard bearings) [mNm] [%]

• Rated voltage/power 230 V/1 W, stack length 12 mm, resistance 750 Ω

• 13 bars aluminum cage,

skewed slots

• Locked rotor and running tests

0 0 500 1000 1500 2000 2500 3000 0 3 6 9 12 15 18 130 150 170 190 210 2300 20 40 60 80 100 120 [m N m ] [ W ] [m A ] [V] torque input power current ≈ linear ≈quadratic

(36)

Instantaneous torque and current

6 8 0.1 0.15 0.2

V = 230 V – locked rotor

2 4 [m N m

] torque mean value

-0.15 -0.1 -0.05 0 0.05 Current [A ] 0 0 5 10 15 20 25 [°] -0.2 -0.15 Current Torque

Second harmonic components in the torque profile (often odd harmonics

because of air-gap asymmetries

→

0.35 mm)

High harmonic content in the current waveform because of the magnetic

saturation

(37)

Line

Line--start single phase synchronous motors

start single phase synchronous motors

• Strictly constant operating speed (n = 60⋅f/p)

• Power ratings ranging from fractional W to a few kW and speed ranging

from 1 rpm (with reduction gears) to 20000 rpm

• Typical appliances requiring pre-defined and repetitive working cycles

Clocks and timers for relay

Printers, recorders, instrumentation

Winding systems for textile industry, …

• Requirements

Self-starting with single-phase supply and load synchronization

(double-phase stator, rotor cages, low inertia loads)

Absence of DC excitation (small rated motors)

• Main types different as concerns the rotor configuration: reluctance,

(38)

Synchronous reluctance motor

θ

b b’

Power balance (linear condition)

p_e: input electric power p_em: converted power

p_ec: power related to the magnetic field ec em e

p

=

+

( )

l

i

dl

i

l

i

di

d

i

d

i

p

=

⋅

ϕ

=

⋅

=

⋅

Ω

⋅

2

+

⋅

2

1 i

d

dl

c

_em

⋅

θ

⋅

=

e.m. torque

( )

dt

di

i

l

i

d

dl

i

l

dt

d

i

dt

d

i

p

_e

⋅

Ω

⋅

+

⋅

θ

=

⋅

=

ϕ

⋅

=

2

dt

di

i

l

i

d

dl

i

l

dt

d

dt

dW

p

_ec ec

⋅

Ω

⋅

+

⋅

θ

⋅

=













_⋅

=

2 2

2

1

2

1 Ω

⋅

=

⋅

Ω

⋅

θ

⋅

=

−

=

_e _ec _em em

i

c

d

dl

p

2

1

Sinchronous speed (ωωωω_e=pΩΩΩΩ)

( )

θ

[

sin2

δ

2 sin2

θ

2 sin

(

4

θ

2

δ

)

]

2 2 2 , ⋅ ⋅ − ⋅ − ⋅ + = p L I p p c_em _b _b

Mean value C_em,0 C_em,2(θ) C_em,4(θ)

( )

θ = ⋅Λ

( )

θ = N ⋅

(

Λ + Λ ⋅ pθ

)

= L + L ⋅ pθ m m N m m l _b _b _b _b _b p s b b p s b ,0 ,2 cos2 ,0 ,2 cos2 2 2 Sinchronous speed (ωωωω_e=pΩΩΩΩ)

(

θ

)

⋅ ⋅ − = θ p L p d dl b b ₂ _sin ₂ 2 ,

( )

t = I ⋅

(

ω t +δ

)

= I ⋅

(

pθ+δ

)

i_b 2 _b cos _e 2 _b cos ib2

( )

t = Ib2 ⋅

[

1+cos

(

2pθ+2δ

)

]

Parallel connected coils Series connected coils

2 2 2 , 0 , q d b q d b Λ − Λ = Λ Λ + Λ = Λ

(39)

Torque profile

0.2 0.4 0.6 0.8 1

inductance

L

_b,0

L

_b,2

δ=0°

δ=π/4

δ=0°

_C

0.3 -1 -0.5 0 0.5 1

coil

current

0 0.2 Electrical angle

δ=π/4

δ=0°

_C

_em,0

e.m. torque

-0.2 -0.1 0 0.1 0.2 2pi 7pi/4 3pi/2 5pi/4 pi 3pi/4 pi/2 pi/4 0

(40)

2 2--phase windings

phase windings

1 θ 1 2

l

₁₁

( )

θ

=

L

₁₁_,₀

+

L

₁₁_,₂

⋅

cos

2 θ

( )

θ

₂₂_,₀ ₂₂_,₂

cos

2 (

θ

π

2 )

₁₁_,₀ ₁₁_,₂

cos

2 θ

22

=

L

+

L

⋅

+

=

L

−

L

⋅

l

( )

θ

₁₂_,₀ ₁₂_,₂

cos

2 (

θ

π

4 )

₁₂_,₀ ₁₂_,₂

sin

2 θ

12

=

L

+

L

⋅

−

=

L

+

L

⋅

l

Identical windings 2

Power balance (linear condition)

(

)

(

)

      ₊ + + +       ₊ ₊ = = + + + ⋅ = ⋅ + ⋅ = dt di i dt di i l dt di i l dt di i l i i d dl i d dl i d dl i l i l dt d i i l i l dt d i dt d i dt d i p m e 1 2 2 1 12 2 2 22 1 1 11 2 1 12 2 2 22 2 1 11 2 22 1 12 2 2 12 1 11 1 2 2 1 1 2 θ θ θ ω ϕ ϕ

( )

t

=

I

⋅

(

ω

t

+

δ

)

i

₁ _m

cos

( )

cos

(

2 )

2

t

=

I

⋅

ω

t

+

δ

−

π

i

_m

If the windings are

identical and are

supplied by a     + + + +     + + = dt i dt i l dt i l dt i l i i d i d i d m 1 2 2 1 2 111 22 2 12 1 2 θ θ θ ω       ₊ + + + +       ₊ ₊ =       ₊ ₊ = dt di i dt di i l dt di i l dt di i l i i d dl i d dl i d dl i i l i l i l dt d p m ec 1 2 2 1 12 2 2 22 1 1 11 2 1 12 2 2 22 2 1 11 2 1 12 2 1 11 2 1 11 2 2 2 1 2 1 θ θ θ ω 2 1 12 2 1 22 2 1 11 2 1 2 1 i i d dl i d dl i d dl c_em θ θ θ + + = m em ec e em p p c p = − = ⋅ω

balanced current set

(2-phase balanced symmetrical system), the torque is constant

(41)

Rotor configurations

• Salient rotor obtained by a cage rotor lamination, cutting some teeth to generate the saliencies

• Cage is kept for starting and

d

q

• Cage is kept for starting and

synchronization purpose

• Asymmetric teeth cutting to weaken the dependence of

starting torque on rotor position

and to limit cogging effects due to slotting (possibly null resultant

d

q

Flux barriers

slotting (possibly null resultant alignment torque acting on the poles)

• Increase of the reluctance effects by inserting suitable flux barriers

q

(42)

Starting and steady

Starting and steady--state operation

state operation

• Starting using asynchronous torque (2-phase

stator winding ↔ rotor cage)

1

2 • At the starting phase ⇒ C

_s

+ C

_A

= C

_m

+ C

_i

o

C

s

: pulsating synchronous torque (ω

m

≠ω

0

/p)

o

C

s

: pulsating synchronous torque (ω

m

≠ω

0

/p)

o

C

A

: asynchronous torque active during the

whole starting (vedi curve 1

and 2)

o

C

m

: load torque

o

C

i

: inertial torque ⇒ J·dω

m

/dt

C

_sm

• Synchronization during the half cycle when

reluctance torque is accelerating ⇒ C

_sm

=C

_m

• Requirements to ease synchronization: low cage resistance (C

_A

↑ when

speed↑), low inertial loads (C

_i

↓)

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

induction motor with the same power rating (larger mean air-gap, absence

of DC excitation)

(43)

Hysteresis synchronous motor

Shaft

Non magnetic cylinder with low mass (brass) Stator having a 2-phase winding generating the main field

S

• Stator flux (S) crossing the

rotor in two points the rotor

surface (2 poles) which rotates

at the synchronous speed

• Pulsating field across the rotor

with low mass (brass)

Hard magnetic material (iron-cobalt alloys, Alnico)

• Pulsating field across the rotor

which generates hysteresis

losses

R

B µ₀H δ B δ

S

H δ J

δδδδ

Rotor field lagging by

δ

with

respect to the stator field

(44)

Electromechanical characteristics

• Torque almost independant from speed during starting phase

⇒ Main dependence on the hysteresis loop area (not on frequency)

⇒ But…presence of eddy current losses

• Rotor and stator field synchronous at steady state

⇒ Operation like a conventiona PM synchronous machine

⇒ Steady-state load angle same as in transient condition

⇒ Possibility to accelerate the loads that can be driven at steady state

• Characteristics with torque on abscissa

• Output power≈ 20 W • Output power≈ 20 W

• Maximum current and torque at starting (1.2 A e 9 Nm)

• Max efficiency 45% at steady state

(45)

Main

Main quantities

quantities from

from data

data--sheets

sheets

Rated starting torque: torque developed after switching on the motor supply system; it is not

guaranteed the reaching of synchronous speed

Running torque: torque developed before reaching the synchronous speed (it can be related to

the maximum).

Synchronous torque: rated synchronous torque

Model 1 2 3 4 5 Starting [Ncm] 11.3 28.3 14.1 31.7 70.6 Synchronous [Ncm] 26.1 26.1 14.1 24.7 19.7 Running [Ncm] 47.3 57.2 14.1 72.0 105.9 Temperature rise [°C] 40 50 50 50 100 Input power [W] 2.5 4.0 4.0 5.0 8.0 Speed [rpm] 1800 (60 Hz) – 1500 (50 Hz)

1. Unidirectional, low energy consumption (2.5 W – 4 VA), use for high temperature or sealing environments 2. Unidirectional, 4 W – 5.75 VA, high torque, use for continuous operation

3. Unidirectional, 4 W – 5.75 VA, presence of anothe gear to obtain till 1 round every 31 days, low torque. 4. Bi-directional, 5 W – 6 VA, capacitor start

5. Bi-directional, 8 W – 11 VA, capacitor start , high torque, intermittent operation with adequate cooling device

(46)

Example with wound stator

Frame with cooling holes

Winding with concentric coils (capacitor start)

(47)

Small PM motors

• Stator with single-phase winding (concentrated coil) with magnetic circuit having some asymmetries to enable the starting

• PMs on the rotor with high coercivity (generally ferrites) mounted on a magnetic cylinder

mounted on a magnetic cylinder

• Non null Mean torque only at synchronous speed

o Sinchronization only during half cycle of the supply

voltage because of the pulsating rotor torque

o Application only to low inertial loads

24-poles rotor

1 _{• Undetermined rotating direction at starting as it depends on}

the initial position

1. Cam with teeth 2. Hooking system 3. Return spring 2

3

the initial position

o adoption of a mechanical device (monodirectional) or electrical one with auxiliary capacitor (bidirectional)

• Number of ‘linking positions’ dependant on the number of poles, displacement between stator and rotor poles defined by the

(48)

Clock motors

Supply cable Reduction gear Stator teeth Asymmetric distribution of the stator teeth to limit cogging effect

bearing

cogging effect

Rotor with surface PM ring (ferrite)

(49)

Single

Single--phase

phase brushless

brushless motors

motors

• Motors generally supplied by a square wave

voltage controlled by an electronic converter

• Stator poles suitably shaped to enable the motor starting

• Winding made by series-connected

concentrated coils

• Rotor PM ring (ferrite or bonded rare earths) cast on the shaft or mounted in a plastic support to be coupled to the shaft

• Very high speed achievable according to the maximum supply voltage and the load

maximum supply voltage and the load

mechanical parameters (from 3000 to 20000

rpm)

• Main applications in small home appliances

(fans, vacuum cleaner, small washing machines) replacing universal or shaded pole motors to

(50)

Conventional

Conventional starting

starting tecniques

tecniques

• Pole shoe shaping to lock the rotor in a position with respect to the winding

axis (asymmetric air-gap profile)

Cogging torque profile more regular tapered air-gap (only two opposite

peaks per period, one stable point)

(51)

Supply

Supply by

by H

H--bridge

bridge converter

converter

• Single phase rectifier with voltage

leveling capacitor V_dc

• Switch commutation to obtain a quadrature condition between the m.m.f. and the PM

field (phase concordance between current field (phase concordance between current

and induced back-emf)

• Adoption of Hall sensor to detect the PM position and control accordingly the switch commutations (a current control is also possible at low speed)

• Problematic positioning/activation of the • Problematic positioning/activation of the

Hall sensors because of the phase lag

caused by the coil inductance at high speed or by magnetic saturation (negative torque must be avoided)

1) Phase advancing tecnique

2) Pulse width control

(52)

Waveforms

Waveforms of

of a

a vacuum

vacuum cleaner

cleaner motor

motor

Technique 1 (30 advance) Tecnique 2 (120 conduction) Conventional

V_dc=50 V - n=5000 rpm

V_dc=330 V - n=20000 rpm

(53)

Half

Half--bridge

bridge converter

converter supply

supply

• Cheap solution requiring only two switches • Stator bifilar winding (subdivision in two

separate strictly coupled coils wound in

opposite direction supplied by only one opposite direction supplied by only one

switch)

• The double of the supplied voltage

applied to the winding terminals ⇒ choice of a suitable wire insulation (double

insulated wire)

• Every semi-coil is supplied by the whole current for half of the period ⇒ the double current for half of the period ⇒ the double

of the turns/pole are needed to obtain the same torque of a conventional winding

(small wire gauges ⇒ difficult wiring, resistance increase)

Overvoltage due to the non-perfect coil coupling

(54)

Comparison

Comparison with

with an

an universal

universal motor

motor

[Nm] [Nm]

Torque-speed

Universal Motor Brushless

High variation with speed

Stiff characteristics

[%] [%]

Efficiency-speed

Universal motor Brushless

with speed

Higher efficiency

[%] [%]

High variation with speed

(55)

Sensorless

Sensorless supply

supply

• Hall sensors are costly, sensitive to

temperature changes and hysteresis errors and troublesome to place ⇒

adoption of alternative tecnique which enable sensor removal

enable sensor removal

• Adoption for small fans (room and cost problems)

• Main problem: Prevent variation of the

rotating direction because of the 2 possible alignment positions (S₁, S₂)

Current pulse wide enough to align the PM with the winding

S₁ S₂

Current pulse wide enough to align the PM with the winding

axis, force current to zero and then supply the motor according

the pre-defined control technique

1) Long duration pulse with very slow current decrease (absence of oscillations around the standstill position)

⇒

Method 1

(56)

Starting

Starting process

process ((method

method 1)

1)

Standstill position 1

Rotor speed

Final position

Standstill position 2

• Clockwise and counter-clockwise rotation according to the current pulse sign • Clockwise and counter-clockwise rotation according to the current pulse sign

(possibility to modify the standstill position by 180°)

• Slow current decrese to avoid oscillations and vibrations, which can lead to an incorrect direction at start if the motor is supplied too soon

• Intervals (t₁, t₂) and (t₂, t₃) suited according to the motor and load characteristics

(57)

Starting

Starting process

process ((method

method 2)

2)

Alignment due to the cogging torque

Free motion determined by the initial energy

• Brief pulse duration (instant t → t ) ⇒ rotor alignment because of the cogging • Brief pulse duration (instant t₅ → t₁) ⇒ rotor alignment because of the cogging

torque generated by the air-gap shaping

• Counter-clockwise rotation indipendently from the current pulse ⇒ clockwise direction achievable only by mirroring the air-gap shape

(58)

Sensorless

Sensorless supply

supply scheme

scheme

• Back-emf measured at the winding teminals by an auxiliary circuit which forces the current to zero (interval S₃-S₄) ⇒ Switching is made with high back-emf values, measure with low back-emf values (low torque)

• Detection of the zero e.m.f.: all switches at OFF, use of two auxialiary resistances (R₁, R₂) much greater than the phase one, V₀ measure when the current is zero

• Measure of the delay after which the current becomes zero with respect to the zero of the back-emf to decide the increase or decrease of the switch conduction

(59)

Single

Single--phase

phase DC

DC brushless

brushless motor

motor

• PM designed to provide a trapezoidal back-emf waveform

• H-bridge converter controlled by a Hall sensor signal

• Current regulated according to a dead beat control strategy

dead beat control strategy

Maximum back

Maximum back e.m.f

e.m.f. zone

. zone

θ₀ θ₁ θ θ₀+π/p θ₁+π/p -I_max I_max 0

Maximum back

Maximum 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 (constant

constant ±

±II

_max_max

)

PM polarity inversion zone

• Current profile can be simulated by numerical

_{PM polarity inversion zone}

Current transition determined by the

voltage equation

L Ri d d U L Ri e U d di _dc dc Ω − Ω − ± = Ω − − ± = θ ϕ θ 0 0

• Current profile can be simulated by numerical

integration (back-emf e

e

₀₀

and inductance LL

pre-calculated by 2D FEM code)

• Choice of the leading angle

leading angle

θθθθθθθθ

₀₀

with respect to

the null-flux position ⇒ maximization of the

mean electromagnetic torque

(60)

Brushless

Brushless motor

motor for

for small

small fan system

fan system

• Raplacement of an existing very low efficient shaded-pole motor

• Self-starting thanks to the PM misaligment because of the presence of the shaded coil slot (asymmetric air-gap not applied as the laminations must be unchanged) • Adoption of a PM ferrite (B_r=0.22 T and H_c=-151 kA/m)

• Assumption to supply by both H bridge (series-connected coils) or by half-bridge converter (bifilar winding) commutated according a Hall sensor signal

(61)

Dynamic model

( )

[

( )

]

( )

_∑

[

( )

]

∑

= =

θ

⋅

τ′′

+

θ

⋅

τ′

=

θ

⋅

Λ′′

+

θ

⋅

Λ′

=

θ

λ

1 1 1 , , 0 , ,

sin

cos

,

sin

cos

,

n k s k s s k s s em n k s k s s k s s s

k

i

k

i

T

k

i

k

i

Flux and torque as functions of

the position and current

determined by interpolating the

results of magnetostatic FEM

2D analyses

∑

k=1

2D analyses

s s s

=

k

⋅

λ

+

L

⋅

i

λ

* _λ ₀

Correction formulas to include 3D effects (PM longer

than the lamination stack, end-winding leakage,

leakage fluxes from the laminations) using a set of 3D

analyses

T

em

=

k

T

⋅

T

em *

Dynamic equations

Numerical solution by a Simulink model

Analisys for the optimal choice of the Hall sensor position and of the winding parameters

(62)

FEM models

2D model

Unchanged mesh because of the rotation of the magnetization axis

3D model

Used also to evaluate the activation flux density 0.09 0.12 zH=-7 mm -0.12 -0.09 -0.06 -0.03 0 0.03 0.06 0.09 -150 -100 -50 0 50 100 150 Bn [T ]

Stator angular coordinate [°] zH=-8 mm

(63)

Model at steady

Model at steady--state speed

state speed

Output characteristics

Optimal sensor positioning

Temperature changes

Scheme for parametric analysis

Winding parameters PM characteristic

(64)

Magnetic flux model

Total flux Back-emf

M.m.f.

θ

(65)

Electromagnetic torque model

Fourier series expansion

θ

3D correction coefficient M.m.f. Current dependant coefficients

(66)

Main results

Check of the 3D correction formulas

(sinusoidal currents)

3D effects evaluation

(sinusoidal currents)

10 15 T_em [mNm] _{FEM 3D} Static measurements -15 -10 -5 0 5 0 60 120 180 240 300 360 Interpolating curves

• constant current supply

• Limited torque and flux increase

• Relevant end-winding leakage

• constant current supply

• good agreement with the measurements,

but slight uncertainties near maximum torque position

o _{approximated measurement set-up}

o difficult improving the 3D air-gap mesh

o presence of mechanical tolerances

o _{uncertainties of the PM and lamination}

(67)

Main results

Hall sensor positioning (steady-state)

Current and back-emf displacement → 0 when θ_H → -30 Starting torque 30 35 40 45 20 25 30 m N m ] [m A ] [N m /A Ω* T_em,0 I_s T_em,0/I_s2 Starting torque

requirements may also be concerned (maximum value for θ_H → 0°) 5 10 15 20 25 30 -60 -50 -40 -30 -20 -10 0 105 10 15 20 [r p m ]· 1 0 -2 [m N m [N_m /A 2 ] θ_H [°] Optimal range 200 250 40 60 θ_H= 0° θ_H= -30° e_s

Higher current and lower speed and output power

-250 -200 -150 -100 -50 0 50 100 150 2.3 2.305 2.31 2.315 2.32 2.325 2.33 2.335 2.34 -60 -40 -20 0 20 40 [V ] [m A ] [s] i_s 3560 rpm 2 W 2720 rpm 1.7 W

speed and output power in case of inaccurate Hall position

High harmonic content in both back-emf and

(68)

Main results

Performances with different windings

(69)

DC servomotors

magnets DC supply (battery) + -V ω magnets i commutator

(70)

No

No--load magnetic network

load magnetic network

+ ℜ_s ℜ₀ M_m=H_c⋅h_m φ₀ ℜ_s

₍

₎

t w t w r t r w r r r c c c c c c c c c c       + + = = ′ + − + = 2 1 2 1 2 2 1 2 1 2 2 1 1 2 1 β β

Slot effect evaluation

1 w‘_c k’_c ℜ_t ℜ_d ℜ_r ℜ_r

(

)

t w t w r t t r c c c c + =     + + = 5 2 1 2 2 2 1 0 P_d 1-2β_c w_c d c c c P w k′ =1− β ′ Carter factor: k_c=1/k’_c Air-gap reluctance: m m c t

w

L

t

k

0

µ

=

ℜ

wm, Lm, hm: larghezza, profondità, altezza magnete

t: ampiezza traferro - k_s:fattore di stipamento L , L : profondità statore, rotore

PM reluctance: m m m m

w

L

h

µ

=

ℜ

0 Teeth reluctance: d d r s d d d

n

w

L

k

h

′

=

ℜ

µ

Stator yoke reluctance

: s s s s

h

L

R

0

2 µ

π

=

ℜ

Rotor yoke reluctance:

r r s r r r

h

L

k

R

µ

π

2 =

ℜ

L₀, L_r: profondità statore, rotore h_s, h_r: altezza statore, rotore

Rs, Rr: raggio medio statore, rotore

µ_s, µ_r, µ_m: permeabilità statore, rotore, magnete w_d, h_d, µ_d: larghezza, altezza, permeabilità dente n’_d: n. medio denti sotto un magnete