CAD package for electromagnetic and thermal analysis using finite elements Flux by CEDRAT Magneto Static application tutorial 2D basic example
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Foreword *(Please read before starting this document) Description of the example The goal of this basic example is to familiarize the user with the Flux Magneto Static application using a simple device. This example contains the general steps and all the data needed to describe the physics,the solving and the postprocessing for the given cases. For this example, the geometry has been previously described in the First steps in using Flux: Geometry and Mesh Tutorial - Basic example. Required knowledge This basic example is designed for the user who is already familiar with the basic functions of Flux software. To obtain this knowledge, first, the user should go through the First steps in using Flux: Geometry and Mesh Tutorial - Basic example. This document explains, in detail, all the actions necessary to build the geometry and mesh of a project in the Flux study domain. Support files included... To view the completed phases of the example project, the user will find the.py files, including the geometry, physics and post processing descriptions. The.py files corresponding to the different study cases in this example are available in the folder: \DocExamples11.1\Examples2D\MagnetostaticApplication\ Supplied files are command files written in Pyflux language. The user can launch them in order to automatically recover the Flux projects for each case. **(.py files are launched by accessing Project/Command file from the Flux drop down menu.) CASE1 CASE2 Supplied files Contents Flux file obtained after launching the.py file TESTCASE_INI.FLU* Geometry, mesh Physbuilt.FLU and physics solving.py Solving process Solved.FLU postprocessing.py Post processing Postprocessed.FLU TESTCASE_INI.FLU** Initial project solving.py Solving process Solved.FLU postprocessing.py Post processing Postprocessed.FLU Note : some directories may contain a main.py enabling the launch of the command files *This file correspond to SENSOR_2D created in the first steps in using Fluxgeometry and mesh tutorial ** This file correspond to the Physbuilt.FLU of CASE 1
Flux Table of Contents 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...7 1.2.1. Main stages for physical description...8 2. Construction of the Flux project...11 2.1. Physical description process...13 2.1.1. Define the physical application...14 2.1.2. Create materials...15 2.1.3. Create face regions...16 2.1.4. Create measuring coils: coil conductors components and coil conductor regions...17 2.1.5. Assign face regions to faces...18 2.1.6. Orient material for face region...19 3. Case 1: static study...21 3.1. Case 1: solving process...23 3.2. Case 1: results post-processing...25 3.2.1. Display default graphic post processing...26 3.2.2. Display arrows of the magnetic flux density on a region boundaries...28 3.2.3. Display isovalues of the magnetic flux density on a 2D grid...29 3.2.4. Compute the magnetic flux density on a point...31 3.2.5. Compute the magnetic force on face regions...32 3.2.6. Plot a 2D curve of the magnetic field strength along a path and export the curve...33 3.2.7. Plot a 2D curve of normal and tangential components of the magnetic field along a path...35 4. Case 2: parametric computation...37 4.1. Case 2: solving process...39 4.2. Case 2: results post-processing...41 4.2.1. Display default graphic post processing (alpha=120 )...42 4.2.2. Create animation of isovalues of the magnetic flux density on face regions versus position parameter...43 4.2.3. Plot a 2D curve of the flux through coil conductors versus an I/O parameter...44 4.2.4. Plot a 3D curve of the magnetic flux density on a path versus an I/O parameter...45 PAGE A
Table of Contents Flux PAGE B MAGNETO STATIC APPLICATION TUTORIAL
Flux General information 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 7 Magneto Static application tutorial PAGE 1
General information Flux PAGE 2 Magneto Static application tutorial
Flux General information 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 Magneto Static application tutorial PAGE 3
General information Flux 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 WHEEL COIL 1+ MAGNET 1 COIL 1- PROBE 1 COIL 2+ MAGNET 2 COIL 2- PROBE 2 Operating principle The rotation of the cogged wheel near the tip of the probes changes the magnetic flux around probes 1 and 2, creating an analog voltage signal that can be measured by the probes. PAGE 4 Magneto Static application tutorial
Flux General information 1.1.2. Studied cases Studied cases Two cases are carried out with the Magneto Static application: case 1: static study (mono value) case 2: multi-parametric static study (multi values) Case 1 The first case is a static study (mono value). In this case, the study is performed in the middle position: the two probes between two teeth. The geometric parameter, which allows us to control the angle of the wheel around Z axis, has a fixed value = 75. The coils are not current supplied (=measuring coils) Case 2 The second case is a multi-parametric static study (multi values) In this parameterized study, the angle of the cogged wheel will vary. The geometric parameter varies in the range [75, 195 ] with a step of 3. Magneto Static application tutorial PAGE 5
General information Flux PAGE 6 Magneto Static application tutorial
Flux General information 1.2. Strategy to build the Flux project Introduction This section presents outlines of physical properties description process of the sensor. Contents This section contains the following topics: Topic See Page Main stages for physical description 8 Magneto Static application tutorial PAGE 7
General information Flux 1.2.1. Main stages for physical description Outline An outline of the physical description process of the sensor is presented in the table below. Stage 1 2 3 4 Definition of the application and definition of the depth of the domain Creation of two materials Creation of four face region Creation of two coils: Two components Four face regions Description Magneto Static 2D (solved with Flux 3D solver) 2D plan (6mm) FERRITE magnet with a linear B(H) characteristic STEEL ferromagnetic material with a non linear B(H) characteristic 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 second magnet of the device 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 PAGE 8 Magneto Static application tutorial
Flux General information Stage Description COIL1P AIR_EXT MAGNET1 WHEEL COIL1N 5 Assignment of face regions AIR WHEEL COIL2P MAGNET2 COIL2N INFINITE 6 Material orientation Magneto Static application tutorial PAGE 9
Construction of the Flux project Flux PAGE 10 Magneto Static application tutorial
Flux 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. Contents This chapter contains the following topics: Topic See Page Physical description process 13 Magneto Static application tutorial PAGE 11
Construction of the Flux project Flux PAGE 12 Magneto Static application tutorial
Flux Construction of the Flux project 2.1. Physical description process Introduction This section presents the definition of the physical properties materials and regions. Contents This section contains the following topics: Topic See Page Define the physical application 14 Create materials 15 Create face regions 13 Create measuring coils: coil conductors components and coil 14 conductor regions Assign face regions to faces 18 Orient material for face region 19 Magneto Static application tutorial PAGE 13
Construction of the Flux project Flux 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 Coils Coefficient 2D domain type Depth of the domain 2D plane 6 mm Automatic Coefficient Application Define Magnetic Magneto Static 2D PAGE 14 Magneto Static application tutorial
Flux Construction of the Flux project 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 Physics Material New Magneto Static application tutorial PAGE 15
Construction of the Flux project Flux 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 Physics Face region New *The region already created and assigned during the creation of the infinite box, however the user need to enter the type of the region. PAGE 16 Magneto Static application tutorial
Flux Construction of the Flux project 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 Physics Electrical components Stranded coil conductor New Data (2) The characteristics of the regions (of coil conductor type) are presented in the table below: Coil conductor type region Face region Component Series or Orientation Turn number 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 Physics Face region New 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 Magneto Static application tutorial PAGE 17
Construction of the Flux project Flux 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. COIL1P AIR_EXT MAGNET1 WHEEL COIL1N COIL2P AIR_WHEEL MAGNET2 COIL2N INFINITE PAGE 18 Magneto Static application tutorial
Flux Construction of the Flux project 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 Physics Face region Orient material for face region Magneto Static application tutorial PAGE 19
Case 1: static study Flux PAGE 20 Magneto Static application tutorial
Flux 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, which allow us to control the angle of the wheel around Z axis, has a fixed value = 75 The coils are not current supplied (=measuring coils) Starting Flux project The starting project is the Flux project TestCase_INI.FLU. This project contains: the geometry description of the device the mesh and computation domain the initial physical description of the contactor Contents This chapter contains the following topics: Topic See Page Case 1: solving process 23 Case 1: results post-processing 25 Magneto Static application tutorial PAGE 21
Case 1: static study Flux PAGE 22 Magneto Static application tutorial
Flux Case 1: static study 3.1. Case 1: solving process Goal The case 1 is solved using the default scenario with reference values. Action Solve case 1. Solving Solve Magneto Static application tutorial PAGE 23
Case 1: static study Flux PAGE 24 Magneto Static application tutorial
Flux Case 1: static study 3.2. Case 1: results post-processing Introduction This section explains how to analyze the principal results of case 1. Contents This section contains the following topics: Topic See Page Display default graphic post processing 26 Display arrows of the magnetic flux density on a region 28 boundaries Display isovalues of the magnetic flux density on a 2D grid 29 Compute the magnetic flux density on a point 31 Compute the magnetic force on face regions 32 Plot a 2D curve of the magnetic field strength along a path and 33 export the curve Plot a 2D curve of normal and tangential components of the 35 magnetic field along a path Magneto Static application tutorial PAGE 25
Case 1: static study Flux 3.2.1. Display default graphic post processing Goal The default graphic post processing is displayed on the device (excluding the infinite box) : - Isovalues of the magnetic flux density - Arrows of the magnetic flux density - Isolines of the vector potential Action (1) Display isovalues Graphic Isovalues Display isovalues Result (1) The following chart shows the isovalues of the magnetic flux density on the device. Continued on next page PAGE 26 Magneto Static application tutorial
Flux Case 1: static study Action (2) Hide previous isovalues and display arrows Graphic Arrows Spatial Group Display arrows Result (2) The following chart shows the arrows of the magnetic flux density on the device. Action (3) Display isolines Graphic Isolines Display isolines Result (3) The following chart shows the isolines of the vector potential on the device. Magneto Static application tutorial PAGE 27
Case 1: static study Flux 3.2.2. Display arrows of the magnetic flux density on a region boundaries Goal The arrows of the magnetic flux density on wheel region boundaries are displayed. Data The characteristics of the arrows are presented in the table below. Arrows on boundary Name Groups Quantity WHEEL_CONTOUR S_WHEEL Magnetic flux density / Vector Graphic Arrows boundary New Result The result is presented in the figure below : PAGE 28 Magneto Static application tutorial
Flux Case 1: static study 3.2.3. Display isovalues of the magnetic flux density on a 2D grid Goal One 2D grid is created midpoint of the second stranded coil. The magnetic flux density isovalues are displayed on the 2D grid. Data (1) 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 Number of Number of Positive X Negative X Positive Y Negative Y disc. elements disc. elements 12 12 30 6 6 20 Rectangular 2D grid in XY plane: appearance Visibility Color visible green Support 2D grid New Data (2) The characteristics of the isovalues are presented in the table below. Isovalues on 2D grid 2D grid Quantity GRID_ONMAGNET Magnetic flux density / Vector Graphic Isovalues New Continued on next page Magneto Static application tutorial PAGE 29
Case 1: static study Flux Result The following chart shows the magnetic flux density on the GRID_ONMAGNET grid PAGE 30 Magneto Static application tutorial
Flux Case 1: static study 3.2.4. 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 Formula POINT1 Center of the magnet B Point defined by its coordinates Coordinates localization Coord. system Region first second 0 0 no constraint PROBE_CS001 MAGNET2 Computation On point New session Quantities computation on points Result The following values show the X and Y components of the magnetic flux density at the above-described point. Magneto Static application tutorial PAGE 31
Case 1: static study Flux 3.2.5. Compute the magnetic force on face regions Goal The value of the magnetic force is computed on the selected face 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. Name FORCE_MAGNET Compute on physic entity Region Spatial group Quantity Magnetic force / Magnitude S_MAGNET2 Magnetic force / x component Magnetic force / y component Computation On physical entity Compute Result The following dialog box shows the result of computation of the magnetic force on the MAGNET2 face region. PAGE 32 Magneto Static application tutorial
Flux Case 1: static study 3.2.6. Plot a 2D curve of the magnetic field strength along a path and export the curve 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. Name SEGMENT Path defined by 2 points Comment Along the magnet Path defined by coordinates Path points Starting point Ending point Discretization Coord. system Coordinates Coordinates by intervals Coord. system First Second First Second PROBE_CS001-15 0 PROBE_CS001 15 0 50 Support Path New Data (2) The characteristics of the curve are presented in the table below. 2D curve (path) Name Comment Path Quantity Magnetic field / CURVE Magnetic field strength along the segment in magnet SEGMENT Magnitude Magnetic field / Normal component Magnetic field / Tangential component Curve 2D curve (Path) New 2D curve (Path) Continued on next page Magneto Static application tutorial PAGE 33
Case 1: static study Flux Result The following curves show the components of the magnetic field strength along the X and Y axes with Absolute view mode. Action Export the curve to excel file Curve 2D curve (path) Excel export PAGE 34 Magneto Static application tutorial
Flux Case 1: static study 3.2.7. Plot a 2D curve of normal and tangential components of the magnetic field along a path Goal The variation of the normal and tangent components of the magnetic field is computed along the selected path and displayed as curve. Data (1) The characteristics of the path are presented in the table below. Name AIR_GAP Arc defined by center, radius and angles Path definition Comment In the air gap Extremities angles Discretiz Coord. Center of arc around Z Radius Region ation by system First Second Starting Ending intervals XY1 0 0-40 70 21.75 AIR_EXT 30 Support Path New Data (2) The characteristics of the curve are presented in the table below. 2D curve (path) Name Comment Path Quantity Magnetic field / CURVE_1 Normal and tangent magnetic Normal component AIR_GAP field along the air gap Magnetic field / Tangential component Curve 2D curve (Path) New 2D curve (Path) Continued on next page Magneto Static application tutorial PAGE 35
Case 1: static study Flux Result The following curves show the normal and tangent components of the magnetic field along the X and Y -axes. PAGE 36 Magneto Static application tutorial
Flux 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 that varies in the range [75, 195 ] with a step of 3. Starting Flux project 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. Contents This chapter contains the following topics: Topic See Page Case 2: solving process 39 Case 2: results post-processing 41 Magneto Static application tutorial PAGE 37
Case 2: parametric computation Flux PAGE 38 Magneto Static application tutorial
Flux Case 2: parametric computation 4.1. Case 2: solving process 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. Name SCENARIO1 Solving scenario Comment study using a geometrical parameter Solving scenario Parameter control Interval Controlled Type Higher parameter Lower limit Method limit step ALPHA Multi-values 75 195 value Step value 3 Solving Solving scenario New Solving Solve Magneto Static application tutorial PAGE 39
Case 2: parametric computation Flux PAGE 40 Magneto Static application tutorial
Flux Case 2: parametric computation 4.2. Case 2: results post-processing Introduction This section explains how to analyze the principal results of case 2. Contents This section contains the following topics: Topic See Page Display default graphic post processing (alpha=120 ) 42 Create animation of isovalues of the magnetic flux density on 43 face regions versus position parameter Plot a 2D curve of the flux through coil conductors versus an 44 I/O parameter Plot a 3D curve of the magnetic flux density on a path versus 45 an I/O parameter Magneto Static application tutorial PAGE 41
Case 2: parametric computation Flux 4.2.1. Display default graphic post processing (alpha=120 ) Action First, the computation step of the geometrical parameterized study is selected (alpha=120 ). Then, the default graphic post processing is displayed via isovalue plots of color shadings. Select the step Data 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 Action Display isovalues Graphic Isovalues Display isovalues Result The following chart shows the magnetic flux density on the selected regions. PAGE 42 Magneto Static application tutorial
Flux Case 2: parametric computation 4.2.2. Create animation of isovalues of the magnetic flux density on face regions versus position parameter Goal The animation of isovalues of the magnetic flux density for different positions of the wheel is created. Data The characteristics of the animation are presented in the table below. Name Animation General Pilot Parameters min max Steps frequency 1/ ANIMATION_1 ALPHA 75 195 2 Build options Build video Display Isovalues 4_ISOVAL _NO_INFI NITE Graphic Animation New Result The animation video is created in the project repertory in a.avi file. Magneto Static application tutorial PAGE 43
Case 2: parametric computation Flux 4.2.3. Plot a 2D curve of the flux through coil conductors versus an I/O parameter 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 Name Name Parameter Lower endpoint 2D curve (I/O parameter) Upper endpoint COILCONDUCTOR1 Circuit COILCONDUCTOR2 CURVE ALPHA 75 195 Flux Flux Curve 2D Curve I/O parameter New 2D Curve (I/O parameter) Result The following curves show the variation of flux through coil conductor in function of the angle variation of the cogged wheel. PAGE 44 Magneto Static application tutorial
Flux Case 2: parametric computation 4.2.4. Plot a 3D curve of the magnetic flux density on a path versus an I/O parameter Goal The variation of the magnetic flux density is computed along the selected path (already defined in case 1) for different positions of the wheel and displayed as curve. Data The characteristics of the curve are presented in the table below Name Path 3D curve (Path + I/O parameter) Parameter Name Min Max CURVE_1 AIR_GAP ALPHA 75 195 Quantity Magnetic flux density / Magnitude Curve 3D Curve (Path + I/O parameter) New 3D Curve (Path + I/O parameter) Result The following curve shows the variation of the magnetic flux density along the path for different positions of the wheel. Magneto Static application tutorial PAGE 45
Case 2: parametric computation Flux PAGE 46 Magneto Static application tutorial