US1995811A - Induction heater - Google Patents

Description

March 26, 1935. T. H. LONG INDUCTION HEATER Filed May 20, 1950 lNvENToR 730/7745 of/j.

ATTRNEY Patented Mar. 26, 1935 UNITED sTATEs INDUCTION HEATER Thomas H. Long, Iwin, Pa., assignor to Westinghouse Electric & Manufacturing Company, a corporation of Pennsylvania Application May 20, 1930, Serial No. 453,908

My invention relates to improvements in heating apparatus and it has particular relation to inductive-heating equipment.

In inductive heating apparatus, constructed and operated according to the teachings 0f the prior art, it has been customary to use a high.- frequency motor-generator set and to correct for low power factor by disposing a plurality of static condensers in series4 or in parallel with-the generator supplying the exciting currentl to the inducing coils. This methodof operating has proved rather expensive, by reason of the cost of the condensers and generator set involved.

On the other hand, it is possible toselect the dimensions of the inducing coil and the frequency of the inducing field, in such manner as to give these properties of the equipment values so related to the characteristics of the charge that a maximum, or a considerably improved, power factor is obtained at relatively low frequencies or standard frequencies such as cycles. Inductiveheating equipment having the requisite tractability in its `properties has a wide range of usefulness.

It is, accordingly, an object of my invention to provide inductive-heating apparatus the properties of which are so inter-related that the ratio of the irreversible energy induced in a hypothetical charge, having the properties of conductors most commonly treated in the apparatus, to the reversible energy induced in the charge is substantially a maximum.

It is a further object of my invention to provide a method for heating a charge wherein the characteristics of the elements partaking in the heating operation are so related to the properties of the charge that the power factor of the" energy developed in the charge is substantially a maximum.

Still another object of my invention is to provide a method of operating an inductive-heating system according to which the charge is so dimensioned that ay maximum power factor -is obtained. A

An additional object of my invention is to provide inductive-heating apparatus wherein the cooperating elements are so related that the first cost of a high-frequency motor-generator set is eliminated.

` A still further object of my invention is to provide inductive-heating apparatus wherein the continued cost arising from the losses engendered in using a high-frequency motor generator set is avoided.

It is still another object of my invention toxincrease' the economy of inductive heating, as applied to industrial processes.

An ancillary object of my invention is to provide inductive-heating apparatus wherein the energy-input distribution inthe charge is substantially uniform.

Another ancillary object of my .invention is to provide inductive-heating apparatus capable of producing a predetermined temperature distribution, in an element treated therein, with a minimum degree of heat conduction.

More specifically stated, it is an object of my invention to provide inductive-heating apparatus wherein the cross section of a charge, its permeability and its conductivity are so related to the frequency of the inducing magnetic field that a substantially maximum power factor is attained at comparatively. low standard frequencies.

According to my invention, I provide an inductive heater dimensioned in compliance with the restrictions defined by a mathematical relation expressing the condition that the value of the vpower factor in terms cf the constants of the apparatus and the properties of an arbitrarily assumed charge, shall have an optimum value. In

-the following analysis, it will be shown that it is possible to use a comparatively low frequency by properly adjusting the remaining variable properties of the heating apparatus.

Other objects of my invention will become evident from the following description, taken in conjunction with the accompanying drawing, in which:

Figure 1 is a sectional view showing schematically an inductive heater constructed according to my invention;

Fig. 2 is a plan view of the apparatus shown in Fig. 1 with outer casing and insulating material removed;

Fig. 3 is a schematic View illustrating a modification of my invention;

Fig. 4 is a sectional view showing schematically the modification shown in Fig. 3;

Fig. 5 is a graph representing the solution of the power-factor problem, as applied to the apparatus shown in Figs. 1 and 2; and

Fig. 6 is a graph representing the solution of the power-factor problem, as applied to the apparatus shown in Figs. 3 and 4.

The apparatus shown in Figs. l and 2 includes a solenoid 1 comprising a plurality of turns of a flattened conductor 3. The cable is surrounded by suitable heat insulating material 4.

Adjacent to the internal surface of the solenoid 1 is a layer of refractory material 5 of torroidal cross section. The charge 7 is disposed within the insulating cylinder 5. Y

Figs. 3 and 4 represent, dia'grammatically, an inductive heater capable of eiiiciently accom- `modating a charge that is rectangular in cross section. In the treatment to be hereinafter described,l the equipment represented in Figs. 3 and 4 will be regarded as having a length that is large, in comparison with its width and depth; that is to say, I shall regard it as extending indefinitely in the direction W while its width 2r and its depth L are denite.

In analyzing the problem, I shall set up and solve the Heaviside-Herz equations for the electro-magnetic iield, thus obtaining the diierential equation which governs the flux distribution in a charge subject to a magnetic iield. In the treatment, it will be implicitly assumed that the wave length, in space, of the inducing current is great in comparison with the dimensions of the apparatus. I

I shall further solve the differential equation for the special case of a cylindrical and an elongated rectangular charge, making certain obviously allowable approximations. Vlin equation defining the special properties of the ux distribution in the charge is thus obtained.

From the relation giving the ux distribution,

I shall obtain the components of the inducedvoltage that give rise to the heatless component and the heat component of the power. The relation involving the ratio of these two values I shall then treat for optimum conditions, solving the equation, thus derived, graphically to obtain an expression relating to properties of the vcharge and the characteristic of the inductive heater.

In the analysis, the physical properties of the elements involved are represented as follows:

R=internal radius of the coil in centimeters r=the radius of the cylindrical charge in centimeters :one half the width of the rectangular charge L=the depth of the charge in centimeters W=the length of the rectangular charge A=conductivity of the charge in mho 4per centimeter cubed A :permeability of the charge H=strength of the magnetic' field, threading the charge, in Gilberts per centimeter =maximum flux density in lines per square centimeter parallel to the axis of the solenoid B..=;S1e12m Where B2 is the z component of B =frequency t=tirne variable J=inducing current I=current density in the charge E=induced voltage per centimeter of length =total ux The field equations are (1) curi H=.4iE (2) curl E=g1o therefore (3) Curl Curl -H=.4^u}( Curl E 5B (4) .41r}\510 s (5) Curl cui-1 B= .mani-104 5B (6) Grad Div B-A?B= -1 .fl'rM--IO s The end eiect in the solenoid may be safely neglected without appreciably aecting the accuracy of the solution and the induction may be regarded Ias having a direction parallel to the axis of the solenoid, i. e., using the conventional coordinates, the components of B are given by therefore (11) becomes (16) Ala-:.anfpiw For a cylindrical charge, the most satisfactory approach to the problem is made withY the help of cylindrical coordinates in which terms (16) becomes Equation (20) is Bessels equation of the zeroth order of which the solution is Now it is at once seen that, since is always finite, it is finite when r=u=0. This restriction may be regarded as a boundary condition.

Hence it follows' that y 1,995,911 o 3 and since it is my purpose to vary :c1 as will be seen hereinafter. (25). B=AJ(") The iiux 90 out of phase with J is given by (26) =A]0(-jmr) 21B! (27) :A 1 Lzz- Lf- JLM (41) K=Ffw The heatless component of the voltage 1s essen- (23) =Albr (mfH-J b1 (11101' tially proportional to J, while the heat comwherein ponent of the voltage is proportional to K and the constants of proportionality do not vary A For brevity I shall write Let 6=the angle the cosine of which is the power factor.

(3) 'SAGU xl'j b x) Hence the power factor is measured by where v X, xs (42) cot 0=7gf=7 fg? To determine A, I apply a second boundary L P Y Kx) vand the equation (30) becomes For a maximum power factor, the derivative with respect to :c of the fraction in :c and r in I equation 43) is 0; that is,

m12 where (36) ci het bei" For brei/ity shall now Write` It is seen'that o comprises two components namely in phase with the inducing current J and which may be taken as equivalent to for all practical purposes. This eld is in phase with the inducing current J.

Hence the total flux in phase with J is given by Q is constant if the assumption is :aaee the gap between the coil and the charge is proportional to the radius of the charge.

`bei' x ber z -f-beix bei' x* f(x)+ x' Equation (51),may besimplied to a form K (sa) wxLkiewfco-gao] .This equation may be solved graphically for :c and its solution for several values for parameter Y ,isshowninFig. 5. s

' duces to the vertical equivalent to rout/.8Min

is greater than 2.5 and has a value determined hy the gap between the coil and the charge. In furnaces constructed according to the teachings of the prior art, a: has avalue greater than '7.03.

- The actual value of :1: that -is chosen for any given case is not arbitrary within the limits but depends on the most convenient value that may be given to Q; that is, to the distance between the coil and the charge. n

In practice, the smallest value that Q has is .05.

t is seen from the curve that a value of 5.25 for as' corresponds to this value of Q.l The relation that dominates the dimensions of` the furnace and the adjustment of the frequency of the current, therefore, reduces to Under ordinary circumstances, c has` a value of unity at the temperatures at which the heater is used, while the maximum value of A is Ai-lii'i. Hence, a more specic expression ior the Equation 54 is l' shall now consider the case wherein the charge has the cross-section of a rectangle the length ci which extends indenitely. In practice, the erom-section oi a charge may he simply an elongated rectangl It has also been found that the solution which will be obtained hereinafter may, with reasonable accuracy, be applied to a charge that has a cross-section in the form of an ellipse having a long major axis and a short minor axis.

Since the cross-section of the charge is indenniteiy long, the eiect at the ends of the charge may be neglected. Hence, ii is expressed with reference to the rectangular coordinates w, in the direction o the length, and r, in the direction ot the width, it is seen that is a function ci r only,

that is,

' Equation i6 holds for any geometric forni Aof charge and, when written in terms oi f and in, reduces'to a2 (s1) aanname-9 de e (se) g=2im where (59) m12.- .amano- I Equation 58 is a linear dierential equation noemen having constant coeicients, and its solution may easily be shown to be cosh mr cos mrfi-j sinh nir sin mr wherein =1 for r=r'1, 2n being the width of the charge.

Again I! =217Vj1 d (61) b o r lo and when the indicated voperation is performed it is found that 28,177 sinh mn cos mrl-i-j cosh mn sin mn (1+j)zn cosh mr; cosmrl--j sinh mr; sin mrl which in more simple ionn appears as cosh 2mr1-l-cos 2mn It is to be noted that the constant m, as dened byv the Equation (59),. is the m o the Equation (18) divided by f 3c i i v In Equation (64) (es) x=2mr==r1ow1mpff 35 sinh x--sin x (66) F@Q -cosi: x-i-cos x sinh x-sn n (67) 'Huy-cosh x-l-cos x 40 A'me total aux 'm phase with the inducing eurrent .i is now given by 1, zama-r) g (en a-mvve e+---/ n (69) afge/Foz) 'and 5'0 i, im S--ffa where 55 R-r .(71) Q- and is assumed toremain constant Q so F'(X)+ iv i @[1 Q31] 72) 5' for) eco i Q RXE?? ee (73) 3?(10575- 1 (QW which may be written ce Fcme-wwam-na} 7@ where .Y Us) Mzxoosh x-cos x sinh n-sin x The solution of the Equation' (74;) for various 75 values of Q is shown in Fig. s. It is seen that, in this case, the dominating inequality is (76) 2.25 f1o1/1.6Mfr 9.91 a more restricted inequality being and is the value determined by the prior art.

It is seen that the rectangular (or elliptic) charge yields a maximum power factor for a width smaller than the diameter of the corresponding cylindrical charge. This property of the system is of` advantage in situations where it is desirable to use a long and narrow charge. It can be applied with facility to apparatus wherein steel strip is normalized.

After the strip passes between a pair of rollers, it traverses an elongated induction heater where it is raised to the temperature that it had before it came under the action of the rollers. It is then rapidly cooled. Steel treated in this manner has more desirable properties than annealed steel.

For p=l and for a maximum value of 4-l04 for A ('15) becomes (7s) 2254079515 f 9.91 for :r1- d0 cycles (T8) becomes When magnetic charges are heated, the permeability is ordinarily of the order of 200.

For such a case, (76) becomes` i having been taken equal to 4104.

I do not wish to be restricted to the speciiic structural details or arrangement of parts herein set fortlnas various modiiications thereof may be eiected without departing from the spirit and ratus in such manner that a predetermined enl ergy-input distribution for the charge is obtained for any given situation.

The energy input per unit time for the cylindrical charge is given by the relation Ell (81) T but by Equation 1 and, by substituting in (81),.it isseen that the absolute value of the energy developed is given by 83) m58;2 berx+bei"x .813)44 berxx-i-beixl For a rectangular charge, the absolute value oif the energy input is given by z mz cosh x-cos x ('84) W .41:42AM cosh x1+cos x1 These relations are of particular interest in certain elds of industry e. g., in rolling mills where it is necessary to relieat an ingot after it has been removed from the mold and prior the rolling operation.

When the ingot is poured, the entire mass of metal may be regarded as having a uniform temperature. As a result of the thermal capacity of the walls of the mold, the ingot, when removed from the mold, is not of uniform temperature throughout but has a maximum temperature in some interior region and has a minimum temperature on its bounding surface.l l

In reheating the ingot before rolling, it is desirable that it be brought back to substantiauy a uniform temperature throughout, the value of will be approximately the same ats-.the temperature at its hottest part when it was removed from the mold.

In general, it is possible to determine the theoretical temperature-distribution characteristic of any ingot of given dimensions, and to sc adjust the properties of the inductive retreating apparatus in which the ingot is treated that the power input in each individual region of the ingot is substantially proportional to the temperature through which the metal in these regions is to be heated. For example, in a cylindrical ingot, the

temperature distribution varies parabolicallyV from the center to the periphery. It is obvious that the constants of the heating apparatus may be so selected that W, in Equation (83), varies substantially as a parabola similar to the inverted temperature-distribution curve.

As a result of such specific arrangement of the apparatw, the heating energy is liberated in individual regions in proportion as it is needed, and it is not necessary to allow time for heat flow from an abnormally heated region to a cooler region. I have found that this process reduces the reheating time from several hours to approximately 10 minutes.

I desire, that only such limitations shall be imposed upon my invention as are indicated in the appended claims.

I claim as my invention:

1. Inductive electrical heating apparatus comprising a coil to be magnetically coupled to a. cy-

lindrical charge, a substantial air gap intervening between said coil and charge and an alternating source of current for energizing said coil, the characteristics of said coil and said source being so related to each other and to the properties of said charge that they substantially obey the relation Y where Y 'l b l wherein ber x be' x-bei x er x F(X)=X ;T; Vxf Y A 2:11-10-1/.8Mfr

berm X+beil2 x rl being the radial distance from the axis of said (X)=m mass o f a point at which W is the energy input b b HJ b A being the conductivity of sa1d mass f(x)=x-fzxel.x a being the permeability of said mass Y s ber x-He x f being the frequency of said magnetic eld Q=R2zz3 x,= 1o-alinea, r1 being the radius of said mass 1 tsm p1=the amplitude of the aux density at the T ithseggifnge Charge periphery of the mass and n Y X being its'conductivity m=1r1/ 10.94131 R being the radius of the inducing coill and being the frequency of the current. i

wherein sinh x-I-sn x F(X) cosh x-icos r' l sinh x-sin x l(x) cosh x-l-cos x SEM-9.5.2. sinh x-sin z R-r Q= 1.

l x= 211'1041/.4pir

2r being the width of the charge A being its conductivity p. being its permeability f being the frequency of the curren 2R being the width of the heating coil.

A3. The method 'of heating a furnace charge, which is in the form of a circular cylinder, from an initial condition in which it has a transverse temperature distribution function which is substantlally a parabola with an'- axis coinciding with the central axis of the cylinder, which consistsv in generating heat Within the cylindrical mass,

the rate of heat generation having a substantially parabolic distribution relative to said central axis.

4. The method o heating a furnace charge, which is in the form of a circular cylinder, from an initial condition in which it has a transverse temperature distribution function whichris substantially a parabola with an axis coinciding with the central axis of the cylinder, which consists in generating heat within the cylindrical mass, the

' rate of heat generation having a distribution which is a parabola substantially similar to the fast-mentioned parabola and is coaxial therewith.

5. The method of heating a furnace charge,V

which is in. the form of a circular cylinder and y which has 'cooled from a substantially uniform elevated temperature condition by heat outow from its side walls, which consists in generating heat by electromagnetic induction .within said cylindrical mass by means of a n'alternating magnetic eld such that the rate W of heat generation ullls the equation v f z .,rrlll2 bei'.I2 x-l-be2 x .812)412 berg Iliff-bei? X1 wherein 6. The method of heating a rectangular conducting Vmass, having the form of a rectangular Y parallelopiped, which has cooled from a substantially uniform elevated temperature condition by heat outflow through two opposite side Walls,

which consists in generating heat within said mass by electromagnetic4 induction through the agency o an alternating magnetic field such that the rate W of heat generation fulils the equation mzl2 cosh x-cos z Aa-ZAM cosh xl-i-cos :x1

x=2fr1o1lniufr 'r being the distance in said mass from the center line parallel to its longest side at which W is the energy input Fano-a! .gaten 2n being the width of said mass and '71. The method of heating a furnace charge, which is in the form of a circular cylinder and which has cooled from a substantially uniform elevated temperature condition by heat outilow from its side walls, which consists in generating heat by electromagnetic induction within said cylindrical mass by means of an alternating niagnetic field such that the rate W of heat generation fullls the equation wherein `1'1 being the radius of said Ymass periphery of the mass and m=1r1lr41jlli the constants of the heating apparatus being so selected that lin the above equation varies substantially as a parabola similar to the inverted temperature-distribution curve. Y 8. The methodl of heating a rectangular con ducting mass, having the form of a rectangular parallelopiped, which has cooled from a substantially uniform elevated temperature condition by heat out-ow through two opposite side walls,

which consists in seneratins heat within wld ter line parallel to its longest side at which W is mass by electro-magnetic induction through the the energy input agency of an alternating magnetic held such that the rate W of heat generation tuliills the equation x: 2'! TH/md 1 3.41%# coahl-i-coo xl t m=r10m l wherein the constants of the heating apparatus being so I selected that W in the above equation varies sub- 10 x=2,10-1/ 4' `T, stantially -as parabola similar to the inverted 10 A temperature-distribution curve. r being the distance in said mass from the cen- THOMAS E. LONG,-

`2nheimrthe widthofsaidmassand 5

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