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TECHNICAL 
L LIBRARY ,_, 

l AD /63t 3 p£ > I 


TECHNICAL REPORT ARLCB-TR-81029 


LOW FREQUENCY INDUCTION HEATING OF LARGE 
DIAMETER STEEL PREFORMS FOR ROTARY FORGING 

David Concordia 



July 1981 


US ARMY ARMAMENT RESEARCH AND DEVELOPMENT COMMAND 

LARGE CALIBER WEAPON SYSTEMS LABORATORY 
BENET WEAPONS LABORATORY 
WATERVLIET, N. Y. 12189 


AMCMS No. 3291.06.7328 
PRON No. M7-4-P4727-M7-1A 


APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED 
















* 


{ 


DISCIAIMLR 

The findings in this report are not to be construed as an official 
Department of the Army position unless so designated by other author¬ 
ized documents. 

The use of trade name(s) and/or manufacturer(s) does not consti¬ 
tute an official indorsement or approval. 


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Destroy this report when it is no longer needed. Do not return it 


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REPORT DOCUMENTATION PAGE 

READ INSTRUCTIONS 

BEFORE COMPLETING FORM 

1. REPORT NUMBER 

ARLCB-TR-81029 

2. GOVT ACCESSION NO. 

3. RECIPIENT'S CATALOG NUMBER 

4. TITLE (and Subtitle) 

LOW FREQUENCY INDUCTION HEATING OF 
DIAMETER STEEL PREFORMS FOR ROTARY 

LARGE 

FORGING 

5. TYPE OF REPORT & PERIOD COVERED 


6. PERFORMING ORG. REPORT NUMBER 

7. AUTHOR(a) 

David Concordia 

8. CONTRACT OR GRANT NUMBER^ 

9. PERFORMING ORGANIZATION NAME AND ADDRESS 

US Army Armament Research & Development Command 
Benet Weapons Laboratory, DRDAR-LCB-TL 

Watervliet, NY 12189 

10. PROGRAM ELEMENT, PROJECT, TASK 

AREA & WORK UNIT NUMBERS 

AMCMS No. 3291.06.7328 

PRON No. M7-4-P4727-M7-1A 

11. CONTROLLING OFFICE NAME AND ADDRESS 

US Army Armament Research & Development Command 
Large Caliber Weapon Systems Laboratory 

Dover, NJ 07801 

12. REPORT DATE 

July 1981 

13. NUMBER OF PAGES 

42 

14. MONITORING AGENCY NAME & ADDRESS (if different from Controlling Office) 

15. SECURITY CLASS, (o 1 this report) 

UNCLASSIFIED 



15a. DECLASSI F| C ATI ON/DOWN G RADI N G 

SCHEDULE 

16- DISTRIBUTION STATEMENT (of this Report) 



Approved for public release; distribution unlimited. 

17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) 

18. SUPPLEMENTARY NOTES 

19. KEY WORDS (Continue on reverse side if necessary and identify by block number) 

Induction Heating 

Magnetic Field 

Magnetic Flux 

Preforms 

Rotary Forge 

20. ABSTRACT (Continue ea reverse aide ft nece-aeary and identify by block number) 

Part I of this report surveys the basic theory of induction heating and 
heat flow in an inductively heated steel cylinder._ Part II describes an 
induction heating system now in use at the Watervliet Arsenal, and applies 
the theory of Part I to this system. 


00 , j ah^ 73 1473 EDmoN OF 1 HOV 65 ,s OBSOLETE UNCLASS IFI ED 


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TABLE OF CONTENTS 


Page 

Subscripts and Symbols Hi 

Part I - Induction Heating 

Introduction > 1 

Terminology ■ 

The Coil Flux 2 

Electrical Parameters 5 

Efficiency 7 

Reference Depth 9 

Power Factor 10 

The Heating Cycle 11 

Part II - The Cheston System 

General Description 15 

Electrical Description 19 

Cooling System 22 

Power Control 22 

Electronic Control Circuits 25 

The Coil 30 

Heating Cycle 33 

References 39 


LIST OF ILLUSTRATIONS 

Fig . 

1. Power Factor 3 

2. Flux Flow 4 

3. P and Q Factors 8 

4. Depth Correction Factor 13 

5. Cheston Induction Heating System 16 

6. Transfer Trolley 17 

7. Tripling Transformers 20 

8. Third Harmonic Voltage 21 

9. Voltage Control 23 

10. Reactor Circuit 26 

11. Electronic Control Circuits 27 


i 



TABLES 


I. 13 Inch Preform Temperatures 
II. 17.5 Inch Preform Temperatures 


Page 


35 

36 




n 



SUBSCRIPTS AND SYMBOLS 


Subscripts : 

g - The air gap 
w - The workpiece 
c - The coil 

Symbols: 


I - Current (amps) 

R - Resistance (ohms) 

0 - The magnetic flux (maxwells) 

H - The magnetic field strength (oersteds) 

B - The flux density (gauss) 

U r - The relative permeability, i.e., the permeability of the material 
divided by the permeability of free space. 

6 - The effective depth of current penetration (cm) 

P - Real power (KIV) 

A - The cross sectional area (cm^) 

P c - The inside perimeter of the coil (cm) 

£ - Voltage (RMS) 
f - Frequency (hertz) 

L - Inductance (henries) 

Z - Impedance (ohms) 

N - Number of turns 
H - The length of the coil (cm) 

(ft - Reluctance ( am P s \ 
maxwells' 

p - Resistivity (ohm-cm) 

T $ - Temperature of surface( °C) 

T c ~ Temperature of center (°C) 

P 0 - Surface power density (cal/sec-cm“) 
a - Radius (cm) 

k - Thermal conductivity (cal/sec-cm-°C) 

Y - Density ( g/cm I * 3 * * 6 ) 

T a - Average temperature(°C) 

C - Specific heat (cal/g^C) 





PART I - INDUCTION HEATING 


INTRODUCTION: 

Induction heating results from a simple and basic phenomenon. 
Faraday's law states that a changing magnetic field will induce a 
current in a conductor that is placed in this field. The resistance 
to the flow of the induced current will result in heating within 
the conductor. (The power causing the heat is equal to I 2 R, where I 
is the current and R is the resistance.) In order to produce a 
changing magnetic field, you must first have a changing current 
within a conductor which will produce the magnetic field. This is 
accomplished by passing an alternating current through the conductor. 
If the conductor is formed into a solenoid, the magnetic field be¬ 
comes concentrated in the center and the result is a practical in¬ 
duction heating coil. 

TERMINOLOGY: 

Magnetic flux, 0, as used herein, refers to the lines of force 
that run between the poles of a magnet. They are abstractions used 
to help visualize what takes place in a magnetic field. A magnetic 
field is the area around a magnet where the flux lines exist. 

The permeability is a property of the material and is often 
given as its value relative to the permeability of free space, y 0 = 

• 4tt maxwel 1 . y./y Q represents the relative permeability (y r ) of a 
amp - cm 


1 



material. The reluctance, <R, is a term used in magnetic circuits, 
analogous to the resistance in electrical circuits. Thus, its value is 
an indication of the resistance to the magnetic flux within a material. 

Reference depth, 6, or effective depth of current penetration, 
in a large diameter workpiece, refers to the depth to which the current 
exists within the workpiece. Alternating current actually exists through¬ 
out the cross section of a conductor. However, since its density decreases 
the greater the distance from the surface, for all practical purposes 

the current may be assumed to exist only from the surface to the 
reference depth. A large diameter workpiece means one in which the 
wall thickness is at least 1.5 times greater than the reference depth. 

The words, "workpiece" and "preform", are used interchangeably in this 
report. 

Real power refers to the power developed as a result of the current 
that is in phase with the voltage. Reactive power is the product of 
the voltage and the current that is 90 degrees out of phase with the 
voltage (see Figure 1). The power factor is the cosine of the angle 
between the voltage and current. 

THE COIL FLUX: 

The magnetic flux produced by the coil, or solenoid, is composed of 
three parts: the flux in the air gap (the space between the coil 
and workpiece), the flux in the workpiece, and the flux in the coil 
(see Figure 2). From the equation B = pH, with y = 1 for the air gap, 


2 


IMAGINARY AXIS 


Lu 

O 


<a 

H 


CO 

X 

< 



<0 

o 

U 


> 

II 

cr 

LU 


< 


3 


Figure 1. Power Factor 







WORKPIECE 


13 0 B R 

COIL 


A-SIDE VIEW 



B-END VIEW 

Figure 2. Flux Flow 
4 
































































it follows that: 

Bg * = H, or 0 = HAg (1) 

Ag 

The flux in the workpiece lags the magnetic field intensity by a 
greater amount as the penetration becomes deeper. Consequently, the flux 
must be represented by a phasor (complex number): 

B w = -A- = PwH(P-jQ), or, 0 W = Uw/yUP-jQ(2) 

A w 


where P and Q are factors introduced to account for the shift in phase 

of the flux. 

The flux within the coil (a cylindrical shape is not assumed), 
which is made from copper, is: 

B r = -! <? .- , = jc = H(l-j), or, 0„ = Wc H(l-i)^ (3) 
A c P C 5 C -2- 

where is a factor introduced to account for spacing between turns, 

and other imperfections, and (1-J) accounts for the phase shift within 
the copper of the coil. The area terms,_^c^c_, result from assuming 
an infinite radius of curvature, so that the area is viewed as a 
rectangle with sides equal to P c and 6 C , g c is used because the flux 
in the copper cannot increase after the dep?h" of penetration exceeds 
one-half the copper thickness, and it is assumed the penetration is 
equal to the copper thickness. 


The total flux can thus be given as: 

0T = HAg + pi w HA v; (P-jQ) + K r P c 6 c H(l-j) 

ELECTRICAL PARAMETERS: 


(4) 


Since E = L 41 and E = N fJS. , then N 


cTT 


dt 

Integrating both sides yields N 
constant which is assumed zero. 

1. Reference is listed at end of report 

2 n " H H n ii n 


= |_ di 

HT cff. 


[ 2 ] 


fd£ dt 

J dt 


fdi 

‘J dt 


or N0 = LI plus a 


5 










Since E = ZI = (j2irfL) I (neglecting coil resistance) then 

L e _= N0 or E = j2-nfN0. If the root-mean-square (RMS) value of 

j 2-rrf L 

the voltage is used (E = E R ^ S f or a sinusoid) and the flux is given 
in maxwells, the equation for the coil voltage becomes 

E = j/2 TTfN c 0T TO' 8 (5) 

Ampere's law states that jpB-dt=y 0 IIf this equation is applied 
to a solenoid, the result is B =y 0 I N or, since B = pH, I = jj 0 H . 

The relative permeability, y_, in this case is one, and if H is given 

yo 

in oersteds, £ in centimeters, and the RMS current is used, the equation 

becoraes 'c = < 6 > 

If a short coil is being considered a term can be added to account 
for the mmf (magnetomotive force, NI) required to overcome the reluctance 
outside the coil due to end effect. The equation then becomes 

I c = _J_ (H£ c + <R 0)^(7) 

.4ttN c /2 T 

where the term, (R0T , has been added to equation 6# According 

. 4ttN c /2 

to Baker^, <R= 1 » 8 _ for a solenoid. 

Pc 

If equation 4 is substituted into equation 5 for the value of 


0 the result is 


E c = /2irfN c H IQ -8 


(p w A w Q ♦ J ttyW + 


1. Reference is listed at end of report. 

^ n ii ii n 11 11 11 

A ' ii ii it ii ii ii I' 


( 8 ) 


6 











If equation 8 is multiplied by equation 6, this gives 

E C I C = 2.5fH 2 £ c HT 8 |^(uA w Q + Kr . P . A )+j(A g + y A w P+ (9) 

Equation 9 gives the complex volt-amperes of the coil where the real term 

is the power input to the coil, which is made up of the power developed 

in the workpiece plus the power lost in the coil copper. If the part of 

the term representing the power in the workpiece is extracted, the result 

is: 

P w = 2.5fH 2 £ c 10" 8 (yA w Q) (10) 

Thus, if you have values for P and Q (see Fig. 3 for a large diameter 
workpiece) and you know the amount of power you want to develop in the 
workpiece, then from Equation 10, you can calculate H, the magnetic field 
strength. If this value of H is substituted into Equation 4, the total 
flux (0j) can be found. And finally, if the value of 0^ is substituted 
into Equation 5, along with the coil voltage, it is possible to calculate 
the number of turns, N c » you will need in order to obtain the power 
desired in the workpiece. If the values of H and N are substituted into 
Equation 6, the current in the coil can be found. Other values can also 
be found from the preceding equations such as coil power factor, coil 
efficiency, etc. 

EFFICIENCY: 

The current flowing in an induction coil is usually quite high, 
so that some means of cooling is required. This can usually be done 
by using a hollow copper coil and circulating water through the coil. 


7 




I 





8 


Figure 3. P and Q Factors 
















































By keeping the coil at or near room temperature, burning of the insulation 
is prevented. Since the resistivity of copper increases with temperature, 
the resistance of the coil can be kept at a minimum. Otherwise, with in¬ 
creased resistance of the coil, the efficiency would decrease. 

The efficiency of the coil is the power developed in the workpiece 
divided by the power input to the coil. In order to calculate this, you 
must know the resistance of the coil. The resistance is, for a single 
turn coi1: 


r = — where the length times the effective depth of current 

£6 C 

penetration gives the area and the perimeter gives the length of current 
travel. If the single turn is divided into N turns, with the length (£) 
the same, the result is: 

R r = = PPc (n) 

~r 5 c ^ 

REFERENCE DEPTH: 


The current that is induced in the workpiece, called Eddy Current, 
decreases in magnitude the deeper the penetration. It has been found 
that this current can be considered to flow in a band near the surface 
of the workpiece and that no Eddy Current exists deeper than this 
depth. The equation for effective depth of current penetration, or 
reference depth, is: 



(12) 


5. Reference is listed at end of report. 

9 







The greater the resistivity, the greater the reference depth. The 
resistivity increases with increasing temperature for most conductors. 
Assuming constant permeability and frequency, the efficiency will in¬ 
crease as the workpiece is inductively heated, due to an increase of 
workpiece resistance. But the permeability does change with magnetic 
field strength and with temperature. For steel, the relationship be¬ 
tween y r and H is given by Baker 1 as: (For H greater than 60 oersteds) 

_ 32,400 . n ,, 

pf —pj- 1 (13) 

Steel changes to a relative permeability of one at the Curie temper¬ 
ature (about 1400°F for steel) and remains at one for all temperatures 
above Curie, i.e., it becomes non-magnetic above the Curie temperature. 
Thus, there is a dramatic increase in reference depth when the Curie 
temperature is reached and, therefore, a large decrease in workpiece 
resistance. This results in a large decrease in coil efficiency when the 
Curie temperature is reached. It can also be seen that this dramatic 
change in p affects the value of H in equation 10 and thus the value of 
0 in Equation 4. This, in turn, affects the relationship between the 
voltage and flux in Equation 5. Therefore, calculations of coil turns 
being done for heating steel must be done for temperatures above and 
below Curie if it is expected to heat above 1400°F. 

POWER FACTOR: 

The power factor of an induction coil is generally less than .5 
lagging. To avoid excessive current draw from the voltage source, 


1. Reference is listed at end of report. 


10 




power factor correcting capacitors are connected in parallel with the 
coil. From Equation 9 the imaginary part gives the reactive power con¬ 
sumed by the coil or, in turn, the volt-amp reactive (VARS) of capacitors 
required to correct the power factor to one. 

Dividing Equation 8 , the voltage, by Equation 6, the current, gives 
the impedance of the coil. The imaginary part is the total inductive 
reactance of the coil. 

X L = 8ir 2 fN 2 lCr 9 - (fl a H-yA w P+ K r pA) 

Since X|_ = 2TrfL, the inductance of the coil may be found and used 
in eouation C = 1 to find the capacitance (C, in farads) re- 

(27rf)2 L 

quired to make the power factor equal to one. 

THE HEATING CYCLE: 

Heating by induction involves heating near the surface of the 
workpiece and having heat conducted toward the center. Basically, 
two things are of concern, viz., (1) How much energy is required to 
raise the workpiece to the temperature desired and (2) What will the 
temperature distribution be at the end of heating. 

Values are available that give the energy per pound required to 
raise a given material to a given temperature. Thus, the energy re¬ 
quired to heat the workpiece can be found. In induction heating, 
energy is usually given in kilowatt hours (KWH). If the power is 
known, the heat time can be found from the relationship: 

Time - JM (14) 

KW 


11 






Consideration must also be given to radiation loss from the workpiece and 
possibly to power line loss from the source to the coil. Also, the 
efficiency of the coil must be considered. The KW in Equation 14 would 
then be: . 

KW = l ji<W (Source) - KW (line loss^J x efficiency^ - KW (radiation loss) 
The temperature difference between surface and center of the work- 
piece is of greatest concern when heating by induction. Assuming a 
constant power input, it has been shown that the following relationship 
exists: 

T s - Tc ■ ^ K, K 2 fc)(15) 

K-] (see Fig. 4) corrects for the fact that the heat is generated to a 
certain depth below the surface with induction heating, and K 2 is a term 
that corrects for a two power level heating cycle. It is theoretically 
possible^to reduce total heat time by using two power levels, with Pi>P2- 
If P-] is the first power level for time, t a , and P 2 is the second power level 
for time, t^, then, K 2 may be found from the equation: 



1 + t b C6] 

!i + Jib 

P 2 t a 


(15a) 


Equation 15a applies only if the temperature difference between surface 
and center reaches equilibrium after each power level is used. This 


time is given by the equation: 

t = yca^ 
4k 


6. Reference is listed at end of report. 


12 









q 



lO <M 


o 


73 


Figure 4. Depth Correction Factor 





























If the time to heat, from Equation 14, is used, P 0 may be found 
from the equation: 

Po = (16) 

2ti 

where, t] is the time to heat the workpiece. 

When power is turned off at the coil, the temperature difference 
between surface and center begins to decrease. In a time, t2, the 
difference in temperature has dropped to 10% of its initial value, 
where: 

t£ = • 154vca^ seconds 0^0 

The time, t 2 , is important because it allows for calculation of 
temperature difference, when time is involved in moving the workpiece 
from the coil to its final destination. 


6. Reference is listed at end of report 


14 





PART II - THE CHESTON SYSTEM 


GENERAL DESCRIPTION: 

This induction system was designed and built by the Cheston Company 
of Rancocas, New Jersey, now called IPE-Cheston of Madison Heights, 
Michigan. The system consists of four induction heating lines, plus 
associated apparatus. Each line is capable of heating approximately 
2.2 tons per hour to a temperature of 1900°F. The basic system covers 
an area of about 1300 square feet, not Including the area covered by 
the transfer trolley tracks and the outside cooling tower. There 
are two levels. The lower level has four induction coil lines running 
parallel to one another (see Figure 5). The Induction coils are located 
in the center of each line. The coil line, on each side of the coil, 
consists of steel plate with fiberglass insulation on the inside and 
removable top covers. Each line has 11 rollers used to oscillate the 
preform back and forth through the induction coil at a speed of about 
2 inches per second. Also, on the lower level, are the closed circuit 
cooling system and the transfer trolley. The upper level contains the 
electrical equipment and control circuits. This includes the main 
supply transformers, tripling transformers, capacitors, reactors, con¬ 
trol boards, relays, meters and temperature readouts. 

Preforms are loaded by overhead cranes onto a 48 foot long roller 
system. A transfer trolley (Figure 6) then transfers the preform 
from the loading rollers to any of the four coil lines. Preform length 
is limited to 180 inches by the size of the trolley and coil lines. 


15 



16 


Figure 5. Cheston Induction Heating System 







I 





17 


Figure 6. Transfer Trolley 




















Preforms are unloaded by the same transfer trolley to a series of rollers 
that move the preform to the rotary forge. 

There are presently four sizes of induction coils used on the system 


are as follows: 



Inside 


Preform 

Diameter 


Diameter 

(in) 

No. Turns 

(in) 

27 

19 

20 

22 

22 

17.5 

19 

26 

15 

17 

29 

13 


All the coils are 21 inches long and use hollow rectangular copper 
tubing; they are water cooled by passing water through the copper in¬ 
side diameter. Studs, brazed to the coil turns and fastened to a 
fiber board, are used to contain the coil. One compression type, 17 
inch diameter coil, has been purchased to test the possibility of in¬ 
creased coil life over the stud type construction. The 19 inch diameter 
coil will also be the compression type. All the coils have a cast 
refractory liner inside the coil and the stud type construction uses 
cast refractory end plates. The compression coils use a transite 
board and a water cooled stainless steel plate on the ends. 

The heating cycle begins with one end of the preform half way 
into the coil and continues until the other end is half way into the 
coil. The direction is then reversed and the preform again travels 
until the end is half way into the coil. This constitutes one count 


18 





as recorded by a counter on the control panel. The preform will oscillate, 
with power to the coil, for the number of counts set on the counter. 

The surface temperature of the workpiece is measured^ it is heat¬ 
ing, by an infrared type temperature instrument. Each coil line has two 
instruments located on each end of the induction coil. Temperature read¬ 
out occurs in digital form on the control panel, with the readout range 
limited to 1500°F - 2500°F. As the workpiece exits the transfer trolley, 
another infrared type instrument measures the surface temperature. This 
readout is automatically recorded on paper to give a final surface 
temperature before the workpiece reaches the forge. 

ELECTRICAL DESCRIPTION: 

Electric power is fed from a 13,200 VAC,three phase, 60 hertz line. 

The voltage is brought down to 480 VAC, three phase, 60 hertz by two 
2000 KVA transformers. The three phase 60 hertz is then converted to 
180 hertz, single phase, by three tripling transformers, which are 
toroidally wound with high permeability steel cores used to accentuate 
the third harmonic component of current; the third harmonic of 60 
hertz being 180 hertz. The tripling transformer circuit is as shown in 
Figure 7. The capacitors are used to correct the power factor. Figure 
8 shows how by connecting the output of the three tripling transformers 
in series, the fundamental component cancels and, since the third 
harmonics are all in phase, they add together. 

The output of the tripling transformers then connects to the in¬ 
duction coil. In parallel are capacitors and two saturable core 


19 



20 


Figure 7. Tripling Transformers 
































-lid -PNIC CCMrCMFHI j ,— Jrd HARMONIC COM«,«£& j 







21 


Figure 8. Third Harmonic Voltage 






















reactors, with a variable inductance^used to control coil voltage. 
COOLING SYSTEM: 

The cooling system consists of two parts. The closed system cir¬ 
culates purified water that is pumped from an 800 gallon storage tank 
through some of the electrical components, including the tripling 
transformers, the capacitors, silicon control rectifiers, reactors 
and bus bar and then, back to the tank. The tank is provided with a 
sand filter that draws water from the tank, through the sand, and 
back to the tank. Water is added, as the need arises, to the tank 
through a deionization tank that purifies the water. 

The open system pumps water from a 2000 gallon storage tank, 
through a heat exchanger coupled to the closed circuit system, then, 
through parallel connections to the coil turns and coil line rollers 
and back through a cooling tower to the tank. The cooling tower has 
two thermostatically controlled fans that operate when the tank water 
temperature exceeds 80°F. The open system uses city water and is 
provided with a conductivity sensor that dumps the water in the tank 
when the conductivity of the water exceeds a pre-set value. Fresh 
city water is added automatically as the water empties, until the 
conductivity is below the set value. The tank water is constantly 
pumped through the sand filter and returned to the tank. 

POWER CONTROL: 

Enough capacitors are used to provide a leading power factor in 
combination with the heating coil and reactors. The more leading the 
power factor, the greater will be the voltage across the coil. This 
is illustrated vectorially in Figure 9. The diagram shows the secondary 


22 




Figure 9. Voltage Control 
23 




























voltage, E, of a transformer, analogous to the output of the tripling 
transformers. R and X|_ represent the resistance and inductive reactance 
of the transformers, and the load represents the impedance from the com¬ 
bination of the heating coil, capacitors and reactors. With E assumed 
constant as the reference phasor, the load is first assumed to have 
a lagging power factor. V-j, the voltage across the induction heating 
coil is then given as: 

V-j = E - I-j (R+jX L ) 

For l£, a leading power factor is shown, and the corresponding 
increase in V 2 can be seen. For 1 3 , a more leading current results 
in a still greater value of V 3 . 

The increase in voltage across the coil, of course, results in an 

increase in power to the load. The reactors are arranged in such a 

way that increasing the inductance of the reactor will increase the 

overall inductance of the circuit. To raise the reactor inductance, 

the permeability of the reactor core must be raised, since L^p. This 

means that the magnetic field strength (H) must be lowered, since pM_ 

H 

as the reactor core becomes saturated. The reactor, in addition to 
being connected in parallel to the heating coil, is connected to a D.C. 
voltage supply. Thus, if the D.C. voltage to the reactor is decreased, 

H will be decreased, p will increase and L will increase. Similarly, 
if the D.C. voltage to the reactor is increased, p will decrease, L 
will decrease and the power factor of the circuit will be less leading, 
resulting in less voltage across the coil. Therefore, by varying the 


24 


D.C. voltage to the reactor, It Is possible to vary the voltage and, thus, 
the power to the heating coil. 

The D.C. voltage to the reactor Is supplied through two silicon 
control rectifiers (SCR's) from a center tapped transformer as shown In 
Figure 10. The transformer is supplied from one phase of the 480V 
60 hertz, three phase transformer secondary. Gate voltage for the SCR s 
comes from the electronic control circuits. 

ELECTRONIC CONTROL CIRCUITS: 

The control circuit is made up of four printed circuit boards: 1) 
the comparator board,(2) relay or current control board,(3) firing 
board and(4) hard firing board. 

Each coil line has a potentiometer for setting the coil voltage 
limit and a potentiometer for the power level to the coil. There is a 
coil voltage meter (red-lined at 800V), a current meter (red-lined at 1400A) 
giving the current drawn from one phase of the 480V, three phase, supply 
transformer and a coil power meter (red-lined at 900KW), along with 
a transducer that senses coil power and outputs it as a 0-1 VDC signal 
that is sent to the comparator board. Other signals sent to the 
comparator board are the coil voltage, as a 0-100 VAC signal, the power 
level, as a 0-5 VDC signal, and the voltage limit setting as a 0-5 VDC 
signal (see Figure 11). The power level setting, and power signal feed 
into a differential amplifier. The voltage signal is rectified and fed 
to another differential amplifier along with the voltage limit signal. 

The outputs of the two differential amplifiers feed to an integrating 
amplifier, and the output of the integrating amplifier feeds to an 


25 


GATE 2 


-W- 

ih/" 


CO 

O 

5 




=j 

§ 

C!) 


< 

tii 

X 


-JH 

"vV~ 

-w- 


r\ 







26 


Figure 10. Reactor Circuit 




























< 
-J z 
o CD 
o co 


o 


o 


co 
cn 
o 
o co 


lL 
CO O 


r> co 

O- LkJ 
t- K- 
ID < 
O O 


27 


Figure 11. Electronic Control Circuits 




































electronic switch that is composed of a NAND gate along with a double 
pole switch. There is also a +5 volt signal into the NAND gate. The 
outputs from the two differential amplifiers also feed to the two con¬ 
tacts on the electronic switch. Depending on whether the electronic 
switch is on or off, either the output from the differential amplifier 
receiving the power signals, or from the differential amplifier re¬ 
ceiving the voltage signal, is sent to an operational amplifier. 

If the voltage from the induction coil is below the voltage limit 
signal, the output of the integrating amplifier will cause the electronic 
switch to disconnect the output from the operational amplifier re¬ 
ceiving the voltage signals and connect the output from the power 
differential amplifier to the operational amplifier. The system is now 
in power control and will automatically adjust coil voltage to maintain 
the power to the coil at the setting of the power control potentiometer. 

If the coil voltage should reach the voltage limit setting, the 
output from the integrating amplifier will cause the electronic switch 
to disconnect the output from the power differential amplifier and 
connect the output from the voltage differential amplifier to the 
operational amplifier. The system is now in voltage control, and will 
automatically prevent the coil voltage from exceeding the voltage 
limit setting. 

The output from the operational amplifier will be a negative 
voltage that combines with a +15 volt signal to produce a variable 


28 


voltage signal between 0-14VDC that outputs from the comparator board. 
This signal is further amplified by the relay board and is input to the 
firing board. The signal goes to the base of a transistor, thus varying 
the bias voltage as the 0-14VDC signal varies. The varying bias voltage 
controls the transistor emitter to collector current which, in turn, 

varies the charging rate of a capacitor. The capacitor is connected 
between the emitter and base one of a unijunction transistor. When the 
voltage across the capacitor reaches a certain value, it causes the 
unijunction transistor to conduct. The primary of a transformer is 
connected to the unijunction transistor so that when it conducts it 
produces a pulse in the secondary of the transformer. This pulse goes 
to the gate of an SCR on the hard firing board. 

The hard firing board contains two transistors, one connected to 
the gate of one SCR in the reactor rectifying circuit, and the other 
transistor connected to the gate of the other SCR. When the pulse 
causes the SCR on the hard firing board to turn on, bias is applied 
to one of the transistors. This provides voltage to the gate of which¬ 
ever SCR has positive voltage on the anode, since the transformer 
supplying voltage to bias the transistor is in phase with the voltage 
to the reactor rectifier SCR's. 

Thus, the voltage from the comparator board varies the charging 
time for the capacitor in the firing board which, in turn, controls 
when the transistor will supply gate voltage to the reactor rectifier 
SCR's. Any variation in the voltage signal from the comparator board 


29 


will vary the reactor current and thus the induction coil voltage, so 
that, through feedback, the reactor current is constantly varying to 
maintain coil power or to limit coil voltage. 

THE COIL: 

The 17 inch coil (presently used on the system for heating a 13 
inch outside diameter, 4.5 inch inside diameter and 90 inch long preform) 
has 29 turns. To show how the equation given in Part I may be used to 
verify mathematically that 29 turns are, indeed, the number required, 
a sample calculation will be given. First, equation 10 must be solved 
for H. The power, P w , in this equation is equal to the power at the 
coil, times the efficiency of the coil. Estimating an efficiency of 
75 percent above Curie temperature and allowing 12 KW power loss in 
the power lines, the power developed at the coil is 900 - 12 = 888 KW. 
Multiplying by the efficiency, the result is (888 KW) x (.75) = 666 KW. 
The frequency is 180 hertz, the length of the coil is 53.53 cm and 
the area of the workpiece is 754 cm^. pr is equal to one, above Curie, 
and Q is equal to .2138 (see Figure 3). The equation then is: 

666,000 = 2.5(180) H 2 (53.53) 10“ 8 (754) (.2138) 
and H is equal to 4141 oersteds. 

Next, equation 4 can be applied to find the total flux, 0-p. Values 
not already given are: 

Ag = 608 cm^ 

P = .2462 

K r = .8 

P c = 136 cm 

e> c = .493 cm 


30 


The equation then is: 


0 T = 4141 


^(608) + (754) (. 2462) + ^8036) (.493) 


(754)(.2138) + -8(136)(.493)^ 


and 0 T is equal to 3397500 - j778609. The magnitude then is 3,485,576 
maxwells. Finally, by applying equation 5, with a coil voltage of 
800 V, the equation is: 

800 = /2tt(180) N c (3485576) 10" 8 


and solving for N c the result is N c = 28.7 turns. Rounding off, the 
result is 29 turns. 

For temperatures below Curie, since H, p, and Q are interrelated, 
it is necessary to assume a value for H, find the corresponding values 
for y and Q and then substitute them into equation 10. If the equation 
is not satisfied, other values of H are tried until the equation is 
satisfied. In this case, a value of H = 2850 oersteds was found. 
Applying this to equation 4 results in a magnitude of flux equal to 
3,290,051 maxwells and, using equation 5, the number of turns is found 
to be 30. By using the number of turns calculated for temperatures 
above Curie, viz., 29, it can be seen from equation 5 that to produce 
the same flux, below Curie, with less turns, less voltage will be 
needed. This only means that the coil voltage, to produce 900 KW, will 
be less below Curie than above. Thus, by using the number of turns 
calculated for above Curie, the 900 KW can be obtained throughout the 


31 






heating cycle without requiring more than the system red-line voltage 
(800 V). 

The current through the 17 inch diameter coil can be found from 
equation 7. Assuming 900 KW, the result is: 

I = 5,181A (above Curie) 

I = 3,794A (below Curie) 

These are the values of current drawn by the coil when 900 KW is 
being delivered to the coil with 29 turns. The change in permeability 
of the steel as it goes above Curie temperature results in a change in 
impedance of the coil-workpiece combination. As a result, to deliver 
900 KW to the coil above Curie temperature requires a greater voltage 
than is required below Curie. The resistance of the coil is, from 
equation 11, 

R„ = (1.15) (1.73 x 10" 6 ) (136) (29) 2 - .0086250Q 

C (53.34) (.494] 

The power lost in heating the coil copper is then given as: 

(above Curie) P = I 2 R = (5181) 2 (.008625) = 232 KW 

(below Curie) P = (3794) 2 (.008625) = 124 KW 
Allowing for loss in the power line to the coil, the power into the coil 
would be: 

900 KW - 12 KW = 888 KW (above Curie) 

900 KW - 6.6 KW = 893 KW (below Curie) 


32 



The efficiency of the coil is: 


888-232 

888 


.74 or 74% (above Curie) 


893-124 = .86 or 86% (below Curie) 
893 


The volt-amperes (VA) consumed by the coil are: 
VA = 800(5181) = 4144800 (above Curie) 

VA = 755(3794) = 2864470 (below Curie) 

The power factor (PF) is: 


PF = 888 KW 

4145 KVA 


.2142 (above Curie) 


PF = 893 

2864 KVA 


.312 (below Curie) 


The values for power factor and efficiency change continuously 
throughout the heating. Thus, the values calculated here actually 
apply only at two specific points in time. They do, however, give 
general values that can be used for calculations above and below the 
Curie temperature and do give useful and sufficiently accurate results 
for calculating the number of coil turns required. 

HEATING CYCLE: 


Temperature profiles of a 13 inch outside diameter, 4.5 inch 
inside diameter preform and a 17.5 inch outside diameter, 6.75 inch 
inside diameter preform were obtained by putting thermocouples at 
various depths and positions. The heating tests were conducted by 


33 






heston personnel as part of the acceptance test for the induction system. 
Tables I and II show results of one heating test for each of the two 
preforms. Sixteen thermocouples were used in each preform. Tables I and 
II show results from only two thermocouples since they show readings on 
the inside and outside surface of the preform. 

To test the accuracy of the equation given in Part I, equation 16 
may be used to calculate the power density, P 0 . Thus, for the 13 inch 
preform test run: 

Pq = — (7-832)(.177 )( 1 0 .795)(1066) = 4.15 cal/sec-cm^ 

2(1920) 

If this value for P 0 is put into equation 15, the result is: 

_ (4J5)(10.795)(.8)(D = 152 °C or 273°F 
s c “ 2(.118) 

This compares to a measured difference of 243°F. Applying equation 17 
the result is: 

t2 = _O54(,7.832)(.177)(10.795)2 = 211 sec or 3 6 m1 „ 

(.118) 

his compares to a measured time of about four minutes. 

Similarly, for the 17.5 inch preform, the values are: 


P o - i 7 . - 832 )(-^J)(13.65)(1093) = 3>2 5 ca ]/ sec _ cm 2 


2(3180) 


T s -T c = (3.25)(13.65)(.85)(.8) 


2(.118) 


128°C or 280°F 


T 2 = 


•154(7.832)(.177)(13.65) 2 

.118 


= 337 sec or 5.62 min 


These compare to measured values of 252°F and 6.5 minutes. 


34 









TABLE I 


13 INCH PREFORM TEMPERATURES 


(13 x 4.5 x 98 

INCH PREFORM, 

4337 STEEL, 17 INCH 

I.D. COIL) 

TIME 

POWER 

TEMPERATURE 

TEMPERATURE 

(min.) 

(KW) 

(inside °F) 

(outside °F' 

5 

900 

228 

702 

10 

900 

577 

1092 

15 

900 

901 

1427 

20 

900 

1155 

1591 

25 

900 

1351 

1763 

30 

600 

1636 

1999 

32 

power off 

1830 

2073 



Power was 900 KW for 28 minutes and 600 KW for 4 minutes^then power 


was shut off. 


35 







TABLE II 


17.5 INCH PREFORM TEMPERATURES 


x 6.75 x 

75 INCH PREFORM, 

4337 STEEL, 22 

INCH I.D. COIL) 

TIME 

POWER 

TEMPERATURE 

TEMPERATURE 

(min.) 

(KW) 

(inside °F) 

(outside °F) 

5 

865 

173 

762 

10 

865 

410 

1073 

15 

865 

652 

1259 

20 

865 

863 

1440 

25 

865 

1038 

1592 

30 

865 

1187 

1752 

35 

600 

1307 

1803 

40 

600 

1379 

1905 

45 

600 

1590 

2021 

50 

600 

1758 

2085 

53 

power off 

1848 

2100 


Power was 865 KW for 32 minutes and 600 KW for 21 minutes / then 
power was shut off. 


36 







The time to heat the preform can be calculated as outlined in Part I 
by applying equation 14. For the 13 inch preform the average power during 
the test run was 865 KW. Using an average efficiency of 77% (the efficien¬ 
cies above and below Curie were calculated earlier as 74 and 86 percent; • 
figuring 60% of the heat time above Curie and a 2% power line loss, the 
average efficiency is 77%), an average radiation loss of 58 KW, (the 
radiation power may be found from the equation 
P = (5.453 x 10' 16 ) (A) (e) (T+459.67) 4 
where T is temperature in degrees Fahrenheit, A is surface area in cm^ 
and e is emissivity), and a value for the energy to raise the preform 
(3240 lbs of steel) to 2000°F, of 308 KWH (from the equation: KWH = 

[.0000487(T)-.00216] [Weight (lbs)J with T in °F and T greater than 
1500°F), the result is: 

Time = _._ 308 _ = .507 hour or 30.4 minutes 

865(.77)-58 


compared to the actual time of 32 minutes, 
the results are: 


Time = 


413 


(760 KW)(.75)-79 KW 


.84 


For the 17.5 inch preform, 


hr. or 50.5 minutes 


compared to the actual time of 53 minutes. 

Of course the specific heat, thermal conductivity and coil efficiency 
are changing continuously with temperature. Thus, the calculation 
procedure outlined here is quite crude in its approach. But it can 
be seen that the results calculated agree quite well with the measured 
values. The procedure can be used as a first approximation to the 


37 




heating time and temperature difference and the process can be refined 
further by actual heating tests. 


38 


References 


1. Baker, R.M., "Design and Calculation of Induction Heating 
Coils", AIEE Transactions, Vol. 76, pt. II., Mar 1957, pp 31-40. 

2. Smith, Ralph J., "Circuits, Devices and Systems", 2nd Edition, 

John Wiley & Sons Inc., 1968, pp. 513-514. 

3. Halliday, D. and Resnick R., "Physics Part II** John Wiley & Sons Inc., 
1968, pp. 857-858. 

4. Matsch, L. W./'Electromagnetic and Electromechanical Machines", 

2nd Edition, Harper & Row, 1972, pp. 8-9. • 

5. Tudbury, C.A., " Basics of Induction Heating’, 1 Rider Publisher, 1960. 

> . 

6. Baker, R.M., "Classical Heat Flow Problems Applied to Induction 
Billet Heating", AIEE Applications and Industry, May 1958, pp. 106-112. 





39 


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