Ansoft Maxwell2D_V12

Ansoft Maxwell 2D Electromagnetic and Electromechanical Analysis

12

electronic design automation software

user’s guide – Maxwell 2D ANSOFT CORPORATION • 225 West Station Square Dr. Suite 200 • Pittsburgh, PA 15219-1119

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

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Contents Contents This 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


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3D/2D Electromagnetic Field Simulation

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 highperformance 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 Benefits

applications

Electromagnetic field simulation Maxwell includes 3D/2D Transient, AC electromagnetic, Magnetostatic, Electrostatic and Electrotransient solvers that accurately solve for force, torque, capacitance, inductance, resistance, and impedance, as well as generate state-space models.

Electromechanical • Motors and generators • Linear or rotational actuators • Relays • MEMS • Magnetic recording heads Electromagnetic • Coils • Permanent magnets • Sensors Power electronic • Transformers • Converters • Bus bars • IGBTs and similar devices EM behavior • Insulation studies • Electrostatic discharge • Electromagnetic shielding • EMI/EMC • Semiconductor • Biomedical

Automatic adaptive meshing Maxwell uses the Ansoft-pioneered automatic adaptive meshing techniques. This robust meshing algorithm automatically creates and refines the finite element mesh as the solution converges, streamlining the solution process and making the software very easy to use. Dynamic link - ePhysics The Maxwell 3D solvers can be dynamically linked with ePhysics’ thermal and stress analysis and are the ideal solution for every electromechanical device requiring cross-disciplinary design analysis. Dynamic link - Simplorer Dynamic links with Simplorer multi-domain system simulation allow accurate high-fidelity component models to be combined with circuits and system architecture to create a powerful, electromagneticbased design flow. Import CAD files can be imported in Maxwell streamlining the design process. Multi-processing and distributed analysis Maxwell can leverage available computing power with multi-processing and distributed analysis options for fast turnaround of your largest designs. Optimization Optimetrics™ 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-processors RMxprt (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.

The new 2D interface provides strong coupling with 3D and many new usability features.

Key features Low-frequency electromagnetic field simulation and analysis using FEM for 3D/2D structures • Transient - nonlinear analysis with: Motion—rotation, translational, non-cylindrical rotation External circuit coupling Permanent magnet demagnetization analysis Core loss computation Lamination modeling for 3D • AC Electromagnetic—Analysis of devices influenced by skin/ proximity effects, eddy/displacement currents • Magnetostatic—Nonlinear analysis with automated equivalent circuit model generation • Electric Field—Transient, Electrostatic/Current flow analysis with automated equivalent circuit model generation Display of data/visualization of results • Field visualization and animations (shaded, contour and vector plots) • Mesh visualization (full, partial) • Current, induced voltage, flux linkage • Power loss, stored energy • Core loss, eddy, excess, hysteresis loss (including the minor loop effects) • Impedance, inductance, capacitance • Force, torque • Custom reports of user-defined solution data

Performance and integration • Distributed Analysis* for parallel computing of parameterized models • 64-bit operating system support • Links to Simplorer®*, ePhysics™*, HFSS™*, RMxprt™*, PExprt™* Integrated 3D modeler featuring ACIS v16 and MFC technology • Standard primitives and multi-sweep functions • Boolean operations: union, subtraction, intersection • Direct import of SAT and DXF files • AnsoftLinks™* for import of STEP, IGES and Pro/E files Automatic, adaptive mesh technology • Fault-tolerant meshing algorithms • Mesh-generation feedback • GUI performs validation and integrity checks • Software identifies artifacts within the imported geometry • Mesh-based model resolution Versatile material manager and material types • User, group and system libraries • Linear, nonlinear anisotropic materials • Material assignment by coordinate type: cartesian, cylindrical or spherical Integrated Optimetrics™* • Geometry and material parameterization • Optimization, sensitivity and statistical analysis *Option available at additional charge.

CAD Files IGES, STEP, DXF, SAT, ProE

AnsoftLinks

™

Simplorer

®

RMxprt

™

Maxwell

®

Optimetrics

™

Electric Machine

PExprt

™

Converters & Transformers

ePhysics

™

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

Maxwell, Simplorer, ePhysics, Optimetrics, PExprt, AnsoftLinks, and HFSS 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 USA T 412-261-3200 F 412-471-9427 E [email protected] W www.ansoft.com

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 designoptimization 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.

OVERVIEW 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.

FEATURED CAPABILITIES • 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

• 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 USA TEL 1.412.261.3200 FA X 1.412.471.9427 EMAIL info @ansoft.com WEB www.ansoft.com

Please consult your local sales representative for pricing and information on this and on other Ansoft products. HFSS, Maxwell, Optimetrics and Q3D Extractor are trademarks of Ansoft Corporation. All other trademarks are the property of their respective owners. © 2005 Ansoft Corporation PH15-1105

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.

v7.0 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

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

Modeling Techniques 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 VHDL-AMS IEEE-endorsed modeling language (standard 1076.1) created to provide a generalpurpose, easily exchangeable and open language for multi-domain analog mixed-signal designs.

CIRCUITS Numerically 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.

transformations and model analogies often employed by singledomain simulation tools.

BLOCK DIAGRAMS Enables the description of signal-flow-based linear, nonlinear, continuous, time-discrete and hybrid systems, making it ideal for dynamic system simulation and closedloop-control applications.

STATE MACHINES Highly efficient modeling technique for event-driven systems, such as logical control found in embedded control systems, space vector controls or PWM for powerelectronic circuits.

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

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

Alternative Power Automotive Hydraulic Machine

• • • •

Mechanical Power SMPS Sensor

FEA-Based Models For 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’ Models SIMPLORER 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.

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

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

• • • •

SIMPLEX Frequency Sweep Worst Case Sensitivity SIMPLORER v7 includes many new statistical design and optimization routines.

Integration Scripting This 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-Simulation SIMPLORER 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.

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

RMxprt

™

v12

Design Software for Electric Machines

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 Benefits

design templates

Fast design RMxprt offers numerous machine-specific, template-based interfaces for induction, synchronous, and electronically and brush-commutated machines that allow users to easily enter design parameters and to evaluate design tradeoffs early in the design process.

Machine types • Induction machines o Single-phase motors o Three-phase motors • Synchronous machines o Line-start PM motors o Salient-pole motors and generators o Non-salient pole motors and generators • Brush commutated machines o DC motors and generators o Permanent magnet DC motors o Universal motors • Electronically commutated machines o Brushless DC motors o Adjustable-speed PM motors and generators o Switched reluctance motors o Claw-pole generators

Performance metrics Critical performance data, such as torque versus speed, power loss, flux in the air gap, power factor and efficiency can be quickly calculated. Robust calculation methods RMxprt uses classical analytical motor theory and equivalent magnetic 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-processor RMxprt is a key part of Ansoft’s motor design methodology. In addition 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 library RMxprt includes a comprehensive database of ANSI and IEC wires. High-fidelity system models RMxprt creates high-fidelity, state-space system models incorporating machines’ physical dimensions, winding characteristics and nonlinear material properties. Engineers can use the resulting behavioral model to explore electronic control topologies, loads, and interactions with drive-system components in Simplorer®. Convenient design sheet output Design 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 optimization RMxprt 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 scripting RMxprt 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.

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

Key features • Machine-specific template editor o Rotor o Stator o Running strategies o Drive circuits • Auto-design feature o Slot size o Coil turns and wire diameter o Starting capacitance o Winding arrangement • Performance curves o Torque o Power o Efficiency

• Output waveforms o Current o Cogging torque o Flux in the air gap • Graphical winding editor • Cross section Editor • Customizable design sheet • Cost evaluation • Integrated parametrics and optimization • State-space model export to Simplorer® • Automated project setup for Maxwell® 2D • Automated geometry and material setup for Maxwell 3D

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.

DESIGN FLOW RMxprt 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. 3TATE3PACE-ODEL

RMXPRT

™

s'EOMETRYs3KEW s-ATERIALS s3TACKING s7INDING s%ND%FFECT )NFO

'EOMETRY WINDINGCHARACTERISTICS ANDNONLINEARMATERIALPROPERTIES

SIMPLORER®

MAXWELL® 0HYSICS BASED0ARAMETERS

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 USA T 412-261-3200 F 412-471-9427 E [email protected] W www.ansoft.com

Presentation

Overview

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

Ansoft Maxwell Field Simulator v12 – Training Seminar

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Maxwell 2D solves the electromagnetic field problems for a given model 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: Electrostatic AC Conduction Electric Fields DC Conduction Magnetostatic Eddy Current Magnetic Fields Transient Magnetic Ansoft Maxwell Field Simulator v12 – Training Seminar

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Different Methods of Electromagnetic Analysis Electromagnetic Analysis

Closed Form

Analytical Techniques

BEM

Numerical Techniques

Iterative

Integral Equations

Differential Equations

Boundary Elements

Finite Difference

Finite Elements

FEM

FDM

Scalar Potentials


Vector Potentials

Components of H-Field

2D Electrostatic

2D Magnetostatic

3D Magnetostatic

3D Thermal

2D Eddy

3D Eddy

3D Electrostatic

2D Transient

3D Transient

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Differential Form of Maxwell’s Equations Faraday' s Law of Induction

∇×Ε =−

Gauss' s Law for Magnetism

∇•B=0

∂Β ∂t

Ampere' s Law

∇×H = J +

Gauss' s Law for Electricity

∇•D=ρ


∂D ∂t

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FEM and adaptive meshing In order to obtain the set of algebraic equations to be solved, the geometry of the problem is discretized automatically 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

Has Stopping Criteria been met?

Refine Mesh

No

Yes

Stop Field Solution

Y X Ansoft Maxwell Field Simulator v12 – Training Seminar

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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 2D Field quantities inside of the triangle are calculated using a 2nd order quadratic interpolation scheme 1

6

2

3

5 4 Ansoft Maxwell Field Simulator v12 – Training Seminar

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FEM Variational Principle Poisson’s equation: ∇ 2 A = − µJ

 1  ∇ A • ∇A  + A • J dV is replaced with energy functional: F ( A) = ∫  2  µ  This functional is minimized with respect to value of A at each node in every triangle


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

[S ][A] = [J ] This can be solved using standard matrix solution techniques such as: Sparse Gaussian Elimination (direct solver) Incomplete Choleski Conjugate Gradient Method (ICCG iterative solver)


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FEM Error Evaluation Put the approximate solution back into Poisson’s equation

∇ 2 Aapprox + µJ = R Since A is a quadratic function, R is a constant in each triangle. The local error in each triangle is proportional to R.


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FEM Percent Error Energy Summation of local error in each triangle divided by total energy n

R(local)i

i =1

Total Energy

Percent Error Energy = ∑

× 100%

Local errors can exceed Percent Error Energy


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Transient Solver Fully Coupled Dynamic Physics Solution Current Source Density

Electric Scalar Potential

Velocity

∂A ∇ × υ∇ × A = J s − σ − σ∇V + ∇ × H c + σv × ∇ × A ∂t Magnetic Vector Potential

Permanent Magnet

Time-varying Electric and Magnetic Fields


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Transient Solver - Magnetic Field Diffusion Magnetic fields “diffuse” into materials at different rates depending on: Material properties of the component Physical size of the component

For a cylindrical conductor, diffusion time is:

uσ a 2 τ= (sec) 2 2.4048 where : u = perm , σ = conductivi ty , a = radius in meters Induced eddy currents always occur in conducting objects due to time-varying fields; however, they may not always be significant


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GUI - Desktop The 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.


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Overview

ACIS solid modeling kernel The underlying solid modeling technology used by Ansoft products is provided by ACIS geometric modeler. ACIS version 16 is presently used. 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


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Supported platforms Windows XP Pro Windows XP Pro x64 Edition Windows Server 2003 Windows Server 2003 x64 Edition Red Hat Enterprise Linux 3, 4 SuSE Linux Enterprise Server 9.3 Solaris 8 -10


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Starting Maxwell Click the Microsoft Start button, select Programs, and select the Ansoft >

Maxwell 12 > Maxwell 12

Or Double click on the Maxwell 12 icon on the Windows Desktop

Adding a Design When 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


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Maxwell Desktop Menu bar

Toolbars

Project Manager with project tree

Property Window

2D Modeler Window

History Tree Progress Window

Message Manager Status bar Coordinate Entry Fields


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Maxwell Desktop – Project Manager Multiple Designs per Project Multiple Projects per Desktop Integrated Optimetrics Setup (requires license for analysis) Project Manager Window

Project

Design

Design Setup

Design Automation •Parametric •Optimization •Sensitivity •Statistical


Design Results

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Overview Maxwell Desktop – 2D Modeler Graphics area

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2D Modeler Window Model

Edge

2D Modeler design tree (history)

Vertex Context menu (right mouse click on 2D modeler window)


Origin

XY Coordinate System

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Geometry Mode To set the geometry mode: 1. Select the menu item Maxwell 2D > Solution Type 2. Solution Type Window: W Choose Geometry Mode: Cartesian XY

Maxwell – Geometry Modes A 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) Z

Y

X R

Z

Φ


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

Magnetic Solution Types Magnetostatic Computes 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 Current Computes 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. Transient Computes 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 Types Electrostatic 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 Conduction Computes 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 Conduction Computes 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. Ansoft Maxwell Field Simulator v12 – Training Seminar

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Set Model Units To 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 Material To set the default material: 1. Using the Modeler Materials toolbar, choose Select 2. Select Definition Window: 1. Type steel_1008 in the Search by Name field 2. Click the OK button


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Modeler – Draw a Rectangle Point 2

Point 1

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 Ansoft Maxwell Field Simulator v12 – Training Seminar

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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


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Modeler – Object Properties Commands (dimensions and history)

In History Tree: Attributes Commands

Attributes (properties of the object)


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Modeler – Attributes

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 Ansoft Maxwell Field Simulator v12 – Training Seminar

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Modeler - Views View > 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 Ansoft Maxwell Field Simulator v12 – Training Seminar

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Changing the View Toolbar

Rotate Around Current Axis

Zoom In/Out

Fit Selected

Predefined View Angles

Pan

Top Rotate Around Rotate Around Screen Center Model Center

Context Menu

Fit All Dynamic Zoom

Right

Left

Bottom

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 Ansoft Maxwell Field Simulator v12 – Training Seminar

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Maxwell V12 Keyboard Shortcuts General Shortcuts F1: Help Shift + F1: Context help CTRL + F4: Close program CTRL + C: Copy CTRL + N: New project CTRL + O: Open... CTRL + S: Save CTRL + P: Print... CTRL + V: Paste CTRL + X: Cut CTRL + Y: Redo CTRL + Z: Undo CTRL + 0: Cascade windows CTRL + 1: Tile windows horizontally CTRL + 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 left Click here to restore view in an RZ model

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.

Predefined View Angles Top

Right

Left

Bottom

Alt + double left Click here to restore view in an XY model Ansoft Maxwell Field Simulator v12 – Training Seminar

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Simple Example Magnetic core with coil Use 2D RZ Magnetostatic Solver

Core (Steel_1008)

Coil (120 Conductors, Copper)


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Setup the geometry mode and solver Choose Cylindrical about Z under Maxwell 2D > Solution Type Choose Magnetostatic Click the OK button

Create Core To create the core: 1. Select the menu item Draw > Rectangle 2. 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


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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 2. Click the OK button 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: 1. Select the Attribute tab from the Properties window. 2. Click the Edit button To set the transparency: 1. Select the Attribute tab from the Properties window. 2. Click the OK button To finish editing the object properties 1. Click the OK button To fit the view: 1. Select the menu item View > Fit All > Active View


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Set Default Material To 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 2. Click the OK button

Create Coil To create the coil for the current to flow: 1. Select the menu item Draw > Rectangle 2. 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 dX: 2.0, dY: 0.0, dZ: 4.0, Press the Enter key

To set the name: 1. Select the Attribute tab from the Properties window. 2. For the Value of Name type: Coil 3. Click the OK button To fit the view: 1. Select the menu item View > Fit All > Active View


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Create Excitation Assign Excitation 1. Click on the coil. 2. Select the menu item Maxwell 2D > Excitations > Assign > Current 3. Current Excitation : General 1. Name: Current1 2. Value: 120 A (Note: this is 120 Amp-turns) 3. Ref. Direction: Positive 4. Click the OK button 5. Note that for RZ models, positive current flows into the screen, however for XY models, positive current flows out of the screen.


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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 > Region 1. Padding Data: One 2. Padding Percentage: 200 3. Click the OK button

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


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Setup Boundary Assign Boundary 1. Change to edge selection mode by choosing: Edit > Select > Edges 2. 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 > Balloon 4. Click the OK button


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Solution Setup - Creating an Analysis Setup To create an analysis setup: 1. Select the menu item Maxwell 2D> Analysis Setup > Add Solution

Add Solution Setup

Setup 2.

Solution Setup Window: 1. Click the General tab: Maximum Number of Passes: 10 Percent Error: 1 2. Click the OK button


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Save Project To 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 Validation To validate the model: 1. Select the menu item Maxwell 3D> Validation Check 2. Click the Close button Note: To view any errors or warning messages, use the Message Manager.

Analyze To start the solution process: 1. Select the menu item Maxwell 2D> Analyze All Validate


Analyze All

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View detailed information about the progress In the Project Tree click on Analysis > Setup1 with the right mouse button und select Profile


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Mesh Overlay Create a plot of the mesh 1. Select the menu item Edit > SelectAll To create a mesh plot: 1. Select the menu item Maxwell 2D > Fields > Plot

Mesh 2.

Create Mesh Window: 1. Click the Done button


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Field Overlays To 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_B 3. Create Field Plot Window 1. Solution: Setup1 : LastAdaptive 2. Quantity: Mag_B 3. In Volume: Allobjects 4. Click the Done button 4. When done, turn off the plot using:

View > Active View Visibility > Filed Reporter


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Field Overlays (cont) Create another 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 > B_Vector 3. Create Field Plot Window 1. Solution: Setup1 : LastAdaptive 2. Quantity: B_Vector 3. In Volume: Allobjects 4. Click the Done button 4. When done, turn off the plot using:



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Field Overlays (cont) Create another 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 > A > Flux_Lines 3. Create Field Plot Window 1. Solution: Setup1 : LastAdaptive 2. Quantity: Flux_Lines 3. In Volume: Allobjects 4. Click the Done button 4. When done, turn off the plot using:


This completes the simple example.


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


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File Structure Everything regarding the project is stored in an ascii file File: .mxwl Double click from Windows Explorer will open and launch Maxwell v12 Results and Mesh are stored in a folder named .mxwlresults Lock file: .lock.mxwl Created when a project is opened Auto Save File: .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)


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Scripts Default Script recorded in v12 Visual Basic Script

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


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Overall Setup Process Design

Solution Type 2. Boundaries

1. Parametric Model Geometry/Materials 2. Excitations 3. Mesh Operations

2. Analysis Setup Solution Setup Frequency Sweep

Mesh Refinement

Analyze

Solve

4. Results 2D Reports Fields

NO

Converged

2. Solve Loop YES Update


Finished P1-47

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Menu Structure Draw – Primitives Modeler – Settings and Boolean Operations Edit – Copy/Paste, Arrange, Duplicate Maxwell 2D – Boundaries, Excitations, Mesh Operations, Analysis Setup, Results


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Modeler – Model Tree Select menu item Modeler > Group by Material

Material

Object

Object Command History

Grouped by Material


Object View

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Modeler – Commands Parametric 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


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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

Toolbar: 2D Objects

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.


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Modeler – Boolean Operations/Transformations Modeler > 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 Toolbar: Boolean

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. Toolbar: Arrange

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 Toolbar: Duplicate

Edit > Scale – Allows non-uniform scaling in the x, y, or z direction Ansoft Maxwell Field Simulator v12 – Training Seminar

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Modeler - Selection Selection Types Object (Default) Face Edge Vertex

Selection Modes All 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 Options From the Display Tab, uncheck Highlight selection dynamically

Selected

Dynamically Highlighted (Only frame of object)


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Modeler – Moving Around Modeler > Snap Mode to set the snaps Tools > Customize… Snap Mode to view Snap Mode toolbar

Toolbar: Snap Mode


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Modeler – Coordinate Systems Can 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 Toolbar: Coordinate System Both Face CS (setting available to automatically switch to face coordinate system in the Modeler Options)

Step 1: Select Face

Step 2: Select Origin

Cone created with Face CS

Step 3: Set X-Axis

New Working CS


Change Box Size and Cone is automatically positioned with the top face of the box P1-55

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2D Measure Modeler > Measure > Position – Location, Distance, and Area Edge – Edge Length Face – Surface Area Object – Surface Area, Object Volume

Position Points


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Options – General Tools > Options > General Options > Project Options Temp Directory – Location used during solution process Make sure it has at least 512MB free disk.

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


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Options – Modeler Options Tools > 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

Typical “Dialog” entry mode window

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


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Converting Older Maxwell Projects (pre-Maxwell v12) to Maxwell v12 From Maxwell v 11 and older, 1. Select the menu item File > Open 2. 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


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Material Setup - Libraries 3-Tier library structure System (global) level – predefined from Ansoft and ships with new upgrades, users cannot modify this User 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 > Materials New Interface for Materials Setting shared with RMxprt


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Overview 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.


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Materials Setup - Editing


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Material Setup – BH curve Robust 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…


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Material Setup - Permanent Magnets Direction 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


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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.

ε 1 0 [ε ] =  0 ε 2  0 0

0 0 , ε 3 

 µ1 [µ ] =  0  0

0

µ2 0

0 0 , µ3 

σ 1 0 0  [σ ] =  0 σ 2 0   0 0 σ 3 

Anisotropic Permitivity

Anisotropic Permeability

Anisotropic Conductivity

Dielectric Loss Tangent

Magnetic Loss Tangent

Electrostatic

yes

no

no

no

no

DC Conduction

no

no

yes

no

no

AC Conduction

yes

no

yes

no

no

Magnetostatic

no

yes

no

no

no

Eddy Current

no

yes

no

no

no

Transient

no

yes

no

no

no

Solver


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

Balloon

Field behaves so that voltage can fringe

Ground at infinity

Matching (Master and Slave)

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.

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

Resistance (DC conduction solver only)

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.

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


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

H-Field Behavior

Default Boundary Conditions (Natural and 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.

Balloon

Field behaves so that magnetic flux can fringe

No fringing at infinity

Matching (Master and 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.


Used to model…

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

Charge Density

The charge density in an object.

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


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Magnetic Field Sources (Magnetostatic) Source

Type of Excitation

Current

The total current in a conductor.

Current Density

The current density 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 (Eddy Current)

Source

Type of Excitation

Current


Parallel Current

The total current in a a group of parallel conductors.

Current Density


Notes: In the Eddy Current solver, current is peak amp-turns. Sources can be solid (with eddy effects) or stranded (without eddy effects).


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Magnetic Field Sources (Transient) Source

Type of Excitation

Current


Current Density


Coil

Current or voltage on a winding representing 1 or more turns

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

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)


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Magnetic Field Sources (Transient) Maxwell 2D > Excitation > Current Value: applies current in amps Type: Solid for windings having a single conductor/turn eddy effects are considered Stranded for windings having many conductors/turns eddy effects are not considered Ref Direction: Positive or Negative


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Magnetic Field Sources (Transient) Maxwell 2D > Excitation > Add Winding Current – 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 > Coil Pick 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 Ansoft Maxwell Field Simulator v12 – Training Seminar

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To Create an External Circuit 2.

3.

Select: Maxwell2D > Excitations > External Circuit > Edit External Circuit > Import Circuit 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) Save circuit as *.amcp file and then Maxwell Circuit > Export Netlist > *.sph file.

I

Model switch1 I W_sw1

Model

Model

V

d1

switch2 V LabelID=VI1

1.

S_sw2

-

D64

+

5.3ohm LabelID=R3

LWinding1

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).

0


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

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


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Core Loss Calculation Method The core loss for electrical steel is based on:

2 p = K h Bmax f + K c (Bmax f ) + K e (Bmax f ) 2

1. 5

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: y p = Cm f x Bmax where: Cm is constant value determined by experiment. fx is the frequency. Bymax is the maximum amplitude of the flux density


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Maxwell 2D > Design Settings The 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).


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Maxwell 2D > Parameters Allows the automatic calculation of parameters following the field solution Includes: Force, Torque, Flux linkage, Core loss, and Matrix


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Maxwell 2D > Model > Motion Setup > Assign Band

1. 2. 3.

Defines the direction and type of motion (translation or rotation) Defines the mechanical parameters such as mass, damping, and load force Defines limits of motion


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Magnetostatic and Electric Solution Setup Start 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.


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Eddy Current Solution Setup


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Transient Solution Setup


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Mesh Operations To 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


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1. Mesh Operations “On selection” applied on the perimeter of the object Element length based refinement: Length Based Skin Depth based refinement: Skin Depth Based

On selection – skin depth based (2 layers)

On selection – length based Ansoft Maxwell Field Simulator v12 – Training Seminar

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

Inside selection – length based


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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)

D = Maximum Surface Deviation

D

Maximum Surface Normal Deviation (degrees) Θ = Maximum Surface r Normal Deviation Θ

D = r (1 − cos(Θ / 2))

Maximum Aspect Ratio

AspectRatio = ri

ro 2 * ri

ro


P1-85

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Manual mesh creation To create the initial mesh: Click Maxwell > Analysis Setup > Apply Mesh Operations To refine the mesh without solving 1. Define mesh operations as previously discussed 2. Click Maxwell > Analysis Setup > Apply Mesh Operations 3. 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


P1-86

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1

Mesh Display 1. 2.

Select an object Select the menu item Maxwell 2D > Fields > Plot Mesh


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2D transient meshing for rotational models “Moving Surface” method used

Stator stationary part master moving surface

Air gap 7 7'

Band

6 6'

5 5'

3

4 4'

3'

2 2'

1 1' slave moving surface

Rotor


moving part(s)

P1-88

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2D transient meshing for translational models “Moving Band” method used Adaptive 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 band Moving part(s)


P1-89

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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


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Overview

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Contour plot


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Shade plot (tone)


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Shade plot (fringe with outline)


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Arrow plot


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Line plot


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Multiple windows and multiple plots


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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


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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


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Fields Calculator – Export Command Exports 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.


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Presentation

Overview Export to Grid Vector data Min: [0 0 0] Max: [2 2 2] Spacing: [1 1 1] Space delimited ASCII file saved in project subdirectory


1

Vector data "" Grid Output Min: [0 0 0] Max: [2 2 2] Grid Size: [1 1 1 0 0 0 -71.7231 -8.07776 128.093 0 0 1 -71.3982 -1.40917 102.578 0 0 2 -65.76 -0.0539669 77.9481 0 1 0 -259.719 27.5038 117.572 0 1 1 -248.088 16.9825 93.4889 0 1 2 -236.457 6.46131 69.4059 0 2 0 -447.716 159.007 -8.6193 0 2 1 -436.085 -262.567 82.9676 0 2 2 -424.454 -236.811 58.8847 1 0 0 -8.91719 -241.276 120.392 1 0 1 -8.08368 -234.063 94.9798 1 0 2 -7.25016 -226.85 69.5673 1 1 0 -271.099 -160.493 129.203 1 1 1 -235.472 -189.125 109.571 1 1 2 -229.834 -187.77 84.9415 1 2 0 -459.095 -8.55376 2.12527 1 2 1 -447.464 -433.556 94.5987 1 2 2 -435.833 -407.8 70.5158 2 0 0 101.079 -433.897 -18.5698 2 0 1 -327.865 -426.684 95.8133 2 0 2 -290.824 -419.471 70.4008 2 1 0 -72.2234 -422.674 -9.77604 2 1 1 -495.898 -415.461 103.026 2 1 2 -458.857 -408.248 77.6138 2 2 0 -470.474 -176.115 12.8698 2 2 1 -613.582 -347.994 83.2228 2 2 2 -590.326 -339.279 63.86

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Getting Help If 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 F1 key. 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 Site If 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


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Overview WebUpdate This 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.


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For Technical Support The 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 America The 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 (781) 229-8900 x0 – Ask for Technical Support 9-4 PST: San Jose, CA (408) 261-9095 x0 – Ask for Technical Support Portland, OR (503) 906-7944 or (503) 906-7947 El Segundo, CA (310) 426-2287 – Ask for Technical Support


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Optimetrics

What is Optimetrics ? ¾

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

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

¾

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 Optimizers 1.

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 handles the 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 setup Integrated with force, torque, matrix Complete support of Transient solution

Optimetrics Module (cont.) Integrated with external circuit Setup variables in Maxwell Circuit Editor

Optimize on ‘voltage’ in Maxwell

Optimetrics Example

Optimization of a starter-alternator pack The pack contains a motor used also as alternator Three-phase claw pole motor Permanent Magnets are added between teeth

Optimization of the Geometry Want to see the influence on the output torque Tooth angle

Magnet thickness

Magnet length

Results

Transient analysis run for the optimized design Initial Peak torque: 63.40 Nm Optimized Peak Torque: 67.42 Nm

Initial

Optimized

Maxwell 2D v12 Chapter 6.0 Chapter 6.0 – Eddy Current Examples 6.1 – Jumping Rings Axisymmetric Model 6.2 – Instantaneous Forces on Busbars

Ansoft Maxwell 2D Field Simulator v12 User’s Guide

6.0 - 1

Maxwell 2D v12

6.1 Eddy Current – Application Note

Introduction This 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 opencircuited. The open-circuit condition is simulated by constraining the total current to zero. A physical layout of the actual device is shown in: open points in rings ring3

ring2

ring1

I1

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 Design Click 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


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Maxwell 2D v12


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

Draw the Solution Region Click on Draw > Rectangle (Enter the following points using the tab key). X: 0, Y: 0, Z: -10 dX: 20, dY: 0, dZ: 20 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 The model consists of three donut-shaped rings. A cross-section of the model is shown below. This is a 2-dimensional axisymmetric drawing; an axisymmetric model 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.


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Maxwell 2D v12


Draw the Rings Click 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 Change its properties: 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 Change its properties: Name: ring3 Material: Copper Color: Yellow


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Maxwell 2D v12


Assign the Sources A 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. Click on Maxwell 2D > Excitations > Assign > Current Name: Current2 Value: 0A Type: Solid Select ring3 from the history tree. Click on Maxwell 2D > Excitations > Assign > Current 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 Boundary 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 three outer edges of the region. Click on Maxwell 2D > Boundaries> Assign > Balloon When done, choose Edit > Select > Object to object selection mode.


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Maxwell 2D v12


Assign the Parameters In 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 Depth Skin 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:

δ =

2

ωµ o µ rσ

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.


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Maxwell 2D v12


Add an Analysis Setup Click 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 Operations In 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: 1000 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.

Mesh operation “On Selection”

Mesh operation “Inside Selection”


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Maxwell 2D v12


Solve the Problem Save 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

View the Solution Data Select 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.

 R11 , L11 R , L  21 21  R31 , L31 Ansoft Maxwell 2D Field Simulator v12 User’s Guide

R12 , L12 R22 , L22 R32 , L32

R13 , L13  R23 , L23  R33 , L33  6.1 - 7

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 ring1 skin effect ring2 proximity effect from I1 ring3 proximity effect from I1 R11

= 3.458e-004 = 4.446e-005 = 1.710e-005 = –6.963e-006 = 4.004e-004 ohms

In this example, with a 1 A peak current in ring1, and with both ring2 and ring3 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.


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Maxwell 2D v12


Plot the Mesh Select 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 Results Now 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.


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Maxwell 2D v12


Compute Total Power Loss in the Coils Select 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 Lines Select all objects Click on Maxwell 2D > Fields > Fields > A > Flux Lines > Done


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Maxwell 2D v12


Verify the total current flowing around each of the rings Click 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 rings Although 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. Click on Maxwell 2D > Fields > Calculator and then perform the following: 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 - 11

Maxwell 2D v12


Plot the current density Hide 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

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.

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


6.1 - 12

Maxwell 2D v12


Plot the current density vector and animate Hide 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 Plots tab. 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.


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Maxwell 2D v12


Calculate the open circuit voltage on ring2 and ring3 Calculate 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:

V2' = − I1 * Z12 = − I1 * (1.722e -5 + jω 1.090e -8 ) = − 1* (1.722e -5 + j2π *10000 *1.090e -8 ) = − 1.722e -5 − j6.849e -4 = 6.851e -4 ∠91.4º (V peak) 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:

V2' = ∫ E • d L =

1 ∫ E • dV area RZ

=

1 ∫ − jω A • d V area RZ

=

2 * π *10000 ∫ − j A • dV 3.1257e −6 RZ

= 6.85e − 4 (Vpeak )


6.1 - 14

Maxwell 2D v12


Calculate the complex magnitude of the voltage To 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 CmplxMag includes both real and imaginary components. Note that the complex magnitude is equal to:

ACmplxMag = Aφ2_ real + Aφ2_ imag 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. Ansoft Maxwell 2D Field Simulator v12 User’s Guide

6.1 - 15

Maxwell v12


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.

1 Re J × B ∗ dV ∫ 2 1 FAC = ∫ J × B dV evaluated at phase (ω t = degrees) 2 FINST = FDC + FAC

FDC =

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.

2D Model


3D Model

6.2 - 1

Maxwell v12


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

Maxwell v12


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


6.2 - 3

Maxwell v12


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. 2. 3. 4.

Click Right on the Analysis folder in the Model Tree and select Add Solution Setup… On the General tab, re-set the Number of passes to 15. Percent Error to 0.01 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.


6.2 - 4

Maxwell v12


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 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.


6.2 - 5

Maxwell v12


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.


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Maxwell v12


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.

XY Plot 1

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0.000006

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Force_DC Setup1 : LastAdaptive Freq='100kHz'

-2.5666E-006

Force_AC Setup1 : LastAdaptive Freq='100kHz'

5.0213E-006

Force_inst Setup1 : LastAdaptive Freq='100kHz'

2.4547E-006

0.000000 1 Y -0.000002

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Maxwell v12


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:

FMST = ∫ (B ⋅ n ) H − 0.5 ( B ⋅ H )n dV

evaluated at phase (ω t = degrees)

Determine the instantaneous component of force at time wt=0 using the Maxwell Stress Tensor method in the calculator: Quantity > B Function > Phase > OK Complex > At Phase Geometry > Line > left > OK Unit Vector > Normal Dot Quantity > H Function > Phase > OK Complex > At Phase Multiply

Loads the B vector Loads the function Phase Evaluates the B vector at phase = wt This enters the edge of the left busbar To determine the unit normal vector for left busbar To take B-dot-Unit Normal Loads the H vector Loads the function Phase Evaluates the H vector at phase = wt This multiplies B and H

Quantity > B Function > Phase > OK Complex > At Phase Quantity > H Function > Phase > OK Complex > At Phase Dot Number > Scalar > 0.5 > OK Multiply

Loads the B vector Loads the function Phase Evaluates the B vector at phase = wt Loads the H vector Loads the function Phase Evaluates the H vector at phase = wt Computes B-dot-H

Geometry > Line > left > OK Unit Vector > Normal Multiply Neg Add Scal? > ScalarX Geometry > Line > left > OK Integrate Add…

Enters the edge of the left busbar To determine the unit normal vector for left busbar This multiplies the quantity times unit normal vector This takes the negative

Multiplies the quantity by 0.5

To extract the x-component of the quantity Enters the edge of the left busbar To integrate the force density and obtain the force in newtons Name: Force_MST


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Maxwell v12


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. XY Plot 2

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Curve Info Force_inst Setup1 : LastAdaptive Freq='100kHz' Force_MST Setup1 : LastAdaptive Freq='100kHz'

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This completes PART 1 of the exercise.


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Maxwell v12


PART 2 - The 3D Eddy Project Now the identical model will be simulated in Maxwell 3D. Setup the Design 1. Click on the menu item Project > Insert Maxwell 3D Design 2. Click on the menu item Maxwell 3D > Solution Type ... • 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


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•

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


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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. 2. 3. 4. 5. 6. 7. 8. 9.

Select the left busbar by clicking on it in the history tree or on the screen. Click on Maxwell > Parameters > Assign > Force Name: Force_Virtual Type: Virtual Click OK to enable the virtual force calculation. Click on Maxwell > Parameters > Assign > Force Name: Force_Lorentz Type: Lorentz Click OK to enable the lorentz force calculation.

Add an Analysis Setup 1. 2. 3. 4. 5.

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


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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 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.


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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.


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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


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Maxwell 2D v12 Chapter 7.0 Chapter 7.0 – Transient Examples 7.1 – Gapped Inductor Model 7.2 – Solenoid Problem with an External Circuit


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7.1

Gapped Inductor – Transient XY Application Note Introduction The 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.


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7.1

Gapped Inductor – Transient XY Application Note Setup the Design Click on the menu item Project > Insert Maxwell 2D Design Click on the menu item Maxwell 2D > Solution Type ... Set Geometry Mode: Cartesian, XY Select the radio button Magnetic: Transient OK

Specify the Drawing Units Click on Modeler > Units Select units: in OK

Create the Model The 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 depth For 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 Change its properties: Name: Core Material: Ferrite Color: Red


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7.1

Gapped Inductor – Transient XY Application Note Draw the Core Windows Click 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_1 and then click on: Modeler > Boolean > Subtract Blank Parts: Core Tool Parts: Rectangle1, Rectangle1_1 Clone objects before subtracting: unchecked Ok

Subtract the Core gap Click 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


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7.1

Gapped Inductor – Transient XY Application Note Draw the Windings Click on Draw > Rectangle X: -1.4, Y: -1.825, Z: 0 dX: 0.8, dY: 0.125, dZ: 0 Change its properties: Name: Coil Material: Copper Color: Green Create the return for the first winding turn: 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 Change its properties: Name: Coil_return Material: Copper Color: Green Create the complete winding by selecting Coil and Coil_return and then choosing: Edit > Duplicate > along line X: 0, Y: 0, Z: 0 dX: 0, dY: 0.25, dZ: 0 Total Number = 15 Do not check Attach to original.

Draw the Solution Region Click on Draw > Region: Padding Data: All Padding Directions Padding Percentage: 100


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7.1

Gapped Inductor – Transient XY Application Note Assign the Outer Boundary 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 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 Sources A 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_14 Choose: Maxwell 2D > Excitations> Assign > Current Name: left Value: 120*sin(2*pi*60*time) + pwl_periodic(ds1, Time) The Add Dataset window will automatically appear to enter the triangular waveform. Name: ds1 Enter the following X,Y coordinates and click OK and Done. X

Y

1

0

0

2

0.00025

20

3

0.00050

0

4

0.00075

-20

5

0.001

0

Type: Solid Polarity: Positive Ok


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7.1

Gapped Inductor – Transient XY Application Note 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 winding Choose Maxwell 2D > Excitations > Set Eddy Effects ... Check the eddy effect for all 30 coils.


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7.1

Gapped Inductor – Transient XY Application Note Add an Analysis Setup Click 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


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7.1

Gapped Inductor – Transient XY Application Note Add Mesh Operations In 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 Restrict Number of Elements: ; Check 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 Restrict Length Of Elements: Uncheck Restrict Number of Elements: ; Check Maximum Number of Elements: 500


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7.1

Gapped Inductor – Transient XY Application Note Create the Mesh before solving Select the menu item Maxwell 2D > Analysis Setup > Apply Mesh Operations

View the Solution Data for the Mesh Select the menu item Maxwell 2D > Results > Solution Data Click on the Mesh Statistics tab to view the starting mesh.


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7.1

Gapped Inductor – Transient XY Application Note Create Output for Current using the Calculator Since 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 plotted To do this, select: Maxwell 2D > Results > Output Variables... Under Report Type, select “Fields”. Choose Category: Calculator Expressions Quantity: Current_in Function: . 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 calculated In 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.


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Maxwell 2D v12

7.1

Gapped Inductor – Transient XY Application Note Solve the Problem Save 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 Mesh Select 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.


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Maxwell 2D v12

7.1

Gapped Inductor – Transient XY Application Note View the Results Now 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 winding vs time.

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


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7.1

Gapped Inductor – Transient XY Application Note Plot Current Density in Coils The 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


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7.1

Gapped Inductor – Transient XY Application Note Plot the Input Current Create 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 XY Plot 1

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7.1

Gapped Inductor – Transient XY Application Note Plot the Losses in the Winding Create 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. XY Plot 2

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7.1

Gapped Inductor – Transient XY Application Note Solve for the sinusoidal current source only Copy 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. XY Plot 1

Ansoft Corporation

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XY Plot 2

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7.2 2D Transient – Application Note

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.

Model

LWinding2

25ohm Rcoil

rectify

170V LabelID=Vsource

D4

+

D1

D2

D3 0

2D RZ Model

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.


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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: 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%

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


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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


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Maxwell v12


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.


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Maxwell v12


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


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Maxwell v12


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


7.2 - 6

Maxwell v12


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: Model

LWinding2

25ohm Rcoil

rectify

170V LabelID=Vsource

D4

+

D1

D2

D3 0

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


7.2 - 7

Maxwell v12


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.


7.2 - 8

Maxwell v12


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.


7.2 - 9

Maxwell v12


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)


7.2 - 10

Maxwell v12


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.


7.2 - 11

Maxwell v12


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). Force Quick Report

Ansoft Corporation

Maxwell2DDesign1

150.00

Curve Info Moving1.Force_z Setup1 : Transient Moving1.LoadForce Setup1 : Transient

100.00

Y1 [newton]

50.00

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

0.00

-50.00

-100.00 0.00

5.00

10.00

15.00

20.00

25.00

Time [ms]


7.2 - 12

Maxwell v12

7.2 2D Transient – Application Note Position Quick Report

Ansoft Corporation

Maxwell2DDesign1

0.00

Curve Info Moving1.Position Setup1 : Transient

-0.50

Moving1.Position [mm]

-1.00

-1.50

-2.00

-2.50

-3.00 0.00

10.00

20.00

30.00

40.00

Time [ms] Speed Quick Report

Ansoft Corporation

50.00

60.00

Maxwell2DDesign1

5.00

Curve Info Moving1.Speed Setup1 : Transient

Moving1.Speed [m_per_sec]

4.00

3.00

2.00

1.00

0.00 0.00

10.00

20.00

30.00 Time [ms]


40.00

50.00

60.00

7.2 - 13

Maxwell v12

7.2 2D Transient – Application Note Winding Quick Report

Ansoft Corporation 150.00

Maxwell2DDesign1

40.00

0.60

Curve Info Current(Winding1) Setup1 : Transient Current(Winding2) Setup1 : Transient

20.00 100.00

FluxLinkage(Winding2) Setup1 : Transient

-0.00

0.40

-20.00

Y1 [A]

InducedVoltage(Winding2) Setup1 : Transient InputVoltage(Winding1) Setup1 : Transient

0.30

Y2 [Wb]

InducedVoltage(Winding1) Setup1 : Transient

50.00

Y3 [V]

0.50

FluxLinkage(Winding1) Setup1 : Transient

-40.00 0.00 0.20 -60.00 -50.00 0.10

-80.00

-100.00

0.00

-100.00 0.00

10.00

20.00

30.00 Time [ms]

40.00

50.00

Loss Quick Report

Ansoft Corporation

60.00

Maxwell2DDesign1

2.50

Curve Info SolidLoss Setup1 : Transient

2.00

Notes: 1) In order to scale the plot and view the solid loss, delete the stranded and core loss traces.

SolidLoss [W]

1.50

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.

1.00

0.50

0.00 0.00

10.00

20.00

30.00 Time [ms]

40.00

50.00

60.00

This completes the exercise. Ansoft Maxwell Field Simulator v12 User’s Guide

7.2 - 14

Maxwell 2D v12 Chapter 9.0 Chapter 9.0 – Basic Exercises 9.1 – 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


9.0 - 1

Maxwell 2D v12

9.1

Basic Exercises – Electrostatic Solver

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 Z Select 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.


9.1-1

Maxwell 2D v12

9.1


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 Change the color and transparency level at your convenience. 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 Change the color and transparency level at your convenience. 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


9.1-2

Maxwell 2D v12

9.1

Basic Exercises – Electrostatic Solver 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 Parameter In 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 object Inner Select the menu item Maxwell > Parameters > Assign > Force


9.1-3

Maxwell 2D v12

9.1


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

Plot the electric field From the modeler history tree, select the plane Global:XZ. On the 3D modeler window, right click and select Fields > E_Vector


9.1-4

Maxwell 2D v12

9.1

Basic Exercises – Electrostatic Solver 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).


9.1-5

Maxwell 2D v12

9.1


Capacitance of a Cylindrical Capacitor in XY The same problem is now solved 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: Cartesian XY Select 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 Change the material to copper Change the color and transparency level at your convenience. Create another circle. Click on the menu item Draw > Circle or click on the icon For the center position, enter 0; 0; 0mm For the radius, enter 1.2 mm; Change the name to Outer Change the material to copper Change the color and transparency level at your convenience. Click on the menu item Draw > Circle or click on the icon For the center position, enter 0; 0; 0mm For the radius, enter 1. mm; Change the name to Air Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.1-6

Maxwell 2D v12

9.1

Basic Exercises – Electrostatic Solver 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 Parameter In addition to the fields, we are interested by the Capacitance value. Capacitance Matrix Select the menu item Maxwell > Parameters > Assign > Matrix Include Voltage1 and Voltage2 in the capacitance computation by checking the radio buttons. Set Voltage1 as a signal line and Voltage2 as ground.

Create Analysis Setup 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%


9.1-7

Maxwell 2D v12

9.1

Basic Exercises – Electrostatic Solver Solve the Problem Select Setup1 from under Analysis in the project tree, right mouse click and select Analyze

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

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.


9.1-8

Maxwell 2D v12

9.1

Basic Exercises – Electrostatic Solver 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 model Click on the menu item Project > Insert Maxwell 2D Design Name the design Plate Click on the menu item Maxwell > Solution Type Select Geometry Mode: Cartesian XY Select 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 Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.1-9

Maxwell 2D v12

9.1

Basic Exercises – Electrostatic Solver 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


9.1-10

Maxwell 2D v12

9.1

Basic Exercises – Electrostatic Solver Assign Executive Parameter Select the menu item Maxwell > Parameters > Assign > Matrix Include Voltage1 and Voltage2 in the capacitance computation

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

Create Analysis Setup Select the menu item Maxwell > Analysis Setup > Add Solution Setup For the Percent Error, enter 1% For the Refinement per Pass (Convergence tab), put 50%

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.


9.1-11

Maxwell 2D v12

9.1

Basic Exercises – Electrostatic Solver Get the capacitance value 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 di electrics) 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.


9.1-12

Maxwell 2D v12

9.3

Basic Exercise – Magnetostatic Force Calculation Force calculation in Magnetostatic Solver This exercise will discuss how to set up a force calculation in the 2D Magnetostatic Solver.

Problem Description As 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.

Actual 3D Coil and Slug


2D Symmetric Coil and Slug about z-axis

9.3-1

Maxwell 2D v12

9.3

Basic Exercise – Magnetostatic Force Calculation Create a New Project Open up Maxwell V12 Click on the menu item Project > Insert Maxwell 2D Design Click on the menu item Maxwell 2D> Solution Type > Magnetostatic Change the geometry mode to Cylindrical about Z

Draw the Slug Click 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 Coil Click 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 Change its color if desired


9.3-2

Maxwell 2D v12

9.3

Basic Exercise – Magnetostatic Force Calculation Add a Region Click 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 project Click on File > Save As: Magnetostatic_Force.mxwl for Basic Exercise Magnetostatic Force calculation

Assign Excitation Select 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) Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.3-3

Maxwell 2D v12

9.3

Basic Exercise – Magnetostatic Force Calculation

Assign Boundary to Region Edges From 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 Calculation Select the Coil and click on the menu item Maxwell2D > Parameters > Assign > Force Name: Force1


9.3-4

Maxwell 2D v12

9.3


Create Analysis Setup Click on Maxwell 2D > Analysis Setup > Add Solution Setup Maximum Number of Passes: 15 Refinement per Pass: 30 Click on OK

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

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


9.3-5

Maxwell 2D v12

9.3


View Calculated Force Result Click on the Force tab in the open Solutions window. The calculated force is updated automatically after each pass.


9.3-6

Maxwell 2D v12

9.3

Basic Exercise – Magnetostatic Force Calculation Plot the Magnitude of Magnetic Flux Density Select 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. Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.3-7

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver 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. Coil OR = 1.25mm Coil IR = 1mm Coil Height = 0.8mm

Slug width = 1mm Slug depth = 1mm Slug Height = 1mm 3D Geometry: Coil and Iron Slug

2D Flux Lines and Flux Density

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 mode Verify 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 CreateRectangle under Rectangle1 in the History Tree, and edit the Position, Xsize and Zsize as shown, and click OK.


9.4 - 1

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver 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 Names Select 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 - 2

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver 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 Region Select 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 Condition View 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 - 3

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver Assign the Excitation Select 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 Calculation Include 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 Setup Right 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. Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.4 - 4

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver Modify Setup and solve a nominal problem In 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 - 5

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver Inspect Results Check 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 - 6

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver Create a Parametric solution Click 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 - 7

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver 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 problem In the Project Manager window, under Optimetrics, right click on ParametricSetup1, 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 - 8

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver 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. SlugHeight Right Click on Results in the Project Manager, and select Create Magnetostatic Report > Rectangular Plot.


9.4 - 9

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver 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 - 10

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver

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 - 11

Maxwell 2D v12

9.4

Basic Exercises – Parametric Solver 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.


9.4 - 12

9.5 Basic Exercise – 2D Transient Inductor using transient source This exercise will discuss how to use transient sources as the excitation for an inductor coil.

Draw the Inductor Click 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 Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.5-1

9.5 Basic Exercise – 2D Transient Click on the menu item Draw > Region: Padding Data: All Padding Directions Padding Percentage: 500 Change the name of the design to: BE_Trans for Basic Exercise Transient

Assign Excitation Select 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:


9.5-2

9.5 Basic Exercise – 2D Transient Create the Excitation The 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 Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.5-3

9.5 Basic Exercise – 2D Transient Assign Balloon Boundary Click 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 Operations The 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 Restrict Length Of Elements: Uncheck Restrict Number of Elements: ; Check Maximum Number of Elements: 250 Select the Coil and click on the menu item Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based. Name: Coil_Inside Restrict Length Of Elements: Uncheck Restrict Number of Elements: ; Check Maximum Number of Elements: 100

Create Analysis Setup Click 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


9.5-4

9.5 Basic Exercise – 2D Transient Solve the Problem Select Setup1 from under Analysis in the project tree, right mouse click and select Analyze

Save the Design Click on File > Save to save the design and results

Plot the Voltage and Current Click 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


9.5-5

9.5 Basic Exercise – 2D Transient Plot the Flux Lines Be 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 Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.5-6

9.6 Basic Exercise – 2D Transient with Circuits Inductor using transient source This exercise will discuss how to use transient sources as the excitation for an inductor coil.

Draw the Inductor Click 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 if desired 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 Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.6-1

9.6 Basic Exercise – 2D Transient with Circuits Click on the menu item Draw > Region: Padding Data: All Padding Directions Padding Percentage: 500 Change the name of the design to: BE_Trans_Ckt for Basic Exercise Transient

Assign Excitation Select 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:


9.6-2

9.6 Basic Exercise – 2D Transient with Circuits Create an External Circuit To 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 Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.6-3

9.6 Basic Exercise – 2D Transient with Circuits 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:

Note: Same name used: Winding_A

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. Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.6-4

9.6 Basic Exercise – 2D Transient with Circuits Assign Balloon Boundary Click 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 Operations The 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 Restrict Length Of Elements: Uncheck Restrict Number of Elements: ; Check Maximum Number of Elements: 250 Select the Coil and click on the menu item Maxwell 2D > Mesh Operations > Assign > Inside Selection > Length Based. Name: Coil_Inside Restrict Length Of Elements: Uncheck Restrict Number of Elements: ; Check Maximum Number of Elements: 100

Create Analysis Setup Click 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


9.6-5

9.6 Basic Exercise – 2D Transient with Circuits Solve the Problem Select Setup1 from under Analysis in the project tree, right mouse click and select Analyze

Save the Design Click on File > Save to save the design and results

Plot the Voltage and Current Click 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


9.6-6

9.6 Basic Exercise – 2D Transient with Circuits Plot the Flux Lines Be 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 legend: Color Map Tab > Number of Divisions: 56 Plots Tab > IsoValType: Line Zoom in to see the plot below.

This concludes the Basic Example for Transient with Circuits Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.6-7

Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Puck Magnet Attractor This example describes how to create and optimize a puck magnet producing an optimal force on a steel plate using the 2D RZ Magnetostatic solver 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


9.8-1

Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Create a New Project Open up Maxwell V12 Click on the menu item Project > Insert Maxwell 2D Design 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 Plate Click 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 Change its color if desired

Draw the Magnet Click 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


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Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor 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 > Faces Click on the magnet and then choose: the menu item Modeler >

Coordinate System > Create > Face CS Click 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


9.8-3

Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Setup the magnet motion To 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 magnet 3. Click the OK button 4. 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.


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Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Add a Region Click 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 project Click on File > Save As: Ex_09_08.mxwl for Basic Exercise Optimization calculation


9.8-5

Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Assign Boundary to Region Edges Click 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 Maxwell 2D > Boundaries > Assign > Balloon Click on the menu item Edit > Select > Objects

Assign Force Calculation Select the Plate and click on the menu item Maxwell2D > Parameters > Assign > Force Name: Force1


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Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Add an Analysis Setup Right 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.


9.8-7

Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Modify Setup and solve a nominal problem In 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.


9.8-8

Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor View the Automatic Adaptive Mesh Convergence Right click on the project tree item Analysis > Setup1 and select Convergence.

View Calculated Force Result Click on the Force tab in the open Solutions window. The calculated force is updated automatically after each pass.


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Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Optimetrics Setup and Solution It 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 Variables Before starting the optimization setup, the appropriate variables must be included in the optimization. Select the menu item Maxwell 2D > Design Properties, click on the Optimization 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.


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Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Setup an Optimization Analysis Select the menu item Maxwell 2D > Optimetrics Analysis > Add Optimization ... In the Setup Optimization window, change the optimizer to: Sequential Nonlinear

Programming Reduce 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. 2. 3. 4. 5. 6. 7.

Name: target Expression: 0.25 Click on Add to create this output variable for the target inductance. Name: cost1 Expression: (target - Force_z) ^2 Click on Add to create this output variable for the cost function. Click on Done to leave the Output Variable window.


9.8-11

Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Setup an Optimization Analysis In 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 Analysis In the Setup Optimization window, change the Condition: Minimze Click OK to leave the Setup Optimization window.


9.8-12

Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Solve the Optimization Analysis In the project tree window, highlight OptimizationSetup1. Select the menu item Maxwell 2D > Analyze All to solve. Solution time is approximately 5 - 10 minutes.

Optimetrics Results Your 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.


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Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Optimetrics Results Choose View: Table to display the results below.


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9.8

Optimetrics Example – Puck Attractor Create Plot of Cost vs Force To 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

XY Plot 1

Ansoft LLC

Maxwell2DDesign1

550.00 Curve Inf o Force1.Force_z Setup1 : LastAdaptive

Force1.Force_z [mNewton]

500.00

450.00

400.00

350.00

300.00

250.00

200.00

0.00

100.00


200.00

300.00 m ove [um ]

400.00

500.00

600.00

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Maxwell 2D v12

9.8

Optimetrics Example – Puck Attractor Create Plot of Cost vs move To create a report: 1. Select the menu item Maxwell 2D > Results > Create Magnetostatic Report

> Rectangular Plot 2.

Choose Quantity: cost1 and click New Report

XY Plot 2

Ansoft LLC

Maxwell2DDesign1

1.00E-001 Curve Info cost1 Setup1 : LastAdaptive

1.00E-002

cost1

1.00E-003

1.00E-004

1.00E-005

1.00E-006

0.00

100.00


200.00

300.00 move [um]

400.00

500.00

600.00

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Maxwell 2D v12

9.10 Basic Exercise - Scripting

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

Save the Project Select the menu item File > Save As… Save the file as scripting_example.mxwl


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Maxwell 2D v12


Start Recording the Script Click 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: dX: 1.0, dY: 0.0, dZ: 0.0, Press the Enter key

Stop Recording the Script Click on the menu item Tools > Stop Script Recording. The file is now saved on the disk.

Delete the Circle Click 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 Circle Click 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.


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Maxwell 2D v12


Open the Script for Editing Locate the file on the hard disk and open with notepad.

Script File Contents Definition 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 oAnsoftApp Dim oDesktop Dim oProject Dim oDesign Dim oEditor Dim oModule Reference defined environment variables using Set. Set oAnsoftApp = CreateObject("AnsoftMaxwell.MaxwellScriptInterface") Set oDesktop = oAnsoftApp.GetAppDesktop() oDesktop.RestoreWindow Set oProject = oDesktop.SetActiveProject("scripting_example") Set oDesign = oProject.SetActiveDesign("Maxwell2DDesign1") Set oEditor = oDesign.SetActiveEditor("3D Modeler") Ansoft Maxwell 2D Field Simulator v12 User’s Guide

9.10-3

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.


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Maxwell 2D v12


Delete the Circle Click 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 Circle Click on the menu item Tools > Run Script. Locate and select the script file and click Open. If successful, the modified cylinder, Circle1, should appear.


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Maxwell 2D v12


Generalize the script to run in any Project and Design To 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.


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Maxwell 2D v12

9.12

Basic Exercises – Eddy Current Solver Introduction to the Eddy Current Solver This 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 Coil A 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 RZ axisymmetric solver.

Cast iron disk

Spiral coil

Simulated 2D model

Actual 3D model

Setup the Design Click on the menu item Project > Insert MaxwellDesign Click on the menu item Maxwell 2D > Solution Type ... Set Geometry Mode: Cylindrical about Z Select the radio button Magnetic: Eddy Current

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

Check the Snap Mode Click on Modeler > Snap mode Verify that Snap To: Grid and Vertex are set. Ansoft Maxwell 2D Field Simulator v12 User’s Guide

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Maxwell 2D v12

9.12

Basic Exercises – Eddy Current Solver Draw the Solution Region Click on Draw > Rectangle (Enter the following points using the tab key). X: 0, Y: 0, Z: -100 dX: 120, dY: 0, dZ: 200 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.

Draw the Spiral Coil Click on Draw > Rectangle X: 17, Y: 0, Z: -1 dX: 2, dY: 0, dZ: 2 Change its properties: 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 Plate Click on Draw > Rectangle X: 0, Y: 0, Z: 1.5 dX: 41, dY: 0, dZ: 1 Change its properties: Name: Plate Material: Cast Iron Color: Red


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Maxwell 2D v12

9.12

Basic Exercises – Eddy Current Solver Assign the Source A 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. Click on Maxwell 2D > Excitations > Assign > Current 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 Boundary 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 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 Parameters In 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


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Maxwell 2D v12

9.12

Basic Exercises – Eddy Current Solver Compute the Skin Depth Skin 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:

δ =

2

ωµ o µ rσ

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 Setup Click 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 Problem Save the project by clicking on menu item File > Save As Select the menu item Maxwell 2D > Validation Check to verify problem setup You 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.

Click on Maxwell 2D > Analyze All Ansoft Maxwell 2D Field Simulator v12 User’s Guide

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Maxwell 2D v12

9.12

Basic Exercises – Eddy Current Solver View the Convergence Select 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.


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9.12

Basic Exercises – Eddy Current Solver Plot the Mesh Select 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.

Compute Total Power Loss in the Plate Click on Maxwell 2D > Fields > Calculator and then perform the following: Quantity > OhmicLoss Geometry > Volume > Plate > OK Integral > RZ Eval ... Evaluate Note: The evaluated loss in the Plate should be about 260 W. Click Done


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Maxwell 2D v12

9.12

Basic Exercises – Eddy Current Solver Compute Total Power Loss in the Coils Select all eight 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 (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 Lines Select all objects Click on Maxwell 2D > Fields > Fields > A > Flux Lines > Done 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 - 7

Maxwell 2D v12

9.12

Basic Exercises – Eddy Current Solver Plot Current Density Scalar in the Plate Hide 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 Coils Select Objectlist1 to select all eight coils in the winding. Click on Maxwell 2D > Fields > Fields > J > JAtPhase > Done


9.12 - 8

Maxwell 2D v12

9.12

Basic Exercises – Eddy Current Solver Plot Ohmic Loss Distribution Hide 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 Vector Rotate 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 - 9

Maxwell 2D v12

9.12

Basic Exercises – Eddy Current Solver Copy the Design and Solve again at DC In 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. Click on Maxwell 2D > Analyze All

Plot Current Density Scalar In 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 - 10

Maxwell 2D v12

9.12

Basic Exercises – Eddy Current Solver Plot the Flux Lines In 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.


9.12 - 11

Maxwell 2D v12

9.13

Basic Exercise: Transient – Large Motion – Rotational 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 from mechanically moving magnetic fields in space, i.e. moving objects. Thus, effects coming from so-called motion induced currents can be considered. 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 with large motion in Maxwell. It is neither the goal to simulate real-world applications, nor to match accurately measured results, nor will these papers show in detail how to setup and work with other Maxwell functionality. Please refer to the corresponding topics.

Quickstart – Rotational Motion Using a Rotational Actuator Example 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. If necessary, 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


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Maxwell 2D v12

9.13

Basic Exercise: Transient – Large Motion – Rotational Perform basic large motion tests „Large Rotational Standstill“ test „Large Rotational Constant Speed“ test „Large Rotational Transient Motion“ test Compute magnetic rigidity and mechanical natural frequency Estimate timestep for transient solver Make a field animation with large motion

Open the Rotational Actuator Model Locate the project Ex_09_13_BasicTransient_MotionRotational_M2dTrs120.mxwl. Open it, activate the design 00_Template and start working from there. You can copy/paste 00_Template into your own working project. The other designs show the fully setup models we will be working on. The model should look like this:

Fig. 1: Rotational actuator example Ansoft Maxwell 2D Field Simulator v12 User’s Guide

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Maxwell 2D v12

Basic Exercise: Transient – Large Motion – Rotational Setup and Verify the Electromagnetic Part Prior to employing large motion, the electromagnetic part of the model should work correctly. Users are well advised not to setup a complex model 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 each individual property should be verified. After that, all properties can be considered together. For this quickstart, please study the winding setup and background. We use stranded windings with constant current (to generate a fixed stator flux vector around which Rotor1 will oscillate later). Also, eddy effects 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 is simulated). 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 the electromagnetic 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 the previous page (00_Template).

Rotational Large Motion – The Maxwell Approach Maxwell separates moving from non-moving objects. All moving objects must be enclosed by one so-called band object. For rotational motion, the band object must be cylindrical with segmented outer surface, i.e. a regular polyhedron. Maxwell considers all moving objects (inside the band) to form one single moving object group.

Fig. 2: Band object separating rotor from stator Ansoft Maxwell 2D Field Simulator v12 User’s Guide

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Maxwell 2D v12

9.13

Basic Exercise: Transient – Large Motion – Rotational 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/dt effects are included in the field solution. Mechanical Transient mode: In case inertia was specified, Maxwell will compute the motion equation in each time step.

Jm · d2ϕm(t) / dt2 + kD(t) · dϕm(t) / dt = Tψ(t) + Tm(t) See Appendix A for a variable explanation.

Apply Large Motion to the Rotational Actuator – Create the Band 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 be considered 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 is not a must. Hide all objects except Rotor1 and Stator1. Determine the required radius:

Modeler > Measure > Position In the geometry, click first on the origin, then move so that the mouse pointer snaps to one outer corner point of Rotor1. Read the Distance value from the Measura Data window (51.05 mm). Then move over so that the pointer snaps to one inner corner point 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.


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Maxwell 2D v12

9.13

Basic Exercise: Transient – Large Motion – Rotational

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 (or dY) field, leaving dZ and dY (or dX) zero. Set the number of segments to 72.

Rename the thus created object to Band1, apply a transparency of 0.9, and maybe use some nicer color. The created Band1 object should look like Fig. 4.


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Maxwell 2D v12

9.13


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 more accurate 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 for the Rotation Axis. On the Data tab, apply zero for the initial position. Thus, motion will start at t = 0 with the rotor position being as drawn. Applying ϕm0 ≠ 0 would start with Rotor1 rotated by ϕm0 from the drawn position. 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.


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Maxwell 2D v12

Basic Exercise: Transient – Large Motion – Rotational Now, we have setup „large rotational standstill“. Positive magnetic torque is generated around the positive z-axis (global coordinate system, Fig. 5). In the project tree > active design > Model, two new entries have been created – MotionSetup1 and Moving1. Clicking on Moving1 inspect the motion setup. Applying the same constant current as before, we can expect the same 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 which the solver will just yield satisfactory results. Band1: For torque computation, the most critical areas are the airgap and its immediate proximity. Thus, the band mesh is crucial for accurate results. We will apply a length based mesh on the surface and inside of Band1. We will restrict the number of elements to 5000. This will do for these tests. Ansoft Maxwell 2D Field Simulator v12 User’s Guide

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Maxwell 2D v12

9.13

Basic Exercise: Transient – Large Motion – Rotational Right mouse click on Band1 > Assign Mesh Operation > Inside Selection > 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 > Inside

Selection > Length Based. Restrict Length of Elements – unchecked, Restrict Number of Elements – checked. Following, first the object names are listed, second the maximum number of elements to apply, and third the name given to the resulting mesh entry: Rotor1 – 1000 – Rotor_Length Stator1 – 1000 – Stator_Length CoilA and CoilB – 100 – Coils_Length (simultaneously selecting CoilA, CoilA_Neg, CoilB, and CoilB_Neg will try to assign 100 triangles to the group, i. e. about 25 triangle 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 Mesh Operations. Watch the progress bar (usually bottom right). Watch the message window (usually bottom left) for a message that says that the Simulation 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.


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Maxwell 2D v12


Fig. 6: Mesh entries

Fig. 7: Resulting mesh

Perform Basic Large Motion Tests These basic tests serve model verification. They can be executed rather quickly. Should they fail in whatever respect, there is no use going further and working with more complex models (like mechanical transients, external circuits, 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 simulation process. 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 Transient Report. > Rectangular Plot, select Category = Torque, and Quantity = Moving.Torque, press New Report, and Close. Your report should show constant force of about 400 mNm.


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Maxwell 2D v12

Basic Exercise: Transient – Large Motion – Rotational 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 constant speed. 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 cogging torque 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 zero position 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 move 180°, i. e. from -90° to +90°, at 5°/step. Right mouse click Analysis > Setup1 > Analyze During solving, you can already open the report Torque(t). The plot is going to build up with each timestep completed. See Fig. 7. Torque(t)

Ansoft Corporation 500.00

12_GeoFull_MagI_MchSpeedslow Curve Info Torque Setup1 : Transient

400.00 300.00

Torque [mNewtonMeter]

200.00 100.00 0.00 -100.00 -200.00 -300.00

Fig. 8: Magnetic torque Tψ(t)

-400.00 -500.00

0.00

20.00

40.00

60.00

80.00

100.00 Time [s]


120.00

140.00

160.00

180.00

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Maxwell 2D v12

Basic Exercise: Transient – Large Motion – Rotational 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:

f0 =

1 2π

cψ J

J in kgm is the total moment of inertia acting on Rotor1. cψ in Nm/rad is the magnetic rigidity. As an analogy it can be 2

understood 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):

cψ =

∆Tψ ∆ϕ m

≈

400 mNm = 2.3 Nm/rad rad(10°)

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. stator flux axis) at f0 < 5 Hz with damped amplitudes.

Fig. 9: Motion setup Ansoft Maxwell 2D Field Simulator v12 User’s Guide

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Maxwell 2D v12

Basic Exercise: Transient – Large Motion – Rotational 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 look like Fig. 9-11. 500.00

Curve Info Torque Setup1 : Transien

400.00

Torque [mNewtonMeter]

300.00 200.00 100.00 0.00 -100.00 -200.00

Fig. 10: Torque Tψ(t)

-300.00 100.00 -400.00

Curve Info Moving1.Speed Setup1 : Transient

80.00

Moving1.Speed [rpm]

60.00 40.00 20.00 0.00 -20.00 -40.00

Fig. 11: Mechanical speed ωm(t)

-60.00 -80.00 50.00

Curve Info Moving1.Position Setup1 : Transient

Moving1.Position [deg]

40.00

30.00

20.00

10.00

0.00

Fig. 12: Mechanical position ϕm(t) 0.00

100.00

200.00

Time [ms]


300.00

400.00

500

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Basic Exercise: Transient – Large Motion – Rotational 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) with respect 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 drawn rotor 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 the total inertia acting on the moving object group. If extra inertia needs to be included (i. e. inertia not geometrically modeled), 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 parts turn 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 can be a constant or a function of t, ωm, or ϕm. Note, that a positive Tm value will accelerate rather than brake.

t

The current simulation time in s.


9.13-13

9.14 Topic – 2D Boundary Conditions 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 2D based 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 Environment The 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

Ansoft Maxwell Field Simulator V12 User’s Guide

9.14-1

9.14 Topic – 2D Boundary Conditions Summary of eight designs to be simulated

1_VectorPotential

2_Balloon

4_Symmetry_Odd and 6_NoSymmetry

3_Balloon_ChangeExcitation 5_Symmetry_Even

7_Matching_Positive Ansoft Maxwell Field Simulator V12 User’s Guide

8_Matching_Negative 9.14-2

9.14 Topic – 2D Boundary Conditions Getting Started Launching Maxwell To 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 Options To 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 Options 2. Maxwell Options Window: 1. Click the General Options tab Use Wizards for data entry when creating new boundaries: ; Checked Duplicate boundaries with geometry: ; Checked 2. Click the OK button 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 3. Click the OK button


9.14-3

9.14 Topic – 2D Boundary Conditions 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 Type Select 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 Model The 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 Units Select the menu item Modeler > Units > Select Units: mm (millimeters) Ansoft Maxwell Field Simulator V12 User’s Guide

9.14-4

9.14 Topic – 2D Boundary Conditions Create Stator and Coils: A User Defined Primitive will be used to create the Stator and Coils

Draw > User Defined Primitive > Syslib > Rmxprt > SRMCore Use 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.


9.14-5

9.14 Topic – 2D Boundary Conditions 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.

Coil3

Coil2

Coil1

Coil4

Coil8 Coil5 Stator Coil7 Coil6 Ansoft Maxwell Field Simulator V12 User’s Guide

9.14-6

9.14 Topic – 2D Boundary Conditions Assign Current Source to Coils Select 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. 2.

Change the Base Name to Current Change the value to 100 Amps


9.14-7

9.14 Topic – 2D Boundary Conditions 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.


9.14-8

9.14 Topic – 2D Boundary Conditions Create the Problem Region One 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.


9.14-9

9.14 Topic – 2D Boundary Conditions Create an Analysis Setup Select the menu item Maxwell 2D > Analysis Setup > Add Solution Setup or right

click on the Analysis in the project window > Add Solution Setup Select General and verify the setting as follows Select Convergence and verify the setting as follows

Set up Boundary Conditions Select the menu item Edit > Select > Edges or right click in the Modeler > Select

Edges Select outer edge of the Stator Click on the menu item Maxwell 2D > Boundaries > Assign > Vector Potential … Accpet the default value and OK.


9.14-10

9.14 Topic – 2D Boundary Conditions Save the Project Select the menu item File > Save

Check the Validity of the Model Select 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

9.14-11

9.14 Topic – 2D Boundary Conditions Solution Data To view the Solution Data, select the menu item Maxwell 2D > Results > Solution Data, or right click on Setup1 under Analysis >

Convergence Here you can view the Profile and the Convergence. Note: The default view for convergence is Table. Click on the Plot radio 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.


9.14-12

9.14 Topic – 2D Boundary Conditions Plot Mesh, H-Field Vector and Flux Line Click 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 .


9.14-13

9.14 Topic – 2D Boundary Conditions 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.


9.14-14

9.14 Topic – 2D Boundary Conditions Create Design2: 2_Balloon Click 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

9.14-15

9.14 Topic – 2D Boundary Conditions Create Design3: 3_Balloon_ChangeExcitation Click 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 Excitation Click 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_3

Current_2

Current_4

Current_1

Current_5

Current_8

Current_6


Current_7

Current_1

Positive

Current_2

Negative

Current_3

Negative

Current_4

Positive

Current_5

Positive

Current_6

Negative

Current_7

Negative

Current_8

Positive

9.14-16

9.14 Topic – 2D Boundary Conditions Run the simulation and compare H Field plot with Design2 2_Balloon that has different excitations.

Design2: 2_Balloon


Design3: 3_Balloon_ChangeExcitation

9.14-17

9.14 Topic – 2D Boundary Conditions Symmetry Boundary Create Design4: 4_Symmetry_Odd Click 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 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).


9.14-18

9.14 Topic – 2D Boundary Conditions Run simulation and view results.

Symmetry: Odd (Flux Tangential)


9.14-19

9.14 Topic – 2D Boundary Conditions Create Design5: 5_Symmetry_Even Click 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). Run simulation and view results.

Symmetry: Even (Flux Normal)


9.14-20

9.14 Topic – 2D Boundary Conditions Create Design6: 6_NoSymmetry Click 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. Run simulation and view results. 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)


9.14-21

9.14 Topic – 2D Boundary Conditions Matching Boundaries (Master/Slave).

Design2: 2_Balloon Design7: 7_Matching_Positive

Slave=Master

Design3: 3_Balloon_ChangeExcitation Design8: 8_Matching_Negative

Slave= — Master

Master


Master

9.14-22

9.14 Topic – 2D Boundary Conditions Matching Boundaries: Master/Slave Create Design7: 7_Matching_Positive Click 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 X axis. 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.


9.14-23

9.14 Topic – 2D Boundary Conditions

Run Simulation and view results.

Slave=Master

Master


9.14-24

9.14 Topic – 2D Boundary Conditions Create Design8: 8_Matching_Negative Click 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. Run Simulation and view results.

Slave=-Master

Master


9.14-25

9.14 Topic – 2D Boundary Conditions 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 2D based 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 Environment The 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


9.14-1

9.14 Topic – 2D Boundary Conditions Summary of eight designs to be simulated

1_VectorPotential

2_Balloon

4_Symmetry_Odd and 6_NoSymmetry

3_Balloon_ChangeExcitation 5_Symmetry_Even

7_Matching_Positive Ansoft Maxwell Field Simulator V12 User’s Guide

8_Matching_Negative 9.14-2

9.14 Topic – 2D Boundary Conditions Getting Started Launching Maxwell To 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 Options To 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 Options 2. Maxwell Options Window: 1. Click the General Options tab Use Wizards for data entry when creating new boundaries: ; Checked Duplicate boundaries with geometry: ; Checked 2. Click the OK button 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 3. Click the OK button


9.14-3

9.14 Topic – 2D Boundary Conditions 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 Type Select 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 Model The 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 Units Select the menu item Modeler > Units > Select Units: mm (millimeters) Ansoft Maxwell Field Simulator V12 User’s Guide

9.14-4

9.14 Topic – 2D Boundary Conditions Create Stator and Coils: A User Defined Primitive will be used to create the Stator and Coils

Draw > User Defined Primitive > Syslib > Rmxprt > SRMCore Use 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.


9.14-5

9.14 Topic – 2D Boundary Conditions 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.

Coil3

Coil2

Coil1

Coil4

Coil8 Coil5 Stator Coil7 Coil6 Ansoft Maxwell Field Simulator V12 User’s Guide

9.14-6

9.14 Topic – 2D Boundary Conditions Assign Current Source to Coils Select 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. 2.

Change the Base Name to Current Change the value to 100 Amps


9.14-7

9.14 Topic – 2D Boundary Conditions 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.


9.14-8

9.14 Topic – 2D Boundary Conditions Create the Problem Region One 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.


9.14-9

9.14 Topic – 2D Boundary Conditions Create an Analysis Setup Select the menu item Maxwell 2D > Analysis Setup > Add Solution Setup or right

click on the Analysis in the project window > Add Solution Setup Select General and verify the setting as follows Select Convergence and verify the setting as follows

Set up Boundary Conditions Select the menu item Edit > Select > Edges or right click in the Modeler > Select

Edges Select outer edge of the Stator Click on the menu item Maxwell 2D > Boundaries > Assign > Vector Potential … Accpet the default value and OK.


9.14-10

9.14 Topic – 2D Boundary Conditions Save the Project Select the menu item File > Save

Check the Validity of the Model Select 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

9.14-11

9.14 Topic – 2D Boundary Conditions Solution Data To view the Solution Data, select the menu item Maxwell 2D > Results > Solution Data, or right click on Setup1 under Analysis >

Convergence Here you can view the Profile and the Convergence. Note: The default view for convergence is Table. Click on the Plot radio 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.


9.14-12

9.14 Topic – 2D Boundary Conditions Plot Mesh, H-Field Vector and Flux Line Click 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 .


9.14-13

9.14 Topic – 2D Boundary Conditions 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.


9.14-14

9.14 Topic – 2D Boundary Conditions Create Design2: 2_Balloon Click 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

9.14-15

9.14 Topic – 2D Boundary Conditions Create Design3: 3_Balloon_ChangeExcitation Click 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 Excitation Click 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_3

Current_2

Current_4

Current_1

Current_5

Current_8

Current_6


Current_7

Current_1

Positive

Current_2

Negative

Current_3

Negative

Current_4

Positive

Current_5

Positive

Current_6

Negative

Current_7

Negative

Current_8

Positive

9.14-16

9.14 Topic – 2D Boundary Conditions Run the simulation and compare H Field plot with Design2 2_Balloon that has different excitations.

Design2: 2_Balloon


Design3: 3_Balloon_ChangeExcitation

9.14-17

9.14 Topic – 2D Boundary Conditions Symmetry Boundary Create Design4: 4_Symmetry_Odd Click 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 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).


9.14-18

9.14 Topic – 2D Boundary Conditions Run simulation and view results.

Symmetry: Odd (Flux Tangential)


9.14-19

9.14 Topic – 2D Boundary Conditions Create Design5: 5_Symmetry_Even Click 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). Run simulation and view results.

Symmetry: Even (Flux Normal)


9.14-20

9.14 Topic – 2D Boundary Conditions Create Design6: 6_NoSymmetry Click 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. Run simulation and view results. 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)


9.14-21

9.14 Topic – 2D Boundary Conditions Matching Boundaries (Master/Slave).

Design2: 2_Balloon Design7: 7_Matching_Positive

Slave=Master

Design3: 3_Balloon_ChangeExcitation Design8: 8_Matching_Negative

Slave= — Master

Master


Master

9.14-22

9.14 Topic – 2D Boundary Conditions Matching Boundaries: Master/Slave Create Design7: 7_Matching_Positive Click 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 X axis. 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.


9.14-23

9.14 Topic – 2D Boundary Conditions

Run Simulation and view results.

Slave=Master

Master


9.14-24

9.14 Topic – 2D Boundary Conditions Create Design8: 8_Matching_Negative Click 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. Run Simulation and view results.

Slave=-Master

Master


9.14-25

Maxwell 2D v12

9.15 Basic Exercise – PM Assignment

Permanent Magnets Assignment This 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 Maxwell Start 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 definition We 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.


9.15-1

Maxwell 2D v12


Orientation of objects as one of the attributes Each object in Maxwell is associated with certain coordinate system. This is called Orientation and 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.


9.15-2

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 leftclick on Global to make it a Working CS again:


9.15-3

Maxwell 2D v12


The Orientation of magnet can now be changed. Object magnet can now be associated with RelativeCS1 coordinate system: Select magnet Edit > Properties Change Orientation from Global to RelativeCS1; OK Select the object magnet again and observe the orientation:

Orientation: Global

Orientation: RealtiveCS1

Specifying properties of Permanent Magnets Change the material of magnet from Vacuum to NdFeB35: Select magnet Edit > Properties Click on Vacuum to enter the material database, find NdFeB35 and click on View/Edit Materials A 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.


9.15-4

Maxwell 2D v12



9.15-5

Maxwell 2D v12


Examples of PM direction of magnetization assignment Direction 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


9.15-6

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


9.15-7

Maxwell 2D v12


Definition of the Solution Space - Region Before 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].


9.15-8

Maxwell 2D v12


Definition of the Boundary Conditions We expect that Region is so large that the magnetic field will not extend beyond Region’s boundary. 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 problem Maxwell 2D > Analysis Setup > Add Solution Setup Accept all default values; OK Maxwell 2D > Analyze All


9.15-9

Maxwell 2D v12


Viewing the results We will plot the magnetic flux lines throughout the solution space Magnetic flux lines: Select All objects (CTRL A or Edit > Select All) Maxwell 2D > Fields > Fields > A > Flux Lines; Done Double-click on the Legend Select 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 assigned This completes the exercise


9.15-10

Ansoft Maxwell2D_V12

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