Study of diamagnetically stabilized non-vertical levitation using the magnetic charge equivalence

Nemoianu, Iosif Vasile; Küstler, G.; Cazacu, Emil

doi:10.3233/jae-2012-1412

Cited by 4 publications

(8 citation statements)

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“…After achieving equilibrium, a way to establish whether it was stable or unstable along a certain direction was to estimate the corresponding discriminant of stability for that direction. This approach was considered to check for stability in the case of a single levitated magnet [27,28] or multiple levitated magnets. As a result of how it was defined (see Section 3.3), a negative value of the discriminant of stability was an indicator of unstable equilibrium.…”

Section: Context Of the Study And Simplifying Hypothesismentioning

confidence: 99%

Self-Organizing Equilibrium Patterns of Multiple Permanent Magnets Floating Freely under the Action of a Central Attractive Magnetic Force

et al. 2022

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The present communication revisits the almost century-and-a-half-old problem of some identical small magnets floating freely on the water’s surface under the action of a superimposing magnetic field created by a stronger magnet placed above them. Originally introduced and performed by Alfred Marshall Mayer and reported in a series of articles starting from 1878 onward, the proposed experiments were intended to provide a model (theoretical and educational) for the building block of matter that, at a microscopic level, is the atom. The self-organizing patterns formed by the repelling small magnets under the influence of a single attractive central force are presented in a slightly different reenactment of the original experiments. Although the set-up is characterized by an axially symmetric magnetostatic structure, and the floated magnets are all identical, the resulting equilibrium patterns are not necessarily symmetrical, as one would expect. To the authors’ best knowledge, the present communication proposes for the first time a quantitative approach to that extremely complex conceptual problem by providing a methodology for computing the equilibrium point coordinates in the case of n = 1…20 floating magnets, as proposed by the original A.M. Mayer experiments. A good agreement between the experiments and computed data was demonstrated for n = 2…15 (1st variant), but it was less accurate while still preserving the experimental set-up configurations for n = 15 (2nd variant)…20. Finally, this study draws the conclusions from the performed experiments and their corresponding computer simulations, identifies some open issues, and outlines possible solutions to address them, as well as future developments concerning the subject in general.

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Section: Context Of the Study And Simplifying Hypothesismentioning

confidence: 99%

Self-Organizing Equilibrium Patterns of Multiple Permanent Magnets Floating Freely under the Action of a Central Attractive Magnetic Force

et al. 2022

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“…Considering the floater as a small permanently magnetized body, its dipole moment modulus writes [17] 0 f r, f…”

Section: Antiparallel Vertical Levitation Principlesmentioning

confidence: 99%

“…An analytical evaluation of the Coulombian integral over the two rectangular pole faces of a magnet yields compact formulae for the flux density field components [17,18]. The superposition principle allows us to determine the total B filed z-component of as the sum of the B and B i z-components:…”

Section: Antiparallel Vertical Levitation Principlesmentioning

confidence: 99%

“…Consequently, the magnets can be reduced to uniform surface charge distributions only on their polar faces [14,15], with absolute value densities [16,17]: σ m, = B r, (for the lifter) and σ m,i = ½│χ│B r,f (for the floater image) [3]. The two quantities B r,  and B r,f represent the remanence of the two real magnets and χ the perpendicular magnetic susceptibility of the pyrolytic graphite plate.…”

Section: Antiparallel Vertical Levitation Principlesmentioning

confidence: 99%

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Theoretical and experimental evaluation on a counterintuitive diamagnetically stabilized levitation setup with permanent magnets

Küstler

Nemoianu

2013

2013 8th International Symposium on Advanced Topics in Electrical Engineering (Atee)

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We report a novel counterintuitive vertical levitation structure involving permanent magnets and at least one stabilizing diamagnetic piece. The setup consists of two permanent NdFeB magnets in a vertical inline configuration. A strong lifter magnet attracts a smaller magnet and compensates its weight. Stability at the equilibrium point is ensured by a diamagnetic pyrolytic graphite plate placed either above or below the levitated magnet. Compared to the classical vertical diamagnetic levitation cases, the magnetic moments of the magnets are antiparallel. Accepted tolerances during the magnetizing process lead to a visible anomaly of the levitated magnet equilibrium point position that apparently defies symmetry. First experiments and calculation results are presented. The proposed setup could find application as a highly sensitive tilt meter or in sensing magnetization angle errors.

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“…Magnetically levitated planar actuators, which greatly simplify the planar motion mechanism and reduce motion mass for realizing friction-less and wear-free high-speed and high-accuracy motion, have become the focus of the research on the high-speed and high-accuracy long-stroke motion system [1][2][3][4][5][6][7][8][9][10][11]. Since the kinematic accuracy of six-degree-of-freedom levitation motion is subjected to even slightest disturbance, the motion must be precisely controlled according to the kinetic characteristics of the system.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the eddy force disturbance on foil-wound coils in magnetic levitated planar motion

Zhou

Liu

et al. 2014

JAE

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Magnetically levitated planar actuators can simplify the planar motion mechanism and thus realize high-speed and high-accuracy motion. The accuracy in the shape of coil, a core part of magnetically levitated planar actuator, is crucial to the performance of actuator. Although the foil-wound coil has high forming precision, the strong eddy current generated in the motion of actuator may pose great interference to magnetic levitation and deteriorate system stability. Based on a thorough analysis of the eddy current and eddy-current force of foil-wound coils in the magnetically levitated planar motion, the paper proposes the calculation model for disturbing eddy force. Results from the simulation show that the model has a relatively high accuracy. It is also indicated that further predictive compensation for the eddy force in the control of precise magnetically levitated actuators can increase the kinematic accuracy and stability of magnetically levitated planar motion system.

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Study of diamagnetically stabilized non-vertical levitation using the magnetic charge equivalence

Cited by 4 publications

References 0 publications

Self-Organizing Equilibrium Patterns of Multiple Permanent Magnets Floating Freely under the Action of a Central Attractive Magnetic Force

Self-Organizing Equilibrium Patterns of Multiple Permanent Magnets Floating Freely under the Action of a Central Attractive Magnetic Force

Theoretical and experimental evaluation on a counterintuitive diamagnetically stabilized levitation setup with permanent magnets

Analysis of the eddy force disturbance on foil-wound coils in magnetic levitated planar motion

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