Mathematical Model of Two-Bridge Multi-Shouldered Adjustable Rectifier Unit Based on Transformer with Rotating Magnetic Field Equipped with Odd Section Count of Both Circular Windings

The purpose of the research under consideration is to develop a mathematical model to calculate the trajectories of the ferromagnetic operating elements (millstones) of an electromagnetic mill, moving in a rotating magnetic field under electrodynamic and hydrodynamic resistance forces being limited by the space of the mill’s working chamber. The millstone motion is described through the equations of plane motion of arbitrary-shaped two-dimensional body. The driving forces of this motion are determined on the basis of the approximation of the tabulated functions connecting the module and the orientation of the equivalent force applied to the millstone, with its position in the working chamber and composite MMF phase of mill inductor winding. These tabulated functions are derived from the estimation of the magnetic field inside a working chamber with millstones, in two-dimensional quasi-stationary approximation, using FEM analysis. The publication contains the approximation algorithm for these tabulated vector functions of a vector argument, mathematical statement of millstones trajectories calculating, and analysis of mathematical experiments results that make it possible to evaluate the adequacy of the model. The developed tool enables conducting quantitative analysis of grinding/mixing process and will help to establish relationships between the electromagnetic mill design parameters and its performance. References 21, figures 6.

Download Full-text

Shear coefficient of spin viscosity estimation through velocity profiles of a ferrofluid under the effect of an external rotating magnetic field of low amplitude and frequency

Magnetohydrodynamics ◽

10.22364/mhd.57.2.1 ◽

2021 ◽

Vol 57 (2) ◽

pp. 139-160

Keyword(s):

Magnetic Field ◽

Mathematical Model ◽

Numerical Solution ◽

Rotating Magnetic Field ◽

Shear Coefficient ◽

Definition Of ◽

Low Amplitude ◽

The Mathematical Model ◽

Numerical Strategy

The present article describes a numerical strategy for the estimation of the shear coefficient of spin viscosity for a ferrofluid sample confined to a cylindrical container and exposed to the effect of an external rotating magnetic field with a low amplitude and frequency. As far as we know, there are no experimental measurements of such coefficient. Furthermore, the few analytical values reported differ in several orders of magnitude. First, we describe briefly the mathematical model of the system and its numerical solution. Then, the definition of the direct and inverse problems is given as a part of the methodology for estimating such coefficient. Finally, we solve the inverse problem using simulated measurements and two global optimization algorithms. We generate this type of measurements by adding white Gaussian noise signals to the numerical solution of the ferrohydrodynamic mathematical model. Several noise levels in the range of 10 to 40 dB were used to increase the number of scenarios for validation purpose. Results showed an excellent agreement between the estimated values and those used in the numerical solution of the mathematical model. A statistical analysis revealed a normal distribution that was dependent on the noise level. This variation did not affect the results, but showed instead the validity of the proposed method. Additionally, this strategy stands as a computational tool for validating experimental results of the future in situ measurements. Tables 7, Figs 11, Refs 17.

Download Full-text