Analytical Model of Modular Spoke-Type Permanent Magnet Machines for In-Wheel Traction Applications

Abstract

This paper proposes an analytical model of modular spoke-type permanent magnet (MSTPM) machines based on air-gap field modulation (AFM) theory. Firstly, a fundamental AFM model of open-circuit MSTPM machines is introduced. The open-circuit air-gap field of MSTPM machines is determined by three fundamental elements including the primitive magnetizing magnetomotive force (MMF) produced by permanent magnet (PM), and two modulators which consist of stator and rotor permeance. The analytical MMF excited by PM (PM-MMF) can be calculated by using magnetic circuit method, while the stator and rotor permeance models are developed based on relative permeance (RP) method. Thereafter, a general model is proposed to calculate the open-circuit back electromotive force (EMF) of MSTPM machines. Further, the winding inductance model is established on the basis of equivalent magnetic circuit method and RP model. Finally, the machine performance is predicted by the analytical model, and verified by both finite element analysis (FEA) and experimental results. Index Terms-Air-gap field modulation, AC machines, spoke-type PM machines, in-wheel traction.  NOMENCLATURE θ Air-gap position μ0 Permeability of vacuum ωRotor mechanical speed (rad/s)Relative rotor permeance at (position θ, moment t) Λr0Average relative rotor permeance Λ s0Average relative stator permeance Λr1 Amplitude of fundamental relative rotor permeance Λs(θ, t) Relative stator permeance at (position θ, moment t) Br(θ, t) Radial air-gap flux density at (position θ, moment t) B ho The h o th harmonic of air-gap flux density ec(t) Back-EMF of a single coil at moment t e kThe k th phase back-EMFThe harmonic of the k th phase back-EMF induced by the ho th harmonic of flux density 

Static and Dynamic Magnetic Pull in Modular Spoke-Type Permanent Magnet Motors

“…The spoke-type permanent magnet motor has been widely studied in home and vehicle appliances because it can concentrate flux and has a high torque density and potential magnet-saving capabilities [1][2][3]. The majority of studies have been mainly focused on the magnet shape [4][5][6][7][8][9][10][11], the analytical model [12,13] and the magnetic barrier, with different shapes and dimensions [14][15][16][17][18][19][20][21], for high-speed spoke-type permanent magnet motors. However, a study on the magnetic pull of modular stators or rotors for modular spoke-type permanent magnet motors has not yet been conducted.…”

Multi-objective Optimization and Performance Comparison of Different Driving Configurations of In-wheel Motors

“…Afterward, Gong et al [11], Ifedi et al [12], and Chung et al [13] developed direct driving IWMs based on outer-rotor radial flux permanent magnet synchronous motor (PMSM) separately. Furthermore, outer-rotor PMSMs with different arrangements of permanent magnets such as Halbach type [14], [15] and Spoke type [16], [17] for direct driving IWMs have been researched. Besides, the design and optimization of diverse concepts of IWMs such as reluctance machines [18], [19] and vernier machines [20], [21] have been conducted.…”

Effect of rotor magnetic isolation dimensions on no‐load performance of ultra‐low speed high torque spoke type permanent magnet motor

“…[13] was to predict the electromagnetic behaviour of a permanent magnet electric motor with a spoke rotor geometry for motorsport applications. Zhang et al [14] proposed an analytical model of modular spoke-type permanent magnet machines based on air-gap field modulation theory.…”

“…Zhang et al. [14] proposed an analytical model of modular spoke‐type permanent magnet machines based on air‐gap field modulation theory.…”