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ОБЩИЕ ВОПРОСЫ АВТОМОБИЛЬНОГО ТРАНСПОРТА
УДК 621.318.4
INDUCTION HEATING OF NON-MAGNETIC SHEET METALS IN THE FIELD OF A FLAT CIRCULAR MULTITURN SOLENOID
Y. Batygin, Prof., D. Sc., A. Gnatov, Prof., D. Sc., Sch. Argun, Assoc. Prof., Ph. D. (Eng.), O. Sabokar, T. Asst., Kharkov National Automobile and Highway University
Abstract. The theoretical analysis of electromagnetic processes in the system for induction heating presented by a flat circular multiturn solenoid positioned above a plane of thin sheet non-magnetic metal has been conducted. The calculated dependences ^ for the current induced in a metal sheet blank and ratio of transformation determined have been obtained. The maximal value of the transformation ratio with regard to spreading the eddy-currents over the whole area of the sheet metal has been determined.
Key words: induction heating, the induction system, the induced current, eddy current, heating of metal.
ИНДУКЦИОННЫЙ НАГРЕВ НЕМАГНИТНЫХ ЛИСТОВЫХ МЕТАЛЛОВ В ОБЛАСТИ ПЛОСКОГО ЦИЛИНДРИЧЕСКОГО МНОГОВИТКОВОГО СОЛЕНОИДА
Ю.В. Батыгин, проф., д.т.н., А.В. Гнатов, проф., д.т.н., Щ.В. Аргун, доц., к.т.н., О.С. Сабокарь, асист., Харьковский национальный автомобильно-дорожный университет
Аннотация. Проведен теоретический анализ электромагнитных процессов в системе индукционного нагрева, представленного плоским круговым многовитковым соленоидом, расположенным над плоскостью тонколистового немагнитного металла. Получены расчетные зависимости для тока, индуцированного в листовом металле, коэффициент трансформации и его максимальное значение.
Ключевые слова: индукционный нагрев, индукторная система, индуцированный ток, вихревые токи, нагрев металла.
1НДУКЦ1ЙНЕ НАГР1ВАННЯ НЕМАГН1ТНИХ ЛИСТОВИХ МЕТАЛ1В У ОБЛАСТ1 ПЛОСКОГО ЦИЛ1НДРИЧНОГО БАГАТОВИТКОВОГО
СОЛЕНО1ДА
Ю.В. Батигш, проф., д.т.н., А.В. Гнатов, проф., д.т.н., Щ.В. Аргун, доц., к.т.н., О.С. Сабокарь, асист., Харк1вський нащональний автомобшьно-дорожнш ушверситет
Анотаця. Проведено теоретичний аналiз електромагнтних процеав у системi тдукцтного нагрiвання, який представлено плоским круговим багатовитковим соленоидом, розташованим над площиною тонколистового немагнтного металу. Отримано розрахунковi залежностi для струму, тдукованого в листовому металi, коефщент трансформацИ' та його максимальне значення.
Ключов1 слова: тдукцтне нагрiвання, тдукторна система, тдукований струм, вихровi стру-ми, нагрiвання металу.
Introduction
Statement of the problem. Induction heating (IH) is heating of a metal object called «a blank» by electric currents. The latter are induced by variable magnetic field of an inductor (singleturn or multiple-turn solenoid). Flow of the eddy-currents is accompanied by heat liberation determined by the effect of Joule-Lenz's law, which results in the object heating [1, 2]. This effect has found a wide industrial application in performing a whole number of working operations, for example, quenching the surfaces of metal products, non-contact heating of liquids, levitation melting of metals, etc. [3, 4].
Publications analysis
Among the latest works devoted to IH there should be mentioned those, which in details describe processes in instruments of the method -generators of transverse magnetic field [5] and generalize the results of integrated studies presented in Russian as well as foreign literature, describe the methods of calculating integral characteristics of the heating processes and the results of physical experiments on industrial units [6].
Interest in IH has been observed in vehicle repair technologies. Here production operations on glass removal, cleaning lacquer coatings, disconnecting bolt joints, softening car body metal coatings before planishing dents, etc. [7].
The idea of using the induction pre-heating in magnetic-pulse metal treatment was suggested yet in the eighties of the 20th century [8]. The authors of the proposal developed and created the system initiating the flow of current in the work tool coil till the moment of force impact. The induction pre-heating allowed sufficient increasy in magnetic-pulse deformation efficiency in whole.
Following the logic of the first proposal of the work authors [8] positive results can be expected at using IH in production operations with magnetic-pulse attraction of preselected areas of thin metals particularly in operations on external planishing of car body elements [7, 9].
A single-sided induction heating system based on IGBT is proposed in the article [4]. Authors have a simulation of the single-sided induction heating system in ANSYS. He simulation results are compared with the experimental results.
And also authors estimate the temperature distribution model by the least squares theory.
From the above-mentioned, it is clear that IH of nonferromagnetic materials in the field of a flat circular multiturn solenoid presents a quite urgent scientific and technical problem, which solving is required for production operations to repair vehicles.
The objective of the research
The objective of the research is theoretical analysis of electromagnetic processes in the system for induction heating presented as a flat circular multiturn solenoid placed above the plane of thin sheet non-magnetic metal.
Electromagnetic processes
When making calculations analytical dependences for induced currents obtained by the authors of the works [10] can be used. The design model in the cylindrical coordinate system with unit director vectors er, e„, ez is presented in fig. 1.
Fig. 1. The design model of the system «inductor-blank»: I(t) - alternating-current source; 1 - multipleturn solenoid; 2 - flat sheet blank
The assumptions accepted.
1. The system has axial symmetry, so that
a
— = 0 (9 - polar angle).
a^
2. The inductor - a flat coil (the number of turns w), which thickness is quite small and its metal is so «transparent» for the existing fields (A^0) that has no effect on the taking place electromagnetic processes.
3. In the inductor there flows the harmonic current I(t), which time parameters allow using in
calculations a known condition of quasi-stationary electromagnetic processes so that
— • I <<1 (here © is a circular frequency of the c
process, c - light velocity in the vacuum condition, l - the most common geometrical dimensions of the system).
4. The radial length of the sheet blank is quite d
large, so that -«1, where d - the metal
R1,2
thickness, R12 - internal and external radius of the field inductor.
The results of the works of reference [9, 10], where electromagnetic processes were studied in the system similar to the considered one but with a single-turn field magnet/inductor we rewrite in a form convenient for numerical estimates.
h
00 _ / \ Jy (r, t) = 4 • jm J f (x) • x2 • e~XdJi ^xdJ
fß2 + X2 )
x¿ a(k)F^M j) * e^^Vd
k=0 % (x) dt
, (1)
I • w where jm = m
'; 1 т
, amplitude of the
(R2 " R1)
excitation current;^ - number of turns; Ri,2 -internal and external radius of the inductor; j(t) -time dependence of the current in the inductor; t - time;
O * (x) = cos (P* )•[ x2 + 2 x-P2 ]-"2-P* • sin(P*)-[1 + x]
Taking into account the specifics of the present task and in accordance with the accepted assumptions the expression (1) can be rewritten as follows:
со h / \
Jy (Г, ф) = 4 jm J f (x)x v4j ^xd J X
<Z a(k)
Fk (x,ßk)
k=0
k(x)
cos y * e fflT
fß2+x2) ^
y
(2)
dx
- corres-
R2 x—2 1 d
where f (x) = — f y • y) •<
x2 R
x—1 d
ponds to uniform distribution of the current
' (p2+x2) ^
density in the inductor;
cos y * e ют
-ф
v J
convolution function corresponds to harmonical time dependence of the excitation current;
j(t)=sin(9) (9=©t - signal phase);
' (p2 +x2) ^
cos y * e
-y
a(k) = •
I 0,5, k = 0; 1,0, k Ф 0;
T
: J cos(^) •(
fß2+xil <ф-ц)
MT dц;
R2
x--2
1 d
f(x)=-2 Í f(y)• y• Ji(y)dy; x2 R
x—1 d
t = ^0-y-d2 - specific time of the field penetration into conducting layer with electric conductivity Y and thickness d.
fy) - the function describing radial distribution of the current density in the inductor; pk - roots of equation
Integrating the expression (2) on re [0;R] we find intensity of the current induced in the metal of a sheet blank in the circle of radius R.
' ßk ^
1 _
(k- d)
sin(ßk) + 2
ßk
(Ь d)
cos(ßk) = 0;
Fk (x) = fl _ cos fßk ))+^ • sin fßk);
I y (r < R, y) =
( 4 • d • w ^
<] f (x)
• x • e
(R2 _ Ri) j
1 _ J0| xR I I x
x
m
h
x
d
<£ a(k ) •
Fk ( x,ßk )
k=0
®k ( x)
(ß2+x2 ) >
---"Ф
cos ф * e fflT
dx. (3)
peculiarities determined by the prosesses of the field penetration at IH of thin metals.
Conclusions
The ratio of transformation is determined as the amplitude ratio of the excitation current and the current induced in a blank in the circle of radius R (area: r < R).
* ( r, ф)=^^={ ] Im V (R - Rl) J
xj f ( x ) • x • e " Xd - Jо f xR ]]x
-(ß
<Z«(k )
Fk ( x,ßk )
k=0
( x )
2 +x2 ) > . Ф
cos ф * e fflT
dx. (4)
From the dependence (4) it follows that the ratio of transformation on the current is directly proportional to the number of turns in the primary coil, thickness of the sheet metal and radius of the circular zone where excitement of the eddy-currents is considered.
Varying the mentioned above parameters allows intensifying electromagnetic coupling between the excitation and induced signals thus raising the level of energy transformation in the metal of the sheet blank.
The maximum value of the transformation ratio is observed at R taking into account distribution of the edd-currents over the whole sheet metal surface.
From the equation (4) we obtain
* = JФmax ( max y
f
4 • d • w
<1 a(k )
v ( R2 - R1) у 0 f
Fk ( x,ßk )
j f ( x) •
x • e " x
k=0
( x )
(ß2+x2 ) >
cos ф * e fflT
dx. (5)
Formulas (2)-(5) are the relations permitting to perform all required numerical evaluation of quality of the processes in the investigated system "inductor - sheet blank" with regard to all
The main results of the theoretical analysis of parameters of the induction heating process of non-magnetic sheet metals depending on their electric conductivity and the time characteristics of current in the coil of a flat multi-turn inductor come to the following statements.
1. The ratio of transformation in the investigated system is determined by the ratio of effective depth of penetration of the field into the conductor and the thickness of the latter, which, to a certain extent specifies the degree of dispersion of concentration of electromagnetic energy in a certain part of the metal sheet blank.
2. The maximal value of the current transformation corresponds to the current operation frequency in the inductor calculated for the equation
f
J m
l
^•(d2 •Мо •Y) '
where d - thickness; - magnetic conductivity
of the vacuum;y - electric conductivity.
References
1. Benenson W. Hand book of Physics / W. Benenson, J.W. Harris, H. Stöcker, H. Lutz (Eds.). Springer Science & Business Media, 2002.
2. Doley J. K. FEM Study on Electromagnetic Formability of AZ31B Magnesium alloy: 6th International Conference on High Speed Forming / J.K. Doley, S.D. Kore, 26-29 May, Daejeon, Korea, 2014. - P. 273-280.
3. Rudnev V. Micah Black, Handbook of Induction Heating / Valery Rudnev, Don Loveless, Raymond L. Cook, Marcel Dek-ker AG, 2002.
4. Song Wang. Single-Sided Electromagnetic Induction Heating Based on IGBT / Song Wang, Guangda Li, and Xiaokun Li. Advances in Mechanical Engineering, 2014. 9 January, Article ID 503849. - P. 1-18.
5. Zinn S. Elements of Induction Heating: Design, Control, and Applications / S. Zinn, S.L. Semiatin, ASM International Year, 1988.
x
m
h
—x
ф
6. Frank W Curtis, High Frequency Induction Heating / Frank W Curtis, Lindsay Publications Inc, 1987.
7. Welcome to BETAG Innovation [Electronic resource]. - 2015. - Available at: www.beulentechnik.com.
8. Belyy I.V., Fertik S.M., Khimenko L.T., Electromagnetic Metal Forming Handbook, 1977. English Translation by Altyno-va M.M. Available at: http://www.mse. eng. ohiostate. edu/_Daehn/ metalforminghb/index.html (accessed 04.11.10).
9. Batygin Yu.V. Basic diagram and practical algorithm removing dents on the body of vehicle by the pulsed electromagnetic attraction / Yu.V. Batygin, A.V. Gnatov // International Journal Of Engineering Sciences & Management. - 2015. - Vol. 5, Issue 1, January- March. - P. 47-51.
10. Batygin Yu.V. Pulsed electromagnetic attraction of sheet metals - Fundamentals and perspective applications / Yu.V. Batygin, S.F. Golovashchenko, A.V. Gnatov // Journal of Materials Processing Technology, Elsevier. - 2013. - № 213 (3). - P. 444-452.
References
1. Benenson W., Harris J.W., Stocker H., Lutz H. (Eds.). Hand book of Physics, Springer Science & Business Media, 2002.
2. J. K. Doley, S. D. Kore «FEM Study on Electromagnetic Formability of AZ31B Magnesium alloy», 6th International Conference on High Speed Forming, 26-29 May, Daejeon, Korea, 2014. pp. 273-280,
3. Valery Rudnev, Don Loveless, Raymond L. Cook. Micah Black, Handbook of Induction Heating, Marcel Dekker AG, 2002.
4. Song Wang, Guangda Li, and Xiaokun Li. Single-Sided Electromagnetic Induction Heating Based on IGBT, Advances in Mechanical Engineering, 9 January, Article ID 503849, 2014. pp. 1-18,
5. Zinn S. and Semiatin S.L., Elements of Induction Heating: Design, Control, and Applications, ASM International Year, 1988.
6. Frank W Curtis, High Frequency Induction Heating, Lindsay Publications Inc, 1987.
7. Welcome to BETAG Innovation [Electronic resource]. - 2015. - Available at: www.beulentechnik.com.
8. Belyy I.V., Fertik S.M., Khimenko L.T., Electromagnetic Metal Forming Handbook, 1977. English Translation by Altyno-va M.M. Available at: http://www.mse. eng. ohiostate. edu/_Daehn/ metalforminghb/i ndex.html (accessed 04.11.10).
9. Batygin Yu. V., Gnatov A.V. Basic diagram and practical algorithm removing dents on the body of vehicle by the pulsed electromagnetic attraction, International Journal Of Engineering Sciences & Management, 2015, Vol. 5, Iss. 1, January-March, pp. 47-51.
10. Batygin Yu.V., Golovashchenko S.F. and Gnatov A.V. Pulsed electromagnetic attraction of sheet metals - Fundamentals and perspective applications, Journal of Materials Processing Technology, Elsevier, 2013. no. 213 (3), pp. 444-452,
Рецензент: О.Я. Никонов, профессор, д.т.н., ХНАДУ.
Статья поступила в редакцию 24 февраля 2016 г.
