Magnetic Flux Controllers in Induction Heating and Melting
MAGNETIC FLUX CONTROLLERS are materials other than the copper coil that are used in induction systems to alter the flow of the magnetic field. Magnetic flux controllers used in power supplying components are not considered in this article. Magnetic flux controllers have been in existence since the development of the induction technique. Michael Faraday used two coils of wire wrapped around an iron core in his experiments that led to Faraday’s law of electromagnetic induction, which states that the electromotive force (emf) induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit. After the development of the induction principle, magnetic flux controllers, in the formof stacks of laminated steel, found widespread use in the development of transformers for more efficient transmission of energy (Ref 1, 2). Magnetic cores gained widespread use in the transformer industry because they increased the amount of magnetic flux produced with the same alternating current. The higher the magnetic flux, the higher the emf, which results in an increase in energy transfer efficiency from the primary winding to the secondary winding. Similar to transformers, magnetic cores were used on early furnaces for induction melting (Ref 1, 2). The benefits of magnetic flux controllers vary depending on the application. For induction heating, magnetic flux controllers can provide favorable and unfavorable paths for magnetic flux to flow, resulting in increased heating in desired areas and reduced the heating in undesirable areas, respectively. Magnetic flux controllers are not used in every induction heating application, but their use has increased (Ref 3, 4).
Optimal Design of Internal Induction Coils
Internal induction heating coils are not so well studied as external. Three main induction coil styles were proposed in pioneering works many years ago: Cylindrical coils, Hair-pin coils and Rod-type coils [1, 2]. It was clear from the very beginning that electromagnetic parameters of the coils of two first styles might be strongly improved by application of magnetic cores. However it was not clearly shown what parameters may be improved and how much, as well as what are the optimal designs of induction coils. Current presentation contains short consideration and comparison of all three styles of coils followed by a detailed analysis of cylindrical internal (ID) coils using modern computer simulation tools. It is shown that it isn’t sufficient to only consider the influence of magnetic core on electrical efficiency of the coil head. The cores reduce dramatically current demand for transfer of required power into the workpiece. In turn it results in strong reduction of voltage drop and power losses in the whole supplying circuitry: coil leads, busswork and matching transformer. Plus much smaller capacitor battery is required. Computer simulation is simple for single-turn cylindrical ID coils and several computer packages may be used. Computer simulation of multi-turn cylindrical ID coils, which are the most common, is a much more complicated task, due to the return leg. The return leg makes the problem 3-D and special methods are required for simulating this case. The authors used a two-dimensional coupled program Flux2D and a program Elta based on a combination of 1D Finite-Difference method and special analytical procedures. INTRODUCTION Induction heating of internal (ID) surfaces is more complicated than heating of external surfaces because of a limited space available for induction coil and for magnetic flux return (magnetic flux back path). There are three main types of inductors for ID heating: central rod, hair-pin and cylindrical. Inductor with a central rod Figure 1. Central rod inductor (left) and hair-pin ID inductor (right) This type of inductor is used not often because of a presence of electrical contact in its circuit. Inductor has a water-cooled rod, which goes through the bore in the work piece. Electric current is supplied to the ends of this rod. No concentrator is required with this inductor. Eddy current induced on the ID surface of the work piece flows along the bore and returns back on the external surface preferably on the side of a busswork connecting the inductor to a heat station. Despite of electrical contact these coils work well with proper maintenance. Minimal bore diameter may be as small as 7 mm. Rotation of the part is desirable but not mandatory. The limitation of these inductors is that the whole internal surface must be heated and there is no real possibility to control the heat pattern in length. Hair-pin ID coil Relatively long ID surfaces may be heated by hair-pin ID coil. These coils must have concentrator preferably from MagnetoDielectric Material (MDM). It is recommended to make an insulation gap between two parts of concentrator. This gap prevents electrical break of concentrator from one conductor to another through the concentrator, resulting in coil short-circuiting. Part rotation is mandatory for this type of induction heating. Hair-pin coils may be successfully used for parts with variation of diameter or wall thickness in length. Coil conductor cross-section may be varied in length in order to provide required power distribution in the part. The other way is variation of concentrator dimensions in the coil length. Hair-pin coils may be used for heating of ID surfaces with diameter above 13 mm. Single-turn cylindrical coils Figure 2. Single-turn ID coil with laminated core [1] (left), modern coil with MDM concentrator (center) and top view of the coil with removed top part of the concentrator (right). Left picture 1coil tubing, 2-thin laminations, 3-bearing ring Similar to OD coils, internal inductors may be singleor multi-turn. Single-turn coils are simple in design and may be successfully used for static heating of relatively short areas of ID surface (Li < 20-30 mm) or for scanning heat treatment. For longer parts the coil current will be too high, resulting in big losses in the coil leads and in the busswork. Minimum diameter of the work piece Dw may be estimated on the following basis:  Minimal internal diameter Dint of the coil may be assumed as 8 mm  Minimum tube wall is 0.5 mm  Radial dimension of cooling channel is 3 mm It gives us an outer coil diameter Di = 17 mm. With coupling gap between the part and coil equal to 1 mm, minimum internal workpiece diameter is 19 mm. For small and medium part diameter (Dw < 100 mm), magnetic flux concentrator is strongly desirable, while for larger coils it is also beneficial. Concentrator facilitates magnetic flux flow inside the coil and as a result improves coil efficiency and dramatically reduces current demand. For a given power transferred into the part, the coil head voltage remains approximately the same with and without concentrator. Lower current means lower losses in coil leads, busswork and matching transformer. In addition required capacitor battery may be several times smaller when the concentrator is installed. Multi-turn cylindrical coils For simultaneous heating of relatively long ID surfaces, multi-turn cylindrical coils may be used. Their design is similar to that of a single-turn coil but additional space is required to pull out the return lead (leg), Figure 3. Figure 3. Multi-turn internal inductor: cross-section (left) and top view with two possible positions of the return leg Design of internal multi-turn coil is shown in Figure 3. Concentrators may have additional discs on the top and bottom, which form the poles. These poles provide more precise heat pattern and improve the coil parameters. Minimal work piece diameter for heating with milti-turn coil may be calculated similar to a case with a single-turn coil. If return leg is 5 mm in diameter, concentrator and insulation thickness is 4 mm and coil tubing radial dimension is 4 mm, minimal workpiece diameter is around 23 mm. Two positions of return leg may be used – central and side, close to the winding (figure 3, right). Electromagnetic field inside the multi-turn coil is essentially three-dimensional even in the case of central position of return leg, when the geometry is axisymmetrical. It is because there are two components of magnetic field in this area. Main field is generated by turns of the coil head. The lines of this two dimensional field are located in Z-R planes. The second field is one-dimensional. It is generated by return leg and its lines form circles around the return legs. OPTIMAL DESIGN OF CYLINDRICAL COILS Before discussing optimal design of internal inductors, it is necessary to show the specific features of ID coils compared to OD ones using a simplified equivalent magnetic circuit (Figure 4). This circuit shows that ampere-turns (IN) of the coil generate magnetic flux  and drive it around the turns of the induction coil. Values of Zm and Rm represent corresponding magnetic resistances (reluctances) of the “active zone” (workpiece and coupling gap under the coil face) and of the return path inside the coil. Compared to O.D. Induction Coils, I.D. Induction Coils have much higher values of Rm relative to Zm. This is due to the small space available for flux to flow inside of the inductor. As a result, more ampere-turns (IN) are required to generate the magnetic flux () required to heat the workpiece. This is also the reason why induction coils with a small coupling gap are more efficient than loosely coupled ones. Ideally, with a coupling gap close to zero, all of the magnetic flux in the “active zone” would flow through the workpiece surface generating eddy currents. In the real world though, the coupling gap is a bypass for magnetic flux in the “active zone”. The smaller the gap between the coil face and the workpiece, the smaller the total magnetic flux and less ampere turns required for its generation. Higher frequency is also beneficial for ID coils, especially for small coils with no magnetic concentrator (core). Figure 4. Equivalent magnetic circuits for I.D. (left) and O.D. (right) induction coils For small I.D. coils without a magnetic flux controller, the value of Rm is often significantly larger than Zm. In these cases, nearly all of the ampere turns are used for driving the flux around the back path and very few are used for heating the workpiece. The power factor, efficiency and coil impedance of these coils are typically very bad. If a good magnetic flux controller is applied as shown in the left hand side of figure 4, then the value of Rm will typically drop several times. This means that the ampere-turns of the coil will also decrease dramatically, leading to very strong improvement in the induction coil
On a New Subclass of p-Valent Close-to-Convex Mappings Defined by Two-Sided Inequality
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