Dual‐frequency induction heating for gear hardening: converter, resonant circuit, and FEM modelling
2018; Institution of Engineering and Technology; Volume: 11; Issue: 14 Linguagem: Inglês
10.1049/iet-pel.2018.5336
ISSN1755-4543
AutoresKamil Kierepka, Piotr LEGUTKO, Piotr Zimoch, Marcin Kasprzak,
Tópico(s)Silicon Carbide Semiconductor Technologies
ResumoIET Power ElectronicsVolume 11, Issue 14 p. 2396-2402 Research ArticleFree Access Dual-frequency induction heating for gear hardening: converter, resonant circuit, and FEM modelling Kamil Kierepka, Kamil Kierepka Department of Power Electronics, Electrical Drive and Robotics, Silesian University of Technology, 2 Krzywoustego St, Gliwice, PolandSearch for more papers by this authorPiotr Legutko, Piotr Legutko Department of Power Electronics, Electrical Drive and Robotics, Silesian University of Technology, 2 Krzywoustego St, Gliwice, PolandSearch for more papers by this authorPiotr Zimoch, Corresponding Author Piotr Zimoch piotr.zimoch@polsl.pl orcid.org/0000-0001-8982-4425 Department of Power Electronics, Electrical Drive and Robotics, Silesian University of Technology, 2 Krzywoustego St, Gliwice, PolandSearch for more papers by this authorMarcin Kasprzak, Marcin Kasprzak Department of Power Electronics, Electrical Drive and Robotics, Silesian University of Technology, 2 Krzywoustego St, Gliwice, PolandSearch for more papers by this author Kamil Kierepka, Kamil Kierepka Department of Power Electronics, Electrical Drive and Robotics, Silesian University of Technology, 2 Krzywoustego St, Gliwice, PolandSearch for more papers by this authorPiotr Legutko, Piotr Legutko Department of Power Electronics, Electrical Drive and Robotics, Silesian University of Technology, 2 Krzywoustego St, Gliwice, PolandSearch for more papers by this authorPiotr Zimoch, Corresponding Author Piotr Zimoch piotr.zimoch@polsl.pl orcid.org/0000-0001-8982-4425 Department of Power Electronics, Electrical Drive and Robotics, Silesian University of Technology, 2 Krzywoustego St, Gliwice, PolandSearch for more papers by this authorMarcin Kasprzak, Marcin Kasprzak Department of Power Electronics, Electrical Drive and Robotics, Silesian University of Technology, 2 Krzywoustego St, Gliwice, PolandSearch for more papers by this author First published: 06 November 2018 https://doi.org/10.1049/iet-pel.2018.5336Citations: 2AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In order to achieve required mechanical properties of hardened elements, such as gear wheels, dual-frequency induction heating may be used. Dual-frequency allows heating only the outline of the gear, due to mixed penetration depth of the subject frequencies. This method of hardening requires the process to be very short as heat may spread by means of conduction. This study presents a 3 kW prototype inverter and its control scheme is used to generate dual-frequency output current. The overall efficiency of the inverter is 96%. An analysis of the output resonant circuit is made to find the resonant frequencies. Finally, circuit and finite element method (FEM) simulations are coupled to analyse the effect of dual-frequency current on the magnetic field, current density, and energy density on the surface of a gear wheel. 1 Introduction High requirements placed on steel elements, associated with obtaining specific mechanical properties, such as adequate surface hardness with unchanged shape and dimensions of the element, require precise heat treatment. Obtaining desired results requires proper processing parameters and full control over the course of the process. Hardened steel elements may be, for example, gears, rods, pipes, sheets etc. Parameters of such elements are subject to significant changes in the treatment process. There is also a need for precise outline hardening of oval elements, e.g. gears, while maintaining the properties of the rest of the steel element. Induction heating method may be used for this purpose [1-4], giving the following advantages: high heating rate, selectivity of the heating area, repeatability of the process providing stability and quality of the obtained product, high energy efficiency. Surface induction hardening is an interdisciplinary process, because it is a combination of electromagnetic, thermal, and metallurgical phenomena. All these phenomena occur when the surface of the material treated in the first stage of the process is heated above the austenitisation temperature and then rapidly cooled in the next stage [4]. The need for reliable and precise outline hardening of oval elements, e.g. irregularly shaped gears (Fig. 1), in a very short time, caused the development of dual-frequency inverters [5-9]. Dual-frequency converters are implemented in many possible configurations described in more detail in papers such as [8-10]. Fig. 1Open in figure viewerPowerPoint Examples of typical gears hardened by induction heat treatment Nowadays, induction heating is widely used for industrial applications. The paper discusses dual-frequency induction heating inverter applied for surface heating of a gear wheel during the hardening process. A current-carrying exciter coil surrounding the work piece induces eddy currents in it. Heat is generated in consequence, accordingly to the Joule–Lenz law. The depth of penetration of induced currents from the surface in irregularly shaped work pieces mainly depends on the material and geometry of work piece and frequency of induced eddy currents. Therefore, it is necessary to conduct a detailed analysis for a particular application. It is not possible to generate equally distributed eddy currents on the surface of a work piece with the use of a single-frequency inverter. The solution is the use of a dual-frequency inverter. The output current i flowing through the exciter coil consists of two components: i = iMF + iHF (MF, medium frequency; HF, high frequency). Properly matched frequencies and amplitudes of both iMF and iHF allow to reach even heat surface distribution. Fig. 2 presents a concept picture for induction heating using a dual-frequency exciting current. Fig. 2Open in figure viewerPowerPoint Example of dual-frequency inverters application area This paper presents the inverter topology and control scheme used to generate the dual-frequency output current, as well as an analysis of the output resonant circuit in order to determine the resonant frequencies. A 3 kW prototype inverter has been built and its efficiency has been measured experimentally to be 96%. A simulation model was created by coupling ANSYS Simplorer circuit model with ANSYS Maxwell finite element method (FEM) model, to determine energy density, magnetic field, and current density in a heated element. 2 Examined inverter topology Fig. 3 shows the circuit diagram of the dual-frequency inverter. This circuit uses a half-bridge configuration consisting of two power silicon-carbide (SiC) field-effect transistors. The transistors used were SCH2080KE SiC MOSFETs with Schottky barrier diodes (SBDs) T1, T2, capacitive voltage divider consisting of two (low ESR, ESL polypropylene) capacitors Cd and a capacitive filter Cf (electrolytic). Fig. 3Open in figure viewerPowerPoint Inverter circuit schematic Laboratory test set-up has been fed from a three-phase diode full-bridge rectifier with an autotransformer connected to three-phase grid (3 × 400 V). As power transistors SiC MOSFETS with SBDs were selected, because of their fast intrinsic body diodes and lower total losses [11-13]. Dynamic parameters of the intrinsic body diode are important, because of hard switching occurrence. 3 Output resonant circuit The inverter is loaded by a resonant circuit connected to its output via a 15:1 transformer. The schematic of the load circuit is shown in Fig. 4 and its photograph is shown in Fig. 5. The parameters of the resonant circuit are given in Table 1. Table 1. Parameters of the resonant circuit Parameter Value L1 8.2 µH L2 580 nH R1 100 mΩ R2 30 mΩ C1 33 µF C2 660 nF Fig. 4Open in figure viewerPowerPoint Output resonant circuit schematic Fig. 5Open in figure viewerPowerPoint Photograph of the output resonant circuit The exciter coil's inductance is equal to 270 nH, but adding the inductance of the copper leads results in a series inductance of ca. 580 nH. In the circuit under consideration, three amplitude resonances occur: an MF series resonance (at frequency fr1), a parallel resonance (at frequency fr2), and an HF series resonance (at frequency fr3). The circuit's impedance is given by (1), absolute impedance is given by (2), and the phase angle is given by (3). The real and imaginary parts of impedance are given by (4) and (5), respectively (1) (2) (3) (4) (5)where (6)Amplitude resonance occurs at angular frequencies fulfilling the following equation (7)Which can be rewritten as (8) (9)where V is the voltage across the resonant circuit and I the current flowing through it. Substituting (2) into (9) results in (10)Thus, (7) can be rewritten as (11)Therefore, to find amplitude resonance frequencies, the following equation must be solved (12)Equation (12) leads to a 12th-order polynomial equation, thus, in compliance with the Abel–Ruffini theorem, a general solution cannot be obtained. The equation may only be solved for given values of L1, L2, C1, C2, R1, and R2. By using the set of parameters of the resonant circuit in question and solving the equation numerically, the values of resonant frequencies were obtained Although the resonant frequencies are dependent on all parameters of the circuit, they can be calculated with simplified formulas (13)–(15) [5] (13) (14) (15)These simplified formulas give results varying from the ones obtained from solving (12) by a few per cent, thus allowing to do a rough calculation and tune the inverter pulse-width modulation (PWM) switching scheme easily. Formulas (13)–(15) may be used, because the reactance of L1 is high for the HF current component iHF. The same is true for C2 and the low-frequency component iMF. Therefore, when analysing HF and MF separately, the L1–C1 branch may be omitted for HF component and the C2 branch may be omitted for MF component, thus simplifying the analyses. Knowing the values of series resonance frequencies is essential, as output power can be regulated by lowering or increasing the difference between the frequency of iMF and fr1 or iHF and fr3. Fig. 6 presents the calculated absolute impedance and phase angle of the resonant circuit as functions of frequency, while Fig. 7 shows the same relations measured with an impedance analyser, by connecting it to the primary winding of the transformer. By comparing the results of calculations (Fig. 6) and measurement (Fig. 7), it can be seen that the calculated resonant frequencies are close to the measured ones. The calculated value of fr3 is ∼266 kHz, while the measured value of fr3 is ∼267 kHz. Similarly, calculated fr1 is ∼9.3 kHz, while the measured value is ∼8.5 kHz. The parallel resonance frequency fr2 is not significant for the inverter operation as no component of the output current has a frequency close to its value. Thus, no phenomena related to this resonance occur. Fig. 6Open in figure viewerPowerPoint Calculated absolute impedance and phase angle of the resonant circuit as functions of frequency Fig. 7Open in figure viewerPowerPoint Results of measuring the absolute impedance and phase angle of the output resonant circuit 4 Inverter control method The idea of obtaining dual-frequency output current by PWM is shown in Fig. 8. The output power of both MF and HF components can be controlled separately. HF current component iHF can be regulated by changing the frequency of the carrier signal, while MF component can be changed by altering the frequency or modulation index of the modulating signal. It should be noted that the presented method allows majority changes of each harmonic, e.g. changing carrier frequency results in a significant change of iHF and a less substantial change of iMF. Fig. 8Open in figure viewerPowerPoint Principle of single simultaneous dual-frequency inverter PWM control system (a) Waveforms of carrier signal (solid line) and modulating signal (dashed line), (b) Inverter output voltage, (c) Inverter output current Forced hard switching operation requires a different approach to achieve optimal efficiency work point. HF resonant class DE inverters (one frequency output current) with series RLC load always work with frequency higher than resonant load frequency to avoid hard switching operation. The described dual-frequency inverter cannot avoid hard switching occurrence. Thus, it is not required to realise phase control. A possible solution to the hard switching problem is the use of SiC MOSFET transistors. 5 Experimental results Laboratory tests were conducted to measure the efficiency of the converter and acquire key waveforms. The control system was tuned to set the frequencies of the carrier and modulating signals close to the series resonant frequencies fr1 and fr2 of the load circuit. Modulation depth was set to 0.8 to avoid overmodulation. Fig. 9 shows waveforms of low-side transistor voltage vT2 and inverter output current i flowing through the resonant circuit. Fig. 9Open in figure viewerPowerPoint Measured drain-source low-side transistor voltage vT2 and output current i The DC-bus voltage VDC was changed by adjusting the autotransformer in equal time intervals (60 s). Equal intervals ensured the same rise time of power transistors temperature. Temperatures were measured by NTC thermistors (NTCLE100E3334JB0) placed by epoxy adhesive on the case of power transistors. The power transistors radiator, load circuit, and work piece (carbon steel pipe) were cooled by independent water coolers. Temperatures of each cooling liquid were measured by a multichannel digital meter (thermocouples type K). Measurements allowed designating active power as a function of the DC-bus voltage. Resistance values of both NTC thermistors were collected at each measured point. Subsequently, the power transistors and radiator were removed from the inverter circuit. Two circuits shown in Fig. 10 were connected in parallel. The value of reference voltage Vref was set at constant value which defined the value of current flowing through the power transistor IT. The value of voltage across the transistors VT was incremented with a step of 1 V in 60 s intervals. NTC thermistors resistances were also measured at each interval. Power dissipation was calculated for each measured point accordingly using (16). The power dissipated in both transistors was graphed as functions of NTC resistances (Figs. 11 and 12). Both functions were approximated by second-order polynomials, thus allowing to obtain (17) and (18). Equations (17) and (18) allow the calculation of power dissipation for each power transistor as a function of NTC thermistor resistance, thus allowing to determine the efficiency during the induction heating process carried out previously (16) (17) (18) Fig. 10Open in figure viewerPowerPoint Power transistor power dissipation test circuit Fig. 11Open in figure viewerPowerPoint Characteristic of power loss in high-side transistor PD1 as a function of NTC thermistor resistance RNTC1 with second-order polynomial approximation Fig. 12Open in figure viewerPowerPoint Characteristic of power loss in low-side transistor PD2 as a function of NTC thermistor resistance RNTC2 with second-order polynomial approximation The efficiency obtained by these calculations is presented as a function of output power in Fig. 13. On average, the efficiency was ∼97%, while being ∼96% at the peak output power. It should be noted, that the measured efficiency takes only transistors and driver circuits power loss into account, while neglecting other losses. Fig. 13Open in figure viewerPowerPoint Converter efficiency as a function of output power 6 Coupled simulation model of a simultaneous dual-frequency inverter In order to illustrate the influence of dual-frequency current of exciter on the load, e.g. a gear, FEM simulation was performed in ANSYS Software. Fig. 14 shows the FEM model of the exciter–gear system made in Maxwell 3D software. Fig. 14, along with Table 2, presents the dimensions of the exciter–gear system. Table 2. Dimensions of the exciter–gear system Parameter Value outer diameter of the coil 73 mm inner diameter of the coil 53 mm height of the coil 10 mm wall thickness of the coil 2.5 mm outer diameter of the gear 46 mm inner diameter of the gear 21 mm height of the gear 10 mm number of teeth of the gear 21 Fig. 14Open in figure viewerPowerPoint FEM model of the exciter–gear system of the simultaneous dual-frequency inverter The exciter material was modelled as copper with parameters set as described in [14]. The gear material (steel C45) has been modelled by using built-in ANSYS magnetic permeability curve, which accounts for the magnetic permeability being a non-linear function of magnetic field [15]. The changes of magnetic permeability with temperature [16] were omitted to simplify the simulations. The calculation mesh has been varied depending on the dimensions and significance of the components of the model. As the simulation was to illustrate the magnetic field distribution and the eddy currents of the gear, the number of mesh elements was as follows: 75,000 elements for the exciter and 250,000 elements for the gear. The dual-frequency exciter current was forced by coupling the FEM model of the exciter–gear system with the circuit model of the resonance converter made in the ANSYS Simplorer software (Fig. 15). As shown in Fig. 15, the peripheral model of the resonant dual-frequency converter include all the components of the actual inverter system, such as a three-phase power supply with diode rectifier loaded with a capacitive filter, a capacitive voltage divider, the series–parallel resonant circuit, a PWM modulator, and parasitic parameters of the exciter-load circuit. Fig. 15Open in figure viewerPowerPoint Circuit model of the resonance converter made in ANSYS Simplorer 7 Discussion of the simulation results As a result of computer simulation of coupled FEM and circuit models, the following results were obtained: distribution of magnetic field B (Fig. 16) and current density distribution J (Fig. 17) in the horizontal plane of the gear. Fig. 16Open in figure viewerPowerPoint Distribution of magnetic field B in the horizontal plane of the gear for a dual-frequency exciter current Fig. 17Open in figure viewerPowerPoint Distribution of current density J in the horizontal plane of the gear for a dual-frequency exciter current Additionally, in order to better visualise the dual-frequency process of hardening a single tooth of a gear, Fig. 18 shows the distribution of energy density E in a single tooth of the gear depending on the distance from the tooth's top (front). Fig. 18Open in figure viewerPowerPoint Distribution of energy density in a single tooth of the gear depending on the distance from the tooth's top for a dual-frequency exciter current By analysing Fig. 18, it can be seen that the highest energy density E occurs at a depth of ∼1 mm – the average energy density is ∼55 J/mm3. Additionally, at the same depth, the highest magnetic induction intensity B, which is ∼25.1 mT (Fig. 16) for an RMS value of both components of the load current of ∼300 A. The low values of magnetic induction B and energy density E obtained from the simulation may be a result of poor coupling (a large distance of ∼5 mm) between the exciter and the gear. By analysing Fig. 17 showing the distribution of current density J, it can be seen that the highest current density occurs around the sides of teeth and the notches of the gear. The maximum current density in this case is ∼938 A/cm2. In order to better illustrate the influence of the exciter's current frequency on the hardening process of the gears, it was decided to simulate the presented exciter-load system separately for each of the current frequency components. Fig. 19 shows the distribution of magnetic field for the MF component of the exciter current of 8 kHz, while in Fig. 20, it is shown for the HF component of 267 kHz. By analysing Figs. 19 and 20, it can be seen that as the exciter's current frequency increases, the magnetic field distribution in the gear changes. For MF, the magnetic field penetrates the gear's inside (Fig. 19), for that reason, the element heats evenly. In the case of inverter operation with HF of the exciter's current, the magnetic field only penetrates into a shallow outline of the gear (Fig. 20). For this reason, temperature rises significantly only on the outer edge of the gear, while the inside remains cooler. Fig. 19Open in figure viewerPowerPoint Distribution of magnetic field B in the horizontal plane of the gear for the exciter current containing only the MF component of 8 kHz Fig. 20Open in figure viewerPowerPoint Distribution of magnetic field B in the horizontal plane of the gear for the exciter current containing only the HF component of 267 kHz A direct comparison between Figs. 16, 19, and 20 shows the advantage of using a dual-frequency exciter current. Using dual-frequency resonant inverters, the magnetic field penetration depth of the gears can be freely controlled. By choosing the frequency components MF and HF of the exciter current, it is possible to control the heating process of any elements with an irregular and complex shape. 8 Conclusion An analysis of all parts of a dual-frequency induction heating system is given by the paper. The control scheme of such inverter was presented and its topology as well as reasons for the use of SiC devices were given. Through an analysis of the load resonant circuit, it has been shown that exact values of resonant frequencies can be obtained only through numerically solving the equations. It has been confirmed that the previously known approximated formulas (13)–(15) result in values close enough to the exact values of resonant frequencies, that they can be used to tune the control scheme. It should be noted that placing a work piece inside the exciter, such as a gear or any other heated element, changes the equivalent resistance of the exciter, thus slightly impacting the resonance frequencies. It has been shown that even with hard switching, it is possible to operate at high efficiency (96% at peak output power) by the means of using SiC devices with very fast intrinsic body diodes. A method of measuring power loss in MOSFETs, when it cannot be measured directly was also presented. Finally, by coupling a circuit model with an FEM model, the whole system was simulated, showing the result of using two frequencies simultaneously for induction heating. 9 References 1Candeo A., Ducassy C., and Bocher P. et al.: 'Multiphysics modeling of induction hardening of ring gears for the aerospace industry', IEEE Trans. Magn., 2011, 47, (5), pp. 918– 921 2Davies E.J.: ' Induction heating handbook' ( Mc-Graw-Hill, New York, USA, 1979) 3Fraczyk A., Jaworski T., and Urbanek P. et al.: 'The design of a smart high frequency generator for induction heating of loads', Prz. Elektrotech., 2014, 90, (2), pp. 20– 23 4Chiu L.H., and Ma C.H.: ' Retained austenite produced by induction hardening of cast iron'. 2017 Int. Conf. on Applied System Innovation (ICASI), Sapporo, 2017, pp. 1837– 1840 5Esteve V., Jordán J., and Dede E.J.: ' Induction heating inverter with simultaneous dual-frequency output'. 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