M.V.K. Chari

Calculating the external magnetic field from permanent magnets in permanent-magnet motors-an alternative method

We present an alternative method for calculating the magnetic field from a set of permanent magnets in a permanent-magnet motor. The method uses a cylindrical coordinate system to model the geometry of the structure enclosing the magnets. A Fourier series expansion yields an alternative to the more familiar multipole expansion given in spherical coordinates. The expansion is developed by using Greens function in cylindrical coordinates. A technique called charge simulation allows computation of an equivalent point charge distribution. Finally, Coulombs law is applied to express the magnetic scalar potential in a mathematically tractable form.

Analysis of the far field of permanent-magnet motors and effects of geometric asymmetries and unbalance in magnet design

In the design of permanent-magnet synchronous machines for naval applications, exterior magnetic fields are of interest. These decay at a rate depending on the number of poles, with magnetic fields due to a higher number of poles decaying more rapidly. We have developed multipole expansion methods to study the effects of geometric asymmetries and unbalanced pole strength on the components of the far field. We have found that, if there is an imbalance in the set of poles, the lower order decay of the unbalanced poles dominates in the far field, and the advantage of using a higher number of poles is diminished. Multipole expansion in combination with the charge simulation method offers a quick and easy method of determining effects of imbalance on the far field of motors at the design stage. We present the results for a variety of imbalances and pole numbers, and discuss the unbalanced terms due to the demagnetization and space imbalance. We also explain the behavior of the far-field decay with the aid of analytical expressions.

The application of finite element method analysis to eddy current nondestructive evaluation

The finite element method for the computation of eddy current fields is presented. The method is described for geometries with a one-component eddy current field. The use of the method for the calculation of the impedance of eddy current sensors in the vicinity of defects is shown. An example is given of the method applied to a C-magnet-type sensor positioned over a crack in a plane-conducting material.

Computation of the External Magnetic Field, Near-Field or Far-Field, from a Circular Cylindrical Magnetic Source using Toroidal Functions

A method is developed for computing the magnetic field from a circular or noncircular cylindrical magnetic source. A Fourier series expansion is introduced which yields an alternative to the more familiar spherical harmonic solution, Elliptic integral solution, or Bessel function solution. This alternate formulation coupled with a method called charge simulation allows one to compute the external magnetic field from an arbitrary magnetic source in terms of a toroidal expansion which is valid on any finite hypothetical external observation cylinder. In other words, the magnetic scalar potential or the magnetic field intensity is computed on a exterior cylinder which encloses the magnetic source. Also, one can compute an equivalent multipole distribution of the real magnetic source valid for points close to the circular cylindrical boundary where the more familiar spherical multipole distribution is not valid. This method can also be used to accurately compute the far field where a finite-element formulation is known to be inaccurate

Advances in the axiperiodic magnetostatic analysis of generator end regions

The end region of turbine generators represents a complicated three-dimensional geometry. In order to reduce the size of the problem, we treat the fields as axiperiodic. A general method for axiperiodic linear magnetostatic problems is developed in this paper, followed by its application to the end region of a turbine generator.

Development of integral equation solution for 3D eddy current distribution in a conducting body

Eddy current analysis finds wide application in electrical machinery and devices, in power system analysis, non destructive testing, continuous casting, ship board applications and others. Finite Element methods such as T-Omega, A-phi and A-V methods do provide solutions of acceptable accuracy for small problems where the element size is comparable to skin-depth. Even for this, a large number of elements are required to model the entire space of the conducting medium and the surrounding air region. Integral equations require modeling of only the conducting parts and therefore offer an alternative approach to the problem. This paper presents an integral equation analysis and its application to a conducting slab with and without a crack excited by a transmission line source, to a slab excited by a dipole source, to phase segregated bus bars and others.

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

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, (Bouwkamp and de Bruijn 1947 J. Appl. Phys.18 562, Cohl et al 2001 Phys. Rev.A 64 052509-1, Selvaggi et al 2004 IEEE Trans. Magn.40 3278). These functions are monotonically decreasing and converge rapidly (Moon and Spencer 1961 Field Theory for Engineers (New Jersey: Van Nostrand Company) pp 368?76, Cohl and Tohline 1999 Astrophys. J.527 86). The introduction of the toroidal harmonic expansion leads to an infinite series solution for which each term can be expressed as an elementary function. This enables one to easily compute the axial and radial forces experienced by an internal or an external point mass.

Employing Toroidal Harmonics for Computing the Magnetic Field From Axially Magnetized Multipole Cylinders

We employ a toroidal harmonic expansion in order to develop a three-dimensional solution for the magnetic field due to a permanent-magnet multipole cylinder. The equations derived in this paper can be used for the optimization and design of various devices that employ cylindrical multipole magnets. The analytical equations employ hypergeometric functions derived from the analytical integration of zeroth-order toroidal functions. Hypergeometric functions are quite general and are very useful for parametric studies.

Modified scalar potential solution for three-dimensional magnetostatic problems

A novel three-dimensional magnetostatic solution based on a modified scalar potential method has been developed. This method has significant advantages over the traditional total scalar, reduced scalar, or vector potential methods. The new method was successfully applied to a three-dimensional geometry of an iron core inductor and a permanent magnet motor. The results obtained are in close agreement with those obtained from traditional methods.

Modified scalar potential finite element solution for electrical machine field problems

A new method titled Modified Scalar Potential Method, for solving magnetostatic problems in electrical machinery and devices, is presented. This technique, like the reduced scalar potential method, results in a mathematically unique and computationally efficient solution, and in addition yields a more accurate solution than its predecessors. The method is applied to 2D and axisymmetric problems and the results are compared with those of other methods where feasible. >