Flux: Examples of Devices xxx Philippe Wendling philippe.wendling@magsoft-flux.com Create, Design, Engineer! www.magsoft-flux.com www.cedrat.com Solenoid 2 1
The Domain Axisymmetry Open Boundary 3 Mesh 3638 Elements 7329 Nodes (2 nd Order) Remeshing (Automatic) 4 2
Flux Lines 5 5 Flux Map 6 6 3
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 7 7 Force vs. Position 8 8 4
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 9 9 Force, Speed, Position 10 10 5
Current vs. Time 11 11 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 12 12 6
Flux Lines 13 13 Power losses density 14 14 7
Position, Speed, Force 15 15 Current 16 16 8
Linear Gear Motor - Geometry Stator Stator winding A B C A B C A B C Stator PM Ferromagnetic air High speed mover PM Ferromagnetic pole High speed mover High speed mover shaft 17 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 18 9
Geometry Air gap length : 1 mm Outside radius : 64 mm Active length of low speed mover : 138.6 mm Active length of high speed mover : 231 mm Stator PM width : 6.3 mm Stator PM height : 3 mm High speed PM width : 23.1 mm High speed PM height : 3 mm High speed yoke inner radius : 18mm High speed yoke outer radius : 33mm PM width Stator slot depth : 14 mm Stator tooth width : 7 mm Winding turns per coils : 39 Winding diameter: 0.8 mm Shaft radius : 18 mm Outside radius 19 Region PA NA PB NB PC NC PA_1 NA_1 PB_1 NB_1 PC_1 NC_1 PA_2 PB_2 NA_2 NB_2 PC_2 NC_2 S_MN STATOR S_MS H_MN H_MS FERROMAGNETIC FERROMAGNETIC_AIR MOVER SHAFT 20 10
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 21 Open Circuit Coil conductor resistance 0.1 ohm Load resistance 10000 ohm 22 11
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 % 23 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 24 12
Initial position t = 0 sec 25 t = 0.1165 sec 26 13
Forces on movers MH mean values : -412.298 N ML mean values : 1977.577 N 29 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 38 14
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 39 Position 41 15
Speed 42 Flux: Transformers and Coils Geometry: Direct Input Import Full or reduced model ¼th 3-phase transformer 43 16
Physical domain in Flux Flux: Transformers and Coils Steady state AC magnetic: common tests (short circuit, open circuit, rated conditions) Single Frequency/Harmonic Transient Magnetic: common tests (short circuit, open circuit, rated conditions) Full signal Steady state thermal : thermal behavior 44 An example: HV transformer 150 MVA - 132 kv / 14.1 kv (courtesy of WTC) Flux Model: Flux: Transformers and Coils The Electric Circuit V1 HV_1 LV_1 R1 V2 HV_2 LV_2 R2 V3 HV_3 LV_3 R3 45 17
Flux: Transformers and Coils Transformer Flux region Description Core, Shunts: Laminated Tank frames: δ<<sheet thickness Shunt for fastening: thin sheet thickness Conductive parts with eddy current Windings, Bus bars, current sources, no eddy currents Magnetic non conductive volume region Surface impedance (face region) Thin conducting surface region Solid conductor volume region Coil conductor volume region or non meshed coils µr µr, ρ µr, ρ thickness µr, ρ Coil component Number of turns 46 Open Circuit Open Circuit Test Case (No Load) Magnetizing current in the primary Saturated core Neglected leakages V1 HV_1 LV_1 R1 R>>1 I=0A V2 HV_2 LV_2 R2 V3 HV_3 LV_3 R3 47 18
Open Circuit 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 48 Open Circuit Flux Computes Results Current in each primary phase Magnetic energy E on the domain Magnetizing current Reactive power/phase E=1/2*L*I² Qtot=2*E*ω Q=Qtot/3 X_1=Q/(I_1)² Magnetizing reactance Xm1, Xm2 Magnetic flux density in core + Bertotti coefficients Iron Losses 49 19
Open Circuit 50 Short-circuit test simulation Principle Magnetizing current neglected Core non saturated low flux density Large flux leakage V1 HV_1 LV_1 R1 R<<1 U=0 V2 HV_2 LV_2 R2 V3 HV_3 LV_3 R3 51 20
Short-circuit test simulation 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 52 Short-circuit test simulation Flux computes Voltage in each primary phase Magnetic energy E on the domain R1, R2, I1, I2 Radial magnetic induction Stray losses density Short-circuit voltages Results Reactive power/phase E=1/2*L*I² Qtot=2*E*ω Q=Qtot/3 X_1=Q/(I_1)² Pj=3*R1*I1²+3*R2*I2² Joule losses in the winding Eddy current losses in the winding Total Stray losses Leakage reactance Xm1, Xm2 53 21
Stray losses Short-circuit test simulation Flux leakage ~Eddy current in conductive parts ~Joule losses - «Stray losses» In Flux use of surface impedance region 54 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 1 b sinh( a / ) sin( a / ) P( eddy) 2 cosh( a / ) cos( a / ) o Short-circuit test simulation Brad 2 a sinh( b / ) sin( b / ) cosh( b / ) cos( b / ) Bax 2 This methods refer to : Calculation of Extra losses in shell transformers windings, T.Ngneugueu, IEEE, 1988. 55 22
Laplace forces analysis Definition 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 56 Thermal analysis of heating Export 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 57 23
Example Eddy Currents Computation of eddy currents in tank Surface Impedance formulation 58 Eddy Current Losses in Coils 1 54 HV TAP HV HV TAP HV 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). 55 108 HV TAP HV leg A HV TAP HV CTC Single section 59 24
FLUX MODEL Axis symm. Just take 3 sections of HV winding and 1 section of LV winding. core 8571.9 A for this area 1004.9 /2 A for this area 60 Current density - hv DC 50Hz 61 25
Current density - lv DC 60 Hz 62 Joule Losses vs. Frequency on HV 63 26
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 Application menu Webinars 64 64 Geometry and Mesh: 50 kw @(1200-1500) rpm 65 27
Cogging torque : B color shade 66 Multi-static analysis : extract torque and flux versus position and current torque versus position for different values of current 600 0 10 20 400 30 40 50 torque (N.m) 200 0-200 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 60 70 80 90 100 110 120 130 140-400 150 160 170-600 position (degree) 180 190 200 67 28
Starting : analysing results Note: the final speed limit is 1173 rpm (we have targeted 1200 rpm) The starting time is around 0.06s 68 Starting : analysing results Display of current versus time 69 29
Flux density in the airgap versus time Examples: Eccentricity PMSM under 50 % dynamic eccentricity healthy PMSM 70 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 71 30
Geometry 72 Mesh 73 31
X component of Flux Density (motion direction) in Gauss 74 Eddy Currents Distribution 75 32
Flux Density in Gauss for different sizes (length x direction) of the target 76 Flux Density in Gauss for different sizes of the target 77 33
Force on Target opposing the motion (in N.) 78 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 79 34
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 80 Geometry 81 35
Mesh 82 X component of Flux Density (motion direction) in Gauss 83 36
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) 84 Eddy Currents Distribution Two Positions 85 37
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 86 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 87 38
SR Machines modelling of complex systems: power electronic converter electromagnetic device control system kinematics of mechanical load How can I build a model? 88 Topology 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 Flux: SR Machines 89 39
Flux: Single Phase Characterization SR-motor magnetization curves: flux-linkage and inductance = f(phase current, rotor position) 0.8 0.7 aligned (60 ) 0.6 Flux-linkage (Wb) 0.5 0.4 0.3 0.2 0.1 unaligned (30 ) 0 0 2 4 6 8 10 12 14 Phase current (A) 90 Flux: SR Machines Specification: Automotive application Traction Power [kw] 55 [kw] Torque [Nm] Speed [rpm] Voltage [V] Dia. of Stator [in] Stack length [in] 100[Nm] 5250[rpm] 288[V] 12 [in] 9 [in] 91 40
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] 92 Flux: Single Phase Characterization Inductance Profile with Current 1.5E-3 1A Inductance PA 0.001 100A Inductance PA 500E-6 200A Inductance PA 300A Inductance PA 0 25 50 75 100 400A Inductance PA 93 41
Static Torque [Nm] Flux: Single Phase Characterization 1[A] 100[A] 200[A] 300[A] 400[A] 94 Flux-linkage Current Curve Flux: Single Phase Characterization 95 42
Flux: Single Phase Characterization 96 External Circuit Connection Flux to Simulink Technology 97 43
System Control by Simulink(matlab) Flux to Simulink Technology 98 Flux to Simulink Technology Speed:2000rpm, Load T:80Nm, Current limit:500a, 99 44
Extension of Model in the 3 rd dimension Flux application 3D 100 Extension of Model in the 3 rd dimension Flux application 3D Webinar Spring 2011 - Flux: SR Machines 101 45
Flux application 3D Extension of Model in the 3 rd dimension: Torque Output 102 Flux SR Machines: Starter/Alternator 104 46
Flux Distribution Flux SR Machines: Starter/Alternator 105 Cumulative Torque Flux SR Machines: Starter/Alternator 106 47
4 Phase Machine Flux SR Machines: Proximity Effects 108 The Mesh Flux SR Machines: Proximity Effects 109 48
External Circuit Connection Flux SR Machines: Proximity Effects Coil modelled as solid Conductors Proximity effects 110 System Control by MATLAB/Simulink Flux SR Machines: Proximity Effects 111 49
Results dynamic simulation Flux SR Machines: Proximity Effects 112 Flux and losses Flux SR Machines: Proximity Effects 113 50
Flux SR Machines: Proximity Effects @3,500 rpm 114 Flux SR Machines: Proximity Effects @1,000 rpm 115 51
Current @1,000 rpm Flux SR Machines: Proximity Effects 116 1. Normal Operation 2. Dynamic Eccentricity 3. Shorted Turn Flux: Failure analysis 117 52
Flux Failure analysis System Control by MATLAB/Simulink 118 System Control by MATLAB/Simulink - Detail Flux Failure analysis R1 R2 119 53
Flux Failure analysis Normal Operation Tooth Force peak 350 N Average torque 0.86 Nm 120 Flux Failure analysis Dynamic Rotor Eccentricity Rotor displaced 0.1 mm Tooth Force peak 550 N Average torque 0.90 Nm 121 54
Flux Failure analysis Shorted Turn Tooth Force peak 300 N Average torque 0.85 Nm 122 Flux in 3D 123 55
Flux in 3D 124 Thank you for your interest in our modelling solutions www.magsoft-flux.com Philippe.Wendling@magsoft-flux.com Tan.Pham@magsoft-flux.com Heide.Lewis@magsoft-flux.com 126 56