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Simulation study of inductive heating of molybdenum sheet suited for rapid prototypes of rigid components of transport systems
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
ScienceDirect ScienceDirect
Transportation Research Procedia 00 (2019) 000–000 Available online at www.sciencedirect.com Transportation Research Procedia 00 (2019) 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Transportation Research Procedia 40 (2019) 449–455 www.elsevier.com/locate/procedia
13th International Scientific Conference on Sustainable, Modern and Safe Transport 13th International 2019), Scientific Conference on Sustainable, and Safe Transport (TRANSCOM High Tatras, Novy Smokovec –Modern Grand Hotel Bellevue, (TRANSCOM 2019),Slovak High Tatras, Novy Smokovec – Grand Hotel Bellevue, Republic, May 29-31, 2019 Slovak Republic, May 29-31, 2019
Simulation study of inductive heating of molybdenum sheet suited Simulation of inductive of molybdenum suited for rapid study prototypes of rigidheating components of transportsheet systems for rapid prototypes of rigid components ofb transport systems a Miroslav Pavelek *, Tibor Donic Miroslav Paveleka*, Tibor Donicb
Department of mechatronics and electronics, University of Zilina, Zilina 01026, Slovakia b Research Centreand of University ofUniversity Zilina. Zilina 01026,Zilina Slovakia Department of mechatronics electronics, of Zilina, 01026, Slovakia b Research Centre of University of Zilina. Zilina 01026, Slovakia
a a
Abstract Abstract This paper deals with the development of the simulation model of the inductive heating of molybdenum sheet. The proposed model is created COMSOL main purpose model of proposed is toheating determine the optimal shape This paperindeals with theenvironment. developmentThe of the simulation of the model inductive of molybdenum sheet. of Themagnetic proposedelement model (ferrite) heating system, through the of electromagnetic field is determine enclosed trough molybdenum Nextelement part of is createdofininductive COMSOL environment. The mainwhich purpose proposed model is to the optimal shape ofsheet. magnetic this publication is dedicated to acquisition thermal-frequency characteristic for giventrough shape molybdenum of magnetic element of heating (ferrite) of inductive heating system, throughofwhich the electromagnetic field is enclosed sheet. Next part of system. The result proposedtomodel can beofused for optimizationcharacteristic of heating element shapeshape as well for optimization of heating control this publication is of dedicated acquisition thermal-frequency for given of as magnetic element of algorithm of result inductive heating system based acquired frequencyof characteristic. system. The of proposed model can beon used for optimization heating element shape as well as for optimization of control algorithm of inductive heating system based on acquired frequency characteristic. © 2019 The Authors. Published by Elsevier B.V. © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility the scientific of the 13th International Scientific Conference on Sustainable, © 2019 The Authors. Published byof Elsevier B.V. committee Peer-review under responsibility of the scientific committee of the 13th International Scientific Conference on Sustainable, Modern (TRANSCOM 2019). Peer-review under responsibility of the scientific Modern and and Safe Safe Transport Transport (TRANSCOM 2019).committee of the 13th International Scientific Conference on Sustainable, Modern and Safe Transport (TRANSCOM 2019). Keywords: molybdenum sheet; inductive heating; magnetic field shaping finite element method. Keywords: molybdenum sheet; inductive heating; magnetic field shaping finite element method.
1. Introduction 1. Introduction This article discusses the development of finite element method (FEM) simulation model of the process of inductive This article the development finite simulation element method simulation modelsheet, of the which processwill of inductive heating. Main discusses issue is development of a of precise model(FEM) of thick molybdenum consider heating. Main is development of aitsprecise model modification of thick molybdenum sheet, which will consider possibilities of issue inductive heating within volumesimulation for the required purposes of its geometric shape (e.g. possibilities of inductive heating within its volume for the required modification purposes of its geometric shape (e.g. design of high-performance thermal shells). Molybdenum is one of the few materials suitable for this purpose in a design thermal shells). Molybdenum is one the few materials suitable for this purpose in a view ofof thehigh-performance long-term high-temperature load of the mold. This is a of suitable ability if durable thermal boxes of storage view of the long-term high-temperature load of the mold. This is a suitable ability if durable thermal boxes of storage * Corresponding author. E-mail address:author. [email protected] * Corresponding E-mail address: [email protected] 2352-1465 © 2018 The Authors. Published by Elsevier B.V. Peer-review©under responsibility of the scientific committee 2352-1465 2018 The Authors. Published by Elsevier B.V. of the 13th International Scientific Conference on Sustainable, Moder n and Safe Transport (TRANSCOM 2019). Peer-review under responsibility of the scientific committee of the 13th International Scientific Conference on Sustainable, Moder n and Safe Transport (TRANSCOM 2019). 2352-1465 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 13th International Scientific Conference on Sustainable, Modern and Safe Transport (TRANSCOM 2019). 10.1016/j.trpro.2019.07.065
Miroslav Pavelek et al. / Transportation Research Procedia 40 (2019) 449–455 Pavelek, Donic / Transportation Research Procedia 00 (2019) 000–000
450 2
systems are required. The mold can be exposed to the temperature gradient of up to 100 °C/mm at the maximum temperature of 2150 °C within the longitudinal direction of the container. For the molybdenum shaping, several processes can be used, while all of them are based on the thermal warming and consequent shaping. It is very important, that whole volume of given molybdenum sheet is heated uniformly, therefore individual thermal processes shall be identified by the simulation firstly. In this way it is possible to avoid any damage of the sample by proper set of pre-heating respectively heating/cooling system of Mo sheets. Currently, the molds are made of molybdenum sheet having a thickness of 0,5 mm, made by powder metallurgy technology, i.e. by plastic deformation and sintering procedure. Specifically, the molybdenum sheet Grade M1 corresponding to the American standard ASTM B386 or GB 3877, where the chemical composition is approximately the same. As heating elements, the inductive heater composed of copper coil is considered. All of the mentioned material properties are precisely defined within proposed simulation model [1-3], while the results are discussed. Nomenclature sa sb sc ca cb cpd f fa fb I σ ρ ε μ H B A J D E QPmax
width of molybdenum sheet length of molybdenum sheet thickness of molybdenum sheet dimension of coil’s wire distance between the coil’s input and output wire distance between coil and molybdenum sheet frequency magnetic material height magnetic material thickness coil current electrical conductivity density relative permittivity relative permeability intensity of magnetic field magnetic flux density magnetic vector potential current density electric inductance electric intensity Amplitude of volumetric power losses within molybdenum sheet
2. Simulation model The simulation model is developed in COMSOL environment as a 3D model with the options for reconfiguration the mutual position between the coil and the molybdenum sheet, the coil material, the frequency and the magnetic material geometry. The model is composed of the molybdenum sheet, coil for inductive heating and magnetic material core. The molybdenum sheet is modeled as a block (domain) with a wanted width(a), depth(b) and thickness(c) and the coil is modeled as a square wire with a wanted thickness (ca) (Fig.1.b). The geometry (Fig.1.) is then complemented by physic setup. The physic used in this model is “Magnetic field (MF)”. The only feature of “MF”, that is used is “COIL”, which specifies the coil domain as a single conductor with current input surface and current output surface. All simulations are set as frequency domain simulation, so we can determine the influence of studied parameters on the amplitude of electromagnetic losse within molybdenum sheet. [4,5] The mentioned “MF” module of the COMSOL environment uses following equations for modeling an electromagnetic field in frequency domain (6).
Miroslav Pavelek et al. / Transportation Research Procedia 40 (2019) 449–455 Pavelek, Donic / Transportation Research Procedia 00 (2019) 000–000
451 3
𝛻𝛻 × 𝐻𝐻 = 𝐽𝐽
(1)
𝐽𝐽 = 𝜎𝜎𝜎𝜎 + 𝑗𝑗𝑗𝑗𝑗𝑗 + 𝐽𝐽𝑒𝑒
(3)
(2)
𝐵𝐵 = 𝛻𝛻 × 𝐴𝐴
(4)
𝐸𝐸 = −𝑗𝑗𝑗𝑗𝑗𝑗
Fig. 1. Model of inductive heater composed of the copper coils
The material parameters and other model settings as final conditions settings of domains can be seen in Table 1. Table 1. Model settings material and final conditions Parameter/Domain
Molybdenum sheet
Coil
Magnetic part
Environment
Material
Molybdenum
Copper
Alloy ferrite powder
Air
Electrical conductivity [S/m]
17.9e6
5.5e7
1e-12
1e-15
Density [kg/m^3]
10280
8700
4980
1.2
Relative permittivity [-]
1
1
1
1
Relative permeability [-]
1.00012
1
2500
1
Ampere’s Law
YES
YES
YES
YES
Magnetic insulation
NO
NO
NO
YES
Coil domain
NO
NO
YES
NO
3. Results Simulation results have been performed for the situation of geometry that is described by main parameters within Table 2.
Miroslav Pavelek et al. / Transportation Research Procedia 40 (2019) 449–455 Pavelek, Donic / Transportation Research Procedia 00 (2019) 000–000
452 4
Table 2. Parameters of the geometry of proposed simulation model. Parameter
sa [mm]
sb [mm]
sc [mm]
ca [mm]
cb [mm]
Value
150
220
1
10
25
Parameter
cpd [mm]
fa [mm]
fb [mm]
I [A]
f [kHz]
Value
(1:1:10)
40
(2.5:2.5:10)
150
(10:10:100)
Fig.2 show power loses of model with different settings of coil-MO_Sheet distance with constant frequency of 25 kHz and magnetic material thickness 10 mm. The maximal power losses of 9 mW/mm^3 are achieved with the coil distance of 1 mm from Mo sheet, while with higher value of the distance the power losses within molybdenum sheet are lower. cpd=1 mm; QP max=9 mW/mm^3
cpd=7 mm; QP max=3.4 mW/mm^3
cpd=4 mm; QP max=6 mW/mm^3
cpd=10 mm; QP max=1.9 mW/mm^3
Fig. 2. Simulation results of inductive heating with variable coil distance.
Pavelek, Donic / Transportation Research Procedia 00 (2019) 000–000 Miroslav Pavelek et al. / Transportation Research Procedia 40 (2019) 449–455
fb=2.5 mm; QP max=6.8 mW/mm^3
fb=7.5 mm; QP max=7.3 mW/mm^3
5 453
fb=5.0 mm; QP max=6.9 mW/mm^3
fb=10.0 mm; QP max=7.5 mW/mm^3
Fig. 3. Simulation results of inductive heating with variable thickness of magnetic material.
Fig.3. shows power losses of proposed simulation model with different settings of the thickness of magnetic material with constant frequency of 25 kHz and the distance between coil and molybdenum sheet of 2 mm. As can be seen the difrences betwwen the electromagnetic losses within molybdenum sheet are minimal but the ferrite core need to by designed considering its maximal operational magnetic flux density [7-9].
) Fig. 4. Frequency Dependency of magnetic energy absorbed by molybdenum sheet (cpd=1 mm; fb=10 mm).
Fig. 4 shows results from the parametric simulation, where operating frequency of electromagnetic filed was varied. It is seen, that magnetic losses and thus the heating power are strongly dependent on operating frequency, while they increase as frequency rises. Considering critical parameters of the ferrite core and heating coil, these is the
Miroslav Pavelek et al. / Transportation Research Procedia 40 (2019) 449–455 Pavelek, Donic / Transportation Research Procedia 00 (2019) 000–000
454 6
most important parameter when skin effect, and core saturation shall be avoided. Proposed model also enables to optimize not only the thermal distribution within the sheet volume, but heating element as well [10]. The simulation of the thermal performance of previously describe inductive heating process is shown on fig. 5. For the identification of the temperature distribution the situation is considered, where the current of the coil is 1000 A and the ferrite core has the thickness of 5 mm. Distance between the heating element and molybdenum sheet is 2 mm, and the operating frequency is 25 kHz. The volumetric density (W/mm 3) is expressed after 140 s, while steadystate conditions have been achieved after this time flow. It is seen that the maximum of 0.3 W/mm 3 was reached at the thermal spots, whereby the highest temperature that was achieved was located around this thermal spot (700 C°) and then are evenly distributed around the heating element. The temperature gradient between the border sides of the sheet and highest temperature spot is 350 C°.
Fig. 5. Simulation results – Volumetric loss density [W/mm^3] (left), Temperature distribution [°C] (right) .
4. Conclusion Presented paper is described the process of the development of simulation model of thick molybdenum sheet considering its inductive heating. For that purpose, the detailed description of the geometry of heating element together with its material properties are given. The investigation of the volumetric losses was initially done, due to further investigation of the temperature distribution. Simultaneous investigation is not possible due to complexity of such physical settings. After parametric investigation of volumetric losses in dependency on operating frequency, selected situation was investigated in thermal domain. Presented model shall serve for the optimization of both heating element as well as for the investigation of thermal distribution within the investigated geometry of molybdenum sheet. Future tasks will be related to the experimental verifications of simulation models and consequently optimization tasks will be realized to tune the validity of proposed simulation model. Acknowledgements The authors would like to thank to the national grant agency APVV for project support No. APVV-0396-15 and No. APVV 14-0284 – Study of useful properties of molded molybdenum sheets applicable for horizontal crystallisation of sapphire monocrystals References [1] Karban, P., Mach, F., Dolezel, I., 2012. Hard-couple model of local direct resistance heating of thin sheets. In: Journal of Computational and Applied Mathematics 236(18), 4725-4731, 2012. https://doi.org/10.1016/j.cam.2012.02.036 [2] Koscelnik, J.; Prazenica, M.; Frivaldsky, M.; et al., Design and Simulation of Multi-element Resonant LCTLC Converter with HF Transformer, Conference: ELEKTRO 10th International Conference Location: Rajecke Teplice, SLOVAKIA Date: MAY 19-20, 2014, Pages: 307-311 Published: 2014 [3] Plansee Group, https://www.plansee.com/en/index.html [15.12.2018]
Miroslav Pavelek et al. / Transportation Research Procedia 40 (2019) 449–455 Pavelek, Donic / Transportation Research Procedia 00 (2019) 000–000
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[4] Mori, K., Maki, S., Tanaka, Y., 2005. Warm and Hot Stamping of ultra-high tensile strenght sheets using resistance heating”. In: CIRP Annals-Manufacturing Technology, 54(), 209-212, 2005. [5] Frivaldsky, Michal; Dobrucky, Branislav; Prazenica, Michal; et al.Multi-tank resonant topologies as key design factors for reliability improvement of power converter for power energy applications, ELECTRICAL ENGINEERING, Volume: 97, Issue: 4m Pages: 287302, Published: DEC 2015 [6] Spanik, P.; Cuntala, J.; Frivaldsky, M.; et al. Investigation of Heat Transfer of Electronic System through Utilization of Novel Computation Algorithms, ELEKTRONIKA IR ELEKTROTECHNIKA, Volume: 123, Issue: 7, Pages: 31-36, Published: 2012 [7] Spanik, P.; Dobrucky, B.; Frivaldsky, M.; et al. Measurement of swtitching losses in power transistor structure, ELEKTRONIKA IR ELEKTROTECHNIKA , Issue: 2, Pages: 75-78, Published: 2008 [8] Maki, S., Harada, Y., Mori, K., Makino, H., 2005. Application of resistance heating technique to mushy state forming of aluminium alloy. In: Journal of materials processing technology 125, 477 – 482, 2002. [9] Dughiero, F., Forzan, M., Pozza, C., Sieni, E., 2012. A translational couple electromagnetic and thermal innovative model for induction welding of tubes. In: IEEE Transactions on Magnetics 48(2), 483-486, 2012. https://doi.org/10.1109/TMAG.2011.2174972 [10] Hargas, L., Hrianka, M., Lakatoš, J., Koniar, D., 2012. Heat Fields Modeling and Verification of Electronic Parts of Mechatronics Systems. In: Metalurgija 49(2), 268 – 272, 2012. https://doi.org/10.5755/j01.eee.123.7.2371
ScienceDirect ScienceDirect
Transportation Research Procedia 00 (2019) 000–000 Available online at www.sciencedirect.com Transportation Research Procedia 00 (2019) 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Transportation Research Procedia 40 (2019) 449–455 www.elsevier.com/locate/procedia
13th International Scientific Conference on Sustainable, Modern and Safe Transport 13th International 2019), Scientific Conference on Sustainable, and Safe Transport (TRANSCOM High Tatras, Novy Smokovec –Modern Grand Hotel Bellevue, (TRANSCOM 2019),Slovak High Tatras, Novy Smokovec – Grand Hotel Bellevue, Republic, May 29-31, 2019 Slovak Republic, May 29-31, 2019
Simulation study of inductive heating of molybdenum sheet suited Simulation of inductive of molybdenum suited for rapid study prototypes of rigidheating components of transportsheet systems for rapid prototypes of rigid components ofb transport systems a Miroslav Pavelek *, Tibor Donic Miroslav Paveleka*, Tibor Donicb
Department of mechatronics and electronics, University of Zilina, Zilina 01026, Slovakia b Research Centreand of University ofUniversity Zilina. Zilina 01026,Zilina Slovakia Department of mechatronics electronics, of Zilina, 01026, Slovakia b Research Centre of University of Zilina. Zilina 01026, Slovakia
a a
Abstract Abstract This paper deals with the development of the simulation model of the inductive heating of molybdenum sheet. The proposed model is created COMSOL main purpose model of proposed is toheating determine the optimal shape This paperindeals with theenvironment. developmentThe of the simulation of the model inductive of molybdenum sheet. of Themagnetic proposedelement model (ferrite) heating system, through the of electromagnetic field is determine enclosed trough molybdenum Nextelement part of is createdofininductive COMSOL environment. The mainwhich purpose proposed model is to the optimal shape ofsheet. magnetic this publication is dedicated to acquisition thermal-frequency characteristic for giventrough shape molybdenum of magnetic element of heating (ferrite) of inductive heating system, throughofwhich the electromagnetic field is enclosed sheet. Next part of system. The result proposedtomodel can beofused for optimizationcharacteristic of heating element shapeshape as well for optimization of heating control this publication is of dedicated acquisition thermal-frequency for given of as magnetic element of algorithm of result inductive heating system based acquired frequencyof characteristic. system. The of proposed model can beon used for optimization heating element shape as well as for optimization of control algorithm of inductive heating system based on acquired frequency characteristic. © 2019 The Authors. Published by Elsevier B.V. © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility the scientific of the 13th International Scientific Conference on Sustainable, © 2019 The Authors. Published byof Elsevier B.V. committee Peer-review under responsibility of the scientific committee of the 13th International Scientific Conference on Sustainable, Modern (TRANSCOM 2019). Peer-review under responsibility of the scientific Modern and and Safe Safe Transport Transport (TRANSCOM 2019).committee of the 13th International Scientific Conference on Sustainable, Modern and Safe Transport (TRANSCOM 2019). Keywords: molybdenum sheet; inductive heating; magnetic field shaping finite element method. Keywords: molybdenum sheet; inductive heating; magnetic field shaping finite element method.
1. Introduction 1. Introduction This article discusses the development of finite element method (FEM) simulation model of the process of inductive This article the development finite simulation element method simulation modelsheet, of the which processwill of inductive heating. Main discusses issue is development of a of precise model(FEM) of thick molybdenum consider heating. Main is development of aitsprecise model modification of thick molybdenum sheet, which will consider possibilities of issue inductive heating within volumesimulation for the required purposes of its geometric shape (e.g. possibilities of inductive heating within its volume for the required modification purposes of its geometric shape (e.g. design of high-performance thermal shells). Molybdenum is one of the few materials suitable for this purpose in a design thermal shells). Molybdenum is one the few materials suitable for this purpose in a view ofof thehigh-performance long-term high-temperature load of the mold. This is a of suitable ability if durable thermal boxes of storage view of the long-term high-temperature load of the mold. This is a suitable ability if durable thermal boxes of storage * Corresponding author. E-mail address:author. [email protected] * Corresponding E-mail address: [email protected] 2352-1465 © 2018 The Authors. Published by Elsevier B.V. Peer-review©under responsibility of the scientific committee 2352-1465 2018 The Authors. Published by Elsevier B.V. of the 13th International Scientific Conference on Sustainable, Moder n and Safe Transport (TRANSCOM 2019). Peer-review under responsibility of the scientific committee of the 13th International Scientific Conference on Sustainable, Moder n and Safe Transport (TRANSCOM 2019). 2352-1465 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 13th International Scientific Conference on Sustainable, Modern and Safe Transport (TRANSCOM 2019). 10.1016/j.trpro.2019.07.065
Miroslav Pavelek et al. / Transportation Research Procedia 40 (2019) 449–455 Pavelek, Donic / Transportation Research Procedia 00 (2019) 000–000
450 2
systems are required. The mold can be exposed to the temperature gradient of up to 100 °C/mm at the maximum temperature of 2150 °C within the longitudinal direction of the container. For the molybdenum shaping, several processes can be used, while all of them are based on the thermal warming and consequent shaping. It is very important, that whole volume of given molybdenum sheet is heated uniformly, therefore individual thermal processes shall be identified by the simulation firstly. In this way it is possible to avoid any damage of the sample by proper set of pre-heating respectively heating/cooling system of Mo sheets. Currently, the molds are made of molybdenum sheet having a thickness of 0,5 mm, made by powder metallurgy technology, i.e. by plastic deformation and sintering procedure. Specifically, the molybdenum sheet Grade M1 corresponding to the American standard ASTM B386 or GB 3877, where the chemical composition is approximately the same. As heating elements, the inductive heater composed of copper coil is considered. All of the mentioned material properties are precisely defined within proposed simulation model [1-3], while the results are discussed. Nomenclature sa sb sc ca cb cpd f fa fb I σ ρ ε μ H B A J D E QPmax
width of molybdenum sheet length of molybdenum sheet thickness of molybdenum sheet dimension of coil’s wire distance between the coil’s input and output wire distance between coil and molybdenum sheet frequency magnetic material height magnetic material thickness coil current electrical conductivity density relative permittivity relative permeability intensity of magnetic field magnetic flux density magnetic vector potential current density electric inductance electric intensity Amplitude of volumetric power losses within molybdenum sheet
2. Simulation model The simulation model is developed in COMSOL environment as a 3D model with the options for reconfiguration the mutual position between the coil and the molybdenum sheet, the coil material, the frequency and the magnetic material geometry. The model is composed of the molybdenum sheet, coil for inductive heating and magnetic material core. The molybdenum sheet is modeled as a block (domain) with a wanted width(a), depth(b) and thickness(c) and the coil is modeled as a square wire with a wanted thickness (ca) (Fig.1.b). The geometry (Fig.1.) is then complemented by physic setup. The physic used in this model is “Magnetic field (MF)”. The only feature of “MF”, that is used is “COIL”, which specifies the coil domain as a single conductor with current input surface and current output surface. All simulations are set as frequency domain simulation, so we can determine the influence of studied parameters on the amplitude of electromagnetic losse within molybdenum sheet. [4,5] The mentioned “MF” module of the COMSOL environment uses following equations for modeling an electromagnetic field in frequency domain (6).
Miroslav Pavelek et al. / Transportation Research Procedia 40 (2019) 449–455 Pavelek, Donic / Transportation Research Procedia 00 (2019) 000–000
451 3
𝛻𝛻 × 𝐻𝐻 = 𝐽𝐽
(1)
𝐽𝐽 = 𝜎𝜎𝜎𝜎 + 𝑗𝑗𝑗𝑗𝑗𝑗 + 𝐽𝐽𝑒𝑒
(3)
(2)
𝐵𝐵 = 𝛻𝛻 × 𝐴𝐴
(4)
𝐸𝐸 = −𝑗𝑗𝑗𝑗𝑗𝑗
Fig. 1. Model of inductive heater composed of the copper coils
The material parameters and other model settings as final conditions settings of domains can be seen in Table 1. Table 1. Model settings material and final conditions Parameter/Domain
Molybdenum sheet
Coil
Magnetic part
Environment
Material
Molybdenum
Copper
Alloy ferrite powder
Air
Electrical conductivity [S/m]
17.9e6
5.5e7
1e-12
1e-15
Density [kg/m^3]
10280
8700
4980
1.2
Relative permittivity [-]
1
1
1
1
Relative permeability [-]
1.00012
1
2500
1
Ampere’s Law
YES
YES
YES
YES
Magnetic insulation
NO
NO
NO
YES
Coil domain
NO
NO
YES
NO
3. Results Simulation results have been performed for the situation of geometry that is described by main parameters within Table 2.
Miroslav Pavelek et al. / Transportation Research Procedia 40 (2019) 449–455 Pavelek, Donic / Transportation Research Procedia 00 (2019) 000–000
452 4
Table 2. Parameters of the geometry of proposed simulation model. Parameter
sa [mm]
sb [mm]
sc [mm]
ca [mm]
cb [mm]
Value
150
220
1
10
25
Parameter
cpd [mm]
fa [mm]
fb [mm]
I [A]
f [kHz]
Value
(1:1:10)
40
(2.5:2.5:10)
150
(10:10:100)
Fig.2 show power loses of model with different settings of coil-MO_Sheet distance with constant frequency of 25 kHz and magnetic material thickness 10 mm. The maximal power losses of 9 mW/mm^3 are achieved with the coil distance of 1 mm from Mo sheet, while with higher value of the distance the power losses within molybdenum sheet are lower. cpd=1 mm; QP max=9 mW/mm^3
cpd=7 mm; QP max=3.4 mW/mm^3
cpd=4 mm; QP max=6 mW/mm^3
cpd=10 mm; QP max=1.9 mW/mm^3
Fig. 2. Simulation results of inductive heating with variable coil distance.
Pavelek, Donic / Transportation Research Procedia 00 (2019) 000–000 Miroslav Pavelek et al. / Transportation Research Procedia 40 (2019) 449–455
fb=2.5 mm; QP max=6.8 mW/mm^3
fb=7.5 mm; QP max=7.3 mW/mm^3
5 453
fb=5.0 mm; QP max=6.9 mW/mm^3
fb=10.0 mm; QP max=7.5 mW/mm^3
Fig. 3. Simulation results of inductive heating with variable thickness of magnetic material.
Fig.3. shows power losses of proposed simulation model with different settings of the thickness of magnetic material with constant frequency of 25 kHz and the distance between coil and molybdenum sheet of 2 mm. As can be seen the difrences betwwen the electromagnetic losses within molybdenum sheet are minimal but the ferrite core need to by designed considering its maximal operational magnetic flux density [7-9].
) Fig. 4. Frequency Dependency of magnetic energy absorbed by molybdenum sheet (cpd=1 mm; fb=10 mm).
Fig. 4 shows results from the parametric simulation, where operating frequency of electromagnetic filed was varied. It is seen, that magnetic losses and thus the heating power are strongly dependent on operating frequency, while they increase as frequency rises. Considering critical parameters of the ferrite core and heating coil, these is the
Miroslav Pavelek et al. / Transportation Research Procedia 40 (2019) 449–455 Pavelek, Donic / Transportation Research Procedia 00 (2019) 000–000
454 6
most important parameter when skin effect, and core saturation shall be avoided. Proposed model also enables to optimize not only the thermal distribution within the sheet volume, but heating element as well [10]. The simulation of the thermal performance of previously describe inductive heating process is shown on fig. 5. For the identification of the temperature distribution the situation is considered, where the current of the coil is 1000 A and the ferrite core has the thickness of 5 mm. Distance between the heating element and molybdenum sheet is 2 mm, and the operating frequency is 25 kHz. The volumetric density (W/mm 3) is expressed after 140 s, while steadystate conditions have been achieved after this time flow. It is seen that the maximum of 0.3 W/mm 3 was reached at the thermal spots, whereby the highest temperature that was achieved was located around this thermal spot (700 C°) and then are evenly distributed around the heating element. The temperature gradient between the border sides of the sheet and highest temperature spot is 350 C°.
Fig. 5. Simulation results – Volumetric loss density [W/mm^3] (left), Temperature distribution [°C] (right) .
4. Conclusion Presented paper is described the process of the development of simulation model of thick molybdenum sheet considering its inductive heating. For that purpose, the detailed description of the geometry of heating element together with its material properties are given. The investigation of the volumetric losses was initially done, due to further investigation of the temperature distribution. Simultaneous investigation is not possible due to complexity of such physical settings. After parametric investigation of volumetric losses in dependency on operating frequency, selected situation was investigated in thermal domain. Presented model shall serve for the optimization of both heating element as well as for the investigation of thermal distribution within the investigated geometry of molybdenum sheet. Future tasks will be related to the experimental verifications of simulation models and consequently optimization tasks will be realized to tune the validity of proposed simulation model. Acknowledgements The authors would like to thank to the national grant agency APVV for project support No. APVV-0396-15 and No. APVV 14-0284 – Study of useful properties of molded molybdenum sheets applicable for horizontal crystallisation of sapphire monocrystals References [1] Karban, P., Mach, F., Dolezel, I., 2012. Hard-couple model of local direct resistance heating of thin sheets. In: Journal of Computational and Applied Mathematics 236(18), 4725-4731, 2012. https://doi.org/10.1016/j.cam.2012.02.036 [2] Koscelnik, J.; Prazenica, M.; Frivaldsky, M.; et al., Design and Simulation of Multi-element Resonant LCTLC Converter with HF Transformer, Conference: ELEKTRO 10th International Conference Location: Rajecke Teplice, SLOVAKIA Date: MAY 19-20, 2014, Pages: 307-311 Published: 2014 [3] Plansee Group, https://www.plansee.com/en/index.html [15.12.2018]
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