Numerical and experimental study of dynamics of two pendulums under a magnetic field

In this article, a two-degree-of-freedom system consisting of two pendulums with magnets embedded in a variable magnetic field is investigated experimentally and numerically. Pivots of the pendulums are coupled by an elastic element. The magnetic interaction originates from permanent magnets, mounted at free ends of the pendulums and current-powered air coils underneath. A novel model for the magnetic force is proposed and verified experimentally. Nonlinear dynamics of the system is examined by means of time series, bifurcation diagrams, phase portraits, and Poincaré sections. Regions of chaotic and regular motion are predicted numerically and justified experimentally. Multiperiodic motion and coexisting solutions are detected, and pictures in basins of their attraction are reported, among other.

Download Full-text

Research on the Magnetic Force of a Blood Pump Driven by Large Gap External Magnetic Field

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.271-272.1636 ◽

2012 ◽

Vol 271-272 ◽

pp. 1636-1640

Author(s):

Xiao Yan Tang ◽

Zhong Yun ◽

Chuang Xiang

Keyword(s):

Magnetic Field ◽

Permanent Magnet ◽

Magnetic Force ◽

Permanent Magnets ◽

Magnetic Field Intensity ◽

Current Theory ◽

Calculation Model ◽

Blood Pump ◽

Single Turn ◽

The Magnetic Field

The calculation model of the single turn rectangle current carrying coil was established. The theoretic formula for calculating the magnetic field intensity of any point in space was derived. For a pair of radial magnetizing permanent magnets, the formula for calculating the magnetic force of permanent magnet in the magnetic field was deduced based on the equivalent current theory of permanent magnet. According to the formula, the influencing factors and the changing rules for the magnetic force of permanent magnet can be seen directly: the current, the coil turns are proportional to its magnetic force, while the coupling distance is inversely proportional to its magnetic force.

Download Full-text

Development of an undulator with a variable magnetic field profile

Journal of Synchrotron Radiation ◽

10.1107/s1600577521000989 ◽

2021 ◽

Vol 28 (2) ◽

pp. 404-409

Author(s):

Takashi Tanaka ◽

Yuichiro Kida ◽

Ryota Kinjo ◽

Tadashi Togashi ◽

Hiromitsu Tomizawa ◽

...

Keyword(s):

Magnetic Field ◽

Magnetic Force ◽

Mechanical Load ◽

Magnetic Measurement ◽

Variable Magnetic Field ◽

Linear Actuator ◽

Free Electron Lasers ◽

Magnetic Field Profile ◽

New Concepts

An undulator generating a magnetic field whose longitudinal profile is arbitrarily varied has been developed, which is one of the key components in a number of proposed new concepts in free-electron lasers. The undulator is composed of magnet modules, each of which corresponds to a single undulator period, and is driven by a linear actuator to change the magnetic gap independently. To relax the requirement on the actuator, the mechanical load on each module due to magnetic force acting from opponent and adjacent modules is reduced by means of two kinds of spring systems. The performance of the constructed undulator has been successfully demonstrated by magnetic measurement and characterization of synchrotron radiation.

Download Full-text

Comparison of closed-form solutions to experimental magnetic force between two cylindrical magnets

EUREKA Physics and Engineering ◽

10.21303/2461-4262.2021.001955 ◽

2021 ◽

pp. 141-146

Author(s):

Sampart Cheedket ◽

Chitnarong Sirisathitkul

Keyword(s):

Magnetic Field ◽

Closed Form ◽

Magnetic Force ◽

Permanent Magnets ◽

Magnetic Levitation ◽

Closed Form Solution ◽

Vertical Tube ◽

Form Solution ◽

Closed Form Solutions ◽

Set Up

The force between permanent magnets implemented in many engineering devices remains an intriguing problem in basic physics. The variation of magnetic force with the distance x between a pair of magnets cannot usually be approximated as x-4 because of the dipole nature and geometry of magnets. In this work, the force between two identical cylindrical magnets is accurately described by a closed-form solution. The analytical model assumes that the magnets are uniformly magnetized along their length. The calculation, based on the magnetic field exerted by one magnet on the other along the direction of their orientation, shows a reduction in the magnetic force with the distance x and a dependence on the size parameters of magnets. To verify the equation, the experiment was set up by placing two cylindrical neodymium iron boron type magnets in a vertical tube. The repulsive force between the identical upper and lower magnets of 2.5 cm in diameter and 7.5 cm in length was measured from the weight on the top of the upper magnet. The resulting separation between the magnets was recorded as x. The forces measured at x=0.004-0.037 m differ from the values calculated using the analytic solution by -0.55 % to -13.60 %. The calculation also gives rise to a practical remnant magnetic field of 1.206 T. When x is much large than the equation of force is approximated as a simple form proportional to 1/x-4. The finding can be directly used in magnetic levitation as well as applied in calculating magnetic fields and forces in other systems incorporating permanent magnets.

Download Full-text

Rayleigh-Bénard Convection of Paramagnetic Liquid under a Magnetic Field from Permanent Magnets

Symmetry ◽

10.3390/sym12030341 ◽

2020 ◽

Vol 12 (3) ◽

pp. 341

Author(s):

Kengo Wada ◽

Masayuki Kaneda ◽

Kazuhiko Suga

Keyword(s):

Magnetic Field ◽

Heat Transfer ◽

Magnetic Induction ◽

Magnetic Force ◽

Permanent Magnets ◽

Cell Pattern ◽

Benard Convection ◽

Rayleigh Benard Convection ◽

Rayleigh Benard ◽

High Magnetic Induction

The convection control is important in terms of the heat transfer enhancement and improvement of the applied devices and resultant products. In this study, the convection control by a magnetic field from block permanent magnets is numerically investigated on the Rayleigh-Bénard convection of paramagnetic fluid. To enhance the magnetic force from the available permanent magnets, pairs of alternating-pole magnets are employed and aligned near the bottom heated wall. The lattice Boltzmann method is employed for the computation of the heat and fluid flow with the consideration of buoyancy and magnetothermal force on the working fluid. It is found that, since the magnetic force at the junction of pair magnets becomes strong remarkably and in the same direction as the gravity, descending convection flow is locally enhanced and the pair of symmetrical roll cells near the magnet junction becomes longitudinal. The local heat transfer corresponds to the affected roll cell pattern; locally enhanced at the magnet junctions and low heat transfer area is shifted aside the magnet outer edge. The averaged Nusselt number on the hot wall also increases proportionally to the magnetic induction but it is saturated at high magnetic induction. This suggests the roll cell pattern is no more largely affected at extremely-high magnetic induction.

Download Full-text

Review on the Actively-Controlled Colloidal Dampers and Investigations on a Colloidal Damper Rendered Controllable under the Variable Magnetic Field Generated by Moving Permanent Magnets

Newest Updates in Physical Science Research Vol. 7 ◽

10.9734/bpi/nupsr/v7/9399d ◽

2021 ◽

pp. 88-115

Author(s):

Barenten Suciu

Keyword(s):

Magnetic Field ◽

Permanent Magnets ◽

Variable Magnetic Field

Download Full-text

Analysis of vibration energy harvester with magnetic spring

ITM Web of Conferences ◽

10.1051/itmconf/20181901030 ◽

2018 ◽

Vol 19 ◽

pp. 01030

Author(s):

Marcin Kulik ◽

Rafał Gabor ◽

Mariusz Jagieła

Keyword(s):

Magnetic Field ◽

Computer Simulation ◽

Resonance Frequency ◽

External Force ◽

Permanent Magnets ◽

Energy Harvester ◽

Magnetic Interaction ◽

Vibration Energy ◽

Vibration Energy Harvester ◽

Numerical Optimisation

In paper an electromagnetic energy harvester with two fixed permanent magnets and one moving suspended vertically by the magnetic interaction between them. The external force imposed on the system causes displacement of the magnet whose magnetic field induces emf in the coil wound around it. In order to obtain the resonance frequency around 25 Hz, the numerical optimisation was carried out. The measured frequency characteristics of the manufactured system compare well with results of computer simulation.

Download Full-text

II. The measurement of magnetic hysteresis

Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character ◽

10.1098/rsta.1902.0002 ◽

1902 ◽

Vol 198 (300-311) ◽

pp. 33-104 ◽

Cited By ~ 4

Keyword(s):

Magnetic Field ◽

Magnetic Force ◽

Permanent Magnets ◽

Magnetic Hysteresis ◽

Physical Processes ◽

Mathematical Expressions ◽

Sheet Iron ◽

Standard Specimens ◽

Simple Instrument ◽

Energy Dissipated

1. Two ideal physical processes have been devised as the foundations of two methods of deducing mathematical expressions for the energy dissipated in magnetic material through magnetic hysteresis; these processes are due to Professor E. Warburg and to the late Dr. J. Hopkinson. In Warburg’s theory the specimen, in the form of a slender wire, is placed in a magnetic field due to a pair of permanent magnets so arranged as to produce magnetic force parallel to the length of the specimen. The mechanical work spent in moving these magnets through such a cycle of changes of position, that the iron is subjected to a cycle of magnetic changes, is clearly equal to the energy dissipated on account of magnetic hysteresis in the specimen. In terms of the magnetic quantities the energy dissipated per cub. centim. per cycle is — ∫I d H or ∫H d I ergs, where H is the magnetic force and I the intensity of magnetisation. Professor J. A. Ewing has applied the principle involved in Warburg’s theory to the design of a simple instrument by which the hysteresis of any specimen of sheet iron (for the range of induction B = 4000 to B = - 4000 C. G. S. units approximately) is determined by comparison with two standard specimens supplied with the instrument, and previously tested for hysteresis by the ballistic method. The principle has also been employed by W. S. Franklin, by H. S. Webb, and by G. L. W. Gill to obtain absolute determinations of hysteresis.

Download Full-text