Air gap permeance in doubly-slotted asynchronous machines

Abstract

Irregularities in the air gap of asynchronous machines are sources of forces, torques, noise, and vibrations. A formal Fourier series expression for the variation in reluctance about the periphery of the air gap has long since been established. A similar formal solution for the variation in permeance, which is generally of greater interest and practical value, has not, to the author's knowledge, been available and is therefore presented here. Glossarv of Svmbolsgap to a smooth surface at R,,.,. k = order number of space harmonic. P = length of air gap. n = number of slots about the air gap. p = number of poles. R, = mean radius to air gap. s = rotor slip. r = subscript for rotor quantities. s = subscript for stator quantities.t = time. [SI U = subscript for rectangular waveshape varying beween zero and unity. ak = Fourier series coefficient for sin ky term. b, = Fourier series coefficient for cos ky term. [m] [m] [m] c k = Ek = bk + j at = ck &. Ad = slot depth. [m] y = peripheral position around air gap. 8 = slot pitch = h / n . A8 = slot width. [rad]cc0 = magnetic permeability of free space. 8 , = angular separation between ys = 0 and yr = 0 at t = 0. $k = arctan ak/bk CO = electrical (synchronous) angular velocity. g(y) = Fourier series for the variation in air gap.[rad][rad][Wm][rad][rad/s] [m] P(Y) = l/g(Y)-b1-l WM 293-1 EC the IEEE Electric Machinery Committee of the IEEE Power Engineering Society for presentation at the IEEE/ PES

Damper winding for noise and vibration reduction of induction machine under sinusoidal conditions

“…The rotating field in the air-gap of AC machines is never perfectly sine, indeed flux density harmonics can be generated by several sources such as spatial distribution of the coils in a finite number of slots (space harmonics), variable thickness of the air-gap [1], [5], [6] (permeance harmonics), eccentricity [7], magnetic saturation or voltages harmonics due to the power supply [8].…”

“…It produces some reactive power 𝑄 𝑐 that the network has not to provide. Its value can easily be estimated by relation (5), taking into account the winding turn ratio.…”

Determination of load capacity for magnetic leadscrew drives

“…An alternative approach to the finite element method is to evaluate the variation of air-gap reluctance or permeance. Hesse [7], for example, derived a formal Fourier series solution for the variation in permeance for a doubly slotted revolving air gap.…”

“…For gap 3, its permeance can be estimated from formulas for calculating permeance of common flux paths. Many authors ( [7], [9]- [11], for example) have discussed the estimation of permeance. Because there are also fluxes between the sides of the nut and the shaft, the permeance corresponding to this path should be estimated and added to .…”

Study and experimentation of a rotor current excited Vernier reluctance machine aimed to direct-driven applications

“…The air gap permeance function is given by the following relation [28]: ε is a coefficient whose value is equal to 1 or -1 and P 0 , P js , P mr and P js-mr are coefficients whose values depend on geometric characteristics (see appendix).…”