I n a sense, coil design for induc-tion heating is built upon a largestore of empirical data whosedevelopment springs from sev-

eral simple inductor geometries such asthe solenoid coil. Because of this, coildesign is generally based on experi-ence. This series of articles reviewsthe fundamental electrical consider-ations in the design of inductors anddescribes some of the most commoncoils in use.

Basic design considerationsThe inductor is similar to a transformerprimary, and the workpiece is equiva-lent to the transformer secondary (Fig.1). Therefore, several of the charac-teristics of transformers are useful inthe development of guidelines for coildesign.

One of the most important featuresof transformers is the fact that the ef-ficiency of coupling between the wind-ings is inversely proportional to thesquare of the distance between them.In addition, the current in the primaryof the transformer, multiplied by thenumber of primary turns, is equal tothe current in the secondary, multipliedby the number of secondary turns. Be-cause of these relationships, there areseveral conditions that should be keptin mind when designing any coil forinduction heating:1) The coil should be coupled to thepart as closely as feasible for maxi-mum energy transfer. It is desirablethat the largest possible number ofmagnetic flux lines intersect the work-piece at the area to be heated. Thedenser the flux at this point, the higherwill be the current generated in the part.

2) The greatest number of flux lines in asolenoid coil are toward the center ofthe coil. The flux lines are concentratedinside the coil, providing the maximumheating rate there.3) Because the flux is most concen-trated close to the coil turns them-selves and decreases farther from

them, the geometric center of the coil isa weak flux path. Thus, if a part wereto be placed off center in a coil, thearea closer to the coil turns would in-tersect a greater number of flux linesand would therefore be heated at ahigher rate, whereas the area of thepart with less coupling would be heatedat a lower rate; the resulting patternis shown schematically in Fig. 2. Thiseffect is more pronounced in high-fre-quency induction heating.4) At the point where the leads andcoil join, the magnetic field is weaker;therefore, the magnetic center of theinductor is not necessarily the geomet-ric center. This effect is most appar-ent in single-turn coils. As the numberof coil turns increases and the fluxfrom each turn is added to that fromthe previous turns, this condition be-comes less important. Due to the im-practicability of always centering thepart in the work coil, the part shouldbe offset slightly toward this area. Inaddition, the part should be rotated, ifpractical, to provide uniform exposure.5) The coil must be designed to pre-vent cancellation of the magnetic field.The coil on the left in Fig. 3 has noinductance because the opposite sidesof the inductor are too close to eachother. Putting a loop in the inductor(coil at center) will provide someinductance. The coil will then heat aconducting material inserted in theopening. The design at the right pro-vides added inductance and is morerepresentative of good coil design.

Because of the above principles,some coils can transfer power morereadily to a load because of their abil-ity to concentrate magnetic flux in thearea to be heated. For example, threecoils that provide a range of heatingbehaviors are:

• a helical solenoid, with the partor area to be heated located within thecoil and, thus, in the area of greatestmagnetic flux;

Coil design and fabrication:basic design and modifications

InductionInductionInductionInductionInduction

by STANLEY ZINN and S. L. SEMIATIN

S. Zinn is executive vice president, Ameritherm,Inc., Rochester , N.Y.; (716) 427-7840.S.L.Semiatin is a project manager in the Center forMaterials Fabrication at Battelle Columbus Divi-sion; (614) 424-7742.This article is excerpted from the book “Ele-ments of Induction Heating,” published by Elec-tric Power Research Institute (EPRI) and dis-tributed by ASM International, (516) 338-5151and used with permission of EPRI

32 HEAT TREATING/JUNE 1988

Ep = primary voltage (V); Ip = primary current (A); Np =number of primary turns; Is = secondary current (A); Ns =number of secondary turns; Es = secondary voltage (V); Rl= load resistance(Ω)

Fig. 1: Electrical circuit illustrating theanalogy between induction heating and thetransformer principle.

Fig. 2: Induction heating pattern producedin a round bar placed off center in a roundinduction coil.

Fig. 3: Effect of coil design on Inductance(from F. W. Curtis, High Frequency Induc-tion Heating, McGraw-Hill, New York, 1950)

enough from the inside of the coil.In multiturn coils, as the heated length

increases, the number of turns gener-ally should increase in proportion. In Fig.11a, the face width of the coil is in pro-portion to the coil diameter. In Fig. 11b,the ratio of the coil diameter to face widthis not suitable; the multiturn coil shownin Fig. 11c provides a more acceptableheat pattern. Multiturn coils of this typeare generally utilized for large-diameter,single-shot heating, in which the quenchmedium can be sprayed between the coilturns (Fig. 11d).

When the length of the coil exceedsfour to eight times its diameter, uniformheating at high power densities becomesdifficult. In these instances, single-turnor multiturn coils that scan the length ofthe workpiece are often preferable.Multiturn coils generally improve the ef-ficiency, and therefore the scanning rate,when a power source of a given ratingis used. Single-turn coils are also effec-tive for heating bands that are narrowwith respect to the part diameter.

The relationship between diameterand optimum height of a single-turn coilvaries somewhat with size. A small coilcan be made with a height equal to itsdiameter because the current is concen-trated in a comparatively small area.With a larger coil, the height should notexceed one-half the diameter. As thecoil opening increases, the ratio is re-duced — i.e., a 2-inch (5.1-cm) ID coilshould have a 0.75-inch (1.91-cm) maxi-mum height, and a 4-inch (10.2-cm) IDcoil should have a 1.0-inch (2.5-cm)height. Fig. 12 shows some typical ra-tios.

Coupling distancePreferred coupling distance depends onthe type of heating (single-shot or scan-ning) and the type of material (ferrousor nonferrous). In static surface heat-ing, in which the part can be rotated butis not moved through the coil, a couplingdistance of 0.060 inch (0.15 cm) frompart to coil is recommended. For pro-gressive heating or scanning, a couplingdistance of 0.075 inch (0.19 cm) is usu-ally necessary to allow for variations inworkpiece straightness. For throughheating of magnetic materials, multiturninductors and slow power transfer areutilized. Coupling distances can be looserin these cases — on the order of 0.25 to0.38 inch (0.64 to 0.95 cm). It is impor-

tant to remember, however, that processconditions and handling dictate coupling.If parts are not straight, coupling mustdecrease. At high frequencies, coil cur-rents are lower and coupling must be

increased. With low and medium fre-quencies, coil currents are considerablyhigher and decreased coupling can pro-vide mechanical handling advantages. Ingeneral, where automated systems areused, coil coupling should be looser.

The coupling distances given aboveare primarily for heat treating applica-tions in which close coupling is required.In most cases, the distance increaseswith the diameter of the part, typical val-ues being 0.75, 1.25, and 1.75 inches (19,32 and 44 mm) or billet-stock diametersof approximately 1.5, 4 and 6 inches (38,102, and 152 mm), respectively.

Effects of part irregularitiesWith all coils, flux patterns are affectedby changes in the cross-section or massof the part. As shown in Fig. 13 (p. 36),when the coil extends over the end of ashaft-like part, a deeper pattern is pro-duced on the end. To reduce this effect,the coil must be brought to a point evenwith or slightly lower than the end ofthe shaft. The same condition exists inheating of a disk or a wheel. The depthof heating will be greater at the endsthan in the middle if the coil overlaps thepart. The coil can be shortened, or thediameter at the ends of the coil can bemade greater than at the middle, therebyreducing the coupling at the former lo-cation.

Just as flux tends to couple heat to agreater depth at the end of a shaft, itwill do the same at holes, long slots, orprojections (Fig. 14, p. 36). If the partcontains a circular hole, an additionaleddy-current path is produced that willcause heating at a rate considerablyhigher than that in the rest of the part.The addition of a copper slug to the holecan effectively correct or eliminate thisproblem. The position of the slug (Fig.15, p. 36) can control the resultant heat-ing pattern. In addition, the slug will mini-mize hole distortion if the part must bequenched following heating.

For slotted parts heated with sole-noid coils (Fig. 16, p. 36), the continuouscurrent path is interrupted by the slot,and the current must then travel on theinside of the part to provide a closed cir-cuit. This is the basis for concentratorcoils. It is of interest to note, however,that with the slot closed, the applied volt-age of the work coil causes a higher cur-rent to flow. This is due to the fact that

35HEAT TREATING/JUNE 1988

Fig. 10: Method of inserting a liner in acoil to widen the flux path

Fig. 11: Selection of single-turn vs. multiturncoils depending on the length-to-diameterration of the workpiece (from F. W. Curtis,High Frequency Induction Heating, McGraw-Hill, New York, 1950)

Fig. 12: Typical proportions of varioussingle-turn coils (from F. W. Curtis, HighFrequency Induction Heating, McGraw-Hill,New York, 1950)

Coil leads

Coil liner

Connection from generatorto coil (braze points)

Top view

Tubing soft-soldered tocoil liner for maximumsurface-to-surface

cooling

Side view showing actual shape of coil

89-mm (3 1/2”) PD gear 12.7 mm (1/2”)

CoilGear Coil

Multiturn,good

Single turn,bad

Coil

Locating stud Spray-quench ring

Gear

19.0 mm (3/4 in.)

25.4 mm(1 in.)

51 mm (2 in.)

Water cooling

25.4 mm(1 in.)

12.7 mm(1/2 in.)

12.7 mm(1/2 in.)

102 mm (4 in.)

29HEAT TREATING/AUGUST 1988

Coil design and fabrication:part 2, specialty coilsby STANLEY ZINN and S. L. SEMIATIN

InductionInductionInductionInductionInduction

C oil designs are based on theheating-pattern require-ments of the application,the frequency, and the

power-density requirements. In addi-tion, the material-handling techniquesto be used for production determine,to a large extent, the coil to be used.If a part is to be inserted in a coil,moved on a conveyor, or pushed endto end, or if the coil/heat station com-bination is to move onto the part, thecoil design must take the appropriatehandling requirements into con-sideration. Accordingly, a variety ofspecialty coil designs have evolved forspecific applications.

Master work coils and coil insertWhen production requirements neces-sitate small batches (as in job-shop ap-plications) and a single-turn coil canbe used, master work coils provide asimple, rapid means of changing coildiameters or shapes to match a vari-ety of parts. In its basic form, a mas-ter work coil consists of copper tub-ing that provides both an electricalconnection to the power supply and awater-cooled contact surface for con-nection to a coil insert (N. B. Stevensand P.R. Capalongo, “Inductor forHigh-Frequency Induction Heating,”U.S. Patent 2,456,091, December 14,1948). A typical design, shown in Fig.1, consists of a copper tube that is bentinto the form of a single-turn coil andsoldered to a copper band that con-forms to the slope of the coil insert

S. Zinn is executive vice president, Ameritherm,Inc., Rochester, N.Y.; (716) 427-7840. S.L.Semiatin is a project manager in the Center forMaterials Fabrication at Battelle Columbus Divi-sion; (614) 424-7742.This article is excerpted from the book “Ele-ments of Induction Heating,” published by Elec-tric Power Research Institute (EPRI) and dis-tributed by ASM International, (516) 338-5151and used with permission of EPRI.

and is recessed. Holes in the insertsthat match tapped holes in the mastercoil securely clamp the inserts to themaster coil, providing good transfer ofelectrical energy and heat removal.Inserts are machined from copperwith a thickness that matches the re-quired heating pattern, and should besomewhat greater in thickness than thedepth of the recess for easy removal.Special coil shapes are easily config-ured. It is important to note that, be-cause of the less-than-optimal cool-ing technique, coil inserts are particu-larly well adapted to processes requir-ing short heating times or those inwhich they are also cooled by thequenching medium.

In machining of coil inserts, caremust be taken to relieve sharp cor-ners, unless it is desired to have adeeper heating pattern in these loca-tions. Fig. 2 shows the effect of sharpcorners on a closely coupled part. Fluxfrom both inductor sides couples to thecomer, which, due to a lack of mass,tends to overheat relative to the restof the pattern. Decoupling of the coilfrom these locations provides the de-sired pattern but tends to reduce over-all efficiency, thus slowing the heat-ing rate and resulting in a deeper case.Relieving or decoupling of only thecorners is a better alternative, par-ticularly when a solid, inductor isused, and the relief can be machinedas required.

Coils for induction scannersCoils for progressive hardening (scan-ning) are built using two techniques.The simpler of the two employs asimple single-turn or multiturn coil witha separate quench ring that can bemounted on the scanner (Fig. 3a,p.30). For larger production runs, adouble chamber coil that incorporates

Fig. 1: Schematic illustration showing thedesign of a master coil with changeableinserts (from M.G. Lozinski, Industrial Ap-plications of Induction Heating, PergamonPress, London, 1969)

Fig. 2: Inductor with a relief designed forthe hardening of the lateral surface of a tem-plate (from M.G. Lozinski, Industrial Appli-cations of Induction Heating, PergamonPress, London, 1969)

31HEAT TREATING/AUGUST 1988

lenges is the creation of an even heat-ing pattern at the end of a bar or shaft.Patterns developed with a pancakeinductor produce a dead spot at thecenter, due to field cancellation in thisarea.

39HEAT TREATING/OCTOBER 1988

Coil design and fabrication:part 3, fabrication principlesby STANLEY ZINN and S. L. SEMIATIN

S. Zinn is executive vice president, Ameritherm,Inc., Rochester, N.Y.; (716) 427-7840. S.L.

InductionInductionInductionInductionInduction

40 HEAT TREATING/OCTOBER 1988

can be extremely large, and if properbracing is not provided; the coil maygradually work harden and finally fail. Typical bracing techniques are il-lustrated in Fig. 2. In Fig. 2a, brassstuds are brazed to every other turn.These studs are then secured to in-sulator posts to hold them in a fixedrelation to each other. Nuts on eachside of the stud at the insulator allowadjustment for characterization of theheating pattern. In Fig. 2b, the insu-lation has been contoured to hold theturns relative to each other after theend turns are secured with studs. The insulation used for bracing ap-plications must meet the criteria forthe coil design. In addition to the in-stallation being capable of withstand-ing the hea t rad ia ted f rom theworkpiece, its electrical capabilitiesmust permit it to with-stand the volt-age between the mounting studs orthe turn-to-turn voltages of the coil.This is of particular concern whenusing high-voltage RF coils where upto 12,000v may be impressed acrossthe total coil. It may be necessary inthese instances to provide slots be-tween the stud locations in the insu-lator boards to increase the electricalcreepage path between the studs. Itmay also be necessary to increase theheat-resistant characteristics of theinsulation by facing the area exposedto the heated surface with a sheet ofhigh-temperature insulation.

For purposes of rigidity, clean-

ness, and protection, it is sometimesdesirable to encapsulate work coils ina plastic or refractory material. Thesame kind of care with respect to volt-age and temperature characteristicsmust be taken with these materials aswith insulating boards. For low-tem-perature induction heating applica-tions, epoxy encapsulation of the coilis quite common. For heating of steelbillets, coils are usually cast in a re-fractory cement to prevent scale fromthe part from falling between the

turns. In coating of coils with refrac-tory materials, care must be taken tomatch the pH of the refractory to that ofthe material being heated; for example,an acidic refractory is required for theferrous scale that drops off during high-temperature heating of steels.

Design considerationsAll coils represent an inductance tothe tank circuit. However, in practice,the working portion of the coil may infact be only a small portion of the in-ductance presented to the tank. Be-tween the output terminals of thegenerator or heat station and the heat-ing portion of the work coil, there maybe a considerable distance of outputlead. In any case, some finite distanceexists between the heat-station termi-nations and the actual coil. Designand construction of these work-coill eads can be a major fac tor indetermining job feasibility.

The effect of lead construction onsystem performance can be best un-derstood with respect to the tank cir-cuit of which it is a part (Fig. 3). Thecoil/load inductance is representedby L2. Each lead connecting the tankcapacitor to the coil has its own in-ductance (L1, L3). If the voltage in thetank, ET, is impressed across the to-tal of these inductances, then somevoltage drop appears across each.The full voltage will thus never ap-pear across the work coil. If the induc-tance of the coil (L2) is approximately10 times the total inductance of theleads (L1 plus L3) or greater, a maxi-mum of 10% of the total voltage willbe lost in the leads. Any loss less thanthis can be considered nominal.

Some coils have many turns, alarge cross-sectional area, and thusfairly high inductance. Hence, thecomparative lead inductance is small.As the frequency increases, coils of-ten become smaller in size, and theirinductance and inductive reactancedecrease. As the distance betweenthe heat station and coil increases,therefore, these lead inductances canbecome critical.

Several coil designs that illustratethe effect of lead design are shown inFigs. 4 and 5. In Fig. 4a, a coil withleads far apart is depicted. The spacebetween the leads presents an induc-

Coil design

Fig. 2: Typical techniques for bracing ofinduction-coil turns (from F.W. Curtis, HighFrequency Induction Heating, McGraw-Hill,New York, 1950)

Table I: Selection of copper tubing for induction coils.