Ansoft_Maxwell2D_V12_2009

Maxwell 2D

AnsoftElectromagnetic and Electromechanical Analysis

ANSOFT CORPORATION • 225 West Station Square Dr. Suite 200 • Pittsburgh, PA 15219-1119

user’s guide – Maxwell 2D

12

electronic design automation software

Ansoft Maxwell Field Simulator v12 User’s Guide 1

The information contained in this document is subject to change without notice. Ansoft

makes no warranty of any kind with regard to this material, including, but not limited to,

the implied warranties of merchantability and fitness for a particular purpose. Ansoft

shall not be liable for errors contained herein or for incidental or consequential

damages in connection with the furnishing, performance, or use of this material.

© 2009 Ansoft Corporation. All rights reserved.

Ansoft Corporation

225 West Station Square Drive

Suite 200

Pittsburgh, PA 15219

USA

Phone: 412-261-3200

Fax: 412-471-9427

Maxwell, ePhysics and Optimetrics are registered trademarks or trademarks of Ansoft

Corporation. All other trademarks are the property of their respective owners.

New editions of this manual will incorporate all material updated since the previous

edition. The manual printing date, which indicates the manual’s current edition,

changes when a new edition is printed. Minor corrections and updates which are

incorporated at reprint do not cause the date to change. Update packages may be

issued between editions and contain additional and/or replacement pages to be

merged into the manual by the user. Note that pages which are rearranged due to

changes on a previous page are not considered to be revised.

Edition: REV2.0

Date: 15 January 2009

Software Version: 12.1

Ansoft Maxwell Field Simulator v12 User’s Guide 2

Contents

ContentsThis document discusses some basic concepts and terminology used throughout the Ansoft Maxwell application. It provides the following information:

Overview

1.0 - Maxwell 2D

Examples – Eddy Current

6.1 – Jumping Rings Axisymmetric Model

6.2 – Instantaneous Forces on Busbars

Examples – Transient

7.1 – Gapped Inductor Model

7.2 - Solenoid Problem with an External Circuit

Examples – Basic Exercises

9.1 – Electrostatic

9.3 – Magnetostatic

9.4 – Parametric

9.5 – Transient

9.6 – Transient with Circuit Editor

9.8 - Optimetrics

9.10 – Scripting

9.12 – Eddy Current

9.13 – Rotational Transient Motion

9.14 – Boundary Conditions

9.15 – Permanent Magnets Assignment

Examples – Motors

11.1 - Permanent Magnet Synchronous Machine

11.2 - Three-phase Induction Machine

11.3 - Permanent Magnet Motor

Maxwell® is a comprehensive electromagnetic field simulation software package for engineers tasked with designing and analyzing 3D/2D structures, such as motors, actuators, transformers and other electric and electromechanical devices common to automotive, military/aerospace and industrial systems. Based on the Finite Element Method (FEM), Maxwell can solve static, frequency-domain and time-varying electromagnetic and electric fields. In addition, the software can be dynamically linked with Simplorer® to create a powerful, system-level electromagnetic-based design flow. This flow enables users to combine complex circuits with accurate component models to design high-performance electromechanical and power electronic systems. Additionally, Maxwell’s 3D solvers have dynamic links to ePhysics™. This allows engineers to perform complex 3D multi-physics studies by linking Maxwell to ePhysics’ thermal and structural solvers.

Key BenefitsElectromagnetic field simulationMaxwell includes 3D/2D Transient, AC Electromagnetic, Magneto-static, Electrostatic and Electrotransient solvers that accurately solve for force, torque, capacitance, inductance, resistance, and imped-ance, as well as generate state-space models.

Automatic adaptive meshingMaxwell uses the Ansoft-pioneered automatic adaptive meshing techniques. This robust meshing algorithm automatically creates and refines the finite element mesh as the solution converges, streamlin-ing the solution process and making the software very easy to use.

Dynamic link - ePhysicsThe Maxwell 3D solvers can be dynamically linked with ePhysics’ thermal and stress analysis and are the ideal solution for every elec-tromechanical device requiring cross-disciplinary design analysis.

Dynamic link - SimplorerDynamic links with Simplorer multi-domain system simulation allow accurate high-fidelity component models to be combined with cir-cuits and system architecture to create a powerful, electromagnetic- based design flow.

ImportCAD files can be imported in Maxwell streamlining the design pro-cess.

Multi-processing and distributed analysisMaxwell can leverage available computing power with multi-pro-cessing and distributed analysis options for fast turnaround of your largest designs.

OptimizationOptimetrics™ provides parametric, optimization, sensitivity, and statistical analysis capabilities to Maxwell. Optimetrics automates the design-optimization process by quickly identifying optimal values for design parameters that satisfy user-specified constraints.

Customized pre-processorsRMxprt (electric machine design) and PExprt™ (magnetic component design) are used to design devices based on a traditional analytical approach. They also can be directly linked to Maxwell and provide fully automated design creation and analytical analysis. Users can perform preliminary studies of design concepts prior to performing rigorous electromagnetic analysis with Maxwell.

applicationsElectromechanical • Motorsandgenerators • Linearorrotationalactuators • Relays • MEMS • MagneticrecordingheadsElectromagnetic • Coils • Permanentmagnets • SensorsPower electronic • Transformers • Converters • Busbars • IGBTsandsimilardevicesEM behavior • Insulationstudies • Electrostaticdischarge • Electromagneticshielding • EMI/EMC • Semiconductor • Biomedical

The new 2D interface provides strong coupling with3D and many new usability features.

3D/2D Electromagnetic Field Simulation

Maxwell,Simplorer,ePhysics,Optimetrics,PExprt,AnsoftLinks,andHFSSaretrademarksofAnsoftCorporation.All other trademarks are the property of their respective owners.

© 2008 Ansoft Corporation 0308

225 West Station Square Drive • Suite 200 • Pittsburgh, PA 15219-1119 USAT 412-261-3200 F 412-471-9427 E [email protected] W www.ansoft.com

Key features

Low-frequencyelectromagneticfieldsimulationandanalysisusingFEM for 3D/2D structures • Transient-nonlinearanalysiswith: Motion—rotation, translational, non-cylindrical rotation External circuit coupling Permanent magnet demagnetization analysis Core loss computation Laminationmodelingfor3D • ACElectromagnetic—Analysisofdevicesinfluencedbyskin/ proximity effects, eddy/displacement currents • Magnetostatic—Nonlinearanalysiswithautomatedequivalent circuit model generation • ElectricField—Transient,Electrostatic/Currentflowanalysiswith automated equivalent circuit model generation

Display of data/visualization of results • Fieldvisualizationandanimations(shaded,contourandvector plots) • Meshvisualization(full,partial) • Current,inducedvoltage,fluxlinkage • Powerloss,storedenergy • Coreloss,eddy,excess,hysteresisloss(includingtheminorloop effects) • Impedance,inductance,capacitance • Force,torque • Customreportsofuser-definedsolutiondata

Performance and integration • DistributedAnalysis*forparallelcomputingofparameterized models • 64-bitoperatingsystemsupport • LinkstoSimplorer®*, ePhysics™*,HFSS™*, RMxprt™*, PExprt™*

Integrated3DmodelerfeaturingACISv16andMFCtechnology • Standardprimitivesandmulti-sweepfunctions • Booleanoperations:union,subtraction,intersection • DirectimportofSATandDXFfiles • AnsoftLinks™*forimportofSTEP,IGESandPro/Efiles

Automatic, adaptive mesh technology • Fault-tolerantmeshingalgorithms • Mesh-generationfeedback • GUIperformsvalidationandintegritychecks • Softwareidentifiesartifactswithintheimportedgeometry • Mesh-basedmodelresolution

Versatile material manager and material types • User,groupandsystemlibraries • Linear,nonlinearanisotropicmaterials • Materialassignmentbycoordinatetype:cartesian,cylindricalor spherical

Integrated Optimetrics™* • Geometryandmaterialparameterization • Optimization,sensitivityandstatisticalanalysis

*Optionavailableatadditionalcharge.

AnsoftLinks™

RMxprt™

Maxwell®

ePhysics™

Optim

etric

s™

CAD FilesIGES, STEP, DXF, SAT, ProE

Simplorer®

Electric Machine

PExprt™

Converters & Transformers

Current density in a busbar system as calculated by Maxwell 3D.

OVERVIEW

FEATURED CAPABILITIES

Optimetrics™ is an optional software module that adds parametric capabilities, optimization algorithms, sensitivity and statistical analyses to Ansoft’s best-in-class electromagnetic-field simulation products—HFSS™, Maxwell® 3D and Q3D Extractor®. Optimetrics automates the design-optimization process for high-performance electronics, such as microwave/RF devices, printed circuit boards, on-chip passives, IC packages and electromechanical components, by quickly identifying optimal values for design parameters that satisfy user-specified constraints and goals.

Optimetrics™ enables users to study the effects of geometry and materials on a design by creating parameters for the dimensions and material constants of the model to be analyzed. Optimetrics then varies these parameters and adjusts the geometry and materials to achieve the desired, user specified, performance goal.

Leveraging previously computed parametric simulation results within its optimizer, Optimetrics enables engineers to understand device

characteristics over a large design space and quickly identify the best performing design that is least sensitive to manufacturing tolerances. Optimetrics, when used in conjunction with HFSS™, Maxwell® 3D and Q3D Extractor®, delivers an innovative and robust design platform from which users gain a greater understanding of the design space and the ability to make insightful design choices.

• Parametric Analysis • User-specified range and number of steps for parameters • Automatic analysis of parameter permutations • Distributed Analysis (cost option) o Automated parser management across multiple hardware platforms and reassembly of data for parametric tables and studies• Sensitivity Analysis • Design variations to determine sensitivities o Manufacturing tolerances o Material properties

This example is a connector designed with HFSS and Optimetrics. The control panel displays design variables (i.e., cost functions, parameters), launches design perturbations and converges to the optimal performance criterion.

Ansoft Corporation • 225 West Station Square Drive • Pittsburgh, PA 15219-1119 USATEL 1.412.261.3200 FAX 1.412.471.9427 EMAIL [email protected] WEB www.ansoft.com

Plea

se co

nsul

t you

r loc

al sa

les re

pres

entat

ive fo

r pric

ing

and

info

rmati

on o

n th

is an

d on

oth

er A

nsof

t pro

ducts

. HFS

S, M

axwe

ll, O

ptim

etrics

and

Q3D

Extra

ctor a

re tr

adem

arks

of A

nsof

t Cor

pora

tion.

Al

l oth

er tr

adem

arks

are t

he p

rope

rty o

f the

ir re

spec

tive o

wner

s. ©

200

5 An

soft

Corp

orati

on

PH15

-110

5

• Optimization • User-selectable cost functions and goal objective o Quasi-Newton method o Sequential Nonlinear Programming (SNLP) o Integer-only Sequential Nonlinear Programming • Automatic analysis of parameter variants until optimum goal obtained• Tuning • User-controllable slide bar for real-time tuning display and results• Statistical Analysis • Design performance distribution versus parameter values

Current sensor optimization results using Maxwell 3D and Optimetrics

Ansoft Corporation • 225 West Station Square Drive • Pittsburgh, PA 15219-1119 USATEL: 412.261.3200 • FAX: 412.471.9427 • EMAIL: [email protected] • WEB: www.ansoft.com

Multi-domain simulation software

Overview

SIMPLORER® is the premier software program for the design and analysis of complex, multi-domain systems commonly found in automotive, aerospace/defense and industrial systems.

Multi-domain system design is challenging and complex. It consists of many interdisciplinary and nonlinear components from multiple domains: electrical, mechanical, thermal and control. The close interaction across domains renders single-domain system simulation tools ineffective. SIMPLORER is the only system engineering tool to offer multiple standard modeling techniques (VHDL-AMS, circuits, block diagrams, state machines, C/C++) that can be used concurrently. It also utilizes the concept of “natures,” allowing components of different engineering domains to interact.

SIMPLORER is the ideal tool for system designs such as:

• Power Systems • Electric Motors and Drives • Powertrains

Modeling Techniques

SIMPLORER v7 offers VHDL-AMS wizard technology, making it easy to leverage the IEEE multi-domain modeling standard.

• Hybrid-electric Propulsion • Other Multi-domain Systems

SIMPLORER allows components to be described as behavioral or physical models using one or any combination of SIMPLORER’s modeling techniques. This eliminates error-prone mathematical

transformations and model analogies often employed by single-domain simulation tools.

VHDL-AMSIEEE-endorsed modeling language (standard 1076.1) created to provide a general-purpose, easily exchangeable and open language for multi-domain analog mixed-signal designs.

CIRCUITSNumerically stable and fast circuit simulator with support for multi-level semiconductor modeling that is optimized to the needs of demanding power-electronic and high-switching-frequency circuit design.

BLOCK DIAGRAMSEnables the description of signal-flow-based

linear, nonlinear, continuous, time-discrete and hybrid systems, making it ideal for

dynamic system simulation and closed-loop-control applications.

STATE MACHINESHighly efficient modeling technique for

event-driven systems, such as logical control found in embedded control systems,

space vector controls or PWM for power-electronic circuits.

v7.0

Models

SIMPLORER Model LibrariesSIMPLORER offers optional application-specific model libraries to enhance productivity and reduce design time:

• Alternative Power • Automotive • Hydraulic • Machine

Integration

FEA-Based ModelsFor models requiring the highest level of fidelity, SIMPLORER provides a direct link to Ansoft’s industry-leading electromagnetic field simulation and design programs: Maxwell®, RMxprt™, and PExprt™. Users can easily create equivalent circuit models from the finite-element analysis (FEA) results and import them directly to SIMPLORER.

Alternatively, users can employ the Transient Simulation coupling link to couple transient FEA directly to SIMPLORER. This powerful feature provides the ultimate in accuracy and flexibility and is ideal for detailed analysis of electromechanical components operating within a system.

Manufacturers’ ModelsSIMPLORER users can access up-to-date manufacturer-specific components online at www.model.simplorer.com. MOSFET, IGBT, ultra capacitors and other components are available to customers as a free download.

Statistical Analysis and Optimization

SIMPLORER includes many advanced analysis capabilities such as parametric sweeps and optimization routines to provide insight into design variations and “trade-offs.” • Parameter Sweep/Table • Monte Carlo • 3D Graphic • Genetic Algorithm • Successive Approximation

• Mechanical • Power • SMPS • Sensor

• SIMPLEX • Frequency Sweep • Worst Case • Sensitivity

Please consult your local sales representative for pricing and information on this and other Ansoft products.SIMPLORER, PExprt and RMxprt are trademarks of Ansoft Corporation. All other trademarks are the property of their respective owners. PL37-0407 © 2004 Ansoft Corporation

SIMPLORER v7 includes many new statistical design and optimization routines.

SIMPLORER v7 now includes a transient simulation coupling link. Users can simultaneously solve a transient FEA project with a transient system simulation.

ScriptingThis powerful feature opens APIs in the SIMPLORER environment, allowing SIMPLORER to be embedded into existing design flows. The scripting capability is language independent so users can work with popular scripting languages, such as Visual Basic®, Java® or Tcl/Tk and interact easily with other tools supporting the Microsoft Com interface, such as MS Office and LabView®

Co-SimulationSIMPLORER allows the integration of proprietary C/C++ programs, MATLAB®/Simulink®, Mathcad® and other specialized programs, allowing SIMPLORER to utilize customized code and existing design control. The direct integration of models in their native environment avoids model translation, saves design time and allows communication and model exchange across departments and between suppliers and OEMs.

RMxprt™ is a versatile software program that speeds the design and optimization process of rotating electric machines. With RMxprt, users can calculate machine performance, make initial sizing decisions, and perform hundreds of “what if” analyses in a matter of seconds. As the entry point for the Ansoft motor and drive design methodology, RMxprt automatically produces both system-level models and geometric data, allowing the preliminary design to be refined and integrated with power electronic and control circuitry.

Key BenefitsFast designRMxprt offers numerous machine-specific, template-based interfaces for induction, synchronous, and electronically and brush-commutat-ed machines that allow users to easily enter design parameters and to evaluate design tradeoffs early in the design process.

Performance metricsCritical performance data, such as torque versus speed, power loss, flux in the air gap, power factor and efficiency can be quickly calculated.

Robust calculation methodsRMxprt uses classical analytical motor theory and equivalent mag-netic circuit methods to compute performance metrics for a specific machine design and accounts for nonlinear magnetic characteristics and 3D effects, such as skew and end-turn.

Model pre-processorRMxprt is a key part of Ansoft’s motor design methodology. In addi-tion to providing classical motor performance calculations, RMxprt can automatically create 3D and 2D geometry and assign material properties and other necessary problem definition data necessary to perform rigorous finite element analysis on the design using Maxwell®.

Wire libraryRMxprt includes a comprehensive database of ANSI and IEC wires.

High-fidelity system modelsRMxprt creates high-fidelity, state-space system models incorporat-ing machines’ physical dimensions, winding characteristics and non-linear material properties. Engineers can use the resulting behavioral model to explore electronic control topologies, loads, and interac-tions with drive-system components in Simplorer®.

Convenient design sheet outputDesign sheets list all the relevant input parameters and calculated parameters and graphically display waveforms including current, voltage, torque and back EMF as well as a detailed winding layout. RMxprt also can output Excel-format design sheets based on the user-defined template.

Design optimizationRMxprt can perform hundreds of “what if” analyses in a matter of minutes, making it a valuable tool for designers needing to make initial sizing and material decisions quickly.

Powerful scriptingRMxprt can be integrated with third party development programs through scripting languages such as VB script, Tcl/TK, JavaScript®, Perl, Excel and MATLAB®. This allows users to customize the design flow and leverage internally developed programs and historical data.

design templatesMachine types • Inductionmachines o Single-phase motors o Three-phase motors • Synchronousmachines o Line-start PM motors o Salient-pole motors and generators o Non-salient pole motors and generators • Brushcommutatedmachines o DC motors and generators o Permanent magnet DC motors o Universal motors • Electronicallycommutatedmachines o Brushless DC motors o Adjustable-speed PM motors and generators o Switched reluctance motors o Claw-pole generators

RMxprt delivers the reports you need to quicklyanalyze and tune your design.

Design Software for Electric Machines

RMxpRt ™ v12

RMxprt, Simplorer and Maxwell are trademarks of Ansoft Corporation.All other trademarks are the property of their respective owners.

© 2008 Ansoft Corporation 0308

225 West Station Square Drive • Suite 200 • Pittsburgh, PA 15219-1119 USAT 412-261-3200 F 412-471-9427 E [email protected] W www.ansoft.com

Key features

• Machine-specifictemplateeditor o Rotor o Stator o Running strategies o Drive circuits• Auto-designfeature o Slot size o Coil turns and wire diameter o Starting capacitance o Winding arrangement• Performancecurves o Torque o Power o Efficiency

• Outputwaveforms o Current o Cogging torque o Flux in the air gap• Graphicalwindingeditor• CrosssectionEditor• Customizabledesignsheet• Costevaluation• Integratedparametricsandoptimization• State-spacemodelexporttoSimplorer®

• AutomatedprojectsetupforMaxwell® 2D• AutomatedgeometryandmaterialsetupforMaxwell3D

design flOWRMxprt is the ideal starting point for a comprehensive electric machine design flow. RMxprt with Maxwell and Simplorer provides an efficient and accurate methodology to design and optimize an electric machine and related electric drive and control system.

RMXPRT™ SIMPLORER®

MAXWELL®

RMxprt™ creates 3D and 2D geometry, assigns materials and sets up boundary conditions for Maxwell. Additionally, any parameter changed in

RMxprt is automatically updated in the finite element project.

Ansoft Maxwell Field Simulator v12 – Training Seminar P1-1

OverviewPresentation

1

Maxwell 2D is a high-performance interactive software package that uses finite element analysis (FEA) to solve electric field and magnetic field problems.



1

Maxwell 2D solves the electromagnetic field problems for a givenmodel with appropriate materials, boundaries and source conditions applying Maxwell's equations over a finite region of space.There are two geometry modes available in Maxwell 2D:

Cartesian (XY) model Axisymmetric (RZ) model

There are six solvers available in Maxwell 2D:ElectrostaticAC Conduction Electric FieldsDC Conduction MagnetostaticEddy Current Magnetic FieldsTransient Magnetic



1

Different Methods of Electromagnetic Analysis

Electromagnetic Analysis

Analytical Techniques

Numerical Techniques

Integral Equations

Differential Equations

Boundary Elements

Finite Difference

Finite Elements

Scalar Potentials

Vector Potentials

Components of H-Field

Closed Form

BEM

FDM

FEM

Iterative

3D Magnetostatic

3D Eddy

3D Transient

2D Magnetostatic

2D Eddy

2D Transient

2D Electrostatic

3D Thermal

3D Electrostatic



1

Differential Form of Maxwell’s Equations

ρ=•∇

∂

∂+=×∇

=•∇

∂

∂−=×∇

Dt

DJH

Bt

ΒΕ

y Electricit forLawsGauss'

Law sAmpere'

MagnetismforLawsGauss'

InductionofLawsFaraday'

0



1

FEM and adaptive meshingIn order to obtain the set of algebraic equations to be solved, the geometry of the problem is discretizedautomatically into small elements (e.g., triangles in 2D). All the model solids are meshed automatically by the mesher.The assembly of all triangles is referred to as the finite element mesh of the model or simply the mesh. Approximate aspect ratio limit in 2D:

X = 10,000Y

Start Field Solution

Generate Initial Mesh

Compute Fields

Perform Error Analysis

Stop Field Solution

Has Stopping

Criteria been met?

Refine Mesh

Yes

No

YX



1

FEM Approximation Functions

The desired field in each element is approximated with a 2nd order quadratic polynomial

Az(x,y) = ao + a1x + a2y + a3x2 + a4xy + a5 y2

Field quantities are calculated for 6 points (3 corners and 3 midpoints) in 2DField quantities inside of the triangle are calculated using a 2nd

order quadratic interpolation scheme1

6 2

354



1

FEM Variational Principle

Poisson’s equation:

is replaced with energy functional:

This functional is minimized with respect to value of A at eachnode in every triangle

JA µ−=∇2

( ) dVJAAAAF ∫

•+

∇•∇=

µ21



1

FEM Matrix Equation

Now, over all the triangles, the result is a large, sparse matrix equation

This can be solved using standard matrix solution techniques such as:

Sparse Gaussian Elimination (direct solver)

Incomplete Choleski Conjugate Gradient Method (ICCG iterative solver)

[ ][ ] [ ]JAS =



1

FEM Error Evaluation

Put the approximate solution back into Poisson’s equation

Since A is a quadratic function, R is a constant in each triangle.

The local error in each triangle is proportional to R.

RJAapprox =+∇ µ2



1

FEM Percent Error Energy

Summation of local error in each triangle divided by total energy

Local errors can exceed Percent Error Energy

( )%100

1×=∑

=

n

i

iREnergy Total

local Energy Error Percent



1

Transient Solver Fully Coupled Dynamic Physics Solution

AvHVtAJA cs ×∇×+×∇+∇−∂∂

−=×∇×∇ σσσυ

Current Source Density

Permanent MagnetMagnetic Vector Potential

Electric Scalar Potential

Velocity

Time-varying Electric and Magnetic Fields



1

Transient Solver - Magnetic Field Diffusion

Magnetic fields “diffuse” into materials at different rates depending on:

Material properties of the componentPhysical size of the component

For a cylindrical conductor, diffusion time is:

Induced eddy currents always occur in conducting objects due to time-varying fields; however, they may not always be significant

metersinradiusatyconductivipermuwhere

au

===

=

,,:

(sec)4048.2 2

2

σ

στ



1

GUI - DesktopThe complex functionality built into the Maxwell solvers is accessed through the main user interface (called the desktop). Problem can be setup in a fairly arbitrary order.A new “validation check” has been added to insure that all required steps are completed.



1

ACIS solid modeling kernel

The underlying solid modeling technology used by Ansoft products is provided by ACIS geometric modeler. ACIS version 16 is presentlyused.Users can create directly models using primitives and operations on primitives.In addition, users can import models saved in a variety of formats (sm2 .gds .sm3 .sat .step .iges .dxf .dwg .sld .geo .stl .prt .asm) When users import models into Ansoft products, translators are invoked that convert the models to an ACIS native format (sat format). Exports directly .sat, .dxf, .sm3, .sm2, .step, .iges



1

Supported platforms

Windows XP ProWindows XP Pro x64 EditionWindows Server 2003Windows Server 2003 x64 EditionRed Hat Enterprise Linux 3, 4SuSE Linux Enterprise Server 9.3Solaris 8 -10



1

Starting MaxwellClick the Microsoft Start button, select Programs, and select the Ansoft > Maxwell 12 > Maxwell 12Or Double click on the Maxwell 12 icon on the Windows Desktop

Adding a DesignWhen you first start Maxwell a new project will be automatically added to the Project Tree.To insert a Maxwell Design to the project, select the menu item Project > Insert Maxwell 2D Design

Toolbar:Insert Maxwell 2D Design

Insert Maxwell 3D Design

Insert RMxprt Design



1

Maxwell Desktop

Status bar

History Tree

Menu bar

Toolbars

ProjectManagerwith projecttree

2D ModelerWindow

Property Window

Progress WindowMessage

Manager

Coordinate Entry Fields



1

Maxwell Desktop – Project ManagerMultiple Designs per Project

Multiple Projects per Desktop

Integrated Optimetrics Setup (requires license for analysis)

Project Manager Window

DesignProject

Design Setup

Design Automation•Parametric•Optimization•Sensitivity•Statistical

Design Results



1

Maxwell Desktop – 2D Modeler

Graphicsarea

Model

2D Modeler design tree(history)

2D Modeler Window

Edge

VertexContext menu(right mouse click on 2D modeler window)

OriginXY

Coordinate System



1

Geometry ModeTo set the geometry mode:

1. Select the menu item Maxwell 2D > Solution Type2. Solution Type Window:

Choose Geometry Mode: Cartesian XY

Maxwell – Geometry ModesA Cartesian (XY) model represents a cross-section of a device that extends in the z-direction. Visualize the geometric model as extending perpendicular to the plane being modeled.An Axisymmetric (RZ) model represents a cross-section of a device that is revolved 360° around an axis of symmetry (the z-axis). Visualize the geometric model as being revolved around the z-axis.

Geometric Model

Cartesian (XY Plane) Axisymmetric (RZ Plane)

XY

Z

Z

R

Φ



1

Set Solution TypeTo set the solution type: select the menu item Maxwell 2D > Solution Type

Magnetic Solution TypesMagnetostaticComputes the static magnetic field that exists in a structure given a distribution of DC currents and permanent magnets. The magnetic field may be computed in structures with both nonlinear and linear materials. An inductance matrix, force, torque, and flux linkage may also be computed from the energy stored in the magnetic field.Eddy CurrentComputes the oscillating magnetic field that exists in a structure given a distribution of AC currents. Also computes current densities, taking into account all eddy current effects (including skin effects). An impedance matrix, force, torque, core loss, and current flow may also be computed from the computed field solution.TransientComputes transient (Time Domain) magnetic fields caused by permanent magnets, conductors, and windings supplied by voltage and/or current sources with arbitrary variation as functions of time, position and speed. It can also be coupled with external circuits. Rotational or translational motion effects can be included in the simulation. Uses a time-stepping solver. Considers source induced and motion inducted eddy effects.

Electric Solution TypesElectrostatic Computes the static electric field that exists in a structure given a distribution of DC voltages and static charges. A capacitance matrix, force, torque, and flux linkage may also be computed from the electric field.AC ConductionComputes the AC voltages and current density distribution in a material having both conductive and dielectric properties given a distribution of AC voltages. An admittance matrix and current flow may also be computed from the calculated fields.DC ConductionComputes the DC currents that flow in a lossy dielectric given a distribution of DC voltages. A conductance matrix and current flow may also be computed from the computed electric field solution.



1

Set Model UnitsTo set the units:

1. Select the menu item Modeler > Units

2. Set Model Units:

1. Select Units: mm

2. Click the OK button

Set Default MaterialTo set the default material:

1. Using the Modeler Materials toolbar, choose Select

2. Select Definition Window:

1. Type steel_1008 in the Search by Namefield




1

Modeler – Draw a Rectangle

Point 1

Point 2

Point 1

Point 2

Coordinate Entry Fields

The Coordinate Entry fields allow equations to be entered for position values.

Examples: 2*5, 2+6+8, 2*cos(10*(pi/180)).

Variables are not allowed in the Coordinate Entry Field

Note: Trig functions are in radians



1

Modeler – Importing .dxf and .dwg CAD files

Check “Import as 2D sheet bodies” so objects come in as sheets and not solids

To change the number of segments on an imported curve:Change to face select mode: Edit > Select > Faces and click on face

Modeler > Surface > Uncover Faces

Change to object select mode: Edit > Select > Objects and click on open polyline

Modeler > Purge History

Modeler > Generate History

Expand the history tree for that polyline and change number of segments as desired

Select the polyline and: Modeler > Surface > Cover Lines



1

Modeler – Object PropertiesIn History Tree:

Commands

(dimensions and history)

Attributes

Commands

Attributes

(properties of the object)



1

Solve Inside – if unchecked meshes but no solution inside (like the old exclude feature in material manager)

Model – if unchecked, the object is totally ignored outside of modeler with no mesh and no solution

Modeler – Attributes



1

Modeler - ViewsView > Modify Attributes >

Orientation – Predefined/Custom View Angles

Lighting – Control angle, intensity, and color of light

Projection – Control camera and perspective

Background Color – Control color of 3D Modeler background

View > Visualization Settings – displayed resolution of curves

View > Active View Visibility - Controls the display of: 3D Modeler Objects, Color Keys, Boundaries, Excitations, Field Plots

View > Options – Stereo Mode, Drag Optimization, Color Key Defaults, Default Rotation

View > Render > Wire Frame or Smooth Shaded (Default)

View > Coordinate System > Hide or Small (Large)

View > Grid Setting – Controls the grid display

Toolbar: Toggle Grid Visibility



1

Changing the ViewToolbar

Context Menu

Shortcuts

Since changing the view is a frequently used operation, some useful shortcut keys exist. Press the appropriate keys and drag the mouse with the left button pressed:

ALT + Drag – Rotate

In addition, there are 9 pre-defined view angles that can be selected by holding the ALT key and double clicking on the locations shown on the next page.

Shift + Drag - Pan

ALT + Shift + Drag – Dynamic Zoom

Pan

Rotate AroundModel Center

Dynamic Zoom

Zoom In/Out

Top

Bottom

Right

Predefined View Angles

Left

Rotate AroundCurrent Axis

Rotate AroundScreen Center

Fit All

Fit Selected



1

Maxwell V12 Keyboard Shortcuts

General ShortcutsF1: HelpShift + F1: Context helpCTRL + F4: Close programCTRL + C: CopyCTRL + N: New projectCTRL + O: Open...CTRL + S: SaveCTRL + P: Print...CTRL + V: PasteCTRL + X: CutCTRL + Y: RedoCTRL + Z: UndoCTRL + 0: Cascade windowsCTRL + 1: Tile windows horizontallyCTRL + 2: Tile windows vertically

Modeller Shortcuts

B: Select face/object behind current selection

F: Face select mode

O: Object select mode

CTRL + A: Select all visible objects

CTRL + SHIFT + A: Deselect all objects

CTRL + D: Fit view

CTRL + E: Zoom in, screen center

CTRL + F: Zoom out, screen center

CTRL + Enter: Shifts the local coordinate system temporarily

SHIFT + Left Mouse Button: Drag

Alt + Left Mouse Button: Rotate model

Alt + SHIFT + Left Mouse Button: Zoom in / out

F3: Switch to point entry mode (i.e. draw objects by mouse)

F4: Switch to dialogue entry mode (i.e. draw object solely by entry in command and attributes box.)

F6: Render model wire frame

F7: Render model smooth shaded

Alt + Double Click Left Mouse Button at points on screen: Sets model projection to standard isometric projections (see diagram below).

ALT + Right Mouse Button + Double Click Left Mouse Button at points on screen: give the nine opposite projections.

Top

Bottom

Right

Predefined View Angles

LeftAlt + double left Click here to restore view in an RZ model

Alt + double left Click here to restore view in an XY model



1

Simple ExampleMagnetic core with coil

Use 2D RZ Magnetostatic Solver

Coil (120 Conductors, Copper)

Core (Steel_1008)



1

Setup the geometry mode and solverChoose Cylindrical about Z under Maxwell 2D > Solution TypeChoose Magnetostatic

Click the OK button

Create CoreTo create the core:

1. Select the menu item Draw > Rectangle2. Using the coordinate entry fields, enter the center position

X: 0.0, Y: 0.0, Z: -3.0, Press the Enter key

3. Using the coordinate entry fields, enter the opposite corner of the rectangle

dX: 2.0, dY: 0.0, dZ: 10.0, Press the Enter key

Continued on Next Page



1

Create Core (Continued)To Parameterize the Height

1. Select the Command tab from the Properties window

2. ZSize: H

3. Press the Tab key

4. Add Variable Window

1. Value: 10mm


To set the name:

1. Select the Attribute tab from the Properties window.

2. For the Value of Name type: Core

To set the material:

1. Select the Attribute tab from the Properties window

2. Click on the button in Material value: set to steel_1008

To set the color:


2. Click the Edit button

To set the transparency:



To finish editing the object properties


To fit the view:

1. Select the menu item View > Fit All > Active View



1

Set Default MaterialTo set the default material:

1. Using the 3D Modeler Materials toolbar, choose Select

2. Select Definition Window:

1. Type copper in the Search by Name field


Create Coil To create the coil for the current to flow:

1. Select the menu item Draw > Rectangle2. Using the coordinate entry fields, enter the center position

X: 2.0, Y: 0.0, Z: 0.0, Press the Enter key

3. Using the coordinate entry fields, enter the opposite corner of the rectangle


To set the name:


2. For the Value of Name type: Coil


To fit the view:

1. Select the menu item View > Fit All > Active View



1

Create ExcitationAssign Excitation

1. Click on the coil.

2. Select the menu item Maxwell 2D > Excitations > Assign > Current3. Current Excitation : General

1. Name: Current1

2. Value: 120 A (Note: this is 120 Amp-turns)

3. Ref. Direction: Positive


5. Note that for RZ models, positive current flows into the screen,however for XY models, positive current flows out of the screen.



1

Define a Region Before solving a project a region has to be defined. A region is basically an outermost object that contains all other objects. The region can be defined by a special object in Draw > Region. This special region object will be resized automatically if your model changes size.

A ratio in percents has to be entered that specifies how much distance should be left from the model.

To define a Region:

1. Select the menu item Draw > Region1. Padding Data: One

2. Padding Percentage: 200


Note: Since there will be considerable fringing in this device, a padding percentage of at least 2 times, or 200% is recommended



1

Setup BoundaryAssign Boundary

1. Change to edge selection mode by choosing: Edit > Select > Edges2. Using the mouse, click on the top, right and bottom edges while holding down the CTRL key.

3. Select the menu item Maxwell 2D > Boundary > Assign > Balloon4. Click the OK button



1

Add Solution Setup

Solution Setup - Creating an Analysis SetupTo create an analysis setup:

1. Select the menu item Maxwell 2D> Analysis Setup > Add Solution Setup

2. Solution Setup Window:

1. Click the General tab:

Maximum Number of Passes: 10

Percent Error: 1




1

Save ProjectTo save the project:

1. In an Ansoft Maxwell window, select the menu item File > Save As.

2. From the Save As window, type the Filename: 2D_simple_example

3. Click the Save button

Model ValidationTo validate the model:

1. Select the menu item Maxwell 3D> Validation Check2. Click the Close button

Note: To view any errors or warning messages, use the Message Manager.

AnalyzeTo start the solution process:

1. Select the menu item Maxwell 2D> Analyze All

Validate Analyze All



1

View detailed information about the progress

In the Project Tree click on Analysis > Setup1 with the right mouse button und select Profile



1

Mesh OverlayCreate a plot of the mesh

1. Select the menu item Edit > SelectAllTo create a mesh plot:

1. Select the menu item Maxwell 2D > Fields > Plot Mesh

2. Create Mesh Window:

1. Click the Done button



1

Field OverlaysTo create a field plot:

1. In the object tree, select the plane for plotting:

1. Using the Model Tree, expand Planes

2. Select Global:XZ

2. Select the menu item Maxwell 2D> Fields > Fields > B > Mag_B3. Create Field Plot Window

1. Solution: Setup1 : LastAdaptive

2. Quantity: Mag_B

3. In Volume: Allobjects


4. When done, turn off the plot using:View > Active View Visibility > Filed Reporter



1

Field Overlays (cont)Create another field plot:



2. Select Global:XZ

2. Select the menu item Maxwell 2D> Fields > Fields > B > B_Vector3. Create Field Plot Window


2. Quantity: B_Vector

3. In Volume: Allobjects





1

Field Overlays (cont)Create another field plot:



2. Select Global:XZ

2. Select the menu item Maxwell 2D> Fields > Fields > A > Flux_Lines3. Create Field Plot Window


2. Quantity: Flux_Lines3. In Volume: Allobjects



This completes the simple example.



1

Screen CapturingTo save the drawing Window or a plot to the clipboard select the menu item: Edit > Copy ImageIn any Windows application, select: Edit > Paste to paste the image



1

File StructureEverything regarding the project is stored in an ascii file

File: <project_name>.mxwl

Double click from Windows Explorer will open and launch Maxwell v12

Results and Mesh are stored in a folder named <project_name>.mxwlresults

Lock file: <project_name>.lock.mxwl

Created when a project is opened

Auto Save File: <project_name>.mxwl.auto

When recovering, software only checks date

If an error occurred when saving the auto file, the date will be newer then the original

Look at file size (provided in recover dialog)



1

ScriptsDefault Script recorded in v12

Visual Basic Script

Remote Solve (Windows Only)Tools > Options > General Options > Analysis Options



1

Overall Setup ProcessDesign

Solution Type

2. Boundaries

2. Excitations3. Mesh

Operations2. Analysis Setup

Solution SetupFrequency Sweep

1. Parametric ModelGeometry/Materials

4. Results2D Reports

Fields

MeshRefinement

Solve

Update

Converged

Analyze

Finished

2. Solve Loop

NO

YES



1

Menu StructureDraw – Primitives

Modeler – Settings and Boolean Operations

Edit – Copy/Paste, Arrange, Duplicate

Maxwell 2D – Boundaries, Excitations, Mesh Operations, Analysis Setup, Results



1

Modeler – Model TreeSelect menu item Modeler > Group by Material

Grouped by Material

Material

Object

Object Command History

Object View



1

Modeler – CommandsParametric Technology

Dynamic Edits - Change Dimensions

Add Variables

Project Variables (Global) or Design Variables (Local)

Animate Geometry

Include Units – Default Unit is meters

Supports mixed Units



1

Modeler – Primitives

2D Draw Objects

The following 2D Draw objects are available:

Line, Spline, Arc, Equation Based Curve,

Rectangle, Ellipse, Circle, Regular Polygon, Equation Based Surface

3D Draw Objects

Note that 3D objects can be pasted into the 2D model window, but they are ignored by the solution

The following 3D Draw objects are available (in Maxwell 3D):

Box, Cylinder, Regular Polyhedron

Cone, Sphere, Torus, Helix, Spiral, Bond Wire

True Surfaces

Circles, Cylinders, Spheres, etc are represented as true surfaces. In versions prior to release 11 these primitives would be represented as faceted objects. If you wish to use the faceted primitives, select the Regular Polyhedron or Regular Polygon.

Toolbar: 2D Objects



1

Modeler – Boolean Operations/TransformationsModeler > Boolean >

Unite – combine multiple primitives

Unite disjoint objects (Separate Bodies to separate)

Subtract – remove part of a primitive from another

Intersect– keep only the parts of primitives that overlap

Split – break primitives into multiple parts along a plane (XY, YZ, XZ)

Split Crossing Objects – splits objects along a plane (XY, YZ, XZ) only where they intersect

Separate Bodies – separates objects which are united but not physically connected into individual objects

Edit > Arrange >Move – Translates the structure along a vector

Rotate – Rotates the shape around a coordinate axis by an angle

Mirror – Mirrors the shape around a specified plane

Offset – Performs a uniform scale in x, y, and z.

Edit > Duplicate >Along Line – Create multiple copies of an object along a vector

Around Axis – Create multiple copies of an object rotated by a fixed angle around the x, y, or z axis

Mirror - Mirrors the shape around a specified plane and creates a duplicate

Edit > Scale – Allows non-uniform scaling in the x, y, or z direction

Toolbar: Boolean

Toolbar: Arrange

Toolbar: Duplicate



1

Modeler - SelectionSelection Types

Object (Default)

Face

Edge

Vertex

Selection ModesAll Objects

All Visible Object

By Name

Highlight Selection Dynamically – By default, moving the mouse pointer over an object will dynamically highlight the object for selection. To select the object simply click the left mouse button.

Multiple Object Selection – Hold the CTRL key down to graphically select multiple objects

Next Behind – To select an object located behind another object, select the front object, press the b key to get the next behind. Note: The mouse pointer must be located such that the next behind object is under the mouse pointer.

To Disable: Select the menu item Tools > Options > Modeler OptionsFrom the Display Tab, uncheck Highlight selection dynamically

Selected

Dynamically Highlighted(Only frame of object)



1

Modeler – Moving AroundModeler > Snap Mode to set the snaps

Tools > Customize…Snap Mode to view Snap Mode toolbar

Toolbar: Snap Mode



1

Modeler – Coordinate SystemsCan be Parameterized

Working Coordinate System

Currently selected CS. This can be a local or global CS

Global CS

The default fixed coordinate system

Relative CS

User defined local coordinate system.

Offset

Rotated

Both

Face CS (setting available to automatically switch to face coordinate system in the Modeler Options)

Toolbar: Coordinate System

Step 1: Select Face Step 2: Select Origin

Step 3: Set X-Axis New Working CS

Change Box Size and Cone is automatically positioned with

the top face of the box

Cone created with Face CS



1

2D Measure Modeler > Measure >

Position – Location, Distance, and Area

Edge – Edge Length

Face – Surface Area

Object – Surface Area, Object Volume

Position Points



1

Options – GeneralTools > Options > General Options > Project Options

Temp Directory – Location used during solution processMake sure it has at least 512MB free disk.

Options - MaxwellTools > Options > Maxwell Options > Solver

Set Number of Processors = 2 for 1 dual-core processor or two single-core processors. Requires additional licenseDefault Process Priority – set the simulation priority from Critical(highest) to Idle (lowest)



1

Options – Modeler OptionsTools > Options > Modeler Options > Drawing for Point and Dialog Entry Modes

Can enter in new dimensions using either Point (mouse) or Dialog entry mode

Alternatively use F3 and F4 to switch between Point and Dialog entry modes

Tools > Options > Modeler Options > Display tab to enable playbackMust close and re-open Maxwell after making change for this setting, to activateVisualization is seen by clicking on primatives in the history tree (under subtract command, for instance)

Typical “Dialog”entry mode

window



1

Converting Older Maxwell Projects (pre-Maxwell v12) to Maxwell v12From Maxwell v 11 and older,

1. Select the menu item File > Open2. Open dialog

1. Files of Type: Ansoft Legacy EM Projects (.cls)

2. Browse to the existing project and select the .cls file

3. Click the Open button

What is Converted?

Converts Entire Model: Geometry, Materials, Boundaries,

Sources and Setup

Solutions, Optimetrics projects and Macros are not converted



1

Material Setup - Libraries 3-Tier library structure

System (global) level – predefined from Ansoft and ships with new upgrades, users cannot modify thisUser Library – to be shared among several users at a company (can be encrypted)Personal libraries - to be used only by single user (can be encrypted)

Add a new material: Tools > Edit Configured Libraries > MaterialsNew Interface for Materials Setting shared with RMxprt



1

Click “Add Material …”. The Material is only available in Project

To add a material in the user or personal library: click on “Export Library” and save it in the desire library.

In the main project window, click on Tools > Configured Libraries. Locate the library to have the material available for all the projects.

Click on Save as default to automatically load library for any new project.



1

Materials Setup - Editing



1

Material Setup – BH curveRobust BH curve entry – can delete points if you make a mistake

Can import data from a file

To export BH curve for use in future, right-mouse-click on curve and select Export to File…



1

Material Setup - Permanent MagnetsDirection of magnetization determined by material’s object’s Orientation and Magnetic Coercivity Unit Vectors.

To modify the Orientation, open the Attribute for the object and change the coordinate system. The default Orientation for permanent magnets is Global CS.

To modify the Magnetic Coercivity Unit Vectors for a permanent magnet material, enter the Materials Library and edit the material.The material coordinate system type can be described in Cartesian, Cylindrical, Spherical The magnetic coercivity has unit vectors corresponding to the chosen coordinate system: for instance X,Y,Z for cartesian.

To rotate a magnet in a parametric simulation and the magnetization direction, you must first rotate the object and second assign the FaceCS, as shown below in the history tree

1. Rotate 2. Create FaceCS



1

Material Setup - Anisotropic Material Properties

ε1, µ1, and σ1 are tensors in the X direction. ε2, µ2, and σ2 are tensors in the Y direction. ε3, µ3, and σ3 are tensors in the Z direction.

Note: Nonlinear anisotropic permeability not allowed in Maxwell 2D.

[ ] [ ] [ ]

=

=

=

3

2

1

3

2

1

3

2

1

000000

,00

0000

,00

0000

σσ

σσ

µµ

µµ

εε

εε

yes

yes

yes

no

no

no

Anisotropic

Permeability

no

no

no

yes

no

yes

Anisotropic

Permitivity

no

no

no

no

no

no

Dielectric Loss Tangent

nonoTransient

nonoEddy Current

nonoMagnetostatic

noyesAC Conduction

noyesDC Conduction

nonoElectrostatic

Magnetic Loss Tangent

Anisotropic ConductivitySolver



1

Planes of symmetry in periodic structures where E is oblique to the boundary.

The E-field on the slave boundary is forced to match the magnitude and direction (or the negative of the direction) of the E-field on the master boundary.

Matching (Master and Slave)

Use this boundary condition when the resistive layer’s thickness is much smaller than the other dimensions of the model.

A resistance boundary models a very thin layer of resistive material (such as that caused by deposits, coatings or oxidation on a metallic surface) on a conductor at a known potential.

Resistance

(DC conduction solver only)

Ground at infinityField behaves so that voltage can fringeBalloon

Boundary Type E-Field Behavior Used to model…

Default Boundary Conditions (Natural and Neumann)

Field behaves as follows:

Natural boundaries — The normal component of D changes by the amount of surface charge density. No special conditions are imposed.

Neumann boundaries — E is tangential to the boundary. Flux cannot cross a Neumann boundary.

Ordinary E-field behavior on boundaries. Object interfaces are initially set to natural boundaries; outer boundaries are initially set to Neumann boundaries.

Symmetry Field behaves as follows:

Even Symmetry (Flux Tangential) — E is tangential to the boundary; its normal components are zero.

Odd Symmetry (Flux Normal) — E is normal to the boundary; its tangential components are zero.

Planes of geometric and electrical symmetry.

Electric Field Boundary Conditions (Electrostatic, DC Conduction, AC Conduction)



1

No fringing at infinityField behaves so that magnetic flux can fringeBalloon

Boundary Type H-Field Behavior Used to model…

Default Boundary Conditions (Naturaland Neumann)

Field behaves as follows:

Natural boundaries — H is continuous across the boundary.

Neumann boundaries — H is tangential to the boundary and flux cannot cross it.

Ordinary field behavior. Initially, object interfaces are natural boundaries; outer boundaries and excluded objects are Neumann boundaries.

Magnetic Vector Potential

Sets the magnetic vector potential on the boundary.

Note: In the Magnetostatic solver, A is RMS while in the Eddy Current solver, A is peak.

Magnetically isolated structures.

Symmetry Field behaves as follows:

Odd Symmetry (Flux Tangential) — H is tangential to the boundary; its normal components are zero.

Even Symmetry (Flux Normal) — H is normal to the boundary; its tangential components are zero.

Planes of geometric and magnetic symmetry.

Impedance

(Eddy Current only)

Includes the effect of induced currents beyond the boundary surface.

Conductors with very small skin depths.

Matching (Masterand Slave)

The H-field on the slave boundary is forced to match the magnitude and direction (or the negative of the direction) of the H-field on the master boundary.

Planes of symmetry in periodic structures where H is oblique to the boundary.

Magnetic Field Boundary Conditions (Magnetostatic, Eddy Current, Transient)



1

The charge density in an object.Charge Density

Notes:

In the Electrostatic solver, any conductor without a source condition will be assumed to be floating.

Source Type of Excitation

Floating Conductor

Used to model conductors at unknown potentials.

Voltage The DC voltage on a surface or object.

Charge The total charge on a surface or object (either a conductor or dielectric).

Electric Field Sources (Electrostatic, DC Conduction, AC Conduction)



1

The current density in a conductor.Current Density


Current The total current in a conductor.

Notes:

In the Magnetostatic solver, current is RMS ampturns.

Permanent magnets will also act as a source in the Magnetostatic solver.

Magnetic Field Sources (Magnetostatic)

Magnetic Field Sources (Eddy Current)

The current density in a conductor.Current Density



Parallel Current The total current in a a group of parallel conductors.

Notes:

In the Eddy Current solver, current is peak amp-turns.

Sources can be solid (with eddy effects) or stranded (without eddy effects).



1

Current or voltage on a winding representing 1 or more turns

Coil



Current Density The current density in a conductor.

Permanent magnets will also act as a source in the Transient solver.

Magnetic Field Sources (Transient)

Current and voltage sources (solid or stranded) can be constant or functions of intrinsic variables: speed (rpm or deg/sec), position (degrees), or time (seconds)Dataset function can be used for piecewise linear functions: Pwl_periodic (ds1, Time)



1


Maxwell 2D > Excitation > CurrentValue: applies current in amps

Type:Solid

for windings having a single conductor/turneddy effects are considered

Strandedfor windings having many conductors/turnseddy effects are not considered

Ref Direction:Positive or Negative



1


Maxwell 2D > Excitation > Add WindingCurrent – applies current in amps

Solid or Stranded

Input current and number of parallel branches as seen from terminal

Voltage – applies voltage (total voltage drop over the length of a solid conductor or the entire winding)

Solid or Stranded

Input initial current, winding resistance, extra series inductance not considered in FEA model, voltage, and number of parallel branches as seen from terminal

External – couples to Maxwell Circuit Editor

Solid or Stranded

Input initial current and number of parallel branches

Maxwell 2D > Excitation > Assign > CoilPick a conductor on the screen and then specify:

Name

Number of Conductors

Polarity: positive, negative, or functional winding direction

Note: Windings in the XY solver will usually have 2 coils: one positive and one negative polarity. Both coils will be added to the appropriate winding by right-mouse clicking on Coil in the project tree and choosing Add to Winding



1

To Create an External Circuit1. Select: Maxwell2D > Excitations > External Circuit > Edit External Circuit > Import Circuit2. After circuit editor opens, add elements to construct the circuit. Note that the name of the

Winding in the circuit (Winding1) must match the name of the Winding in Maxwell (Winding1)

3. Save circuit as *.amcp file and then Maxwell Circuit > Export Netlist > *.sph file.

0

LWinding15.3ohmLabelID=R3

-

+

ModelV

switch2

V

S_sw2

D64

Model

d1

ModelI

switch1

I

W_sw1

Labe

lID=V

I1

Note: The dot on the winding symbol is used as the positive reference for the current (positive current is oriented from the "dotted" terminal towards to "un-dotted" terminal of the winding as it passes through the winding).



1

Maxwell 2D > Excitation > Set Eddy EffectsNeed to enable the calculation of eddy effects in objects

Maxwell 2D > Excitation > Set Core LossFor objects with zero conductivity (such as a laminated core), you can calculate the core lossNote that the core loss coefficients must be defined in the material setup



1

Core Loss Calculation Method

The core loss for electrical steel is based on:

where:Kh is the hysteresis coefficient. Kc is the classical eddy coefficient. Ke is the excess or anomalous eddy current coefficient due to magnetic domains. Bmax the maximum amplitude of the flux density. f is the frequency.

The power ferrite core loss is based on:

where:Cm is constant value determined by experiment. fx is the frequency. Bymax is the maximum amplitude of the flux density

( ) ( ) 5.1max

2max

2max fBKfBKfBKp ech ++=

yxm BfCp max=



1

Maxwell 2D > Design SettingsThe Design Settings window allows you to specify how the simulator will deal with some aspects of the design. Tabs vary by solver used (the panel below is for the transient solver)Set the Symmetry Multiplier (For Transient XY Solutions only).

Set the Material Threshold for treating materials as conductors vs. insulators.Set Preserve Transient Solution options (For Transient Solutions Only).Set transient coupling with Simplorer on the Advanced Product Coupling tab (For Transient Solutions Only)Set the Model Depth (Maxwell2D XY Transient Designs Only).Set the default Background material (Maxwell2D Designs Only).



1

Maxwell 2D > ParametersAllows the automatic calculation of parameters following the field solution

Includes: Force, Torque, Flux linkage, Core loss, and Matrix



1

Maxwell 2D > Model > Motion Setup > Assign Band

1. Defines the direction and type of motion (translation or rotation)

2. Defines the mechanical parameters such as mass, damping, and load force

3. Defines limits of motion



1

Magnetostatic and Electric Solution SetupStart the menu of solution setup by: Maxwell > Analysis Setup > Add Solution Setup …For Magnetostatic solver on Solver tab, suggest setting nonlinear residual = 0.001. On default tab choose Save Defaults to set this value for all future projects.



1

Eddy Current Solution Setup



1

Transient Solution Setup



1

Mesh OperationsTo assign Mesh operations to Objects, select the Menu item: Maxwell 2D > Assign Mesh Operations

1. On Selection is applied on the surface of the object

2. Inside Selection is applied through the volume of the object

3. Surface approximation is applied to set faceting guidelines for true surface objects



1

1. Mesh Operations “On selection”applied on the perimeter of the object

Element length based refinement: Length BasedSkin Depth based refinement: Skin Depth Based

On selection – length based

On selection – skin depth based (2 layers)



1

2. Mesh Operations “Inside selection” - applied throughout the volume of the objectElement length based refinement: Length Based

Inside selection – length based



1

3. Mesh Operations “Surface Approximation”For true surfaces, perform faceting control on a face-by-face basis

Select Mesh operation > Assign > Surface approximation and specify one or more settings:

Maximum surface deviation (length)

Maximum Surface Normal Deviation (degrees)

Maximum Aspect Ratio

ro

ri rirooAspectRati*2

=

D

Θr

D = Maximum Surface Deviation

Θ = Maximum Surface Normal Deviation

))2/cos(1( Θ−= rD



1

Manual mesh creationTo create the initial mesh: Click Maxwell > Analysis Setup > Apply Mesh OperationsTo refine the mesh without solving

1. Define mesh operations as previously discussed

2. Click Maxwell > Analysis Setup > Apply Mesh Operations3. Click Maxwell > Analysis Setup > Revert to Initial Mesh to restart to the initial mesh

To view mesh information: Click Maxwell > Results > Solution Data and click on the tab Mesh Statistics



1

Mesh Display1. Select an object

2. Select the menu item Maxwell 2D > Fields > Plot Mesh



1

2D transient meshing for rotational models

“Moving Surface” method used

Band

Air gap

Rotor

Stator

12345671'2'3'4'5'6'7'

master moving surface

slave moving surface

stationary part

moving part(s)



1

2D transient meshing for translational models

“Moving Band” method usedAdaptive meshing not used, so user must manually create the mesh or link to a solved MS or Eddy design

The band area is re-meshed at each time step

The stationary region and moving part(s) are not re-meshed

If you link the mesh to a solved MS or Eddy design:

The entire mesh from the linked design is transferred to the transient design.

The mesh in objects inside and outside of the band never changes as motion occurs.

If the starting transient position is the same as the linked MS or Eddy design, then the linked mesh in the band object is reused.

If the starting transient position is the different than the linked MS or Eddy design, then the linked mesh in the band object is completely deleted. The band is then re-meshed based only on mesh operations in the transient solver. Any mesh or mesh operation on the band in the linked MS or Eddy Design is ignored. The key point is that mesh operations are always required on the band object (use inside selection) for Maxwell 2D transient designs.

For subsequent positions as the object(s) move in the band, the mesh operations on the band in the transient design are re-applied at every timestep and a new mesh is created.

Stationary region

Moving part(s)

band



1

Post Processing

Two Methods of Post Processing Solutions:

Viewing Plots

Manipulating Field Quantities in Calculator

Five Types of Plots:

1. Contour plots (scalars): equipotential lines, ...

2. Shade plots (scalars): Bmag, Hmag, Jmag, …

3. Arrow plots (vectors): B vector, H vector, …

4. Line plots (scalars): magnitude vs. distance along a predefined line

5. Animation Plots



1

Contour plot



1

Shade plot (tone)



1

Shade plot (fringe with outline)



1

Arrow plot



1

Line plot



1

Multiple windows and multiple plots



1

Animation plot

Various types of animated plots are possible:

Animate with respect to phase angle (eddy solver)

Animate with respect to time (transient solver)

Animate with respect to position (for parametric analysis)

Animate with respect to shape change (for parametric analysis)

Export to .gif or .avi format



1

Fields Calculator

To bring up the Fields Calculator tool

1. Select the menu item Maxwell->Fields->Calculator

Typical quantities to analyze:

1. Flux through a surface

2. Current Flow through a surface

3. Tangential Component of E-field along a line

4. Average Magnitude of B-field in a core

5. Total Energy in an object



1

Fields Calculator – Export CommandExports the field quantity in the top register to a file, mapping it to a grid of points. Use this command to save field quantities in a format that can be read by other modeling or post-processing software packages. Two options are available:

1. Grid points from file: Maps the field quantity to a customized grid of points. Before using this command, you must create a file containing the points.

2. Calculate grid points: Maps the field quantity to a three-dimensional Cartesian grid. You specify the dimensions and spacing of the grid in the x, y, and z directions.



1

Export to Grid

Vector data <Ex,Ey,Ez>

Min: [0 0 0]

Max: [2 2 2]

Spacing: [1 1 1]

Space delimited ASCII file saved in project subdirectory

Vector data "<Ex,Ey,Ez>"Grid Output Min: [0 0 0] Max: [2 2 2] Grid Size: [1 1 10 0 0 -71.7231 -8.07776 128.0930 0 1 -71.3982 -1.40917 102.5780 0 2 -65.76 -0.0539669 77.94810 1 0 -259.719 27.5038 117.5720 1 1 -248.088 16.9825 93.48890 1 2 -236.457 6.46131 69.40590 2 0 -447.716 159.007 -8.61930 2 1 -436.085 -262.567 82.96760 2 2 -424.454 -236.811 58.88471 0 0 -8.91719 -241.276 120.3921 0 1 -8.08368 -234.063 94.97981 0 2 -7.25016 -226.85 69.56731 1 0 -271.099 -160.493 129.2031 1 1 -235.472 -189.125 109.5711 1 2 -229.834 -187.77 84.94151 2 0 -459.095 -8.55376 2.125271 2 1 -447.464 -433.556 94.59871 2 2 -435.833 -407.8 70.51582 0 0 101.079 -433.897 -18.56982 0 1 -327.865 -426.684 95.81332 0 2 -290.824 -419.471 70.40082 1 0 -72.2234 -422.674 -9.776042 1 1 -495.898 -415.461 103.0262 1 2 -458.857 -408.248 77.61382 2 0 -470.474 -176.115 12.86982 2 1 -613.582 -347.994 83.22282 2 2 -590.326 -339.279 63.86



1

Getting HelpIf you have any questions while you are using Ansoft Maxwell you can find answers in several ways:

Ansoft Maxwell Online Help provides assistance while you are working.

To get help about a specific, active dialog box, click the Help button in the dialog box or press the F1key.

Select the menu item Help > Contents to access the online help system.

Tooltips are available to provide information about tools on the toolbars or dialog boxes. When you hold the pointer over a tool for a brief time, a tooltip appears to display the name of the tool.

As you move the pointer over a tool or click a menu item, the Status Bar at the bottom of the Ansoft Maxwell window provides a brief description of the function of the tool or menu item.

The Ansoft Maxwell Getting Started guide provides detailed information about using Maxwell to create and solve 3D EM projects.

PDF version of help manual at: ../Maxwell/Maxwell12/help/maxwell_onlinehelp.pdf for printing.

Ansoft Technical Support

To contact Ansoft technical support staff in your geographical area, please log on to the Ansoft corporate website, www.ansoft.com and select Contact.

Your Ansoft sales engineer may also be contacted in order to obtain this information.

Visiting the Ansoft Web SiteIf your computer is connected to the Internet, you can visit the Ansoft Web site to learn more about the Ansoft company and products.

From the Ansoft Desktop

Select the menu item Help > Ansoft Corporate Website to access the Online Technical Support (OTS) system.

From your Internet browser

Visit www.ansoft.com

http://www.ansoft.com/

http://www.ansoft.com/



1

WebUpdateThis new feature allows you to update any existing Ansoft software from the WebUpdate window. This feature automatically scans your system to find any Ansoft software, and then allows you to download any updates if they are available.



1

For Technical SupportThe following link will direct you to the Ansoft Support Page. The Ansoft Support Pages provide additional documentation, training, and application notes. Web Site: http://www.ansoft.com/support.cfm

Application Support for North AmericaThe names and numbers in this list may change without notice

Technical Support:

9-4 EST:

Pittsburgh, PA

(412) 261-3200 x0 – Ask for Technical Support

Burlington, MA


9-4 PST:

San Jose, CA


Portland, OR

(503) 906-7944 or (503) 906-7947

El Segundo, CA

(310) 426-2287 – Ask for Technical Support

http://www.ansoft.com/support.cfm

http://www.ansoft.com/support.cfm

Optimetrics

What is Optimetrics ?Optimetrics enables engineers to determine the best design variation among a model's possible variations.

Create the original model, the nominal design, and then define design parameters that vary

Optimetrics includes five unique capabilities: 1. Parametrics: Define one or more variable sweep definitions, each specifying a series of variable

values within a range. Easily view and compare the results using plot or table to determine how each design variation affects the performance of the design.

2. Optimization: Identify the cost function and the optimization goal. Optimetrics automatically changes the design parameter(s) to meet the goal. The cost function can be based on any solution quantity that can be computes, such as field values, R,L,C force, torque, volume or weight.

3. Sensitivity: Determine the sensitivity of the design to small changes in variables in the vicinity of a design point. Outputs include: Regression value at the current variable value, First derivative of the regression, Second derivative of the regression

4. Tuning: Variable values are changed interactively and the performance of the design is monitored. Useful after performing an optimization in which Optimetrics has determined an optimal variable value, and you want to fine tune the value to see how the design results are affected.

5. Statistical: shows the distribution (Histogram) of a design output like force, torque or loss caused by a statistical variation (Monte Carlo) of input variables.

Five Unique Optimizers1. Quasi Newton - This optimizer approximates the gradient of a user-defined cost function in its search for

the minimum location of the cost function. This gradient approximation is only accurate enough if there is little noise involved in the cost function calculation. The cost function calculation involves FEA, which possesses finite accuracy.

2. Pattern Search - This optimizer performs a grid-based simplex search, which makes use of simplices: triangles in 2D space or tetrahedra in 3D space. The cost value is calculated at the vertices of the simplex. The optimizer mirrors the simplex across one of its faces based on mathematical guidelines and determines if the new simplex provides better results. If it does not produce a better result, the next face is used for mirroring and the pattern continues. If no improvement occurs, the grid is refined. If improvement occurs, the step is accepted and the new simplex is generated to replace the original one. Pattern Search algorithms are less sensitive to noise.

3. Sequential Nonlinear Programming - The main advantage of SNLP over quasi Newton is that it handlesthe optimization problem in more depth. This optimizer assumes that the optimization variables span a continuous space. [Note: this is better for optimizations with only a few variables]

4. Sequential Mixed Integer NonLinear Programming - To be able to optimize on number of turns or quarter turns, the optimizer must handle discrete optimization variables. The SMINLP optimizer can mix continuous variables among the integers, or can have only integers, and works if all variables are continuous. [Note: this is used for optimizations where some variables must be integers such as wire gauge size and is better for optimizations having only a few variables]

5. Genetic Algorithm - The Genetic Algorithm (GA) search is an iterative process that goes through a number of generations (see picture below). In each generation some new individuals (Children / Number of Individuals) are created and the so grown population participates in a selection (natural-selection) process that in turn reduces the size of the population to a desired level (Next Generation / Number of Individuals). [Note: this is better for optimizations having many variables]

Optimetrics Module (cont.)

Distributed Parametrics and Optimization

Seamless setupIntegrated with force, torque, matrixComplete support of Transient solution

Optimetrics Module (cont.)Integrated with external circuit

Optimize on ‘voltage’in MaxwellSetup variables in

Maxwell Circuit Editor

Optimetrics ExampleOptimization of a starter-alternator packThe pack contains a motor used also as alternatorThree-phase claw pole motorPermanent Magnets are added between teeth

Optimization of the Geometry

Want to see the influence on the output torque

Tooth angle Magnet thickness Magnet length

ResultsTransient analysis run for the optimized designInitial Peak torque: 63.40 NmOptimized Peak Torque: 67.42 Nm

Initial Optimized

Ansoft Maxwell 2D Field Simulator v12 User’s Guide

Maxwell 2D v12

6.0 - 1

Chapter 6.0

Chapter 6.0 – Eddy Current Examples6.1 – Jumping Rings Axisymmetric Model

6.2 – Instantaneous Forces on Busbars


6.1Eddy Current – Application Note

6.1 - 1

Maxwell 2D v12

IntroductionThis example investigates the classical “jumping rings” experiment using a 2D axisymmetric eddy current model. Three rings are stacked on top of each other around a common axis. The bottom ring provides a 10 kHz excitation that induces eddy currents and losses in the other two rings. These rings are repelled from ring1 and can be suspended by the magnetic field as the current in ring1 is increased.

The model consists of three solid copper rings. The bottom ring1has a peak current of 1A, while ring2 and ring3 have no excitation and are open-circuited. The open-circuit condition is simulated by constraining the total current to zero. A physical layout of the actual device is shown in:

After the problem is solved, you can do the following:

View the impedance matrix.

Calculate the power loss using two independent methods, and compare it to the loss in the convergence table.

Calculate the induced voltage (V2’) across the open ends of ring2.

The analysis includes all skin and proximity effects in the calculation of the impedance matrix, power losses, and voltage.

Setup the DesignClick on the menu item Project > Insert Maxwell 2D Design

Click on the menu item Maxwell 2D > Solution Type ...

Set Geometry Mode: Cylindrical about Z

Select the radio button Magnetic: Eddy Current

open pointsin rings

I1

ring3

ring2

ring1



6.1 - 2

Maxwell 2D v12

Specify the Drawing UnitsClick on Modeler > Units > Select units: cm

Draw the Solution RegionClick on Draw > Rectangle (Enter the following points using the tab key).

X: 0, Y: 0, Z: -10dX: 20, dY: 0, dZ: 20

Change its properties:Name: RegionTransparency: 0.9

Select View > Fitall > Active View to resize the drawing window.Select wireframe view by selecting: View > Render > Wire Frame.

Create the ModelThe model consists of three donut-shaped rings. A cross-section of the model is shown below. This is a 2-dimensional axisymmetric drawing; an axisymmetricmodel is rotated 360° around the z-axis (displayed as the v-axis in the drawing).

To create the cross-section of the rings:Draw a circle named ring1 with a center at (1,0), a radius of 0.1 cm, 36 segments, colored red.Draw a circle named ring2 with a center at (1,0.5), a radius of 0.1 cm, 36 segments, colored green.Draw a circle named ring3 with a center at (1,0.8), a radius of 0.1 cm, 36 segments, colored yellow.



6.1 - 3

Maxwell 2D v12

Draw the RingsClick on Draw > Regular Polygon

X: 1, Y: 0, Z: 0

dX: 0.1, dY: 0, dZ: 0

Segments: 36

Change its properties:

Name: ring1

Material: Copper

Color: Red

Click on Draw > Regular Polygon

X: 1, Y: 0, Z: 0.5

dX: 0.1, dY: 0, dZ: 0

Segments: 36


Name: ring2

Material: Copper

Color: Green

Click on Draw > Regular Polygon

X: 1, Y: 0, Z: 0.8

dX: 0.1, dY: 0, dZ: 0

Segments: 36


Name: ring3

Material: Copper

Color: Yellow



6.1 - 4

Maxwell 2D v12

Assign the SourcesA current of 1A will be assigned to the ring1 while 0A will be assigned to both ring2

and ring3. This forces the total current flow around these rings to be zero in order to model the “open-circuit” condition.

Select ring1from the history tree.

Click on Maxwell 2D > Excitations > Assign > Current

Name: Current1

Value: 1A

Type: Solid

Select ring2 from the history tree.


Name: Current2

Value: 0A

Type: Solid

Select ring3 from the history tree.


Name: Current3

Value: 0A

Type: Solid

Note: Choosing Solid specifies that the eddy effects in the coil will be considered. On the other hand, if Stranded had been chosen, only the DC resistance would have been calculated and no AC effects in the coil would have been considered.

Assign the Outer BoundaryThe boundary must be set on the solution region.

Choose Edit > Select > Edges to change the selection mode from object to edge.

While holding down the CTRL key, choose the three outer edges of the region.

Click on Maxwell 2D > Boundaries> Assign > Balloon

When done, choose Edit > Select > Object to object selection mode.



6.1 - 5

Maxwell 2D v12

Assign the ParametersIn this example, the compete [3x3] impedance matrix will be calculated. This is done by setting a parameter.

Click on Maxwell 2D > Parameters > Assign > Matrix

Check each of the three sources: Current1, Current2, Current3

Compute the Skin DepthSkin depth is a measure of how current density concentrates at the surface of a conductor carrying an alternating current. It is a function of the permeability, conductivity and frequency

Skin depth in meters is defined as follows:

where:

ω is the angular frequency, which is equal to 2πf. (f is the source frequency which in this case is 10000Hz).

σ is the conductor’s conductivity; for copper its 5.8e7 S/m

µr is the conductor’s relative permeability; for copper its 1

µο is the permeability of free space, which is equal to 4π×10-7 A/m.

For the copper coils, the skin depth is approximately 0.066 cm which less than the diameter of 0.200cm for the conductors.

σµωµδ

ro

2=



6.1 - 6

Maxwell 2D v12

Add an Analysis SetupClick Right on Analysis in the Model Tree and select Add Solution Setup

On the General tab, re-set the Percent Error to 0.01

On the Solver tab, re-set the Adaptive Frequency to 10kHz

Add Mesh OperationsIn order to accurately compute the mutual resistance terms in the impedance matrix, a uniform mesh is needed in all conductors.Select all three coils in the history tree and then Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based.

Name: Coils_Inside

Restrict Length Of Elements: Uncheck

Restrict Number of Elements: Check

Maximum Number of Elements: 1000Note that by choosing “Inside Selection” instead of “On Selection”, the mesh operation is applied evenly through the area of the conductors as opposed to being applied only on the outer perimeter of the conductor.

Mesh operation “On Selection”

Mesh operation “Inside Selection”



6.1 - 7

Maxwell 2D v12

Solve the ProblemSave the project by clicking on menu item File > Save AsSelect the menu item Maxwell 2D > Validation Check to verify problem setupClick on Maxwell 2D > Analyze All

View the Solution DataSelect the menu item Maxwell 2D > Results > Solution Data Click on the Convergence tab to view the adaptive refinement.Note the total loss is approximately 0.0002003 W.

Click on the Mesh Statistics tab to view the refined mesh.

Click on the Matrix tab to display the 3x3 impedance matrix. By default, the results are displayed as [R, Z] but can be also shown as [R, L] or as coupling coefficients.

333332323131

232322222121

131312121111

,,,,,,,,,

LRLRLRLRLRLRLRLRLR



6.1 - 8

Maxwell 2D v12

The diagonal resistance terms represent the self-resistance of each coil due to the DC component and skin effects, as well as the proximity effects in all other conductors. The off-diagonal resistance terms result from proximity effect currents induced in one coil due to excitation in the other coil.

The diagonal inductance terms represent the self-inductance of each coil, while the off-diagonal terms represent the mutual inductance due to coupling.

The matrix results should closely resemble the results shown in the following matrix. The negative resistance R13 means that the current in ring1 induces a current in ring3, which actually reduces the AC resistance of ring3:

The diagonal term R11 is made up of the following resistive components due to ring1, ring2, and ring3. (The ring1 DC resistance is obtained by running a separate simulation a 0.1Hz. The R11 term as well as ring2 and ring3 proximity terms are taken from the matrix above. Finally, The ring1 skin effect term is calculated as the difference between of all of these terms.)

ring1 DC resistance = 3.458e-004

ring1 skin effect = 4.446e-005

ring2 proximity effect from I1 = 1.710e-005

ring3 proximity effect from I1 = –6.963e-006

R11 = 4.004e-004 ohms

In this example, with a 1 A peak current in ring1, and with both ring2 andring3 open-circuited, the total power loss can be calculated by hand from the impedance matrix using the following formula:

P = ½*I2peakR11 = ½*12*4.006e–4 = 2.003e–4 (Watts) This value also corresponds to the Total Power Loss in the convergence

table.



6.1 - 9

Maxwell 2D v12

Plot the MeshSelect all objects and click on Maxwell 2D > Fields > Plot Mesh and zoom in.

When done, hide the plot by selecting View > Active View Visibility > Fields Reporter and unchecking the Mesh1 plot.

View the ResultsNow that you have generated a solution, you can analyze the results. Specifically, what you want to calculate and display are:

The total power loss, total current flow, and rotational current flow in the rings.

Flux lines plot.

Current density plot for ring2 and ring3.

Animated current density vector plot.

Induced voltage (V2‘) across the open-circuit point in ring2.



6.1 - 10

Maxwell 2D v12

Compute Total Power Loss in the CoilsSelect all three coils in the history tree and then Modeler > List > Create > Object List . ‘Objectlist1’ appears under ‘List’ in the History Tree.

Click on Maxwell 2D > Fields > Calculator and then perform the following:

Quantity > OhmicLoss

Geometry > Volume > Objectlist1> OK

Integral > RZ

Eval ... Evaluate

The evaluated loss in the Coils should be about: 2.003e-004 (W). This value is equal to the power calculated by hand from R11 in the impedance matrix.

Click Done.

Plot Flux LinesSelect all objects

Click on Maxwell 2D > Fields > Fields > A > Flux Lines > Done



6.1 - 11

Maxwell 2D v12

Verify the total current flowing around each of the ringsClick on Maxwell 2D > Fields > Calculator and then perform the following:

Quantity > J > ScalarPhi

Complex > Real

Geometry > Surface > ring1> OK

Integral > XY (Note this is a surface integral of J dot dA)

Eval ... Evaluate

Note that the current in ring1 is close to 1 A. Repeating these steps for ring2 and ring3 yields a net current ~0 A, which represents an open-circuited ring.

Click Done.

Calculate the rotating current in the open ringsAlthough the net current flow in ring2 and ring3 is zero, there is a small rotating current flowing down one side and back on the opposite of each open ring. Taking the absolute value of J will return two times the current flowing in the open rings.


Quantity > J > ScalarPhi

Complex > Real

Abs

Geometry > Surface > ring1> OK

Integral > XY

Eval ... Evaluate

The magnitude of the total current in ring1 is displayed. Note that the current in ring1 is close to 1 A. Now repeat the above procedure for rings 2 and 3, yielding currents of 0.087 and 0.048A. The current flowing along each side of ring2 is a “rotational” eddy current equal to ½ * 0.087 = 0.044A. For ring3, the current flowing along each side of is ½ * 0.048 = 0.024A. This current flows in opposite directions on either side of ring2 and ring3 unlike the current flow in ring1, which is only in one direction.

Click Done.



6.1 - 12

Maxwell 2D v12

Plot the current densityHide the Region by selecting View > Active View Visibility and un checking Region.

Select ObjectList1 in the history tree.

Click on Maxwell 2D > Fields > Fields > J > JatPhase > Done

Modify the scale of the plot to observe the current density in ring2 and ring3 by selecting: Click on Maxwell 2D > Fields > Modify Plot Attributes > J > Ok

On the Scale tab, select Use Limits and set Min: -53000 and Max: 53000

Click on Apply and Close.

Note: On ring1, the skin effect causes higher current density on the surface. Current density is higher towards the axis of symmetry due to the DC spirality effect.

Note: On ring2 and ring3, the rotational eddy currents cause positive and negative current density.



6.1 - 13

Maxwell 2D v12

Plot the current density vector and animateHide the previous plots by selecting: View > Active View Visibility > Fields Reporter

Rotate the view by holding down ALT and then left mouse drag.

Select Objectlist1

Click on Maxwell 2D > Fields > Fields > J > J_Vector > Done

After the plot is displayed, double left clicking on the legend select the Plotstab.

Choose plot: J_Vector1 and change the Vector plot spacing to: Min = 0.02 and Max = 0.02.

Select the Marker/Arrow tab and reduce the size of the arrows by sliding the size “slider” to the left.

Select the Scale tab and set to Auto.

In the Project Window, right click on J_Vector1 and click Animate > OK.

Click on Export to save the animation as a .gif or .avi movie file.



6.1 - 14

Maxwell 2D v12

Calculate the open circuit voltage on ring2 and ring3Calculate the voltage (V2‘) induced across the open-circuit point in ring2. This voltage is the negative of the voltage that is required to ensure that the total current flow around ring2 is zero. It can be calculated by hand from the impedance matrix using the following formula:

The open circuit voltage (V2‘) can also be calculated by integrating the average electric field in ring2 around its circumference using the following formula, where E = – jωA, ω = 2 pi (10000), and area = 3.1257e-6:

peak) (V 91.4º6.851e j6.849e .722e1

)1.090e *10000*2j (1.722e *1

)1.090e j (1.722e * *

4-

4-5-

8-5-

8-5-1

121'

2

∠=

−−=

+−=

+−=

−=

π

ωIZIV

)(85.6

1257.310000**2

1

1

4

6

'2

Vpeake

VdAje

VdAjarea

VdEarea

LdEV

RZ

RZ

RZ

−

−

=

•−=

•−=

•=

•=

∫

∫

∫

∫

π

ω



6.1 - 15

Maxwell 2D v12

Calculate the complex magnitude of the voltageTo calculate the complex magnitude of the voltage using the plane calculator, choose Data/Calculator, then select:

Quantity > A

Scalar > ScalarPhi

Complex > CmplxMag, since A_vector is a complex number, the CmplxMagincludes both real and imaginary components. Note that the complex magnitude is equal to:

To multiply by w; select:

Number > Scalar > 2 > Ok

Function > Freq > Ok

Constant > Pi

*

*

*

To divide by area; select:

Number > Scalar > 1 > Ok

Geometry > Surface: ring2 > Ok

Integral > XY > Eval

Exchange > Pop

/

Finally, do an RZ integration to determine the voltage across the ends of ring2.

Geometry > Volume: ring2 > Ok

Integral > RZ > Eval

The open circuit voltage induced across the open point in ring2 is 6.86e-004 V. This equals the voltage calculated by hand from Z12 in the impedance matrix, as well as that calculated by integrating the average electric field. This is the complex magnitude of the voltage. The real and imaginary components can be individually determined by substituting Complex/Imag and Complex/Real in the steps above. These voltages are: V2'(real) = -1.80e-005 and V2'(imaginary) = -6.85e-004 which are nearly the same as the voltage calculated by hand on the previous page.

Reference: “Prediction and Use of Impedance Matrices for Eddy-Current Problems,”IEEE Transactions on Magnetics, Kent R. Davey and Dalian Zheng, vol. 33 pp. 2478-2485, 1997.

This completes the Jumping Rings exercise.

2_

2_ imagrealCmplxMag AAA φφ +=

Maxwell v12 6.2

Eddy Current – Application Note

Instantaneous Forces on Busbars in Maxwell 2D and 3D

This example analyzes the forces acting on a busbar model in Maxwell 2D and 3D. Specifically, it provides a method for determining the instantaneous force on objects having sinusoidal AC excitation in the Eddy Current Solver. Force vectors in AC problems are a combination of a time-averaged “DC” component and an alternating “AC” component. The alternating component fluctuates at a frequency twice the excitation frequency. Both of these components can be calculated using the formulas below so that the instantaneous force can be determined. Three different force methods are used in this example: Virtual, Lorentz, and the Maxwell Stress Tensor.

ACDCINST

AC

DC

FFF

degreestωphaseatevaluateddVBJF

dVBJF

+=

=×=

×=

∫

∫ ∗

)(21

Re21

Description This example will be solved in two parts using the 2D Eddy Current and 3D Eddy Current solvers. The model consists of two 4mm parallel copper busbars separated by a center-center spacing of 16mm. The excitation frequency is 100kHz.

Ansoft Maxwell Field Simulator v12 User’s Guide

3D Model
2D Model
6.2 - 1

Maxwell v12 6.2


PART 1 - The 2D Eddy Project A 2D model of the busbars will be simulated first. Access the Maxwell Project Manager and create a new 2D project called 2dbars. Open the project and change to the Eddy Current solver with an XY drawing plane. Setup the Design

1. Click on the menu item Project > Insert Maxwell 2D Design 2. Click on the menu item Maxwell 2D > Solution Type ...

• Set Geometry Mode: Cartesian, XY • Select the radio button Magnetic: Eddy Current

3. Draw the Solution Region • Click on Draw > Rectangle (Enter the following points using the tab key).

• X: -150, Y: -150, Z: 0 • dX: 300, dY: 300, dZ: 0

• Change its properties: • Name: Region • Transparency: 0.9

• Select View > Fitall > Active View to resize the drawing window. • Select wireframe view by selecting: View > Render > Wire Frame.

Create the Model Now the model can be created. This model also consists of a left and right busbar that have a 4mm square cross-section, however a length of 1 meter is assumed so that the results must be scaled to compare to 3D. Create the Left Busbar

• Click on Draw > Rectangle • X: -12, Y: -2, Z: 0 • dX: 4, dY: 4, dZ: 0

• Change its properties: • Name: left • Material: Copper • Color: Red

6.2 - 2 Ansoft Maxwell Field Simulator v12 User’s Guide

Maxwell v12 6.2


Create the Right Busbar

• Click on Draw > Rectangle • X: 8, Y: -2, Z: 0 • dX: 4, dY: 4, dZ: 0

• Change its properties: • Name: right • Material: Copper • Color: Red

Assign the Boundaries and Sources The current is assumed to be 1A at 0 degrees in the left busbar and -1A at 60 degrees in the right busbar. A no-fringing vector potential boundary will be assigned to the outside of the 2D problem region which is also the default boundary for all 3D projects. This forces all flux to stay in the solution region.

1. The boundary must be set on the solution region. • Choose Edit > Select > Edges to change the selection mode from object to edge. • While holding down the CTRL key, choose the four outer edges of the region. • Click on Maxwell 2D > Boundaries> Assign > Vector Potential

• Value: 0 • Phase: 0 • OK

• When done, choose Edit > Select > Object to object selection mode.

2. Select left from the history tree • Click on Maxwell 2D > Excitations > Assign > Current

• Name: Current1 • Value: 1A • Phase: 0 • Type: Solid • Reference Direction: Positive

3. Select right from the history tree. • Click on Maxwell 2D > Excitations > Assign > Current

• Name: Current2 • Value: 1A • Phase: 60 • Type: Solid • Reference Direction: Negative


Maxwell v12 6.2


Turn on the Eddy Effects in the winding In order to consider the skin effects in the busbars, you must manually turn on the eddy effect.

1. Choose Maxwell 2D > Excitations > Set Eddy Effects ... 2. Verify that the eddy effect is checked for both the left and right conductors.

Assign the Parameters In order to automatically calculate force on an object, it must be selected in the Parameters panel. In 2D, only the virtual force can be automatically calculated. Later, the Lorentz force will be calculated manually in the Post Processor after solving the project.

1. Select the left busbar by clicking on it. 2. Click on Maxwell 2D > Parameters > Assign > Force 3. Click OK to enable the force calculation.

Add an Analysis Setup

1. Click Right on the Analysis folder in the Model Tree and select Add Solution Setup… 2. On the General tab, re-set the Number of passes to 15. 3. Percent Error to 0.01 4. On the Solver tab, re-set the Adaptive Frequency to 100kHz.

Solve the Problem

1. Save the project by clicking on menu item File > Save As 2. Select the menu item Maxwell 2D > Validation Check to verify problem setup 3. Click on Maxwell 2D > Analyze All.


Maxwell v12 6.2


View the Results

1. Select Maxwell 2D > Results > Solution Data… and click on the Force tab. The force results are reported for a 1 meter depth of the model. The DC forces are shown below.

2. Now select Type:AC<Mag,Phase> This shows the magnitude of the force F(x)Mag is approximately 5e-6 (N) and the phase F(x)Phase is -2.0 radians or -120 degrees.


Maxwell v12 6.2


Create a Plot of Force vs. Time The average, AC, and instantaneous components of the Lorentz force can be plotted vs. phase by creating named expressions in the calculator using the formulas at the beginning of the application note.

1. Determine the time-averaged component of Lorentz force: • Click on Maxwell 2D > Fields > Calculator and then perform the following: • Quantity > J • Quantity > B > Complex > Conj > Cross • Scalar X > Complex > Real • Number > Scalar > 0.5 > OK • Multiply • Geometry > Volume > left > OK • Integrate • Add… Name: Force_DC • Click OK

2. Determine the AC component of Lorentz force:

• Quantity > J • Quantity > B > Cross • Scalar X • Function > Phase > OK • Complex > AtPhase • Number > Scalar > 0.5 > OK • Multiply • Geometry > Volume > left > OK • Integrate • Add… Name: Force_AC • Click OK

3. Determine the instantaneous (DC + AC) component of Lorentz force. In the Named Expressions

panel: • In the Named Expressions window, select Force_DC and Copy to stack • Select Force_AC and Copy to stack • Add • Add… Name: Force_inst • Click OK and Done to close the calculator window.


Maxwell v12 6.2


4. Create a plot of Force vs. Phase. Now that the force quantities have been created, a plot of these

named expressions can been created.

• Select Maxwell 2D > Results > Create Fields Report > Rectangular Plot • Change the abscissa X: from the default Freq to Phase. • Category: Calculator Expressions • Quantity: Force_DC, Force_AC, Force_inst (hold down shift key to select all three at once) • New Report > Close • Right mouse click on the legend and select: Trace Characteristics > Add… • Category: Math • Function: max • Add > Done • Double left mouse click on the legend and change from the Attribute to the General tab. • Check Use Scientific Notation and click on OK. Note: The "max" values match the results from Solution Data > Force. I can also be observed that the forces fluctuate at 2 times the excitation frequency since there are two complete cycles over 360 degrees as shown below.

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00Phase [deg]

-0.000008

-0.000006

-0.000004

-0.000002

0.000000

0.000002

0.000004

0.000006

Y1

Ansoft Corporation Maxwell2DDesign1XY Plot 1Curve Info max

Force_DCSetup1 : LastAdaptiveFreq='100kHz'

-2.5666E-006

Force_ACSetup1 : LastAdaptiveFreq='100kHz'

5.0213E-006

Force_instSetup1 : LastAdaptiveFreq='100kHz'

2.4547E-006


Maxwell v12 6.2


6. Finally, the instantaneous force on the left busbar can be calculated using an alternate method, the

Maxwell Stress Tensor method. This method is different than both the Lorentz force and virtual force methods. The Maxwell Stress Tensor method is extremely sensitive to mesh. The force on an object can be determined by the following equation:

( ) )()(5.0 degreestωphaseatevaluateddVnHBHnBFMST =⋅−⋅= ∫ Determine the instantaneous component of force at time wt=0 using the Maxwell Stress Tensor

method in the calculator:

Quantity > B Loads the B vector Function > Phase > OK Loads the function Phase Complex > At Phase Evaluates the B vector at phase = wt Geometry > Line > left > OK This enters the edge of the left busbar Unit Vector > Normal To determine the unit normal vector for left busbar Dot To take B-dot-Unit Normal Quantity > H Loads the H vector Function > Phase > OK Loads the function Phase Complex > At Phase Evaluates the H vector at phase = wt Multiply This multiplies B and H Quantity > B Loads the B vector Function > Phase > OK Loads the function Phase Complex > At Phase Evaluates the B vector at phase = wt Quantity > H Loads the H vector Function > Phase > OK Loads the function Phase Complex > At Phase Evaluates the H vector at phase = wt Dot Computes B-dot-H Number > Scalar > 0.5 > OK Multiply Multiplies the quantity by 0.5 Geometry > Line > left > OK Enters the edge of the left busbar Unit Vector > Normal To determine the unit normal vector for left busbar Multiply This multiplies the quantity times unit normal vector Neg This takes the negative Add Scal? > ScalarX To extract the x-component of the quantity Geometry > Line > left > OK Enters the edge of the left busbar Integrate To integrate the force density and obtain the force in newtons Add… Name: Force_MST


Maxwell v12 6.2


7. Create a plot of the Maxwell Stress Tensor Force vs. Phase.

• Select Maxwell 2D > Results > Create Fields Report > Rectangular Plot • Change the abscissa X: from the default Freq to Phase. • Category: Calculator Expressions • Quantity: Force_inst, Force_MST Note: The slight difference in these curves is due to mesh error in the stress tensor calculation.

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00Phase [deg]

-0.000008

-0.000006

-0.000004

-0.000002

0.000000

0.000002

0.000004

Y1

Ansoft Corporation Maxwell2DDesign1XY Plot 2Curve Info

Force_instSetup1 : LastAdaptiveFreq='100kHz'

Force_MSTSetup1 : LastAdaptiveFreq='100kHz'

This completes PART 1 of the exercise.


Maxwell v12 6.2


PART 2 - The 3D Eddy Project Now the identical model will be simulated in Maxwell 3D. Setup the Design


• Select the radio button Magnetic: Eddy Current 3. Draw the Solution Region

• Click on Draw > Box (Enter the following points using the tab key). • X: 0, Y: -150, Z: -150 • dX: 10, dY: 300, dZ: 300

• Change its properties: • Name: Region • Transparency: 0.9

• Select View > Fitall > Active View to resize the drawing window. • Select wireframe view by selecting: View > Render > Wire Frame.

Create the Model Now the model can be created. This model also consists of a left and right busbar that have a 4mm square cross-section and a length of 10mm. Create the Left Busbar

• Click on Draw > Box • X: 0 Y: -12, Z: -2 • dX: 10, dY: 4, dZ: 4

• Change its properties: • Name: left • Material: Copper • Color: Red

Create the Right Busbar

• Click on Draw > Box • X: 0 Y: 8, Z: -2 • dX: 10, dY: 4, dZ: 4

• Change its properties: • Name: left • Material: Copper


Maxwell v12 6.2


• Color: Red

Assign the Boundaries and Sources The current is assumed to be 1A at 0 degrees in the left busbar and -1A at 60 degrees in the right busbar. The default boundary in Maxwell 3D in no-fringing. So a boundary does not need to be explicitly assigned.

1. To assign the source current, the four (4) end faces of the conductors must be selected. Choose Edit > Select > Faces to change the selection mode from object to face.

2. Zoom in to the busbars using:View > Zoom In 3. Click on the front face of the left busbar.

• Click on Maxwell > Excitations > Assign > Current • Name: Current1 • Value: 1A • Phase: 0 • Type: Solid

4. Select View > Rotate > Model Center to spin the bubars around to see the other face of the left busbar. Select it and then:

• Click on Maxwell > Excitations > Assign > Current • Name: Current2 • Value: 1A • Phase: 0 • Type: Solid • Click on Swap Direction to be sure that the red directional arrow is pointing out of

the conductor 5. Click on the front face of the right busbar.

• Click on Maxwell > Excitations > Assign > Current • Name: Current3 • Value: 1A • Phase: 60 • Type: Solid

6. Select View > Rotate > Model Center to spin the bubars around to see the other face of the left busbar. Select it and then:

• Click on Maxwell > Excitations > Assign > Current • Name: Current4 • Value: 1A • Phase: 60 • Type: Solid • Click on Swap Direction to be sure that the red directional arrow is pointing out of

the conductor


Maxwell v12 6.2


Turn on the Eddy Effects in the winding In order to consider the skin effects in the busbars, the eddy effect must be turned on.

1. Choose Maxwell 3D > Excitations > Set Eddy Effects ... 2. Verify that the eddy effect for left and right is checked. 3. Un-check the displacement current calculation.

Assign the Parameters In order to automatically calculate force on an object, it must be selected in the Parameters panel. In Maxwell 3D, you can calculate both virtual and Lorentz force. Note however that Lorentz force is only valid on objects with a permeability = 1.

1. Select the left busbar by clicking on it in the history tree or on the screen. 2. Click on Maxwell > Parameters > Assign > Force 3. Name: Force_Virtual 4. Type: Virtual 5. Click OK to enable the virtual force calculation. 6. Click on Maxwell > Parameters > Assign > Force 7. Name: Force_Lorentz 8. Type: Lorentz 9. Click OK to enable the lorentz force calculation.

Add an Analysis Setup

1. Click Right on the Analysis folder in the Model Tree and select Add Solution Setup… 2. On the General tab, re-set the Number of passes to 15. 3. Percent Error to 0.01 4. On the Solver tab, re-set the Adaptive Frequency to 100kHz. 5. Click OK to save the setup.

Solve the Problem

1. Save the project by clicking on menu item File > Save 2. Select the menu item Maxwell 3D > Validation Check to verify problem setup 3. Click on Maxwell 3D > Analyze All.


Maxwell v12 6.2


View the Results

3. Select Maxwell 3D > Results > Solution Data… and click on the Force tab. Notice that the 3D results are reported for a 10mm depth while the 2D results were for 1meter depth. The DC forces are shown below.

4. Now select Type:AC<Mag,Phase> This shows the magnitude of the force F(x)Mag is approximately 5e-6 (N) and the phase F(x)Phase is -2.0 radians or -120 degrees.


Maxwell v12 6.2


Create a Plot of Force vs. Time The time-averaged, AC, and instantaneous components Lorentz force can be plotted vs. time by creating named expressions in the calculator using the formulas at the beginning of the application note.

1. Determine the time-averaged component of Lorentz force: • Click on Maxwell 3D > Fields > Calculator and then perform the following: • Quantity > J • Quantity > B > Complex > Conj > Cross • Scalar Y > Complex > Real • Number > Scalar > 0.5 > OK • Multiply • Geometry > Volume > left > OK • Integrate • Add… Name: Force_DC • OK

2. Determine the AC component of Lorentz force:

• Quantity > J • Quantity > B > Cross • Scalar Y • Function > Phase > OK • Complex > AtPhase • Number > Scalar > 0.5 > OK • Multiply • Geometry > Volume > left > OK • Integrate • Add… Name: Force_AC • OK

3. Determine the instantaneous (DC + AC) component of Lorentz force. In the Named Expressions

panel: • In the Named Expressions window, select Force_DC and Copy to stack • Select Force_AC and Copy to stack • Add • Add… Name: Force_inst • Click on OK and Done to close the calculator window.


Maxwell v12


6.2 - 15

6.2


4. Create a plot of Force vs. Phase. Now that the force quantities have been created, a plot of these named expressions can been created. • Select Maxwell 3D > Results > Create Fields Report > Rectangular Plot • Category: Calculator Expressions • Change the abscissa X: from the default Freq to Phase. • Quantity: Force_DC, Force_AC, Force_inst (hold down shift key to select all three at once) • New Report > Close • Right mouse click on the legend and select: Trace Characteristics > Add… • Category: Math • Function: Max • Add > Done • Double left mouse click on the legend and change from the Attribute to the General tab. • Check Use Scientific Notation and click on OK. Note that these values match the results on

the Solution Data > Force. Also, since forces fluctuate at 2 times the excitation frequency, there are two complete cycles in 360 degrees shown below.

This completes PART 2 of the exercise. Reference: MSC Paper #118 "Post Processing of Vector Quantities, Lorentz Forces, and Moments in AC Analysis for Electromagnetic Devices" MSC European Users Conference, September 1993, by Peter Henninger, Research Laboratories of Siemens AG, Erlangen


Maxwell 2D v12

7.0 - 1

Chapter 7.0

Chapter 7.0 – Transient Examples7.1 – Gapped Inductor Model

7.2 – Solenoid Problem with an External Circuit


7.1Gapped Inductor – Transient XY Application Note

7.1 - 1

Maxwell 2D v12

IntroductionThe Maxwell 2D Field Simulator’s XY transient solver can be used to demonstrate the difference between sinusoidal and non-sinusoidal excitation in a gapped inductor. In addition, the fringing flux effect on AC losses can be considered in this device.

The inductor consists of a ferrite core with a gap in the center leg. The winding has 15 copper turns which are connected in series. The inductor is excited by a 120A-60Hz sinusoidal current and a 20A-1kHz triangular current superimposed on it.

Although no motion occurs in this problem, the transient time-stepping solver is needed because of the complex waveform of the current.

After the problem is solved, the user can do the following:

View the flux lines and power loss density in the winding.

Plot the instantaneous power loss in the winding vs. time.

Calculate the average power loss over time.

A second simulation will be done using only a sinusoidal excitation in order to compare the losses.



7.1 - 2

Maxwell 2D v12

Setup the DesignClick on the menu item Project > Insert Maxwell 2D Design


Set Geometry Mode: Cartesian, XY

Select the radio button Magnetic: Transient

OK

Specify the Drawing UnitsClick on Modeler > Units

Select units: in

OK

Create the ModelThe model consists of a core and a winding. Note that each turn of the winding is exactly modeled and is “solid” in order to accurately determine the AC losses.

Set the model depthFor all transient XY models, the depth must be specified. Then all losses and force results reported are for that particular depth.

Click on Maxwell 2D > Model > Set Model Depth ...

Model Depth: 1 in

OK

Draw the Core Click on Draw > Rectangle

X: -2.5, Y: -3, Z: 0

dX: 5, dY: 6, dZ: 0


Name: Core

Material: Ferrite

Color: Red



7.1 - 3

Maxwell 2D v12

Draw the Core WindowsClick on Draw > Rectangle

X: -1.5, Y: -2, Z: 0

dX: 1, dY: 4, dZ: 0

Duplicate the window by selecting the window and choosing:

Edit > Duplicate > along line

X: 0, Y: 0, Z: 0

dX: 2, dY: 0, dZ: 0

Total Number: 2

Do not check Attach to original.

OK

Select Core, Rectangle1, Rectangle1_1and then click on:

Modeler > Boolean > Subtract

Blank Parts: Core

Tool Parts: Rectangle1, Rectangle1_1

Clone objects before subtracting: unchecked

Ok

Subtract the Core gapClick on Draw > Rectangle

X: -0.5, Y: -0.2, Z: 0

dX: 1, dY: 0.4, dZ: 0

Select Core, Gap and then click on:

Modeler > Boolean > Subtract

Blank Part: Core

Tool Parts: Rectangle_2

Clone objects before subtracting: unchecked

Ok



7.1 - 4

Maxwell 2D v12

Draw the WindingsClick on Draw > Rectangle

X: -1.4, Y: -1.825, Z: 0

dX: 0.8, dY: 0.125, dZ: 0


Name: Coil

Material: Copper

Color: Green

Create the return for the first winding turn:


X: 0, Y: 0, Z: 0

dX: 2, dY: 0, dZ: 0

Total Number: 2


OK


Name: Coil_return

Material: Copper

Color: Green

Create the complete winding by selecting Coil and Coil_return and then choosing:


X: 0, Y: 0, Z: 0

dX: 0, dY: 0.25, dZ: 0

Total Number = 15


Draw the Solution RegionClick on Draw > Region:

Padding Data: All Padding Directions

Padding Percentage: 100



7.1 - 5

Maxwell 2D v12

Assign the Outer BoundaryThe boundary must be set on the solution region.Choose Edit > Select > Edges to change the selection mode from object to edge.

While holding down the CTRL key, choose the three outer edges of the region.Click on Maxwell 2D > Boundaries> Assign > BalloonWhen done, choose Edit > Select > Object to object selection mode.

Assign the SourcesA 120A 60Hz sinusoidal current will be assigned to the 15 series turns in the inductor.

In addition, a 20A 1kHz triangular current source will be added on top of the sinusoidal current. The winding consists of a go and a return for the left and right sides of the winding. A simple sinusoidal function with be used to create the 60Hz component while a dataset “ds1” will be used to create the triangular component of current.

In the history tree, select: Coil, Coil_1, ... Coil_14Choose: Maxwell 2D > Excitations> Assign > CurrentName: leftValue: 120*sin(2*pi*60*time) + pwl_periodic(ds1, Time)

The Add Dataset window will automatically appear to enter the triangular waveform.

Name: ds1Enter the following X,Y coordinates and click OK and Done.

Type: SolidPolarity: PositiveOk

5

4

3

2

YX

00.001

-200.00075

00.00050

200.00025

001



7.1 - 6

Maxwell 2D v12

In the history tree, select: Coil_return, Coil_return1, ... Coil_return14

Choose Maxwell 2D > Excitations > Assign > Current

Name: right

Value: 120*sin(2*pi*60*time) + pwl_periodic(ds1, Time)

Name: ds1

Enter the following X,Y coordinates and click OK and Done:

Type: Solid

Polarity: Negative

Ok

Turn on the Eddy Effects in the windingChoose Maxwell 2D > Excitations > Set Eddy Effects ...

Check the eddy effect for all 30 coils.



7.1 - 7

Maxwell 2D v12

Add an Analysis SetupClick on Maxwell 2D > Analysis Setup > Add Solution Setup ...

On the General Tab:

Stop Time: 0.05 sec

Time Step: 0.00025 sec

On the Save Fields Tab:

Type: Linear Step

Start: 0 sec

Stop: 0.05 sec

Step Size: 0.01 sec

Click on: Add to List >>

OK



7.1 - 8

Maxwell 2D v12

Add Mesh OperationsIn the transient solvers, the mesh is not automatically created. It must either be linked to a magnetostatic or eddy current design, or you can manually create it. In this example, the mesh will be manually created.

In the history tree, select all 30 conductors and then Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based ...

Name: Coils_Inside

Restrict Length of Elements: Uncheck


Maximum Number of Elements: 500

Note that by choosing “Inside Selection” instead of “On Selection”, the mesh operation is applied evenly through the area of the conductors as opposed to being applied only on the outer perimeter of the conductor.

Select the core and then Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based.

Name: Core_Inside






7.1 - 9

Maxwell 2D v12

Create the Mesh before solvingSelect the menu item Maxwell 2D > Analysis Setup > Apply Mesh Operations

View the Solution Data for the MeshSelect the menu item Maxwell 2D > Results > Solution Data

Click on the Mesh Statistics tab to view the starting mesh.



7.1 - 10

Maxwell 2D v12

Create Output for Current using the CalculatorSince the input current is not an automatic output, this must be created manually.

Select the menu item Maxwell 2D > Fields > Calculator ...

Select the menu item Quantity > J > Scal? > ScalarZ

Geometry > Coil > OK

Integrate

Add...

Name: Current_in

OK

Done

Make the named expression available to be plottedTo do this, select: Maxwell 2D > Results > Output Variables...

Under Report Type, select “Fields”.

Choose Category: Calculator Expressions

Quantity: Current_in

Function: <none>.

Name: type in a variable such as I_in

Click on “Insert Quantity into Expression” and then Add.

This output will now be available for plotting. Click on Done to leave the Output Variables window.

Specify when expression will be calculatedIn the project tree, right click on Analysis > Setup1 and click on Properties. Under the Output Variables tab click on Add to add the newly created parameter for I_in. Be sure that the Evaluation Time Step = 0.00025s which is the same as the solve time step under the General tab. Select OK to exit.



7.1 - 11

Maxwell 2D v12

Solve the ProblemSave the project by clicking on menu item File > Save As

Select the menu item Maxwell 2D > Validation Check to verify problem setup

Click on Maxwell 2D > Analyze All

Plot the MeshSelect all objects and click on Maxwell 2D > Fields > Plot Mesh.

When done, hide the plot by selecting View > Active View Visibility > Fields Reporter and unchecking the Mesh1 plot.



7.1 - 12

Maxwell 2D v12

View the ResultsNow that you have generated a solution, you can analyze the results. Specifically, what you want to calculate and display are:

Flux lines plot at t=0.02sec.

Current density plot for the winding t=0.02sec.

The current and instantaneous average power loss for the windingvs time.

Plot Flux LinesSet the timestep = 0.02sec by selecting: View > Set Solution Context > 0.02sec > OK

Alternatively, you can set the solution context by double-clicking on the Time box in the lower left corner of the modeling window.

Select all objects by selecting CTRL-A




7.1 - 13

Maxwell 2D v12

Plot Current Density in CoilsThe current density in the coils will be greater near to the gap in the core because fringing flux caused induced proximity losses in the copper.

Create an object list including only the copper coils:

In the history tree, select coil and coil_return.

Click on Modeler > List > Create > Object List

Create the plot by selecting Objectlist1in the history tree.

Click on Maxwell 2D > Fields > Fields > Jz > Done



7.1 - 14

Maxwell 2D v12

Plot the Input CurrentCreate the plot of the named expression.

Select Maxwell 2D > Results > Create Transient Report > Rectangular Plot

Category: Output Var. Cache

Quantity: OVC(I_in)

New Report

0.00 10.00 20.00 30.00 40.00 50.00Time [ms]

-150.00

-100.00

-50.00

0.00

50.00

100.00

150.00

OV

C(I_

in)


OVC(I_in)Setup1 : Transient



7.1 - 15

Maxwell 2D v12

Plot the Losses in the WindingCreate the plot of the named expression. To do this,

Select Maxwell 2D > Results > Create Transient Report > Rectangular Plot

Category: Loss and Quantity: SolidLoss

New Report

Right mouse click on the legend and select: Trace Characteristics > Add...

Category: Math and Function: avg

Click on Add and Done and the average losses (approx. 4.35W) will be displayed in the legend.

2.00

4.00

6.00

8.00

10.00

12.00

Solid

Loss

[W]

Ansoft Corporation Maxwell2DDesign1XY Plot 2Curve Info avg

SolidLossSetup1 : Transient 4.3540

0.00 10.00 20.00 30.00 40.00 50.00Time [ms]

0.00



7.1 - 16

Maxwell 2D v12

Solve for the sinusoidal current source onlyCopy the MaxwellDesign1 and paste it in the Project tree area to create MaxwellDesign2

Remove all excitations for the windings and reassign them without the triangular dataset component.

Resolve the project by selecting Maxwell 2D > Solve. The average power loss (approx. 3.41W) is smaller than the previous simulation (approx. 4.35W) which included the triangular current component. Also, you can see that the power loss is sinusoidal at twice the excitation frequency.

0.00 10.00 20.00 30.00 40.00 50.00Time [ms]

-150.00

-100.00

-50.00

0.00

50.00

100.00

150.00

OV

C(I_

in)


OVC(I_in)Setup1 : Transient

0.00 10.00 20.00 30.00 40.00 50.00Time [ms]

0.00

1.00

2.00

3.00

4.00

5.00

6.00

Solid

Loss

[W]

Ansoft Corporation Maxwell2DDesign2XY Plot 2Curve Info avg

SolidLossSetup1 : Transient 3.4118

Maxwell v12

2D Transient – Application Note

7.2 - 1

7.2


A Solenoid Problem with an External Circuit

This example models an AC solenoid using Maxwell 2D. A full wave bridge rectifying drive circuit will be setup to drive the solenoid. Description A model of an AC solenoid using an external circuit will be simulated using the 2D RZ transient solver. The source is a 170V 60Hz sinusoidal voltage which is rectified using a full-wave bridge. The mechanical force for a spring and gravity are modeled using an equation. The force, loss, position, speed and winding current, flux, and voltage will be determined.

2D RZ Model

D1

D2

D3

D4

Model

rectify

LWinding225ohmRcoil

+ 170VLabelID=Vsource

0

Maxwell v12


7.2 - 2

7.2


Setup the Design


Set Geometry Mode: Cylindrical about Z Select the radio button Magnetic: Transient

Specify the Drawing Units

1. Click on Modeler > Units 2. Select units: in > OK

Import the Model Now the model can be created. Since this is a complicated geometry, the model will be imported from an old Maxwell 2D model file *.sm2.

1. Click on: Modeler > Import … 2. Navigate to find the file: Ex_7_02_Solenoid.sm2

Draw the Solution Region

1. Click on Draw > Region Padding Data: Pad Individual Directions Padding Percentage: X = +/- 300% Z = +/- 100%

3. Select View > Fitall > Active View to resize the drawing window. 4. Select wireframe view by selecting: View > Render > Wire Frame

NOTE: For 2D RZ designs, the –X limit will be the Z-axis if the padding percentage is large enough. Otherwise, if the -X padding percentage creates a region with –X > 0, then the region will have a “hole” in the model.

Maxwell v12


7.2 - 3

7.2


Assign the Materials Since the model was imported, no material properties have been assigned. Select the objects one at a time and assign the appropriate material properties.

1. Select the coil and the shadering and choose: Modeler > Assign Material > copper > OK

2. Select the endstop, flange, housing, plunger and top_nut and choose: Modeler > Assign Material > steel_1008 > OK

3. Select the Band and choose: Modeler > Assign Material > Vacuum > OK

Assign the Boundaries and Sources A no-fringing vector potential boundary will be assigned to outside of the 2D problem region. This forces all flux to stay in the solution region.

1. Choose Edit > Select > Edges to change the selection mode from object to edge. 2. While holding down the CTRL key, choose the top, right, and bottom outer edges of the region.

Note that the left edge does not need a boundary because it is automatically the axis of symmetry in a RZ model.

3. Click on Maxwell 2D > Boundaries> Assign > Vector Potential Value: 0 OK

4. When done, choose Edit > Select > Object to object selection mode.

Because the solenoid is a converted “AC” solenoid, it contains a copper “shading ring” which may have eddy currents induced in it. A zero voltage source must be set on the shade ring in order to properly represent a shorted single turn winding and to see if the eddy currents are significant or not.

1. Select the shadering and click on the menu item: Maxwell 2D > Excitations > Assign > Coil… Name: shadering Number of Conductors: 1 Polarity: Positive (into the screen) OK

Maxwell v12


7.2 - 4

7.2


2. Click on the menu item: Maxwell 2D > Excitations > Add Winding…

Name: Winding1 Type: Voltage and Solid Initial Current: 0 Resistance: 0 (for solid windings, resistance calculated by the solver) Inductance: 0 (coil inductance always calculated by the solver) Voltage: 0 (zero voltage represents a shorted turn, with no source) Number parallel branches: 1

3. In the project tree, right mouse click on shadering under Excitations and click on the menu item Add to Winding and

4. In the Add to Winding window, Winding1 will be selected and then click on OK.

Maxwell v12


7.2 - 5

7.2


5. Select the Coil and click on the menu item: Maxwell 2D > Excitations > Assign > Coil… Name: Coil Number of Conductors: 2250 Polarity: Positive (into the screen) OK

6. Click on the menu item: Maxwell 2D > Excitations > Add Winding … Name: Winding2 Type: External and Stranded (Note: stranded is assigned since the coil has 2250 turns). Initial Current: 0 Number parallel branches: 1 OK

7. In the project tree, right mouse click on coil under Excitations and click on the menu item Add to Winding

In the Add to Winding window, highlight Winding2 click on OK. The project tree should look like this:

8. Create an External Circuit To access Maxwell Circuit Editor, choose Maxwell 2D > Excitations > External Circuit >

Edit External Circuit… Select Edit Circuit… from the Edit External Circuit dialog

Maxwell v12


7.2 - 6

7.2


Click on File > New to create a new schematic Click on the Components tab in the Project Manager Window Expand Maxwell Circuit Elements to view the library elements Expand Passive Elements and click on DIODE and drag this component onto the sheet:

Name: D1 mod: rectify

Copy this diode three times creating D2, D3, and D4 and rotate them using CTRL-R before connecting together to form the full-wave bridge as shown below.

Select Passive Elements > DIODE_Model and drag this component onto the sheet: Name: rectify

Maxwell v12


7.2 - 7

7.2


Under Maxwell Circuit Elements > Dedicated Elements select Winding and drag this

component onto the sheet In the properties window change the following:

Name: Winding2 Note that this name has to be exactly the same name as used in the Winding

definition described previously in Maxwell > Excitations > Add Winding Under Maxwell Circuit Elements > Passive Elements select Res and drag this component

onto the sheet: Name: coil R: 25 ohms

Under Maxwell Circuit Elements > Sources select Vsin and drag this component onto the sheet, hit ESC to end insertion:

Name: source Va: 170 volts VFreq: 60 Hz

Connect all of the elements together using Draw > Wire and add a ground using Draw > Ground.

The circuit should look like this:

Click on Edit > Save As: ex07_02_solenoid.amcp Click on Maxwell Circuit > Export Netlist:

File Name: ex07_02_solenoid.sph

D1

D2

D3

D4

Model

rectify

LWinding225ohmRcoil

+ 170VLabelID=Vsource

0

Maxwell v12


7.2 - 8

7.2


9. Link the circuit file to the Maxwell project

Without closing the Maxwell Circuit Editor, return to the Maxwell project click on Cancel. Then choose Import Circuit… from the Edit External Circuit dialog and select

ex07_02_solenoid.sph

A window should indicate that the model imported successfully.

Clicking on the Circuit Path tab will verify the linked circuit file *.amcp.

Maxwell v12


7.2 - 9

7.2


Turn on the Eddy Effects in the winding In order to consider the skin effects in the busbars, you must manually turn on the eddy effect.

1. Choose Maxwell 2D > Excitations > Set Eddy Effects ... 2. Check the eddy effect for the shadering and choose OK.

Apply Mesh Operations The transient solver does not use the automatic adaptive meshing process, so a manual mesh needs to be created. Note that after the mesh operations are assigned, clicking on them in the history tree will shade the appropriate objects in the modeler window (assuming they are in wireframe view first).

1. Select the band and click on the menu item Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based.

Name: Band_Inside Restrict Length Of Elements: Uncheck Restrict Number of Elements: Check Maximum Number of Elements: 1000

2. Select the shadering and click on the menu item Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based.

Name: Shadering_Inside Restrict Length Of Elements: Uncheck Restrict Number of Elements: Check Maximum Number of Elements: 50

3. Select the coil, endstop, flange, housing, plunger, and top_nut and click on the menu item Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based.

Name: Other_Objects_Inside Restrict Length Of Elements: Check Maximum Length: 0.05 in (Note: be sure to set units = in) Restrict Number of Elements: Uncheck

Setup the Motion The plunger is the moving object and is surrounded by the band. (Note: moving objects are never allowed to touch the band. The minimum air gap is 0.002 inches when the solenoid is "fully" closed.) Positive motion is defined as upwards or in the positive Z direction. The starting position is -0.100 inch (or open) so the plunger will move upwards (and close) when the solenoid is energized.. The load force acts downward against the direction of motion and consists of: gravity (-0.04N), a spring preload force (-50N), and a variable compression spring force (-5530 * position) which is zero at the starting position and increases as the plunger closes. The units for the intrinsic variable "position" are meters.

Maxwell v12


7.2 - 10

7.2


1. Select the band object by clicking on it on the screen or in the history tree. 2. Choose: Maxwell 2D > Model > Motion Setup > Assign Band

On the Type tab, the Motion Type will always be Translation for RZ models. On the Type tab, the Moving Vector will Global:Z.

Set Positive as the direction of the moving vector.

On the Data tab: Initial Position: -0.1 in Translate Limit Negative: -0.1 in Translate Limit Positive: 0 in

On the Mechanical tab: Consider Mechanical Transient: Check Velocity: 0 m_per_sec Mass: 0.004 kg Damping: 1e-005 N-sec/m Load Force: -5530 * (.00254 + position) -0.04 -50 (units are in Newtons)

Maxwell v12


7.2 - 11

7.2


Create Analysis Setup

Click on Maxwell > Analysis Setup > Add Solution Setup General Tab

Stop Time: 0.05 s Time Step: 0.0002 s

Save Fields Tab Type: Linear Step Start: 0 s Stop: 0.05 s Step Size: 0.005 s Click on: Add to List >>

Solve the Problem

1. Save the project by clicking on menu item File > Save As 2. Select the menu item Maxwell 2D > Validation Check to verify problem setup 3. Click on Maxwell 2D > Analyze All.

Maxwell v12


7.2 - 12

7.2


Create Output Plots vs. Time The force, loss, position, speed and winding current, flux, and voltage will be plotted vs. time.

1. To create these plots select: Maxwell 2D > Results > Create Quick Report… 2. Select: Force, Loss, Position, Speed, and Winding

3. In the force plot below, Force_z is only the magnetic component of force (upwards) while

LoadForce is gravity, spring preload force, and a variable compression spring force (downwards).

0.00 5.00 10.00 15.00 20.00 25.00Time [ms]

-100.00

-50.00

0.00

50.00

100.00

150.00

Y1 [n

ewto

n]

Ansoft Corporation Maxwell2DDesign1Force Quick ReportCurve Info

Moving1.Force_zSetup1 : Transient

Moving1.LoadForceSetup1 : Transient

Note: When magnetic force exceeds load force (at Time = 4.2msec) armature starts to close

Maxwell v12


7.2 - 13

7.2


0.00 10.00 20.00 30.00 40.00 50.00 60.00Time [ms]

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

Mov

ing1

.Pos

ition

[mm

]

Ansoft Corporation Maxwell2DDesign1Position Quick ReportCurve Info

Moving1.PositionSetup1 : Transient

0.00 10.00 20.00 30.00 40.00 50.00 60.00Time [ms]

0.00

1.00

2.00

3.00

4.00

5.00

Mov

ing1

.Spe

ed [m

_per

_sec

]

Ansoft Corporation Maxwell2DDesign1Speed Quick ReportCurve Info

Moving1.SpeedSetup1 : Transient

Maxwell v12


7.2 - 14

7.2


This completes the exercise.

0.00 10.00 20.00 30.00 40.00 50.00 60.00Time [ms]

0.00

0.50

1.00

1.50

2.00

2.50

Solid

Loss

[W]

Ansoft Corporation Maxwell2DDesign1Loss Quick ReportCurve Info

SolidLossSetup1 : Transient

Notes: 1) In order to scale the plot and view the solid loss,

delete the stranded and core loss traces. 2) The solid losses in the shading ring are very

small, since the current is a rectified to be nearly DC. If the full wave bridge rectifier is eliminated so the solenoid uses AC voltage, the shading ring will have a more significant effect on both the losses and force.

0.00 10.00 20.00 30.00 40.00 50.00 60.00Time [ms]

-100.00

-80.00

-60.00

-40.00

-20.00

-0.00

20.00

40.00Y1

[A]

0.00

0.10

0.20

0.30

0.40

0.50

0.60

Y2 [W

b]

-100.00

-50.00

0.00

50.00

100.00

150.00

Y3 [V

]

Ansoft Corporation Maxwell2DDesign1Winding Quick ReportCurve Info

Current(Winding1)Setup1 : Transient

Current(Winding2)Setup1 : Transient

FluxLinkage(Winding1)Setup1 : Transient

FluxLinkage(Winding2)Setup1 : Transient

InducedVoltage(Winding1)Setup1 : Transient

InducedVoltage(Winding2)Setup1 : Transient

InputVoltage(Winding1)Setup1 : Transient


Maxwell 2D v12

9.0 - 1

Chapter 9.0

Chapter 9.0 – Basic Exercises9.1 – Electrostatic

9.2 – DC Conduction

9.3 – Magnetostatic

9.4 – Parametric

9.5 – Transient

9.6 – Transient with Circuit Editor

9.7 – Post Processing

9.8 – Optimetrics

9.9 – Meshing

9.10 – Scripting

9.11 – Linear ECE

9.12 – Eddy Current

9.13 – Rotational Transient Motion

9.14 – Boundary Conditions

9.15 – Permanent Magnets Assignment

9.16 – Magnetostatic Actuator Example


9.1Basic Exercises – Electrostatic Solver

9.1-1

Maxwell 2D v12

Introduction on the Electrostatic Solver

This note introduces the Electro Static solver based on some simple examples. This solver is meant to solve the static electric field without current flowing in conductors (conductors are in electrostatic equilibrium). The conductors are considered perfect such that there is no electric field inside conductors.

Capacitance of a Cylindrical Capacitor in RZ

Suppose we have a long coaxial line. We want to know what is the electric field distribution based on the potential (or the charges) that are applied on each conductor. We also want to determine the capacitance. We use an R-Z representation. We will then solve the same problem using an XY representation.

Draw the Model

Click on the menu item Project > Insert Maxwell 2D Design

Click on the menu item Maxwell > Solution Type

Select Geometry Mode: Cylindrical about ZSelect the radio button Electrostatic

Click on the menu item Draw > Rectangle or click on the icon

For the rectangle position, enter 0; 0; - 4 mm

For the opposite corner of the rectangle, enter 0.6; 0; 21 mm or enter for dx, dy, dz 0.6; 0; 25mm;

Change the name to Inner

Change the material to copper

Change the color and transparency level at your convenience.



9.1-2

Maxwell 2D v12

Create a second Rectangle

For rectangle position, enter 0.6; 0 ;- 4 mm

For dx, enter 0.4 mm, for dz, enter 25 mm or enter 1.0; 0 ; 21 mm for the position of the opposite corner.

Change the name to Air

Change the material to Air


Create a third rectangle

For center position, enter 1.0; 0; - 4mm

For dx, enter 0.2 mm, for dz, enter 25 mm or enter 1.2; 0 ; 21 mm for the position of the opposite corner.

Change the name to Outer

Assign material to copper


Select the menu item Draw > Region.

For the padding data, choose Pad All Directions

For the Padding Percentage, enter 300 for positive X direction and 0 for all other directions



9.1-3

Maxwell 2D v12

Assign Excitation

Based on the assumptions that the conductors are in electrostatic equilibrium, we assign voltage potential on the object itself. In other words, we do not solve inside conductors, we assume that all the conductor parts are at the same potential.

Apply voltage excitation to object Inner

Select the object Inner

Select the menu item Maxwell > Excitations > Assign > Voltage. As an alternative, once the object is selected, you can right click and select Assign Excitations > Voltage.

For the voltage, enter -1kV

Apply voltage excitation to object Outer

Select the object Outer

select the menu item Maxwell > Excitations > Assign > Voltage.

For the voltage, enter 1kV

Assign Executive ParameterIn addition to the fields, we are interested by the Capacitance value as well

as the force applied to the inner armature.

Capacitance Matrix

Select the menu item Maxwell > Parameters > Assign > Matrix

Include Voltage1 and Voltage2 in the capacitance computation by checking the radio buttons of the Signal Line column

Force computation


Select the menu item Maxwell > Parameters > Assign > Force



9.1-4

Maxwell 2D v12


Select the menu item Maxwell > Analysis Setup > Add Solution Setup

For the Percent Error, enter 0.5%

For the Refinement per Pass (Convergence tab), put 50%

Solve the ProblemSelect Setup1 from under Analysis in the project tree, right mouse click and select Analyze

Plot the electric fieldFrom the modeler history tree, select the plane Global:XZ.

On the 3D modeler window, right click and select Fields > E_Vector



9.1-5

Maxwell 2D v12

Get the capacitance value

From the Project window, right click on Setup1. From the context menu, select the entry Solutions

Select the tab entry Matrix

In our problem, we only have two conductors, therefore the capacitance values are symmetrical.

Select the tab entry Force. It gives you the force applied to the inner object. Note that the force is essentially zero since the model is magnetically balanced.

The analytical value of the capacitance per meter for an infinite long coaxial wire is given by the following formula:

C = 2πε0 / ln(b/a) (a and b being the inside and outside diameters)

The analytical value would is therefore 1.089e-10 F/m (a =0.6mm, b=1mm)

In our project, then length of the conductor is 25 mm, therefore the total capacitance is. 2.723pF. We obtain a good agreement with the obtained result. 2.722 pF.

Note: in the Convergence tab, you have access to the total energy of the system. We find 5.4459e-6 J. It is exactly 2000 times the capacitance (2000V being the difference of potential).



9.1-6

Maxwell 2D v12

Capacitance of a Cylindrical Capacitor in XY

The same problem is now solved using an XY representation

Draw the Model



Select Geometry Mode: Cartesian XYSelect the radio button Electrostatic

Click on the menu item Draw > Circle or click on the icon

For the center position, enter 0; 0; 0mm

For the radius, enter 0.6 mm;

Change the name to Inner



Create another circle.



For the radius, enter 1.2 mm;

Change the name to Outer





For the radius, enter 1. mm;

Change the name to Air



9.1-7

Maxwell 2D v12

Assign Excitation

Based on the assumptions that the conductors are in electrostatic equilibrium, we assign voltage potential on the object itself. In other words, we do not solve inside conductors, we assume that all the conductor parts are at the same potential.

Apply voltage excitation to object Inner


Select the menu item Maxwell > Excitations > Assign > Voltage. As an alternative, once the object is selected, you can right click and select Assign Excitations > Voltage.

For the voltage, enter -1kV

Apply voltage excitation to object Outer

Select the object Outer

select the menu item Maxwell > Excitations > Assign > Voltage.

For the voltage, enter 1kV

Assign Executive Parameter

In addition to the fields, we are interested by the Capacitance value.

Capacitance Matrix


Include Voltage1 and Voltage2 in the capacitance computation by checking the radio buttons. Set Voltage1 as a signal line and Voltage2 as ground.



For the Percent Error, enter 0.5%




9.1-8

Maxwell 2D v12

Solve the Problem

Select Setup1 from under Analysis in the project tree, right mouse click and select Analyze


From the Project window, right click on Setup1. From the context menu, select the entry Solutions

Select the tab entry Matrix

The analytical value of the capacitance per meter for an infinite long coaxial wire is given by the following formula:

C = 2πε0 / ln(b/a) (a and b being the inside and outside diameters)

The analytical value would is therefore 1.089e-10 F/m (a =0.6mm, b=1mm)

This matches the obtained value.



9.1-9

Maxwell 2D v12

Capacitance of a planar capacitor

In this example we illustrate how to simulate a simple planar capacitor made of two parallel plates. The bottom plate is modeled and the top plate is considered by using only the edge of the dielectric (air).

Draw the modelClick on the menu item Project > Insert Maxwell 2D Design

Name the design Plate


Select Geometry Mode: Cartesian XYSelect the radio button Electrostatic

Select the menu item Draw > Rectangle to create a plate

For the first position corner, enter 0;0 mm

For the Xsize, enter 25 mm

For the Ysize, enter 2mm

For the material property, enter pec (perfect conductor)

Name the first box DownPlate

Select the menu item Draw > Rectangle to create a plate

For the first position corner, enter 0;0mm

For the Xsize, enter 25 mm

For the Ysize, enter 3mm

Name the box Region

For the material property, enter air



9.1-10

Maxwell 2D v12

Assign Excitation

Select the object DownPlate, select the menu item Maxwell > Excitations > Assign > Voltage. As an alternative, once the object is selected, you can right click and select Assign Excitations > Voltage.

For the voltage, enter 0V

Select the upper edge of the Region, select the menu item Maxwell > Excitations > Assign > Voltage.

For the voltage, enter 1V



9.1-11

Maxwell 2D v12

Assign Executive Parameter


Include Voltage1 and Voltage2 in the capacitance computation

We ground Voltage2. We will obtain just a 1 by 1 matrix.



For the Percent Error, enter 1%


Solve the Problem

Select Setup1 from under Analysis in the project tree, right mouse click and select Analyze. The problem is really easy, therefore the solution is obtained almost immediately.



9.1-12

Maxwell 2D v12


From the Project window, right click on Setup1. From the pull down menu, select Solutions, then the Matrix tab

The analytical value of the capacitance for two parallel plates is given by:

C = A/ d *ε0 (A is the area of the plate and d is the thickness of the dielectrics)

If we consider the plate to be 25mm by 25 mm, using the above formula, we obtain 5.53 pF (the dielectric is 1mm thick).

We obtain 221.35pF. This value should be considered as the capacitance of the two parallel plates with a 1 meter depth. If we rescale this value by multiplying by 0.25mm we find 5.53pF as well.

9.3Basic Exercise – Magnetostatic Force Calculation

9.3-1Ansoft Maxwell 2D Field Simulator v12 User’s Guide

Maxwell 2D v12

Force calculation in Magnetostatic SolverThis exercise will discuss how to set up a force calculation in the 2D Magnetostatic Solver.

Problem DescriptionAs shown in the following picture, a coil and slug are drawn in a plane using RZ symmetry. The coils carry a current that exert a vertical force on the ferromagnetic slug.

2D Symmetric Coil and Slug about z-axis

Actual 3D Coil and Slug



Maxwell 2D v12

Create a New ProjectOpen up Maxwell V12


Click on the menu item Maxwell 2D> Solution Type > Magnetostatic

Change the geometry mode to Cylindrical about Z

Draw the SlugClick on the menu item Draw > Rectangle

X,Y, Z: 0,0,-10, Enter (default units are in mm)

DX, DY, DZ: 5,0,15, Enter

Change its name from Rectangle1 to Slug

Select the Slug and change its material to Steel 1008

Change its color if desired

Draw the CoilClick on the menu item Draw > Rectangle

X, Y, Z: 6,0,0, Enter

DX, DY, DZ: 4,0,20, Enter

Change its name to: Coil

Change its material to: Copper




Maxwell 2D v12

Add a RegionClick on the menu item Draw > Region:

Select Pad all Directions and type 100 in Padding Percentage

You should see a message indicating that the –X direction is set to zero due to RZ-symmetry about the Z-axis.

Select Region and click on the menu item View > Hide Selection > All views.

Save your projectClick on File > Save As:

Magnetostatic_Force.mxwl for Basic Exercise Magnetostatic Force calculation

Assign ExcitationSelect the Coil and click on the menu item Maxwell2D > Excitations > Assign > Current:

Name: Current1

Value: 1000

Ref. Direction: Negative (so positive current will be in the negative Y direction)



Maxwell 2D v12

Assign Boundary to Region EdgesFrom the object tree, select Region

Click on the menu item Edit > Select > All Object Edges

Click on the menu item Maxwell2D > Boundaries > Balloon

Assign Force CalculationSelect the Coil and click on the menu item Maxwell2D > Parameters > Assign > Force

Name: Force1



Maxwell 2D v12

Create Analysis SetupClick on Maxwell 2D > Analysis Setup > Add Solution Setup

Maximum Number of Passes: 15

Refinement per Pass: 30

Click on OK


View the Automatic Adaptive Mesh ConvergenceRight click on the project tree item Analysis > Setup1 and select Convergence.



Maxwell 2D v12

View Calculated Force ResultClick on the Force tab in the open Solutions window.

The calculated force is updated automatically after each pass.



Maxwell 2D v12

Plot the Magnitude of Magnetic Flux DensitySelect the object tree item Global: XZ plane under Planes

Select the menu item Maxwell2D > Fields > Fields > B > Mag_B

Click OK on the Create Field Plot window.

This Concludes the Magnetostatic Force Calculation Basic Exercise.


9.4Basic Exercises – Parametric Solver

9.4 - 1

Maxwell 2D v12

2D Parametric study using a coil and iron slug. An RZ Magnetostatic problem will be used to demonstrate the setup of a parametric solution using Optimetrics in Maxwell 2D. The coil current and the dimensional length of an iron slug will be varied and the force on the slug will be observed.

Click on the menu item Project > Insert Maxwell 2D Design.

Click on the menu item Maxwell 2D > Solution Type > Magnetostatic, and select Cylindrical about Z,from the pull down menu.

Set the Units and the Snap Mode. Click on the menu item Modeler > Units . . . , and select mm.

Click on Modeler > Snap modeVerify that Snap To: Grid and Vertex are set.

2D Geometry: Iron Slug inside a coil. Draw the coil: Click on the menu item Draw > Rectangle, and arbitrarily choose a starting point and opposite corner for what will be the coil.

Double click on CreateRectangleunder Rectangle1 in the History Tree, and edit the Position, Xsizeand Zsize as shown, and click OK.

2D Flux Lines and Flux Density3D Geometry: Coil and Iron Slug

Coil OR = 1.25mm

Coil IR = 1mm

Coil Height = 0.8mm

Slug width = 1mm

Slug depth = 1mm

Slug Height = 1mm



9.4 - 2

Maxwell 2D v12

Draw the Slug: Click on the menu item Draw > Rectangle, and arbitrarily choose a starting point and opposite corner for what will be the slug.

Double click on CreateRectangle under Rectangle2 in the History Tree, and edit the Position, Xsize and Zsize as shown.

Enter the text ‘SlugHeight’ for the Value of Zsize. After selecting OK, the Add Variable box appears. Assign the Value for SlugHeight as 1mm, and click OK.

Note: By defining a variable name (SlugHeight) it becomes a design variable. Similarly, if an object is moved, it’s move distance can be assigned a variable. The Design Variables are accessible in the Property window by clicking on the Design name in the Project Manager. Or they can be viewed by clicking: Maxwell 2D > Design Properties . . .

Note: The parameter for Xsize is defined using the predefined constant, pi, and an equation that calculates the equivalent 2D cross-section of a 1mm2 slug which was used in the 3D Exercise. Other predefined constants can be found by selecting from the menu, Project > Project Variables, and selecting Constants tab.

Assign Materials and NamesSelect the Rectangle1 object in the Design Tree and double click it to edit it’s properties.

Name: Coil

Material: Select copper from the material database.

Color: Change the color to Orange, and click OK.



9.4 - 3

Maxwell 2D v12

Similarly, select the Rectangle2 object in the Design Tree and double click it to edit it’s properties.

Name: Slug

Material: Select steel_1008 from the material database.

Color: Change the color to Blue, and click OK.

Create the RegionSelect from the menu, Draw > Region.

Select the Pad Individual Directions radio button and assign padding percentages as shown below and Click OK.

Since this model is symmetric about the Z-axis, the X=0 boundary is the line of symmetry.

Assign the Boundary ConditionView the full geometry by selecting from the menu, View > Fit All > Active View, or simply type the shortcut Ctrl+D.

Choose the Edge selection mode by selecting from the menu, Edit > Select > Edges , or right click in the drawing space and click Select Edges.

While holding down the Ctrl key, select the top, bottom, and right edges of the Region.

From the menu, select Maxwell 2D > Boundaries > Assign > Balloon . . .

Change back to the Object selection mode by selecting from the menu, Edit > Select > Objects.



9.4 - 4

Maxwell 2D v12

Assign the ExcitationSelect the Coil from the History Tree.

From the menu, select Maxwell 2D >Excitations > Assign > Current . . .

Leave Name as Current1 and set Value: AmpTurns and click OK.

Define ‘AmpTurns’ as 100 in the Add Variable window, and click OK.

Assign the Force CalculationInclude a force calculation by selecting the Slug from the History Tree.

Select from the Menu, Maxwell 2D > Parameters > Assign > Force . . .

Change the name to SlugForce, in the Force Setup window.

Add an Analysis SetupRight Click on Analysis in the Model Tree and select Add Solution Setup.Click OK to accept the defaults for now.

Add the Force as an Output Variable. Select from the menu, Maxwell 2D > Results > Output Variables . . .

Select SlugForce.Force_z in the Quantity: window and click on Insert Into Expression.

Insert a minus sign in the Expression text box in front of Slugforce.Force_z, this will result in a positive force.

Enter ‘SlugForce’ as the Name and select Add.

Click Done.



9.4 - 5

Maxwell 2D v12

Modify Setup and solve a nominal problemIn the project tree, double click on Setup1 under the Analysis folder.

Change the default Maximum Number of Passes to 15. Change the default Percent Error to 0.5.

In the Convergence tab, select SlugForce to be displayed in the Convergence, as shown below. Click OK.

Find the Validate icon in the tool bar. (It looks like a green check mark). This will check the problem setup.

Solve the problem by right clicking on Setup1 in the Project manager. Click on Analyze.



9.4 - 6

Maxwell 2D v12

Inspect ResultsCheck the solution by again right clicking on Setup1 and select Convergence . . .

Plot flux results:Select the Coil, Slug, and Region objects by using ctrl+A.

From the menu, select Maxwell 2D > Fields > Fields > B > Mag_B, click Done in the Create Field Plot window.

Similarly, select Maxwell 2D > Fields > Fields > A > Flux Lines, click Done in the Create Field Plot window.

In the project tree under Field Overlays, right click on Mag_B1 and check Plot Visibility. Do the same for Flux_Lines1 so that both plots are visible.



9.4 - 7

Maxwell 2D v12

Create a Parametric solutionClick on the Menu item Maxwell 2D > Optimetrics Analysis > Add Parametric . . .

Click Add. . . in the Add/Edit Sweep window to define the parameters to be swept in the analysis.

Select SlugHeight from the Variable pull-down menu, and assign Start =1 mm, Stop =2 mm, and Step = 0.2, and click the Add >> button.

Similarly, select AmpTurns from the Variable pull-down menu, and assign Start =100, Stop =200, and Step = 50, and click the Add >> button.

Click OK.

Click on the Table tab to inspect the combination of solutions that have been created. There should be 18 solutions since we defined 6 variations of SlugHeight and 3 variations of AmpTurns.

Next, select the Calculations tab to define which outputs will be calculated for each parametric solution.

Then, click on the Setup Calculations . . . Button in the lower left corner of the Calculations tab.



9.4 - 8

Maxwell 2D v12

The Add/Edit Calculation window should appear :

Select: Category: Output Variables. Quantity: SlugForce (a previously defined Output Variable).

Click Add Calculation.

Click Done.

In the Options Tab, click both boxes for Save Fields And Mesh, and Copy Geometrically Equivalent Meshes.

Solve the Parametric problemIn the Project Manager window, under Optimetrics, right click onParametricSetup1, and select Analyze.

Note: the solving criteria is taken from the nominal problem, Setup1 . Each parametric solution will re-mesh if the geometry has changed or the energy error criteria is not met as defined in Setup1.



9.4 - 9

Maxwell 2D v12

View the solution progress:

In the Project Manager window, right click on ParametricSetup1, and select View Analysis Result . . .

Click the Table button to view all the results in tablature form.

The full parametric solution should take about 1 minute depending on the speed of the machine.

Graph the Force vs. AmpTurns vs. SlugHeightRight Click on Results in the Project Manager, and select Create Magnetostatic Report > Rectangular Plot.



9.4 - 10

Maxwell 2D v12

In the New Report – New Traces window, Select the Trace tab:

Select: Category: Output Variables. Quantity: SlugForce (a previously defined Output Variable).

X: SlugHeight, and Y: SlugForce.

Select the Families tab:

Ensure that that AmpTurns is selected as the Sweeps variable.

Click on New Report, Click on Close.

The plot will appear as shown on next page, the markers can be added by double clicking on the trace and checking the Show Symbol check box.

Right click in the plot and select Export Data . . . to export the data to a file.

The axis can be edited by double clicking on the x or y axis.

The title can be changed by editing the name in the Project Tree.



9.4 - 11

Maxwell 2D v12

A 3D surface can be created by right clicking on Results in the Project Tree and selecting Create Magnetostatic Report > 3D Rectangular Plot.

Edit the 3D Cartesian Plot window as shown below. Click New Report, Close.

This is the end of the 2D Parametrics Basic Exercise.



9.4 - 12

Maxwell 2D v12

Animate the flux plot:Since the SlugHeight and AmpTurns were parametrically varied, the flux plot can be animated with respect to either of these variables.

In the Project Manager window, right click on the Flux_lines plot and select Animate…

In the Setup Animation window, choose:

Swept Variable: SlugHeight

Select values: (select all values in the list)

Choose OK to create the animated plot.

After viewing the plot, choose: Export… to save as a .gif movie file.


9.5Basic Exercise – 2D Transient

9.5-1

Inductor using transient sourceThis exercise will discuss how to use transient sources as the excitation for an inductor coil.

Draw the InductorClick on the menu item Project > Insert Maxwell 2D Design

Click on the menu item Maxwell 2D > Solution Type

Geometry Mode: Cylindrical About Z

Magnetic: Transient

Click on the menu item Draw > Rectangle

Start Position: 0,0,0

X Size: 2mm

Z Size: 20 mm

Change its name to: Core

Change its material to: ferrite

Change its color to green

Select the Core and click on the menu item Edit > Copy

Click on the menu item Edit > Paste, the new objects name is Core1

In the object tree click on Core1 and then click on CreateRectangle

In the Properties window change the following:

Position: 0,0,1mm

X Size: 5mm, Z Size: 18mm

Click on the name Core1 and change its properties

Name: Coil

Material: Copper

Color: Yellow

Select Coil and Core and then click on 2D Modeler > Boolean > Subtract:

Blank Part: Coil

Tool Part: Core

Clone objects before subtracting: checked



9.5-2

Click on the menu item Draw > Region:



Change the name of the design to:

BE_Trans for Basic Exercise Transient

Assign ExcitationSelect the Coil and click on the menu item Maxwell 2D > Excitations > Assign > Coil:

Name: Coil

Number of Conductors: 150

Polarity: Positive (into the screen)

Click on the menu item Maxwell 2D > Excitations > Add Winding

Name: Winding_A

Type: Voltage

Stranded: Checked

Initial Current: 0.0 amps

Resistance: 25 ohm

Inductance: 0 H

Voltage: 0 V (Note: This will be changed on the next page)

Number of parallel branches: 1

Select Winding_A from the project tree under Excitation and right mouse click and select Add Coils …

In the Add Terminals window, select: Coil and click Ok.

The project tree should look like this:



9.5-3

Create the ExcitationThe excitation for this problem will be a voltage source with a 1KHz triangular wave superimposed on a 50 Hz sine wave that has a 50 volt DC offset.

Click on the menu item Maxwell 2D > Design Datasets and then Add a new dataset

Name: DSet_A

Coordinates:

X1 = 0 Y1 = 0

X2 = 250e-6 Y2 = 1

X3 = 750e-6 Y3 = -1

X4 = 1e-3 Y4 = 0

Click Ok and Done.

Select Winding_A from the Project Tree and right mouse click and select Properties and type in the following:

Change Voltage: 0 V that was specified on the previous page to: Voltage: V_DC + Vp*sin(2*PI*50*Time) + 5*pwl_periodic (DSet_A, Time)

Click on OK and in the dialog window enter 50 for V_DC, click on OK

In the next dialog window enter 25 for Vp, click on OK

The first term is the DC offset and the 2nd is peak voltage of the sine wave



9.5-4

Assign Balloon BoundaryClick on the menu item Edit > Select > Edges

Select one of the edges of the background region

Click on the menu item Edit > Select > Select Edge Chain

Click on the menu item Maxwell 2D > Boundaries > Assign > Balloon

Name: Balloon1

Apply Mesh OperationsThe transient solver does not use the automatic adaptive meshing process, so a manual mesh needs to be created.

Select the Core and click on the menu item Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based.

Name: Core_Inside




Select the Coil and click on the menu item Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based.

Name: Coil_Inside




Create Analysis SetupClick on Maxwell2D > Analysis Setup > Add Solution Setup

General Tab

Stop Time: 20 ms

Time Step: 100 us

Save Fields Tab

Type: Linear Count

Start: 0 sec

Stop: 20 msec

Count: 11

Click on: Add to List



9.5-5


Save the DesignClick on File > Save to save the design and results

Plot the Voltage and CurrentClick on Maxwell 2D > Results > Create Transient Report > Rectangular plot:

Select Category: Winding

Select Quantity: InputVoltage(Winding_A)

Click on: New Report

Select Quantity: Current(Winding_A)

Click on: Add Trace

Click on: Close



9.5-6

Plot the Flux LinesBe sure that the 2D Modeler window is in the active view window.

Select the menu item View > Set Solution Context

Time: 0.01 sec

Select all of the objects by clicking on Edit > Select All

Click on Maxwell 2D > Fields > Fields > A > Flux Lines

Click on Done

Double click on the plot lgend:

Color MapTab > Number of Divisions: 56

Plots Tab > IsoValType: Line

Zoom in to see the plot below.

This concludes the Basic Example for Transient Sources


9.6Basic Exercise – 2D Transient with Circuits

9.6-1

Inductor using transient sourceThis exercise will discuss how to use transient sources as the excitation for an inductor coil.

Draw the InductorClick on the menu item Project > Insert Maxwell 2D Design

Click on the menu item Maxwell 2D > Solution Type

Geometry Mode: Cylindrical About Z

Magnetic: Transient

Click on the menu item Draw > Rectangle

Start Position: 0,0,0

X Size: 2mm

Z Size: 20 mm

Change its name to: Core

Change its material to: ferrite


Select the Core and click on the menu item Edit > Copy

Click on the menu item Edit > Paste, the new objects name is Core1

In the object tree click on Core1 and then click on CreateRectangle

In the Properties window change the following:

Start Position: 0,0,1mm

X Size: 5mm, Z Size: 18 mm

Click on the name Core1 and change its properties

Name: Coil

Material: Copper

Color: Yellow

Select Coil and Core and then click on 2D Modeler > Boolean > Subtract:

Blank Part: Coil

Tool Part: Core

Clone objects before subtracting: checked



9.6-2

Click on the menu item Draw > Region:



Change the name of the design to:

BE_Trans_Ckt for Basic Exercise Transient

Assign ExcitationSelect the Coil and click on the menu item Maxwell 2D > Excitations > Assign > Coil:

Name: Coil

Number of Conductors: 150

Polarity: Positive (into the screen)

Click on the menu item Maxwell 2D > Excitations > Add Winding

Name: Winding_A

Type: External

Stranded: Checked

Initial Current: 0.0 amps

Number of parallel branches: 1

Select Winding_A from the project tree under Excitation and right mouse click and select Add Coils …

In the Add Terminals window, select: Coil and click Ok.

The project tree should look like this:



9.6-3

Create an External CircuitTo access Maxwell Circuit Editor, right mouse click on Excitations and select External Circuit > Edit External Circuit

Select Edit Circuit from the Edit External Circuit dialog

Maximize the Ansoft Maxwell Circuit Editor window on the screen.

Click on File > New to create a new schematic

Select the Components tab and choose Maxwell Circuit Elements > Dedicated Elements > Winding and drag this component onto the sheet

Select the Winding on the schematic.

In the properties window change the following:

Name: Winding_A

Note: This name has to be exactly the same name as used in the Winding definition described previously in Maxwell > Excitations > Add Winding

Select Sources > VSin drag this component onto the sheet, hit ESC to end insertion:

Va: 100 volts

VFreq: 50 Hz

Select Source > VSin drag this component onto the sheet:

Va: 10 volts

VFreq: 1000 Hz

Select Passive Elements > Res and drag this component onto the sheet:

R: 25 ohms



9.6-4

Connect all of the elements together using Draw > Wire and add a ground using Draw > Ground.

Select Probes > Voltmeter and place it between the two voltage sources and ground.

The circuit should look like this:

Click on File > Save As:

BE_Circuit.amcp for Basic Exercise Circuit (Note directory where file is saved.)

Click on Maxwell Circuit > Export Netlist:

File Name: BE_Circuit.sph (Note directory where file is saved.)

Link the circuit file to the Maxwell project

In the Maxwell BE_Trans_Ckt.mxwl project click on Import Circuit from the Edit External Circuit dialog and select BE_Circuit.sph

The Edit External Circuit Panel should appear as below with a check in the Has Inductor in Circuit box.

To verify the location of the imported .sph file, click on Circuit Path tab.

Note: Same name used: Winding_A



9.6-5

Assign Balloon BoundaryClick on the menu item Edit > Select > Edges

Select one of the edges of the background region

Click on the menu item Edit > Select > Select Edge Chain


Name: Balloon1

Apply Mesh OperationsThe transient solver does not use the automatic adaptive meshing process, so a manual mesh needs to be created.

Select the Core and click on the menu item Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based.

Name: Core_Inside




Select the Coil and click on the menu item Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based.

Name: Coil_Inside




Create Analysis SetupClick on Maxwell > Analysis Setup > Add Solution Setup

General Tab

Stop Time: 20 ms

Time Step: 100 us

Save Fields Tab

Type: Linear Count

Start: 0 sec

Stop: 20 msec

Count: 11

Click on: Add to List



9.6-6


Save the DesignClick on File > Save to save the design and results

Plot the Voltage and CurrentClick on Maxwell 2D > Results > Create Transient Report > Rectangular plot:

Select Category: NodeVoltage

Select Quantity: NodeVoltage(IVoltmeter)

Click on: New Report

Select Category: Winding

Select Quantity: Current(Winding_A)

Click on: Add Trace

Click on: Close



9.6-7

Plot the Flux LinesBe sure that the 2D Modeler window is in the active view window.Select the menu item View > Set Solution Context

Time: 0.01 secSelect all of the objects by clicking on Edit > Select AllClick on Maxwell 2D > Fields > Fields > A > Flux Lines

Click on DoneDouble click on the plot legend:

Color Map Tab > Number of Divisions: 56Plots Tab > IsoValType: Line

Zoom in to see the plot below.

This concludes the Basic Example for Transient with Circuits


9.8Optimetrics Example – Puck Attractor

9.8-1

Maxwell 2D v12

Puck Magnet AttractorThis example describes how to create and optimize a puck magnet producing an optimal force on a steel plate using the 2D RZ Magnetostaticsolver and Optimetrics in the Ansoft Maxwell 2D Design Environment.

The optimization obtains the desired force = 0.25N by varying the air gap between the plate and the puck using a local variable.

Magnet

Steel Plate



9.8-2

Maxwell 2D v12

Create a New ProjectOpen up Maxwell V12


Click on the menu item Maxwell 2D> Solution Type

Change the geometry mode to Cylindrical about Z

Solver should be: Magnetic: Magnetostatic

Verify that mm are units under Modeler > Units

Draw the PlateClick on the menu item Draw > Rectangle

X,Y, Z: 0,0,0, Enter (default units are in mm)

dX, dY, dZ: 5,0,1, Enter

Change its name from Rectangle1 to Plate

Select the Plate and change its material to Steel 1008


Draw the MagnetClick on the menu item Draw > Rectangle

X, Y, Z: 0,0,2 Enter

dX, dY, dZ: 2,0,2 Enter

Change its name to: Magnet

Change its material to: NdFe30

Change its color to Red



9.8-3

Maxwell 2D v12

Create the relative coordinate system for the puck magnetization:The default magnetization direction for NdFe30 is in the X-direction. Since magnetization in the Z-direction is desired for this example, a face coordinate will be created:

Change to face select mode using: Edit > Select > FacesClick on the magnet and then choose: the menu item Modeler > Coordinate System > Create > Face CSClick on the lower left corner of the magnet and the upper left corner of the magnet to create the face coordinate system.

Change back to object select mode using: Edit > Select > Objects

Assign the relative coordinate system to the Puck object:To assign the relative coordinate system:

In the History Tree, select the object Magnet.

Ín the attributes window, change the attribute Orientation to FaceCS1. To change the value, click on the value Global and select the new coordinate system from the pull-down list.

In the history tree, change back to the Global coordinate system by clicking on Global under Coordinate Systems



9.8-4

Maxwell 2D v12

Setup the magnet motionTo create the variable allowing the magnet to move parametrically:

1. Select the magnet and then Edit > Arrange > Move 2. Click twice on the lower left corner of the magnet3. Click the OK button4. The properties window appears automatically. Under command tab set the

Move Vector value to 0, 0, move. Press Enter.

5. The Add Variable window appears automatically. Set the value of the variable move to 0mm.



9.8-5

Maxwell 2D v12

Add a RegionClick on the menu item Draw > Region:

Select Pad all Directions and type 300 in Padding Percentage

Reset the view by choosing: View > Fit All > All Views

You should see a message indicating that the –X direction is set to zero due to RZ-symmetry about the Z-axis.

Save your projectClick on File > Save As:

Ex_09_08.mxwl for Basic Exercise Optimization calculation



9.8-6

Maxwell 2D v12

Assign Boundary to Region EdgesClick on the menu item Edit > Select > Faces

With the CTRL key depressed click on the top, right, and bottom edges.


Click on the menu item Edit > Select > Objects

Assign Force CalculationSelect the Plate and click on the menu item Maxwell2D > Parameters > Assign > Force

Name: Force1



9.8-7

Maxwell 2D v12

Add an Analysis SetupRight Click on Analysis in the Model Tree and select Add Solution Setup.

Set Maximum Number of Passes: 15

Percent Error: 0.1%

Click OK.

Add the Force as an Output Variable.Select from the menu, Maxwell 2D > Results > Output Variables . . .

Select Force1.Force_z in the Quantity: window and click on Insert Into Expression.

Enter ‘Fz’ as the Name and select Add.

Click Done.



9.8-8

Maxwell 2D v12

Modify Setup and solve a nominal problemIn the project tree, double click on Setup1 under the Analysis folder.

On the Convergence tab, check Use Output Variable Convergence and the Output Variable: Fz will be displayed in the Convergence, as shown below.

Set Max Delta Per Pass: 0.1%

Click OK.

Find the Validate icon in the tool bar. (It looks like a green check mark). This will check the problem setup.

Solve the problem by right clicking on Setup1 in the Project manager. Click on Analyze.



9.8-9

Maxwell 2D v12

View the Automatic Adaptive Mesh ConvergenceRight click on the project tree item Analysis > Setup1 and select Convergence.

View Calculated Force ResultClick on the Force tab in the open Solutions window.

The calculated force is updated automatically after each pass.



9.8-10

Maxwell 2D v12

Optimetrics Setup and SolutionIt is possible to optimize position in order to obtain the specified force. For this optimization, the position will be varied to obtain a desired force of 0.25N.

Specify the Optimization VariablesBefore starting the optimization setup, the appropriate variables must be included in the optimization.

Select the menu item Maxwell 2D > Design Properties, click on theOptimization radial button in order to specify that move be used in an optimization solution.

Check the Include box.

Set the Min = 0mm, and Max = 1mm.

Select OK to exit.



9.8-11

Maxwell 2D v12

Setup an Optimization AnalysisSelect the menu item Maxwell 2D > Optimetrics Analysis > Add Optimization ...In the Setup Optimization window, change the optimizer to: Sequential Nonlinear ProgrammingReduce the Max No of Iterations: 10 so the solution will not do to many iterations.

Click Setup Calculations... and then Output Variables…

In the Output Variables window, enter the following:

1. Name: target2. Expression: 0.253. Click on Add to create this output variable for the target inductance.

4. Name: cost15. Expression: (target - Force_z) ^26. Click on Add to create this output variable for the cost function.

7. Click on Done to leave the Output Variable window.



9.8-12

Maxwell 2D v12

Setup an Optimization AnalysisIn the Add/Edit Calculation note that both target and cost1 are now listed.

Highlight cost1 and click Add Calculation.

Click Done to leave the Add/Edit Calculation window

Setup an Optimization AnalysisIn the Setup Optimization window, change the Condition: Minimze

Click OK to leave the Setup Optimization window.



9.8-13

Maxwell 2D v12

Solve the Optimization AnalysisIn the project tree window, highlight OptimizationSetup1.

Select the menu item Maxwell 2D > Analyze All to solve. Solution time is approximately 5 - 10 minutes.

Optimetrics ResultsYour Optimetrics Results will be similar to the following results.Select the menu item: Maxwell 2D> Optimetrics Analysis > Optimetrics Results

Check Log Scale to display the plot below.



9.8-14

Maxwell 2D v12

Optimetrics ResultsChoose View: Table to display the results below.



9.8-15

Maxwell 2D v12

Create Plot of Cost vs ForceTo create a report:

1. Select the menu item Maxwell 2D > Results > Create Magnetostatic Report > Rectangular Plot

2. Leave the default settings and click New Report

0.00 100.00 200.00 300.00 400.00 500.00 600.00move [um]

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

Forc

e1.F

orce

_z [m

New

ton]

Ansoft LLC Maxwell2DDesign1XY Plot 1

Curve Info

Force1.Force_zSetup1 : LastAdaptive



9.8-16

Maxwell 2D v12

Create Plot of Cost vs moveTo create a report:

1. Select the menu item Maxwell 2D > Results > Create Magnetostatic Report > Rectangular Plot

2. Choose Quantity: cost1 and click New Report

0.00 100.00 200.00 300.00 400.00 500.00 600.00move [um]

1.00E-006

1.00E-005

1.00E-004

1.00E-003

1.00E-002

1.00E-001

cost

1

Ansoft LLC Maxwell2DDesign1XY Plot 2

Curve Info

cost1Setup1 : LastAdaptive


9.10Basic Exercise - Scripting

9.10-1

Maxwell 2D v12

Scripting the Creation of a Model Object This exercise will discuss how to record, modify and run a script for automating generation of a circle. The following tasks will be performed:

Record a script in which a circle is created.Modify the script to change the circle’s radius and height.Run the modified script.

Create the ProjectClick on the menu item File > NewClick on the menu item Project > Insert Maxwell 2D Design

Save the ProjectSelect the menu item File > Save As…Save the file as scripting_example.mxwl



9.10-2

Maxwell 2D v12

Start Recording the ScriptClick on the menu item Tools > Record Script. By default the script will be recorded in Visual Basic format.

Specify the name of the file as script.

Draw the Circle The radius for our initial circle object will be 1mm.

Click on the menu item Draw > Circle

Using the coordinate entry field, enter the center position:

X: 0.0, Y: 0.0, Z: 0.0, Press the Enter key

Using the coordinate entry field, enter the radius:


Stop Recording the ScriptClick on the menu item Tools > Stop Script Recording.

The file is now saved on the disk.

Delete the CircleClick on the menu item Edit > Select > By Name. Select Circle1 and click OK.

Click on the menu item Edit > Delete.

Run the Script to Recreate the CircleClick on the menu item Tools > Run Script.

Locate and select the script file and click Open.

If successful, the original circle, Circle1, should be back.

We can now explore the contents of the script file.



9.10-3

Maxwell 2D v12

Open the Script for EditingLocate the file on the hard disk and open with notepad.

Script File ContentsDefinition of environment variables. Dim is the generic visual basic variable type.

' ----------------------------------------------' Script Recorded by Maxwell Version 12.0' 11:38 AM Aug 09, 2007' ----------------------------------------------Dim oAnsoftAppDim oDesktopDim oProjectDim oDesignDim oEditorDim oModule

Reference defined environment variables using Set.

Set oAnsoftApp = CreateObject("AnsoftMaxwell.MaxwellScriptInterface")Set oDesktop = oAnsoftApp.GetAppDesktop()oDesktop.RestoreWindowSet oProject = oDesktop.SetActiveProject("scripting_example")Set oDesign = oProject.SetActiveDesign("Maxwell2DDesign1")Set oEditor = oDesign.SetActiveEditor("3D Modeler")



9.10-4

Maxwell 2D v12

Create the circle.

All of the parameters needed to create the circle are defined in this line of code. Here we will modify the Radius of the circle by changing the appropriate text.

oEditor.CreateCircle Array("NAME:CircleParameters", "CoordinateSystemID:=", -1, "IsCovered:=", true, "XCenter:=", "0mm", "YCenter:=", "0mm", "ZCenter:=", "0mm", "Radius:=", "1mm", "WhichAxis:=", "Z"), Array("NAME:Attributes", "Name:=", "Circle1", "Flags:=", "", "Color:=", "(132 132 193)", "Transparency:=", 0,"PartCoordinateSystem:=", "Global", "MaterialName:=", "vacuum",

"SolveInside:=", true)

Modify Script

Locate the line containing the Radius and change the numerical values to 5mm:

>> "Radius:=", "1mm", "WhichAxis:=", "Z"),>> "Radius:=", “5mm", "WhichAxis:=", "Z"),

Save the file and return to Maxwell.



9.10-5

Maxwell 2D v12

Delete the CircleClick on the menu item Edit > Select > By Name. Select Circle1 and click OK.

Click on the menu item Edit > Delete.

Run the Script to Create the Modified CircleClick on the menu item Tools > Run Script.

Locate and select the script file and click Open.

If successful, the modified cylinder, Circle1, should appear.



9.10-6

Maxwell 2D v12

Generalize the script to run in any Project and DesignTo run the script in order to create your circle in a different project. Change the following lines in the script.

Set oProject = oDesktop.SetActiveProject("scripting_example")Set oDesign = oProject.SetActiveDesign("MaxwellDesign1")

Set oProject = oDesktop.GetActiveProject()Set oDesign = oProject.GetActiveDesign()

This Completes the Scripting Exercise.


9.12Basic Exercises – Eddy Current Solver

9.12 - 1

Maxwell 2D v12

Introduction to the Eddy Current SolverThis example introduces the Eddy Current solver based on a simple example with a disk above a coil. This solver calculates the magnetic fields at a specified sinusoidal frequency. Both linear and nonlinear (for saturation effects) magnetic materials can be used. Also, eddy, skin and proximity effects are considered.

2D Geometry: Iron Disk above a Spiral CoilA sinusoidal 500 Hz current will be assigned to an eight turn spiral coil underneath of a cast iron disk. The coil induces eddy currents and losses in plate. The 2D model will be setup as shown below using the 2D RZaxisymmetric solver.

Setup the DesignClick on the menu item Project > Insert MaxwellDesign


Set Geometry Mode: Cylindrical about Z

Select the radio button Magnetic: Eddy Current

Specify the Drawing UnitsClick on Modeler > Units > Select units: cm

Check the Snap ModeClick on Modeler > Snap mode

Verify that Snap To: Grid and Vertex are set.

Cast irondisk

Spiral coil

Actual 3D modelSimulated 2D model



9.12 - 2

Maxwell 2D v12

Draw the Solution RegionClick on Draw > Rectangle (Enter the following points using the tab key).

X: 0, Y: 0, Z: -100

dX: 120, dY: 0, dZ: 200


Name: Region

Transparency: 0.9

Select View > Fitall > Active View to resize the drawing window.

Select wireframe view by selecting: View > Render > Wire Frame.

Draw the Spiral CoilClick on Draw > Rectangle

X: 17, Y: 0, Z: -1

dX: 2, dY: 0, dZ: 2


Name: Coil

Material: Copper

Color: Yellow

Click on Edit > Duplicate > Along Line

Input the first point of the duplicate vector: X: 0, Y: 0, Z: 0

Input the second point of the duplicate vector: dX: 3.1, dY: 0, dZ: 0

Set Total Number: 8

Do not check Attach To Original Object and choose OK.

Draw the PlateClick on Draw > Rectangle

X: 0, Y: 0, Z: 1.5

dX: 41, dY: 0, dZ: 1


Name: Plate

Material: Cast Iron

Color: Red



9.12 - 3

Maxwell 2D v12

Assign the SourceA current of 125A will be assigned to each coil. This will result in a total of 1000

A-turns being assigned to the complete winding.

Select Coil, Coil_1, ... Coil _7 from the history tree.


Name: Current

Value: 125 A

Type: Solid

Note: Choosing Solid specifies that the eddy effects in the coil will be considered. On the other hand, if Stranded had been chosen, only the DC resistance would have been calculated and no AC effects in the coil would have been considered. Stranded is appropriate when the skin depth is much larger than the stranded conductor thickness, for example when using Litz wire. Note that the induced eddy effects in the plate will be calculated in either case.

Assign the Outer BoundaryThe boundary must be set on the solution region.

Choose Edit > Select > Edges to change the selection mode from object to edge.

While holding down the CTRL key, choose the three outer edges of the region.

Click on Maxwell 2D > Boundaries> Assign > Balloon

When done, choose Edit > Select > Object to object selection mode.

Assign the ParametersIn this example, the compete [8x8] impedance matrix will be calculated. This is done by setting a parameter.

Click on Maxwell 2D > Parameters > Assign > Matrix

Check each of the eight sources: Current_1, Current_2, ... Current_8



9.12 - 4

Maxwell 2D v12

Compute the Skin DepthSkin depth is a measure of how current density concentrates at the surface of a conductor carrying an alternating current. It is a function of the permeability, conductivity and frequency

Skin depth in meters is defined as follows:

where:

ω is the angular frequency, which is equal to 2πf. (f is the source frequency which in this case is 500Hz).

σ is the conductor’s conductivity; for cast iron its 1.5e6 S/m

µr is the conductor’s relative permeability; for cast iron its 60

µο is the permeability of free space, which is equal to 4π×10-7 A/m.

For cast iron the plate the skin depth is approximately 0.24 cm.

After three skin depths, the induced current will become almost negligible. The automatic adaptive meshing in Maxwell 2D does an excellent job of refining the mesh in the skin depth, so that mesh operations are not needed.

Add an Analysis SetupClick Right on Analysis in the Model Tree and select Add Solution Setup

On the General tab, re-set the Maximum Number of Passes to 15

On the Solver tab, re-set the Adaptive Frequency to 500Hz

Solve the ProblemSave the project by clicking on menu item File > Save AsSelect the menu item Maxwell 2D > Validation Check to verify problem setupYou will get a warning about Boundaries and Excitations. To clear this warning, simply return to the eddy effect screen by choosing: Maxwell 2D > Excitations > Set Eddy Effects > OK. This tells the solver that you have checked the eddy setup and that you have correctly set the eddy effect on the appropriate objects.


σµωµδ

ro

2=



9.12 - 5

Maxwell 2D v12

View the ConvergenceSelect the menu item Maxwell 2D > Results > Solution Data Click on the Convergence tab to view the adaptive refinement.Note the total loss is approximately 284 W.

Click on the Matrix tab to display the 8x8 impedance matrix. By default, the results are displayed as [R, Z] but can be also shown as [R, L] or as coupling coefficients.



9.12 - 6

Maxwell 2D v12

Plot the MeshSelect all objects and click on Maxwell 2D > Fields > Plot MeshWhen done, hide the plot by selecting View > Active View Visibility > Fields Reporter and unchecking the Mesh1 plot.

Compute Total Power Loss in the PlateClick on Maxwell 2D > Fields > Calculator and then perform the following:Quantity > OhmicLossGeometry > Volume > Plate > OKIntegral > RZEval ... Evaluate

Note: The evaluated loss in the Plate should be about 260 W.

Click Done



9.12 - 7

Maxwell 2D v12

Compute Total Power Loss in the CoilsSelect all eight coils in the history tree and then Modeler > List > Create > Object List . ‘Objectlist1’ appears under ‘List’ in the History Tree.


Quantity > OhmicLoss

Geometry > Volume > Objectlist1> OK

Integral > RZ (Note: RZ is a volume integral, XY is a surface integral)

Eval ... Evaluate

The evaluated loss in the Coils should be about 24 W

Click Done.

Note: The total power loss for the plate and the coils = 260+24 = 284W which matches the loss result in the convergence table.

Plot Flux LinesSelect all objects


Note that the flux lines are attracted to the plate since it is magnetic. Also, skin effects are present in the plate since there are eddy currents flowing in it. This can be seen best if you zoom into the plate



9.12 - 8

Maxwell 2D v12

Plot Current Density Scalar in the PlateHide the Region by selecting View > Active View Visibility and un checking Region.

Resize the view by selecting View > Fit All > All Views

Verity that the view is wireframe by selecting: View > Render > Wire Frame

Select the plate.

Click on Maxwell 2D > Fields > Fields > J > JAtPhase > Done

Plot Current Density Scalar in the CoilsSelect Objectlist1 to select all eight coils in the winding.

Click on Maxwell 2D > Fields > Fields > J > JAtPhase > Done



9.12 - 9

Maxwell 2D v12

Plot Ohmic Loss DistributionHide previous plots by selecting View > Active View Visibility > Fields Reporter and unchecking the previous plots.

Select all objects

Click on Maxwell 2D > Fields > Fields > Other > Ohmic_Loss

Or right mouse click after object Plate is selected, then Fields > Other > Ohmic_Loss

After the plot is displayed, change to a log scale by double left clicking on the legend and change to Log on the Scale tab.

Animate Current Density VectorRotate the view by holding down ALT and then left mouse drag.

Select the Plate

Click on Maxwell 2D > Fields > Fields > J > J_Vector

After the plot is displayed, double left clicking on the legend select the Plots tab.

Choose plot: J_Vector1 and change the Vector plot spacing to: Min = 0.5 and Max = 0.5.

In the Project Window, right click on J_Vector1 and click Animate > OK.



9.12 - 10

Maxwell 2D v12

Copy the Design and Solve again at DCIn order to show the difference between the AC case and the DC case, copy the design and re-run it at 0.001Hz (which is essentially DC).

In the project window, select MaxwellDesign1 and choose Edit > Copy

Click on the green project folder and choose Edit > Paste. MaxwellDesign2 should appear.

Under MaxwellDesign2, choose Analysis > Setup > Solver and change the adaptive frequency = 0.001 Hz.


Plot Current Density ScalarIn the project window, just click on JAtPhase1 to display the current density plot. Note that there is no significant current induced in the plate at 0.001 Hz.



9.12 - 11

Maxwell 2D v12

Plot the Flux LinesIn the project window, just click on Flux_Lines1 to display the flux lines plot. Note that the flux lines penetrate in and through the plate. While saturation is considered at DC, no AC skin effects or shielding occurs.

This is the end of the Eddy Current Basic Exercise.


9.13Basic Exercise: Transient – Large Motion – Rotational

9.13-1

Maxwell 2D v12

Large Motion – its Quick Implementation Using the Maxwell 2D Transient Solver

Maxwell Transient is able to consider interactions between transient electromagnetic fields and mechanical motion of objects.

Maxwell Transient (with motion) includes dB/dt arising frommechanically moving magnetic fields in space, i.e. moving objects. Thus, effects coming from so-called motion induced currents can beconsidered.

In Maxwell rotational motion can occur around one single motion axis.

This paper represents a quick start to using rotational motion. It will exercise rotational motion in Maxwell 2D using a rotational actuator(experimental motor) example.

Subsequent papers will demonstrate rotational motion in more depth, non-cylindrical rotational motion using a relays example, as well as translational motion which a solenoid application will serve as an example for.

The goal of these papers is solely to show and practice working withlarge motion in Maxwell. It is neither the goal to simulate real-worldapplications, nor to match accurately measured results, nor will thesepapers show in detail how to setup and work with other Maxwell functionality. Please refer to the corresponding topics.

Quickstart – Rotational Motion Using a Rotational ActuatorExample

Maxwell Transient with large motion is a set of advanced topics. Users should have thorough knowledge on Maxwell fundamentals as well as Maxwell Transient (without motion) prior to approaching large motion. Ifnecessary, please consult the proper training papers, help files, manuals, and application notes.

We will exercise the following in this document:

Create a new or read in an existing rotational actuator model – to serve as an experimental testbench for large motion

Prepare and adapt this existing actuator model to our needs

Apply large motion to the rotational actuator

Create the band object

Setup rotational motion

Mesh



9.13-2

Maxwell 2D v12

Perform basic large motion tests

„Large Rotational Standstill“ test

„Large Rotational Constant Speed“ test

„Large Rotational Transient Motion“ test

Compute magnetic rigidity and mechanical naturalfrequency

Estimate timestep for transient solver

Make a field animation with large motion

Open the Rotational Actuator ModelLocate the projectEx_09_13_BasicTransient_MotionRotational_M2dTrs120.mxwl. Open it, activate the design 00_Template and start working from there. You cancopy/paste 00_Template into your own working project. The other designsshow the fully setup models we will be working on.

The model should look like this:

Fig. 1: Rotational actuator example



9.13-3

Maxwell 2D v12

Setup and Verify the Electromagnetic PartPrior to employing large motion, the electromagnetic part of the modelshould work correctly. Users are well advised not to setup a complexmodel completely at once and then try to simulate, but rather work in steps. Especially in cases eddy current effects, external circuits, and large motion are included, the correctness of the setup for eachindividual property should be verified. After that, all properties can beconsidered together.

For this quickstart, please study the winding setup and background.

We use stranded windings with constant current (to generate a fixedstator flux vector around which Rotor1 will oscillate later). Also, eddyeffects will be excluded.

Verify the symmetry multiplier being set to 1. In the project tree: RMB click on Model > Set Symmetry Multiplier (the full geometry issimulated).

Verify the model depth being set to 25.4 mm. In the project tree: RMB click on: Model > Set Model Depth (taken from the original 3D project).

Perform a test simulation on the electromagnetic part alone. If desired, play with various excitations, switch eddy effects in Stator1 and Rotor1 on and off, vary material properties, etc. For each test check theelectromagnetic fields for correctness.

Refer to the corresponding topics on materials, boundaries, excitations, meshing, transient simulations without motion, and post processing.

If the electromagnetic part without motion effects yielded correct results, make sure to re-apply the same model setup as elaborated at theprevious page (00_Template).

Rotational Large Motion – The Maxwell ApproachMaxwell separates moving from non-moving objects.

All moving objects must be enclosedby one so-called band object.

For rotational motion, the band objectmust be cylindrical with segmentedouter surface, i.e. a regular polyhedron.

Maxwell considers all moving objects(inside the band) to form one singlemoving object group.

Fig. 2: Band object separating rotor from stator



9.13-4

Maxwell 2D v12

Constant Speed mode:

If the model is setup to operate in constant speed mode (see below), Maxwell will not compute mechanical transients. However, changing magnetic fields owing to speed ωm, i. e. dB/dteffects are included in the field solution.

Mechanical Transient mode:

In case inertia was specified, Maxwell will compute the motionequation in each time step.

See Appendix A for a variable explanation.

Apply Large Motion to the Rotational Actuator – Create theBand Object and Mesh

First, let‘s examine the moving parts to comply with Maxwell‘s conventions:

All moving objects can be separated from the stationary objects and can be combined to one single rotating group. All moving objects beconsidered to perform the same cylindrical motion.

Create the band object:

We want a regular polyhedron that encloses all moving objects.

Outer surface segmentation should be between 1° and 5°, i. e. we will have between 360 and 72 outer surface segments.

The band object should preferably cut through the middle of the airgap, leaving about the same space to Rotor1 and Stator1. However, this isnot a must.

Hide all objects except Rotor1 and Stator1.

Determine the required radius:

Modeler > Measure > PositionIn the geometry, click first on the origin, then move so that themouse pointer snaps to one outer corner point of Rotor1. Readthe Distance value from the Measura Data window (51.05 mm). Then move over so that the pointer snaps to one inner cornerpoint of Stator1. Read the Distance value (53.75 mm).

See Fig. 3 next page.

Thus, band should have a radius of 52.4 mm. Here, 52.5 mm was used.

Jm · d2ϕm(t) / dt2 + kD(t) · dϕm(t) / dt = Tψ(t) + Tm(t)



9.13-5

Maxwell 2D v12

Fig. 3: Rotor1 radius measurement

Draw the band:

Draw > Regular Polygon, have X = 0, Y = 0, Z = 0 for the Center position. When asked for the Radius, enter 52.5 into the dX (ordY) field, leaving dZ and dY (or dX) zero. Set the number of segments to 72.

Rename the thus created object to Band1, apply a transparencyof 0.9, and maybe use some nicer color.

The created Band1 object should look like Fig. 4.



9.13-6

Maxwell 2D v12

Fig. 4: Band object Band1

We have now created Band1 that encloses all rotating objects(only Rotor1 in this example).

72 outer segments means a new segment every 5°. For moreaccurate simulations we should apply more segments.

Setup rotational motion:

In the history tree, right mouse click on the Band1 object and choose: Assign Band...This automatically separates moving from stationary objects.

Under Motion Type, check Rotational for the Motion Type, leave Non-Cylindrical unchecked, and select Global:Z – Positive forthe Rotation Axis.

On the Data tab, apply zero for the initial position. Thus, motionwill start at t = 0 with the rotor position being as drawn. Applyingϕm0 ≠ 0 would start with Rotor1 rotated by ϕm0 from the drawnposition. Leave Rotate Limit unchecked (allowing the rotor to spin continuously) and leave Non-Cylindrical unchecked.

Under Mechanical, uncheck Consider Mechanical Transient and apply an Angular Velocity of zero.



9.13-7

Maxwell 2D v12

Now, we have setup „large rotational standstill“. Positive magnetictorque is generated around the positive z-axis (global coordinatesystem, Fig. 5). In the project tree > active design > Model, two newentries have been created – MotionSetup1 and Moving1. Clicking on Moving1 inspect the motion setup.

Applying the same constant current as before, we can expect thesame constant magnetic torque (provided a good mesh).

Fig. 5: Motion setup

Mesh

Meshing is a very critical issue with respect to simulation speed and accuracy. For here, we will apply a rather coarse mesh only, by whichthe solver will just yield satisfactory results.

Band1:

For torque computation, the most critical areas are the airgapand its immediate proximity. Thus, the band mesh is crucial foraccurate results.

We will apply a length based mesh on the surface and inside of Band1. We will restrict the number of elements to 5000. Thiswill do for these tests.



9.13-8

Maxwell 2D v12

Right mouse click on Band1 > Assign Mesh Operation > InsideSelection > Length Based.

Rename this mesh entry to Band_Length,

Restrict Length of Elements – unchecked,

Restrict Number of Elements – checked, set to 5000, OK.

For all other objects we will also just restrict the number of elements –for simplicity reasons only. The mesh will be assigned one by one. For each,

right click the object > Assign Mesh Operation > InsideSelection > Length Based. Restrict Length of Elements – unchecked,

Restrict Number of Elements – checked.

Following, first the object names are listed, second themaximum number of elements to apply, and third the namegiven to the resulting mesh entry:

Rotor1 – 1000 – Rotor_Length

Stator1 – 1000 – Stator_Length

CoilA and CoilB – 100 – Coils_Length (simultaneouslyselecting CoilA, CoilA_Neg, CoilB, and CoilB_Neg will tryto assign 100 triangles to the group, i. e. about 25triangle in each coil will result)

Background1 – 1000 – Background_Length.

Once done assigning, you should see project tree entries like Fig. 5.

Assign a solution setup:

In the project tree, right mouse click Analysis > Add Solution Setup... ClickOK to accept the default values for now.

We need this setup just to allow meshing and check the mesh, we will care about its values later.

In the project tree right mouse click Analysis > Setup1 > Apply MeshOperations. Watch the progress bar (usually bottom right). Watch themessage window (usually bottom left) for a message that says that theSimulation has been successfully completed. Now, meshing is done.

Select View > Set Solution Context leaving Time = -1 (the simulation has not yet started) and then click on OK.

Select all objects except for Background1. Maxwell > Fields > Plot Mesh. Your mesh plot should look similar to Fig. 6.



9.13-9

Maxwell 2D v12

Fig. 7: Resulting meshFig. 6: Mesh entries

Perform Basic Large Motion TestsThese basic tests serve model verification. They can be executed ratherquickly. Should they fail in whatever respect, there is no use going furtherand working with more complex models (like mechanical transients, externalcircuits, eddy currents, etc.).

Simulate the „Large Rotational Standstill“ test:

Refer to design 11_GeoFull_MagI_MchStandstill.

Setup Solution

In the project tree, double click on: Setup1.

Set 20 ms for the stop time. Set 5 ms for the time step.

Leave all other properties of Setup1 untouched. Exit by OK.

We have now told Maxwell Transient to simulate five timesteps only(icl. zero), because we are expecting a quasi magnetostatic result.

Right mouse click Analysis > Setup1 > Analyze will start the simulationprocess. Its progress can be monitored in the progress window.

Post process:

We will just look at the force function at the moment.

In the project tree, right mouse click Results > Create TransientReport. > Rectangular Plot, select Category = Torque, and Quantity = Moving.Torque, press New Report, and Close.

Your report should show constant force of about 400 mNm.



9.13-10

Maxwell 2D v12

Perform the “Large Rotational Constant Speed“ test:

Refer to design 12_GeoFull_MagI_MchSpeedslow.

We will now operate the rotational actuator at a very slow constantspeed.

Remember, there is only one magnetic excitation present in the model– namely constant coil current with stranded windings. Alternatively, Rotor1 could have been assigned permanent magnet properties. Eddy effects are switched off for all objects.

We can now use Transient with Large Motion to monitor coggingtorque effects.

Setup motion

In the project tree, underModel right mouse click on MotionSetup1 and select Properties.

Under Data, set Initial Position to -61 deg.

Under Mechanical, set Angular Velocity to 1 deg_per_sec.

Rotor1 as drawn has a -29° offset. This is taken to be the zeroposition for the transient solver. By giving an extra -61°, positive rotation of 1 °/s starts at: -61 -29 = -90°.

Setup Solution

Right mouse click on Analysis > Setup1 > Properties.

Set Stop Time to 180 s.

Set Time Step to 5 s

By rotating at a speed of 1 °/s 180 s long, Rotor1 will move180°, i. e. from -90° to +90°, at 5°/step.

Right mouse click Analysis > Setup1 > AnalyzeDuring solving, you can already open the report Torque(t). The plot isgoing to build up with each timestep completed. See Fig. 7.

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00Time [s]

-500.00

-400.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

400.00

500.00

Torq

ue [m

New

tonM

eter

]

Ansoft Corporation 12_GeoFull_MagI_MchSpeedslowTorque(t)Curve Info

TorqueSetup1 : Transient

Fig. 8: Magnetic torque Tψ(t)



9.13-11

Maxwell 2D v12

Perform the „Large Rotational Transient Motion“ test:

We will now operate the actuator as a one-body oscillator.

Inertia will be specified as well as some damping.

We can expect Rotor1 to oscillate around the stator flux axis (y-axis) at some natural frequency f0, which can be approximated as:

Jc

f ψ

π21

0 =

J in kgm2 is the total moment of inertia acting on Rotor1.

cψ in Nm/rad is the magnetic rigidity. As an analogy it can beunderstood as a mechanical spring spanned between Rotor1 and Stator1, whose force coming from the magnetic field.

We can roughly calculate rigidity c from the cogging torque function(stable limb):

Nm/rad3.2)rad(10

mNm400=

°≈

∆∆

=m

Tc

ϕψ

ψ

Assuming inertia J = 0.0024 kgm2, an approximated f0 = 5 Hz results.

This is sufficient for estimating the necessary timestep as far as mechanical oscillations are regarded.

Refer to design 13_GeoFull_MagI_MchTransient.

Motion Setup (Model > MotionSetup > Properties):

Under Data, set Initial Position = 0.

Under Mechanical (see Fig. 9), set

Consider Mechanical Transient = checked

Initial Angular Velocity = 0,

Moment of Inertia = 0.0024 kgm2,

Damping = 0.015 Nm·s/rad, and Load Torque = 0.

This causes 15 mNm resistive torque at 1 rad/s speed.

We thus expect oscillation between -29° and +29° (w. r. t. statorflux axis) at f0 < 5 Hz with damped amplitudes.

Fig. 9: Motion setup



9.13-12

Maxwell 2D v12

Solution Setup:

Under Analysis > Setup1 > Proporties, set

Stop Time = 0.5 s, Time Step = 0.01 s

From f0, we can expect a >200 ms cycle. At 10 ms timestep we will sample one cycle >20 times.

Analyze this design. Open the already generated report Torque(t).

This and the two additional reports for speed and position should looklike Fig. 9-11.

-400.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

400.00

500.00

Torq

ue [m

New

tonM

eter

]

Curve InfoTorque

Setup1 : Transien

-80.00

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

Mov

ing1

.Spe

ed [r

pm]

Curve InfoMoving1.Speed

Setup1 : Transient

0.00 100.00 200.00 300.00 400.00 50Time [ms]

0.00

10.00

20.00

30.00

40.00

50.00

Mov

ing1

.Pos

ition

[deg

]

Curve InfoMoving1.Position

Setup1 : Transient

Fig. 10: Torque Tψ(t)

Fig. 11:Mechanical speed ωm(t)

Fig. 12:Mechanical position ϕm(t)

0



9.13-13

Maxwell 2D v12

The transient reports have been created using:

Category: Speed, Quantity: Moving.Speed, and

Category: Position, Quantity: Moving.Position.

Fig. 10-12 on the previous page:

Tψ looks as expected from previous simulations.

ωm corresponds to Tψ‘s first derivative and is correct.

ϕm oscillates around +29°, which is the stator flux axis (y) withrespect to the initial position.

Appendix A: Variable Explanation:

ϕm(t) Mechanical angular position in rad (angles can also be given in degrees).

ϕm0 Initial ϕm in rad. Note that the drawnrotor position is considered as ϕm0 = 0.

dϕm(t) / dt, ωm(t) Mechanical angular speed in rad/s.

ωm0 Initial ωm in rad/s.

d2ϕm(t) / dt2 Mechanical angular acceleration in rad/s2.

Jm Moment of inertia in kg·m2. This is thetotal inertia acting on the moving objectgroup. If extra inertia needs to beincluded (i. e. inertia not geometricallymodeled), just add this to Jm.

kD(t) Damping koefficient in Nm·s/rad. For kD= 1 Nm·s/rad, resistive torque of 1 Nm would be generated if the moving partsturn at 1 rad/s. kD can be a function of t, ωm, or ϕm.

Tψ Magnetically generated torque in Nm.

Tm Mechanical extra torque in Nm, this canbe a constant or a function of t, ωm, orϕm. Note, that a positive Tm value will accelerate rather than brake.

t The current simulation time in s.

Ansoft Maxwell Field Simulator V12 User’s Guide

9.14Topic – 2D Boundary Conditions

9.14-1

Assigning Boundary Conditions

Boundary Conditions

Boundary conditions enable you to control the characteristics of planes, faces, or interfaces between objects. Boundary conditions are important to understand and are fundamental to solution of Maxwell’s equations.

Purpose of the Exercise

This exercise introduces various boundary conditions used in Maxwell 2Dbased on a simple example with coils and steel core. The user will learn how to use Vector Potential, Balloon, Symmetry and Matching Boundary (Master and Slave).

Ansoft Maxwell Design EnvironmentThe following features of the Ansoft Maxwell Design Environment are used to create the models covered in this topic

2D Sheet Modeling

User Defined Primitives (UDPs): SRMCore

Boolean Operations: Separate Bodies

Boundaries/Excitations

Current: Stranded

Boundaries: Vector Potential, Balloon, Symmetry, Master/Slave,

Analysis

Magnetostatic

Field Overlays:

H Vector



9.14-2

Summary of eight designs to be simulated

1_VectorPotential 2_Balloon

3_Balloon_ChangeExcitation

4_Symmetry_Odd and 6_NoSymmetry

5_Symmetry_Even

7_Matching_Positive 8_Matching_Negative



9.14-3

Getting Started

Launching MaxwellTo access Maxwell, click the Microsoft Start button, select Programs, and select

Ansoft and then Maxwell 12. Or double click the icon on the desktop.

Setting Tool OptionsTo set the tool options:

Note: In order to follow the steps outlined in this example, verify that the following tool options are set :

1. Select the menu item Tools > Options > Maxwell 2D Options2. Maxwell Options Window:

1. Click the General Options tab

Use Wizards for data entry when creating new boundaries: Checked

Duplicate boundaries with geometry: Checked


3. Select the menu item Tools > Options > Modeler Options.4. 3D Modeler Options Window:

1. Click the Operation tab

Automatically cover closed polylines: Checked

2. Click the Drawing tab

Edit property of new primitives: Checked




9.14-4

Opening a New Project

To open a new project:

1. In an Maxwell window, click the on the Standard toolbar, or select the menu item File > New.

2. Select the menu item Project > Insert Maxwell 2D Design, or click on the icon.

3. Save the project with name “Ex_9_14_BasicBoundaryCondictions” to your own folder. Change the name of the design from “Maxwell2DDesign1” to “1_VectorPotential”.

Set Solution TypeSelect the menu item: Maxwell 2D > Solution Type > Magnetostatic, or right mouse click on 1_VectorPotential and select Solution Type.The Geometry Mode should be: Cartesian, XY

Creating 2D ModelThe example that will be used to demonstrate how to assign boundary conditions does not represent any real-world product. The intent of this write-up is rather to demonstrate how boundary conditions are implemented.

Set Model UnitsSelect the menu item Modeler > Units > Select Units: mm (millimeters)



9.14-5

Create Stator and Coils: A User Defined Primitive will be used to create the Stator and Coils

Draw > User Defined Primitive > Syslib > Rmxprt > SRMCoreUse the values given in the panel below to create the Stator and Coils

Click on the object just created in the drawing window and in the panel on the left change its name from SRMCore1 to Stator.Change the Material from vacuum to nickel.



9.14-6

The stator and coils were created as one entity and they need to be separated.

1. Click on the Stator-Coil group so that they are selected

2. Select the menu item Modeler > Boolean > Separate Bodies, the result will be a single stator and eight coil cross-sections.

As was done with the Stator, change the name, materials, and color for Coils. The material property for the Stator will be nickel, and the material property for the Coils will be copper. The name and color for each object is given below.

Coil1Coil4

Coil3 Coil2

Stator

Coil5

Coil6

Coil8

Coil7



9.14-7

Assign Current Source to CoilsSelect all eight coils by holding down the CTRL key and using your mouse or selecting from tree on the left hand side of the GUI

Select the menu item Maxwell 2D > Excitations > Assign > Current or right click > Assign Excitations > Current

1. Change the Base Name to Current

2. Change the value to 100 Amps



9.14-8

The project tree now shows eight separate Excitations, each of them is pointing out of the plane (along Z axis):

Changing directions of Excitations

Right click on Excitations > List …, hold down CTRL key and select Current_2, Current_4, Current_6 and Current_8, then click on “Properties”, change direction from Positive to Negative.



9.14-9

Create the Problem RegionOne of the main differences between Maxwell V11 and V12 is that a Background Region is not automatically created when a project is started. A separate object needs to be specifically created.

To create a rectangular region simply select Draw > Region, or click the icon from standard toolbar. The size of this rectangular region is based on dimensions of the existing objects. Change Padding Percentage to 20.

Click View > Fit All > All Views, or CTRL + D.



9.14-10

Create an Analysis SetupSelect the menu item Maxwell 2D > Analysis Setup > Add Solution Setup or right click on the Analysis in the project window > Add Solution SetupSelect General and verify the setting as follows

Select Convergence and verify the setting as follows

Set up Boundary ConditionsSelect the menu item Edit > Select > Edges or right click in the Modeler > Select EdgesSelect outer edge of the Stator

Click on the menu item Maxwell 2D >

Boundaries > Assign > Vector Potential …

Accpet the default value and OK.



9.14-11

Save the ProjectSelect the menu item File > Save

Check the Validity of the ModelSelect the menu item Maxwell > Validation Check, or click on the icon

The problem won’t solve unless each item has a check mark.

Analyze Select the menu item Maxwell 2D > Analyze All, or click on the icon



9.14-12

Solution DataTo view the Solution Data, select the menu item Maxwell 2D > Results > Solution Data, or right click on Setup1 under Analysis > ConvergenceHere you can view the Profile and the Convergence.

Note: The default view for convergence is Table. Click on the Plotradio button to view a graphical representations of the convergence data.

Note: You don’t have to wait for the solution to be done to do this. You can do this while the simulation is running, all information will update automatically after each pass is done.



9.14-13

Plot Mesh, H-Field Vector and Flux LineClick on the menu item Edit > Select All Visible or Select All, or use CTRL + A , or select everything from the history tree window, then right mouse click in the modeler and select Plot Mesh .Do the same, select all objects, then right mouse click in the modeler and select Fields > H > H_Vector, and Fields > A > Flux Lines .



9.14-14

The following H-field vector plot will appear, which is the result of the current excitation on the left side.

If the plot is not as nice as you may want to see, you can double click on the legend bar, then change various settings under Color map / Scale / Marker / Arrow or Plots tabs.



9.14-15

Create Design2: 2_BalloonClick on design 1_VectorPotential in the Project Manager window and then right mouse click and select Copy

Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 1_VectorPotential1 has been created, change the design name to 2_Balloon.

Click on VectorPotential1 under Boundaries in the Project Manager, and press “Delete” from keyboard to remove the boundary condition.

Right click in the modeler and select Select Edges, to change from object selection mode to edge selection mode.

Left mouse click on one of the edges of the Region, then right mouse click and select All Object Edges to select all edges of the Region.

Right mouse click again, Assign Boundary > Balloon…

Run the simulation and compare H Field plot with the previous design that has vector potential boundary.

Balloon on all edges of the Region Zero Vector Potential on the outer edge of the Stator



9.14-16

Create Design3: 3_Balloon_ChangeExcitationClick on design 2_Balloon in the Project Manager window and then right mouse click and select Copy

Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 2_Balloon1 has been created, change the design name to 3_Balloon_ChangeExcitation.

Modify Current ExcitationClick on Excitations > Current_3 in the

Project window, you will see a Properties

window under Project window, change from

Positive to Negative in the Direction row. Also,

Change Current_7 from Positive to Negative

Change Current_4 and Current_8 from

Negative to Positive.

The purpose is to change the current

excitation as shown in the graph below.

Current_2

Current_1

Current_8

Current_7

Current_3

Current_4

Current_5

Current_6

PositiveCurrent_8

NegativeCurrent_7

NegativeCurrent_6

PositiveCurrent_5

PositiveCurrent_4

NegativeCurrent_3

NegativeCurrent_2

PositiveCurrent_1



9.14-17

Run the simulation and compare H Field plot with Design2 2_Balloon that has different excitations.

Design2: 2_Balloon Design3: 3_Balloon_ChangeExcitation



9.14-18

Symmetry BoundaryCreate Design4: 4_Symmetry_Odd

Click on design 2_Balloon in the Project Manager window and then right mouse click and select CopyClick on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 2_Balloon1 has been created, change the design name to 4_Symmetry_Odd.Select all objects and right mouse click in the modeler > Boolean > Split, choose XZ plane to create half geometry.

In the history tree, double click on CreateRegion under Vacuum > Region, change –Y Padding Percentage to 0.Remove the Balloon boundary, reassign the Balloon boundary to three edges (not on the symmetry edge).Change to Edge selection mode and click on the edge of the Region along X axis, right mouse click in the modeler > Assign Boundary > Symmetry, choose Odd (Flux Tangential).



9.14-19

Run simulation and view results.

Symmetry: Odd (Flux Tangential)



9.14-20

Create Design5: 5_Symmetry_EvenClick on design 4_Symmetry_Odd in the Project Manager window and then right mouse click and select Copy

Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 4_Symmetry_Odd1 has been created, change the design name to 5_Symmetry_Even.

Select the Symmetry boundary and change it to Even (Flux Normal).


Symmetry: Even (Flux Normal)



9.14-21

Create Design6: 6_NoSymmetryClick on design 4_Symmetry_Odd in the Project Manager window and then right mouse click and select Copy

Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 4_Symmetry_Odd1 has been created, change the design name to 6_NoSymmetry.

Select the Symmetry boundary and delete it.


The result should look the same as Design4: 4_Symmetry_Odd because odd symmetry or flux tangential is the default boundary condition.

No Symmetry: by default an Odd (Flux Tangential boundary is assigned)



9.14-22

Matching Boundaries (Master/Slave).

Slave=Master

Master


Slave= — Master

Master

Design7: 7_Matching_Positive Design8: 8_Matching_Negative



9.14-23

Matching Boundaries: Master/Slave

Create Design7: 7_Matching_PositiveClick on design 6_NoSymmetry in the Project Manager window and then right mouse click and select Copy.

Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 6_NoSymmetry1 has been created, change the design name to 7_Matching_Positive.

Select all objects and right mouse click in the modeler > Edit > Boolean > Split, choose YZ plane.

Change –X Padding Percentage of the Region to be 0.

Remove the existing Balloon boundary and redefine it on two edges of the Region that are not on X and Y axis.

Change to Edge selection mode and select the edge of the Region that is along Xaxis. Right mouse click in the modeler > Assign Boundary > Master. Be sure that the master vector arrow is pointing in the positive X direction. If not use Swap Direction.

Select the edge of the Region that is along Y axis. Right mouse click in the modeler > Assign Boundary > Slave. Be sure that the slave vector arrow is pointing in the positive Y direction. If not use Swap Direction.

Choose Master1 from the pull down menu, and Relation as Bs = Bm.



9.14-24

Run Simulation and view results.

Slave=Master

Master



9.14-25

Create Design8: 8_Matching_NegativeClick on design 7_Matching_Postitive in the Project Manager window and then right mouse click and select Copy.Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 7_Matching_Postitive1 has been created, change the design name to 8_Matching_Negative.Change the Slave boundary Relation to Bs = - Bm.


Slave=-Master

Master



9.14-1

Assigning Boundary Conditions

Boundary Conditions

Boundary conditions enable you to control the characteristics of planes, faces, or interfaces between objects. Boundary conditions are important to understand and are fundamental to solution of Maxwell’s equations.

Purpose of the Exercise

This exercise introduces various boundary conditions used in Maxwell 2Dbased on a simple example with coils and steel core. The user will learn how to use Vector Potential, Balloon, Symmetry and Matching Boundary (Master and Slave).

Ansoft Maxwell Design EnvironmentThe following features of the Ansoft Maxwell Design Environment are used to create the models covered in this topic

2D Sheet Modeling

User Defined Primitives (UDPs): SRMCore

Boolean Operations: Separate Bodies

Boundaries/Excitations

Current: Stranded

Boundaries: Vector Potential, Balloon, Symmetry, Master/Slave,

Analysis

Magnetostatic

Field Overlays:

H Vector



9.14-2

Summary of eight designs to be simulated

1_VectorPotential 2_Balloon

3_Balloon_ChangeExcitation

4_Symmetry_Odd and 6_NoSymmetry

5_Symmetry_Even

7_Matching_Positive 8_Matching_Negative



9.14-3

Getting Started

Launching MaxwellTo access Maxwell, click the Microsoft Start button, select Programs, and select

Ansoft and then Maxwell 12. Or double click the icon on the desktop.

Setting Tool OptionsTo set the tool options:

Note: In order to follow the steps outlined in this example, verify that the following tool options are set :

1. Select the menu item Tools > Options > Maxwell 2D Options2. Maxwell Options Window:

1. Click the General Options tab

Use Wizards for data entry when creating new boundaries: Checked

Duplicate boundaries with geometry: Checked


3. Select the menu item Tools > Options > Modeler Options.4. 3D Modeler Options Window:

1. Click the Operation tab

Automatically cover closed polylines: Checked

2. Click the Drawing tab

Edit property of new primitives: Checked




9.14-4

Opening a New Project

To open a new project:

1. In an Maxwell window, click the on the Standard toolbar, or select the menu item File > New.

2. Select the menu item Project > Insert Maxwell 2D Design, or click on the icon.

3. Save the project with name “Ex_9_14_BasicBoundaryCondictions” to your own folder. Change the name of the design from “Maxwell2DDesign1” to “1_VectorPotential”.

Set Solution TypeSelect the menu item: Maxwell 2D > Solution Type > Magnetostatic, or right mouse click on 1_VectorPotential and select Solution Type.The Geometry Mode should be: Cartesian, XY

Creating 2D ModelThe example that will be used to demonstrate how to assign boundary conditions does not represent any real-world product. The intent of this write-up is rather to demonstrate how boundary conditions are implemented.

Set Model UnitsSelect the menu item Modeler > Units > Select Units: mm (millimeters)



9.14-5

Create Stator and Coils: A User Defined Primitive will be used to create the Stator and Coils

Draw > User Defined Primitive > Syslib > Rmxprt > SRMCoreUse the values given in the panel below to create the Stator and Coils

Click on the object just created in the drawing window and in the panel on the left change its name from SRMCore1 to Stator.Change the Material from vacuum to nickel.



9.14-6

The stator and coils were created as one entity and they need to be separated.

1. Click on the Stator-Coil group so that they are selected

2. Select the menu item Modeler > Boolean > Separate Bodies, the result will be a single stator and eight coil cross-sections.

As was done with the Stator, change the name, materials, and color for Coils. The material property for the Stator will be nickel, and the material property for the Coils will be copper. The name and color for each object is given below.

Coil1Coil4

Coil3 Coil2

Stator

Coil5

Coil6

Coil8

Coil7



9.14-7

Assign Current Source to CoilsSelect all eight coils by holding down the CTRL key and using your mouse or selecting from tree on the left hand side of the GUI

Select the menu item Maxwell 2D > Excitations > Assign > Current or right click > Assign Excitations > Current

1. Change the Base Name to Current

2. Change the value to 100 Amps



9.14-8

The project tree now shows eight separate Excitations, each of them is pointing out of the plane (along Z axis):

Changing directions of Excitations

Right click on Excitations > List …, hold down CTRL key and select Current_2, Current_4, Current_6 and Current_8, then click on “Properties”, change direction from Positive to Negative.



9.14-9

Create the Problem RegionOne of the main differences between Maxwell V11 and V12 is that a Background Region is not automatically created when a project is started. A separate object needs to be specifically created.

To create a rectangular region simply select Draw > Region, or click the icon from standard toolbar. The size of this rectangular region is based on dimensions of the existing objects. Change Padding Percentage to 20.

Click View > Fit All > All Views, or CTRL + D.



9.14-10

Create an Analysis SetupSelect the menu item Maxwell 2D > Analysis Setup > Add Solution Setup or right click on the Analysis in the project window > Add Solution SetupSelect General and verify the setting as follows

Select Convergence and verify the setting as follows

Set up Boundary ConditionsSelect the menu item Edit > Select > Edges or right click in the Modeler > Select EdgesSelect outer edge of the Stator

Click on the menu item Maxwell 2D >

Boundaries > Assign > Vector Potential …

Accpet the default value and OK.



9.14-11

Save the ProjectSelect the menu item File > Save

Check the Validity of the ModelSelect the menu item Maxwell > Validation Check, or click on the icon

The problem won’t solve unless each item has a check mark.

Analyze Select the menu item Maxwell 2D > Analyze All, or click on the icon



9.14-12

Solution DataTo view the Solution Data, select the menu item Maxwell 2D > Results > Solution Data, or right click on Setup1 under Analysis > ConvergenceHere you can view the Profile and the Convergence.

Note: The default view for convergence is Table. Click on the Plotradio button to view a graphical representations of the convergence data.

Note: You don’t have to wait for the solution to be done to do this. You can do this while the simulation is running, all information will update automatically after each pass is done.



9.14-13

Plot Mesh, H-Field Vector and Flux LineClick on the menu item Edit > Select All Visible or Select All, or use CTRL + A , or select everything from the history tree window, then right mouse click in the modeler and select Plot Mesh .Do the same, select all objects, then right mouse click in the modeler and select Fields > H > H_Vector, and Fields > A > Flux Lines .



9.14-14

The following H-field vector plot will appear, which is the result of the current excitation on the left side.

If the plot is not as nice as you may want to see, you can double click on the legend bar, then change various settings under Color map / Scale / Marker / Arrow or Plots tabs.



9.14-15

Create Design2: 2_BalloonClick on design 1_VectorPotential in the Project Manager window and then right mouse click and select Copy

Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 1_VectorPotential1 has been created, change the design name to 2_Balloon.

Click on VectorPotential1 under Boundaries in the Project Manager, and press “Delete” from keyboard to remove the boundary condition.

Right click in the modeler and select Select Edges, to change from object selection mode to edge selection mode.

Left mouse click on one of the edges of the Region, then right mouse click and select All Object Edges to select all edges of the Region.

Right mouse click again, Assign Boundary > Balloon…

Run the simulation and compare H Field plot with the previous design that has vector potential boundary.

Balloon on all edges of the Region Zero Vector Potential on the outer edge of the Stator



9.14-16

Create Design3: 3_Balloon_ChangeExcitationClick on design 2_Balloon in the Project Manager window and then right mouse click and select Copy

Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 2_Balloon1 has been created, change the design name to 3_Balloon_ChangeExcitation.

Modify Current ExcitationClick on Excitations > Current_3 in the

Project window, you will see a Properties

window under Project window, change from

Positive to Negative in the Direction row. Also,

Change Current_7 from Positive to Negative

Change Current_4 and Current_8 from

Negative to Positive.

The purpose is to change the current

excitation as shown in the graph below.

Current_2

Current_1

Current_8

Current_7

Current_3

Current_4

Current_5

Current_6

PositiveCurrent_8

NegativeCurrent_7

NegativeCurrent_6

PositiveCurrent_5

PositiveCurrent_4

NegativeCurrent_3

NegativeCurrent_2

PositiveCurrent_1



9.14-17

Run the simulation and compare H Field plot with Design2 2_Balloon that has different excitations.




9.14-18

Symmetry BoundaryCreate Design4: 4_Symmetry_Odd

Click on design 2_Balloon in the Project Manager window and then right mouse click and select CopyClick on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 2_Balloon1 has been created, change the design name to 4_Symmetry_Odd.Select all objects and right mouse click in the modeler > Boolean > Split, choose XZ plane to create half geometry.

In the history tree, double click on CreateRegion under Vacuum > Region, change –Y Padding Percentage to 0.Remove the Balloon boundary, reassign the Balloon boundary to three edges (not on the symmetry edge).Change to Edge selection mode and click on the edge of the Region along X axis, right mouse click in the modeler > Assign Boundary > Symmetry, choose Odd (Flux Tangential).



9.14-19


Symmetry: Odd (Flux Tangential)



9.14-20

Create Design5: 5_Symmetry_EvenClick on design 4_Symmetry_Odd in the Project Manager window and then right mouse click and select Copy

Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 4_Symmetry_Odd1 has been created, change the design name to 5_Symmetry_Even.

Select the Symmetry boundary and change it to Even (Flux Normal).


Symmetry: Even (Flux Normal)



9.14-21

Create Design6: 6_NoSymmetryClick on design 4_Symmetry_Odd in the Project Manager window and then right mouse click and select Copy

Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 4_Symmetry_Odd1 has been created, change the design name to 6_NoSymmetry.

Select the Symmetry boundary and delete it.


The result should look the same as Design4: 4_Symmetry_Odd because odd symmetry or flux tangential is the default boundary condition.

No Symmetry: by default an Odd (Flux Tangential boundary is assigned)



9.14-22

Matching Boundaries (Master/Slave).

Slave=Master

Master


Slave= — Master

Master

Design7: 7_Matching_Positive Design8: 8_Matching_Negative



9.14-23

Matching Boundaries: Master/Slave

Create Design7: 7_Matching_PositiveClick on design 6_NoSymmetry in the Project Manager window and then right mouse click and select Copy.

Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 6_NoSymmetry1 has been created, change the design name to 7_Matching_Positive.

Select all objects and right mouse click in the modeler > Edit > Boolean > Split, choose YZ plane.

Change –X Padding Percentage of the Region to be 0.

Remove the existing Balloon boundary and redefine it on two edges of the Region that are not on X and Y axis.

Change to Edge selection mode and select the edge of the Region that is along Xaxis. Right mouse click in the modeler > Assign Boundary > Master. Be sure that the master vector arrow is pointing in the positive X direction. If not use Swap Direction.

Select the edge of the Region that is along Y axis. Right mouse click in the modeler > Assign Boundary > Slave. Be sure that the slave vector arrow is pointing in the positive Y direction. If not use Swap Direction.

Choose Master1 from the pull down menu, and Relation as Bs = Bm.



9.14-24


Slave=Master

Master



9.14-25

Create Design8: 8_Matching_NegativeClick on design 7_Matching_Postitive in the Project Manager window and then right mouse click and select Copy.Click on the project name Ex_9_14_Basic_BoundaryConditions, right click and select Paste, a new design called 7_Matching_Postitive1 has been created, change the design name to 8_Matching_Negative.Change the Slave boundary Relation to Bs = - Bm.


Slave=-Master

Master


9.15Basic Exercise – PM Assignment

9.15-1

Maxwell 2D v12

Permanent Magnets AssignmentThis exercise will discuss how to set up a permanent magnet (PM) material to an object. This procedure is applicable for Magnetostatic and Transient Solvers.

Start working with MaxwellStart Maxwell V12

If a new project is not open click on Project > New

Project > Insert Maxwell 2D Design

Maxwell 2D > Solution Type > Magnetic: Magnetostatic; Geometry Mode: Cartesian, XY

Problem definitionWe are interested to solve the magnetic field of a Circular PM placed in vacuum. The material of PM is NdFeB35 and the magnet is magnetized in the direction 30 degrees relative to the Global X direction.



9.15-2

Maxwell 2D v12

Orientation of objects as one of the attributesEach object in Maxwell is associated with certain coordinate system. This is called Orientationand it is specified under attributes for each object. Let us create an object (circle with the center in [0,0,0] and radius of 1 mm) and observe its Orientation. Click on the menu item Draw > Circle

X,Y, Z: 0, 0, 0 Enter

DX, DY, DZ: 1, 0, 0 Enter

Edit > Properties; Select Attribute Tab

Change the name from Circle1 to magnet

Before clicking OK see that one of the attributes displayed is Orientation. The Orientation of this object is Global. This means that our object magnet is currently associated with the Global coordinate system. Global Coordinate system exists by default in a newly inserted Maxwell Design. Left-clicking on Global allows changing the Orientation to other coordinate system, provided, of course, that some other coordinate system exists. Click OK to close the window.



9.15-3

Maxwell 2D v12

Orientation can also be viewed graphically. First, make sure that this feature is enabled:

Tools > Options > Modeler Options select Display Tab and check Show orientation of selected objects

Select the object magnet (left-click on magnet from the history tree). The Orientation is shown as small arrows starting from the origin. These should not be confused with the Coordinate System axes arrows which are bigger and display x or y next to arrows. The visibility and size of Coordinate System axes arrows can be controlled from: View > Coordinate System > Small

Create a new Coordinate System (CS) with x-axis rotated 30 degrees relative to x-axis of the Global CS:

Modeler > Coordinate System > Create > Relative CS > Rotated

On the Status Bar (bottom right) change the CS type from Cartesian to Cylindrical and specify

R, Phi, Z: 1, 30, 0 Enter

The newly created CS automatically becomes a working CS (small w sign is displayed next to the icon of a Working CS). Expand Coordinate Systems form History Tree and left-click on Global to make it a Working CS again:



9.15-4

Maxwell 2D v12

The Orientation of magnet can now be changed. Object magnet can now be associated with RelativeCS1 coordinate system:

Select magnetEdit > PropertiesChange Orientation from Global to RelativeCS1; OK

Select the object magnet again and observe the orientation:

Orientation: Global Orientation: RealtiveCS1

Specifying properties of Permanent MagnetsChange the material of magnet from Vacuum to NdFeB35:

Select magnetEdit > PropertiesClick on Vacuum to enter the material database, find NdFeB35 and click on View/Edit MaterialsA Permanent Magnet (PM) with linear characteristic is uniquely defined by specifying two of the following: Coercive Field, Remanent Flux Density, Relative Permeability. Coercive Field and Relative Permeability are chosen by default to be specified. If any other combination of quantities is know instead, select Calculate Properties for PM (see next page) and specify the two known quantities. The remaining quantity will be determined automatically.The direction of magnetization is specified by a unit vector (see next page) relative to the Coordinate System associated with the given object, that is relative to the Orientation of the object. If the Orientation of the object is Global, the unit vector will be specified relative to the Global CS. Maxwell also allows to specify the type of the Coordinate System (upper right corner – see next page). Thus Cartesian, Cylindrical and Spherical CS type can be defined. This means that if the Orientation of the object is Global and CS type Cartesian, the unit vector will be specified as X, Y, and Z relative to the Cartesian Global CS. And, e.g., if the Orientation of the object is RelativeCS1 and CS type is Cylindrical, the unit vector will be specified as R, Phi and Z relative to the Cylindrical RelativeCS1 CS. Hence, the right direction of magnetization is specified by the appropriate combination of object’s Orientation, CS type and Unit Vector. Click OK to approve the material definition and to perform the assignment.



9.15-5

Maxwell 2D v12



9.15-6

Maxwell 2D v12

Examples of PM direction of magnetization assignmentDirection of Magnetization in the Global X direction

Orientation: Global; CS Type: Cartesian; Unit Vector X, Y, Z: 1, 0, 0

Direction of Magnetization in the direction 30 degrees relative to Global X direction

Orientation: Global; CS Type: Cartesian; Unit Vector X, Y, Z: 1, 0.5, 0

OR

Orientation: RelativeCS1; CS Type: Cartesian; Unit Vector X, Y, Z: 1, 0, 0



9.15-7

Maxwell 2D v12

Direction of Magnetization in the outward radial direction

Orientation: Global; CS Type: Cylindrical; Unit Vector R, Phi, Z: 1, 0, 0

Direction of Magnetization in the inward radial direction

Orientation: Global; CS Type: Cylindrical; Unit Vector R, Phi, Z: -1, 0, 0



9.15-8

Maxwell 2D v12

Definition of the Solution Space - RegionBefore proceeding to define the solution space make sure that the direction of magnetization is 30 degrees relative to Global X direction, as required by the problem definition (see page 9.15-1).

FEM requires that a finite solution space is defined prior solving the problem. This solution space in Maxwell is called Region. The Region can be very conveniently defined using the following command:

Draw > Region and specify Padding Percentage 500. Padding Percentage of 500% creates a rectangle which extends 5 times the diameter of the circle in each direction. As the diameter of the circle is 2 mm and 5 times 2 mm is 10 mm, the corners of the rectangle will be [-11, -11] and [11, 11].



9.15-9

Maxwell 2D v12

Definition of the Boundary ConditionsWe expect that Region is so large that the magnetic field will not extend beyond Region’sboundary. This situation corresponds to the boundary condition specifying the magnetic vector potential (A) zero on the edges of Region:

Select Region and Edit > Select > All Object Edges

Maxwell 2D > Boundaries > Assign > Vector Potential and leave the value zero; OK

Define Analysis and solve the problemMaxwell 2D > Analysis Setup > Add Solution Setup

Accept all default values; OK

Maxwell 2D > Analyze All



9.15-10

Maxwell 2D v12

Viewing the resultsWe will plot the magnetic flux lines throughout the solution spaceMagnetic flux lines:

Select All objects (CTRL A or Edit > Select All)Maxwell 2D > Fields > Fields > A > Flux Lines; DoneDouble-click on the LegendSelect Color Map Tab and specify 40 in the Number of Divisions field; Apply; Close Zoom in

We can see that the flux lines are really oriented 30 degrees relative to the Global Coordinate System. This means that the magnetization of the magnet is correctly assignedThis completes the exercise

Date post:	30-Oct-2014
Category:	Documents
Upload:	lev-foxhill
View:	79 times
Download:	1 times

Ansoft_Maxwell2D_V12_2009

Documents