Note: Descriptions are shown in the official language in which they were submitted.
BACKGROUND OF '~IE INVENTION
Thermall~ regulated heating elements of a wide variety of typeshave existed for some time. Most often these elements have utilized some form
of feedback control system in which the temperature produced is sensed and
the source of electrical energization to the heating element is controlled
either in a continuous, proportional or step-wise switching fashion to achieve
more-or-less constant temperature. Utilizing a wide variety of thermal sensors
and various control systems, these approaches continue to be successfully used
in many applicatlons.
However, there are many situations requiring temperature regulation
which the prior art feedback control systems are not capable of handling
adequately.
One of these situations involves differential thermal loading of
the heating element over its extent, such that its various parts operate at
different temperatures. In order to satisfactorily regulate temperature under
such a loading condition with the prior art feedback control systems, the
heating element must be subdivided into a plurallty of smaller heating elements
and each one must be provided with independent sensing means and feedback con-
trol, etc. In general, this approach is far too clumsy, unreliable and ex-
pensive.
A second situation in which the prior art feedback control systems
are not adequate is where the heating element itself is so small as to make
adequate monitoring of its temperature by a separ~te sens~ng means impractical.
In some instances it has been possible to cope with these situations by utilizing
a thermally dependent parameter of the beating element as a means of sensing
its own temperature. For example, it is possible in some instances to energlze
a heating element in a pulsed manner and sense the resistance of the heating
element during the portion of the po~er suppl~ cycle when it is not energized.
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If the cycle of alternate energization and temperature sensing is made short
in comparison to the thermal time constants o~ the heating element and its load,such a scheme can be used to alter the duty cycle of energization by means of
a feedback control system to produce a constant temperature. However, the re-
sultant apparatus is complex and relatively expensive.
Another instance in which traditional means of feedback temperature
control is inappropriate occurs when the thermal time constants associated
with the heating element and thermal load are so short that they exceed the
speed of response of the thermal sensor and the control system. Typically
these situations arise when the heating element is extremely small but can
; also occur in heating elements of great extent but low mass such as in a long
filamentary heater.
The~above and many other difficult thermal regulation problems
could be reliably, simply and inexpensively solved if there were an electricallyresistive heating element which provided adequate intrinsic self-regulation
of temperature despite changes in thermal load.
Description of the Prior Art
In the induction heating furnace prior art, a known means of tem-
perature control has been to select the ferromagnetic material of the inductive
heating members in such a way that the power induced in them by induct~ve
coupling from an AC primary circuit was automatically regulated by ma~erial
parameters.
In particular, it was reaIized in the prior art that ferromagnetic
materi~undergo a thermodynamic phase transition from a ferromagnetic phase
to a paramagnetlc phase at a temperature known as the Curie temperature. This
transition is accompanied by a marked decline in the magnetic permeability of
the ferromagnetic material. Consequently, when the inductive heating members
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approach the Curle temperature, the consequent declIne in magnetic permeability
significantly lessens magnetic coupling from the primary circuit of the in-
duction furnace, thereby achieving temperature regulation in the region of the
Curie temperature of the ferromagnetic inductive heating members.
However, this prior art, which is exemplified by United States
Patents 1,975,436, -437, and -438, does not teach how the declining magnetic
permeability at the Curie temperature may be used to control the temperature
of a non-inductively coupled heating element. Furthermore, this prior art does
not suggest that the transition which occurs at the Curie point may be utilized
~n combination with the skin effect phenomenon in a composite material in such
a way as to provide intrinsic temperature regulation, with either ohmmic or
inductive coupling to the power supply.
The principal object of the present invention is to provide a re-
s~stive heating element which is intrinsically self-regulating at a substantially
constant temperature despite large changes in thermal load.
A second object of the present invention ~s to provide such a re-
sistive heat~ng element which is self-regulating at a temperature determined
by a physical parameter of the materials used to make the heating element.
A third object of the present invention is ~o provide a resistive
heating element which utilizes the skin effect, ~hereby alternatlng currents
are most heavily concentrated near the surface of a conductor, as a means to
achieve lntrinsic temperature regulation.
A fourth object of the present invention is to provide a resistive
heating element in which localized variations in ~hermal load over the surface
extent of the heating element are locally compensated to achieve a high degree
of tempeTature constancy uniformly over the extent of the heating element.
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A fifth object o~ the present invention is to provide a resistive
heating element in which a high degree of temperature stability despite signif-
icant fluctuations in thermal load is achieved without resort to complex feed-
back systems to control electrical energization.
A sixth object of the present invention is to provide a resistive
heating element in which a high degree of temperature control can be achieved
merely ~y energization with a constant-current alternating source operating
typicall~ in the frequency range from 8-20 MHz.
To the above ends, an electrically resistive heating element according
to the present invention comprises: a substrate member of a non-magnetic material
having high thermal and electrical conductivity, and a surface layer of a fer-
romagnetic material having a Curie temperature in the region about which tem-
erature control is desired, the surface layer extending substantially the full
length of the heating element. By energizing the heating element so provided
~th a constant-current R.F. source, current is confined substantiall~ entirely
to the ferromagnetic surface layer until the temperature of the h0ating element
rises into the region of the Curie temperature of the ferromagnetic material.
As the Curie temperature is approached, the declining magnetic per-
meability~of the ferromagnetic surface layer markedly reduces the skin effect
causing a mlgratioD or spreading of the current into the non-magnetic member
of the heating element. As a result of this spreadingJ the resistance of the
heating element declines sharply near the Curie temperature such that at con-
stant current, the power dissipated by the heating element likewise declines.
By selection of the materials and physical dimensions of the heating element,
the frequency and the constant current of the AC source, it is possible to
achieve a high degree of temperature regulation in a narrow range around the
Curie temperature of the ferromagnetic layer despite consideTable changes in
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thermal lGad.
Moreover, any localized variations in thermal load on the heatlng
element are automatically compensated, since the resistance of any axial
portion of the heating element, however shoTt, is a function of its temperature.
The high thermal conductivity of the non-magnetic member is a further aid in
equalizing temperature over the extent of the heating element~ The heating
element according to the present invention can provide accurate temperature
regulation despite extremely small physical size. A further feature is that
the constant current R.F. source can ~e significantly cheaper than the complex
~eedback-controlled power supplies of the prior art.
T~e above and other features, ob~ects and advantages of the present
invention, together with the best means contemplated by the inventors thereof
for carrying out their invention will become more apparent from reading the
following description of a preferred embodiment and perusing the associated
drawlngs in which:
Brief Description of the Drawings
Figure 1 is a partially schematic representation showing a heating
element according to the present inventi ;
Figure 2 is a schematic representation of a cyllndrical heating
element and its current density profile;
Figure 3 is a graph of power versus temperature illustratlng the
operational advantages of the present in~ention;
Figure ~ is a cross-sectional view of a fluid conduit employing the
heating element of the present invention;
Figure S is a view partly in section and partl~ in elevation of a
soldering iron tip employ-ing the teachings of the pTesent invention.
Detailed Description o a Preferred Embodiment
~n Figure 1 there is shown a simplified cylindrical heating element
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1 connected ~n series circuit relationship with an R.F. source 3 and an on-off
switch 5. R.~. source 3 might provide hlgh frequency alternating current
power typically in the range from 8-20 MHz, for example> and might desirably
include constant current regulation for reasons that will appear from what
follows.
Although the cylinders lllustrated in Figures 1, 2 and ~ of thls
application are plainly circular cylinders, it is to be understood that the
use of the term "cylinder" in this application is by no means limited to the
speclal case of circular cylinders; it is intended that this term encompass
cylinders of any cross-sectional shape except where otherwise indicated.
Furthermore, although the electrical circuit arrangements illustrated all
employ direct or ohmmic connection to a source of alternating current electric
power, it is to be understood that the invention is not so limited since the
range of its application also includes those cases where the electric power
source is electrically coupled to the heating element inductively or capacitive-
1~.
Heating element 1 is traversed along ~ts major axis or length by a
high frequency alternating current from R.F. source 3. The efect of this
current is to cause I R heating or "Joule" heating. ~f, as suggested above,
R.F. source 3 is provided with constant current regulat~on, then I2 is a con-
stant and the power absorbed by heating element 1 from R.F. source 3 ls pro-
portional to the resistance R of element 1 between the points of connection
to ~he external circuit.
As can also be seen in Figure 1, ~eat~ng element 1 has a composite
s~tructure in which an inner core or su~strate 7, which might be made of copper
or other non-magne~ic, electrically and thermally conductive material is sur-
rounded by or clad by a sheath or plating in the form of layer 9 which is made
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of a magnetic material such as a ferromagnetic alloy having a resistivity higher
than the res~stivity of the conductive material of core 7.
In Figure 2, the current density profile across the cross-section
of a conductor carrying high frequency current is illustrated. If the conductor
is in the form oE a circular cylindrical conductor of radius r, then the cur-
rent density profile has the general form, under condltions of relatively high
frequenc~ excitation, illustrated by characteristic 11 in Figure 2, showing a
marked increase in current density in the surface regions of conductor 1'.
As will be apparent to those skilled in the art, characteristic 11
clearly illustrates the "skin eff0ct" whereby alternating currents are concen-
trated more heavily in the surface regions of the conductor than in the interior
volume thereof. The high concentration of current at the surface region of the
conductor is more pronounced the higher the frequenc~ is. However, from what
follows it is also obvious that the skin effect ls dependent upon the magnetic
permeability of the conductor: In a "thick" conductor having a planar surface
and a thickness T, energized by an alternating current source connected to pro-
duce a current pa~allel to the surface, the current density under the influence
of the skin effect can be shown to be an exponentially decreasing function of
the distance from the surface of the conductor:
j Cx~ ~ jO e x/s, where
j Cx2 is the current densit~ ~n amperes per sq. meter at a d~stance
x in the conductor measured from~the surface,
O is the current magnitude at the surface, and
s is the "skin depth" which ~n mks unlts is given by s z~2/~
for T ~ s-
Where ~ is the permeability o$ the material of conductor, a is theelectrial conductivity of the materlal of the conductor and w is the radian
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frequency of the alternating current source. ln discusslng the relationship
of the skin effect ~o the magnetic properties of materials, it is convenient
to talk in terms o~ the relative permeability ~r, where ~r is the permeability
normalized to ~v, the permeability~of vacuun~ and ~v = 4~ x 10 7 henry/meter.
Thus, ~r = ~ = ~ . For non-magnetic materials, ~r = 1.
The ~oregoing relationship of current density as a function of dis-
tance from the sur~ace, although derived for a thick planar conductor, also
holds for circular cylindrical conductors having a radius of curvature much
larger than the skin depth s.
I0 Although it is not necessar~ to examine quantitatively the effects
of these relationships, it is worth noting and understanding that for ferro-
magnetic alloys, which have values of ~r in the range of 100 or more when
operating below their Curie temperatures, the dependence of the above expressions
upon ~ results in a markedly steeper drop of current away from the surface of
a ferromagnetic conductor as compared to a non-magnetic conductor, for which
~r = 1.
As temperature approaches the Curie temperature of a ferromagnetic
conductor, however, the relative permeability declines quite rapidly and
approaches a value very near 1 for temperatures above the Curie temperature.
The corresponding effect on the current density profile of a purely magnetic
cylindrical conductor 1' of radlus r is illustrated by Figure 2.
~e lower part of Figure 2 is a graph of~current density j across
the diameter of conductor 1'. For temperatures well belo~ the Curie temperature,
current density profile 11 shows the expected high current density at the sur-
face of conductor 1' tapering rapidly to a very low current in the interlor of
conductor 1'. Profile 13, on the other hand, illustrates the current densit~
for a temperature in the region of the Curie temperature of the ferromagnetic
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material of conductor 1': the character~stic shows a considerable lessening
of the skin effect with only a moderate falling off of current away from the
surfaces of conductor 1'.
Qualitatively, these ef~ects are entirely comprehensible from the
foregoing material concerning the marked decline of ~ as temperature rises to
near the Curie temperature of a ferromagnetic material: since ~r for a magnetic
material approaches 1 near the Curie temperature, the current density profile
approaches the shape of the current density profile for a non-magnetic conductor.
Turning now to Figure 3, a graph of power versus temperature for
two differen~ heating elements is shown. Characteristic 15 is for a uniform
ferromagnetic conductor such as, for example, the conductor 1' shown in
~gure 2, carrying a constant current Il. As shown, characteristic 15 exhibits
a sharp drop in power absorbed from an R.F. energizing source such as R.F.
source 3 in Figure 1, as the Curie temperature Tc is approached. Following
this sharp drop in power, characteristic 15 levels off at a level labeled
Pmin in Figure 3.
Characteristic 16 in Figure 3 shows a typical power versus ~emperature
curve for a composite heating elemen~ such as element 1 in Figure 1 in which a
non-magnetic conductive core is surrounded by a ferromagnetic surface layer.
Characteristic 16 also illus~rates the very similar behavior of a hollow,
cylindrical non-magnetic conductor which hasbeen provided with a ferromagnetic
layer on its inside surface, or indeed any composite conductor formed princi-
pally of a non-magnetic conductive member with a ferromagnetic surface layer
according to the present invention. Although qualitatively the shape of
characteris~ic 16 is similar to that for characteristic 15, it is to be noted
that characteristic 16 descends more nearly vertically to a lower value of
minimum power input.
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A third characteristic 17 illustrates the effect of increasing the
current carried by the composite heating element to a new value I2 which is
greater than Il. As illustrated, characteristic 17 shows the effect of such
a current increase where I2 has been selected 5~ as to produce the same level
o$ minimum power Pmin as was obtained in the case of the characteristic for a
unlform ferromagnetic conductor 15 operating at current Il.
The significance of such a current increase can be appreciated by
considering the pair of thermal load lines 19 and 21. Load lines 19 and 21
are graphs of total power lost through conduction, convection, and radiation,
shown as a function of temperature. As w~ll be apparent to those skilled in
; the art, load line 19 is for a condition of greater thermal lossiness than
load line 21. For example, line 19 might represent the thermal load when a
fluid coolant is brought into contact with the heating element.
Since at thermal equilibrium the power input to a heating element
equals the power lost by radiation, conve~ction, and conduction, resulting in
a steady temperature, the points of intersection of lines 19 and 21 with the
characteristics 15, 16 and 17 represent equilibria from ~hich both the steady
state power input and temperature can be r~ad.
B~ considering the six intersectlons of lines 19 and 21 with
characte~istics 15-17, the~following facts may be deduced: ~1) good temperature
regulation despite variations in thermal load requires that the points of inter-section for all thermal loads to be encountered in use should lie, insofar as
possible, ~n t~e nearly vertlcal porti~n o~ the character~stic llne; ~2~ the
ideal characteristic line would have a long, straight vertical section such
that widely varying thermal loads could be accommodated without any variation
in temperature; (3) characteristic line 17 in Figure 3 ~hich is representative
of heating elements-havinga composite structure with a non-magnetic conductive
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core and a ferromagnetic surface layer, operat~ng at the relatively h~gher
current ~2' most nearly approaches the ideal since both thermal load lines
19 and 21 intersect characteristic 17 defining equilibria whlch lie on the long,
straight, nearly vertically falling portion of characteristic 17.
The reason for the superior temperature regulating performance of
the composite heating element as shown by characteristics 16 and 17 of Figure
3 is relatively simple to understand in a qualitative way.
Since both current and frequency are constants, the power input to
the heating element (P=I2R) is directly proportional to the resistance of the
heating element as a function of temperature, R~T). As temperature rises and
approaches the Curie temperature of the ferromagnetic material concerned,
magnetic permeability ~ drops to approach the permeabilit~ of vacuum (~r = 1)
as a limit beyond the Curie temperature, Tc. The consequent slgnificant re-
duction in skin effect causes current, which flowed almost entirely in the
surface layer of the heating element at low temperatures, to migrate or spread
.lnto the body of the heating element such that more and more current flows
through the interior as temperature rises near T ~ Since the available cross-
section for current flow is thus increased and since most of the current is
flowing in a highly conductive medium, resistance drops causing a corresponding
drop in power consumption.
In the case of the composite heating element accordi~g to the present
invention, only a relatively thin surface layer of the heating element is
formed of ferromagnetic materialj while the rema~nder consists of a substrate
mem~er made of non-~agnetic material havIng high electrical conductivi*y.
Consequently, the decline in resistance and power consumption which is ex-
perienced with a purely ferromagne~ic hea~ing element is greatly increased by
the use of a non-magnetic, highly conductive core.
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As already noted, when cur~ent is held constant, power is proportional
to the r~sistance of the heating element, Consequently, the maximum power and
the minimum power which will be supplied to the heating element are proportional
to the maximum and minimum resistance of the heating element. Since the ratio
o~ maximum power to minimum power determines the range over which the heating
element can adequately malntaln constant temperature, this ratio and the cor-
responding ratio, RmaX/Rmin, are significant indicia of performance. It can
be shown that max ~ ~r max ~ min , where ~r and ~ represent the permeabllitY
min ~r min ~ max
and conductivity of the material as before.
For ferromagnetic materials, the ratio ~ min/~ max is sufficiently
close to 1 such that to a good approximation, Rmax = I~r m~x I. Since ~r
r min
max has values which fall in the range from lO0-600 for commercially available
magnetic materials, and further since ~r min (the value above Tc) is approximately
equal to l, the ratio RmaX/Rmin has a range of values for ferromagnetic materials
from approximately ~ to ~ , or approximately 10 to 25.
By the use of the composite construction~according to the present
invention, this modest ratio of resistances can be vastly increased by selection
of the relative cross-sectional areas and conductivities of the non-magnetic
member and its ferromagnetic surface layer. Through the choice of the Curie
temperature by means of alternative ferromagnetic materials, the temperature
; at which regulation will take place is also variable.
Turning now to Pigure 4, there is shown a novel application o~ the
present invention to form a heated con~duit for the transmission of ~luid such
as, for example, crude oil over long distances while maintaining the fluid at
a selected elevated temperature design0d to minimize viscosity. The conduit 23
of Figure 4 comprises a hollow cylindrical core 2S which may be made of copper
or a less expensive non-magnetic material, for example. Surrounding and
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immediately adjacent and in contact with the surface of core 25 is a ferromag-
netic layer 27 which is in good thermal and electrical contact with core 25
substantially throughout its length.
As insulative later 29 which might be made of a plastic chosen to
withstand the environment in which conduit 23 will be used surrounds core 25
and layer 27, electrically and thermall~ separating them from an outer sheath
31 which might be a woven mesh of fine copper wires; or any other suitable con-
ductive sheath material.
Although not shown, a source of R.F. current to energize conduit
23 would be connected between sheath 31 and core 25 and layer 27. Typically,
sheath 31 would be operated at ground potential in order to avoid accidental
short circuits.
rn Figure 5 is shown an add~tional application of the present
invention to a soldering iron tip 33 of conical shape. Tip 33 is comprised of
an outer non-magnetic shell 35 which might be made of copper or molybdenum,
for example, and which is in good thermal and electrical contact with an inner
ferromagnetic shell 37, thus forming a composi~e self-regulating heating element
~n accordance with the present inventlon. An inner conductive~ non-magnetic
stem 39 extends axially into conical shells 35 and 37 and may be joined to
inner shell 37 as by spot welding, for example. An ~.F. source 41 ig shown
schematically ~nterconnected between stem 39 and outer shell 35.
Soldering iron tip 33 makes paTticularly good usc of the advantages
o the composite heating element structure of the present invention. As will be
obvious to those skilled in the art, the path of current flow ~hrough the
structure of tip 33 is along stem 39 to its point of juncture with inner shell
37 and axially along the conical inside surface of tip 33 in an expanding current
flo~ path to return to R.F. source 41. Were it not for the teachings of the
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present ~nvention, such a current flo~ path would lnevitably produce excessive
absorption of electric power at the apex portion of soldering iron tip 33, since
the cross-section of the current flow path is smallest at this point and the
resistance would in the usual case be higher therefore. The result would be
that unless large amounts of copper were used in the formation of outer shell
35, the apex region of tip 33 would be overheated while portions near the broad
base of the cone received inadequate heat.
However, according to the present invention, such overheating of the
apex region of tip 33 does not occur since at each axlal cross-section of the
current flow path the local dissipation of R.F. energy is governed by the ther-
mal characteristics detailed in Figure 3 of this application. Consequently,
each portion of the current flow path will adjust its temperature to very nearly
the desired regulated value despite significant changes in current-path cross-
sectional area, or differential thermal loading.
Although the invention has been described with some particularity
in reference to a set of preferred embodiments which, taken together, comprise
the best mode contemplated by the inventors for carrying out their invention,
it will be obvious to those skilled in the art that many changes could be made
and many apparently alternative embodiments thus derived without departing from
the scope of the invention. Consequently, it is intended that *he scope of the
invention be interpreted only from the following claims.
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