Flux field formulation and back-iron analysis of tubular linear machines

In electromagnetic machines, ferromagnetic material is one of the key components that affect the magnetic field and thus the output performance significantly. The objective of this paper is to study the influence of ferromagnetic material on magnetic field distribution of tubular electromagnetic linear machines. Generic magnetic field models are obtained for linear machines with various structure designs based on magnetic vector potential and Bessel functions. The magnetic field model is validated with numerical results from finite element calculations. The comparison between them shows that the flux model fits closely with the numerical computation. The obtained analytical model can be employed to study the flux density distribution of machine designs with single-sided, double-sided, and non back irons. It shows that the use of back iron, especially for the internal side, helps to greatly enhance the radial component of magnetic field. This component contributes to the axial force generation of tubular linear machines. The study could be useful for the design optimization of permanent-magnet linear machines.