Prediction of temperature of hot strip in finishing mill

Transcription

1 , pp Prediction of temperature of hot strip in finishing mill Jong-Hyeon Lee 1, Jeong-Seok Kang 1, Jin-Taek Kim, Byung-Joon Baek 1* 1 School of Mechanical System Engineering, Automobile Hi-Technology Research Center, Chonbuk National University, JeonJu, , Korea Sung-Hyuk Lim 2, Jun-Seok Lim 2, Hyeong-Jin Kim 2 2 Technical Research Center, Hyundai Steel Company Dangjin, Chungnam, , Korea Abstract. This study focuses on predicting the temperature distribution of strip ranging from FET to FDT of an actual finishing mill process. Heat transfer phenomena generated in strip were modeled using a finite difference method. A simulator to predict the temperature distribution of strip was created in consideration of different heat transfer phenomena such as plastic heating, frictional heating and contact heat transfer generated in a finishing mill process. Keywords: Finishing mill, Water jet spray, Work roll, Steel strip 1 Introduction Unstable temperature distribution and wrong temperature prediction of strip in the hot strip finishing mill process causes facilities many problems such as deterioration of material quality due to wave and twist, reduction in roll lifespan and allocation of rolling load. Thus, it is necessary to accurately predict the temperature of strip in a finishing mill process. Based on finite elements method, C.G.SUN et al predicted the change in the temperature inside strip generated in a finishing mill process. This method proved effective for predicting the change in bar temperature generated by an edge heater [1]. Daniel Weisz-Patrault et al studied the effects of work roll on the temperature of strip through the observation of heat transfer due to contacts between work roll and strip in a finishing mill process [2]. Stuart W. Churchill et al could assess temperature rise and heat transfer phenomena under certain wall temperature based on a formula established through Rayleigh number test and laminar boundary layer theory [3]. Madakasira Prabhakar Phaniraj et al used semi-empirical method for recrystallization and particle growth, conducted a simulation using common programs, and explained the deformation and load of strip and the changes in the diameter and temperature of rolling during a finishing mill process [4]. To improve finite elements method which too much time and expense is required to apply to an actual production process, J. H. Lee et al configured On-Line model to ensure the accuracy of calculation and to reduce the time of interpretation using least square method and dimensional analysis [5]. ISSN: ASTL Copyright 2016 SERSC

2 A model to predict the temperature in a hot strip finishing mill process was developed in this study. This model is expected to increase the effects of facilities such as the prevention of quality deterioration due to the wave and twist of materials along with the allocation of rolling loads. 2 Analysis model Figure 1 shows the overall layout of a finishing mill process. Fig. 1. Layout of Finishing mill process 3 Differential equation analysis and Boundary Conditions Based on the governing equation of heat transfer in Equation (1), a simulation was created using Forward-Time Central-Space (hereinafter referred to as FTCS) method among finite difference methods. ρc p T t = k 2 T 2 x + q (x) (1) k T x (± H 2 ) = h side [T (± H 2 ) T sur] + εσ [T 4 (± H 2 ) T sur 4 ] (2) There occur conduction, convection cooling, radiative cooling and water cooling in free areas. As the surface temperature of strip is high with approximately 1000, the cooling effect of natural convection, forced convection and emissivity is great. Convection cooling and radiative cooling are calculated according to Equation (2), while water cooling is calculated based on the area and amount of water-injection, spray cooling coefficient and water temperature. 50 Copyright 2016 SERSC

3 Heat transfer phenomena such as conduction, plastic heating, frictional heating and contact heat transfer occur in a rolling area, and are calculated according to q (x) in Equation (1). 4 Results and Discussion The effects of the conditions of water spray injection on FDT were observed. Figure 2.a. shows the results of calculating the conditions of water spray injection. The temperature in the center during the calculation process rose 7 times. Temperature rise was largely caused by internal plastic heating. It is found that the rolling is caused by work roll at the related locations. Temperature changes rapidly because of frictional heating and contact heat transfer at the top and bottom of a rolling area. In the calculation process before the first rolling area, temperature changes rapidly three times at the top and the bottom, which is surface cooling by FSB spray. A large degree of surface cooling after the first rolling is caused by 2. After the second rolling, spray is applied to only the surface of the top, and so, the temperature at the top only changes rapidly. During the overall rolling process, the top is slightly cooled a few times by spray with a small amount of water injection. Figure 2.b. shows the contour of internal temperature distribution change of strip assessed on one dimension in a thickness direction during a finishing mill process. Nodes are distributed in the range from Number 0, which refers to the top surface, to Number 5, which refers to the bottom surface. Figure 2.b. shows the results represented according to the numbers of calculated nodes without considering the change in thickness. Table 1. Water jet spray flow rate of Simulation case FSB 1 FSB 2 FSB Flow rate 100% 100% 100% 100% 80% 80% 70% 60% 60% Fig. 2. a. Temperature change of strip in Simulation case Copyright 2016 SERSC 51

4 Fig. 2.b. Temperature distribution of strip in Simulation case An analysis was conducted on the results of calculating 12,000 sets of operation data. A learning factor was excluded from calculation conditions. A learning factor was to give feedback on temperature error on the delivery side of finishing mill, which was calculated through on-line model. A learning factor is a constant to compensate for temperature error to occur in calculating the temperature of the following material. According to the calculation results shown in Figure 3, the average error rate of FDT is 0.29% and standard deviation thereof is The reason of this relatively large standard deviation is that error rate is classified into two ranges of -6.5 to 0% and 0.5 to 8% and data is distributed in them. Error rate is calculated according to Equation (3). Error rate(%) = Measured FDT Calculated FDT Measured FDT 100 (3) Fig. 3. Normal distribution on error factor ratio of calculated FDT and measured FDT 52 Copyright 2016 SERSC

5 Fig. 4. Normal distribution on error factor ratio of measured FDT and calculated FDT by learning factor Figure 4 shows the result of calculation where a learning factor is applied under the condition of steel grade shown in Figure 3. According to the calculation result, average error rate of FDT is -0.11% and standard deviation is , which shows that data density is very high. There is a difference between Figure 3 and Figure 4 only in whether or not a learning factor is applied. It is found that, to make an accurate calculation without applying a learning factor, there is a need to modify certain variables in Equations. 5 Conclusion A simulator was developed to predict the temperature behavior of strip during a finishing mill process by analyzing a cooling model considering plastic heating, frictional heating, contact heat transfer and water jet through this study. Explicit method, which is among finite difference methods, was used to predict the temperature behavior of strip. The accuracy of calculation was improved and the time of calculation was reduced through the differentiation of the distance between calculated nodes. A simulator was created using GUI of Matlab. As the result of calculating 12,000 steel grades using a created simulator, it was found that the variables of calculation formulas should be improved to fully meet FDT without applying a learning factor. References 1. Sun, C. G., Park, H.D., Hwang, S.M.: Prediction of Three Dimensional Strip Temperatures through the Entire Finishing Mill in Hot Strip Rolling by Finite Element Method, ISIJ International, Vol.42, page 629~635 (2002) 2. Weisz-Patrault, D., Ehrlacher, A., Legrand, N., Labbe, N., Horsky, J., Luks, T., Analysis of roll gap heat transfers in hot steel strip rolling through roll temperature sensors and heat transfer models, Key Engineering Materials, , pp (2012) Copyright 2016 SERSC 53

6 3. Churchill, S. W., Chu, H. H.S.: Correlating equations for laminar and turbulent free convection from a vertical plate, International Journal of Heat and Mass Transfer, Vol.18, Issue.11, page 1323~1329 (1975) 4. Phaniraj, M.P., Behera, B.B., Lahiri, A.K.: Thermo-mechanical modeling of two phase rolling and microstructure evolution in the hot strip mill Part 1. Prediction of rolling loads and finish rolling temperature, Journal of Materials Processing Technology 170, page 323~335 (2005) 5. Lee, J.H., Choi, L.W., Kwak, W.J., Hwang, S. M.: The development and application of online model for the prediction of strip temperature in hot strip rolling, The 5th Rolling Symposium, page 336~345 (2004) 6. Kim, H. J.: Predictions of Strip Temperatures for Finishing Mill of Gwangyang Hot Rolling Line #3, The 5th Rolling Symposium, page 349~358 (2004) 54 Copyright 2016 SERSC