As part of an industrial project, our team carried out a comprehensive analysis, experimental validation, and mathematical modeling of an induction heating process for steel tubular billets. The aim was to optimize heating modes and improve energy efficiency through a science-based approach.

🔧 Experimental Campaign

We conducted a full-scale experimental study using 270 mm diameter billets made of steel grade 14541. The heating was performed in a horizontal induction furnace consisting of six inductors, each operating in a pulsed mode (PWM) at power levels of up to 80%.

Internal temperature measurements were recorded using type N thermocouples embedded radially in the billet and connected to a Pico Technology TC data logger. The heating process simulated realistic operation with a pushing interval of 70 mm per cycle. Peak electrical current in the inductors reached 2600 A.

The heating regime targeted progressive increase of billet temperature:

• Zone 1–2: 490°C
• Zone 3: 720°C
• Zone 4: 950°C
• Zone 5: 1090°C
• Zone 6: 
• Final Temperature of 1190°C

Temperature distribution across the billet was analyzed at each stage. The maximum radial temperature gradient in early zones reached ~300°C, reducing to under 100°C in later stages. Notably, peak temperatures shifted inward in zones 5–6 due to increased radiative losses from the billet surface.

A holding period of 9 minutes at 10% power was also modeled, followed by a reheating stage after an idle pause — confirming temperature recovery and thermal inertia of the system.

🧠 Development of a Predictive Software Model

To complement the physical tests, we developed a custom simulation tool based on the non-stationary heat conduction equation. This tool was tailored to:

• The geometry of the furnace and billet;
• Variable thermal properties of steel 14541;
• Skin effect and depth-dependent heat generation;
• Control logic of each inductor using adjustable PWM cycles;
• Dynamic adjustment of power based on surface pyrometer feedback.

The model calculated the temperature profile of the billet as it moved through the furnace, predicting not only surface temperatures but also internal thermal gradients. A key feature of the model is synchronized operation of the first two inductors based on real-time sensor input, ensuring precision from the initial heating stage.

📊 Validation & Technological Implementation

The software model was validated against experimental data, with excellent agreement across all temperature zones. We confirmed compliance with thermal and material balance, and used this validated tool to generate optimized heating mode maps.

These maps are now ready for industrial implementation, enabling:

• Energy-efficient heating;
• Improved temperature uniformity;
• Reduced risk of overheating or surface degradation;
• Better metallurgical consistency at the final rolling or forming stage.

This project reflects our full-cycle expertise — from physical testing and data acquisition to algorithm design and deployment-ready software. Our team successfully bridged experimental and numerical approaches, delivering a high-fidelity, physics-based digital tool tailored to real-world production needs.