New infinitesimal method for the analysis and synthesis of AC machines winding

The paper describes a new universal infinitesimal method which enables the analysis and synthesis of arbitrary AC motor windings. The method is based on the notion of the local angular density of conductors n(α) = dN(α)/dα. It will be proved the proportionality B(α) ≈ ∫
_n
(α)dα for the magnetic flux density in the air gap. The function n(α) can be arbitrary, i.e. of continual or impulse character. In a special case, when the function n(α) is given in the form of Dirac impulses, this new method generates the same results as the classical method. Spatial functions n(α), B(α) may be evolved into Fourier series. The first harmonic components of these functions serve to the electromagnetic design of the induction or synchronous motor. Higher harmonic components serve to the calculation of the differential leakages. New method enables to calculate linkage fluxes, and self as well as mutual inductances of any stator and rotor windings, too.