A THREE DIMENSIONAL ANALYTICAL CALCULATION OF THE AIR-GAP MAGNETIC FIELD AND TORQUE OF COAXIAL MAGNETIC GEARS

Abstract

In order to solve the defects that the end-efiect of magnetic fleld is ignored in two dimension (2-D) analytical method or 2-D flnite element method (FEM); meanwhile, mass computer resource and time for parametric design or optimization are wasted in three dimension (3-D) FEM, a concise and e-cient 3-D analytical approach is put forward for the calculation of the air-gap magnetic fleld and torque of coaxial magnetic gears. Based on the cylindrical coordinates where a coaxial magnetic gear is in, the equivalent current model and vector magnetic potential equation of permanent magnets in high speed permanent magnetic ring are constituted. By superposed magnetic ∞ux density of every tile permanent magnets on high speed permanent magnetic ring in cylindrical coordinates, a air-gap magnetic fleld 3-D analytical formula is set up without ferromagnetic pole-pieces; in the interest of modulated air-gap magnetic fleld 3-D analytical formula with ferromagnetic pole-pieces, three types boundary conditions using state equations of contact surfaces between ferromagnetic pole-pieces and air-gap are established by a thorough analysis of the modulate mechanism of ferromagnetic pole-pieces. Finally, magnets of the low speed permanent magnetic ring are reduced to a distribution of equivalent current, which experience the Lorentz force in modulated magnetic fleld of high speed permanent magnetic ring for torque calculation. The integrals in all aforementioned calculation are axial, so the end-efiect is embodied in above analytical model and more precise than 2-D analytical method or 2-D FEM. As the calculation results, the formula is accurate but faster than the 3-D FEM. The analytical model is suited for programmable calculation and that will make the structural and parametric design or optimization of coaxial magnetic gears simple and timesaving.