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Magnetic field simulation in the air gap of DC electric motor

QuickField simulation example

In the lab air space is modelled by the current layer ef, magnetic permeability of steel assumed to be infinite. Problem field is replaced by the sheet of conducting paper of proper shape (abcdefg). Obtaining the lines of magnetic field is replaced by the lines of equal electric potential in the conducting sheet. This replacement is correct, as the picture of the field H in the air and field U in the sheet looks the same. Current flows in at line ef and goes out from line ab. Lines of equal electric potential are measured by digital voltmeter.

Problem type
Liner plane-parallel magnetostatic problem.

Geometry
Air region is defined by contour abcdefg. Dimensions: ab=2 mm, ag=32o, cd=68 mm, bc=45o, de=30o, ef=55 mm. Action of other parts of the motor is modeled by boundary conditions.>
model of dc motor model of the equivalent conducting sheet

Given
Relative magnetic permeability of steel of rotor and stator μ=1000.
Relative magnetic permeability of air μ= 1.
Current density in the coil j=1 A/mm².
Electric power of motor 45 kW.

Task
Draw the lines of magnetic field in DC electric motor in the non-ferromagnetic region. Calculate pole dissipation coefficients for two formulations. First - the coil is defined by current distribution, the magnetic permeability of steel is finite. Second - simplified formulation: steel assumed to be with infinite permeability and the coil is modeled by current layer.

Solution

Results
Flux density in DC electric motor:
DC motor air gap simulation

Model type Leakage flux Full flux Ratio
Realistic model 1.11 mWb 52.93 mWb 0.021
Simplified model (laboratory unit) 3.39 mWb 78.87 mWb 0.043