Analytical modelling of a slotless tubular interior permanent magnet machine considering iron poles permeability

An analytical method is proposed to model the magnetic field distribution across a slotless tubular interior permanent magnet machine. In order to consider the permeability of both permanent magnets and iron poles of the slider, in the proposed approach, instead of choosing each one as an individual sub-domain, they are taken as an integrated sub-domain. Therefore, the governing partial differential equation alters from Poisson equation to the governing magnetostatics equation for inhomogeneous (space-dependent permeability) materials. The solution is derived through separation of variables method in which a Sturm-Liouville problem is encountered. The solution and its important mathematical properties, such as the orthogonality and generalised Fourier series, are fully addressed. These properties are very helpful for creating linear interface equations in terms of the integral coefficients. In addition, since the number of sub-domains is decreased, the total number of the unknowns of the final matrix of equations is reduced effectively. To validate the proposed method, a case study is simulated by the aid of computer software and its results are compared with those of finite element method. It has been observed that the results are in good agreement.