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Exercise N 7. Magnetic field simulation in the air gap of DC electric motor
Task
Draw the lines of magnetic field in DC electric motor in the nonferromagnetic 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.
Problem type
Liner planeparallel magnetostatic problem.
Geometry
Air region is defined by contour abcdefg. Dimensions: ab=2 mm, ag=32^{o}, cd=68 mm, bc=45^{o}, de=30^{o}, ef=55 mm. Action of other parts of the motor is modeled by boundary conditions.>
Given data
Relative magnetic permeability of steel of rotor and stator μ=1000.
Relative magnetic permeability of air μ= 1.
Current density in the coil j=1000000 A/m^{2}.
Electric power of motor 45 kW.
Simplified model (laboratory unit)
Coil is replaced by the current layer ef, magnetic permeability of steel assumed to be infinite. Problem field is replaced by the sheet of electroconducting 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.
Solution
 Model of real motor: due to symmetry at line Od H_{t}=0, at line Oa A=0.
 Simplified model (laboratory unit): H_{t}=0 at the steel surface (lines defga and bc) and axis of symmetry Od, at the line Oa A=0.
Results
Flux density in DC electric motor:
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 
Please, see problems lab7.zip and lab7exp.zip
