Bài tập mô phỏng điện từ trường

The symmetry: The infinite box: Dimension of infinite box mm Type of The geometrical parameters are: Name of the SECT Thickness of the upper part of fixed magnetic circuit, MAGCIR

CAD Package for Electromagnetic and Thermal

Analysis using Finite Elements

Tutorial of translating

motion

FLUX is registered mark

This tutorial was updated on 2 July 2009 Ref.: K205-A-10-EN-07/09

CEDRAT

15 Chemin de Malacher - Zirst

38246 MEYLAN Cedex

FRANCE Phone: +33 (0)4 76 90 50 45 Fax: +33 (0)4 56 38 08 30 Email: cedrat@cedrat.com Web: http://www.cedrat.com

CONVENTIONS USED

To make this tutorial easier to read, we use the following typeface conventions:

• All comments are written in the same way as this sentence

• All dialog text between the user and FLUX2D is written in courier font:

Name of the region to be created:

Below are presented the conventions used for the dialog between the user and FLUX2D:

Italic text Messages or questions displayed on the screen by FLUX2D

User input to FLUX2D, such as the coordinates of a point

The ↵ character symbolizes the Return/Enter key

You only have to enter enough of the response to remove any ambiguity between the response you want and other valid ones In which case enter the

character shown in square brackets [ ]

word (shown in angled brackets < >)

FLUX2D graphical input, such as selecting a line or a point

↵ The reply is by default To enter a default response, simply press the

Return/Enter key

• If you are not familiar with FLUX2D yet, we advise you to run through this

entire tutorial and to refer, if necessary to the given cases

• If you are already a FLUX2D user, we advise you to redo only

the PREFLUX 2D, SOLVER_2D and POSTPRO_2D sections, in order to discover the new possibilities of FLUX2D

TABLE OF CONTENTS

1 REALIZED STUDY 3

2 GEOMETRY 5

2.1 Regions 8

2.2 Mesh 9

2.3 Materials 11

2.4 Sources 12

2.5 Boundary conditions 12

3 PREFLUX 2D: ENTERING THE GEOMETRY, THE MESH AND THE PHYSIC 15

3.1 Starting FLUX2D 15

3.2 Starting PREFLUX 2D 18

3.3 Entering the geometry 21

3.4 Activating the Geometry command 22

3.5 Create geometric tools 24

3.6 Create the fixed part of the magnetic core 30

3.7 Create the moveable part of the magnetic core 43

3.8 Create translating airgap and displacement regions 47

3.9 Create the domain 53

3.10 Building the mesh 58

3.11 Construct the mesh 79

3.12 Creating the regions and assign physical properties 84

3.13 Creating the TRA file 116

3.14 Saving data and leaving PREFLUX 2D 117

4 SOLVER_2D: SOLVE THE PROBLEM 119

4.1 Choosing the problem 119

4.2 Define a parameter 120

4.3 Activate the parameterization tools 120

4.4 Parameterize the CORE position 121

4.5 Run the solver 126

5 POSTPRO_2D: ANALYZE THE RESULTS 127

5.1 Starting POSTPRO_2D 127

5.2 Choosing the problem 127

5.3 Display the results 129

5.4 Visualize the color-shaded plot of flux density 131

5.5 Curves and vectors of the magnetic flux density 133

5.6 Compute local and global quantities 142

5.7 Leave POSTPRO_2D 148

6 ELECTRIFLUX: CONSTRUCT THE SUPPLY CIRCUIT 151

6.1 About ELECTRIFLUX 151

6.2 Start ELECTRIFLUX 152

6.3 Create a new circuit 152

6.4 Name the circuit 153

6.5 Construct the electric circuit 153

6.6 About the ELECTRIFLUX graphic display 158

6.7 Leave ELECTRIFLUX 160

7 PREFLUX 2D: PHYSICAL PROPERTIES FOR TRANSIENT MAGNETIC 161

7.1 Start PREFLUX 2D 161

7.2 Creating the TRA file 176

7.3 Saving data and leaving PREFLUX 2D 177

8 PREPARE THE SOLVING PROCESS 178

9 SOLVER_2D: SOLVE THE PROBLEM 182

9.1 Choosing the problem 182

9.2 Define a parameter 184

9.3 Run the solver 192

10 POSTPRO_2D: ANALYZE THE RESULTS 196

10.1 Starting POSTPRO_2D 196

10.2 Choosing the problem 197

10.3 Time variation of the current in the coil 198

10.4 Time variation of the mechanical quantities 203

10.5 Time variation of the magnetic flux and of the inductance of the coil 211

10.6 Leave POSTPRO_2D 216

PART A: DESCRIPTION OF THE STUDY

1 REALIZED STUDY

The aim of this tutorial is to get familiarized with the use of the translating motion feature of FLUX

software – section Flux2D The tutorial deals with the study of the cylindrical electromagnet of an

electrovalve, with a conical airgap, in two different cases:

Case 1 : the initial and final positions of the mobile core of the electromagnet, for

the value NI = 1800 A⋅turns of the total current in the coil;

Case 2 : the study of dynamic behavior of the electromagnet when the coil is

DC constant voltage of U = 24 V supplied and the motion of the

mobile core is determined by both electromagnetic force and the force of

a spring;

Translatingairgap(TAG region)

Shell airgap(LINAGregion)

AIR_MOBILE

Upperdisplacementarea (DEPLT

Lowerdisplacementarea (DEPLTregion

CORE

MAGCIRCOIL

MAGCIRSymmetry

axis

In Case 1, you will learn the commands for FLUX modules:

- PREFLUX 2D: definition of the geometry, building of the mesh and assignment of physical properties

- SOLVER_2D: solving of the problem

- POSTPRO_2D: analysis of the results

Case 2 differs from case 1 by the supply of the coil, the presence of spring attached to the core and

by the type of the application, which is of transient magnetic type You simply need to create the supply circuit and redefine the physical properties using the following modules:

ELECTRIFLUX : creating the supply circuit

PREFLUX 2D : assignment of the physical properties

SOLVER_2D : solving of the problem

POSTPRO_2D : analysis of the results

2 GEOMETRY

The geometry of the electromagnet is described in millimeters [mm] The SECT geometric

parameter allows us to modify the thickness of the upper and lateral zones of the fixed magnetic

core region called MAGCIR

The INFINITE region is used to extend the study domain up to infinity The points and lines of the

INFINITE region are automatically created by FLUX

32

0.5

SECT

47 6245

The geometry includes two coordinate systems, one immobile, called AXI_SYMMETRIC and another mobile, called MOBILE, that are related through the DIST parameter

The symmetry:

The infinite box:

Dimension of infinite box (mm) Type of

The geometrical parameters are:

Name of the

SECT Thickness of the upper part of fixed magnetic circuit, MAGCIR 8 DIST Distance between mobile and immobile coordinate systems 0 ; - 6.5

The coordinate systems are:

Name Type of system Coordinate system of

definition

Type of

Coordinates of the points defining the MAGCIR region in the AXI_SYMMETRIC

8 31.5

Coordinates of the points defining the displacement region DEPLT

in the AXI_SYMMETRIC coordinate system

8 50

Coordinates of the points defining the translating airgap region TAG

in the AXI_SYMMETRIC coordinate system

2.1 Regions

The computation domain of the magnetic field consists of seven surface regions and one line region

fixed parts of the computation domain

2.2 Mesh

The mapped and automatic mesh generators are used to mesh the computation domain of the

magnetic field

upper and lower displacement areas;

lateral part of the MAGCIR region

The three distinct areas are meshed by quadrangular elements

Lower displacement area Upper displacement area

19 x 3

• The other surfaces are meshed using the mesh point and mesh line generators For most of the

cases of meshing we will use point meshand elsewhere we use arithmetic mesh line

Zoom 2

Zoom 1

Zoom 1: Mesh of the upper DEPLT area Zoom 2: Mesh of the lower DEPLT area

2.3 Materials

The problem that we are going to study contains the following materials:

• An isotropic nonlinear magnetic material called STEEL in the CORE and MAGCIR regions

The material is defined by an analytical magnetization curve B(H) with:

magnetic flux density at saturation Bs = 1.9 T

slope relative to the origin µr = 500

The solid conductor behavior of the magnetic core is considered in this tutorial; consequently, the

model of STEEL material considers also the value ρ = 0.2e-6 Ωm for the resistivity

• AIR region as well as the COIL region have the properties of vacuum

2.4 Sources

In Case 1 the coil is supplied by a total current of 1800 A

In Case 2 the coil of 225 turns is supplied by a DC voltage source of 24 V The electrical resistance

of the coil is 3 Ω

2.5 Boundary conditions

Along the symmetry axis and at infinity a Dirichlet condition is imposed, corresponding to null value of the local magnetic flux

PART B: EXPLANATION OF CASE 1

3 PREFLUX 2D: ENTERING THE GEOMETRY,

THE MESH AND THE PHYSIC

This chapter lists the commands used to build the geometry of the device and the mesh of the computation domain and to create and assign the physical properties This is the first step to study a device by finite element method with FLUX2D

3.1 Starting FLUX2D

FLUX2D uses several programs managed by a supervisor To activate it on WINDOWS, you have

to click on the menus:

Start, Programs, Cedrat, FLUX 10

The FLUX Supervisor window is then displayed:

Program manager

My programs

Directory manager

FLUX View

Project Files

Menu bar Tool bar

The different parts of the FLUX Supervisor window are described hereafter:

• Options (memory, license, etc.)

• Help (link to online Users Guide for FLUX)

Program manager Displays the FLUX modules

The different modules are grouped by “family” in different folders Each module is shown as an item in the tree

You can expand a folder by clicking on the sign

You can start a module by double-clicking on its name, e.g., Geometry

• DOS Shell

• Windows Explorer You can add links to other programs here, as you wish

• the model geometry for the selected 2D project file (*.TRA)

• the FLUX View logo, if no problem is selected

The FLUX2D supervisor window is displayed

First, you should create a new directory to work in it and access your new working directory by

(e.g., C:\users\customers\cedrat)

Now, you can run any FLUX2D program by double-clicking with the mouse on the corresponding

menu

3.2 Starting PREFLUX 2D

To run PREFLUX 2D, in the tree at the left, in Construction, you should double-click on the

following menu:

Title bar

Menus bar Data tree

Graphic scene toolbar

Status bar

Context bar

Graphic scene

History

Menus and toolbar

The different parts of the PREFLUX 2D window are described below

Element Function

• Software name and version number

• Name of the current project

• Project, Application, View, Display, Select

• Geometry, Mesh, Physic, Tools, Help

Context bar Access to the toolbar corresponding to the contexts:

• Geometry, Mesh, Physic

Tool and menu bar

Project

Access to the commands of Project menu:

• New, Open…, Save, Close, Exit

• Undo

• Commands of creation of the geometric entities

• Check of the geometry

• Commands for the creation of mesh entities

• Actions on the mesh

• Check of the mesh

• Commands for the creation of physic entities

• Actions on the physic

• Check of the physic

Element Function Toolbar of the graphic scene

• Refresh view, Zoom all, Zoom region

• Standard 1 view, Standard 2 view, Opposite view, Direction of view, View on X, View on Y, View

on Z, Four views mode

Display

Access to the commands of Display menu:

• Display of coordinate systems, points, lines, faces, volumes, surface regions, volume regions

Access to the commands of Display menu of the

Geometry context:

• Display of surface elements, points numbers, lines numbers

Access to the commands of Display menu of the

Access to the commands of the Select menu:

• Activate the selection filter, Select points, Select lines, Select faces, Select volumes, Select surface regions, Select volume regions

3.3 Entering the geometry

The first step in the numerical modeling of an electrovalve is the description of the device geometry and the computation domain

3.3.1 Creating a new problem

Each time that you run a FLUX2D program, you should select the name of the problem to be treated

or define a new problem

To create a new problem, you should use:

• either the menus below

To save the current project under the Electrovalve name, you should use:

• either the menus below:

Project

Save

• or the icon below:

The Save window is then displayed and you must perform tasks 1 and 2 in the next figure

1 Enter ELECTROVALVE as

Preflux2D project name

2 Click on Save button to

save the Preflux2D project

3.4 Activating the Geometry command

Then, you should check that the Geometry context is selected

• by the icon:

We call entity any object that helps with the geometry construction In the geometry module, we

distinguish several entities They are visible in the tree data bar under the rubric names Domain,

Tools , Geometric entities (see next figure)

• The Domain rubric defines the space limit of the study

• The Tools rubric consists of all geometric facilities that Flux2D allocates to build the geometry

• The Geometric entities rubric contains basic objects to construct the geometry

Geometric entities Geometric tools

A property sheet corresponds to each entity, where all specific characteristics are saved A property sheet is presented in the form of a dialogue box that contains:

• a title bar with the type of entity

• different tabs containing the specific characteristics of the entity

• buttons to validate the information or to close the sheet

To identify the entity Different tabs of the entity Specific characteristics of the entity

Validation / Cancel / Help buttons

To create a new entity, you should first open the corresponding New Entity property sheet, and then

enter the data

To open a New Entity property sheet, you can use several methods All these methods are presented below with the example of the Geometric Parameter Of course, these methods are also applicable

to the other entities

• from the Data toolbar:

Click on the icon

The New Geometric parameter property sheet is opened

• from the Geometry menu:

Select Geometric parameter and then click on

New

⇒The New Geometric parameter property

sheet is opened

• from the Data tree:

1 Right click on Geometric parameter

2 ⇒ The New Geometric

parameter property sheet is

opened

• from the Data tree (short cut):

Double click on Geometric Parameter The New Geometric Parameter property sheet is opened

3.5 Create geometric tools

The general rule to construct the geometry of the computation domain is first defining the points, and then connecting themselves by lines that generate the faces

PREFLUX 2D contains several tools, which helps the creation of points and lines You can find them into the Tools rubric in the Data tree bar

Tools

• Geometric parameter is a variable in which you can save a value or a mathematical expression

• Coordinate system can be defined by yourself All geometric entities are defined within a

specific coordinate system

• Transformation is a geometrical function that permits the creation of new objects, starting from

objects already created

We will use all these facilities to construct the geometry more easily

Defining parameters simplifies problem entry and allows modifications to be made more easily later Many types of changes can be made by modifying only the definition of the parameters instead of modifying all the individual points, lines, or nodes that might be built using that parameter

The coordinates of points, arcs, circles, and coordinate systems can be entered using geometric parameters or mathematical expressions This allows us to rapidly modify the geometric dimensions

A parameter is defined by a name, a comment and a mathematical expression

The mathematical expressions may contain:

or meters, or kilometers, or any other unit In this way, you can modify the scale of a geometric feature without entering each point or item all over again Parameters can be created at any time during the geometry description

The reference values of the parameters are presented in the following table

DIST Distance between the mobile and immobile coordinate system 0

The first parameter that we will create is the SECT parameter that will allow us to quickly modify

the shape of the MAGCIR region

Follow the program sequence below:

• either select the following menus:

• or in the tree at the left, in the Data tab:

click with the right button of the mouse, in Geometry, Geometric tools, on

Geometric parameter

The following contextual menus appear

Select New

• or double click on Geometric parameter in the tree

The Edit Geometric Parameter window is then displayed and to create the geometric parameter SECT you must perform tasks 1 to 5 in the next figure

1 Enter SECT as Name of

Parameter

2 Enter Thickness of the

upper magnetic circuit as Comment

3 Enter 8 as Algebraic

expression for the parameter

4 Click on the Ok button to

create the parameter

Note:

You can enter the name of the projects, regions and parameters in lowercase or uppercase They will automatically be converted to uppercase

The geometric parameter SECT is then created

The New Geometric Parameter properties sheet is then opened Here will be defined the

second geometric parameter DIST It allows us to modify the position of the mobile magnetic core

1 Enter DIST as Name of

Parameter

2 Enter Distance between

the mobile and immobile coordinate systems as Comment

3 Enter 0 as Algebraic

expression for the parameter

4 Click on the Ok button to

create the parameter

5 Click on the Cancel button

to quit this window

3.5.1 About the modification / deletion of an entity

To modify an entity you should first open its property sheet, and then modify its characteristics

The main method to open a property sheet of an entity is presented below related to the geometric

parameter (entity) SECT from the Data tree

1 Click on the symbol + (if necessary) to open the entity list

2 Right click on SECT

3 Select Edit or Delete in the contextual menu

⇒The Edit Geometric Parameter window of SECT is

opened or

⇒The entity SECT is deleted

3.5.2 Create the coordinate systems

Using the geometric parameters and defining more coordinate systems allow us to describe and modify the geometry much more easily

All geometric entities, including points and geometric transformations are defined within a specific coordinate system Each coordinate system is defined by the coordinates of its origin, the orientation

of the axes, the type of coordinate system and the units of length and angle

The coordinate systems are identified by a name, a comment, a type of coordinates, a type of system (global or local), length units, angle units, coordinates of the origin, orientation

We will use in this tutorial a global co-ordinate system called AXI_SYMMETRIC and a local

co-ordinate system – name MOBILE (see table below) The units are millimeter for length and

degree for angle

The two coordinate systems are cartesian The first name was choosing to remember the type of this 2D problem that must be defined when assign the physical properties

Name Type of system Coordinate system of definition Coordinate type (mm) X (mm) Y Rot Z ( °)

To create a new coordinate system, you should use:

• either the following menus:

Geometry

Coordinate system

New

• or the following icon:

• or in the tree at the left, in the Data tab:

click with the right button of the mouse, in Geometry, Geometric tools, on

Coordinate system

The following contextual menus appear

Select New

• or double click on Coordinate system in the tree

The New Coordinate System window is then displayed and to create the coordinate system

AXI_SYMMETRIC, you must perform tasks 1 to 11 in the next figure

1 Enter AXI_SYMMETRIC as Name of

Coordinate System

2 Enter Axi symmetric

coordinate system as Comment

3 Select Cartesian as Type of

Coordinate System

4 Select Global as being Defined

with respect to the Global Coordinate System

5 Select MILLIMETER as Length Unit

6 Select DEGREE as Angle Unit

7 Enter 0 as Origin: first component

8 Enter 0 as Origin: second

The AXI_SYMMETRIC coordinate system is then created

The local coordinate system MOBILE is defined depending on the global one through DIST parameter The two extreme positions of the mobile magnetic core with respect to the fixed parts are defined by the values DIST = 0 mm for the initial position, and DIST = – 6.5 mm for the final position

The different entities such as points, transformations, and objects created in local coordinate system are automatically reported to the global coordinate system

In the following New Coordinate System property sheet we will define the local coordinate system

4 Select Local as being Defined with

respect to the Global Coordinate System

5 Select AXI_SYMMETRIC as parent

coordinate system

6 Enter 0 as Origin: first component

7 Enter DIST as Origin: second

To display the coordinate system, you can:

• either select the following menus:

View

Display Coordinate System

• or click on the following icon:

At this step, we have finished to define the tools that will help us to enter the points Now, we will enter points and lines

3.6 Create the fixed part of the magnetic core

Now that the parameter and coordinate systems have been created, we will enter the points to define the fixed part of the magnetic core Points can be entered as a set of coordinates in a specified

coordinate system, or as an image of an existing point through a geometric transformation

3.6.1 About point of view

The easiest way to adjust the view as you want is to use the scrolling wheel of your mouse in order

to enlarge the picture By keeping pressed the right mouse button and moving, you move the object The same manipulation with the left one will rotate the object around the center of the screen

Nevertheless, there are several predefined tools to change the point of view of the graphic display All are accessible via the View menu:

Select View and then click on

the desired option

3.6.2 Enter the points of the MAGCIR region

Points can be entered in PREFLU 2D as a set of coordinates in a specified coordinate system, or using geometric transformations To define the point coordinates we can use numbers, parameters or Fortran expressions

When the coordinates of a point are modified, all the geometric entities linked to this point (lines, surfaces, ) will automatically be updated

You may notice that the points on your screen are not assigned the same numbers as the ones we use for convenience in this tutorial Please do not be worried about this discrepancy Whenever we use a point number in our instructions, we will also include a short description about the location of that point, so that you will be able to choose the proper one from your own screen

We will create the thirteen points of the MAGCIR region in the AXI_SYMMETRIC coordinate system, as presented in the table below

To create a point, you should use:

• either the following menus:

Geometry

Point

New

• or the following icon:

• or in the tree at the left, in the Data tab:

click with the right button of the mouse, in Geometry,Geometric entities,

on Point

The following contextual menus appear

Select New

• or double click on Point in the tree

The New Point window is then displayed and to create the first point, you must perform tasks 1 to

6 in the next figure

1 Select the Geometric Definition

tab

2 Select Point defined by its Parametric Coordinates as

Type of the Point

3 Select AXI_SYMMETRIC as Coordinate

System for definition

4 Enter 5 for the First coordinate

5 Enter –20.5 for the Second coordinate

6 Click on the OK button to create the

point

The point number 1 is then created

To create the second point, you must perform tasks 1 to 3 in the next figure

1 Enter 3 for the First coordinate

2 Enter –20.5 for the Second coordinate

3 Click on the OK button to create the

point

The point number 2 is then created

Then you must create all the other points until the next to last one listed in the previous table

Finally, to create the last point of the previous table, you must perform tasks 1 to 4 in the next figure

1 Enter 32 for the First coordinate

2 Enter 23 for the Second coordinate

3 Click on the OK button to create the

point

4 Click on the Cancel button to quit

this window