WOLFRAM SYSTEM MODELER

Educational example: iron core with airgap

# Wolfram Language

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`SystemModel["Modelica.Magnetic.FluxTubes.Examples.BasicExamples.QuadraticCoreAirgap"]`
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# Information

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

Educational example of a magnetic circuit containing an iron core and an airgap:

A current ramp is applied in positive electric direction through the exciting coil, causing a rising magnetomotive force (mmf) in positive magnetic direction of the electromagnetic converter. The mmf in turn causes a magnetic flux through the circuit in the direction indicated by the flux sensor. From that magnetic flux, flux density can be calculated in every element of the magnetic circuit. Flux density is used to derive magnetic field strength. Magnetic field strength times length of the flux line gives magnetic potential difference of each element. The sum of all magnetic potential differences is covered by the mmf of the exciting coil.

Using the parameter values, the results can be validated by analytic calculations:

element cross sectionlength rel. permeability B H mmf
left leg a*a l - a μr flux / cross sectionB/(μr0)H*length
upper yokea*a l - a μr flux / cross sectionB/(μr0)H*length
right leg a*a l - a - deltaμr flux / cross sectionB/(μr0)H*length
airgap a*a delta 1 useful flux / cross sectionB/μ0 H*length
lower yokea*a l - a μr flux / cross sectionB/(μr0)H*length
total Σ mmf = N*I

Note that there is a leakage flux path present. Therefore the total magnetic flux of in core splits into

• the useful flux through the airgap and
• the leakage flux through the leakage element.

However, the magnetic voltage across the airgap and the leakage model are equal. The ratio of the useful flux over the flux in the core is equal to `1 - σ`. In the core the magnetic flux is the same in every element as they are connected in series. For the calculation of the length of flux lines inside the core, a medium flux line (dashed line) is used.

Additionally, a measuring coil is placed in the airgap. Due to Faraday's law, the time derivative of flux causes an induced voltage both in the exciting coil (in positive direction) and in the measuring coil (in negative direction). Since current and therefore flux are a linear time dependent ramp, induced voltages are constant during that ramp and zero otherwise. Note that usage of nonlinear magnetic material would change that result due the nonlinear relationship between magnetic field strength and flux density.

Note the proper usage of electric and magnetic grounds to define zero potential.

# Parameters (7)

l Value: 0.1 Type: Length (m) Description: Outer length of iron core Value: 0.01 Type: Length (m) Description: Side length of square cross section Value: 1000 Type: Real Description: Relative permeability of core Value: 0.001 Type: Length (m) Description: Length of airgap Value: 0.1 Type: Real Description: Leakage coefficient Value: 500 Type: Integer Description: Number of turns of exciting coil Value: 1.5 Type: Current (A) Description: Maximum exciting current

# Components (15)

excitingCoil Description: Ideal electromagnetic energy conversion Type: Cuboid Description: Flux tube with rectangular cross-section; fixed shape; linear or non-linear material characteristics Type: Cuboid Description: Flux tube with rectangular cross-section; fixed shape; linear or non-linear material characteristics Type: Cuboid Description: Flux tube with rectangular cross-section; fixed shape; linear or non-linear material characteristics Type: Cuboid Description: Flux tube with rectangular cross-section; fixed shape; linear or non-linear material characteristics Description: Ideal electromagnetic energy conversion Type: Cuboid Description: Flux tube with rectangular cross-section; fixed shape; linear or non-linear material characteristics Type: Ground Description: Zero magnetic potential Type: Ground Description: Ground node Type: RampCurrent Description: Ramp current source Type: MagneticFluxSensor Description: Sensor to measure magnetic flux Type: Ground Description: Ground node Type: VoltageSensor Description: Sensor to measure the voltage between two pins Description: Leakage reluctance with respect to the reluctance of a useful flux path (not for dynamic simulation of actuators) Type: RealExpression Description: Set output signal to a time varying Real expression