Mechanical Properties of a Ferrofluid Seal: Three-Dimensional Analytical Study Based on the Coulombian Model

Abstract—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 mag-netic energy of the ferrofluid seal by using only the three-dimensional equations of the magnetic field created by ring permanent magnets ra-dially magnetized. Our study corresponds to the specific case when the ferrofluid is submitted to a very high magnetic field. Under these conditions, 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 kAm−1. Consequently, the magnetic parti-cles 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 and an inner non-magnetic 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. More-over, 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. ha l-0