Magnetic pressure and shape of ferrofluid seals in cylindrical structures

Abstract

This paper presents a three-dimensional analytical model for studying the shape and the pressure of ferrofluid seals submitted to intense magnetic fields produced by permanent magnet ironless structures. This three-dimensional analytical approach is based on the exact calculation of the magnetic field components created by ring permanent magnets whose polarizations are either radial or axial. We assume that the ferromagnetic particles of the ferrofluid are saturated and the static behaviour of the ferrofluid seal depends on both the magnetic field produced by the permanent magnets and the saturation magnetization of the ferrofluid particles. In our applications, ferrofluid seals are always submitted to very high magnetic fields. Consequently, the accurate knowledge of the ferrofluid seal shape as well as the magnetic pressure inside the ferrofluid seal is very useful for the design of devices using both permanent magnets and ferrofluid seals. It is emphasized here that our structures are completely ironless and thus, there are no iron-base piston for these structures. Then, this paper makes a review of the main structures using ring permanent magnets and ferrofluid seals. For each ironless structure, the shape and the pressure of the ferrofluid seals are determined. To our knowledge, this way of characterizing the static behaviour of ferrofluid seals submitted to intense magnetic fields appears for the first time in the literature. Indeed, we think that a three-dimensional analytical model is interesting for such a study because it is simple to use and has a very low computational cost.

Magnetic Force Between Inclined Circular Loops (Lorentz Approach)

“…The vast majority of this attention has been given to the purely coaxial geometries [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. More recently the focus has been shifted to calculation of the mutual inductance and magnetic force between circular coils with lateral and angular misalignments [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Calculation of the Mutual Inductance and the Magnetic Force Between a Thick Circular Coil of the Rectangular Cross Section and a Thin Wall Solenoid (Integro-Differential Approach)

“…The differential coefficient is taken with respect to that coordinate. As is evident in [29][30][31][32][33][34][35][36][37][38][39][40], the magnetic force may be calculated by simple differentiation in cases where a general formula for the mutual inductance is available. This formula exists in our case, and the magnetic force between the coils can be calculated with the following expression:…”

Ironless transducer for measuring the mechanical properties of porous materials

“…It is made of a voice-coil motor such as those used in traditional electrodynamic loudspeakers. However, this motor is ironless, 21,22 and the viscoelastic suspension is replaced by ferrofluid seals 23 in order to vanish the major electrical and mechanical nonlinearities, 24,25 respectively. Furthermore, the motor is constituted by a stack of three permanent magnet rings 20 mm high with an inner diameter of 49.7 mm.…”

“…The inner face of the motor presents also a strong gradient of the magnetic field where the magnetic field reverses, i.e., at the interface between two rings. These regions, where the magnetic pressure is the most important, 23 define the position of ferrofluid seals, which guide the piston along the "x" direction 28,29 and ensure the airtightness between the two cavities ͑Fig. 3͒.…”