3-D Semi-Analytical Model of a Superconducting Axial Flux Modulation Machine

Abstract

This article presents a 3-D semi-analytical model of a partially superconducting axial flux modulation machine for the computation of the flux density distribution, the torque and the Eddy-current losses in the armature. The modulation of the superconducting coil magnetic field by the superconducting bulks is calculated by solving the Maxwell's equations in scalar potential with the variable separation method. Using Fourier series analysis and the convolution theorem, the bulk region is modelled by a domain with a spatially variable magnetic permeability. This variable permeability enables considering a diamagnetic bulk as well as a more complex magnetic behavior using the Bean model. The results of the proposed model are compared with 3-D finite elements models and good agreement is obtained for a significantly reduced computation time. The proposed model appears to be a suitable tool for optimisation and sizing processes.

Non-Linear 3-D Semi-Analytical Model for an Axial-Flux Reluctance Magnetic Coupling

“…Finally, one can note that, in the Cartesian frame, the height of the PM and SP is 𝐷 = 𝑅 2 − 𝑅 1 , a pole width is 𝜏 = 𝑅 𝑚 𝜋 𝑝 ⁄ , the PM width is 𝛼 𝜏 2 ⁄ and the SP width is 𝛽 𝜏 2 ⁄ . The linearization to the mean radius is a common method to simplify the modelling of axial-flux actuator and has been successfully applied for various topologies in previous works [8], [9] [19].…”

“…The limit in the x-direction is fixed at 𝐿 = 3𝐷, this value is defined from our experience of previous models [19].…”

“…Thus, (13) . We can similarly define 𝑯 𝒖 𝒊 , 𝚽 𝒊 and 𝑴 𝒖 𝒊 for the magnetic field, the scalar potential and magnetization in each region, the vector concatenation structure in 3-D is presented in [19]. Moreover, 𝝁 𝒄,𝒙 𝑰𝑰𝑰 , 𝝁 𝒄,𝒚 𝑰𝑰𝑰 and 𝝁 𝒄,𝒛 𝑰𝑰𝑰 denotes the permeability convolution matrices for the different components of the constitutive relation whose concatenation structure is also presented in [19].…”

“…Cauchy's product) which allows to consider complex space distribution of the magnetic permeability. In a recent article, we improved the method by applying it to an axial-flux superconducting flux modulation machine [19]. The proposed 3-D model was a cartesian model considering subdomains with a permeability variable in two directions allowing to approach the magnetic behavior of superconducting bulks.…”

“…In this article, we apply the method presented in [19] to propose a new 3-D semi-analytical model of the axial-flux reluctance coupling of Fig. 1.…”