This paper presents a general method for studying the mechanical properties of a ferrofluid seal by using a three-dimensional analytical approach based on the coulombian model of a magnet. The fundamental Maxwell's equations lead us to define the concept of magnetic energy of the ferrofluid seal by using only the threedimensional equations of the magnetic field created by ring permanent magnets radially magnetized. Our study corresponds to the specific case when the ferrofluid is submitted to a very high magnetic field. Under these conditions, we assume that the mechanical properties of the ferrofluid depend only on the magnetic field created by the permanent magnets. Throughout this paper, the remanence polarization J of the magnets used is higher than 1T. The magnetic field we use in order to align the magnetic particles is very intense, greater than 400 kA/m. Consequently, the magnetic particles are assumed to be saturated and the magnetic field they create can be omitted. In this paper, a cylindrical structure consisting of two outer ring permanent magnets radially magnetized and an inner nonmagnetic cylinder is considered. In addition, a ferrofluid seal is placed between them. The calculation of the magnetic pressure of the ferrofluid seal has been analytically established in three dimensions in order to determine its shape. Moreover, the geometrical evolution of the ferrofluid seal shape is presented when the inner non-magnetic cylinder crushes the ferrofluid seal. The radial stiffness of the ferrofluid seal is determined in three dimensions when the inner cylinder is decentered. Furthermore, a way of obtaining the ferrofluid seal static capacity is discussed.
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