Flux: Examples of Devices - 北京天源博通科技有限公司 ... · · 2013-10-25Region STATOR FERROMAGNETIC FERROMAGNETIC_AIR H_MN H_MS MOVER ... The unequal amplitude of BEMF

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Create, Design, Engineer!

Flux: Examples of Devicesxxx

www.magsoft-flux.comwww.cedrat.com

Philippe [email protected]

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Solenoid

2

3

The Domain

Axisymmetry

Open Boundary

4

Mesh

3638 Elements

7329 Nodes (2nd Order)

Remeshing (Automatic)

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5

Flux Lines

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6

Flux Map

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4

7

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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8

Force vs. Position

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5

9

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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10

Force, Speed, Position

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6

11

Current vs. Time

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12

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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14

Power losses density

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8

15

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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19

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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21

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


viscous friction coefficient - 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


viscous friction coefficient - 0.1


• external characteristics

Mass – 0 kg


viscous friction coefficient - 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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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


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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


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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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48

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


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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


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Stray losses

Flux leakage~Eddy current in conductive parts

~Joule losses - « Stray losses »

In Flux use of surface impedance region


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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.


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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

54

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

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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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94


Static Torque [Nm]

400[A]

300[A]

200[A]

100[A]

1[A]

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Flux-linkage Current Curve

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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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102

Flux application 3DExtension of Model in the 3rd dimension: Torque Output

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Flux SR Machines: Starter/Alternator

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105


Flux Distribution

106


Cumulative Torque

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108

Flux SR Machines: Proximity Effects

4 Phase Machine

109


The Mesh

49

110


External Circuit Connection

Coil modelled as solid Conductors –Proximity effects

111


System Control by MATLAB/Simulink

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112


Results – dynamic simulation

113


Flux and losses

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114


@3,500 rpm

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@1,000 rpm

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116


Current @1,000 rpm

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Flux: Failure analysis1. Normal Operation2. Dynamic Eccentricity3. Shorted Turn

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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



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122

Flux Failure analysisShorted Turn



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Flux in 3D

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Flux in 3D

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Thank you for your interest in our modelling solutions

www.magsoft-flux.com

[email protected]@[email protected]

Documents

Flux: Examples of Devices - 北京天源博通科技有限公司 ... · · 2013-10-25Region STATOR FERROMAGNETIC FERROMAGNETIC_AIR H_MN H_MS MOVER ... The unequal amplitude of BEMF