flux2d tutorial ms2d

Copyright – August 2009

CAD Package for Electromagnetic and Thermal

Analysis using Finite Elements

Flux® 2D Application

Tutorial of Magnetostatics

Flux is a registered trademark.

Flux software : COPYRIGHT CEDRAT/INPG/CNRS/EDF Flux tutorials : COPYRIGHT CEDRAT

This tutorial was edited on 18 August 2009

Ref.: K205-10-EN-08/09

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38246 Meylan Cedex FRANCE

Phone: +33 (0)4 76 90 50 45 Fax: +33 (0)4 56 38 08 30 Email: [email protected]

Web: http://www.cedrat.com

Foreword

About the tutorial

The objective of this document is to discover and master the various functionalities of the software using the example of a simple device. This tutorial contains the general steps and all the data needed to describe the physics and the computation of the sensor model. Geometry and mesh of the sensor model are already described in the Flux 2D Generic Tutorial of Geometry and Mesh.

Required knowledge

Before proceeding with this tutorial, the user must understand the functionalities of the Flux software. The user can gain this knowledge by initially completing the Generic tutorial. The Flux 2D Generic Tutorial of Geometry and Mesh explains in detail all actions to build the geometry and mesh of the study domain.

Path The files corresponding to the different cases studied in this tutorial are

available in the folder: …\DocExamples\Examples2D\MagnetostaticApplication\

Command files and Flux files

The files provided for this tutorial are: • command files,

come in handy to build the Flux projects • Flux files

already built project files

The use of files is explained in the table below.

the user can To describe … follow execute the

command file recover the Flux file*

the geometry and mesh

2D Generic Tutorial GeoMesh_2D.py SENSOR_2D.FLU

the physics § 2.1of this tutorial GeoMeshPhys.py GEO_MESH_PHYS.FLU Case 1 § 3. of this study Case1.py CASE1.FLU Case 2 § 4. of this study Case2.py CASE2.FLU

* Flux files are ready to be meshed and then solved.

Flux®10 Table of Contents

PAGE A

Table of Contents 1. General information .................................................................................................................1

1.1. Overview .......................................................................................................................................3 1.1.1. Description of the studied device....................................................................................4 1.1.2. Studied cases .................................................................................................................5

1.2. Strategy to build the Flux project ..................................................................................................6 1.2.1. Main phases for physical description..............................................................................7

2. Construction of the Flux project ...............................................................................................9 2.1. Physical description process.......................................................................................................10

2.1.1. Define the physical application .....................................................................................11 2.1.2. Create materials ...........................................................................................................12 2.1.3. Create face regions ......................................................................................................13 2.1.4. Create measuring coils: coil conductors components and coil conductor regions.......14 2.1.5. Assign face regions to faces.........................................................................................15 2.1.6. Orient material for face region ......................................................................................16

3. Case 1: static study ...............................................................................................................17 3.1. Case 1: solving process..............................................................................................................18 3.2. Case 1: results post-processing..................................................................................................19

3.2.1. Compute and display isovalues of the magnetic flux density on volume regions ........20 3.2.2. Compute and display arrows of the magnetic flux density in faces region...................21 3.2.3. Create 2D grid for computation and display isovalues of the magnetic flux

density...........................................................................................................................22 3.2.4. Compute and display isovalues of the magnetic flux density on a 2D grid ..................23 3.2.5. Compute and display isovalues of the magnetic field strength on a 2D grid................24 3.2.6. Compute the magnetic flux density on a point .............................................................25 3.2.7. Plot a 2D curve of the magnetic field strength along a path.........................................26 3.2.8. Compute the magnetic force on face regions...............................................................28

4. Case 2: parametric computation............................................................................................29 4.1. Case 2: solving process..............................................................................................................30

4.1.1. Create sensors .............................................................................................................31 4.1.2. Define the solving scenario and solve the project ........................................................32

4.2. Case 2: results post-processing..................................................................................................33 4.2.1. Display a color-shaded plot of the magnetic flux density (alpha=120°) .......................34 4.2.2. Display arrows of the magnetic flux density (alpha=120°) ...........................................35 4.2.3. Plot a 2D curve of the flux through coil conductors versus an I/O parameters (for

alpha=120°) ..................................................................................................................35

Flux® 10 General information

Tutorial of Magnetostatics PAGE 1

1. General information

Introduction This chapter contains the presentation of the studied device and the Flux

software.

Contents This chapter contains the following topics:

Topic See Page Overview 3 Strategy to build the Flux project 6

General information Flux®10

PAGE 2 Tutorial of Magnetostatics



1.1. Overview

Introduction This section presents the studied device (a variable reluctance speed sensor)

and the strategy of the device description in Flux.

Contents This section contains the following topics:

Topic See Page Description of the studied device 4 Studied cases 5



1.1.1. Description of the studied device

Studied device The device to be analyzed is a variable reluctance speed sensor.

The studied device consists of: • a cogged wheel (made of steel) with three teeth • two probes with a magnet (made of ferrite) and a coil around each

The physical model of the studied device is presented in the figure below.

PROBE 2

COIL 2-

COIL 2+

MAGNET 1

COIL 1-

COIL 1+

WHEEL

MAGNET 2

PROBE 1

Operating principle

The rotation of the cogged wheel near the tip of the probes changes the magnetic flux, creating an analog voltage signal that can be measured in probes.



1.1.2. Studied cases

Studied cases Three cases are carried out in a Magneto Static application:

• case 1: static study • case 2: multi-parametric computation

Case 1 The first case is a static study.

This study is a very easy problem of Magneto Statics. In this study, a magneto static analysis of the sensor is performed in a medium position: the two probes between two teeth. A geometric parameter α, which allow us to control the angle of the wheel around Z axis, has a fixed value α = 75° The coils are not current supplied (=measuring coils)

Case 2 The second case is a parametric computation.

The angle of the cogged wheel will vary. In this parameterized study, the geometric parameter is the angle α that varies in the range [75°, 195°] with a step of 3°.



1.2. Strategy to build the Flux project

Introduction This section presents outlines of physical properties description process of the

sensor.


Topic See Page Main phases for physical description 7



1.2.1. Main phases for physical description

Outline An outline of the physical description process of the sensor is presented in

the table below.

Stage Description

1

Definition of the application and definition of the depth of the domain

• Magneto Static 2D (solved with Flux 3D solver)

• 2D plan (6mm)

2 Creation of two materials

• FERRITE – magnet with a linear B(H) characteristic

• STEEL – ferromagnetic material with a non linear B(H) characteristic

3 Creation of four face region

• AIR_EXT region, corresponding with the air surrounding the device

• AIR_WHEEL region, corresponding with the air in the cogged wheel

• MAGNET1 region corresponding with the first magnet of the device

• MAGNET2 re region corresponding with the first magnet of the device

4

Creation of two coils: • Two components • Four face regions

• COIL_CONDUCTOR1 • COIL_CONDUCTOR2 • COIL1N region, corresponding with the

negative part of the first coil • COIL1P region, corresponding with the

positive part of the first coil • COIL2N region, corresponding with the

negative part of the second coil • COIL2P region, corresponding with the

positive part of the second coil

Continued on next page



Main phases for physical description, Continued

Outline (continued)

Stage Description

5 Assignment of face regions

INFINITE

AIR WHEEL

AIR_EXT

COIL1P

MAGNET1

COIL1N

COIL2P

MAGNET2

COIL2N

WHEEL

6 Material orientation

Flux® 10 Construction of the Flux project


2. Construction of the Flux project

Introduction This chapter contains the physical description of the sensor. For a more

detailed description of the basic geometry of the sensor, the user should reference the Flux 2D Generic Tutorial of Geometry and Mesh. The user must have good understanding of all functionalities of the Flux preprocessor.

Starting Flux project

The starting project is the Flux project GEO_MESH.FLU. This project contains: • the geometry description of the contactor • the mesh of the computation domain

New Flux project

The new Flux project is GEO_MESH_PHYS.FLU.


Topic See Page Physical description process 10

Construction of the Flux project Flux®10


2.1. Physical description process

Introduction This section presents the definition of the physical properties – materials and

regions.


Topic See Page Define the physical application 11 Create materials 12 Create face regions 13 Create measuring coils 14 Assign face regions to faces 15 Orient material for face region 16



2.1.1. Define the physical application

Goal First, the physical application is defined. The required physical application is

the Magneto Static 2D application.

Data The characteristics of the application are presented in the table below.

Magneto Static 2D application

Definition 2D domain type Depth of the domain Solver Coils

Coefficient 2D plane 6 mm Flux3D solver Automatic

Coefficient



2.1.2. Create materials

Goal Two materials are created directly for the physical description of the sensor;

the two materials are characterized by their magnetic properties: • the first material is FERRITE defined for the coiled magnets • the second material is STEEL defined for the cogged wheel

Data The characteristics of the materials are presented in the tables below.

B(H) linear magnet described in the Br module Name Remanent flux density (T) Relative permeability

FERRITE 0.8 1

B(H) isotropic analytic saturation (arctg 2 coef.)

Name Initial relative permeability Saturation magnetization (T)

STEEL 5000 1.9



2.1.3. Create face regions

Goal Five face regions are necessary for the physical description of the sensor.

Five following face regions will be created: • the AIR_EXT region, corresponding with the air surrounding the device • the AIR_WHEEL region, corresponding with the air in the cogged wheel • the MAGNET1 region, corresponding with the first magnet of the device • the MAGNET2 region, corresponding with the second magnet of the device • the WHEEL region, corresponding with the cogged wheel

The INFINITE region, already created during the infinite box creation, will be edited to activate its physical properties.

Data The characteristics of the face regions are presented in the table below.

Face region Name Type Material Color

AIR_EXT Air or vacuum region Turquoise AIR_WHEEL Air or vacuum region Turquoise INFINITE* Air or vacuum region Turquoise MAGNET1 Magnetic non-conducting region FERRITE Magenta MAGNET2 Magnetic non-conducting region FERRITE Magenta

WHEEL Magnetic non-conducting region STEEL Cyan

*The region already created and assigned during the creation of the infinite box, however the user need to enter the type of the region.



2.1.4. Create measuring coils: coil conductors components and coil conductor regions

Goal Two coils are created to measure the flux density.

About coil In magnetic applications, a coil is represented by one face region or by a

group of face regions of the coil conductor type. The value I of the current in a wire (or turn) of the coil is set by means of an electric component (of coil conductor type) associated to the coil.

Data (1) The characteristics of the electric components (of coil conductor type) are

presented in the table below:

Stranded coil conductor with imposed current (A) Name comment Value

COIL_CONDUCTOR1 Coil conductor on the first coil 0 COIL_CONDUCTOR2 Coil conductor on the second coil 0

Data (2) The characteristics of the regions (of coil conductor type) are presented in the

table below:

Coil conductor type region

Face region Component Orientation Turn number Series or parallel Color

COIL1N COIL_CONDUCTOR1 negative 1000 series red COIL1P COIL_CONDUCTOR1 positive 1000 series red COIL2N COIL_CONDUCTOR2 negative 1000 series red COIL2P COIL_CONDUCTOR2 positive 1000 series red

• the COIL1N region, corresponding with the negative part of the first coil • the COIL1P region, corresponding with the positive part of the first coil • the COIL2N region, corresponding with the negative part of the second coil • the COIL2P region, corresponding with the positive part of the second coil



2.1.5. Assign face regions to faces

Goal The INFINITE region has been already assigned during the creation of the

infinite box. The nine regions (AIR_EXT, AIR_INT, WHEEL, COIL1P, COIL1N, MAGNET1, COIL2P, COIL2N, and MAGNET2) are assigned to faces.

Outline The region assignment is presented in the figure below.

INFINITE

AIR_WHEEL

AIR_EXT

COIL1P

MAGNET1

COIL1N

COIL2P

MAGNET2

COIL2N

WHEEL



2.1.6. Orient material for face region

Goal An orientation of the material region is needed to describe physics.

Data The orientation of the material region is related in the table below

Orient material for face region Name Oriented type Coordinate system Angle

MAGNET1 Direction PROBE_CS 0 MAGNET2 Direction PROBE_CS001 0

Flux® 10 Case 1: static study


3. Case 1: static study

Case 1 The first case is a static study.

This study is a very easy problem of Magneto Statics. In this study, a magneto static analysis of the sensor is performed in a medium position: the two probes between two teeth. A geometric parameter α, which allow us to control the angle of the wheel around Z axis, has a fixed value α = 75° The coils are not current supplied (=measuring coils)


The starting project is the Flux project GEO_MESH_PHYS.FLU. This project contains: • the geometry description of the device • the mesh and computation domain • the initial physical description of the contactor

Project name The Flux project is saved under the name of CASE1.FLU


Topic See Page Case 1: solving process 18 Case 1: results post-processing 19

Case 1: static study Flux®10


3.1. Case 1: solving process

Introduction This section explains how to solve case 1.

Flux module The Flux module is Preflu2D.

Action Case 1 is solved using the default scenario with reference values.



3.2. Case 1: results post-processing

Introduction This section explains how to analyze the principal results of case 1.


Topic See Page Compute and display isovalues of the magnetic flux density on volume regions

20

Compute and display arrows of the magnetic flux density in faces region

21

Create 2D grid for computation and display 22 Compute and display isovalues of the magnetic flux density on a 2D grid

23

Compute and display isovalues of the magnetic field strength on a 2D grid

24

Compute the magnetic flux density on a point 25 Plot a 2D curve of the magnetic field strength along a path 26 Compute the magnetic force on face regions 28



3.2.1. Compute and display isovalues of the magnetic flux density on volume regions

Goal The scalar quantities of the magnetic flux density are computed on the

selected volume region and displayed via isovalue plot of color shadings.

Data The characteristics of the isovalues are presented in the table below:

Isovalues on face region Face region Formula AIR_EXT COIL1P COIL1N COIL2P COIL2N

MAGNET1 MAGNET2

WHEEL

Mod(B)

Result The following chart shows the magnetic flux density on the AIR_EXT,

COIL1P, COIL1N, COIL2P, COIL2N, MAGNET1, MAGNET2, and WHEEL face regions.



3.2.2. Compute and display arrows of the magnetic flux density in faces region

Goal The vector quantities of the magnetic flux density are computed in the

selected face regions and displayed in the form of arrows.

Data The characteristics of the arrows are presented in the table below.

Arrows in Face regions

Volume region Formula AIR_EXT COIL1P COIL1N COIL2P COIL2N

MAGNET1 MAGNET2

WHEEL

(B)

Result The following arrows show direction and magnitude of the magnetic flux

density in the AIR_EXT, COIL1P, COIL1N, COIL2P, COIL2N, MAGNET1, MAGNET2 and WHEEL face regions.



3.2.3. Create 2D grid for computation and display isovalues of the magnetic flux density

Goal One 2D grid is created midpoint of the second stranded coil

Data The characteristics of the 2D grid are presented in the table below.

Rectangular 2D grid in XY plane: definition 2D grid origin coordinates Name Comment Coordinate system First Second

GRID_ONMAGNET For the magnet PROBE_CS 0 0

Rectangular 2D grid in XY plane: definition Characteristics along X Characteristics along Y

Positive X Negative X Number of disc. elements Positive Y Negative Y Number of

disc. elements 12 12 30 6 6 20

Rectangular 2D grid in XY plane: appearance

Visibility Color visible green



3.2.4. Compute and display isovalues of the magnetic flux density on a 2D grid

Goal The scalar quantities of the magnetic flux density are computed on the 2D

grids and displayed via isovalue plots of color shadings.

Data The characteristics of the isovalues are presented in the table below.

Isovalues on 2D grid

2D grid Formula GRID_ONMAGNET Mod(B)

Result The following chart shows the magnetic flux density on the

GRID_ONMAGNET grid



3.2.5. Compute and display isovalues of the magnetic field strength on a 2D grid

Goal The scalar quantities of the magnetic flux density are computed on the 2D

grids and displayed via isovalue plots of color shadings.

Data The characteristics of the isovalues are presented in the table below.

Isovalues on 2D grid

2D grid Formula GRID_ONMAGNET Mod(H)

Result The following chart shows the magnetic field strength on the

GRID_ONMAGNET grid



3.2.6. Compute the magnetic flux density on a point

Goal The magnetic flux density is computed on the selected point.

Data The characteristics of the point are presented in the table below.

Quantities computation on points

Name Comment FormulaPOINT1 Center of the magnet B

Point defined by its coordinates

Coordinates localization Coord. system Region first second 0 0 no constraint PROBE_CS001 MAGNET2

Result The following values show the X and Y components of the magnetic flux

density at the above-described point.



3.2.7. Plot a 2D curve of the magnetic field strength along a path

Goal The variation of the magnetic flux density is computed along the selected path

and displayed as curve.

Data (1) The characteristics of the path are presented in the table below.

Path defined by 2 points

Name Comment Definition Discretization SEGMENT Along the magnet by coordinates 50

Path defined by coordinates

Path points Starting point Ending point

Coordinates Coordinates Coord. system First Second Coord. system First Second

PROBE_CS001 -15 0 PROBE_CS001 15 0

Data (2) The characteristics of the curve are presented in the table below.

2D curve (XYZ path)

Name Comment Path Formula

CURVE Magnetic field strength along the segment in magnet SEGMENT H

Continued on next page



Result The following curves show the components of the magnetic field strength

along the X and Y -axes.



3.2.8. Compute the magnetic force on face regions

Goal The value of the magnetic force is computed on the selected volume region

and the result of computation is displayed in the dialog box.

Data The characteristics of the magnetic force computation are presented in the

table below.

Predefined magnetic force

Name Face region FORCE_MAGNET MAGNET2

Result The following dialog box shows the result of computation of the magnetic

force on the MAGNET2 face region.

Flux® 10 Case 2: parametric computation


4. Case 2: parametric computation

Case 2 The second case is a parametric computation.

The angle of the cogged wheel will vary. In this parametric study, the geometric parameter is the angle α that varies in the range [75°, 195°] with a step of 3°.


The starting project is the Flux project GEO_MESH_PHYS.FLU. This project contains: • the geometry description of the device • the mesh and computation domain • the initial physical description of the contactor

Project name The new Flux project is saved under the name of CASE2.FLU.


Topic See Page Case 2: solving process 30 Case 2: results post-processing 33

Case 2: parametric computation Flux®10


4.1. Case 2: solving process

Introduction This section explains how to prepare and solve case 2.

Flux module The Flux module is Preflu_2D.


Topic See Page Create sensors 31 Define the solving scenario and solve the project 32



4.1.1. Create sensors

Goal Two sensors are created to compute the magnetic flux through the coils

Data The characteristics of the sensors are defined in the table below.

Predefined sensor : Flux through a coil conductor

Name Coil Conductor FLUX_PROBE1 COIL_CONDUCTOR1 FLUX_PROBE2 COIL_CONDUCTOR2



4.1.2. Define the solving scenario and solve the project

Goal The scenario with the controlled geometrical parameter is defined for a

varying solving process.

Data The characteristics of the solving scenario are presented in the tables below.

Solving scenario

Name Comment Type SCENARIO1 study using a geometrical parameter multi-values

Solving scenario

Parameter control Interval Controlled

parameter Type Lower endpoint

Upper endpoint Method Step value

ALPHA Multi-values 75 195 step value 3

Action Solve CASE 2 using the scenario 1 with parametric study.



4.2. Case 2: results post-processing

Introduction This section explains how to analyze the principal results of case 2.


Topic See Page Display a color-shaded plot of the magnetic flux density 34 Display arrows of the magnetic flux density 35 Display arrows of the magnetic flux density 35



4.2.1. Display a color-shaded plot of the magnetic flux density (alpha=120°)

Goal First, the computation step of the geometrical parameterized study is selected

(alpha=120°). Then, the scalar quantities of the magnetic flux density are computed on the selected face regions and displayed via isovalue plots of color shadings.

Data (1) The characteristics of the scenario and computation step selection are

presented in the table below.

Scenario and computation step

Computation step Scenario Parameter name Value SCENARIO1 ALPHA 120

Data (2) The characteristics of the isovalues are presented in the table below.

Isovalues on face region

Face region Formula AIR_EXT COIL1N COIL1P COIL2N COIL2P

MAGNET1 MAGNET2

WHEEL

Mod(B)

Result The following chart shows the magnetic flux density on the selected regions.



4.2.2. Display arrows of the magnetic flux density (alpha=120°)

Goal First, the computation step of the geometrical parameterized study is selected

(alpha =120). Then, the scalar quantities of the magnetic flux density are computed on the selected face regions and displayed via arrows.

Data (1) The characteristics of the scenario and computation step selection are

presented in the table below.

Scenario and computation step

Computation step Scenario Parameter name Value CASE2 ALPHA 120

Data (2) The characteristics of the arrows are presented in the table below.

Arrows on face region

Face region Formula AIR_EXT COIL1N COIL1P COIL2N COIL2P

MAGNET1 MAGNET2

WHEEL

(B)

Result The following chart shows the magnetic flux density on the selected regions.



4.2.3. Plot a 2D curve of the flux through coil conductors versus an I/O parameters (for alpha=120°)

Goal The values of the flux through the two coil conductor versus the angular

position of the cogged wheel are computed and displayed in a curve

Data The characteristics of the curve are presented in the table below

2D curve (I/O parameter)

Parameter Formula Name Comment Name Lower

endpoint Upper

endpoint sensors

Flux_probe1 CURVE Flux through coil conductor ALPHA 75° 195° Flux_probe2

Result The following curves show the variation of flux through coil conductor in

function of the angle variation of the cogged wheel.

flux2d tutorial ms2d

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