# Shape - Typical designs with sector angles of pi/2 [90 degrees], and 2pi/3 [120 degrees] are shown below.

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1 Sector Torus Cores Started 01 Jun 012 By Newton E. Ball Definitions - Torus - Restricted to Circular Torus, the solid shape formed by the rotation of a circular area, about an axis that is external to the circle. Sector - Angle subtended, at the axis by a partial torus, referred to as a Sector Torus. Rod - Right circular cylinder of ferromagnetic material, with the same crossection diameter as adjacent Sector Torus core pieces. Core - Solid assembly of ferromagnetic material, forming a closed path for magnetic flux. The path is usually linked by turns of magnet wire, close to the core. Winding - All of the Sector Torus and rod portions of each core, are to be closely surrounded by layers of magnet wire, each turn, of which, links the magnetic flux path. All of the turns that are in series, constitute a winding. Pitch - The closely spaced turns of a winding form a spiral. The turn to turn distance is inversely quantified as pitch, in turns per inch, or turns per meter. Lay - The spiral winding of a layer has a right handed or left handed sense, corresponding to the sense of right or left handed threads. That is, the winding layer can be right lay or left lay.. Coherent Winding - If all of the layers of a winding have the same pitch, and the same lay, then the winding is said to be coherent. Gap - The portion of magnetic path that is empty of ferromagnetic material, is a gap. Gaps are used to store magnetic energy. Gaps usually have parallel walls, perpendicular to the direction of magnetic flux. Gaps are usually filled with solid material, such as plastic, that is not ferromagnetic. Working Gap - In a motor, generator, or actuator, the portion of a gap that is filled or emptied of ferromagnetic material, during torque or thrust generation, is called the working gap. Shape - Typical designs with sector angles of pi/2 [90 degrees], and 2pi/3 [120 degrees] are shown below.

2 -Sector Torus Core, 90 o, -Sector Torus Core, 120 o A Axial & Canted Views- Axial & Canted Views- Material - For the cores of high frequency inductors, coupled inductors, and transformers, in switching power service, the material is usually ferrite, a power alloy, such as Ferroxcube 3F3, or Fair-Rite Alloy 78. For motors, generators, and motorgenerators, the material is usually laminated silicon steel. Purposes - Minimizing copper losses- A good core shape minimizes the length of every turn, by providing maximum ratio of core area to wire turn length. The circular crossection does this. Any other shape has greater perimeter to area ratio. The number of wire layers needs to be minimized, because outer layers require greater wire length. Core shapes minimize layer count, by maximizing the winding width, as a proportion if magnetic path length. A full torus core, assembled from sectors, can be wound over it's

3 entire path length, further, no toroid winder is required. The winding is produced on a mandrel, by an ordinary coil winder, and slipped over the core at assembly. This 100% path length coverage, also applies to oval and other shapes, assembled from round rod cores, used with sector torus cores. Providing for energy storage - Magnetic energy storage is a necessary function in all inductors, and coupled inductors. Gapped ferrite energy storage has the feature that the gap, where the energy is stored, is lossless. Some gapped shapes produce some loss, due to interaction of fringing flux, with nearby windings. Dividing the total gap into smaller gaps, magnetically in series, dramatically reduces fringing. Sector Torus Cores can be shimmed at every core joint, to provide multiple equal gaps. Minimizing core loss - While the specific flux density may be run at the same peak level, as a pot core, or other shape, giving the same specific core loss, The core assembled from Sector Torus, and rod segments, has much lower volume, than other shapes, typically by a factor of three. To obtain core loss, the specific loss, or loss density, is multiplied by the core volume. Thus the total core loss is much lower for the Sector Torus core than for any standard shape. Fit to available board space - Most shapes, when mounted on a printed circuit board, require area outside of the core footprint, for terminations. The planar shapes assembled from rods, and sector tori, [plural of torus] have open central areas, available for board terminations. Cores assembled from Sector Torus and rod shapes, can compete for height with other planar core shapes, with the same height over the board, and much lower core weight, and core volume. Minimize Weight - Aboard aircraft, spacecraft, and satellites, weight is a very expensive attribute, because of fuel costs. The same three to one advantage, in core volume, translates directly into core weight. The weight of copper of the first two winding layers, is about the same as that of the first two layers of usual magnetic components. To the extent that there are more than two layers in the usual design, there is a copper weight advantage to the Sector Torus designs. Typical Ferrite Assemblies - Assemblies can be planar and simple, like the torus and oval shown,

4 or a planar shape can be more complex: A wide variety of 3D shapes can be useful. One example: If the problem were to fit inductive energy storage into a cube, this is a good place to start. Note that there are eight gaps, so that each gap can be quite narrow, minimizing fringing effects. : Windings - The cores are to be surrounded, over virtually all of their magnetic path length, by turns of magnet wire, usually round magnet wire. There are strong reasons

5 why coherent winding layers are preferred. The figure below, illustrates windings of AWG 20 wire, for use with 1/4" rod or sector torus cores, wound on mandrels, with layer 2 then threaded onto layer 1, ready for insertion of rod cores, or of sector torus cores. The left view is of Layer 1. The center view is of layer 2. The right view shows the point in the assembly, when layer 2 is threaded onto layer 1, ready for core insertion. As a sector torus core is inserted, The wire of the second layer, is forced toward the inside of the sector turn, finding a place such that the composite winding is only one layer deep at the outside of the sector torus turn. If a rod core is inserted, then the relative position, shown in the right view, remains. After all of the core, constituting the complete, closed magnetic path, has been inserted, then a partial turn, at each end of each layer, is unwound, stripped of coating, and formed for termination. The termination may be to a terminal, or directly to a printed circuit board, by surface mount, or through hole mounting. These terminations are typically the principal mounting for the entire magnetic assembly. Ends of core pieces, may be held in alignment by a short piece of thin wall shrink tubing, or dilated plastic tubing. In the case where inductive energy storage is desired, circular plastic shims separate the core ends, under the tubing. In the example winding shown, the layers are right lay, and both have pitch, slightly greater than the diameter of the AWG 20 magnet wire. Use in Motors - Cores assembled from Sector Tori [plural of torus] and rods, allow winding shapes to adapt to available space, while always surrounding a circular crossection. The motor, shown in part below, has a specified case length and diameter. It is a unidirectional motor only, no reverse operation, no generator operation. motors of this sort need only two phases. A continuous winding surrounds the cores on opposite sides of the rotor.

6 Views - At the top left is a canted view of the magnetic core parts only. Top right adds rotor, bearings, and shaft. Below is an axial view, showing how each winding fits a quadrant of the motor. Adapter, wound core to rotor - At each of the eight ends of the cores to be wound, shown above, is a core part that is not to be wound. These parts called adapters, have constant crossection area along their length, but the shape changes from circular, at the wound core end, to trapezoidal, at the rotor end, so that the short dimension minimizes the angle from center, on the rotor. The adapter is shown in bold lines below.

7 * Two Phase Two Coil - In the motor shown above, a single winding surrounds two core sections, on opposite sides of the rotor, with the winding crossing outside of the rotor. in two places. The motor is said to have two coils, or two calipers. Caliper designates the stationary mounting of the core and coil, and forms a quadrant of the stator. Two Phase Four Coil - Two more calipers, occupying the upper vacant stator quadrants, can be added to this motor design, doubling it's torque. The coils of a phase may be connected in series, or in parallel, depending on whether higher voltage or higher current is desired. Three Phase - A motor-generator, or reversible motor or generator, or actuator, is usually equipped with three phases of drive. 120 degree Sector Torus shapes, fit these configurations, with three or six caliper, coil and core sets.. Rotor - The rotor has a center layer, perforated in the pattern shown at the left, below. The rotor has also two identical outer layers perforated in a different pattern, and shown with the center layer, at the right.

8 This rotor has 22 rotor poles per side, describing the cross-rotor magnetic polarization. These poles never reverse polarity, and hysteresis, or permanent magnet effect, is all to the good. This fixed magnetic polarization, keeps the core losses in the rotor very low. Motor Drive - Caliper motors utilizing sector torus magnetic cores are designed to be electronically driven. A typical drive circuit is shown in a mixed block diagram, and schematic form below

9 Use in Actuators - Linear electric actuators use the same sector torus and rod cores. They are aranged as shown here. Only one caliper, of two or three calipers, is shown. Arrows indicate direction of travel. All of the sector torus, and rod portions, shown, are to be wound with a continuous winding. Voids in the ferromagnetic armature, are not shown. Actuator Drive - Actuators are driven by the same circuit, as the one shown for motors, except that a linear position encoder is substituted for the shaft encoder.

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