industrial electrical engineering and automation lund university, sweden iron loss calculation in a...

Industrial Electrical Engineering and AutomationLund University, Sweden

Iron Loss Calculation in a Claw-pole Structure

Avo Reinap

David Martinez Muñoz

Mats Alaküla

© Avo R Iron loss calculation in a claw-pole structure

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Objective

• Core loss calculation in a claw-pole structure– Estimation of magnetic loading MEC vs. FEM– Estimation of magnetic losses according to B locus

• Core loss model verification– Core loss measurement of a single-phase claw-pole motor

• Optimal size for the claw-pole structure


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Construction of the motor

• Magnetring – plastic bounded ferrite (PA12);– lateral polar magnetization;

• Claw-pole halves – soft magnetic composite

(Somaloy500+LB1);– A progressive radius of the

claw-poles causes difference between the rest positions and a starting torque;

housing

magnet

inner core half outer core half

shaft

coil


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Core loss formulation• Loss separation

– The formulation is the same for an alternating and rotating field

• Hysteresis loss– Rate of change of energy used to affect magnetic domain wall

motion

• Eddy-current loss (classical eddy currents)– Due to induced currents flowing in closed paths within

magnetic material

• Anomalous loss– Eddy current loss due to magnetic domain wall motion

anomalouseddyhysteresiscore PPPP


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Core loss calculation

• On the basis of the variation and location of magnetic loading the specific core loss can be predicted

• Magnetic loading evaluation is based on – Magnetic Equivalent Circuit (MEC)– 3D Finite Element (FE) modeling;

• A posteriori core loss prediction approach• The hysteresis loss calculation and the loss coefficients

differ between the alternating and rotating field

T

a

T

en

h dtdt

d

Tkdt

dt

d

TkfBkp

0

2/3

0

21

8.11

2ˆ BB


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Core loss energy per cycle

• The specific core loss energy per remagnetization revolution at constant speed ω

• Loss coefficients are derived from the measurements that consider sinusoidal magnetization

• In general, the flux density locus forms an ellipse that is a combination of alternation and circular rotation

2

0

2/32/1

2

0

2

8.12ˆ dd

dkd

d

dkBkw ae

nh

locuscore

BB

linecomp

circlecomp

ellipsecomp w

B

Bw

B

Bw

2

major

minor

major

minor 1


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Magnetic Equivalent Circuit

• A model of 1D elements describes the main flux paths in the 3D core at the alignment position;

• The node potential method is used to calculate the scalar magnetic potential, branch fluxes and magnetic loading for each element;

ememec GnodenodeeM 21

ΦGu 45454545 GFGuu


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Magnetic Equivalent Circuit

• When the rotor is located at any other position different from the alignment position, there will be flux flow through the symmetric surfaces;

• The extended formulation that considers the connection between the node points on the periodicity surfaces

zzNrzzr P 00 ,2,,,

0

0

11

11

'14

10

14

93 u

u

u

uGMP


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Finite Element Analysis

• The FE method allows to discretize the machine in a larger number of 3D elements;

• The solution of the magnetostatic problem is calculated at a number of positions in the excitation cycle;

• A commercial package, Opera-3D, is used for FE field calculations;

00 SH


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3D FE Core Loss Calculation

3D FE DBAS (ARBITARY POSITION)

TABLE (WRITE) IN=ELEM OUT=XYZ

3D FE DBAS(θ) (CYCLE POSITION)

TABLE(θ) (WRITE) IN=XYZ OUT=RB(XYZ)

TABLE (READ) IN=RB(XYZ) OUT=DBAS

$COMI CORELOSS VOLUME ACTION=INTEG

TABLE(θ) (READ FILES) CALCULATE FIELD COMPONENTS FIELD DERIVATIVE

TABLE (WRITE FILE) RBX RBY RBZ

END OF EXCITATION CYCLE?

no

yes

• Core loss calculation is carried out according to the magnetic loading in the centre of each hexahedral element;

• The trajectory of the field locus over excitation cycle is calculated for each element;

• The predicted specific loss is attached to the core geometry;


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Magnetic loading

• The magnitude of flux density components BθBrBz

– At the alignment position the radial Br and the axial Bz

components are dominating– The rotation gives rise to the circumferential Bθ component


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The trajectory of field locus• The ratio of the minor axis of ellipse to the major axis

determines the contribution of the alternating and rotating components to the total core losses;– The flux alternation (a line) occurs mainly in the base core– The flux density loci are close to a circle in the claw-poles– The flux variation forms ellipse in the flanks

mod

mod

major

minor

max

min

B

B

B

B


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Specific hysteresis loss energy

• Alternation (B vector forms a line)– Dissipated energy due to

magnetization cycle equals to the area of hysteresis loop

• Rotation (B vector forms a circle)– Specific rotational hysteresis loss

per cycle can be expressed in terms of four elements;

23

2

223

2

2

1

21

21

1

1

as

a

s

as

a

saw circleh

23

22

111

aaB

Bs

s

nh

lineh BkHdBw

The static loss energy is the work required to overcome magnetic friction and to magnetize the core during the magnetization period, which in turn is equivalent to the area of the major hysteresis loop


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Hysteresis loss

• No local minima (minor hysteresis loops)

• No biased field variation (asymmetric hysteresis loop)

• A rotational field causes nearly twice the loss, compared to the loss produced by an alternating field with the same peak value at a midrange flux density;

• At saturation the loss caused by a rotation field decreases to the levels well below that caused by an alternating field;


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Dynamic core loss• The dynamic loss energy per magnetization cycle depends on the

frequency of the cycle• The loss energy is calculated according to the average of the position rate

of change

1

1

2/2221294.1N

k

n

zkrkkn

dynlocusdyn

Bf BBBfkw It is advantageous to use a single formulation combining all the dynamic losses, since then the loss coefficients can be calculated more easily from the measurements


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Static loss measurement• A calibrated dc motor is

used to estimate:– the mechanic loss energy

(Wfrict) to turn the shaft of the mechanic system;

– the total loss energy (Wfrict +Whyst) to turn the shaft when the claw-pole core is included;

• The static characteristics differ 60% between – the shaft magnetic torque

seen from the dc motor – the cogging measured from

the mechanic equilibrium

ellipsehystfrict

hystfrictadcm

WTW

dTdTdiW

2

2

0

2

0

2

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.015

-0.01

-0.005

0

0.005

0.01

0.015

period T= 14.20 [s] frequency fm

= 0.07 [Hz]to

rqu

e T

, [N

m]

Tf rict

Tdcm

Tdcm

- Tf rict

Tcog


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Dynamic loss measurement

• The higher rotation speed gives rise to– Windage loss (Pdyn,mech)

of the mechanic system (no claw-pole core included);

– Dynamic core loss (Pdyn,core) of the claw-pole stator that includes air dynamic losses in the air-gap and friction between the shaft and core;

10-1

100

101

102

0

5

10

15

20

25

loss

ene

rgy

per

revo

lutio

n, [

mJ]

frequency fe, [Hz]

measured mechanic loss energymeasured core loss energyestimated core loss energy

mechdyncoredynellipsehystfrict

adcm

PPfWTf

ifP

,,2

2


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Optimization

Num

ber

of p

oles

Length to width ratio

Inner radius

• Optimization routine looks for the optimal combination of the size and pole numbers for the claw pole motor, while the stator volume is constant;

• The inner radius of the inner stator is varied from 0 to 20mm;

• The length to width ratio of the cross-section of the claw-pole structure is changed from ¼ to 4;

• The number of poles is changed from 4 to 44;


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4 8 12 16 200

5

10

15

20

number of poles

inne

r ra

dius

Tem

[Nmm]

10 20

30

30

40

40

50

50

60

60

60

70

70

70

80

80

80

90

90

90

100

100

100

110

110

110

120

120

4 8 12 16 200

5

10

15

20

number of poles

inne

r ra

dius

m

[V]

5060

70

70

80

80

80

90

90

90

90

100

100

100

100

110

110

110

120

120

120

130

130

130

140140

150

150

Peak torque• Peak torque and flux linkage of a claw-pole structure as a function of inner

radius and pole number

Flux density 0:0.1:1.5 T


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4 8 12 16 200

5

10

15

20

number of poles

inne

r ra

dius

Whyline [mJ]

6

6

7

7

8

8

8

9

9

9

10

10

10

10

11

11

11

11

12

4 8 12 16 200

5

10

15

20

number of poles

inne

r ra

dius

Whyellipse [mJ]

89

10

11

11

12

12

13 13

13

14

14

14

14

15

15

15

15 16

16

Hysteresis Loss• Hysteresis loss due to field loci of a claw-pole structure as a

function of inner radius and pole number

The specific hysteresis loss 0:200:2000 J/m3


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Optimal core size

• Soft magnetic composite (SMC) core has advantage of– Forming complex isotropic 3D core;– Lower dynamic core losses at

higher frequencies;

• The torque of the outer rotor motor that depends on the number of poles is limited by the leakage between the adjacent poles


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Summary

• The simple MEC is sufficient to select the size of the core and to predict magnetic loading

• Unless proper material data are used, the calculation method does not give reliable results

• Hysteresis loss measurements show 35% higher loss than it was expected from the calculations

• The dynamic core loss is underestimated as much as 60% at 100Hz;

industrial electrical engineering and automation lund university, sweden iron loss calculation in a...

Documents

specific loss

automationcore loss

iron loss calculation

location of magnetic

d core

scalar magnetic potential

d elementsthe solution

field locus