A Study on the 2-D Temperature Distribution of the Strip due to Induction Heater

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1 , pp A Study on the 2-D Temperature Distribution of the Strip due to Induction Heater Jong-Hyun Lee 1, Jin-Taek Kim 1, Sung-Hyuk Lim 2, Do-Gyun Jung 2, Hyeong-Jin Kim 2, Byung-Joon Baek 1* 1 School of Mechanical System Engineering, Chonbuk National University, Jeonju, , Korea 2 Technical Research Center, Hyundai Steel Company, Dangjin, Chunnam, , Korea. Abstract. Lowering the temperature drop of the hot strip in hot rolling process results in the increased rolling load and qulaity deterioration. The induction heating is the competitive way to heat the cooled bar. In this study, a twodimensional thermal analysis has been performed to predict the temperature distribution along the width direction passing through the induction heater. In addition, correction coefficient for the amount of the cooling, Setting Power efficiency of the Induction Heater and heating efficiency is proposed to improve the prediction value. Keywords: Reheating facility, Roughing mill, Finishing mill, Induction heater 1 Introduction Hot rolling process consists of heating the bar for a suitable material for deformation temperature in the reheating furnace, forming some standard bar in Roughing mill, Finishing mill, cooling in run out table (ROT) process and down coiling. The hot strip passing through the Roughing mill and Finishing mill cooled down due to the heat transfer to the cold environment. Lowering the bar temperature results in the increased rolling load and a twist or wave occurs in the strip. Therefore, extra heating is needed to compensate the heat loss. The induction heating is the competitive way to heat the cooled bar. Rudnev [1,2] reported a comprehensive study of induction heating prior to hot working. A few case studies are also provided to illustrate the capabilities of numerical simulation. The ability to model the induction heating process is very important to control and to optimize the processing parameter. The mechanism of the energy transformation in induction heating with magnetic flux concentrator is carried out in [3]. In this study, a two-dimensional thermal analysis has been performed to predict the temperature distribution along the width direction passing through the induction heater. In addition, correction coefficient for the amount of the cooling, Setting Power efficiency of the Induction Heater and heating efficiency is proposed to improve the prediction value. ISSN: ASTL Copyright 2015 SERSC

2 2 Induction Heater Model Fig. 1 shows the process of rolling equipment from Roughing mill to Finishing mill with bar heater and edge to increase the bar temperature. The bar is heated by induction heating and cooled down passing through the area exposed to air by convection and radiation heat transfer. Fig. 1 Diagram of hot rolling process 3 Governing Equation A two-dimensional heat transfer model is used to approximately predict the temperature of the bar. The two-dimensional heat transfer model consists of the following equations by selecting the width of the x-coordinate direction of the material, the thickness direction in the y-direction. 2 T + 2 T + q = 1 T x 2 y 2 k t (1) Here q represents a heat generation rate of the bar. Heat generation rate is applied to hot bar by the induction heater. The equation is expressed in equation (2) by using the induced current equation, the efficiency of the induction heater, input power, size and depth of penetration depth of material.[4,5] q (x) = f(q, σ, H, w) J(x) 2 = 2x H 2(x H) Q e δ 2e δ +e δ H w v t H 2H IH δ 2H e δ δ e δ (2) 4 Results and Discussion Fig. 2 illustrates the comparison of the results of present study and that of literature [6]. One-dimensional temperature distribution in the thickness direction is analyzed in this case. The temperature difference between present result and that of literature shows is 3 o C at surface, 1 o C at 1/4 point of the thickness and is 1 o C at center of the bar cross section. It was found that the maximum deviation is within 3% error. This temperature difference can be occurred because of differences in physical properties that is not same with the value used in the reference paper. 2 Copyright 2015 SERSC

3 Fig. 3 shows the results obtained by using the commercial software of STAR-CCM+ to validate our code developed using MATLAB. It can be seen that the temperature rises significantly at the surface by the effect of induction heating and penetrates into the depth of the thickness of the bar. It is found out that this temperature distribution is agrees fairly well with MATLAB code and experimental results, which validates the methodology that is adopted in this study. Fig.2 Comparison of temperature distribution.. Fig.3 Temperature from STAR-CCM+. Two dimensional MATLAB code was developed based on the algorithm tested by previous 1-D code. Fig. 4 shows the temperature distribution across the width direction of the cold bar. The bar at temperature of 22 o C enters the bar heater and heated to the target temperature through the heater. The temperature increases from center to the surface due to the effect of skin depth of the induction current. It is noted that the temperature keeps nearly uniform across the width direction, while significant drops near the edge area. It represents the need of extra heating by edge heater of the hot mill process. It was also compared with experimental data measured by CA type thermocouples at several locations of the stainless steel. Table 1 shows the quantitative comparison of simulated temperature and measured temperature. The temperature rise by induction heating is 32 o C and maximum temperature difference occurs at surface of the bar with 2.8 % deviation. Fig. 5 shows the thermal image of the hot strip taken by the IR camera (FLIR SC2500, FLIR). The thermo-graphic data are analyzed using the software FLIR Altair. The image illustrates the surface temperature of the hot strip moving through the actual hot rolling process. Temperature to be increases is T =20 o C. The inlet temperature of the hot bar entering bar heater increases from 1150 o C to 1170 o C at the exit of the bar heater. Table 1. Comparison with measured temperature. Surface P=8 1/4 P=16 1/2 P=24 Cold bar test ( o C) Temperature calculated ( o C) Temperature difference ( o C) Copyright 2015 SERSC 3

4 Fig.4. Temperature distribution with measured temperature. Fig. 5 Temperature rising 20 o C on the head. Fig. 6 shows the surface temperature distribution of hot strip heated by 2 bar heaters. The temperature increases uniformly) across the width direction with setting temperature value ( T = 40 o C, T = 20 o C) while passing through the 2 heaters. However, temperature drop near edge area cannot be avoided due to the cooling of the side surface. This edge effect occurs at 13% length of the width. It was also compared with experimental data measured by IR camera. It represents fairly good agreement between numerical and experimental results BH1(Inlet BH2(Outlet) IR(Outlet) IR(OutletLeft) BH1(Inlet BH2(Outlet) IR(Outlet) IR(OutletLeft) (a) T = 40 o C (b) T = 0 o C Fig. 6 Temperature distribution of hot strip across the width direction. 4 Copyright 2015 SERSC

5 5 Conclusion Numerical simulation has been performed to investigate the temperature distribution of the bar in hot mill process. The domain of hot mill process from Roughing mill to Finishing mill is transformed to time dependent problem passing through the position of the bar. The temperature was modified using the experimental data to improve the accuracy of the predicted value. The skin depth of the bar is predicted to investigate induction current affected area. A significant decrease in temperature is found from the surface to center of the bar.. Heating efficiency of the real model in the width direction were predicted by applying internal heat generation distribution about the Cold bar test, and Cold bar test for temperature rise amounts were calculated by back calculation method then, heating rate of surface in the width direction was calculated and verified. The temperature increases uniformly across the width direction with setting temperature value while passing through the heaters. However, temperature drop near edge area cannot be avoided due to the cooling of the side surface. This edge effect occurs at 13% length of the width. Acknowledgments. The authors like to express their sincere gratitude to HYUNDAI STEEL COMPANY for their financial support, thank the Rolling Technology Development Team for their helpful mill data and discussion. References 1. D.U. Furrer and S.L Semiatin : Simulation of Induction Heating Prior to Hot Working and Coating, ASM Handbook, Volume 22B, Metals Process Simulation. (2010) 2. Rudnev, V. I., Loveless, D., Schweigert, K., Dickson, P., and Rugg, M., : Efficiency and Temperature Considerations in Induction Re-Heating of Bar, Rod and Slab, Industrial Heating, pp (2000) 3. Feng Li, Xue Kun Li, Tian Xing Zhu, Qian Zhe Zhao, Yi Ming Kevin Rong : Modeling and Simulation of Induction Heating with Magnetic Flux Concentrator, Applied Mechanics and Materials, pp , 983 (2012) 4. K.F. Wang, S. Chandrasekar, and H.T.Y. Yang : Finite-Element Simulation of Moving Induction Heat Treatment, Journal of Materials Engineering and Performance, Volume 4, Issue 4, pp.460~473 (1995) 5. Martin Fisk : Simulation of Induction Heating in Manufacturing, Licentiate thesis (2008:42) 6. Kim, H. J. : A Numerical Study on Temperature Profiles of Steel Plates Heated by Induction Heater, KSME 2003 Conference, pp.1412~1416 (2003) Copyright 2015 SERSC 5