An improved analytical solution for predicting magnetic forces in permanent magnet motors

Abstract

This paper describes an analytical model for analyzing magnetic forces developed in permanent magnet motors of radial field topology. The slotting effect is taken into consideration by solving the boundary value problem of the air gap field. The solution is expressed in the form of Fourier series with which the analysis of the harmonic contents in the magnetic forces can be readily performed. In particular, the curvature effect or the flux focusing effect in the slot opening regions is taken into consideration. The results of magnetic forces obtained from this model are verified with numerical simulations using the finite element method and experimental results.

2D analytical modeling of a wholly superconducting synchronous reluctance motor

“…Compared to the FE simulations, one can see that the analytical calculation well tracks the electromagnetic torque. The torque characteristic shown in figure 15 presents the same behavior of the classical result obtained for a conventional 4-pole Synchronous Reluctance Motor [3][4][5]. One can observe that a maximum torque of around 7000 N.m is obtained for a value of θ 0 equal to 22.5°.…”

“…The analytical solutions in the hole sub-domain and in the other sub-domains have been computed with a finite number of harmonic terms N and K as indicated in table 1. Outer radius of bulks 9.5 cm R 3 Inner radius of the windings 10 cm R 4 Outer radius of the windings 12.5 cm R 5 Outer radius of the outer airgap (cryostat yoke) 14.5 cm R 6 Outer radius of the magnetic yoke 18 cm The corresponding flux density distributions (radial and tangential components) in the middle of the air-gap (at r =9.75 cm) under no-load condition (θ 0 = 0°) and load condition (θ 0 = 22.5°) are plotted, respectively, in figure 13 and figure 14. The effect of the HTS bulks on the flux density waveforms is very clear.…”

“…As can be seen in figure 1, the rotor contains a ring of Q holes domains between the Q HTS bulks which are difficult to handle in the analytical prediction of the air-gap magnetic field. Analytical approaches for the magnetic field computation in classical ferromagnetic machines using sub-domains method can be found in the literature [4][5][6][7]. However, the proposed analytical models relate to ironcored electrical machine and cannot be used for the analysis of the proposed air-cored machine with HTS bulks.…”

Analytical calculation of open-circuit magnetic field distribution of slotless brushless PM machines

“…In the case of slotted structure, the technique by which the slotting effect has been implemented is mentioned in the last column of Table 1. Normally the slotting effects are taken into account using one of the following techniques: (1) Carter's factor [1]; (2) relative permeance model [3,6,16,22,30]; (3) complex relative permeance model [26,32,36]; (4) Schwarz-Christoffel mapping [21,38]; and (5) subdomain technique [9,29,33,34,37,[39][40][41][42][45][46][47][49][50][51][52], where the first four approaches are among conformal transformation techniques. Zhu et al [42] have briefly explained the advantages and disadvantages of these techniques.…”

Time- and Spatial-Harmonic Content in Synchronous Electrical Machines

“…This period is called the mechanical time period or the basic time period (T m ), it is the time the rotor needs to perform one revolution. Usually the magnetic field is expressed using auxiliary quantities such as the magnetic scalar potential (ψ) [5]- [7] or the magnetic vector potential (A) [8]- [16]. If the end effects are neglected, ψ and A are independent of z.…”