L11 - Torque · L11: Torque Rotating electrical machine has to provide torque – breaking and driving Avo R Design of Electrical Machines 2 Industrial Electrical Engineering and

L11 - Torque

EIEN20 Design of Electrical Machines, IEA, 2016 1

Industrial Electrical Engineering and AutomationLund University, Sweden

L11: Torque

Rotating electrical machine has to provide torque – breaking and driving

Avo R Design of Electrical Machines 2

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Magnetic forces

• Gap flux density B=0.7-1.0T causes magnetic stress tensor δ=B2/2μ0 =0.2-0.4MPa or N/mm2

• A3 example– Normal stress 190kN/m2,

3460N, net force is zero– Shear stress 14kN/m2,

250N, 7.25Nm

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

200

400

600

800

1000

1200

mag

netic

stre

ss,

m [k

N/m

2 =kP

a]

magnetic flux density, Bg [T]

0 30 60 90 120 150 180 210 240 270 300 330 360

-3

-2

-1

0

1

2

3

4

x 105

angle , [deg]

Mag

netic

she

ar s

tress

in th

e ai

rgap

(

), [N

/m2 ]

gnL(), [N/m2]

gtL(), [N/m2]

gn0(), [N/m2]

gt0(), [N/m2]


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Content• Torque requirement vs torque density

– Direct torque drive “is usual” requirement from applications

– Size of electrical machine becomes bulky for low speeds and direct drives

• Integration and architecture– Torque division between production (Electrical

Machine) and transmission (Gear Box)– Torque vs size, size vs cooling

• Sizing equations• Torque quantity and quality

L11 - Torque



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nSpecific torque & architecture

• Mechanical transmissions are capable to transfer higher (contact) loads at low speed5000kN/m2 (Nm/m3)

– Depends of material durability

• Electrical machines are attractive at higher speedsand their torque capability is lower 50kN/m2 (Nm/m3)

– Depends on cooling and machine topology

Grabcad.com Avo R Design of Electrical Machines 6

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Integration and realization

• Design specification of compo-nent active volumes for torque production and transmission

• Identification and realization of non-active volumes

– Support, housing, bearing, termination, end-turns

• Integration and improvements– Manufacturability, ability to cool,

Electricbike.com


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Gear design• Different types of geared

transmissions• Transmission stress K-factor

– Limited by contact load stress on the flank of the working tooth

– Gear durability depends on materials and load cycles

• Specific transmission volumeis related to gear ratio, K-factorand torque

ratiogearNNm

mm

KTbd g

g

g

1

2121

12

S.P.Radzevich Avo R Design of Electrical Machines 8

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Machine design

• Specify topology and scaling rules• Determine main design parameters

– Outer radius Ro– Number of poles Np– Stator to rotor size ratio Kz

• Determine torque capability and cooling requirement-0.05 0 0.05

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

gap radiustooth ref nodesyoke ref nodes

rt

stttst

rt

ggo

g

o

g

o

gz

VVVV

VLRLRR

LRLRLR

RR

K

1

1222

2

2

2

L11 - Torque



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nShear stress small machine

• Outer radius and length of the electrical machine: L=Ro=20…60 mm

• Number of poles: Np=8 (6…10)

• Peak value of current density in the winding: Jc=5, 10 15, 20 A/mm2

• Volumetric size difference between rotor and stator: Kz=1/√2, 1/√3, 1/√4

5 10 15 202

2.5

3

3.5

4

4.5

5

5.5

6

current density, J A/mm2

oute

r rad

ius,

Ro

[cm

]

Magnetic shear stress, [kN/m2] @ Rg/Ro=1/2

10

10

20

20

20

30

30

40

40

50

60

5 10 15 20current density, J A/mm2


20

20

40

40

40

60

60 80

100

5 10 15 20current density, J A/mm2


20

40

40

40

60

60

60

80

80

100

100

120

20

30

40

50

60

70

80

90

100

Jcpk=10A/mm2, =10-60kN/m2

=24nΩm, qc=500W/dm3


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20 Nm drive weight estimation

• K=1N/mm2 transmission type and the achievable reduction rate• approximate weight of active components• 10A/mm2 is selected as a reference current density for specific

torque of electrical machines

• Gear ratios by columns

– 1:1-1:10– 1:1, 1:4-1:100– 1:3 – 1:10– 1:20 – 1:200

HD component– 1:20 – 1:200

HD unit


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Shear stress medium machine

• Outer radius and length of the electrical machine: L=Ro=80…160 mm

• Number of poles: Np=8 (6…18)

• Peak value of current density in the winding: Jc=5, 10 15, 20 A/mm2

• Volumetric size difference between rotor and stator: Kz=1/√2, 1/√3, 1/√4

20

30

30

40

40

40

50

50

50

60

60

60

70

70

70

80

80

90

90 100

110


oute

r rad

ius,

Ro

[cm

]


5 10 15 208

9

10

11

12

13

14

15

16

40

60

60

80

80

80

100

100

100

120

120

120

140

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160



5 10 15 20

60

80

80

100

100

100

120

120

120

140

140

140

160

160

180



5 10 15 2060

70

80

90

100

110

120

130

140

Jcpk=10A/mm2, =35-140kN/m2

=24nΩm, qc=500W/dm3


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1000 Nm drive weight estimation

• K=5N/mm2 transmission type and the achievable reduction rate• approximate weight of active components• 10A/mm2 is selected as a reference current density for specific

torque of electrical machines

single stage double stage planetary gear two-stage planetary gear harmonic gear unit0

50

100

150

200

250

300

350

specific gear ratio, mg [-]

activ

e w

eigh

t, m

[kg]

• Gear ratios by columns

– 1:1-1:10– 1:1, 1:4-1:100– 1:3 – 1:10– 1:9 – 1:100– 1:20 – 1:200

L11 - Torque



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nMachine size specification

• Geometric constrains• Size given by the available

space in a system• Size specified by standards

(NEMA, IEC, DIN, …)– Frame– Mounting (Flange, Foot, …)– Power, speed, voltage,

performance and characteristics

L

D


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Design = Construction + Energy Conversion

• Lorenz force → current sheet → magnetic forces in air-gap

• Facilitate subsequent magnetic coupling →arrangements of magnets

• Torque density and ripple• Design for

– Energy conversion density– manufacturability


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Magnetic circuits

• Magnetic core provides mechanic support and construction• Soft and hard magnetic materials

– Solid, laminated or powder cores – high μ & Bsat vs Ploss

– Discrete, multipole magnets – high BrHc vs cost & integration

• Establish magnetic coupling – linkage vs leakageAvo R Design of Electrical Machines 16

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Electric circuits

• Initially referred as 3φ symmetric and sinusoidal• Insulated electric conductor (Wire) wound as coils or formed as waves• Distributed or concentrated windings

– Arrangement measured by winding factor - ratio of actual MMF to full-pitched winding MMF

• Manufacturability and assembling

L11 - Torque



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0.5 1 1.5 22

3

4

5

6

q

Np

Vcu/Vfe, -

0.40.60.81

1.21.41.6

1.8

2

0.5 1 1.5 22

3

4

5

6

q

Np

Pfe, W

6

7

8910

0.5 1 1.5 22

3

4

5

6

q

Np

Pcu, W

300

350

400

400

450

0.5 1 1.5 22

3

4

5

6

q

Np

pm, C

95

100

105

105

110

115

0.5 1 1.5 22

3

4

5

6

q

Np

w, C

108110

112114

114

116

118

0.5 1 1.5 22

3

4

5

6

q

Np

Qc, W/m2

11001200

1300

1400

Thermal circuits

• Thermal circuits – easy heat paths– Outcome of integration and assembling

• Sources – power losses, Loads or sinks – cooling medium,

• Temperature dependencies and limits


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Radial flux machine cores• Impact of soft magnetic material on construction of

radial flux electrical machines • Stator cores: roto-moulded, roto-moulded with inserts,

compression moulded and laminated

• Short and wide– Ø240/310-H60

• Long and slender– Ø175/100-H112

• Same activevolume 1.8 dm3


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Concentrated distributed windings


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Torque as a function of position

-100 -80 -60 -40 -20 0 20 40 60 80 100-20

-10

0

10

20

30

40

50

60

q=0.214

q=0.286q=0.357q=0.429q=0.500q=0.571

q=0.643q=0.714

q=0.786q=0.857

Ns=9,Np=14,q=0.214Ns=12,Np=14,q=0.286Ns=15,Np=14,q=0.357

Ns=18,Np=14,q=0.429

Ns=21,Np=14,q=0.500Ns=24,Np=14,q=0.571

Ns=27,Np=14,q=0.643


-100 -80 -60 -40 -20 0 20 40 60 80 100-20

-10

0

10

20

30

40

50

60

q=0.188

q=0.250q=0.313q=0.375q=0.438q=0.500q=0.563q=0.625q=0.688q=0.750


Ns=18,Np=16,q=0.375

Ns=21,Np=16,q=0.438Ns=24,Np=16,q=0.500

Ns=27,Np=16,q=0.563


-100 -80 -60 -40 -20 0 20 40 60 80 100-10

0

10

20

30

40

50

q=0.150

q=0.200

q=0.250q=0.300q=0.350q=0.400q=0.450q=0.500

q=0.550

q=0.600

Ns=9,Np=20,q=0.150

Ns=12,Np=20,q=0.200Ns=15,Np=20,q=0.250

Ns=18,Np=20,q=0.300

Ns=21,Np=20,q=0.350Ns=24,Np=20,q=0.400

Ns=27,Np=20,q=0.450

Ns=30,Np=20,q=0.500Ns=33,Np=20,q=0.550

Ns=36,Np=20,q=0.600

-100 -80 -60 -40 -20 0 20 40 60 80 100-10

0

10

20

30

40

50

q=0.136q=0.182

q=0.227q=0.273q=0.318q=0.364q=0.409q=0.455q=0.500

q=0.545

Ns=9,Np=22,q=0.136

Ns=12,Np=22,q=0.182Ns=15,Np=22,q=0.227

Ns=18,Np=22,q=0.273

Ns=21,Np=22,q=0.318Ns=24,Np=22,q=0.364

Ns=27,Np=22,q=0.409

Ns=30,Np=22,q=0.455Ns=33,Np=22,q=0.500

Ns=36,Np=22,q=0.545

L11 - Torque



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nTorque capability vs core realisation


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Design

• Design is an (iterative) process of development(rather than a final solution as a product)

• The design of electrical machinery is both an art and a science

– Many factors involved with conflicting requirements

• Design will always remain stimulating and challengingengineering profession


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Design

• Design process has distinguished steps– Physical understanding – the essence of a physical system– Mathematical modelling – description of system and structure– Analysis – focus on consequences ’split apart’– Synthesis – focus on causatives ’pile up’– Cost functional (Optimization) – focus on improvements

• Designer seeks for / explores the optimal (or the most reasonable) combination of a structure, materials and functionality of a device

• Cost efficient solution is usually more crucial than the technically optimal device


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Computer Aided Design

• Efficient use of computational power and information• CAD, CAE, CAM

Conceive DesignManufactureDevelop

ValidateConcept design

Product layout

Detailed device modelling

Tool design

Drawings

Analysis

CADIDEAS

Requirements

CAM

CAE

L11 - Torque



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nDesign environment

• The design environment is established in Matlab

– Approximate design model– Analysis and optimization– Visualization and administration

• Finite element modelling– Focus on a field problem– Improvement of a design model

APPROXIMATE DESIGN MODEL

NUMERICAL ANALYSIS

OPTIMIZATION


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Design target

• Quantitative and qualitative parameters

• Optimization target– max(power/cost)– max(efficiency/cost)– T/V, T/J, ΔT/T

• Manufacturability• Integrability

• Ageing TEAM– Temperature + chemical

processes– Electric: partial discharge– Ambience: moisture– Mechanic: stress,

vibration

It is essential to consider that the design

goal is to exceed rather than just to meet

performance and reliability requirements


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Design factors

• Economic– Most inportant, lowest price wins – BUT life time cost is

getting mote important than sales price (LCC / LCA).• Material

– Magnetic (soft and hard), electric and insulation materials determine the limits, and are continually improved.

• Specifications– Standards for size, speed, voltage, current

• Special factors– Reliability, size, weight, noise, ...

• Technical factors – main design features


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Main design features• Electric

– # of phases, type of winding, current density, ... Jm

• Magnetic– Max flux density, iron losses, inductances, ... Bm

• Dielectric– Insulation (strand-to-strand, coil-to-coil, coil-ground),

electrical breakdown, routing, ... Um

• Thermal– Coolant (air, water, ...), calculation of temperature rise m

• Mechanical– Critical speed, acoustics, moment of inertia, forces during

short circuit ... σm

L11 - Torque



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nCircuits and loadings

• Electric – I, J– Winding distribution:

highest utilization of active conductors producing torque at all rotor positions

• Magnetic – Φ, B– Maximize magnetic

coupling with the expense of the lowest excitation loss

• Thermal – Ploss, q– Maximize energy transfer

within the thermal limit

• Mechanic – F, σ– Maximal mechanic output

with minimal stress in the materials

• Dielectric – Ubd, – Maximize (electrical

breakdown) safety with the minimal space


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Design object: PMSM

• High efficiency • No rotor losses• High torque/power

density

• Expensive material• Flux weakening difficult• Line start difficult

• Temperature dependence• Magnetic protection, short circuit current• …


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Sizing formulation• The Dis

2L Output Coefficient – Essen’s rule– Ideal interpretation of magnetic circuits and loading as

waveforms in an air-gap– the mechanical power from the active air gap power

– The torque is independent of the number of poles– Large le/τp – difficult to cool, Small le/τp – high leakage

inductance– The actual current densities, tooth flux densities etc are not

included

)cos()(22

)cos(

)(12

1 gapgaprmssgisisismech

gapgapgapgapgapmech

KBlDkk

VAPP


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Sizing formulation• The Dos

3L Output Coefficient– Considers magnetic circuits and loading– Relate the pole flux and stator current to the air gap flux

density, the slot current density and express the output torque

is

e

csis

g

tsis

g

is

e

csis

g

is

e

csis

g

is

e

tsis

g

isosormssgos

is

os

is

os

is

isosgapgapcuismech

ll

BkB

PBkB

b

ll

BkB

ll

BkB

Pll

BkB

a

lDJBDD

DDb

DDa

lDkkkT

11

21

211

3)(1

23

31

2

12

)(2

)()cos(28

L11 - Torque



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nSizing formulation

• The D2.5L Output Coefficient– Multiplication of the two (previous) sizing equations– Useful expression that considers the temperature rise of the

machine

)(

)()cos(24

5.2)5.2()()(1

5.21

isosoos

iso

os

isrmssrmsscug

isosgapgapismech

lDDDf

DDJKkB

lDkkT


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Limitations• Magnetic limitations in core material:

– Teeth: B < 1.55 – 2 T– Core: B < 1.4 – 1.7 T

• Voltage limitations– Insulation in slots subject to high overvoltages

• Slot openings– Open: high fill factor, low tooth utilisation, longer effective air

gap– Semi closed: low fill factor, straight teeth,

• Random vs. Formed Coils– Formed fill factor 50% vs. Random fill 30%– Random wound bracing difficult -> varnish dip


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Machine design

• Quantitative and qualitative design parameters– e.g. torque versus torque ripple

• Specify two types of loadings in order to get torque– Magnetic loading B [Vs/m2] – limited by magnetic saturation– Electric loading K [A/m] – limited by thermal constrains– Torque – T=kD2LKB, k=π/(2√2)

• Estimate the sources of loss for the specified loadings– Thermal design – hot spot at specified cooling conditions

• Focus on qualitative parameters– Torque ripple, cogging torque


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Torque Components• Cogging torque

Attraction between the PM field and the stator slotting.PM + stator slotting -> ripple;

• PM torqueInteraction between the PM field and the mmf distribution.PM field + stator mmf -> constant torque;PM field + stator mmf harmonics -> ripple.

• Reluctance torqueAttraction between the rotor anisotropy, stator mmf and slotting.Synchronous stator mmf + rotor anisotropy -> constant torque;Stator mmf harmonics + rotor anisotropy -> ripple.

L11 - Torque



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Remedial strategies to reducethe torque ripple

Stator• Skewing• Notches• Fractional-slot windings


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Remedial strategies to reducethe torque ripple

Rotor• Stepped skewing• Optimum PM pole arc

width• Different PM pole arc

width• PM pole-shifting• Shaped pole surface


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No effectsConst ↓Harm ↓↓

Const ↓Harm ↓↓

Fund ↓Harm ↓↓

ReducedFract-slot windings

Peak ↓Freq ↑

No effectsNo effectsNo effectsPeak ↓Freq ↑

Notches

ReducedConst ↓Harm ↓↓


Fund ↓Harm ↓↓

Neutra-lisedSkewing

REL cogging

REL torquePM torqueBack emfCogging

Torque

Ripple reduction on the stator side


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nPeak ↓Freq =

ReductionConst ↓Harm ↓↓

Fund ↓Harm ↓↓

Peak ↓Freq =

Shapedpole surf.

Peak ↓Freq =



Fund ↓Harm ↓↓

Peak ↓Freq ↑

PM pole-shifting

ReductionConst ↓Harm ↓↓


Fund ↓Harm ↓↓

ReductionDif Pm arc width

Reduction(Fund)ReductionReductionReductionReduction

(Fund)Opt PM arc width

ReducedConst ↓Harm ↓↓


Fund ↓Harm ↓↓

Reduction(up to Ns)

Steppedskewing

REL cogging

REL torquePM torqueBack emfCogging

Torque

Ripple reduction on the rotor side

L11 - Torque



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nAssignment A5

• Assignment in two sections: assignmenttask

– Introductory study on normalised parameters

– Continuation of A3, A4, parameter estimation and characteristics

• Parameters: Imax, psim, Lnand ksii=Lsy/Lsx

• Characteristics: circle diagram, torque-speed and power-speed

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

1

1

1

1

1

11

11.2

1.2

1.2

1.2

-0.8 -0.8

-0.6 -0.6

-0.4 -0.4

-0.2 -0.2

0 0

0.2 0.2

0.4 0.4

0.6 0.6

0.8 0.8

0.6

0.6

0.6

0.8

0.8

0.8

1

1

1

1. 2

1 .2

1 .2

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

Lsx*=0.44 Lsy*=0.44 Psim*=0.90


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Summary

• Rotating electrical machine has to provide torque – breaking and driving

• Design requirements: gearless, brushless, coreless, lossless, priceless, …. , results to a challenging “negotiation”

• Usually the torque comes with ripple

Documents

L11 - Torque · L11: Torque Rotating electrical machine has to provide torque – breaking and driving Avo R Design of Electrical Machines 2 Industrial Electrical Engineering and