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Патент USA US2408191

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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.
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