Levitation of Conductive and Magnetically Anisotropic Ball

Spałek, D.

doi:10.1109/tmag.2018.2887216

Cited by 6 publications

(12 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us consider a magnetically anisotropic and conducting ball in an axially‐symmetric stationary field (Fig. 5 ) in which the axial component (far from the ball along the z ‐axis) is given by polynomial of N items (extension of [2, 3 ]) as follows:

B_{z} = B_{0} + \sum_{k = 1}^{N - 1} G_{k} z^{k},

where B 0 and G k are given constants.…”

Section: Magnetostatic Levitationmentioning

confidence: 99%

“…a) Maxwell stress tensor [2, 3, 5, 14, 16 ]

{bold-italicσ}_{z} = - H_{z} B + {bold-italici}_{z} \frac{1}{2} bold-italicH bold-italicB,

generalised method leads to the force

F_{z} = F_{M z} + normalΔ F,

where integral over the sphere including the ball with radius R is equal to

\begin{matrix} right leftthickmathspace.5em \\ F_{M z} & = - 2 π R^{2} \int_{0}^{π} (}{, - \frac{B_{z} B_{r}}{μ_{0}} + (\frac{B_{r}^{2}}{2 μ_{0}} + μ_{0} \frac{B_{θ}^{2}}{2 μ_{θ θ}^{2}}) \cos θ) \\ \cdot \sin θ normald θ, \end{matrix}

and Δ F is the volume integral of non‐zero value for the anisotropic ball ([2, 3 ], Appendix 1).…”

Section: Magnetostatic Levitationmentioning

confidence: 99%

“…Levitation driven by magnetic alternating field is often applied in many technological solutions and enables, e.g. spotless melting [1–4 ]. There is also a certain interest in electrostatic levitation forced by electric charge [5 ].…”

Section: Introductionmentioning

confidence: 99%

“…The paper considers both electrostatic and magnetostatic levitations driven only by material forces acting on dielectric, paramagnetic, and ferromagnetic materials. Static levitation forces act either separately [1, 7, 8 ] or together with other electromagnetic forces ([2, 4, 11–13 ] and Table 1 ).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Electrostatic and magnetostatic levitations of ball – forces, stability and oscillations frequencies

Spałek

2020

IET Science, Measurement &Amp; Technology

View full text Add to dashboard Cite

The study presents approaches to both electrostatic and magnetostatic levitations. For anisotropic balls, both dielectric and magnetic field distributions are derived in analytical forms by means of the variable separation method. Distributions are given by power functions and polynomials either Legendre's (for the electrostatic problem) or the associated polynomials (for the magnetostatic problem). The levitation forces are evaluated by means of four methods, i.e. Maxwell stress tensor generalised method, co‐energy method, material force density, and equivalent dipole analysis for both levitations. Levitation forces versus either electric permittivity or magnetic permeability are presented. The stability of the equilibrium points is investigated. The frequencies of free and damped oscillations are evaluated.

show abstract

B_{z} = B_{0} + \sum_{k = 1}^{N - 1} G_{k} z^{k},

where B 0 and G k are given constants.…”

Section: Magnetostatic Levitationmentioning

confidence: 99%

“…a) Maxwell stress tensor [2, 3, 5, 14, 16 ]

{bold-italicσ}_{z} = - H_{z} B + {bold-italici}_{z} \frac{1}{2} bold-italicH bold-italicB,

generalised method leads to the force

F_{z} = F_{M z} + normalΔ F,

where integral over the sphere including the ball with radius R is equal to

\begin{matrix} right leftthickmathspace.5em \\ F_{M z} & = - 2 π R^{2} \int_{0}^{π} (}{, - \frac{B_{z} B_{r}}{μ_{0}} + (\frac{B_{r}^{2}}{2 μ_{0}} + μ_{0} \frac{B_{θ}^{2}}{2 μ_{θ θ}^{2}}) \cos θ) \\ \cdot \sin θ normald θ, \end{matrix}

and Δ F is the volume integral of non‐zero value for the anisotropic ball ([2, 3 ], Appendix 1).…”

Section: Magnetostatic Levitationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Electrostatic and magnetostatic levitations of ball – forces, stability and oscillations frequencies

Spałek

2020

IET Science, Measurement &Amp; Technology

View full text Add to dashboard Cite

show abstract

“…Spałek [8], he proposed the solution of analytical method for maglev problem for conductive balls and magnetically anisotropic. The magnetic field uses swirl currents in the conductive balls and magnetic.…”

Section: Introductionmentioning

confidence: 99%

Model predictive control of magnetic levitation system

Alkurawy

Mohammed

2020

IJECE

View full text Add to dashboard Cite

In this work, we suggest a technique of controller design that applied to systems based on nonlinear. We inform the sufficient conditions for the stability of closed loop system. The asymptotic stability of equilibrium and the nonlinear controller can be applied to improvement the stability of Magnetic Levitation system(MagLev). The MagLev nonlinear nodel can be obtained by state equation based on Lagrange function and Model Predictive Control has been used for MagLev system.

show abstract

Electrostatic levitations of anisotropic dielectric oblate and prolate spheroids

Spałek

2023

Electr Eng

View full text Add to dashboard Cite

The paper presents analytical approach to electrostatic field for dielectric spheroids problem. For both oblate and prolate spheroids fields distributions are derived. The variable separation method is applied. Electrostatic force is evaluated with the help of the Maxwell stress tensor generalized method, material force density, coenergy and equivalent dipole. Levitation forces for both oblate and prolate dielectric spheroids versus axis permittivities and spheroids height are presented.

show abstract

Levitation of Conductive and Magnetically Anisotropic Ball

Cited by 6 publications

References 9 publications

Electrostatic and magnetostatic levitations of ball – forces, stability and oscillations frequencies

Electrostatic and magnetostatic levitations of ball – forces, stability and oscillations frequencies

Model predictive control of magnetic levitation system

Electrostatic levitations of anisotropic dielectric oblate and prolate spheroids

Contact Info

Product

Resources

About