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Create, Design, Engineer!
Flux: Examples of Devicesxxx
www.magsoft-flux.comwww.cedrat.com
Philippe Wendlingphilippe.wendling@magsoft-flux.com
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Solenoid
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The Domain
Axisymmetry
Open Boundary
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Mesh
3638 Elements
7329 Nodes (2nd Order)
Remeshing (Automatic)
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5
Flux Lines
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Flux Map
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4
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Force vs. Position
Multistatic
Motion between -0.015” and +0.415”
Curves force vs. position for line current varying from 0.25 A to 2.00 A, sampling of 0.25 A
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Force vs. Position
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5
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Dynamic Study
Coil is connected to a voltage source
Mass is associated to the plunger
The plunger is free to move
The current is transient
No eddy current in this case
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Force, Speed, Position
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6
11
Current vs. Time
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Dynamic Study With EC
Coil is connected to a voltage source
Mass is associated to the plunger
The plunger is free to move
The current is transient
The Eddy currents are taken into account in this case
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7
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Flux Lines
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Power losses density
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Position, Speed, Force
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Current
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Linear Gear Motor - Geometry
Stator
Stator PM
Stator winding
Ferromagnetic air
Ferromagnetic poleHigh speed mover PM
High speed mover High speed mover shaft
A B C A B C A B C
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The Device
Number of stator slots: 9
Number of stator PM pole pairs: 11
Number of active ferromagnetic pole pieces: 14
Number of active high speed mover PM pole pairs: 3
Rated speed of low speed mover: 0.3 m/s
Rated speed of high speed mover: 1.4 m/s
Steel : M800_50A
Remanence of PMs : 1.1 T
Relative permeability : 1.05
Gear ratio : 14:3
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Geometry
Air gap length : 1 mmOutside radius : 64 mmActive length of low speed mover : 138.6 mmActive length of high speed mover : 231 mmStator PM width : 6.3 mmStator PM height : 3 mmHigh speed PM width : 23.1 mmHigh speed PM height : 3 mmHigh speed yoke inner radius : 18mmHigh speed yoke outer radius : 33mmStator slot depth : 14 mmStator tooth width : 7 mmWinding turns per coils : 39Winding diameter: 0.8 mmShaft radius : 18 mm
Outside radius
PM width
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Region
STATOR
FERROMAGNETIC FERROMAGNETIC_AIRH_MN H_MS
MOVER
PA NA PB NB PC NC
PA_1 NA_1 PB_1 NB_1 PC_1 NC_1PA_2
NA_2
PB_2
NB_2
PC_2
NC_2
SHAFT
S_MN
S_MS
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Kinematics
Stator, winding, and stator PMs – fixed
Ferromagnetic poles and air – move slow
Translation along one axis with velocity – 0.3 m/s
High speed PMs, mover, shaft – move high
Translation along one axis with velocity – 1.4 m/s
Air – compressible
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Open Circuit
Coil conductor resistance – 0.1 ohm
Load resistance – 10000 ohm
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Mesh
Completed with automatic mesh
Total number of nodes --> 28574
Number of elements not evaluated : 0 %
Number of excellent quality elements : 99.54 %
Number of good quality elements : 0.45 %
Number of average quality elements : 0.01 %
Number of poor quality elements : 0 %
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BEMF
Moving distance : 2 high speed magnet pole pitch = 92.4 mm
Time steps : 140
Total time : 0.066 sec
The unequal amplitude of BEMF is caused by end effect
peak value = 15 V, rms value = 10.5 V
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Initial position t = 0 sec
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t = 0.1165 sec
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Forces on moversMH mean values : -412.298 N
ML mean values : 1977.577 N
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Couple of load
Modify kinematic setting
Move low – coupled of load• Initial position – 30 mm
• internal characteristics
Mass – 7 kg
constant friction coefficient - 0
viscous friction coefficient - 0.1
friction coefficient proportional to the square speed – 0
• external characteristics
Mass – 0 kg
constant friction coefficient - 0
viscous friction coefficient - 0
friction coefficient proportional to the square speed – 0
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Couple of load
Modify kinematic setting
Move high – coupled of load• Initial position – 20 mm
• internal characteristics
Mass – 7 kg
constant friction coefficient - 0
viscous friction coefficient - 0.1
friction coefficient proportional to the square speed – 0
• external characteristics
Mass – 0 kg
constant friction coefficient - 0
viscous friction coefficient - 0
friction coefficient proportional to the square speed – 0
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Position
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Speed
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Flux: Transformers and Coils
Geometry:
Direct Input
Import
Full or reduced model
¼th 3-phase transformer
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Flux: Transformers and Coils
Physical domain in Flux
Steady state AC magnetic:
common tests (short circuit, open circuit, ratedconditions) – Single Frequency/Harmonic
Transient Magnetic:
common tests (short circuit, open circuit, ratedconditions) – Full signal
Steady state thermal :
thermal behavior
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An example:HV transformer 150 MVA - 132 kV / 14.1 kV
(courtesy of WTC)Flux Model:
The Electric CircuitV1
V2
V3
HV_1
HV_2
HV_3
LV_1
LV_2
LV_3 R3
R2
R1
Flux: Transformers and Coils
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Transformer Flux region Description
Core, Shunts:Laminated
Magnetic non conductive volume region
µr
Tank frames:δ<<sheet thickness
Surface impedance (face region)
µr, ρ
Shunt for fastening:thin sheet thickness
Thin conducting surface region
µr, ρthickness
Conductive parts with eddy current
Solid conductor volume region
µr, ρ
Windings, Bus bars, current sources, no eddy currents
Coil conductor volume region or non meshed coils
Coil component Number of turns
Flux: Transformers and Coils
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Open Circuit Test Case (No Load)
Magnetizing current in the primary
Saturated core
Neglected leakagesR>>1I=0AV1
V2
V3
HV_1
HV_2
HV_3
LV_1
LV_2
LV_3 R3
R2
R1
Open Circuit
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Color shades of B Arrows of B
Joule losses on the tank: 10 W
Energy on the domain: 73 Joules
Magnetizing reactance
Iron losses on the core (Bertotti): 416 Joules
Open Circuit
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Flux Computes Results
Current in each primary phase
Magnetizing current
Magnetic energy E on the domain
Reactive power/phaseE=1/2*L*I²Qtot=2*E*ω Q=Qtot/3
X_1=Q/(I_1)²
Magnetic flux density in core
+ Bertotti coefficients Iron Losses
Magnetizing reactanceXm1, Xm2
Open Circuit
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Open Circuit
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Principle
Magnetizing current neglected
Core non saturated – low flux density
Large flux leakageR<<1U=0
V1
V2
V3
HV_1
HV_2
HV_3
LV_1
LV_2
LV_3 R3
R2
R1
Short-circuit test simulation
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Color shades of B Arrows of B
Joule losses on the tank: 1395 W Stray losses
Energy on the domain: 1024 Joules Leakage Reactance
Laplace forces
Joule losses in the windings
Short-circuit test simulation
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Flux computes Results
Voltage in each primary phase
Short-circuit voltages
Magnetic energy E on the domain
Reactive power/phaseE=1/2*L*I²Qtot=2*E*ω Q=Qtot/3
X_1=Q/(I_1)²
R1, R2, I1, I2Pj=3*R1*I1²+3*R2*I2² Joule losses in the winding
Radial magnetic induction
Eddy current losses in the winding
Stray losses density Total Stray losses
Leakage reactanceXm1, Xm2
Short-circuit test simulation
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Stray losses
Flux leakage~Eddy current in conductive parts
~Joule losses - « Stray losses »
In Flux use of surface impedance region
Short-circuit test simulation
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Eddy current losses in the winding Losses per conductor per winding linked to radial magnetic
induction Brad
In Flux: export on 2D grid of B in the coil use formula
BaxBrad bb
bba
aa
aabeddyP
o
22
2 )/cos()/cosh(
)/sin()/sinh(
)/cos()/cosh(
)/sin()/sinh(1)(
This methods refer to : “Calculation of Extra losses in shell transformers windings”, T.Ngneugueu, IEEE, 1988.
Short-circuit test simulation
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Laplace forces analysisDefinition
dF(t)=PVEC(J,B) = F1+F2(t) with F1 = 1/2Re(JxB*) and F2(t) = cos(2wt).F21+sin(2wt).F22
Display color shades or arrows of Laplace force density on coils DF Laplace/DV = Component F1 (Fundamental)
DF Laplace/DV 2w = Pulsating component F2(t) (double frequency)
Compute total force
Integral of the above quantities in all coils
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Thermal analysis of heatingExport Joule losses from short-circuit simulation
For example the Joule losses on the tank
Define a Steady State Thermal application
Use of thin conducting region with exchange and thermal source
Create a spatial parameter for import
Imported losses will be used as heat source
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Example Eddy Currents
Computation of eddy currents in tank – Surface Impedance formulation
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Eddy Current Losses in Coils
HV
HV
TAP
HV
HV
TAP
HV
HV
TAP
HV
HV
TAP
leg A
1
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55
108
• Section1 to section 54 are series.• Section55 to section 108 are series.• Then, upper and lower part are parallel
connected.• Each section is consist with 9-turn
continuously transposed conductors (CTC).
Single section
CTC
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FLUX MODEL – Axis symm.
Just take 3 sections of HV winding and 1 section of LV winding.
8571.9 A for this area
1004.9 /2 A for this area
core
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Current density - hv
DC
50Hz
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Current density - lv
DC 60 Hz
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Joule Losses vs. Frequency on HV
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Application: Rotating machines
Dedicated tools:
Flux “Overlays”:Motor templates
to define models quickly
Flux/SPEED LINK:Import SPEED geometries
in Flux with automatic meshing
for any « speed » motor
Webinars 64
Applicationmenu
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Geometry and Mesh: 50 kW @(1200-1500) rpm
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Cogging torque : B color shade
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Multi-static analysis : extract torque and flux versus position and current
torque versus position for different values of current
-600
-400
-200
0
200
400
600
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88
position (degree)
torq
ue
(N
.m)
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
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Starting : analysing results
Note: the final speed limit is 1173 rpm (we have targeted 1200 rpm)
The starting time is around 0.06s
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Starting : analysing results
Display of current versus time
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Examples: Eccentricity
Flux density in the airgap versus time
healthy PMSM
PMSM under 50 % dynamic eccentricity
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Some Sensor
Positioning Sensor
Resolver,
Speed Sensor
Reluctance,
Proximity Sensor
Capacitive or eddy current.
Speed Sensor
Reluctance eddy current, Induced Voltage,
Current Sensor
Flux Linkage
Etc..
Example of counting sesnor
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Geometry
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Mesh
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X component of Flux Density (motion direction) in Gauss
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Eddy Currents Distribution
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Flux Density in Gauss for different sizes (length – x direction) of the target
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Flux Density in Gauss for different sizes of the target
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Force on Target opposing the motion (in N.)
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Times to solve
161 position samples per geometry
40 mm with a sampling of .25 mm
9 minutes for 161 samples
7 size samples (1.0, 2.5, 5.0, 7.5, 10.0, 12.5, 15.0)
51 minutes to solve 7X161 samples
Includes eddy currents due to the motion
2D solution – no net current through the target
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3D Solution
The permanent magnet is actually cylindrical, the target is hexahedral. The radius of the cylindrical magnet is 5 mm, the square base of the target is 10mmx10mm
The 2D approximation overstates the amount of Field hitting the target. A 3D computation will be more representative of the problem.
The same geometry is entered in the 3D application of Flux, solved for constant motion and including eddy current.
In this case, the problem is symmetrical and only half of the domain is needed. A symmetry with parallel magnetic field is defined along the symmetry
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Geometry
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Mesh
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X component of Flux Density (motion direction) in Gauss
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Difference 2D/3D
In the 2D computation, the maximum peak flux density is 95 G.
In the 3D computation, the maximum peak flux density is 22 G.
The spatial frequency of the signal is however the same in both cases. (cf FFT of signal for 2D and 3D)
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Eddy Currents DistributionTwo Positions
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Time to solve
161 position samples per geometry
40 mm with a sampling of .25 mm
518 minutes (8h 38 min) for 161 samples
Average 3m22s par sample
At each new sample, the program remesh a buffer area around the moving part. The solving time includes the time needed to remesh. The elements are second order (second order mesh).
The space taken by the solution on disk is just short of 5GB.
To make a comparison of the results, a modified geometry with a narrower target has been solved. The width of the target is in the direction orthogonal to the motion. A target of 1mm wide will barely affect the field. The next section shows the results for a target of 3 mm
87
SR Machines
laminated stator and rotor poles
only stator poles are excited by coils
low rotor inertia
simple and robust construction with complex control (position transducer)
sequence of anti-clockwise excitations of phases results in clockwise movement of rotor (minimum reluctance)
applications: automotive, textile machines, electrical traction, robotics, aerospace, fail safe application …
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SR Machines
modelling of complex systems: power electronic converter
electromagnetic device
control system
kinematics of mechanical load
How can I build a model
?
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Flux: SR MachinesTopology defined using the overlay?
A dedicated interface adapted to the vocabulary of the user (number teeth, radius of rotor and stator, …)
Possibility to define the whole motor with a few number of parameters
The mesh is done automatically
The winding tool
Easily define classical windings
Associate coils and regions automatically
Import a SPEED defined topology
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90
Flux: Single Phase Characterization
SR-motor magnetization curves:
flux-linkage and inductance = f(phase current , rotor position)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 2 4 6 8 10 12 14
Phase current (A)
Flu
x-l
ink
ag
e (
Wb
)
aligned (60°)
unaligned (30°)
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Flux: SR Machines
Specification: Automotive application
TractionPower [kw] 55 [kw]
Torque [Nm] 100[Nm]
Speed [rpm] 5250[rpm]
Voltage [V] 288[V]
Dia. of Stator [in] 12 [in]
Stack length [in] 9 [in]
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Flux: SR Machines
Phases 3
Number of Poles 6/4
Stator Dia. 11.8 [in]
Rotor Dia. 6.6 [in]
Air gap length 0.02 [in]
Stack length 8 [in]
Shaft Dia. 2.09 [in]
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Flux: Single Phase CharacterizationInductance Profile with Current
0
500E-6
0.001
1.5E-3
25 50 75 100
1AInductance PA
100AInductance PA
200AInductance PA
300AInductance PA
400AInductance PA
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Flux: Single Phase Characterization
Static Torque [Nm]
400[A]
300[A]
200[A]
100[A]
1[A]
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Flux: Single Phase Characterization
Flux-linkage Current Curve
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Flux: Single Phase Characterization
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Flux to Simulink TechnologyExternal Circuit Connection
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Flux to Simulink TechnologySystem Control by Simulink(matlab)
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Flux to Simulink TechnologySpeed:2000rpm, Load T:80Nm, Current limit:500A,
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Flux application 3DExtension of Model in the 3rd dimension
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Flux application 3DExtension of Model in the 3rd dimension
Webinar Spring 2011 - Flux: SR Machines
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Flux application 3DExtension of Model in the 3rd dimension: Torque Output
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Flux SR Machines: Starter/Alternator
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Flux SR Machines: Starter/Alternator
Flux Distribution
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Flux SR Machines: Starter/Alternator
Cumulative Torque
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108
Flux SR Machines: Proximity Effects
4 Phase Machine
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Flux SR Machines: Proximity Effects
The Mesh
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Flux SR Machines: Proximity Effects
External Circuit Connection
Coil modelled as solid Conductors –Proximity effects
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Flux SR Machines: Proximity Effects
System Control by MATLAB/Simulink
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Flux SR Machines: Proximity Effects
Results – dynamic simulation
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Flux SR Machines: Proximity Effects
Flux and losses
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Flux SR Machines: Proximity Effects
@3,500 rpm
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Flux SR Machines: Proximity Effects
@1,000 rpm
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116
Flux SR Machines: Proximity Effects
Current @1,000 rpm
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Flux: Failure analysis1. Normal Operation2. Dynamic Eccentricity3. Shorted Turn
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118
Flux Failure analysisSystem Control by MATLAB/Simulink
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Flux Failure analysisSystem Control by MATLAB/Simulink - Detail
R1
R2
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120
Flux Failure analysisNormal Operation
• Tooth Force peak 350 N
• Average torque 0.86 Nm
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Flux Failure analysisDynamic Rotor Eccentricity
• Rotor displaced 0.1 mm
• Tooth Force peak 550 N
• Average torque 0.90 Nm
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122
Flux Failure analysisShorted Turn
• Tooth Force peak 300 N
• Average torque 0.85 Nm
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Flux in 3D
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124
Flux in 3D
126
Thank you for your interest in our modelling solutions
www.magsoft-flux.com
Philippe.Wendling@magsoft-flux.comTan.Pham@magsoft-flux.comHeide.Lewis@magsoft-flux.com
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