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EMDtool

Summary

Material Basic isotropic material class.

Materials are normally instantiated with the static methods

  • Material.create

  • Material.from_specs

    PROPERTIES

  • Material/BH_extrapolation_method is a property.

  • Material/data is a property.

  • iron_loss_computation_method Iron loss computation method.

This property allows an option to toggle the iron loss computation method. Indeed, the loss_density method of the Material class calls the method with its name equal to this property.

However, subclasses may have a different loss_density method. Help for Material/iron_loss_computation_method is inherited from superclass MATERIALBASE

  • stacking_factors - list of stacking factors per each element

Methods

Class methods are listed below. Inherited methods are not included.

* harmonic-approximation BH-curve (eq. (47) in Arkkio’s thesis)

* Material/add_domain is a function.

this = add_domain(this, domain)

* clear_copy New independent copy of the material.

* create Create material

mat = Material.create(material_object)

Return a clear_copy of material_object.

mat = Material.create(matid)

Create a material from library, see get_defaultMaterial

mat = Material.create()

Create an empty Material object.

* initialize_material_data Calculate reluctivities etc.

Compute reluctivities and extrapolate BH data.

Reluctivity data as a function of B^2 is saved to this.data .

* detach Clear elements, domains, etc.

* differential_reluctivity Return reluctivity and its derivative.

[nu, dnu] = differential_reluctivity(this, Bvector, true)

Return reluctivity and its derivative w.r.t. B ^2 computed with the harmonic approximation

[H, dHdB] = differential_reluctivity(this, Bvector)

Return magnetic field strength vector and the differential reluctivity tensor. Only works in 2D.

* extrapolate_BH_langevin Extrapolate BH data with constant magnetization.

[Bext, Hext] = extrapolate_BH_langevin(B, H) extrapolate given BH data by assuming a constant magnetization beyond the given range.

Returns original BH data appended by extrapolated data.

* extrapolate_BH_data Extrapolate given BH data.

[Bext, Hext] = extrapolate_BH_data(this, B, H) extrapolate BH data with the method specified in this.BH_extrapolation_method:

  • ‘langevin’ : fitting a single Langevin function to the data, using Material.extrapolate_BH_langevin

  • ‘constant’ : extrapolate using constant magnetization equal to the last datapoint in the given BH data. Uses Material.extrapolate_BH_constant

  • ‘linear’ : linear extrapolation of BH curve. Uses Material.extrapolate_BH_linear

  • for other approaches, please subclass Material.

Returns original BH data appended by extrapolated data.

* extrapolate_BH_langevin Extrapolate BH data with Langevin approach.

[Bext, Hext] = extrapolate_BH_langevin(B, H) extrapolate given BH data by fitting the single-valued Langevin function to the data; specifically by matching the value and slope at the end of the given BH curve.

Returns original BH data appended by extrapolated data.

* extrapolate_BH_linear Extrapolate BH data with linear extrapolation.

Returns original BH data appended by extrapolated data.

* fit_Langevin1 Process BH data with Langevin approach.

fit_Langevin1(this)

Process given BH data (this.B, this.H). Given data range is used as such. Extrapolation to higher flux densities is performed by fitting the single Langevin function to the data, and using it for extrapolation.

fit_Langevin1(this, ‘monotonicity_factor’, c)

Additional improve the reluctivity-monotonicity of the given data with the following approach:

  1. Compute nu = H / B

  2. Make nu monotonic.

  3. Compute H_monotonic = nu * B

  4. Replace H := (1-c)H_original + cH_monotonic.

  5. Proceeed as earlier.

Even a small monotonicity factor can often improve the convergence of nonlinear problems.

NOTE: Original BH data is not modified.

* from_specs Create material from specs.

Call syntax:

mat = Material.from_specs(‘name’, name, ‘B’, B_curve_vector, ‘H’, H_curve_vector, ‘property_name_1’, value_1, …)

* init_for_problem Initialize object for problem.

Normally, this method does very little apart from determining the stacking factors. It could be used to initialize hysteresis models or similar in subclasses on Material, though.

* initialize_material_data Initialize reluctivity curves etc.

initialize_material_data(this)

Process given BH data (this.B, this.H). Given data range is used as such. Extrapolation to higher flux densities is performed by this.extrapolate_BH_data

initialize_material_data(this, ‘monotonicity_factor’, c)

Additional improve the reluctivity-monotonicity of the given data with the following approach:

  1. Compute nu = H / B

  2. Make nu monotonic.

  3. Compute H_monotonic = nu * B

  4. Replace H := (1-c)H_original + cH_monotonic.

  5. Proceeed as earlier.

Even a small monotonicity factor can often improve the convergence of nonlinear problems.

NOTE: Original BH data is not modified.

* iron_loss_density_frequency_domain_Bertotti Iron loss density computed

with the frequency-domain Bertotti model.

WARNING: make sure the that the solution used contains a full fundamental period of the flux density waveforms.

WARNING: many concentrated winding configurations result in sub-harmonics in the rotor field. In this case, multiple electrical periods should be analysed, and the use_entire_solution keyword argument set to true when calling MaterialBase.losses.

* iron_loss_density_time_domain_Steinmetz Iron loss density from modified Steinmetz

model.

[p_hysteresis, p_eddy, p_excess] = iron_loss_density_time_domain_Steinmetz(this, Bdata), where

  • Bdata : flux density data structure returned from MaterialBase.get_B_data .

The loss components are computed as follows:

p_hysteresis = hysteresis loss density = ch ** abs(Bx^a ** dBx/dt^b) + abs(By^a * dBy/dt^b)

where a=b=1 by default, if not given in this.material_properties.steinmetz_exponents = 1x2 vector

p_eddy = eddy loss density = ce * ( (dBx/dt)^2 + (dBy/dt)^2 )

p_excess = all-zero.

WARNING: For now, the method also supports a legacy syntax, with the input arguments (this, timestamps, Bx, By). This syntax is used by the time_domain_Steinmetz function. In this case, the returned loss densities are in W/kg.

* loss_density Iron/material loss density method.

[p_hysteresis, p_eddy, p_excess] = loss_density(this, Bdata), where

  • Bdata : flux density waveform data returned by get_B_data .

Return values:

  • Elementwise hysteresis, eddy, and exces loss densities, expressed in W/m^3. Help for Material/loss_density is inherited from superclass MATERIALBASE

* plot_BH Plot BH curves etc.

* Material.process_BH is a function.

[Bnu, Bdnu] = process_BH(BH, varargin)

* raw_reluctivity Evaluate (non-differential) reluctivity.

nu = raw_reluctivity(this, B2)

* save_to_excel Save material specs to Excel.

* set_step Set new time-step.

set_step(this, kstep, t, varargin)

Does nothing by default

* Material/shift_elements is a function.

this = shift_elements(this, Ne)

* Material/thermal_conductivity is a function.

l = thermal_conductivity(this)