Determination of electromagnetic forces in magnetic field calculations

A procedure is outlined for determining the electromagnetic force in the equation of motion for an electrical machine. Instead of approximating the inductance, the force is determined directly from the magnetic field distribution corresponding to a specific relative position of the electromechanical system components. The field pattern is most intricate, with the magnetic induction changing most abruptly, in the regions of strong fringing at corners of teeth or salient poles in the air gap. Calculations for plotting the magnetic field by the method of finite elements or finite differences yields most accurate results when the selected surfaces pass through points where components of magnetic induction have discontinuities or overshoots. The procedure is demonstrated on a machine with rectangular slots on both sides of the air gap and with the magnetic cores made of E1A steel. The magnetization curves for all components of the ferromagnetic structure are approximated. In calculating electromagnetic forces on the conductors in slots by this method, it has been found to be most expedient to treat them as tension forces.