R.M. Del Vecchio

Loss separation measurements for several electrical steels

Loss separation measurements were made on regular grain oriented 3% Si steels of four sheet thicknesses, one thickness of high permeability oriented 3% Si steel, two grades of nonoriented Si steel, a low carbon steel, a primary recrystallization oriented low alloy iron sample, and an amorphous metal sample. The Bn dependence of hysteresis loss Ph for all samples except the oriented Si steels was close to n=1.6, in good agreement with the Steinmetz value. All the oriented Si steels had n values close to 2.

Computation of losses in nonoriented electrical steels from a classical viewpoint (invited)

Nonoriented electrical steels approximate a classical continuum with respect to magnetic and electrical properties. A calculation based on fields which vary smoothly from point to point should therefore be appropriate. At each point, the paths taken by the magnetic fields in the B–H plane are influenced by eddy currents and the eddy currents in turn depend on the B–H paths. This mutual interaction prevents hysteresis and eddy current losses from being independent. The full electromagnetic problem, including these interactions, can be solved for simple geometries. At present we are restricted to solving unidirectional flux problems where convenient hysteresis models may be applied. These yield a reasonable description of complex hysteresis paths with only a limited amount of experimental input. Using a hysteresis model and numerical techniques, loss calculations for both sinusoidal and distorted flux waveforms in thin laminations were performed and are compared with experimental data.

Magneto-thermal coupled finite element calculations in multiconductor systems

In this paper we present, the calculation of temperature transients in devices where the electromagnetic and heat, transfer processes are coupled. We have extended the finite element electromagnetic code (WEMAP) in such a manner that the calculated power loss densities in a multiconductor system are used as the heat, sources for a transient thermal solution in subregions of the original problem geometry. These subregions are enclosed by surfaces on which either temperature, or a convection boundary condition is known. The implementation of this capability will be shown by way of an example.

Micromagnetics calculation for two-dimensional thin-film geometries using a finite-element formulation

Micromagnetics problems in two dimensions are formulated in terms of a finite-element description. The free energy, including exchange, anisotropy, external field, and demagnetization contributions, is approximated by means of integrals over linear triangular finite elements and minimized with respect to the nodal variables. By enforcing the constraint that the magnetization vectors at the nodes have constant magnitude, the resulting minimization equations are nonlinear. They are solved using Gauss-Seidel iteration. The finite-element description allows calculations to be performed for arbitrary two-dimensional geometries. In the examples presented, the magnetization distributions obtained were in agreement with expectations based on domain theory. >

Eddy-current losses in a conducting plate due to a collection of bus bars carrying currents of different magnitudes and phases

Losses in bus bars carrying AC current and passing near the tank wall in transformers can contribute significantly to stray losses and can produce high temperatures on the tank wall. Usually these losses are mitigated by moving the bus bars farther away from the wall or by placing a shield of high conductivity and low permeability on the tank wall near the bus bars. Although these losses in the wall or shield can be calculated by modern finite-element codes, an analytical method would obtain these losses quickly during the design phase. We present such a method here. The method works for an arbitrary collection of bus bars carrying currents from different phases. Applications to other situations where long cables or bus bars carrying AC currents and running parallel to a conducting plate are also possible.

A program to compute magnetic fields, forces, and inductances due to solid rectangular conductors arbitrarily positioned in space

The computer program BUS3D was developed to compute the magnetic field and vector potential produced by a collection of rectangular busbars carrying DC current and arbitrarily oriented in space, using exact analytic expressions. The field and vector potential expressions are used in numerical integrations to obtain forces on individual busbars and inductances or mutual inductances between collections of busbars. The program has been checked against known results found in the literature. BUS3D has been used in the design of electromagnetic launch system component interconnections and in the analysis of a rail gun. An example of a rail gun configuration is presented to show the various options BUS3D offers.

WEMAP-a computer aided instructional tool for electromagnetics

WEMAP is an electromagnetic analysis computer code for teaching electromagnetics to power engineering students. WEMAP is a stand-alone interactive graphics system for electromagnetic analysis, which includes electrostatics, magnetostatics, eddy currents (time harmonic as well as transient), and permanent magnet fields. These capabilities are described, and examples are given to illustrate how this program can enhance the classroom presentation of some of the electromagnetic phenomena. >

Calculation of magnetic domain wall bowing and eddy current losses in an infinite sheet of bar‐like domains

An analytic solution has been obtained for the magnetic field distribution and eddy current losses associated with an infinite array of regularly spaced 180° domain walls which are allowed to bow during their motion. Wall motion was constrained to satisfy a sinusoidal total flux boundary condition. The field solution was solved self‐consistently with the domain wall equation of motion. Calculated losses were always lowered relative to the plane wall case. Difficulties were encountered in the numerical iteration scheme as the degree of bowing increased. Using an approximation for the high bowing case, a physical instability occurred before bowing became too severe.

New solid armature design concept (for railguns)

Solid armatures in railgun applications experience extreme mechanical, thermal, and electromagnetic conditions. They must be able to survive a launch without undue bore damage, and yet have as small a mass as possible. A novel solid armature concept is presented, some of the factors influencing its design are examined, and some relationships are established among the physical parameters which characterize its operation. A novel feature of the armature design is the separation of the finger or fiber contact design from the bulk of the armature which simply transports current across the rails. This latter region should be transposed, because in virtually all practical cases, the current nonuniformity due to the velocity-skin effect would otherwise be large. The transposed region could be made different material than the contact region. This different material need not be mechanically strong, since it will be probably be imbedded in a matrix. Its selection can therefore be based on different criteria, such as achieving low mass. >

Calculation of the reversible part of the magnetization curves at any angle to the rolling direction for polycrystalline silicon steel

Polycrystalline Goss oriented electrical steel contains a distribution of grain orientations which has been shown, in previous work, to be characterized by one rms angle. Approximating the grains by long rods, theoretical single crystal reversible magnetization curves were averaged over the empirical grain directional distribution and the results compared with experimental curves above the knee where the magnetization is predominantly reversible. When the rms angle is chosen to give a best fit to the magnetization curve in the rolling direction, good fits are obtained for the family of magnetization curves at other angles to the rolling direction. The empirical relation between the induction at 10 Oe, B10, and rms angle is also reproduced. The methods described here may be used for electrical steel having any specified orientation.