industrial electrical engineering and automation lund university, sweden iron loss calculation in a...
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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
© Avo R Iron loss calculation in a 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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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;
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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;
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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;
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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
© Avo R Iron loss calculation in a claw-pole structure
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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;