Effect of rotor eccentricity on the magnetic field in the air-gap of a non-salient-pole machine

A method of calculation is developed for the determination of the magnetic field in the air-gap of an idealized machine without salient poles and with an eccentric rotor. The basic case of a concentric rotor is considered first, simplifying assumptions being made to render the problem amenable to calculation.The magnetic potential at any point is governed by the currents flowing in the windings and also by the magnetization induced on the cylindrical surfaces of the rotor and the stator. The potential functions appropriate to the stator, rotor and air-gap are determined for several elementary conductor arrangements, and hence the complex potential function is derived at any point in the air-gap.The eccentric annulus representing the air-gap when the rotor is displaced is related to a concentric annulus by means of a conformal transformation. Hence the complex potential is known at any point in the eccentric air-gap, and expressions are thence derived for the potential and flux functions at any point in the gap due to a single current-carrying conductor placed arbitrarily in either stator or rotor.Finally, the application of the principal results of the analysis is exemplified by the calculation of the radial magnetic field at the surface of an eccentric rotor with an arbitrary stator winding.