Computation of the Magnetic Field Generated by Helicoidal Toroidal Permanent Magnets

Abstract

This article presents an analytical numerical procedure to compute the\ud magnetostatic field generated from permanent magnets shaped by a helicoidal geometry of a toroidal kind. The transversal section of these magnets is pseudorectangular, and the magnetization model that has been used is based on the equivalent magnetic charge. The modulus of the magnetization vector M has a constant value in all points of the magnet case study. M has the same direction as the binormal in each\ud point of the barycentric curve relative to the helicoidal magnet of a toroidal kind. The procedure proposed to evaluate the magnetic field is shown by computing the distribution of the magnetic flux B on a surface parallel to one of the four surfaces that surround the magnet. This evaluation has been performed with reference to a discrete set of points belonging to the same surface. Successively, a bidimensional interpolant function is used to virtually evaluate B in each point of the previous surface that contains the points where B has been actually computed. The results are presented using a three-dimensional representation of vector B obtained by the computation

Interaction Magnetic Force Calculation of Permanent Magnets Using Magnetization Charges and Discretization Technique

“…Many authors have proposed different methods for determining the magnetic field generated by permanent magnets of different shapes (Muscia, 2012;Tsai & Hsu, 2007;Zhang et al, 2000) and different approaches for determining interaction forces between them Ravaud et al, 2009aRavaud et al, , 2010Greconici et al, 2010). Simplified and robust formulations of the interaction forces created by permanent magnets are proposed.…”

Evaluation of Forces and Torques Generated by Toroidal Helicoidal Magnetic Fields

“…Moreover, τ Ws correctly decreases when W tends to K m , that is when |r WUm | increases and the corresponding moduli |r W | and |r W | decrease [see Figure 6(b), Eqs. (B2), (26), (32), (38) and the trends of τ Ws (ξ, |r WUm |)].…”

“…The magnetic inductions B Sa (P ) and B Sb (P ) have been computed with the magnetic charges method [23][24][25][26][27][28][29][30] as illustrated in Section 3. The choice of the points was performed following the procedure described in [6].…”

“…In order to perform the computation of the forces and moments applied by the magnet A to the magnet B the magnetic charges method [23][24][25][26][27][28][29][30] has been considered. This approach integrates Maxwell equations…”

“…Additionally, the time computation was very high and also various 3D CAD/CAE models were very difficult to manage. On the contrary, even though complex formulations are necessary, the magnetic charges method [23][24][25][26][27][28][29][30] allows a quick and accurate evaluation of the forces/moments applied to the moving permanent magnet E. In the following paragraphs we describe how the magnetic charges model has been implemented to perform the calculations and the results obtained regarding certain relative positions between the magnets A and E.…”