WOLFRAM SYSTEMMODELER

CoilDesign

Calculation of winding parameters (wire diameter, number of turns et al.) and recalculation with optionally chosen parameters; to be adapted to particular design tasks

Wolfram Language

In[1]:=
SystemModel["Modelica.Magnetic.FluxTubes.Examples.Utilities.CoilDesign"]
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

This model example shows dimensioning of a winding (wire diameter, number of turns) based on desired operating conditions (voltage, temperature, current density, conductor filling factor) for a given cross-section area of the winding. It can be modified according to the parameters given and sought after for a particular design project.

The calculated winding resistance and number of turns can be used as input parameters to the electrical subsystem of a device to be modelled. Operating voltage V_op can be minimum, nominal and maximum voltage respectively as specified for a particular design project. In conjunction with the setting of the operating temperature T_op, this enables for analysis of the device under worst-case conditions (e.g., minimum required magnetomotive force, maximum allowed ohmic losses, minimum and maximum force respectively).

For manufacturing of a winding, the obtained wire diameter d_wireCalculated must be rounded to that of an available wire. In order to analyse the influence of this rounding, one can enter the chosen wire diameter d_wireChosen and number of turns N_chosen as optional input. Calculation of the resulting winding parameters enables for comparison with the ones obtained otherwise.

Parameters (23)

rho_20

Value: 0.0178e-6

Type: Resistivity (Ω·m)

Description: Resistivity of conductor material at 20 degC (default: Copper)

alpha_20

Value: 0.0039

Type: LinearTemperatureCoefficient (¹/K)

Description: Temperature coefficient of conductor material's resistivity at 20 degC (default: Copper)

T_op

Value: 293.15

Type: Temperature (K)

Description: Operating temperature of winding

rho

Value: rho_20 * (1 + alpha_20 * (T_op - (20 - Modelica.Constants.T_zero)))

Type: Resistivity (Ω·m)

Description: Resistivity at operating temperature

h_w

Value:

Type: Length (m)

Description: Height of winding cross-section

b_w

Value:

Type: Length (m)

Description: Width of winding cross-section

A_w

Value: h_w * b_w

Type: Area (m²)

Description: Cross-section area of winding

l_avg

Value:

Type: Length (m)

Description: Average length of one turn

V_op

Value:

Type: Voltage (V)

Description: Operating voltage (nominal/ minimum/ maximum voltage depending on design objective)

J_desired

Value: 4e6

Type: CurrentDensity (A/m²)

Description: DESIRED current density at operating temperature and voltage resp.

c_condFillChosen

Value: 0.6

Type: Real

Description: CHOSEN conductor filling factor = total conductor area without insulation/ total winding area

N_calculated

Value: V_op / (rho * l_avg * J_desired)

Type: Real

Description: CALCULATED number of turns

d_wireCalculated

Value: sqrt(4 * A_w * c_condFillChosen / (pi * N_calculated))

Type: Diameter (m)

Description: CALCULATED wire diameter (without insulation)

A_wireCalculated

Value: pi * d_wireCalculated ^ 2 / 4

Type: Area (m²)

Description: Calculated wire cross-section area

R_calculated

Value: rho * N_calculated * l_avg / A_wireCalculated

Type: Resistance (Ω)

Description: Winding resistance at operating temperature and voltage resp. with CALCULATED number of turns and wire diameter

P_calculated

Value: V_op ^ 2 / R_calculated

Type: Power (W)

Description: Winding's ohmic losses at operating temperature and voltage resp. with CALCULATED number of turns and wire diameter

d_wireChosen

Value: d_wireCalculated

Type: Diameter (m)

Description: CHOSEN available wire diameter (without insulation)

N_chosen

Value: N_calculated

Type: Real

Description: CHOSEN number of turns

A_wireChosen

Value: pi * d_wireChosen ^ 2 / 4

Type: Area (m²)

Description: Wire cross-section area resulting from CHOSEN wire diameter

R_actual

Value: rho * N_chosen * l_avg / A_wireChosen

Type: Resistance (Ω)

Description: Winding resistance at operating temperature and voltage resp. resulting from CHOSEN number of turns and wire diameter

P_actual

Value: V_op ^ 2 / R_actual

Type: Power (W)

Description: Winding's ohmic losses at operating temperature and voltage resp. resulting from CHOSEN number of turns and wire diameter

J_actual

Value: V_op * 4 / (R_actual * pi * d_wireChosen ^ 2)

Type: CurrentDensity (A/m²)

Description: Current density at operating temperature and voltage resp. resulting from CHOSEN number of turns and wire diameter

c_condFillActual

Value: N_chosen * pi * d_wireChosen ^ 2 / (4 * A_w)

Type: Real

Description: Conductor filling factor resulting from CHOSEN number of turns and wire diameter