A General Method for Calculating the External Magnetic Field from a Cylindrical Magnetic Source using Toroidal Functions

Selvaggi, Jerry P.; Salon, S.J.; Chari, O Kwon Cvk

doi:10.2172/881294

Cited by 3 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, the H-field can be calculated using Heuman's Lambda function [33] or using separation of variables in polar coordinates applied to magnetic gears [34]. Selvaggi [35] introduce a Hfield calculation employing toroidal harmonics.…”

Section: A Literature Review On Analytical Field Computationmentioning

confidence: 99%

Generalized and Reduced Analytical Formulation for Ultra-Fast 3-D Field and Vector Potential Calculation From Arch-Shaped Axially Magnetized Bodies in Electrical Machines

2020

View full text Add to dashboard Cite

Arch-shaped axially magnetized bodies tend to appear frequently in electrical machine analysis such as in overhang parts of classical radial-flux machines as well as in main parts of axial-flux machines. The calculation of 3-D fields originating from these bodies is demanding. 3-D FEA suffers from high computational burden as well as no knowledge of the field origin. Analytic techniques involve the use of elliptic integrals and complex numbers for numerical evaluation, which makes them significantly slower than 3-D FEA.In this paper, a new analytical technique is proposed to speed up the computation by factor 20 for the global magnetic field created by a generic magnetized body, by removing complex numbers and reducing the analytic equations significantly without any loss of precision. As a result, it can compete with conventional 3-D FEA. In addition, integral methods may contribute to the wider use of parallel processing techniques. The original expressions for the vector potential are also provided, which has its own benefits and applications. Finally, the showcased magnetized body is assessed against 3-D FEA and discussed in terms of practical applications.

show abstract

Section: A Literature Review On Analytical Field Computationmentioning

confidence: 99%

Generalized and Reduced Analytical Formulation for Ultra-Fast 3-D Field and Vector Potential Calculation From Arch-Shaped Axially Magnetized Bodies in Electrical Machines

2020

View full text Add to dashboard Cite

show abstract

“…A number of recent articles by Cohl et al have made useful contributions to potential theory and multipole analysis [3,6,19]. The authors of this paper have used, with great success, the toroidal expansion to solve a number of problems in electromagnetics [4,[20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 97%

The Newtonian force experienced by a point mass near a finite cylindrical source

Selvaggi¹,

Salon²,

Chari³

2007

Class. Quantum Grav.

View full text Add to dashboard Cite

The Newtonian gravitational force experienced by a point mass located at some external point from a thick-walled, hollow and uniform finite circular cylindrical body was recently solved by Lockerbie, Veryaskin and Xu (1993 Class. Quantum Grav. 10 2419). Their method of attack relied on the introduction of the circular cylindrical free-space Green function representation for the inverse distance which appears in the formulation of the Newtonian potential function. This ultimately leads Lockerbie et al to a final expression for the Newtonian potential function which is expressed as a double summation of even-ordered Legendre polynomials. However, the kernel of the cylindrical free-space Green function which is represented by an infinite integral of the product of two Bessel functions and a decaying exponential can be analytically evaluated in terms of a toroidal function. This leads to a simplification in the mathematical analysis developed by Lockerbie et al. Also, each term in the infinite series solution for the Newtonian potential function can be expressed in closed form in terms of elementary functions. The authors develop the Newtonian potential function by employing toroidal functions of zeroth order or Legendre functions of half-integral degree, Q m− 1 2 (β) (Bouwkamp and de

show abstract

“…10 Also, it has been used for calculating the external field from permanent magnet motors. [11][12][13][14] It has recently been used for determining the gravitational potential. [15][16][17] Figure 1 illustrates the geometry of the problem.…”

Section: Introductionmentioning

confidence: 99%

An application of toroidal functions in electrostatics

Selvaggi

Salon

Chari

2007

American Journal of Physics

View full text Add to dashboard Cite

Quantitative analysis of the damping of magnet oscillations by eddy currents in aluminum foil Am. J. Phys. 80, 804 (2012) Rolling magnets down a conductive hill: Revisiting a classic demonstration of the effects of eddy currents Am. J. Phys. 80, 800 (2012) A semiquantitative treatment of surface charges in DC circuits Am. J. Phys. 80, 782 (2012) Relation between Poisson and Schrödinger equations Am. J. Phys. 80, 715 (2012) Magnetic dipole moment of a moving electric dipole Am.A method employing the use of toroidal functions is introduced for calculating the scalar potential and the electric field from a charged conducting ring. This method is an alternative to the well-known elliptic integral formulation and is usually easier to formulate than the elliptic integral solution.

show abstract

A General Method for Calculating the External Magnetic Field from a Cylindrical Magnetic Source using Toroidal Functions

Cited by 3 publications

References 8 publications

Generalized and Reduced Analytical Formulation for Ultra-Fast 3-D Field and Vector Potential Calculation From Arch-Shaped Axially Magnetized Bodies in Electrical Machines

Generalized and Reduced Analytical Formulation for Ultra-Fast 3-D Field and Vector Potential Calculation From Arch-Shaped Axially Magnetized Bodies in Electrical Machines

The Newtonian force experienced by a point mass near a finite cylindrical source

An application of toroidal functions in electrostatics

Contact Info

Product

Resources

About