Approximate analytical solution for induction heating of solid cylinders

Jankowski, Todd A.; Pawley, Norma H.; Gonzales, Lindsey M.; Ross, Craig A.; Jurney, James D.

doi:10.1016/j.apm.2015.10.006

Cited by 50 publications

(22 citation statements)

References 14 publications

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“…For the induction heating, a model considering the effect of the initial temperature and the effect of the power/energy in the working volume was considered A simplified temperature calculation can be performed based on the determined Nagaoka coefficient. As a function of time, the unified cross-sectional temperature can be calculated according to the following formula [33]:…”

Section: Induction-heating System Optimizationmentioning

confidence: 99%

A CPS-Based Simulation Platform for Long Production Factories

Iannino

Colla

Denker³

et al. 2019

Metals

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Production technology in European steel industry has reached such a level, that significant improvements can only be reached by through process optimization strategies instead of separately improving each process step. Therefore, the connection of suitable technological models to describe process and product behavior, methods to find solutions for typical multi-criterial decisions, and a strong communication between involved plants is necessary. In this work, a virtual simulation platform for the design of cyber-physical production optimization systems for long production facilities focusing on thermal evolution and related material quality is presented. Models for describing physical processes, computers, software and networks as well as methods and algorithms for through process optimization were implemented and merged into a new and comprehensive model-based software architecture. Object-oriented languages are addressed and used because they provide modularity, a high-level of abstraction and constructs that allow direct implementation and usage of the cyber-physical production systems concepts. Simulation results show how the proper connection between models, communication, and optimization methods allows feasibility, safety and benefits of cyber-physical production systems to be established. Furthermore, the software architecture is flexible and general and thus, can be transferred to any steel production line as well as outside the steel industry.

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Section: Induction-heating System Optimizationmentioning

confidence: 99%

A CPS-Based Simulation Platform for Long Production Factories

Iannino

Colla

Denker³

et al. 2019

Metals

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“…For an ideal solenoid, the magnetic field is H0=NI/L′ where N is the winding number. The value of the magnetic field for a short cylinder is corrected by the so-called modified Nagaoka coefficient Kn [5,6]. The correction coefficient Kn for a finite-length coil is expressed as Kn=trueK¯n1−D2d2+D2d2newlinetrueK¯n=1+1.536β2+0.274β41+1.036β2−8β3π where K¯n is the Nagaoka coefficient and β=d2L′.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…A mathematical model of the coupled electromagnetic-thermal problem is then calibrated with experiments to extract the temperature dependent model parameter α. The parameter α corrects the so-called modified Nagaoka coefficient which has mainly been assumed constant in the literature [5,6]. In principle, this parameter is temperature dependent and it changes during the heating process.…”

Section: Introductionmentioning

confidence: 99%

Inverse Model for the Control of Induction Heat Treatments

et al. 2019

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In this work, we present and test an approach based on an inverse model applicable to the control of induction heat treatments. The inverse model is comprised of a simplified analytical forward model trained with experiments to predict and control the temperature of a location in a cylindrical sample starting from any initial temperature. We solve the coupled nonlinear electromagnetic-thermal problem, which contains a temperature dependent parameter α to correct the electromagnetic field on the surface of a cylinder, and as a result effectively the modeled temperature elsewhere in the sample. A calibrated model to the measurement data applied with the process information such as the operating power level, current, frequency, and temperature provides the basic ingredients to construct an inverse model toolbox, which finally enables us to conduct experiments with more specific goals. The input set values of the power supply, i.e., the power levels in the test rig control system, are determined within an iterative framework to reach specific target temperatures in prescribed times. We verify the concept on an induction heating test rig and provide two examples to illustrate the approach. The advantages of the method lie in its simplicity, computationally cost effectiveness and independence of a prior knowledge of the internal structure of power supplies.

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“…However, the coil required for the planar induction heating is significantly different from the traditional spiral coils, in which the magnetic field distribution is difficult to effectively concentrated, the air impedance of the system loop is too large and the heating temperature is not uniform and difficult to control accurately [5][6][7]. The efficiency of the planar induction heating extensively depends on the effective conversion of the electromagnetic field of the coil and the reasonable matching of the In recent years, in order to apply the induction heating process more effectively, many scholars have conducted more research on induction heating [11][12][13][14][15][16][17][18][19], including numerical modeling of induction heating process and electromagnetic field conversion mechanism analysis. Numerical approaches are adopted in the power distribution and temperature prediction during induction heating process [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

“…Jankowski T.A. [18] presents a multiple-scale perturbation method to solve the multi-physics mathematical model of induction heating process in a cylindrical coil. Streblau M. [19] uses a multi-physics mathematical model to analysis the electromagnetic and thermal fields in axial symmetric inductor system.…”

Section: Introductionmentioning

confidence: 99%

Analytical Modeling of the Temperature Using Uniform Moving Heat Source in Planar Induction Heating Process

Ning

Liang

2019

Applied Sciences

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The planar induction heating possesses more difficulties in industry application compared with traditional spiral induction coils in mostly heat treatment processes. Numerical approaches are adopted in the power distribution and temperature prediction during the induction heating process, which has a relatively low computational efficiency. In this work, an analytical calculation model of the planar induction heating with magnetic flux concentrator is investigated based on the uniform moving heating source. In this model, the power density in the surface of the workpiece induced by coils is calculated and applied into the analytical model of the temperature calculation using a uniform moving heat source. Planar induction heating tests are conducted under various induction coil parameters and the corresponding temperature evolution is obtained by the infrared imaging device NEC R300W2-NNU and the thermocouples. The final surface temperature prediction is compared to the finite element simulation results and experimental data. The analytical results show a good match with the finite element simulation and the experimental results, and the errors are in reasonable range and acceptable. The analytical model can compute the temperature distribution directly and the computational time is much less than the finite element method. Therefore, the temperature prediction method in this work has the advantage of less experimental and computational complexity, which can extend the analytical modeling methodology in induction heating to a broader application.

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Approximate analytical solution for induction heating of solid cylinders

Cited by 50 publications

References 14 publications

A CPS-Based Simulation Platform for Long Production Factories

A CPS-Based Simulation Platform for Long Production Factories

Inverse Model for the Control of Induction Heat Treatments

Analytical Modeling of the Temperature Using Uniform Moving Heat Source in Planar Induction Heating Process

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