We present analytical formulations, based on a coulombian approach, of the magnetic field created by permanent-magnet rings. For axially magnetized magnets, we establish the expressions for the three components. We also give the analytical 3-D formulation of the created magnetic field for radially magnetized rings. We compare the results determined by a 2-D analytical approximation to those for the 3-D analytical formulation, in order to determine the range of validity of the 2-D approximation.

No abstract

This paper deals with the calculation of the force and the stiffness between two ring permanent magnets whose polarization is axial. Such a configuration corresponds to a passive magnetic bearing. All the calculations are determined by using the Coulombian model. This paper also discusses the optimal ring dimensions in order to have a great force or a great stiffness between the rings. Such properties are commonly searched in passive magnetic bearings and we propose a three-dimensional method allowing to optimize these parameters. Furthermore, an important result is established in this paper: the exact relative position of the rings for which the force is the strongest depends on the air gap dimension. As the expressions presented in this paper give this exact relative position, manufacturers can easily optimize their passive magnetic bearings. It is noted that this result is new because the curvature effect is taken into account in this paper. Furthermore, such semi-analytical expressions are more precise than the numerical evaluation of the magnetic forces obtained with the finite element method. In addition, semi-analytical expressions have a low computational cost whereas the finite element method has a high one. Thereby, as shown in this paper, such calculations allow an easy optimization of quadripolar lenses or devices using permanent magnets. Index TermsMagnetic forces, analytical calculation, ring permanent magnet, magnetic bearing

This paper deals with the calculation of the force and the stiffness between two ring permanent magnets whose polarization is axial. Such a configuration corresponds to a passive magnetic bearing. All the calculations are determined by using the Coulombian model. This paper also discusses the optimal ring dimensions in order to have a great force or a great stiffness between the rings. Such properties are commonly searched in passive magnetic bearings and we propose a three-dimensional method allowing to optimize these parameters. Furthermore, an important result is established in this paper: the exact relative position of the rings for which the force is the strongest depends on the air gap dimension. As the expressions presented in this paper give this exact relative position, manufacturers can easily optimize their passive magnetic bearings. It is noted that this result is new because the curvature effect is taken into account in this paper. Furthermore, such semi-analytical expressions are more precise than the numerical evaluation of the magnetic forces obtained with the finite element method. In addition, semi-analytical expressions have a low computational cost whereas the finite element method has a high one. Thereby, as shown in this paper, such calculations allow an easy optimization of quadripolar lenses or devices using permanent magnets. Index TermsMagnetic forces, analytical calculation, ring permanent magnet, magnetic bearing

Articles you may be interested inDevelopment of a highly efficient hard disk drive spindle motor with a passive magnetic thrust bearing and a hydrodynamic journal bearingThe stiffness of magnetic bearings composed of only two permanent magnet rings is limited. To increase this stiffness, stacked structures are used. Conventionalstacking is obtained by placement of the magnetizations in opposition. This article presents another type of stacking with rotating magnetization direction (RMD), which improves the stiffness by about a factor of 2 in comparison with the conventional stack. 6634

Abstract-This paper presents the exact analytical formulation of the three components of the magnetic field created by a radially magnetized tile permanent magnet. These expressions take both the magnetic pole surface densities and the magnetic pole volume density into account. So, this means that the tile magnet curvature is completely taken into account. Moreover, the magnetic field can be calculated exactly in any point of the space, should it be outside the tile magnet or inside it. Consequently, we have obtained an accurate 3D magnetic field as no simplifying assumptions have been used for calculating these three magnetic components. Thus, this result is really interesting. Furthermore, the azimuthal component of the field can be determined without any special functions. In consequence, its computational cost is very low which is useful for optimization purposes. Besides, all the other expressions obtained are based on elliptic functions or special functions whose numerical calculation is fast and robust and this allows us to realize parametric studies easily. Eventually, we show the interest of this formulation by applying it to one example: the calculation and the optimization of alternate magnetization magnet devices. Such devices are commonly used in various application fields: sensors, motors, couplings, etc. The point is that the total field is calculated by using the superposition theorem and summing the contribution to the field of each tile magnet in any point of the space. This approach is a good alternative to a finite element method because the calculation of the magnetic field is done without any simplifying assumption.

Abstract-This paper presents an improvement of the calculation of the magnetic field components created by ring permanent magnets. The three-dimensional approach taken is based on the Coulombian Model. Moreover, the magnetic field components are calculated without using the vector potential or the scalar potential. It is noted that all the expressions given in this paper take into account the magnetic pole volume density for ring permanent magnets radially magnetized. We show that this volume density must be taken into account for calculating precisely the magnetic field components in the near-field or the far-field. Then, this paper presents the component switch theorem that can be used between infinite parallelepiped magnets whose cross-section is a square. This theorem implies that the magnetic field components created by an infinite parallelepiped magnet can be deducted from the ones created by the same parallelepiped magnet with a perpendicular magnetization. Then, we discuss the validity of this theorem for axisymmetric problems (ring permanent magnets). Indeed, axisymmetric problems dealing with ring permanent magnets are often treated with a 2D approach. The results presented in this paper clearly show that the two-dimensional studies dealing with the optimization of ring permanent magnet dimensions cannot be treated with the same precisions as 3D studies.

No abstract