Experimental Research of Induction Heating in Inner Hollow of Cylindrical Solenoid

DOI: http://dx.doi.org/10.24018/ejers.2020.5.8.2053 Vol 5 | Issue 8 | August 2020 986  Abstract—Purpose: The experimental research of magnetic field strength distribution and induced current density in tubular metal blank depending on its position inside cylindrical inductor. Methodology: Electrodynamics problem solution using mathematical methods for analytical calculations. Expressions for fields and currents flowing in non-magnetic metals under a multi-turn cylindrical solenoid influence have been derived from Maxwell’s equations system. The accepted mathematical assumptions and simplifications do not affect the correctness of the results. Conducting the experiment to determine magnetic field strength inside solenoid hollow and induced currents density on surface of non-magnetic metal billet. Results: The obtained experimental distributions of magnetic field strength and induced currents when a billet is completely placed inside cylindrical inductor hollow correspond to the previously derived analytical relations and coincide with the fundamental physical concepts of the ongoing processes in the system. With partial placement of the billet inside the inductor, there is an abrupt increase in the tangential magnetic field strength. An extremum is observed in the end zone of a billet in this case. This is due to induced currents concentration in this area as well as on cylindrical surface of a billet. Scientific novelty. Average induction heating velocities correspond to the calculated values for the materials of the processed samples used in the experiment. Thus it testifies to the effectiveness of using this processing technology equally, both non-magnetic metals and magnetic. The practical significance of the results lies in the possibility of assessing the qualitative indicators of the level of induced currents and thermal effects in the end parts of non-magnetic cylindrical blanks with partial overlapping by an inductor for performing operations.

 Abstract-Purpose: The experimental research of magnetic field strength distribution and induced current density in tubular metal blank depending on its position inside cylindrical inductor. Methodology: Electrodynamics problem solution using mathematical methods for analytical calculations. Expressions for fields and currents flowing in non-magnetic metals under a multi-turn cylindrical solenoid influence have been derived from Maxwell's equations system. The accepted mathematical assumptions and simplifications do not affect the correctness of the results. Conducting the experiment to determine magnetic field strength inside solenoid hollow and induced currents density on surface of non-magnetic metal billet. Results: The obtained experimental distributions of magnetic field strength and induced currents when a billet is completely placed inside cylindrical inductor hollow correspond to the previously derived analytical relations and coincide with the fundamental physical concepts of the ongoing processes in the system. With partial placement of the billet inside the inductor, there is an abrupt increase in the tangential magnetic field strength. An extremum is observed in the end zone of a billet in this case. This is due to induced currents concentration in this area as well as on cylindrical surface of a billet. Scientific novelty. Average induction heating velocities correspond to the calculated values for the materials of the processed samples used in the experiment. Thus it testifies to the effectiveness of using this processing technology equally, both non-magnetic metals and magnetic. The practical significance of the results lies in the possibility of assessing the qualitative indicators of the level of induced currents and thermal effects in the end parts of non-magnetic cylindrical blanks with partial overlapping by an inductor for performing operations.

I. INTRODUCTION
Induction heating is being used in many industries, but for repair aims it mostly used in automobile industry. Depending on the configuration of inductor-tool there can be conducted different technological operations such as flattening of dents on car bodies (external non-contact alignment) or taking off stickers and glasses etc.
[1], [2]. This paper presents the consideration of characteristics of the tool typically intended for bolt joints reconnection, extrusion of different clamp types, dismantling of complex structures units which can't be brought to desired form by traditional methods without losing its of functionality. Induction heating of such type allows local and quick destroy the corrosion layer on details, which in many cases Published on August 31, 2020. V. Strelnikova, Kharkiv National Automobile and Highway University, Ukraine.
(e-mail: v.strelnikova91 gmail,com) caused the complications during listed operations performance. Today many engineering solutions based on the description of similar electrodynamic problem, but they cannot be called universal [3], [4]. For this reason, in the development of high-efficiency inductor systems, the key stages are a complete analytical review of a specific unsolved problem and conducting an experiment in the laboratory, in order to identify the main factors that influence on the obtaining of the desired result.
In the design of the induction heating equipment, in particular tool-inductor, there can be distinguished two intersecting problems. The first one is problem with achievement of simultaneous processing throughout the whole metal billet, which is often the case of the multipurpose use of induction heating systems. It leads to second onemathematical complications in drawing up an adequate model without introducing physical assumptions that distort it.
The purpose of this paper is the experimental determination of the magnetic field strength and the density of induced currents distribution dependences in the metal of the tubular blank from its position in the internal hollow of the cylindrical inductor.

II. FORMULATION OF THE PROBLEM
A conditional move of the tubular blank along the cylindrical inductor central axis ( Fig.1) holds the preservation of azimuthal symmetry.
Despite this, the displacement of the blank in the direction that does not satisfy the condition   1 1 lR  , leads to the inhomogeneity of the magnetic field and the appearance of edge effects in the end zone of the tubular billet. In the future, this will entail a complication of the mathematical model, because of the need to introduce a component describing these edge effects. The experiment was dedicated to determination of magnetic field strength in axis direction of its inner hollow and superficial distribution of induced currents in metal billet with its different longitudinal placement in the inductor. Of particular practical and physical interest is the behavior of these parameters on the end surface of the billet.

III. CALCULATION MODEL
Consider the basic mathematical model of the process of induction heating of tubular blanks, described in [5].
There are main assumptions that have been used for the experiment planning: − the presence of a gap between wires leading to power installation can be neglected and it can be supposed that there is circular symmetry when 0     (φ is the azimuthal angle); − the energy of the excited magnetic field is concentrated in the inner hollow of the solenoid and on its inner surface, the longitudinal z-component of the intensity will be equal to: The fundamental solution system of (1) is Bessel's modified functions of the first order -I1(z), K1(z) [7].
According to this for non-zero field components (in where A(p), B(p), C(p)arbitrary constants of integration.
The arbitrary constants of integration in (2) and (3) can be found using corresponding boundary conditions. − for magnetic field strength      (2) 01 where Wwinding turns number of exciting solenoid; Z0wave resistance of vacuum. Assuming that the induced current flows along the azimuth in a solid cylindrical blank of radius -R1 and length l, can be find the L-image of J(p) by the law of total current: The equation (5) can be simplified if it takes into account the actual conditions for performing repair operations that require induction heating of the working objects.
After necessary identical transformations in (5) obtained the following      (6) As the expression (6) contains uncertainties, opening them, in the original space can be obtained a directly proportional relationship between the exciting current of the solenoid and the current induced in the metal of the heated cylindrical billet.
The result (7) indicates that the magnitude of the induced current in cylindrical induction heating systems with working frequencies about 30 to 50 kHz and steel nonmagnetic blanks (about 0. , and length about 2Rl.
Because the wavelength is greater than the penetration depth the tubular blank assumed as solid, therefore, the thickness of the walls is not taken into account in the calculations [8].

B. Heating objects:
Tubular blanks of L62 brass (diamagnetic, based on the properties of the copper alloy as the main component) and aluminum (paramagnetic).

C. Progress of the experiment:
Proceeding from the statement of the problem, the tubular blank was placed as follows: 100%, 75%, 50% and 25% of the blank length in the inner inductor hollow.
As shown in Fig.1b the induction sensor was placed between the inductor and the tubular blank. It was decided to measure the magnetic field strength at 10 points with an offset step x = 5 mm, for this purpose, using an electronic oscilloscope, the readings of the EMF were recorded in mV for each of the four blank positions.
Further, using Faraday's law (8) for the sensor and knowing that the strength of the magnetic field varies according to the harmonic law obtained the following dependences: where S -sensor's area, S = 1·10 -6 m 2 ; N -sensor's turns number, N = 100.
Because the experiment was carried out using high frequencies at which the field does not penetrate through the blank, the statement Hmi = ji, is true, then the current induced in the blank will be numerically equal to: where jiinduced current density Induced currents density distributions in relative units for different blank materials are showed in Fig.2 and Fig.3.   The flow of eddy currents is accompanied by the release of Lenz-Joule heat [6]. Suppose that in the absence of heat transfer heating occurs only in that part of the blank where the eddy currents are concentrated. We give numerical estimates of the heating carried out under laboratory conditions, using the dependence derived in [5]. The indicator of this evaluation is the dynamic characteristic of the processthe average induction heating speed: The main results of the study include the following: 1. The obtained experimental distributions of the magnetic field strength and induced currents with the complete placement of the blank in the cylindrical inductor hollow correspond to the analytic relations derived earlier and coincide with the fundamental physical concepts of the proceeding processes. 2. It is shown that the magnitude of the induced current of this idealization for cylindrical induction heating systems is established solely by the winding turns number of the exciting solenoid and doesn't depend either on the temporal characteristics of the electromagnetic processes or on the system geometry. 3. When the blank is partially placed in the inductor inner hollow, there is an abrupt increase in the tangential magnetic field strength. In this case, an extremum is observed in the end zone of the blank. This is due to the concentration of induced currents in this area, as well as on the cylindrical surface of the billet. 4. Average heating velocities correspond to the calculated values for the processed samples materials used in the experiment, which indicates the efficiency of induction heating both of non-magnetic metals and magnetic ones.