Basics of Induction Heating (vols. 1&2)

Citation preview

This book is written to pre sent the fundamental principle s of the indu ction heat ing art and of commercial induction heating equipment in a manner readily understood and enjoyed by any read er familiar with the simple rul es of electric it y. It expla ins what inducti on he ating is and how 1t works; it describes and explains th e operation of the more common types of industrial induction heating machines in use toda y; it pre sents mat erial to assist in developin g a qu ant it ative un ders tanding for new appl ication s; and it deals with electrical and thermal aspects in detail and touc hes more briefly upon some of the mech anical pr ob lems associated with fixturin g. Intend ed for stude nt s in high schools, technical institutes, and indu strial train ing courses, thi s text is useful for sho p men enga ged in operating, maintaining, and tooling indu ction heating equipmen t. Graduate engineers who h ave not had the opportunity of devoting time to this subjec t will benefit great ly from this book. It is hop ed that those who read it will not only be reward ed by having clone so, but will also derive some enjoyment, and that the y will be stimulate d to fu rther studr of the subj ect. T he book is quantitative; it uses numbers. It is not enough to say tha t the power is larg e, or th at the workpiece is hot, or that the rate of heating is fast, or that the frequen cy is hi gh. To be mean ingful, we must express these quantities as so many kilowatts or degrees per second or cycles per second. There are many numeri cal que stions and problems, becau se the best way to learn is by doing.

llaslcs of

lncluctlon heatln9

basics of lncluctlon heating. lty CHESTER A. TUDBURY,M.S. Otief Engineer New RochelleThermatoolCorp.

VOL.I

JOHN F. RIDER PUBUSHER,INC., NEW YORK London: CHAPMAN & HALL, LTD.

Copyright May 1960 by John F. Rider Publishe r , Inc.

All rights reserved. This book or any parts thereof may not be reproduced in any form or in any language without permission of the publisher. L ibrary of Congress Catalog Number 60-8958 Printed

in the United States of America

PREFACE

This book is written to present the fundamental principles of the induction heating art and of commercial induction heating equipment in a manner readily understood and enjoyed by any reader familiar with the simple rules of electricity. It explains what induction heating is and how it works; it describes and explains the operation of the more common types of industrial induction heating machines in use today; it presents material to assist in developing a quantitative understanding for new applications ; and it deals with electrical and thermal aspects in detail and touches more briefly upon some of the mechanical problems associated with fixturing. Intended for students in high schools, technical institutes, and industrial training courses, this text is useful for shop men engaged in operating, main- taining, and tooling induction heating equipment. Graduate engineers who have not had the opportunity of devoting as much time to this subject as I have will benefit from reading this book. It is hoped that those who read it will not only be rewarded by having done so, but will also derive some enjoyment, and that they will be stimulated to further study of the subject. Induction heating is like the elephant which was encountered by two blind people. Not having approached from the same direction , they formed very different first impressions. An intricate induction hardening machine for tiny gyroscope spindles, located in an air-conditioned room , operates in accordance with the same laws as a massive induction furnace in a smoky foundry, melting a thousand pounds or more of seething alloy. They are two aspects of the same elephant. This book is written in the belief that an understanding of the basic laws leads the way to an understanding of each specific ' application. The book is quantitative; it uses numbers. It is not enough to say that the power is large, or tha t the workpiece is hot, or that the rate of heating is fast , or that the frequency is high. To be meaningful , we must express these quantities as so many kilowatts or degrees or degrees per second or cycles per second. There are many numerical questions and problems, because the best way to learn is by doing. However , this book does not delve into higher

141324 V

Louisia naState Library State Capitol Grounds Baton Rou ge, Louisiana

PREFACE

mathematics. Even though much of what it presents was discovered as a result of much study, by many people, of differential equations, Bessel functions, and the like, it is not necessary for the rest of us to repeat that labor. The time thus saved releases us to forge ahead creatively rather than simply repeating what has already been done. It is hoped that Basics of Induction Heating will help the reader to do so. I wish to express my appreciation to David G. Osterer, Vice President of the New Rochelle Tool Corporation, for having persuaded me to undertake this project in the first place, and to my patient wife, Ruthena Warr en Tudbury, who saw to it that, once having started this book, I completed it. CHESTER

New Rochelle, New York May 1960

vi

A. TUDBURY

CONTENTS VOL . I -

Preface

BASICS

OF INDUCTION

.......................

Induction

Heating

Eddy Currents

.. ......................

in Industry

HEATING

.. .......................

. ...............

.

V

... ........ ................. ............................................... 1

.... ...............

............................... ................... .............. 12

The Thin Sleeve ......................................................................................................... 19 Solid Bar in Solenoidal Coil .............. ................

. ...................................... 24

Skin Effect .................................................................................................................... 33 Questions and Prob lems .. ........... .... . ............................... .....

.............. 38

Electrical

Effici~ncy . ....... .. ........ .............................................. ....... ...

Reference

Depth

Equivalent

Resistance of Workpiece

40

................................ ..... ............ . ................ ............................ 44

Resistance of Heating

.......... ...................... ................................ 47

Coil . ............................................... .... ........... .... .. ........... 54

Questions and Problems ....................................... ......... ............. ........................ 59 Graphical Method for Finding

Efficiency ... .................................................

Factors Which Affect Efficiency ....................................... Rectangular

Workpieces

Hollow Workpieces

61

. ................ ......... 66

..........................................................................,............... 73

............................................... .................................................... 77

Odd -Shaped Workpieces

................................ .... .. ... ................................ ... ..

81

Questions and Problems ............................... ,........................................................ 86 Some Basic Facts about Heat ...... Heat Flow in Workpiece Calculation

and Problems

Induction

Heating

Mechanical

Coils

Index

96

Applications

....... .......... .. .

Forces on Coils

............. ...

.. .........................................

............................... ............ ...101

.__ .... __ .. .........................

Summary .................... Glossary

87

..........

of Through-Heating

Questions

............................ .... ......................

......................108 .. ....... .......110 .. .... ............. .......... ...120 ..... . ................. 126

...... .. .. ...

........................................ ....

. .. ... .......... . 127 . .... ...................

-....131

INDUCTION

HEATING

IN INDUSTRY

Commercial Importance of Induction Heating

INDUCTION HEATING

MAYBE USED IN TH E MANUFACTUR E OFAUTOMOB ILES , AIRCRAFT, TRACTORS, EARTH-MOVING EQU IPMENT , MUNITIONS, TYSET S, DIESEL ENG ~ ETC . If you have had the opportunity of visiting a modern high-production metalworking factory, you have probably seen induction heating machines. Induction heating has taken its place as a modern industrial tool, and many familiar everyday products of today's industry depend, in some measure, upon it. Automobiles, aircraft, earth-moving equipment, tractors, munitions, TV sets, diesel engines, and many other items contain parts which have been heated by induction at some stage of manufacturing. The purpose of induction heating may be to harden a part, and thus to prevent wear; to make the metal plastic for forging or hot-forming into a desired shape; to braze or solder two parts togethe r ; to melt and mix the ingredients which go into the high-temperature alloys which make jet engines possible; or for any number of other applications. Induction heating, however, is no cure-all. True, there are jobs which can be done better by induction than by any other method. There are some things which are done every day by induction which we do not know how to do at all by any other methods. Induc;tion must either stand on its own merits competitively or else not be used. It must -either cost less or have some other outstanding advantage over other possible methods. And there are applications where induction heating is definitely inferior. It is taken for granted today that k~y people in industrial plants will have some familiarity with induction heating - what it can and cannot do. (1-1)

INDUCTION

HEATING

IN INDUSTRY

Jobs Done By Induction Heating Induction heating is particularly useful where highly repetitive operations are performed. Once an induction heating machine is properly adjusted, part after part is heated with identical results. Usually, no further attention on the part of the operator is required, except for the loading and unloading of the workpieces. The ability of induction heating to heat successive parts identically means that the process is adaptable to completely automatic operation, where the workpieces are loaded and unloaded mechanically with no operator present.

Induction heating has made it possible to locate operations, such as hardening, in production lines along with other machine tools instead of in remote separate departments. This saves the time of transporting parts from one part of the factory to another. Induction heating is clean; it does not throw off unpleasant heat. Hence, working conditions around induction heating machines are good, and comparable to those around other modern metalworking machine tools. They do not give off the smoke and dirt which are sometimes associated with heat-treating departments and forge shops. Another desirable characteristic of induction heating is its ability to heat only a small portion of a workpiece. For example, in forming the ends of ball studs used in steering linkages of automobiles, it is unnecessary to heat the whole part. Only the end to be formed is heated to bright red forging temperature. It is then thrust into a forging machine, known as an upsetter, where the round ball end is formed in 4 or 5 strokes. Meanwhile another part is heated, and is readied for the forming operations. (1-2)

INDUCTION

HEATING

IN INDUSTRY

Jobs Done By Induction Heating (contd .)

Some High Produdion Parts ~ hich have been Heated by lndud1on ~

CRANKSHAFTS

~

CAMSHAFTS

1-1 r

-

AXLES HAFTS DRILLCHUCKS GEARS UNIVERSAL JOI_NTS

There are many other high-production applications of induction heating as shown in the illustrations above. All induction heating applications are not automatic, and do not involve high production. An example is the widespread use of induction for melting. Special alloys, both ferrous and non ferrous , are brewed in induct ion melting furnaces . The flexibility and cleanliness of induction melting cannot be duplicated by conventional steel mill and foundry methods.

IINDU CTION HEATING intheFOU NDR YI l '

•

f

w

Induction

(1-3)

INDUCTION

HEATING

IN INDUSTRY

What Induction Heating Is

Even though you may not have first-hand experience with induction heating machines in an industrial plant, you may have observed evidences of the process many times-for example, the heating caused by magnetic losses in transformer cores and in motor laminations. This type of induction heating is undesirable , and electrical designers do all they can to discourage it. However, an entire industry has been built around the ingenious beneficial use of a phenomenon which had previously been considered strictly undesirable. Induction heating is often confused with dielectric heating by people who only know that both processes involve high-frequency electrical power. But there is a big difference between induction and dielectric heating. Each depends upon quite different electrical phenomena. Induction heating is useful for heating conducting materials and depends upon a varying magnetic field; but induction heating does not always require high frequency. Dielectric heating, on the other hand, is useful for heating materials which are commonly thought of as being nonconducting. It depends upon highfrequency electric fields. The frequencies used are generally higher (usually much higher) than those used in induction heating. Dielectric heating is used, for example, for heating plastic preforms before molding, sealing plastic parts such as handba gs and toys , drying sand cores used in foundries, curing glue in plywood, drying rayon cakes, and for many similar applications. This book is about Induction in a varying magnetic field.

Heating - the heating

(1-4)

of conducting

parts

INDUCTION

HEATING

IN INDUSTRY

Induction Heating Coils The varying magnetic field required for induction heating is produced by a-c flowing in an induction heating coil. The frequency of this a-c ranges anywhere from 60 cycles or lower to several million cycles. An important part of what we shall study in this book is the determination of the best frequency for a given situation. The induction heating coils, which are sometimes called inductors, have many sizes and shapes . Some consist of tiny turns of small copper tubing and are for heating sewing needles for hardening. Others are massive assemblies of copper bars and tubes, and are large enough to heat aluminum billets 3 feet in diameter by 8 feet long for extruding. Whatever their shape and size, all induction heating coils operate on the same basic principles . This will become more and more evident in the pages which foflow. Three common types of coils are illustrated on this page. Additional types will appear later .

made ofrectangular copper tubing with mitered and brazed joints

rectangular copper tube forcooling water

n

J

cooling topportion ofworkpieces water inlet \ cold workpieces heated astheytravel through coil entering coil

CHANNEL ORSLOT COIL

(1-5)

INDUCTION

HEATING

IN INDUSTRY

Induction Heating Machines

An induction heating machine is defined as a device or group of devices which supply controlled amoun t s of a-c to the induction heating coil and physically support the coil and the workpiece . They may also incorporate automatic loading and unloading and special controls such as temperature . These devices often perform oth er related functions such as quenching, progressively movin g the workpiece , and squee zing two parts to g ether for brazing. The most commonly used types of induction heating machines are motor generator, vacuum tube oscillator , line frequency (60 cycle), spark-gap oscillator, mercury-arc inverter , and static magnetic frequency multiplier. Motorgenerator induction heatin g machines come in ratings from a few kw to several thousand , with frequencies of 540 cps , 1000 cps (1 kc), 2 kc, 3 kc, 4.2 kc, 10 kc, up to 30 kc. At least one-half of all the power used for induction heating is supplied by this type of machine.

5-l

;::::-; 70 u>C

MAXIMUM POSSIBLE ELECTRICAL EFFICIENCY vs.RESISTIVITYCOPPER HEATING COILFREQUENCY SUFFICIENTLY HIGH TOBENO LIMITING FACTOR -NONMAGNETIC WORKPIECE

60

G)

u

:::

50

Cl)

0 u

-

·.: u

40• 30

Cl)

LLI

20 10 0

10

20

30

40

Resistivity

50

60

70

80

90

100

- microhm - inch

What can be done about workp iece resistivity? Not very much. If our assignment is to heat aluminum billets, we are committed to working with the properties with which nature endowed aluminum. (1-69)

FACTORS

WHICH

AFFECT

EFFICIENCY

How Frequency Affects Electrical Efficiency

Seepage11-49) for theactual curve 1 .0

HEATING OK ANYWHERE ABOVE

ao

-=4 d2

2 ( :;

( 4

IN HERE, YOU'D BETTER CHECK FURTHER

4

RATIO O F DIAMETER TO REFERENCE DEPTH 00

(2

NO GOODI

Here is a factor which we can control (at least within the limits of the available equipment or , if new machines are to be ordered , within the limits of our budget). Frequency does not appear as such on the curves on page (1-64), but it is there. As you recall, frequency is one of the controlling factors determining reference dep t h. The higher the frequency, the smaller the reference depth, and the larger the electrical size of the workpiece (a 0 / d 2 ). The highest efficiency curve is the one for an electrical size of infinity. Of course this is a condition which we never encounter in practice, but it does show the limiting values. The curve for a diameter of 10 reference depths, however, is almost as high everywhere as the curve for infinity, and the curve for a size of 4 run s a close third. Thus, there is little to be gained by making the frequency so high that the electrical diameter of a round bar is greater than 4 reference depths. If you refer to the curve of K n 2 on page (1-48) , you will notice that a 0 / d 2 equals 4.0 comes at the upper end of th e steep part of the curve. K n 2 at this point is already 0.74, whereas the highest value it can ever have, even with infinite ao/ d 2 , is 1.0. It is no coincidence that elect r ical efficiency falls off rapidly below an electrical size of 4. The sharp decrease in efficiency in this region is a manifestation of the reduced wo r kpiece reflected resistance reof sulting from the lowered KR2 • In fact, a quick test for the practicability a proposed induction heating job is to calculate a 0 / d 2 and consult the KR2 curve. (1-70)

FACTORS

WHICH

AFFECT

EFFICIENCY

How Frequency Affects Electrical Efficiency (contd.)

' Before leaving the subject of frequency, let us take another look at the efficiency curves on page (1-64). The only thing which we can accomplish by varying frequency is to move vertically from one efficiency curve to another. We cannot do anything about C 2 or any of the factors which affect C2 by varying the frequency. No matter how high the frequency, the maximum efficiency when heating copper at room temperature with a copper coil is SO%. The use of a high frequency cannot compensate for low resistivity , low permeability , or a poorly designed coil. Frequency 1. Efficiency

affects electrical

efficiency in the following

ways :

increases with frequency.

2. Frequency must be high enough. An a 0 / d 2 of at least 4.0 is safe. a 0 / d2 between 2 and 4 is questionable, and below 2 it is usually unsatisfactory. 3. There is no advantage in increasing beyond a certain value. Once a 0 / d2 is 4.0 or higher, there is little to be gained by further increase of frequency. 4. Frequency cannot compensate for low resistivity, permeability, or quality of coil design. The maximum possible efficiency with a given workpiece is limited by its resistivity and permeability .

Example (1). Is heating a ¼-inch steel rod to forging temperature a good application for induction heating with 10 kc?

(2200 °F)

Example (2). How about heating the same rod to 1000° F for stress relieving with 10 kc? Assume permeability equal to 40.

(1-71)

FACTORS

WHICH

AFFECT

EFFICIENCY

How Coil Geometry Affects Electrical Efficiency Coil geometry includes the ratios of workpiece diameter to coil diameter, and of coil diameter to coil length. When the former is high, we say that the coupling is close. More of the magnetic field set up by the coil threads through the workpiece. When the latter is low , the coil is long compared with its diameter. End effects are smaller in proportion than when the coil is short compared with its diameter . Again , more of the magnetic lines of force set up by the coil thread through the workpiece. Anything which tends to cause more of the magnetic field to pass through the workpiece also increases the electrical efficiency. But the extent of this increase depends upon other factors. When heating a magnetic steel bar with high frequency, the ratio of workpiece diameter to coil diameter may have very little effect upon electrical efficiency. But when heating a nonferrous material such as aluminum with a low frequency, this ratio may be all important . These facts can be seen by studying the curves on page (1-64). The only way in which coil geometry affects these curves is through its effect upon C 1 • If the other three factors, namely (a) workpiece resistivity, (b) workpiece permeability, and (c) ratio of workpiece diameter to reference depth (a 0 / d 2 ), are such that we are already way out to the right on the X axis and at the same time are using an effiC'iency curve which is nearly horizontal, then coil geometry is relatively unimportant. But if we are on the steep part of the curves, a small change in C2 on the X axis will cause a large change in efficiency. Thus, you can see that coil geometry is particularly important when heating low-resistivity nonmagnetic materials. It may even determine whether a job is economically feasible or not.

CoilOeomeli'g qflecfiEfficiency on the ifeeppqlfof thecu,ve! 100%

----

- ----

~

·--

PERMEABILITYU). SIZE - J RESISTIVITY

MUCH MORE EFFECTHERE THAN HERE

0 E....-.J.,__--'----

---

- - -l----+

C2 THE SAME CHANGE IN COIL GEOMETRY

(1-72)

FACTORS AFFECTING EFFICIENC Y

We must live with these

- -

0

FREQUENCY } COIL GEOMETRY ~ But we CAN do something about these!

~

[

RECTANGULAR Rectangular

WORKPIECES

Workpieces

Thesame basic principles thatwelearned forsolid round barsapply to rectan ularworkpieces

Workpieces whose cross-sectiona l shape is rectangular can be heated by induction in the same manner as round bars. The same basic principles apply. One of the most common methods is to place the rectangular part inside a rectangular or round heating coil. We know that skin effect is necessary :for induction heating of a round bar. This is also true of rectangular bars. Instead of flowing in c ircular paths, the eddy currents now try to follow the surface outline. They tend t o stay close to the surface. The degree of skin effect in a rectangular workpiece depends upon the same general factors that it does in round bars. The bigger the cross section and the higher the frequency (or both), the more pronounced is skin effect.

Reference depth is found for a rectangular bar by the same equation as that used for the round bar. It has practically the same meaning, but we must find a new ratio to replace the ratio of workpiece diameter to reference depth. You remember that this ratio was very important in determ ining the electrica l size of a round bar. The diameter in number of reference depths was important in determining the electrica l behavior of the round bar. We need to know this ratio to calculate the resistance which the workpiece reflects into the coil circuit and to calculate the electrical efficiency. For rectangular slabs, the ure of electrical size. The rectangular workpiece is applicability of induction

ratio of thickness to reference depth is the meassmaller of the two cross-section dimensions of a the more important one used to determine the heating . Why? · (1-73)

RECTANGULAR

WORKPIECES

Electrically Large Rectangular Workpieces The equivalent resistance of an electrically large workpiece is practically the same as that of a thin sleeve around its circumference . Its thickness is equal to the reference depth and its cross section equals the reference depth multiplied by its heated length. The length of the induced current path in the sleeve is approximately the same as the perimeter of the workpiece.

Example (1). An 8-inch-long aluminum bar whose cross section is 2 X 5 inches is placed in a 10-turn coil through which 3-kc current is flowing. The aluminum is at room temperature. Find the resistance which the workpiece reflects into the coil circuit. 6 Solution. p of aluminum (room d = 3 160 ✓ l.l 2 X 10- = 0 0610 · h 2 3 X 10a . me . 6 temperature) 1.12 X 10- ohm-inch. (Ratio smaller dimension of slab) / d 2 2.0/ 0.0610 = 33.. Therefore, the workpiece is electrically large.

=

=

R

2

•u

= N12 p2 X

length area

= 102 1.12

X

10- 6 (2 + 2 0.0610 (8)

+ 5 + 5)

= 3210

X

l0--6

0

h m.

Example (2). Suppose that the inside of the coil of Example (1) is rectangu lar , with dimensions of 3 X 6 inches. This shape is obtained by winding a copper strip or thick rectangular copper tubing on a rectangular mandrel. Take the space factor equal to 0.85. Find the electrical efficiency, assuming that the inside wall of the coil turns is large compared to the reference depth in copper. Solution. Reference depth in • ✓ 0.68 X 10- 6 d1 3.160 0.0475 mch. 3.0 X 1O-8 copper coil = d 1 where Therefore, the mean length per turn (ML T) in copper is 6 + 6 + 3 + 3 + 4 (0.0475) = 18.2 inches . The width of 1 turn is (length X sf) / number of turns, or 8.0 (0.85) / 10 = 0.68 inch. Therefore the area for current flow in the coil is 0.68 (0.0475) or 0.0323 in 2 •

=

Ri

= N1 (MLT)

=

Pi

area 10 (18.2) (0.68 X 10- 6 ) 0.0404

= 3830

=

X lQ- 6 ohm

3210

3830

+ 3210

= 0.456 or

45.6%.

(1-74)

/

RECTANGULAR

WORKPIECES

Smaller Rectangu lar Workp ieces Suppose that one dimension of the cross section of a rectangular bar is not large relative to reference depth. Another factor is needed in calculating workpiece resistance. This is K n~- We had a curve [page (1-48) J from which we could find Kn 2 for the round bar. But the curve of Kn 2 for the case we are studying now is slightly different. In the first place, the independent variable is the ratio of thickness divided by reference depth. In the second place, the shape of the curve is somewhat different. Contrary to what happens in the case of the round bar, the curve gives values of K n2 which are greater than 1 over a short range. But for high values, both curves give K n2 equal to 1. Both curves show K n 2 to be very low for small values of the ratio. Here is the curve of K n2 for a rectangular section in which one dimens ion is large, but the other is electrically smaller.

0.8

i-----;---t--

i----+-

0.7

1----;-----,t-t--

1-

0.6 f---+-¾-+0.5 t---+ 0.4

Rectangular workpiece vs. Thickness/Reference depth

---+

-t-+---+

t-- -+-t-

-

0.3 I---+..._

-

__

0.2 t----

0 0 ----

I

-----

234567 -'----------

-

'---------

rH.,cKNEss;RE FER~Nc :~oi:PrH·

The curve is particu larly useful in calculating what happ~ns in workpieces which are wide and thin. Sheet steel or sheet meta ls of various kinds are examples. Usually in these cases, it is sufficiently accurate to consider only the currents which flow across the face of the sheet , ignoring the relatively small effect of the current which necessarily flows perpendicular to the thickness at the edges, where it turns around to go the other way. R2

= 2 LP2d2W ( 1-75)

N i 2 Kn2

RECTANGULAR

WORKPIECES

Numerical Examples

ELECTR ICALLY SMALL RECTANGULARWORKPIECE ,

Get KR2 from Curve •

✓

·

2f W

.

R2eq =

.

Ld2 2

2 NI KR2

Example (1). Find the equivalent

resistance referred to the coil when heating a brass strip 0.020 X 2.0 inches at 1000 ° F in an 18-tum coil 6 inches long whose space factor is 0.75 and whose inside dimensions are 1.0 X 4.0 inches using 450 kc.

Solution. The resistivity ohm-inch,

of brass at 1000 ° F from page (1-18) is 4.5 X 10- 6 depth at 450 kc is

so the reference

6

d

4.5 X 10= 3160 'V/ 0.4 5 X 106 = 0.010

h • me .

The ratio of thickness to reference depth is therefore 0.020/ 0.010, or 2.0. From the curve on page (1-75), KR2 corresponding to T / d 2 = 2.0 is 0.815.

R _ 2 P2 W N 2-

1

L d2

= 79,000

2

K

X 10- 6

_ 2.0 (4.5) X 10- 6 (2.0) (18.0) 2 (0.815)'

R2 -

= 0.0792

Example (2). Find the electrical

Solution. The reference

6.0 (0.010) ohm.

efficiency

in Example

(1).

depth in copper at 68 ° F and 450 kc is 8

. h / 0.68 X 10= 3160 '\J 0.4 X 106 = 0.00 388 me . 5 The MLT is 2.0 + 8.0 = 10.0 inch. The width per tum is [ 6.0(0.7 5)] / 18 = 0.25 inch. Therefore, carrying area is equivalent to 0.25 (0.00388) = 0.000970 = 9.7 X d1

R1 -

o.58

X lQ-

6

(lO) (l 8 ) = 12.62

9.7 X lo--4

_ '17 e-

X

10- 2 = 0.1262 ohm.

0.0792 _ + 0 _0792 _- 0.386, or 38.6 ol10 • 0 1262 (1-76)

the current10- 4 in 2.

HOLLOW

WORKPIECES

Hollow Workpiec'ls You will recall that the eddy currents are very tiny in the layers near the center of a solid round workpiece compared with their size near the surface. A small hole drilled along the centerline would have very little effect. There would be no appreciable change in the eddy-current distribution. We also have learned that the magnetic field gets weaker as we go deeper. This is because the eddy currents in each layer weaken the field "inside that layer. If the wall thickness of a hollow workpiece is large compared to reference depth, there will be no magnetic field inside the empty space. This phenomenon is sometimes utilized for shielding. 0

{J,1/01/ow Watl"iu't,-M'/MF.i'.~l //J.flY. .1!;;:}lq/4Wtll/ll,9ffft!l!~@¼l •'f!l:'rllc

F TUBE AND ALONG EOG

1:rJSJJ'i//.f.~ :r.~:,1« :'tWi"r,;,,1? :':\'il.11.'!J}J:' JiJ:IP!, ·;1.~m,·

Tube welding by induction enabled thinner wall tubing to be welded than had previously been practicable by conventional electrical methods. Production rates are several times higher than with non-electrical methods.

(1-119)

MECHA:r-lICAL

FORCES

ON COILS

Induction Heating Coils vs. Electromagnets You have probably noticed the similarity in appearance between some of the induction heating coils which we have sketched and electromagnets which operate such devices as relays.

Relaycoil

An induction heating coil, in addition to heating the workpiece, also exerts a mechanical force on the workpiece . This is true even when the workpiece is not of a material which can be lifted by ordinary magnets. Large mechanical forces can be developed between induction heating coils and workpieces of such materials as aluminum, copper, and brass (as well as of steel). We all know that there is a force of attraction between a coil carrying d-c and an iron or steel plunger partly inside the coil. The plunger is drawn toward the center of the coil. We also know that nonferrous materials like aluminum or copper would be unaffected by the coil carrying d-c. If the direction of the d-c were to be reversed, the force on the steel plunger would still be in the same direction. The coil and the plunger would attract each other. If low-frequency a-c were used instead of d-c, there would still be a force of attraction but there would be pulsations. The magnetic parts of a-c relays and magnets are constructed of laminated steel. They are not solid, because eddy currents would be induced, and heating would result. (1-120)

MECHANICAL

FORCES

ON COILS

Force between Coil and Workpiece If the frequency of the a-c is sufficiently high (or if the plunger is large enough) for appreciable eddy currents to be induced, this situation may reverse. These are the same conditions which make for efficient induction heating - namely, large electrical size.

When a current-carrying conductor is in a magnetic field, a force is exerted on the conductor. The direction of the force is at right angles to the conductor and to the direction of the field, and can be predicted by the left-hand (or motor) rule. The magnitude of the force depends upon the magnitude of the current and upon the strength of the magnetic field. Let us see how the left-hand rule applies to eddy currents induced by an induction coil. We have seen that eddy currents can exist only if there is a magnetic field. We have seen that eddy currents tend to reduce the field but that it is impossible for them to eliminate it completely . Eddy currents in this respect are like the currents in armatures of motors. They exist in a magnetic field. A force is exerted upon the conductor in which they ffow (in this case, the workpiece).

FORCE ON CON ~ UCTOR

T

-

..;

-

. . . . . .. . . . . . I

I

I

I

l

l

l

I

'

T

' T

'I

.

-

FORCES' ARE INWARD

T

T'

I

)C)CVYVXIV)(V

;.

..----0000000000---

I

X

X

. .:::

tEFT-HANO RULE ('MOTOR' RULE) Let us apply the left-hand rule to the case of a hollow workpiece centered inside a solenoidal coil. The same forces exist in a solid nonmagnetic bar inside a solenoid coil. If the bar is centered in the coil, or if it protrudes from each end so that fringing of the field is the same at both ends, there is no net tendency for axial motion. (1-121)

MECHANICAL

FORCES

ON COILS

Forces on Pancake Coils The force between the heating coil and the workpiece manifests itself particularly with pancake heating coils which are used for heating fl.at surfaces. Unless the coil is carefully braced, it will move away from the workpiece each time the power is applied. This not only disturbs the uniformity of the airgap between the coil and the workpiece, altering the heat pattern, but it also weakens the coil itself. Repeated flexing of the copper gradually makes it brittle and it finally fails by cracking. This same force of repulsion is well known to designers of power transformers and generators. Constant-current transformers for such applications as series street lighting circuits have utilized this principle for many years. When the current in the secondary or load circuit tends to increase, the repulsion between the primary winding and the secondary winding increases. The secondary winding moves away from the primary winding, decreasing the mutual coupling, and restoring the secondary current to substantially the same value as before the change.

CONSTANT -CURRENT TRANSFORMER

THE COIL AND WORKPIECE REPEL EACH OTHER [LEFT-HAND RULE) (1-122)

FORCE ON WORKPIECE

MECHANICAL

FORCES

ON COILS

Forces on a Solid Bar

Forceson a SolidBar :· --

- BAR IS ONLY PART WAY INSIDE COIL

··rl·tt -------

-- ---

---~

NET FORCE

X)(tJ xt( .:!.R·

,· ~;

-- -

~:;::r,.,..JQi

a:1'~f;fafe,i

A LUMI NU M BAR IS FO RCED AWAY FROM CENTER OF COIL BY FO RCES O N IN DUCED CURRENTS

MagneticMafe,ial IN DUCTION HEATER FEEDS ITSELF

AB

TEMP

When a nonmagnetic bar is placed part way inside a solenoidal induction heating coil to heat a portion of one of its ends, the fringing flux causes a component of force which tends to expell the bar from the coil. There is no counterbalancing force at the other end of the bar. In the case of light nonferrous materials such as aluminum, means frequently must be provided for keeping the bar from being thrown bodily out of the coil when the power is turned on.

An interesting variation of this phenomenon occurs when a column of steel billets is heated progressively to a temperature above the Curie point in a long coil using a low frequency. At the entrance end of the coil, the steel is magnetic; the billets tend to be drawn into the coil. But on the other end, where they are above Curie temperature and are nonmagnetic , there is a force of repulsion between the coil and the induced current in the billets . It is possible to tilt such a coil so t hat gravity , aided by these electromagnetic forces and by the vibration from the low frequency , causes the billets to move by themselves into the cold end and out of the hot end of the coil. (1-123)

MECHANICAL

FORCES

ON COILS

Stirring Effect in Melting Furnace

In a coreless induction melting furnace, the workpiece is a charge of melted metal in a nonconducting, heat-resistant crucible. The compressive forces which we found in the hollow sleeve also exist in the outer layers of the melted charge. They give rise to motion of the liquid metal. This is known as the stirring effect. It is one of the advantages of induction melting furnaces, as it tends to make the composition of the metal uniform throughout the various parts of the crucible. Further advantage is taken of this phenomenon in levitation melting. One of the problems in melting certain metals is the contamination of the metal by the material of the crucible with which it is in contact. It is possible to shape a coil in such a way that a charge can be melted while it is being supported in mid-air (or a vacuum) by the electromagnetic forces associated with the induction heating. This process is in industrial use for ' small charges of high-purity materials.

f"

-, LEVITATION MELTING TAKES ADVANTAGE OFTHE STIRRING EFFECT SUPPORTING

FORCES ON MELTED METAL BECAUSE OF INDUCED CURRENTS

HEATING COIL

I

•

000-1

0-\

/

\.J "-.../

·:.~ ..

I

.............. \

....._._. . ..

I

I

.

(1 -124)

FORCES

,.

MECHANICAL

FORCES

ON COILS

Forces between Induction Coil and Workpiece at Low Frequency With low-frequency induction heating , the currents are larger and the magnetic fields stronger than with high-frequency induction heating. This is because the reference depth is greater, and the resistance of the workpiece to eddy currents lower. Larger currents must therefore be induced in order to develop the same 12R power. It follows that the forces between heating coils and workpieces are larger with low frequency than with high frequency. It is not uncommon for the frequency of a melting furnace installation to be chosen on the basis of optimum stirring effect. Too high a frequency may result in too little stirring; too low a frequency gives too violent an effect. This erodes the crucible, and may even tend to throw some of the charge out of the crucible entirely .

crucible

1//h'/A

~ll 1 1 1

D

end boa rd s of insulating material

D

D D □

studs intension supports insulati materia

D

□ □ □

studs brazed to coil turns

V///

1/////.1

1111 1 1

V/////.

1//

EXAMPLESOF COIL BRACING The electromechanical forces between coil just as they affect the workpiece. ing, it is necessary to brace the turns motion and damage because of these mechanical forces become troublesome

the coil and the workpiece affect the Especially with low-frequency heatof induction coils securely against forces . It is only in rare cases that in high-frequency induction heating .

(1-125)

SUMMARY Induction Heating In this volume we have seen what happens electrically and thermally inside a workpiece when it is heated by induction, and we have studied the heat ing coil from the standpoint of its effect upon the workpiece. In Volume II we shall examine how the heating coil reacts wit h the induction heating machine which supplies the electrical power to it. We shall learn how the var ious types of induction heating machines work , and we shall study the peculiar characteristics of each.

✓,....

1ff}~:

..~.

Book1 covered relationships . betweenthe WORKPIECE and the COIL

BookI I coversrelationships betweenthe COILand the INDUCTION HEIITING - also//ow the MIICHINES vario us kindsof machines work. ,., .

~l-126~

GLOSSARY TO VOLUME I Ampere turns - A measure of magnetizing force equal to the product coil current in amperes and the number of turns. Anneal -

of

To soften by heating.

Axial - Parallel

to the axis or centerline.

Blackbody radiation loss emissivity is 100%. Charge -

Heat loss (kw / in 2 ) from a hot surface whose

The material to be melted in the crucible of a furnace.

Coil geometry - Shape and dimensions tween coil and workpiece.

of heating

coil and of airgap be-

Contouring - Shaping the inside of a heating coil ( especially a one-turn coil) for controlling the heat distribution along the workpiece surface. Close coupling piece.

Very little space between the heating coil and the work-

Conventional direction of current flow ternal circuit. Crucible nace.

Refractory

container

From positive to negat ive in ex-

for holding

Curie temperature - The temperature magnetic material is unity .

above which the permeability

Current density -

Current

Density -

of 1 cubic inch of material

Weight

the charge in a melting

divided by cross-sectional

of a

area, in amperes / in 2 •

in lb.

Dielectric heating - The housing of nonconducting high-frequency electr i c field. Dyne -

fur-

material by means of a

Unit of force in the CGS system.

Eddy currents material.

Currents

induced

Effective value of current -The

by transformer

action in a volume of

value of current based on its heating effect.

Electrical efficiency - That percentage of power input to the heating coil which appears as heat in the workpiece. Electrically large workpiece - A workpiece whose ratio of diameter to ref erence depth is greater than 4. Equivalent resistance - A fictitious resistance which , if heating coil current flowed through it , would draw the same power as the workpiece. Equivalent sleeve - A hollow sleeve in which the current density is uniform, having the same electrical characteristics as the solid workpiece which it represents. (1-127)

GLOSSARY

Erg - The amount of energy expended by a force of 1 dyne acting through a distance of 1 cm. Flux density Franklinian Frequency -

Density of a magnetic field in lines per in 2 •

current flow -

From positive to negative in external circuit.

Number of complete cycles per second .

Fringing - The weakening of the magnetic field near the end of a heating coil because of the spreading out of the lines of force. Heating coil -A coil through which a-c flows to set up the alternating netic field required for induction heating a workpiece.

mag-

Heat content - The energy required to raise 1 lb of material from 68°F to a given temperature (kwh / lb). Hysteresis loop-A loop formed 'when flux density Bin a magnetic material . is plotted against magnetizing force H for one cycle of magnetization. Hysteresis Joss - Power loss (other than eddy current) rial caused by reversals of a magnetic field. Induction heating - The heating of conducting magnetic field.

in a magnetic mate-

parts by means of a varying

Induction thermal factor - A factor which, when multiplied by the differ ence between surface and center temperatures, yields surface power density. Induction melting furnace tion heating.

A furnace in which metal is melted by induc-

Inductor block - A one-turn heating coil, usually made from solid copper bars or forgings, sometimes elaborately machined. Interpolation - Estimating the magnitude points by assuming linear (proportional)

of a variable between two given variation over that region .

Joule - A unit of energy, equal to 1 watt-second; 0.7376 ft-lb. Laminated -

also 10 millions ergs, or

Made of thin sheets.

Load - Workpiece. Lenz's Law - An induced current tends to oppose. the flux which induced it. Levitation melting - Melting a charge which is supported netic forces without any crucible.

by electromag-

Line-frequency machine - An induction heating machine utilizing line-frequency current in the heating coil.

power

Loose coupling - Having a large space between heating coil and workpiece. (1-128)

GLOSSARY

Magnetic field - A magnetized Magnetic steel unity.

region.

Steel whose permeability

Magnetizing force turns / inch.

The strength

is substantially

of a magnetic

greater

than

field in air, in ampere-

Maximum value of current -The highest value above the zero axis which an alternating current reaches during a cycle. Mean length per turn - The average length of one turn of a heating coil. Mercury inverter - An induction heating power source utilizing vapor tubes for frequency conversion.

mercury

Motor generator - A rotating higher than line frequency.

power at

Nonferrous -

Containing

machine for producing

electrical

no iron.

Nonmagnetic - Applying as that of air (unity).

to any material

whose permeability

is the same

Permeability - A measure of how magnetic a material is, being the unitless ratio of flux density in thjl material divided by what the density would have been in air. Power - Rate of doing work (joules / sec; watts; kw) . Quenching - Quickly cooling from above the critical temperature purpose of hardening. Radial - Perpendicular

for the

to the axis or centerline.

Radiation loss - Heat loss in kw / in 2 radiated away from a hot surface. Reference depth - The wall thickness Reflected resistance -

Equivalent

Relay - An electromagnetic means of moving contacts.

of an equivalent

sleeve.

resistance.

device for closing and opening

a circuit by

Resistance factor - A factor by which the circumference of a workpiece is multiplied to obtain the length of the current path in its equiva lent sleeve. Shielding - Preventing eddy currents from being induced in a conducting body by interposing a conducting plate or shield between it and the source of a varying magnetic field. Skin eHect - The tendency of a-c to flow more densely near the surface of a conducting body. Space factor - The total length of a heating coil divided by the prodttct of the number of turns times the width per turn . (1-129)

GLOSSARY Spark-gap oscillator - An induction heating power source wherein trains of oscillations are triggered by sparks jumping across gaps between conducting surfaces. Specific heat - The energy required to raise the temperature rial 1° F, in kwh / lb- ° F .

of 1 lb of mate-

Split return coil - A heating coil where useful heating is concentrated near the "go" portion, with relatively little heating under the "return" portion. Solenoid coil Stirring effect forces.

A coil wound in helical form. The motion of a melted charge caused by electromagnetic

Surface harden - To harden a shallow layer on the surface of a workpiece without hardening the interior. Surface heating - Heating a shallow layer on the surface of a workpiece without heating the interior. Thermal conduction - A natural process whereby heat moves from one location in a solid mass toward a cooler location. Thermal conductivityThe rate at which heat energy is conducted through a 1-inch solid cube of material from one face to the opposite face, when the temperature difference is 1 F 0 • Through heating as possible.

Heating the entire volume of a workpiece

Vacuum tube generator - A power source for induction lizes a high-power vacuum tube oscillator.

as uniformly

heating which uti-

Vector - An arrow whose length is proportional to the effective value of a voltage or current and whose direction indicates the phase angle. Workpiece -

The part which it is desired to heat.

Workpiece shortness factor - A factor used in calculating reflected resistance which accounts for the fringing of the magnetic field at the ends of the heating coil.

(1-130)

INDEX TO VOLUME I Basic electrical rules, 1-14 Blackbody radiation, 1-104 British thermal uoit (Btu), 1-90 Brown, Hoyler, Bierwirth, 1-11 Coils: dimensions, 1-51 effect oo efficiency, 1-72 mechanical forces, l-121 resistance, 1-54 types, l-5 Commercial induction heating, 1-1 Constant current transformer, 1-122 Contouring, 1-85 Convection, 1-103 Conventional current fiow, 1-18 Cooling after power is off, 1-105 Curie temperature, 1-13, 1-66 Density of materials, 1-95 Dielectric heating, 1-4 Dyne, 1-89 Eddy current losses, 1-11 Eddy currents: definition, 1-13 effect of size and frequency, 1-26 in solid bar, 1-24 Effective value of current, 1-28 Efficiency, electrical: definition, 1-40 factors affecting, 1-43, 1-65 graphical method, 1-61 importance of, 1-42 maximum possible, 1-69 Electrical size, 1-47, 1-48 Electromagnet, 1-120 Energy, 1-90, 1-91 Equivalent resistance, 1-40, 1-47 Equivalent sleeve, 1-44, 1-48 Erg, 1-89 Faraday, 1-9, 1-11 Frankliniao fiow, 1-18 Frequency: effect on efficiency, 1-70 units, 1-27 Fringing, 1-51 Gear heating, 1-82 Heat content: curves, 1-93 definition, 1-92 Heat time, 1-101, 1-106 History of induction heating, 1·9 Hollow workpieces, 1-77 Hysteresis loop, 1-12 Hysteresis losses, 1-12 Induced voltage, 1-14 Induction heating definition, 1-4 Induction heating machines, l-6

Induction thermal factor: curves, 1-102 definition, 1-101 Inductor block, 1-85 Jobs done by induction heating, 1-2 Joule, 1-89 Laminations, 1-26 Left-hand rule, 1-121 Lenz's Law, 1-22 levitation melting, 1-124 Line-frequency machines, 1-7 Machines, 1-6 Magnetic core in coil, 1-113 Magnetic frequency multipliers, 1-7 Magnetic field: of conducto r, 1-18 of d-c coil, 1-23 Maximutn value of current, 1-28 Mean length per turn, 1-54 Mechanical forces, 1-120 Melting furnace, 1·3, 1· 124 Mercury-arc inverters, 1-7 Motor generators, 1-6 Odd-shaped workpieces, 1-81 Ohm's Law, 1-14 Pancake coil, 1-114, 1-122 Permeability: definition, 1-45 effect on efficiency, 1-66 function of magnetizing force, 1-67 Power: affected by voltage ., 1-21 definition, 1-91 for heating, 1-87, 1-101, 1-106 in resistance, 1-14 Power density, 1-20 Practicability test, 1-70 Quantitative approach, 1-16 Radiation: curve, 1-104 losses, 1-103 Rectangular workpiece, 1-73 Reference depth: definition, 1-44 equation, 1-45 large size, 1-49 Reflected resistance, 1-78 Resistance: of conductor, 1-14 of workpiece, 1-44, 1-46 referred to coil, 1-50, 1-78 Resistance factor: curve for rounds, 1-48 curve for slabs, 1-75 definition, 1-47 for hollow parts, 1-80

(1-131)

INDEX Resistivity: definition , 1-14 effect on efficiency, 1-68 cable, 1-17 Right-hand rules, 1-18 Rudd, W . C., 1-11 Shortness factor: curves, 1-52 definition, 1-51 Skin effect: affected by permeability, 1-34 affected by resistivity, 1~35 definition, 1-32 in heating coils, 1-56 Solid bar, 1-24, 1-28 Space factor, 1-54, 1-57 Spark -gap oscillators, 1-7 Specific heat, 1-87, 1-90 Spectrum of induction heating, 1-8 Spiral coil, 1-114 Split return coil, 1-116 Stansel, N. R, 1-11

Stirring effect, 1-124 Strickland, H. A., 1-11 Surface heating, 1-82, 1-100 Temperatu re distribution, 1-36, 1-100 Temperature-time curves, 1-99 Thermal conductivity: curves, 1-98 definition, 1-97 Thick sleeve, 1-118 Thin sleeve, 1-19 Through heating: calculations , 1-101 effect of power, 1-32, 1-100 odd-shaped parts, 1-81 Transformer cores, 1-26 Tube welding, 1-119 Vacuum tube oscillators, 1-6 Vaughan, J. T ., 1-11 Vector, 1-29 Work, 1-12, 1-89 Workpiece resistance, 1-44

(1-132)

basics of

lncluctlon heating

I .

I.

basics of lnclUctlon heating lty CHESTER A.TUDBURY,M.S. O.ief Engineer New RochelleThermatoolCorp.

YOL.2

JOHN F. RIDER PUBLISHER, INC., NEW YORK London: CHAPMAN & HALL, LTD.

Copyright May 1960 by John F. Rider Publisher,

Inc.

All rights reserved. This book or any parts thereof may not be reproduced in any form or in any language without permission of the publisher.

Library Printed

of Congress

Catalog Number 60-8958

in the United States of America

PREFACE

This book is written to present the fundamental principles of the induction heating art and of commercial induction heating equipment in a manner readily understood and enjoyed by any reader familiar with the simple rules of electricity. It explains what induction heating is and how it works; it describes and explains the operation of the more common types of industrial induction heating _machines in use today; it presents material to assist in developing a quantitative understanding for new applications; and it deals ~ith electrical and thermal aspects in detail and touches more briefly upon some of the mechanical problems associated with fixturing. Intended for students in high schools, technical institutes, and industrial training courses, this text is useful for shop men engaged in operating, maintaining, and tooling induction heating equipment. Graduate engineers who have not had the opportunity of devoting as much time to this subject as I have will benefit from reading this book. It is hoped that those wh ·o read it will not only be rewarded by having done so, but will also derive some enjoyment, and that they will be stimulated to further study of the subject. Induction heating is like the elephant which was encountered by two blind people. Not having approached from the same direction, they formed very different first impressions. An intricate induction hardening machine f.or tiny gyroscope spindles, located in an air-conditioned room, operates in accordance with the same laws as a massive induction furnace in a smoky foundry, melting a thousand pounds or more of seething alloy. They are two aspects of the same elephant. This book is written in the belief that an understanding of the basic laws leads the way to an understanding of each specific application . The book is quantitative; it uses numbers. It is not enough to say that the power is large, or that the workpiece is hot, or that the rate of heating is fast, or that the frequency is high . To be meaningful, we must express these quantities as so many kilowatts or degrees or degrees per second or cycles per second. There are many numerical questions and problems, because the best way to learn is by doing. However, this book does not delve into higher

V

PREFACE

mathematics. Even though much of what it presents was discovered as a result of much study, by many people , of differential equations , Bessel functions, and the like, it is not necessary for the rest of us to repeat that labor. The time thus saved releases us to forge ahead creatively rather than simply repea t ing what has already been done. It is hoped t hat Basics of Induction Heating will help the reader to do so . I wish to express my appreciation to David G. Osterer , V ice President of the New Rochelle Tool Corporation, for having persuaded me to undertake this project in the first place, and to my patient wife , Ruthena Warren Tudbury, who saw to it that, once having started this book, I completed it.

New Rochelle , New York May 1960

CHESTER

A. TUDBURY

"

CONTENTS

VOL. II - BASICS

OF INDUCTION

HEATING

Preface .................................................................... . ........ .. .... ............................... v Review of Basic Alternating Electrical Characteristics Questions and Problems

Currents

..........................

of Heating Coils ................. ..

1

..........

9

MG Operating Characteristics .............................................................................. Capacitors and Transformers for MG Equipment ....... ..................................

20 21 25 35 42

Setting Up a New Job with MG Equipment

47

Motor Generators for Induction Heating ....... .................................................... The Inductor Altern'ktor .......... ... .... ...... ............... ........... ............ ..

of MG Sets ....

Parallel Operation

MG Rating and Protection Questions

................................................

and Problems

51

. .................. ..... ....

...... ........ ........... ................. 54

............................................................... ................... .. 59

Vacuum Tube Generators

.......................................... .......................... .... 60

Loading an Oscillator

.......

Three-Phase

.............. .......................... .................................................... 76

Rectifiers

... .... . .... ....... ............. ...... . .............. ..... ........ ........ 68

Questions and Problems Line-Frequency Spark-Gap

Induction

Oscillators

Mercury Inverters

............................................................. ....... 85 93

......... .................. ............ ........... .....................................

95

Frequency

Questions

and Problems

High-Frequency

Heating

........................................................... .. ....................

Magnetic

Proximity

.................. ........ ......... 84

Multipliers

.

. ................................................................ 97

..................

············· ·········· l00

Resistance of a Conductor

...101

Effect ....................................................................................... ........... ....107

High-Frequency Transmission ..............................................................................113 Fixtures ............................................................................................................ ...........116 Controls

...................................................................................................................... 119

Spurious Radiation ....................................................................................................124 Questions and Problems ......................................................................... ...............126 Glossary Cumulative

........................................................................................ ...............................127 Index

..................... ................................................................................131

REVIEW

f

OF BASIC ALTERNATING

CURRENTS

Review of A-C Circuits

I

I

IS INDUCE IN TURNS The four induction heating coil characteristics which we studied in Volume I have to do with relationships between the coil and the workpiece. Next we shall study the relationships between the coil and the electrical circuit of which it is a part. Before doing so, let us review some facts about a-c circuits. You recall from your studies of elementary electricity that self-inductance results when the magnetic field set up by an electric circuit links that same circuit. All induction heating coils have self-inductance. The magnetic field of the coil not only induces voltages in the workpiece, but also in the turns of the coil itself. These induced voltages are in such a direction that they tend to reduce the a-c flowing in the coil . The stronger the coil current, the stronger the field, and the higher is this back induced voltage. The higher the frequency, the higher is the voltage which a field of given strength will induce. These facts lead to a familiar equation : ?;"iJ.."'*'fl~.£/.;~-.."'!~-4:~~i:: '~• .Y, .•~- .._ . . , ~ ., •••

~ ~

i: :f· .,'·

~f:: ~

!· ~

i !' l

~;~

(2-1)

REVIEW

OF BASIC

ALTERNATING

CURRENTS

Inductance and Reactance The voltage required to force a-c of I amperes (effective) at a frequency of f cycles per second through an inductance of L henrys is (21rfL) I volts. Whenever such a current flows through an inductance, this voltage will appear as a drop across its terminals. The quantity 21rfL is called inductive reactance. The commonly used symbol for inductive reactance is XL, and its units are ohms. The equations for the voltage across a resistance and for the voltage across a reactance are very similar in appearance , but there is an important difference. In the case of a resistance, the voltage is in phase with the current, but in an inductive reactance, the current lags the voltage by 90 electrical degrees .

I

VOLTAGES ACROSS RESIS TANCE AND INDUCTANCE ARE 90 ° OUT OF PHASE R..t....

I

~ ~ER=IR

XL~

~ ~EL=IXL

~

~

-t:_+-1x, R

I

XL

..,.... L L .,~., Eo

ER

I

2 2 2 Eo = CIR> + CIXL>

I

CURRENTAND VO LTAGE ARE IN PHASE

L

CURRENTLAGS VOLTAGE BY 90 ELECTRICAL DEGREES

IR

When a-c flows through a resistance and an inductance voltage drop across the two elements is a combination of voltage drops. It is not correct to add the two voltages cause their maximum values occur at different times in addition must be by vectors.

I

in series, the total the two individual arithmetically bethe a-c cycle. The

Vector addition is done by attaching the tail of one vector to the point of the next, until all vectors to be added have been used. The vector sum is a new vector whose tail is at the starting point and whose po'int is at the point of the last vector added. (2-2)

REVIEW

OF BASIC

ALTERNATING

CURRENTS

Inductance and Reactance - Numerical Examples Let us numerically examine our thinking about inductance, inductive reactance, and circuits which contain resistance and inductive reactance. The inductance in the circuit sketched is 3.5 µh; resistance is 0.05 ohm; frequency is 10 kc.

I

Example

(1).

Find the inductive

reactance

XL of the coil, in ohms.

11

Example (2). Find the voltage drop across the inductive the current is 750 amperes. Example (3 ). Find the voltage drop across the resistance is 750 amperes .

reactance

when the current

Example (4). Sketch the vector diagram of the two voltage previous examples.

,,

1

'

I

I

Example (5). Find the total voltage inductance in series.

when

drops in the

drop across the resistance

and the

Example

(6).

How much true power in kw is drawn by this circuit?

Example

(7 ). How much apparent power _in kva is drawn by this circuit?

Example (8). How much reactive power in kvar (kilovolt-amperes is drawn by this circuit? Example

(9).

reactive)

What is the impedance in ohms of this circuit?

Example (10). What is the tector

relationship

(2-3)

between kw, kvar, and kva?

REVIEW

OF BASIC AL TERNA TING CURRENTS

Capacitors

A capacitor

consists basically of conducting plates separated from each other by insulating material called a dielectric. When a steady unchanging voltage is applied to a capacitor, there is a short burst of cur r ent while the plates become charged, but after that there is no current. When an a-c voltage is impressed on a capacitor, the plates are charged first in one polarity and then the other. The charge rushing alternately toward and away from the plates constitutes a-c in the wires leading to the capacitor. Capacitors , therefore, have the property of blocking the flow of d-c while permitting the flow of a-c. They are used for this purpose in high-frequency oscillators used in induction heating. The electrical size of a capacitor is described by its capacitance in farads (or, more frequently, in microfarads, which are millionths of a farad) . Capacitance is a measure of how much charge is stored on the plates for a given applied voltage. The bigger the area of the plates, the more room for charge, and the higher is the capacitance. The closer the plates are together, the more they affect each other, and the larger is the capacitance. The material of the dielectric between the plates is important, some materials giving rise to high er capacitances than others. The effective value of a-c which flows through a capacitor for a given voltage is higher when the frequency is higher because the capacitor becomes charged and discharged more often. These facts are summarized in the familiar relationship between voltage, current, and frequency shown below.

(2-4)

REVIEW

OF BASIC ALTERNATING

CURRENTS

Capacitive Reactance The voltage required to force a-c of I amperes (effective) at a frequency of f cycles per second through a capacitance of C farads is [1/ (27TfC)] I volts. Whenever a-c flows through a capacitor, this voltage appears across its terminals. The quantity 1/ (27TfC) is called capacitive reactance. Its symbol is Xe, and its unit is the ohm.

"

,.

EL=IXL VECTOR DIAGRAM

~

go• go•

CURRENT LAGS VOLTAGE ACROSS AN INDUCTANCE BY90°

- I

l./1naB -UT -C -UR -RE .NT LEADS VOLTAGE ACROSS BY90° A CAPACITOR Ec=IXc

CIRCUITCONTAINING RESISTANCE, INDUCTANCE,AND CAPACITANCE XL 1-

I•

R

Xe

~..l\.l'V"--{-;--

E,*.E,~E,1

The relationship between the voltage across a capacitive reactance and the current through it differs from the corresponding relationship for an induc tive reactance in two important respects. First, the voltage across a capacitor decreases with frequency, whereas the voltage across an inductance increases with frequency. Second, the phase relation between the voltage across a capacitor and the current through it are opposite from what they are in the case of an inductance. The current through a capacitor leads the voltage across the capacitor by 90 electrical degrees. When a-c Hows through a capacitor in series with other circuit elements such as resistances and inductances, the total voltage across all the elements is found by vector addition. (2-5)

REVIEW

OF BASIC ALTERNATING

CURRENTS

Impedance

- PEDANCEZ IS THERATIO OF THEVO ~~ROSS A CIRCUIU)IVIDEDB'!_THECU

--

-

The impedance of an a-c circuit may be nothing more than a resistance R, or a reactance X, if one of these is the only element in the circuit. But if several of these elements are present, then impedance is a combination of them.

q V II (,)

X I

THIS ISTHE IMPEDANCE TRIANGLE FOR ASERIES CIRCUIT CONTAINING R= 3; ·XL= 20; Xc = 16

~

X

R•3 The impedance of a series circuit can be visualized with a right triangle in which R is the base, (X L - X e) the altitude, and Z is the hypotenuse (long side). Let us do some numerical examples. (2-6)

REVIEW

OF BASIC AL TERNA TING CURRENTS

Numerical Examples

Example (1). Find the reactance (b) 10 kc; (c) 450 kc. Example (2). Find the reactance 3 kc; (b) 450 kc; (c) 2 me.

of a 1-µf capacitor of a 1-milihenry

at:

(a) 60 cycles;

(mh) choke coil at: (a)

Example (3). What is the impedance of a circuit consisting of a resistance of 10 ohms, a capacitance of 0.015 µf, and an inductance of 8.35 mh in series at: (a) 10 kc? (b) 450 kc? (c) 2 me?

Sol11tlons

(2-7)

REVIEW

OF BASIC ALTERNATING

CURRENTS

Power - True, Reactive, and Apparent

These quantities are used so often in induction heating work that it is essential that we agree precisely upon how they should be understood. We do not always bother to state whether we are talking about true, appar ent, or reactive power. We assume that the units give us this information. For instance, if we say that a heating coil requires 1300 kva at 38.5¾ power factor, what we really mean is that the apparent power is 1300 kva. The true power is 1300 X 0.385 = 500 kw. The reactive power is (1300) 2 - (500) 2 = 1200 kvar. We could have said that the coil requires 500 kw at 38.5¾ powerfactor, in which case we would have meant that the true power is 500 kw, and that the apparent power is 500/ 0.385 = 1300 kva, and that the reactive power is 1200 kvar. We must be meticulous in our use of the units kw, kvar , and kva. Sometimes true power and apparent power are equal. This is true when the power-factor is unity. 500 kw at 100¾ power-factor and 500 kva at 100¾ power-factor mean the same thing. Sometimes reactive power and apparent power are identical. This is true of a pure capacitance. If a capacitor takes 1200 kvar, its apparent power is also 1200 kva. So 1200 kvar and 1200 kva at zero power-factor mean the same thing.

(2-8)

ELECTRICAL

CHARACTERISTICS

OF HEATING

COILS

Heating Coil Inductance and Resistance The self-inductance of an induction heating coil, as viewed from its input terminals, is a combined property of the coil and the magnetic field established by the coil. It is a measure of how many lines of force link the coil as the result of an a~pere Bowing in the coil. Most induction heating coils have higher inductance when there is no workpiece in them. We have seen that the eddy currents in the workpiece weaken the magnetic field of a coil. This reduces the inductance.

Presenceof workpiece reducescoil inductance

LAMINATED,SO THAT EACH THIN PIECEIS ELECTRICALLY SMALL

INDUCTANCEOF THE COILIS MUCH HIGHERTHAN WITHOUTCORE

j

PRACTICALLY NO EDDY CURRENTS IN CORE

Steel workpieces even below the Curie temperature also reduce the inductance of a heating coil. The only condition under which this is not true is when the electrical size is so small that the workpiece is only borderline for induction heating. This happens when the workpiece is too small or the frequency is too low. The eddy currents are not strong enough in the steel bar to override the core effect, and the inductance of the coil increases. This situation is provided purposely in the design of iron-core transformers. The self-inductance of the primary winding is far greater with a properly designed core than without. The magnitude of the no-load (or magnetizing) current is many times reduced, even though there necessarily are some small eddy currents in the laminations of the core. It is also common practice to increase the inductance of coils used for such applications as chokes by means of laminated cores.

ELECTRICAL

CHARACTERISTICS

Heating Coil Inductance

OF HEATING

COILS

and Resistance (contd.)

The larger the airgap, the greater the number of lines of force threading through the coil, and the greater is its inductance. The eddy currents inside the workpiece reduce only the portion of the magnetic field which otherwise would occupy the space where the workpiece is placed. They cannot reach out and affect the field between the piece and the coil. However the area through which flux can exist in the airgap is reduced by the amount of the area of the workpiece. We have seen that the inductance of a coil without its workpiece is usually greater than with it. From the sketch on the previous page, we see that the total magnetic flux through the coil consists of three components. A few lines pass through the turns of the coil. Most of the lines usually pass through the airgap . Some lines are in the workpiece. Except with very low frequency or extremely close coupling, the airgap lines have the greatest effect in determining the inductance. The higher the frequency, the more this is the case .

._,

R1

1ij11j11U.N■

X1

.

R2

Xg

~1

X2

Xg

,

..,.,.,,,. ji~It ·)· ..

X2

}x1

THIS IS A TYPICAL IMPEDANCE TRIANGLEFOR AN INDUCTION HEATING COIL AND WORKPIECE COMBINATION

'---'~

~ RtotolR2~

The resistance which an induction heating coil presents to the rest of the circuit is the sum of the resistance of the coil (at the frequency used) plus the reflected resistance of the workpiece. We studied these in connection with electrical efficiency . In most induction heating coils ( except where their dimensions are small compared with reference depth) the reactance arising from the lines passing through the turns is approximately equal to to the resistance of the coil and the reactance reflected by the workpiece is approximately equal to its reflected resistance. (2-10)

ELECTRIC Matching

A L CH A R ACTE RI STIC S OF HEATING

COILS

=~

,,,,,m:mmmm·::mm···· ··· · ~~"', ,,,,,,,,, BULBS!11 ~ { . . ;:=

2 - volt utomobi

•

•

t '· '

Matching means causing an induction heating coil or indu ctor to dra w the desired amount of power when it is connected to the induction he at i ng machine with w hich it is to be used . The power drawn by an induc ti on heating coil depends upon the voltage and the coil resistance and reacta n ce. For a .given coil and workpiece combination, and at a given frequency, the re is only one value of voltage which will result in the desired amo unt of power. Most other electrical loads have the same limitation. Fo r instanc e, a light bu lb designed for use in a 12-volt automobile electrical system will not glow at full brilliance if used on a 6-volt system. It will bu rn ou t if used on a 115-volt house lighting system . The voltage which is impressed upon an induction heating coil by the machine to which it is connected must be just right if the amount of po wer which is drawn is to be the desired value. It is not always feasible to des ign the coil so that it can utilize directly t he rated voltage of a par tic ular machine. The size and shape of the area to be heated determine the size and shape of the coil. Sometimes 1-turn coils do the heating better t han multi-turn coils . Some coils must be small , and y et draw high power. Ot hers must be large, yet dra w low power. Usually it is necessary to make the coil the size and shape needed for the job and then , if necessary, match it to the machine by means of transformers. In almost all cases, the rated voltage of the machine is higher than needed; therefore step-down transformers ar e used.

ELECTRICAL

CHARACTERISTICS

OF HEATING

COILS

Transformer Ratios for Matching

Transformers for matching induction heating coils usually step down the voltage and step up the current. If they were perfect transformers, the primary voltage divided by the secondary voltage and the secondary cur rent divided by the primary current would both be exactly equal to the turn ratio. But they are not perfect. The actual secondary voltage is lower than the answer obtained by dividing the primary voltage by the turn ratio. The actual secondary current is lower than the answer obtained by multiplying the primary current by the turn ratio. In practice, we must compensate for this by using a turn ratio which is lower than the rat io of actual voltages and higher than the ratio of actual currents. The amount of this compensation depends upon the design of the transformer. Here are two numerical examples.

Example (1). Suppose that a 3-kc inductor block (1-turn) for hardening a pin bearing on a crankshaft requires 32 volts at its terminals for it to draw the required power of 150 kw. The rated voltage output of the available 3-kc motor generator is 800 volts . Specify the transformer which should be used. Example (2). A certain 450-kc vacuum tube type oscillator has a rated output (tank) current of 125 amperes. The induction heating coil which we wish to use with this machine requires 750 amperes. The oscillato r characteristically has constant output current, regardless of the load impedance connected to it. Specify the transformer which is needed.

800 32

=25

Ei1111~le 2.

Useratioslightlylo•erthanis:1 Useratioslightlyhigher than6:1

(2-12)

ELECTRICAL

CHARACTERISTICS

OF HEATING

COILS

Matching Coil and Load to Source

It is sometimes possible to design the coil and load combination so that it draws the desired power at rated voltage without the use of matching transformers. This is particularly applicable when multi-turn coils are used for heating columns of parts progressively as they are pushed through the coil. Sometimes taps are provided near the ends of the coils so that the final adjustment of matching can be made on the job. Choosing the correct transformer for a given job is frequently by trial and error. The coil or inductor is built so that it will heat the desired area of the workpiece, regardless of the voltage of the machine with which it is to be used. Then it is tried, using the nearest available transformer, and readings are taken on the machine in meters . From these readings, it is usually possible to calculate the correct voltage. This calculation utilizes the fact that the power drawn varies with the square of the voltage . (2-13)

ELECTRICAL

CHARACTERISTICS

OF HEATING

COILS

Numerical Example

Example. It is desired to use the full power output of a 50-kw, 10-kc induction heating machine for the surface hardening of a bearing surface . A 1-turn inductor was constructed and tried, using the only ava il ab le transformer which happened to have a 17 : 1 ratio. The rated voltage of the machine is 220 volts. It was found that with ?.20 volts impressed on the primary of the transformer, the power drawn from the machine was 18 kw. Assuming perfect transformers, what ratio should have been used?

Some induction heating machines are furnished with variable ratio trans formers so that different voltages can be impressed upon various coils.

A misconception

which sometimes confuses the operator is the assumption that, because the induction heating machine has a certain rating, each coil connected to it will draw that rated power. (2-14)

ELECTRICAL

CHARACTERISTICS

OF HEATING

COILS

Tuning the Induction Coil to Resonance TUNING,OR POWER-FACTOR CORRECTING, CAPACITOR BANK

Tuning refers to the use of capacitors in conjunction with the heating coil. The purpose is to reduce the current drawn from the source. With fixed frequency equipment, this amounts to power-factor correction. In oscillators, the capacitor is part of a resonant tank circuit . It functions somewhat differently, since the frequency is free to take whatever value it must for the circuit to resonate. The current drawn from the source by the capacitor leads the voltage by 90 °. It combines with the coil current vectorially, resulting in a need for less current from the source. If just the right capacitor is used, the parallel combination of coil and capacitor can be made to draw the same current from the source as if it were a pure resistance. A high current circulates between the coil and the capacitor, with only enough current being drawn from the source to supply the power. (2-15).

ELECTRICAL

CHARACTERISTICS

OF HEATING COILS

Economic Importance of Tuning

(ruNING hll(IHS SAVINGS - in sp(lce(Ind money/I

Tuning of the sort just described is used in motor-generator and linefrequency installations. Suppose a heating coil is matched to a 3-kc, 800volt rotating generator and draws 150 kw at a lagging power-factor of 25%, If no tuning were used , the generator would be called upon to supply 600 kva. With tuning, it is possible to use a 150-kva generator, operating at unity power-factor. The size and cost of a rotating generator depends upon its kva rating, so this represents a considerable saving. The cost of the capacitor bank is far less than the saving in generator capacity . (2-16)

ELECTRICAL

CHARACTERISTICS

0F HEATING

COILS

Electrical Changes When the Workpiece Heats

The electrical characteristics at the terminals of an induction heating coil change when the temperature of the workpiece rises because of the changes in resistivity and permeability which take place in the workpiece. The resistance R 1 of the turns themselves, the reactance X 1 due to the lines of force through them, and the reactance Xg due to the lines through the airgap do not change. The resistivity of most materials which are heated by induction increases with temperature, sometimes in the order of 10 to 1 or higher. In the case of a steel workpiece which is heated through its Curie temperature, an added factor is the sudden permeability change from a high value to unity.

12R2 ._.__ USEFULPOWER__ INDEPENDENT OF WHICH IS DEVELOPED REACTANCE VALUES IN WORKPIECE ~ INDEPENDE NT OF 2 2 TOTAL INPUT= 1 R, + t R2 GENERATOR USED~We've _seen

HEATING THE COIL TURNS

USEFUL OUTPUT = t 2

R

2

ELECTRICAL EFFICIENCY =

t I

2

2

'L

..I.,

~

R2

R1+I

2R

2

" R

I

+R

this

before!

2

The most important effect of the changes in reflected resistance and reactance of the workpiece is on the electrical efficiency. If the reflected resis tance decreases, the efficiency also decreases, but if the reflected resistance increases, the efficiency improves. This is true for any type of induction heating generator. Changes in reflected reactance do not affect the efficiency; however, they, along with changes in reflected resistance, do affect the generator performance. This effect is different for various generators, depending upon whether the frequency is fixed, whether the voltage tends to stay constant, whether the coil current tends to be constant, etc. (2-17)

ELECTRICAL

CHARACTERISTICS

OF HEATING

COILS

Electrical Changes When Heating Steel and Nonmagnetic Materials

ELECTRICAL CHANGES WHEN THE WORKPIECE HEATS IMPEDANCE TRIANGLES OF COIL CONTAINING A STEEL WORKPIECE

VECTOR DIAGRAMS

ELECTRICAL EFFICIENCY OF HEATING STEEL WORKPIECES -TYPICAL CURVES (NOT TO SCALE)

100%

ti z

0

cr,J

X 0

u

BELOW CRITICAL

!!!

..J

ii: IL

< u

UJ

j:

J

ii:

u

< u

ii:

N6i~~ 1-

ix

uUJ

x..11-U V

-1-""

'- ...al_.... Rr Rz

~--...?' HOT C SAME AS COLD>

J UJ

>