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Patented Sept. 24, 1946 2,408,190 UNITED STATES PATENT OFFICE 2,408,190 MAGNETIC INDUCTION HEATING OF THIN WALLED NONMAGNETIC METALLIC TUBES Robert M. Baker, Pittsburgh, Pa., assignor to Westinghouse Electric Corporation, East Pitts burgh, Pa., a corporation of Pennsylvania Application January 27, 1944, Serial No. 519,866 1 2 Claims. (Cl. 219-13) Heat can be generated in a piece of metal or other conducting material by Wrapping a heat ing~coil helically, or otherwise, around the piece, and ‘causing alternating current of suitable mag nitude and frequency to flow in the coil. The current produces a pulsating magnetic ?eld in side the heating-coil which induces circulating electrical currents in the work~piece that add heat to it. This type of heating is called induc tion heating with longitudinal magnetic flux be cause the flux lines which interlink the work piece are axially directed inside the heating— coil, and has many applications in industrial processes, of which hardening 0r heat~treating of surfaces, heating slugs in a continuous process for forging, and brazing are a few examples. My invention relates to this type of heat-treat 2 magnetic induction heating with longitudinal flux for heat-treating hollow nonmagnetic cylin drical metallic materials with frequencies in the rotating machine range; and it is among the objects of my invention to efficiently convert electrical energy of low frequency and relatively high power-factor into heat for heating border line sizes of thin-wall nonmagnetic metal tubes. Advantages, features and objects of my inven tion will be discernible from the following de scription thereof which is to be taken in connec_ tion with the accompanying schematic drawing for illustrating the principles thereof. In the drawing which is not to scale: Figure 1 is an axial or longitudinal view of an induction heating system embodying my inven tion, for heating a metal tube, Fig. 2 is a transverse view of the heating-coil and tube of Fig. 1, duction heating has the advantages of concen 20 Fig. 3 is a curve for indicating the induced trating the heat in a small space so that the current distribution in a piece of metal being work-piece can be quickly heated up, Whether it inductively heated with a coil-current having a is stationary or travelling, and of permitting the frequency such that the induced currents in the degree of heating to be accurately controlled. However, the maximum amount of power that 25 metal do not penetrate to the center thereof, Fig. 4 is a graphic representation of a curve can be e?lciently and eifectively introduced into useful for ascertaining the induction heating rate the work-piece depends on the physical relation of non-magnetic metallic cylinders, under cer ships between the heating-coil and the work tain conditions, and ment. Compared to other heat-treating systems, in piece, and their characteristics. Generally, the frequencies used for induction heating of metal Fig. 5 is a graphic representation of the heat ing rate or power input to a particular hollow brass cylinder as a function of the frequency depend on the size and the electrical and mag netic properties of the Work—piece, and may vary from common commercial frequencies of 25 to 60 cycles per second for heating joints in iron pipes, of the current supplied to the induction heating coil, the abscissae being on a logarithmic scale. to a few million cycles for soldering small non- 7 magnetic pieces of metal. Low frequencies up to 10,000 cycles, or slightly more, can be obtained Magnetic induction heating can be eXplained brie?y with reference to Figs. 1 and 2 which show a hollow cylinder or tube 2 of a nonmagnetic metal centrally inside a surrounding heating with high power from rotating electrodynamic machines; but for high power at high frequencies, coil 4 in the form of a helix of hollow copper say about 14,000 cycles and above, one must 40 tubing, the heating-coil being hollow so that it may be water cooled in any suitable manner. resort to spark-gap oscillators or tube-oscillators. The heating-coil derives its energy from an A very successful recent application of such in alternator or induction generator 6 to the output duction heating involving high- or radio of which it is connected by any suitable circuit frequency power is the treating of electrolytic tin-plate for brightening and solidifying its tin coating. In a. process of this kind, disclosed in copending application Serial No. 464,040 of Glenn E. Stoltz and myself, ?led October V31, 1942, the tinned surface of an electrolytically tinned fer 46 including, if desired, power-factor correcting capacitors 8 and i0, either in series or in parallel with the heating-coil, or both as shown. The alternator 6 is of any common type for delivering alternating current at frequencies up to approxi rous strip is melted while moving through a 50 mately 10,000 to 12,000 cycles per second, more or less, at high power, and is driven by an elec helical‘heating-coil at a speed of about 1000 feet tric motor i2 of controllable speed for control per minute, the heating-coil being supplied with ling the frequency of the alternator output. electrical energy at a rate of about 1200 kilowatts When a current I is caused to flow in the heat but at a frequency of 200,000 cycles. My invention is directed to the application of 55 ing-coil 4, a magnetic field is produced having magnetic flux lines F which are longitudinal 2,aoe,190 3 4 surface of the piece being heated; )‘ is the fre inside the heating-coil. A part of these ?ux lines interlinks tube 2 and causes a countercurrent CI to be induced in the tube, as illustrated by the respective arrows in Fig. If the wall of the tube 2 is suf?ciently thick and the frequency of quency in cycles per second; and Cr is a func tion of the product of K and a, the parameter Ka being used so as to make the heating formula perfectly general and applicable to any frequency and any cylinder. For this G function the supplied current sufficiently high, the induced current density is highest at the outer surface of the tube and decreases exponentially in the‘di (3) rection radially inward, as shown in Fig, 3 where 10 and a is the radius of the cylinder in centimeters. the ordinates are current densities and the ab The G function for solid cylinders is shown in scissae depths below the surface. To use gen Fig. 4, as a function of the product of K and a, and can be derived either experimentally or eralities by which such curve obtains and cor respondingly compute the induction heating in volves complex mathematics and complicated mathematically. For a hollow cylinder having a thick wall, by formulae. For a simpli?ed approach, a factor known as the depth of current penetration has been introduced, this factor being generally des~ thick wall meaning one having a thickness ap preciably greater, for a given frequency, than the depth of current penetration so that the in duced current can distribute itself in accordance with the curve A——B—C of Fig. 3, formula 2 is applicable when multiplied by the ratio of the ignated by the symbol 6. This depth of current penetration is considered as the radial or inward depth from the outer surface of a material being inductively heated to which a current of uniform density must penetrate in order to produce the same heating as that of the actually induced cur cross-sectional area of a solid cylinder to that of the hollow cylinder, because of the lesser metal volume of the hollow cylinder. rent of non-uniform density distributed radially For a solid cylinder, the foregoing G function or inwardly from the surface in the manner illus~ 25 becomes equal to about trated by the curve A——B—-C of Fig. 3. In general, for nonmagnetic metals, A 1/? K0 5 = c'\/-?- centimeters (1) when the depth of current penetration is less than about 1/2 the radius of the cylinder, so that Where 1‘ is the electrical resistivity of the metal in ohm-centimeters; f is the frequency in cycles per second of the current ?owing in the heating coil, and c is a constant depending on the con formula 2 for such case, can be simpli?ed to 35 watts per square centimeter of the outer surface of the cylinder which is directly within the coil. The total watts induced in the cylinder would be 0 can be assumed to be about 5030 for substan the value of W’ multiplied by such outer surface. tially ?at materials, varying only slightly there The required watts per square centimeter will .ii) from for curved materials, within about 15%. depend, of course, on how much heat is to be For a brass material, such as later described, the added to the piece, and can be computed from the actual heating produced by the actual current to desired increase in its temperature, the time in a depth 6 beneath the surface, along the curve which such heating is to be effected, and the spe portion A-B, is about 87% of the total heating, ci?c heat and volume of the material to be heated provided the wall thickness is over about three in this time. For moving material, the volume times 6. can be relatively very large. For economical low cost apparatus and effi If formulae 1 and 2 are used to determine the cient induction heating, it has generally been ac frequency for heating a thin-wall cylinder hav cepted, and it has been the practice, to induc tively heat tubular non-magnetic materials in a 50 ing a wall-thickness less than about 1/6 of its outer diameter, and it is assumed that the depth manner so that the depth of current penetration of current penetration is to be equal to or less is materially less than the wall thickness. than the wall thickness, values are obtained For solid cylinders, a ratio between the radius which are higher than I have found necessary of the cylinder and the depth of current pene for economical and effective heating, I con tration of not less than about 4:1 has been recom sider this to be an important discovery. One mended in the Northrup Patent 1,694,792 of De reason is that there have been instances where cember 11, 1928. For such condition, in which frequencies were indicated that could be obtained the depth of current penetration is considerably only with spark-gap or tube-oscillator equip less than the distance to the center of a solid ments. For example, consider a hollow brass metal, so that substantially all the current dis cylinder with a resistivity of '7><10—6 ohm-centi tributes exponentially as shown in Fig. 3, the rate meters, having a diameter of 10 centimeters and of heating can be expressed in watts per cubic a wall thickness of .1 of a centimeter. From centimeter of the part of the cylinder which is formula 1, the frequency required for a depth of radially encompassed by the heating-coil, pro vided end effects can be ignored, which is the 65 current penetration equal to the wall thickness should be case when the coil length is about 5 times the spacing between the outer surface of a cylinder being heated and the inside diameter of the ?guration of the outer surface of the material being inductively heated. For general purposes, heating-coil. This heating is expressed by the formula watts per cubic centimeter where H is the peak magnetizing force in oersteds at the 70 In accordance with my invention lesser fre quencies can be used, although the depth pene tration is several times the wall thickness of the hollow cylinder, for in such case the hollow cyl inder can be considered as the short-circuited secondary of an air-cored transformer, with sub 5 2,408,190 stantially uniform current density through the thickness of the Wall. Referring to Fig. 3, at the point where the depth of current penetration line cuts the ex 6 accurate. The vertical dotted line It indicates the frequency at about which the depth of cur rent penetration passes the wall thickness, the depth of current penetration for frequencies to the right of this line it being less than the wall ponential curve, the current density would ap pear to be signi?cantly less than that at the thickness. In other words, for wattages requir outer surface of the cylinder. However, I believe ing frequencies intersecting the curve to the right that in a thin-wall cylinder, the thin wall pre of f5 formula 2 or 4 can be used; but for wattages vents the current from distributing in accordance at or below that for the horizontal part of the with the curve-portion embracing B-—C, so that 10 curve, lower frequencies can actually be used than the current density near the inner surface of the would be indicated by curve D—E—F. cylinder is raised, thereby providing a more uni The two frequencies fr and it comes closer to form distribution of current in the wall than is gether as the ratio of the diameter of the hollow indicated by a curve such as Fig. 3. cylinder to its wall thickness is decreased. fr The power input to a thin-wall hollow cylinder 15 can be represented by the formula by an alternating source having a frequency yielding a depth of penetration, according to for mula 1, which is greater than the wall thickness, is no longer represented by formula 2, but I have found that it can be represented by the formula 20 and it can be represented by the formula (6) fr=l5?;;10° (7) f6=25.t::10° The ratio of these frequencies is, therefore, watts per square centimeter of the outer sur face of the hollow cylinder, which is directly in 25 side the heating coil; where d is the outer diam (8) =.1e7 % eter of a cylinder in centimeters; and t is the thickness of the cylinder wall in centimeters, This shows that the two frequencies coincide My invention, in its general aspects, can be approximately when the outside diameter of the explained with reference to Fig. 5 in which the 80 hollow cylinder is six times the wall thickness, ordinates represent watts per unit of the square and become farther apart as the ratio of the di of magnetizing force per square centimeter of ameter to wall thickness increases. Accordingly, outer cylindrical surface within the effective by thin wall I mean a tube in which the wall heating-coil boundaries, and the abscissae rep thickness is less than about 1/6 of the outer di resent the frequencies for obtaining such watt 35 ameter. ages for the aforesaid brass cylinder. Curve If satisfactory power input can be obtained at D—E—-F is derived from formula 4 and. repre a frequency is, it is also possible to obtain the sents the least frequencies, according to prior same satisfactory input at a lower frequency down practice, at which the corresponding ordinate to fr, so that the most economical or available watts were thought to be obtainable. Curve 4.0 power source can be chosen. The lower frequency G—E—H is derived from formula 5 when the heating-coil and. cylinder are considered an air cored. transformer, or When the depth of cur rent penetration is greater than the wall thick ness. also results in an improved power factor at the heating-coil terminals. In the speci?c case of the brass cylinder, frequencies of 17,000 to 18,000 cycles are at present beyond the range of rotary The two curves can be joined by a section 45 alternators, but frequencies of 10,000 and below K—-L for producing a representative curve are easily obtainable. Since uniform heating can G_K—I_r-—F under which the hollow brass cyl be obtained, in accordance with my invention, inder actually absorbs power, so that the parts with lower frequencies, it is evident that such a brass cylinder can be e?iciently heated at mini of the curves D—E—-L and K—E—H therebelow can be ignored for practical purposes. 50 mum cost with rotary equipment. It is seen that the power input increases rap While I have described my invention in con nection with a hollow cylinder, it is apparent that idly at ?rst as the frequency is increased, then it is generally applicable to thin-wall nonmag the power input levels off and becomes constant with increased frequency, and finally increases netic metal tubes of other shapes so long as the again with frequency. I explain this in the fol 55 inner dimensions are, on the whole, more than lowing manner. At very low frequencies the about 6 times the maximum thickness of the wall, depth of current penetration is greater than the as a whole. Of course, irregularities or peculiar wall thickness and the heating is proportional to the square of the induced voltage and, there shapes may give other relations, of less than 1/5, in a, limited region, without operating outside the fore, of the frequency. However, when the in 60 scope of my invention. duced current becomes approximately equal to The resistivity of a material changes with tem the current in the heating-coil, increasing the perature; but for materials having small changes frequency does not induce any greater voltage of resistivity with temperature, any value in the in the work~piece so that the heating remains range of temperatures in which the material is constant until the frequency reaches a value such 65 inductively heat-treated will yield results satis that the depth of current penetration becomes factory for practical purposes. Where the re less than the wall thickness and the current den sistivity changes may be large, however, the aver sity distribution follows more closely the curve of age value of resistivity between the temperatures Fig. 3. When this arises, the heating in the of the material immediately before and after in work-piece is represented by formula 2 or 4 in 70 duction heating is desirable for determining stead of formula 5. power input, while the maximum value is desir In Fig. 5, the vertical dotted line fr indicates able for frequency determinations, in order to an arbitrary value of frequency where the input operate with a factor of safety; although in gen has almost reached the flat part of the curve, eral the average value can, as a rule, be used 90% of the value being considered satisfactorily 75 without too serious discrepancies. 2,408,190 7 I claim as my invention: l. A method of e?lciently and effectively mag n etically inductively heating hollow nonmagnetic metallic cylindrical material having an outer di " 01, in centimeters, generally in excess of @3185 its wall-thickness t, in centimeters, which. method comprises passing the hollow cylin 8 2. A method of ei?ciently and effectively mag netically inductively heating hollow nonmagnetic metallic cylindrical material having a minimum outer dimension d, in centimeters, in excess of ‘ six times the thickness 15 of its wall, in centi meters, which method comprises placing the ma terial centrally in an axial alternating magnetic field having a frequency in cycles per second dri material in the direction of its axis through which is greater than an induction heating-coil, and energizing the heating-coil from a rotary alternator delivering 10 an alternating current having a. frequency in cycles per second, in a range between but less than l53r10° 25.6r10° id t2 ‘(11371 where r in ohm-centimeters is the resistivity of 25.6110” t2 the material. ROBERT M. BAKER. Where T is the resistivity of the material in ohm 20 centimeters.