Abstract
This paper describes the application of the method of separation of variables and the use of Fourier series for solving the Laplace´s and Poisson´s equations on the study and analysis of the magnetic field produced in a linear motor with Halbach array. Equations for predicting the 2D magnetic flux density distribution produced in the air gap were developed. The model was validated by means of finite element analysis and by measurements carried on a prototype of the linear motor. Theoretical results helped understand the behaviour of the magnetic flux density in the air gap and to obtain the values of the static propulsion force and normal force in such machine.
Highlights
Fourier series can be applied on the solution of many problems in Electrical Engineering, especially on the study of electrical circuits and on the electric and magnetic field analysis
For comparison and validation of the analytical model, curves are obtained by numerical analysis and by measurements, under the same conditions of current and position used in the analytical method
The numerical analysis allowed to foresee the behaviour of the distribution of the magnetic flux density in the structure of the linear motor, especially in the ferromagnetic core of the armature, considered infinitely permeable in the analytical model
Summary
Fourier series can be applied on the solution of many problems in Electrical Engineering, especially on the study of electrical circuits and on the electric and magnetic field analysis. Joseph Fourier (1768-1830) in his Théorie Analytique de la Chaleur, in 1822 [1] It allows the representation of a periodic nonsinusoidal function in terms of an infinite sum of sines and cosines. In order to obtain the equations of fields in the electric motors, the solution of Laplaces and Poissons equations can be involved. These equations are subject of study in Electrical Engineering courses, principally due to their application on electromagnetic problems
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