S. Zinn is an independent consultant on induction heating; (585) 427-7840. S.L. Semiatin is a project manager in the Center for Materials Fabrication at Battelle Columbus Division, (614) 424-7742. This article is excerpted from the book "Elements of Induction Heating.' published by Electric Power Research Institute (EPR) and distributed by ASM International. (516) 338-5151 and used with permission of EPRI
In a sense, coil design for induction heating is built upon a large store of empirical data whose development springs from several simple inductor geometries such as the solenoid coil. Because of this, coil design is generally based on experience. This series of articles reviews the fundamental electrical considerations in the design of inductors and describes some of the most common coils in use.
Basic Design Considerations
The inductor is similar to a transformer primary, and the workpiece is equivalent to the transformer secondary (Fig. 1). Therefore, several of the characteristics of transformers are useful in the development of guidelines for coil design.
One of the most important features of transformers is the fact that the efficiency of coupling between the windings is inversely proportional to the square of the distance between them. In addition, the current in the primary of the transformer, multiplied by the number of primary turns, is equal to the current in the secondary, multiplied by the number of secondary turns. Because of these relationships, there are several conditions that should be kept in mind when designing any coil for induction heating:
1) The coil should be coupled to the part as closely as feasible for maximum energy transfer. It is desirable that the largest possible number of magnetic flux lines intersect the workpiece at the area to be heated. The denser the flux at this point, the higher will be the current generated in the part.
2) The greatest number of flux lines in a solenoid coil are toward the center of the coil. The flux lines are concentrated inside the coil, providing the maximum heating rate there.
3) Because the flux is most concentrated close to the coil turns themselves and decreases farther from them, the geometric center of the coil is a weak flux path. Thus, if a part were to be placed off center in a coil, the area closer to the coil turns would intersect a greater number of flux lines and would therefore be heated at a higher rate, whereas the area of the part with less coupling would be heated at a lower rate; the resulting pattern is shown schematically in Fig. 2. This effect is more pronounced in high-frequency induction heating.
4) At the point where the leads and coil join, the magnetic field is weaker; therefore, the magnetic center of the inductor is not necessarily the geometric center. This effect is most apparent in single-turn coils. As the number of coil turns increases and the flux from each turn is added to that from the previous turns, this condition becomes less important. Due to the impracticability of always centering the part in the work coil, the part should be offset slightly toward this area. In addition, the part should be rotated, if practical, to provide uniform exposure.
5) The coil must be designed to prevent cancellation of the magnetic field. The coil on the left in Fig. 3 has no inductance because the opposite sides of the inductor are too close to each other. Putting a loop in the inductor (coil at center) will provide some inductance. The coil will then heat a conducting material inserted in the opening. The design at the right provides added inductance and is more representative of good coil design.
Because of the above principles, some coils can transfer power more readily to a load because of their ability to concentrate magnetic flux in the area to be heated. For example, three coils that provide a range of heating behaviors are:
a helical solenoid, with the part or area to be heated located within the coil and, thus, in the area of greatest magnetic flux;
a pancake coil, with which the flux from only one surface intersects the workpiece; and
an internal coil for bore heating, in which case only the flux on the outside of the coil is utilized.
In general, helical coils used to heat round workpieces have the highest values of coil efficiency and internal coils have the lowest values (Table I). Coil efficiency is that part of the energy delivered to the coil that is transferred to the workpiece. This should not be confused with overall system efficiency.
Besides coil efficiency, heating pattern, part motion relative to the coil, and production rate are also important. Because the heating pattern reflects the coil geometry, inductor shape is probably the most important of these factors. Quite often, the method by which the part is moved into or out of the coil can necessitate large modifications of the optimum design. The type of power supply and the production rate must also be kept in mind. If one part is needed every 30 seconds but a 50-second heating time is required, it will be necessary to heat parts in multiples to meet the desired production rate. Keeping these needs in mind, it is important to look at a wide range of coil techniques to find the most appropriate one.
Simple solenoid coils are often relied on in medium-to-high-frequency applications such as heat treatment. These include single- and multiple-turn types. Fig. 4 illustrates a few of the more common types based on the solenoid design. Fig. 4a is a multiturn, single-place coil, so called because it is generally used for heating a single part at a time. A single-turn, single-place coil is also illustrated (Fig. 4b). Fig. 4c shows a single-turn, multiplace coil, in this design, a single turn interacts with the workpiece at each part-heating location. Fig. 4(d) shows a multiturn, multiplace coil.
More often than not, medium-to-high-frequency applications require specially configured or contoured coils with the coupling adjusted for heat uniformity. In the simplest cases, coils are bent or formed to the contours of the part (Fig. 5). They may be round (Fig. 5a), rectangular (Fig. 5b), or formed to meet a specific shape such as the cam coil (Fig.5c). Pancake coils (Fig. 5d) are generally utilized when it is necessary to heat from one side only or when it is not possible to surround the part. Spiral coils (Fig. 5e) are generally used for heating bevel gears or tapered punches. Internal bores can be heated in some cases with multiturn inductors (Fig. 5f). It is important to note that, with the exception of the pancake and internal coils, the heated part is always in the center of the flux field.
Regardless of the part contour, the most efficient coils are essentially modifications of the standard, round coil. A conveyor or channel coil, for example, can be looked at as a rectangular coil whose ends are bent to form "bridges" in order to permit parts to pass through on a continuous basis. The parts, however, always remain "inside" the channels where the flux is concentrated. Fig. 6 illustrates similar situations in which the areas to be hardened are beside the center of the coil turns, and thus are kept in the area of heaviest flux.
Heating of internal bores, whether for hardening, tempering, or shrink fitting, is one of the major problems most commonly confronted. For all practical purposes, a bore with a 0.44-inch (1.1 cm) internal diameter is the smallest that can be heated with a 450 kHz power supply. At 10 kHz, the practical minimum ID is 1.0 inch (2.5 cm).
Tubing for internal coils should be made as thin as possible, and the bore should be located as close to the surface of the coil as is feasible. Because the current in the coil travels on the inside of the inductor, the true coupling of the maximum flux is from the ID of the coil to the bore of the part. Thus, the conductor cross section should be minimal, and the distance from the coil OD to the part (at 450 kHz) should approach 0.062-inch (0.16 cm). In Fig.7a, for example, the coupling distance is too great; coil modification improves the design, as shown in Fig. 7b. Here, the coil tubing has been flattened to reduce the coupling distance, and the coil OD has been increased to reduce the spacing from coil to work.
More turns, or a finer pitch on an internal coil, will also increase the flux density. Accordingly, the space between the turns should be no more than one-half the diameter of the tubing, and the overall height of the coil should not exceed twice its diameter. Figs. 7c and 7d show special coil designs for heating internal bores. The coil in Fig. 7d would normally produce a pattern of four vertical bands, and therefore the part should be rotated for uniformity of heating.
Internal coils, of necessity, utilize very small tubing or require restricted cooling paths. Further, due to their comparatively low efficiency, they may need very high generator power to produce shallow heating depths.
Because magnetic flux tends to concentrate toward the center of the length of a solenoid work coil, the heating rate produced in this area is generally greater than that produced toward the ends. Further, if the part being heated is long, conduction and radiation remove heat from the ends at a greater rate. To achieve uniform heating along the part length, the coil must thus be modified to provide better uniformity. The technique of adjusting the coil turns, spacing, or coupling with the workpiece to achieve a uniform heating pattern is sometimes known as "characterizing" the coil.
There are several ways to modify the flux field. The coil can be decoupled in its center, increasing the distance from the part and reducing the flux in this area. Secondly, and more commonly, the number of turns in the center (turn density) can be reduced, producing the same effect. A similar approach - altering a solid single-turn inductor by increasing its bore diameter at the center - achieves the same result.
In Fig. 8a, the coil turns have been modified to produce an even heating pattern on a tapered shaft. The closer turn spacing toward the end compensates for the decrease in coupling caused by the taper. This technique also permits "through the coil" loading or unloading to facilitate fixturing. A similar requirement in the heat treatment of a bevel gear is shown in Fig. 8b. Here, because of the greater part taper, a spiral-helical coil is used. With a pancake coil, decoupling of the center turns provides a similar approach for uniformity.
Multiturn vs. Single-Turn
Heating-pattern uniformity requirements and workpiece length are the two main considerations with regard to the selection of a multiturn vs. a single turn induction coil. A fine-pitch, multiturn coil closely coupled to the workpiece develops a very uniform heating pattern. Similar uniformity can be achieved by opening up the coupling between the part and the coil so that the magnetic flux pattern intersecting the heated area is more uniform. However, this also decreases energy transfer. Where low heating rates are required, as in through heating for forging, this is acceptable. When high heating rates are needed, however, it is sometimes necessary to maintain close coupling. The pitch of the coil must be opened to prevent overloading of the generator.
Because the heating pattern is a mirror image of the coil, the high flux field adjacent to the coil turns will produce a spiral pattern on the part. This is called "barber poling," and can be eliminated by rotating the workpiece during heating. For most hardening operations, which are of short duration, rotational speeds producing not less than 10 revolutions during the heating cycle should be used.
If part rotation is not feasible, heating uniformity can be increased by using flattened tubing, by putting a step in the coil, or by attaching a liner to the coil. Flattened tubing should be placed so that its larger dimension is adjacent to the workpiece. The stepping of coil turns (Fig. 9) provides an even, horizontal heating pattern. Stepping is easily accomplished by annealing the coil after winding and pressing it between two boards in a vise. A coil liner is a sheet of copper soldered or brazed to the inside face of the coil. This liner expands the area over which the current travels. Thus, a wide field per turn can be created. The height of this field can be modified to suit the application by controlling the dimensions of the liner. When a liner is used, the current path from the power supply passes through the connecting tubing (Fig.10). Between the two connections, the tubing is used solely for conduction cooling of the liner.
In fabricating coils with liners, it is necessary only to tack-braze the tubing to the liner at the first and last connection points, with further tacks being used solely for mechanical strength. The remainder of the common surfaces between tubing and liner can then be filled with a low temperature solder for maximum heat conduction, because the coil-water temperature will never exceed the boiling point of water, which is well below the flow point of the solder. This may be necessary because the copper may be unable to conduct heat fast enough from the inside of the coil.
In multiturn coils, as the heated length increases, the number of turns generally should increase in proportion. In Fig. 11a, the face width of the coil is in proportion to the coil diameter. In Fig. 11b, the ratio of the coil diameter to face width is not suitable; the multiturn coil shown in Fig. 11c provides a more acceptable heat pattern. Multiturn coils of this type are generally utilized for large-diameter, single-shot heating, in which the quench medium can be sprayed between the coil turns (Fig. 11d).
When the length of the coil exceeds four to eight times its diameter, uniform heating at high power densities becomes difficult. In these instances, single-turn or multiturn coils that scan the length of the workpiece are often preferable. Multiturn coils generally improve the efficiency, and therefore the scanning rate, when a power source of a given rating is used. Single-turn coils are also effective for heating bands that are narrow with respect to the part diameter.
The relationship between diameter and optimum height of a single-turn coil varies somewhat with size. A small coil can be made with a height equal to its diameter because the current is concentrated in a comparatively small area. With a larger coil, the height should not exceed one-half the diameter. As the coil opening increases, the ratio is reduced— i.e., a 2-inch( 5.1-cm) ID coil should have a 0.75-inch (1.91-cm) maximum height, and a 4-inch (10.2-cm) ID coil should have a 1.0-inch (2.5-cm) height. Fig.12 shows some typical ratios.
Preferred coupling distance depends on the type of heating (single-shot or scanning) and the type of material (ferrous or nonferrous). In static surface heating, in which the part can be rotated but is not moved through the coil, a coupling distance of 0.060 inch (0.15 cm) from part to coil is recommended. For progressive heating or scanning, a coupling distance of 0.075 inch (0.19 cm) is usually necessary to allow for variations in workpiece straightness. For through heating of magnetic materials, multiturn inductors and slow power transfer are utilized. Coupling distances can be looser in these cases — on the order of 0.25 to 0.38 inch (0.64 to 0.95 cm). It is important to remember, however, that process conditions and handling dictate coupling. If parts are not straight, coupling must decrease. At high frequencies, coil currents are lower and coupling must be increased. With low and medium frequencies, coil currents are considerably higher and decreased coupling can provide mechanical handling advantages. In general, where automated systems are used, coil coupling should be looser.
The coupling distances given above are primarily for heat treating applications in which close coupling is required. In most cases, the distance increases with the diameter of the part, typical values being 0.75,1.25, and 1.75 inches (19, 32 and 44 mm) or billet-stock diameters of approximately 1.5,4 and 6 inches (38, 102, and 152 mm), respectively.
Effects of Part Irregularities
With all coils, flux patterns are affected by changes in the cross-section or mass of the part. As shown in Fig.13, when the coil extends over the end of a shaft-like part, a deeper pattern is produced on the end. To reduce this effect, the coil must be brought to a point even with or slightly lower than the end of the shaft. The same condition exists in heating of a disk or a wheel. The depth of heating will be greater at the ends than in the middle if the coil overlaps the part. The coil can be shortened, or the diameter at the ends of the coil can be made greater than at the middle, thereby reducing the coupling at the former location.
Just as flux tends to couple heat to a greater depth at the end of a shaft, it will do the same at holes, long slots, or projections (Fig.14). If the part contains a circular hole, an additional eddy-current path is produced that will cause heating at a rate considerably higher than that in the rest of the part. The addition of a copper slug to the hole can effectively correct or eliminate this problem. The position of the slug (Fig.15) can control the resultant heating pattern. In addition, the slug will minimize hole distortion if the part must be quenched following heating.
For slotted parts heated with solenoid coils (Fig.16), the continuous current path is interrupted by the slot, and the current must then travel on the inside of the part to provide a closed circuit. This is the basis for concentrator coils. It is of interest to note, however, that with the slot closed, the applied voltage of the work coil causes a higher current to flow. This is due to the fact that the resistive path, now around the periphery of the part, is considerably shorter. The increase in current then produces a considerably higher heating rate with the same coil.
When two separate regions of a workpiece are to be heated, but are close together (Fig. 17), it is possible that the magnetic fields of adjacent coil turns will overlap, causing the entire bar to be heated. To avoid this problem, successive turns can be wound in opposite directions. By this means, the intermediate fields will cancel, and the fields that remain will be restricted. It should be noted that, as shown in Fig.17, lead placement is critical. Having the return inductor spaced far from the coil leads would add unneeded losses to the system. Another example of a counterwound coil is shown in Fig.18; the coil in Fig. 18b is the counterwound version of the one in Fig.18a. This type of coil can be used effectively in an application in which the rim of a container is to be heated while the center remains relatively cool.
Another technique that can be utilized in the above circumstances involves the construction of a shorted turn or "robber" placed between the active coil turns. In this case, the shorted loop acts as an easy alternative path for concentration of the excess flux, absorbing the stray field. It is therefore sometimes called a flux diverter. As for the active coil turns, the robber must be water cooled to dissipate its own heat. A typical construction is shown in Fig.19.
Shorted coil turns are also used effectively to prevent stray-field heating on very large coils where the end flux field might heat structural frames.
Flux robbers or flux diverters can also be used in fabricating test coils when it is desired to determine the optimum number of turns empirically. In these situations, a few additional turns are provided that can be added or removed as required. These can be shorted with a copper strap or temporarily brazed while tests are made and removed pending the outcome of the heating trials.