scholarly journals MATHEMATICAL MODEL TO CALCULATE THE TRAJECTORIES OF ELECTROMAGNETIC MILL OPERATING ELEMENTS

2021 ◽  
Vol 2021 (2) ◽  
pp. 26-34
Author(s):  
O. Makarchuk ◽  
◽  
D. Calus ◽  
V. Moroz ◽  
◽  
...  
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Driving Forces ◽  
Fem Analysis ◽  
Plane Motion ◽  
Rotating Magnetic Field ◽  
Hydrodynamic Resistance ◽  
Design Parameters ◽  
Two Dimensional ◽  
Working Chamber

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.

NUMERICAL MODELING OF INDUCTION HEATING FOR TWO-DIMENSIONAL GEOMETRIES

1993 ◽  
Vol 03 (06) ◽  
pp. 805-822 ◽  
Author(s):  
S. CLAIN ◽  
J. RAPPAZ ◽  
M. SWIERKOSZ ◽  
R. TOUZANI
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Numerical Method ◽  
Induction Heating ◽  
Two Dimensional ◽  
Time Periodicity ◽  
Model Equations ◽  
Thermal Phenomena ◽  
The Magnetic Field ◽  
Different Time Scales

We present both a mathematical model and a numerical method for simulating induction heating processes. The geometry of the conductors is cylindrical and the magnetic field is assumed to be parallel to the invariance axis. The model equations have current tension as prescribed data rather than current intensity. In particular, the formulation of the electromagnetic problem uses the magnetic field as the unknown function. The numerical method takes into account the time periodicity of the prescribed tension and deals with the two different time scales of electromagnetic and thermal phenomena.

Interaction of a pair of ferrofluid drops in a rotating magnetic field

2018 ◽  
Vol 846 ◽  
pp. 121-142 ◽  
Author(s):  
Mingfeng Qiu ◽  
Shahriar Afkhami ◽  
Ching-Yao Chen ◽  
James J. Feng
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Hydrodynamic Interaction ◽  
Dipole Interaction ◽  
Rotating Magnetic Field ◽  
Viscous Drag ◽  
Planetary Motion ◽  
Two Dimensional ◽  
Initial Separation ◽  
Mutual Induction

We use two-dimensional numerical simulation to study the interaction between a pair of ferrofluid drops suspended in a rotating uniform magnetic field. Numerical results show four distinct regimes over the range of parameters tested: independent spin, planetary motion, drop locking and direct coalescence. These are in qualitative agreement with experiments, and the transition between them can be understood from the competition between magnetophoretic forces and viscous drag. We further analyse in detail the planetary motion, i.e. the revolution of the drops around each other while each spins in phase with the external magnetic field. For drops, as opposed to solid microspheres, the interaction is dominated by viscous sweeping, a form of hydrodynamic interaction. Magnetic dipole–dipole interaction via mutual induction only plays a secondary role. This insight helps us explain novel features of the planetary revolution of the ferrofluid drops that cannot be explained by a dipole model, including the increase of the angular velocity of planetary motion with the rotational rate of the external field, and the attainment of a limit separation between the drops that is independent of the initial separation.

Spin-up of a magnetically driven tornado-like vortex

2013 ◽  
Vol 736 ◽  
pp. 641-662 ◽  
Author(s):  
Tobias Vogt ◽  
Ilmārs Grants ◽  
Sven Eckert ◽  
Gunter Gerbeth
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Driving Forces ◽  
Axisymmetric Flow ◽  
Rotating Magnetic Field ◽  
Turbulent Vortex ◽  
Force Magnitude ◽  
Order Of Magnitude ◽  
Converging Flow ◽  
Concentration Condition

AbstractThe spin-up of a concentrated vortex in a liquid metal cylinder with a free surface is considered experimentally and numerically. The vortex is driven by two flow-independent magnetic body forces. A continuously applied rotating magnetic field provides the source of the angular momentum. A pulse of about one order of magnitude stronger travelling magnetic field drives a converging flow that temporarily focuses this angular momentum towards the axis of the container. A highly concentrated vortex forms that produces a funnel-shaped surface depression. We explore experimentally the duration, the depth and the conditions of formation of this funnel. Additionally, we measure the axial velocity and calculate the axisymmetric flow field of this transient vortex at a lower force magnitude. The spin-up vortex is similar to the corresponding developed time-averaged turbulent vortex driven by the same magnetic forces (Grants et al., J. Fluid Mech., vol. 616, 2008, pp. 135–152). There are two main differences. First, the maximum swirl concentration condition cannot be expressed as a constant ratio of the two driving forces. Second, a much higher degree of swirl concentration is feasible. We explain these differences as due to a much lower turbulence during the spin-up.

scholarly journals A comparative analysis of the parameters of a rotating magnetic field inductor when using concentric and loop windings

2021 ◽  
pp. 12-18
Author(s):  
V. I. Milykh ◽  
M. G. Tymin
Keyword(s):  
Magnetic Field ◽  
Single Layer ◽  
Rotating Magnetic Field ◽  
Geometrical Parameters ◽  
Stator Winding ◽  
Electromagnetic Parameters ◽  
Working Chamber ◽  
Three Phase ◽  
Technological Processing ◽  
The Magnetic Field

Introduction. Three-phase inductors of a rotating magnetic field are used in grinders, separators and stirrers for the technological processing of bulk and liquid substances. This occurs in a cylindrical working chamber under the influence of ferromagnetic elements in the form of pieces of iron wire, which move together with the field. Problem. By analogy with three-phase induction motors, for the stator of inductors a concentric winding is adopted, which is a diametric single-layer winding. When moving from such motors to an inductor, its operating conditions have changed due to the significantly increased non-magnetic space inside the inductor compared to the motor clearances. The difference in the frontal parts of the phase windings has become essential for the electromagnetic parameters and the structure of the magnetic field in the inductor working chamber. Therefore, a loop shortened stator winding, which is symmetrical, can be considered as an alternative to a concentric diametric winding. Goal. The aim of the work is to compare the dimensional and electromagnetic parameters of a rotating magnetic field inductor in two versions of its three-phase winding: concentric single-layer diametrical and loop shortened two-layer. Methodology. Comparison of the windings is carried out through a detailed analysis of the geometrical parameters of their frontal parts, as well as through numerical-field calculations of the electromagnetic parameters of the inductor as a whole and the distribution of the magnetic field in its working chamber. Results. A significant difference in the geometrical parameters of the frontal parts of the two windings under inductor conditions was revealed. The loop version of the winding makes it possible to reduce the length of the winding conductor, its active resistance, as well as the reactance of its frontal dissipation. At the same time the asymmetry of the phase windings is excluded and an increase in the homogeneity of the magnetic field in the inductor working chamber is provided. Originality. The scientific novelty of the work lies in the development of a method of comparative analysis of the windings under the conditions of the rotating magnetic field inductor and in revealing the advantages of a loop shortened winding compared to the used concentric diametric winding. Practical value. The loop shortened stator winding recommended for the inductor will eliminate the asymmetry of its electromagnetic system. Thereby, the quality of its work in the technological processing of different substances is significantly increased due to ensuring the homogeneity of the magnetic field in the working chamber. At the same time, the copper conductor of the winding is still saved, and the efficiency of the inductor is also increased by reducing the power of electrical losses.

Sign in / Sign up

Export Citation Format

Share Document