Force effect of a circular rotating magnetic field of a cylindrical electric inductor on a ferromagnetic particle in process reactors

The object of research is the force effect of a circular magnetic field of cylindrical inductors with alternating current windings on the actuator element of technological reactors – a ferromagnetic particle. Technologies using a rotating magnetic field and ferromagnetic particles (RMF and FP) are increasingly used in industry, in devices for fine and ultra-fine grinding, mixing and activation, in the construction and chemical industries, in energy-saving and environmental systems.In previous studies, the authors proposed a method for calculating the force effect on ferromagnetic particles (FP) of an elliptical rotating magnetic field (RMF) of an external cylindrical inductor with a symmetrical alternating current winding. In this work, based on this technique, formulas for the force effect on the FP of the fundamental harmonic of RMF of cylindrical inductors with different numbers of pole pairs are derived and analyzed.It is shown that for a hard magnetic and saturated magnetically soft (soft-magnetic) particle in a circular field of a cylindrical inductor with the number of pole pairs greater than one, the magnitude of the magnetic displacement force does not depend on the orientation of the magnetic moment of the ferromagnetic particle, and the direction of action of this force is determined by the angle between the circular field induction vector and the magnetic moment of the particle. While maintaining the similarity of the inductors and the equality of the amplitude of the magnetic induction on the surface of the inductor bore, the magnetic displacement force does not retain the similarity, in particular, while maintaining the values of the magnetic moment of the particle, this force is inversely proportional to the radius of the bore of the cylindrical inductor.Examples are given of the use of formulas for calculating the ratio of displacement forces to the weight of a particle and the calculation of forces for an unsaturated soft-magnetic particle, where, due to the dependence of the magnetic moment on the field strength, the calculation formulas are modified and take on a slightly different form than the formulas for a particle with a constant modulus magnetic moment.The research results will be useful for engineers and researchers involved in the research, development, design and operation of reactors with RMF and FP technologies.