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This paper presents an analytical method for modeling the no-load air gap flux density of a surface-mounted and a consequent-pole linear Vernier hybrid machine (LVHM). The approach is based on simple magneto-motive force (MMF) and permeance functions to account for the doubly-slotted air gap of the LVHM. These models are used to determine the flux linkage, induced electromotive force (EMF) and average thrust force of each machine. The accuracy of the two analytical models is validated by comparison with 2D finite element method (FEM) solutions. Based on the analytical models, it is found that the working harmonics of both surface-mounted and consequent-pole LVHMs are essentially the same. However, the magnitudes of these working harmonics in the consequent-pole LVHM are invariably greater than those of surface-mounted LVHM. Further, using the analytical model, the contribution to the thrust force of the machine by each individual working harmonic can be shown clearly, and is used to explain why the consequent-pole LVHM has improved performance despite using only 50% of the permanent magnet (PM) material compared to the surface-mounted LVHM.

Analytical Modeling of Surface-Mounted and Consequent-Pole Linear Vernier Hybrid Machines