Optimal Shape Design of Inductor Coils for Surface Hardening

A shape optimization problem is considered related to the design of induction hardening facilities. The mathematical model consists of a vector potential formulation for Maxwell's equations coupled with the energy balance and an ODE to describe the solid-solid phase transition in steel during heating. Depending on the shape of the coil we control the volume fraction of the high temperature phase. The coil is modeled as a tube and is defined by a unit-speed curve. The shape optimiza- tion problem is formulated over the set of admissible curves. The existence of an optimal control is proved. To obtain the form of the shape gradient of the cost functional, the material derivative method is applied. Finally, the first order necessary optimality conditions are estabished for an optimal tube

Optimal Shape Design of Inductor Coils for Surface Hardening

A shape optimization problem is considered related to the design of induction hardening facilities. The mathematical model consists of a vector potential formulation for Maxwell's equations coupled with the energy balance and an ODE to describe the solid-solid phase transition in steel during heating. Depending on the shape of the coil we control the volume fraction of the high temperature phase. The coil is modeled as a tube and is defined by a unit-speed curve. The shape optimiza- tion problem is formulated over the set of admissible curves. The existence of an optimal control is proved. To obtain the form of the shape gradient of the cost functional, the material derivative method is applied. Finally, the first order necessary optimality conditions are estabished for an optimal tube

Numerical Analysis of Inhomogeneous Inductive Heating of Forging Parts

In this research work has been investigated the topic of the inhomogeneous induction heating. The idea is to realize an heating process which allows to heat a billet of steel in different zones at different temperatures. Comparing the traditional induction heating method and the inhomogeneous induction heating it comes that the second one allows to save 5.6% of the energ

Thermo-mechanical problems in induction heating of steel

We discuss a 3D model that is capable for describing mechanical deformations of steel through induction hardening processes. It consists of a reduced system of Maxwell's equations, the heat transfer equation and a system of equations describing the mechanical state of the steel workpiece. In a first step the model is applied to simulation of an axisymmetrical induction hardening device, which is a wide-spread industrial equipment. We present numerical results obtained for a steel tube hardening

Analysis and simulations of multifrequency induction hardening

We study a model for induction hardening of steel. The related differential system consists of a time domain vector potential formulation of the Maxwell's equations coupled with an internal energy balance and an ODE for the volume fraction of {\sl austenite}, the high temperature phase in steel. We first solve the initial boundary value problem associated by means of a Schauder fixed point argument coupled with suitable a-priori estimates and regularity results. Moreover, we prove a stability estimate entailing, in particular, uniqueness of solutions for our Cauchy problem. We conclude with some finite element simulations for the coupled system

Sensitivity analysis of an eddy current problem related to induction heating

We study a mathematical model for the inductive heating of steel.It consists of a vector potential formulation of Maxwells equations coupled with a heat equation and an evolution equation for the volume fraction of high temperature phase in steel. An important task for practical applications of induction heating it to find the optimal coupling distance between inductor and workpiece. To this end, we employ the speed method to investigate the sensitivity of solutions to the state equations with respect to perturbations of the inductor coil. We show the existence of strong material derivatives for the state variables and apply the structure theorem to characterize the Eulerian derivative of the cost functional

Modélisation et simulation d'une plaque en acier 4340 chauffée par induction utilisant un modèle de simulation par éléments finis : prédiction et optimisation numérique /

RÉSUMÉ : Le traitement thermique par induction est une technologie importante dans l'industrie manufacturière. Avec sa vaste gamme d'applications allant du chauffage à la fusion, du brasage au soudage et du scellement des bouchons au collage, c'est souvent la clé pour ajouter de la valeur à un processus particulier dans l'industrie. Ceci est réalisé par le fait que le chauffage par induction fournit un taux de chauffage plus élevé que tout autre procédé de chauffage commercial disponible. En raison du chauffage rapide et de la bonne reproductibilité, il est couramment utilisé pour chauffer des matériaux conducteurs à la température exacte. La capacité de génération de chaleur en profondeur en combinaison avec une intensité de chaleur élevée rapidement et dans des régions bien définies sur la pièce est une caractéristique très attrayante de cette technologie conduisant à un temps de cycle de processus réduit avec une qualité reproductible. Néanmoins, beaucoup reste à faire pour construire le meilleur profil de température possible, c’est pour cela qu’il est nécessaire de caractériser et de contrôler l’effet des paramètres de contrôle du procédé. L’objectif de cette étude consiste alors à l’étude des paramètres géométrique, électromagnétique et mécanique intervenant en chauffage par induction, destinée à une géométrie tridimensionnelle à l’acier 4340 avec inducteur asymétrique. Pour bien mener cette étude, le projet est structuré en trois grandes parties combinant la simulation, la planification d’expérience, l’analyse statistique et l’optimisation pour la création d’un modèle prédictif du profil de température. À partir des équations de Maxwell pour l’électromagnétisme et les équations de transfert de chaleur, les phénomènes physiques ont été modélisés en éclairant les lois du comportement mécanique des matériaux et en établissant la densité de courant externe. Le problème a été entamé par la méthode des éléments finis avec un modèle en 3D et réalisé dans le logiciel COMSOL. Plusieurs simulations, et des mesures de profil de température ont été effectués pour chaque partie du modèle et permettent de confirmer avec succès les hypothèses du modèle et de vérifier la qualité des résultats de la simulation. Les conclusions de ce travail ont pointé l’aspect rentable des techniques utilisées et ont donné accès à l’industrie pour des recettes simples et fiables consacrées à la conception des profils de température uniformes et plus optimisés et qui rendent possible la production des composantes mécaniques de haute performance. -- Mot(s) clé(s) en français : Traitement thermique par induction, Acier 4340, Plaque, Simulation, Profil de température, Taguchi, ANOVA, Prédiction. -- ABSTRACT : Induction heat treatment is an important technology in the manufacturing industry. With its wide range of applications ranging from heating to fusion, brazing to welding, and cap sealing to gluing, this is often the key to adding value to a particular process in industry. This is achieved by the fact that induction heating provides a higher heating rate than any other commercial heating method available. Due to the rapid heating and good reproducibility, it is commonly used to heat conductive materials to the exact temperature. The ability to generate heat at depth in combination with high heat intensity quickly and in well-defined regions on the part is a very attractive feature of this technology leading to reduced process cycle time with reproducible quality. However, much remains to be done to build the best possible temperature profile, which is why it is necessary to characterize and monitor the effect of the process control parameters. The objective of this study is then to study the geometric, electromagnetic and mechanical parameters involved in induction heating, intended for a three-dimensional geometry in 4340 steel with asymmetric inductor. To properly conduct this study, the project is structured in three main parts combining simulation, experiment planning, statistical analysis and optimization to create a predictive model of the temperature profile. From Maxwell's equations for electromagnetism and heat transfer equations, physical phenomena have been modeled by illuminating the laws of mechanical behavior of materials and by establishing the external current density. The problem was started by the finite element method with a model in 3D and carried out in the software COMSOL. Several simulations, and temperature profile measurements were performed for each part of the model and allow to successfully confirm the model assumptions and to check the quality of the simulation results. The conclusions of this work pointed out the cost-effective aspect of the techniques used and gave access to the industry for simple and reliable recipes devoted to the design of uniform and more optimized temperature profiles and which make possible the production of mechanical components of high performance. -- Mot(s) clé(s) en anglais : Induction heat treatment, 4340 steel, Plate, Simulation, Temperature profile, Taguchi, ANOVA, Prediction

Recent scientific research on electrothermal metallurgical processes

A wide range of industrial metallurgical heating and melting processes are carried out using electrothermal technologies. The application of electrothermal processes offers many advantages from technological, ecological and economical point of view. Although the technology level of the electro heating and melting installations and processes used in the industry today is very high, there are still potentials for improvement and optimization due to the increasing complexity of the applications and the strong requirements regarding the performance and quality of the products but also regarding the reduction of time and costs for the development of new processes and technologies. In this paper recent applications and future development trends for efficient heating and melting by electrothermal technologies in metallurgical processes are described along selected examples like induction heating for forging or rolling of billets, heat treatment of strips and plates, press-hardening processes, induction surface hardening of complex geometries, induction welding as well as induction melting processes

Induction heating converter's design, control and modeling applied to continuous wire heating

Induction heating is a heating method for electrically conductive materials that takes advantage of the heat generated by the Eddy currents originated by means of a varying magnetic field. Since Michael Faraday discovered electromagnetic induction in 1831, this phenomena has been widely studied in many applications like transformers, motors or generators' design. At the turn of the 20th century, induction started to be studied as a heating method, leading to the construction of the first industrial induction melting equipment by the Electric Furnace Company in 1927. At first, the varying magnetic fields were obtained with spark-gap generators, vacuum-tube generators and low frequency motor-generator sets. With the emergence of reliable semiconductors in the late 1960's, motor-generators were replaced by solid-state converters for low frequency applications. With regard to the characterization of the inductor-workpiece system, the first models used to understand the load's behavior were based on analytical methods. These methods were useful to analyze the overall behavior of the load, but they were not accurate enough for a precise analysis and were limited to simple geometries. With the emergence of computers, numerical methods experienced a tremendous growth in the 1990's and started to be applied in the induction heating field. Nowadays, the development of commercial softwares that allow this type of analysis have started to make the use of numerical methods popular among research centers and enterprises. This type of softwares allow a great variety of complex analysis with high precision, consequently diminishing the trial and error process. The research realized in last decades, the increase in the utilization of numerical modeling and the appearance and improvement of semiconductor devices, with their corresponding cost reduction, have caused the spread of induction heating in many fields. Induction heating equipments can be found in many applications, since domestic cookers to high-power aluminum melting furnaces or automotive sealing equipments, and are becoming more and more popular thanks to their easy control, quick heating and the energy savings obtained. The present thesis focuses on the application of induction heating to wire heating. The wire heating is a continuous heating method in which the wire is continuously feeding the heating inductor. This heating method allows high production rates with reduced space requirements and is usually found in medium to high power industrial processes working 24 hours per day. The first chapters of this study introduce the induction heating phenomena, its modeling and the converters and tanks used. Afterwards, a multichannel converter for high-power and high-frequency applications is designed and implemented with the aim of providing modularity to the converter and reduce the designing time, the production cost and its maintenance. Moreover, this type of structure provides reliability to the system and enables low repairing times, which is an extremely interesting feature for 24 hours processes. Additionally, a software phase-locked loop for induction heating applications is designed and implemented to prove its flexibility and reliability. This type of control allows the use of the same hardware for different applications, which is attractive for the case of industrial applications. This phase-locked loop is afterwards used to design and implement a load-adaptative control that varies the references to have soft-switching according to load's variation, improving converter's performance. Finally, the modeling of a continuous induction wire hardening system is realized, solving the difficulty of considering the mutual influence between the thermal, electromagnetic and electric parameters. In this thesis, a continuous process is modeled and tested using numerical methods and considering converter's operation and influence in the process.Postprint (published version