Computation Time Analysis of the Magnetic Gear Analytical Model

Abstract

This article focuses on the computation time and precision of a linear 2D magnetic gear analytical model. Two main models of magnetic gears are studied: the first with an infinite relative permeability of yokes, and the second with a finite relative permeability of yokes. These models are based on the subdomain resolution of Laplace and Poisson equations. To accurately compute the magnetic field distribution, it is necessary to take into account certain harmonics of the various rings and other system harmonics due to modulation. Global system harmonics, which increase the value of computation time, must also be taken into account. If the magnetic gear has a high pole number, then computation time increases even more and no longer allows for system optimization. This article proposes to compute magnetic field distribution using different harmonic selection methods in order to significantly reduce the computation time for the magnetic torque without any loss of accuracy.

Gear ratio optimization of a full magnetic indirect drive chain for wind turbine applications

“…3. To compute it, a 2-D magneto static model, developed by [17] without any magnetic field computation in yokes and by [18] with magnetic field computation in yokes, is used with radial magnetization of magnets, constant remanence of the magnets and a constant relative permeability for all materials. This analytical model requires to solve Poisson's and Laplace's equation (6) in the k region of the system [19] (yokes region, permanent magnet region, air gap region and each air space between pole pieces) where ( ) and ( ) are the magnetic vector potential and the radial magnetization distribution respectively, and are the cylindrical coordinates.…”

“…From these boundary conditions, it is possible to obtain a matrix system of equations Z where the constants of integration presented in (7)- (8) are the unknowns of the problem. The dimension of the matrix Z presented in (11) is dependent of the number of harmonics taken into account in the air space between pole pieces (region III), the number of pole pieces and the number of harmonics taken into account in the other regions (region X, I, II, IV, V and VI) [18]. This matrix must be inverted to determine the magnetic field distribution.…”

“…Comparison can then be drawn between the magnetic torque of the internal and external rings obtained with the analytical model and finite element model with a rotation of the internal ring while keeping the pole-piece ring and the external ring fixed (Fig.5). [18]. In this example: = 2, = 7 and = 9 (flux line distribution is not represented in pole pieces because the analytical model does not permit to compute the magnetic vector potential in these regions).…”

“…For high power application like wind turbines (on the order of the MW), magnetic gears have high pole number which increases the dimension of the matrix Z (11) and then the computation time. To reduce the computation time, [18], an harmonics selection method is proposed. It permits to build the matrix system of the analytical model only with harmonics which generate magnetic fields.…”

Analytical iron loss model for the optimization of magnetic gear

“…On the downside, mechanical gearboxes cause production interruptions and require repairs, thus increasing operating costs [2], [3]. In this context, one attractive solution consists of developing a conversion chain featuring a medium-speed generator and a magnetic gear [4] (with non-contact power transmission) (Fig. 1c).…”