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Flux www.cedrat.com Example Creation date Characterization of a ferromagnetic material 2009 Author : Pascal Ferran - Université Claude Bernard Lyon Ref. FLU2_MS_MAG_06 Program Dimension Version Physics Application Work area Flux 2D 10.3 Magnetic Static Magnetic FRAMEWORK Presentation General remarks In this example, we’ll see the characterization of materials with the method of the torus. To do so, we’ll consider a coil torus with 2 coils (primary and secondary). The torus material is characterized by a model defined by the combination of a straight line and a curve with tangent arc. Js and µr are the parameters of this model. A sinusoidal current is injected in the primary coil, an induced voltage is measured at the secondary coil. The magnetic field H corresponds to the current, the magnetic induction field corresponds to the voltage. Th B(H) curve enables us to characterize the material. We’ll consider the original B(H) curve and the one « measured » via the torus. Objective - Computation of the magnetic induction in the torus from the voltage at the terminals of the secondary coil. - Computation of the magnetic field H in the ferromagnetic torus The parameters the user can change are: Average relative permeability of the magnetic material (MUR) Magnetic polarization at material saturation (JS) Maximum current (I_MAX) injected in the primary coil Number of spires of the primary and secondary coils (NP, NS) Theoretical reminders See Annex Properties CEDRAT S.A. 15, Chemin de Malacher Inovallée – 38246 MEYLAN Cedex (France) – Tél : +33 (0)4 76 90 50 45 – Email : [email protected] Flux - Rated average radius of the torus: R_MOY = 28.75 mm - Rated number of spires in the primary and secondary coils : Np = 4000 spires and Ns = 1000 spires -Rated characteristics of the torus material : Js = 1.2 T and µr = 500 - Maximal value of the direct current injected in the primary coil : I_MAX = 1 A - Measurements are made in direct mode Illustration Main characteristics Some results … Curv B(H) of the material considering the different computation modes (all parameters are rated) PAGE 2 Characterization of a ferromagnetic material Flux FRAMEWORK Distribution of the surface density of the magnetic flux (I = 1A, Np = 4000, Ns= 1000, r = 500 et Js = 1,2T) (all parameters are rated) To go further … - Impact of the airgap in a magnetic circuit with toric shape Study of current sensors Characterization of material via the method of the torus in 3D … Characterization of a ferromagnetic material PAGE 3 MODEL IN FLUX Flux MODEL IN FLUX Domain Dimension 2D Depth THICKNESS Infinite Box Disk Length unit. mm Angle unit. degrees Size Out. Radius : 150mm Periodicity In. radius : 100mm Symmetry Characteristics none Repetition number : Offset angle : Even/odd periodicity Application Properties Geometry / Mesh Full model in the FLUX environment Mesh 2nd order type Mesh Number of nodes 10133 Input Parameters Name Type Description Rated value THICKNESS ALPHA I_MAX Js Geometrical Physical Physical Physical 7 mm 1 1A 1.2 T MUR Physical Np Physical Ns Physical Problem’s depth Current variation coefficient Current maximal intensity Magnetic polarization at material saturation Average relative permeability of the material Number of spires of the primary coil Number of spires of the secondary coil PAGE 4 500 4000 1000 Characterization of a ferromagnetic material Flux MODEL IN FLUX Material Base NAME B(H) model Magnetic property J(H) model Electrical property D(E) model Dielectric property K(T) model K(T) characteristics RCP(T) model RCP(T) characteristics MATERIAL Analytical isotropic saturation MUR - Js Regions NAME AIR INFINITE Nature Surface region Air region or vacuum - Surface region Air region or vacuum - MAGNETIC_CIRCUI T Surface region Non conductive magnetic region MATERIAL - - - - - - - - - - Np spires – Negative orientation of the current - - - - - - - - - Type Material Mechanical Set Corresponding circuit component Electrical characteristics Current source Thermal characteristics Possible source thermal PRIMARY_COIL_MINUS Surface region Coil conductor type region PRIMARY_FIELD NOM Nature PRIMARY_COIL_PLUS Surface region SEC_MINUS Line region Type Coil conductor type region Coil conductor type region Matériau associé Ens. mécanique Composant circuit associé - - SEC_PLUS Line region Coil conductor region - PRIMARY_FIELD SECONDARY_COIL SECONDARY_COIL Caractéristiques électriques Np spires – Positive orientation of the current Ns spires – Negative orientation of the current Source de courant Caractéristiques thermiques - - Ns spires orientation current - - - - - - - Source de éventuelle chaleur Characterization of a ferromagnetic material – type Positive of the PAGE 5 MODEL IN FLUX Flux Mechanical Set Fixed part : Compressible part : Type Characteristics Miscellaneous Mobile part : Type of kinematics Internal characteristics: External characteristics : Mechanical stops Electrical circuit Component Type PRIMARY_FIELD Coil conductor SECONDARY_COIL Coil conductor Characteristics Imposed current : I_MAX x ALPHA Imposed current : 0 Associated Region PRIMARY_COIL_MINUS PRIMARY_COIL_PLUS SEC_MINUS SEC_PLUS Electric scheme Solving process options Type of linear system solver Type of non-linear system solver Automatically chosen Parameters Precision Newton Raphson Automatically defined 0.0001 Method for computing the relaxation factor Nb iterations 100 Automatically defined Thermal coupling Advanced characteristics Solving Scenario SCENARIO_1 Name of parameter ALPHA Duration of the solving PAGE 6 Controllable parameter Physical 40 seconds Variation method Steps list Interval definition Step selection 0.0 to 1.0 0.01, 0.02, 0.05, 0.075, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 Operating System Windows XP 32 bits Characterization of a ferromagnetic material Flux ANNEX ANNEX Theoretical reminders Magnetic induction measurement We can measure the voltage at the terminals of the secondary coil and deduct from it the average flux in the magnetic circuit from the following relation : vs NS d dt avec B S From which we get : B vs H Computation 1 NS 2 f S Let’s calculate H with the Ampere’s theorem formula : H dl j Nj ij c In this case, the current circulating in the secondary coil is equal to 0 and we integrate H along the average contour of the torus (average radius = = R_MOY). Result: ALPHA I _ MAX NP H 2 R _ MOY Coming from : H Characterization of the magnetic material used ALPHA I _ MAX NP 2 R _ MOY In Flux, a material can be characterized by having the following magnetic property: Isotropic analytical saturation (arctg, 2 coef.) ». The corresponding mathematical expression of the B(H) model is : Characterization of a ferromagnetic material PAGE 7 ANNEX Notations and symbols Flux symbol description vs unit Voltage at the terminals of secondary c Average flux in the magnetic circuit Magnetic induction field Torus section Magnetic field Peak value of the current carried by the primary coil Torus average radius Number of spires of the primary coil Number of spires of the secondary coil Coefficient allowing the adjustment of the of the current value to its maximal value B S H I_MAX R_MOY Np Ns ALPHA V Wb T m² A/m A m Numerical applications Presentation Analytical computation of the different values seeked for the below working point : - Determination of H It is now possible of determine the value of H at the defined working point by applying the Ampere theorem : H Determination of B (Flux formula) Property of the magnetic material : Js = 1.2 T - µr = 500 Torus average radius : R_MOY = 28.75 mm Number of spires : Np = 4000 spires – Np = 1000 spires Maximal intensity : I_MAX = 1 A Current ratio: ALPHA = 0.05 ALPHA I _ MAX NP 0.05 1 4000 1107 A / m 2 R _ MOY 2 28.75 10 3 From the determined H value, it is possible to find the corresponding value of the B : ( µr 1 ) µ0 H arctg 2 Js (500 1) 4 10 7 1107 2 1.2 7 B 4 10 1107 arctg 2 1 . 2 B µ0 H 2 Js B 0.56 T PAGE 8 Characterization of a ferromagnetic material