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Estimation of Camber Generation in Rough Rolling Process
16th IFAC Symposium on Automation in Mining, Mineral and Metal Processing August 25-28, 2013. San Diego, California, USA
Estimation of Camber Generation in Rough Rolling Process Youngil Kang *, Yong-Joon Choi**, Gijang Oh***, Sangchul Won**** *Graduate Institute of Ferrous Technology, POSTECH, Pohang, Korea (Tel: +82-54-279-9278; e-mail: [email protected]). **Technical Research Laboratories, POSCO, Pohang, Korea (e-mail:[email protected]) **Technical Research Laboratories, POSCO, Pohang, Korea (e-mail:[email protected]) *** Department of Electrical Engineering, POSTECH, Pohang, Korea (e-mail: [email protected])} Abstract: In this paper, a method predicting camber generation during rough rolling process is proposed. Using previous studies on mathematical model of camber in roughing mill process, mechanisms of camber generation is presented using Frenet formula. Curvature of the strip is obtained using least square curve fitting method to centerline of the strip. Previous mathematical relation of strip curvature before rolling and after rolling is introduced and verified using FEM simulator describing rough rolling process. The FEM (Finite Element Method) simulator is composed of commercial FEM software DEFORM 3D combined with MATLAB. Assuming that initial tangent vector of the strip after rolling is measured; shape of the strip is estimated using Frenet formula. Simulational results where reasonable parameters are applied show that proposed mathematical relation of camber generation is appropriate. Keywords: Roughing Mill Process, Camber, FEM, Lateral motion, Frenet formula
1. INTRODUCTION Hot rolling process is one of the main processes among steel making process. Its role is making thin strip from thick strip while maintaining pre-determinate temperature during rolling. Since quality of final steel product is strongly related with uniformity of strip thickness, most control algorithm in hot rolling process is focused mainly on regulating thickness of strip to desired value. Meanwhile, there are several abnormal behaviours during hot rolling process such as lateral motion or steering of strip. Due to these abnormal behaviours, suspension of rolling process could be happen which is related with deterioration of productivity. Also, continuous lateral motion or steering of strip could be one of the reasons of frequent substitution of main equipment such as work rolls. Since all these things are directly connected with conductivity of hot rolling process, prevention of lateral motion and steering of strip is good topic for study.
This paper consists of several chapters. At first, mathematical relation of camber and factors of camber is studied on chapter 2. Simulational results from the FEM simulator is shown on chapter 3. On Chapter 4, conclusion of this paper is mentioned. 2. Mechanism of Camber Generation Camber and lateral motion of the strip is well known behaviours which are shown during hot rolling process. Fig. 1 shows what is camber and lateral motion of strip. The concept of camber is steering of strip during rolling process. Difference of mass flow between work-side and drive-side of process is direct reason of camber generation. Quantification of camber is mainly defined as using curvature concept along a point on centerline of strip. On the other hand, lateral motion of the strip is defined as distance between center of roll and centerline of strip.
Although a lot of researches have been conducted to study the reason of those behaviours, it is not yet investigated how those factors work and as a result lateral motion and steering of strip are generated. Asymmetric properties of rolling process such as difference of temperature distribution, thickness deviation of strip, roll gap, rolling force, and stiffness of roll between work side and drive side of process are considered as factors bringing such abnormal behaviours.
Camber and lateral motion of the strip is related with each other. That means, lateral motion is one of the most important factors intensifying camber generation and the reverse is also
This paper studies how steering of strip (or camber) is generated. Mathematical model of camber generation due to 978-3-902823-42-7/2013 © IFAC
lateral motion, entry strip thickness deviation, and roll gap difference is induced from previous studies of rolling process. Mathematical representation of camber generation is verified by using FEM simulator combined with MATLAB. From simulational results, proposed mathematical relation between camber and factors of camber is confirmed as useful and shape of the strip after rolling could be estimated using Frenet formula as well.
436
10.3182/20130825-4-US-2038.00076
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
437
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
rolling could be also possible. Fig. 4 shows comparison between estimated curvature and actual curvature after rolling in the case of equation (2) and (3). It is clear that equation (3) is more precise mathematical model then equation (2).
elasticity. Shape of strip is shown as follows. Entry thickness deviation follows sine function with magnitude 5mm. Specification of strip and roll is listed in table 1.
-5
equation (2)
x 10 curvature(mm-1)
5
estimation actual
0
-5
0
20
40
60
80 step equation (3)
-5
x 10
(a) FEM Simulator on DEFORM 3d
100
curvature(mm-1)
5
120
140
estimation actual
0
-5
0
20
40
60
80
100
120
140
step
(b) Shape of Strip
Fig 4. Comparison between equation (2) and (3)
Fig 2. FEM simulator
Shape of strip after rolling 60
Table 1. Dimension of rolling process 40
Value 1100 9200 107 87 650 2080 1200
Temperature of strip( ) Max. Magnitude of wedge(mm)
20 y direction(mm)
Specification Width(mm) Length(mm) Entry strip thickness(mm) Exit strip thickness(mm) Roll Radius(mm) Length of roll(mm)
-20
-40
5
-60
-80 2000 -5
curvature(mm-1)
2
curvature of strip before rolling
x 10
0
6000
8000 10000 x direction(mm)
12000
14000
16000
Using Frenet formula of equation (1), shape of strip could be estimated assuming that initial tangent vector of strip after rolling is measured. Fig. 5 shows proposed method is useful for estimating shape of curve after rolling.
-1
0
20
40
60
80 100 step wedge of strip before rolling
120
140
4 wedge(mm)
4000
Fig 5. Shape of strip after rolling
1
-2
estimation actual
0
4. Conclusion
2
In this paper, mechanism of camber generation is studied. Based on previous researches on lateral motion and camber, two mathematical model of curvature after rolling is introduced. FEM simulator for hot rolling process is used to verify which model is more appropriate.
0 -2 -4
0
20
40
60
80
100
120
140
step
REFERENCES
Fig 3. Curvature and wedge of strip before rolling
K. Nakajima, T. Kajiwara, and H. Matsumoto, (1980). ³Automatic side-walk control in hot strip mill´, Proc. of Japanese Spring Conference for the Technology of Plasticity,vol. 116, pp. 61-64
Based on the fitted curve of centerline of the strip, curvature and wedge of strip before rolling is derived as depicted in Fig 3. After FEM simulation, wedge of strip after rolling could be obtained using same way. Since wedge profile of strip before and after rolling is known, estimation of curvature after 438
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
M. Okada et al., (2005). ³VSS control of strip steering for hot rolling mills´, IFAC World Congress T. Ishikawa et al., (1988). ³Fundamental study on snaking in strip rolling´, ISIJ, vol. 28 T. Shiraishi, H. Ibata, A. Mituza, et al., (1991). ³Relation between camber and wedge in flat rolling under restrictions of lateral movement´, ISIJ, vol. 31, pp. 583587 Y.J. Choi et al., (2009). ³PID sliding model control for steering of lateral moving strip in hot strip rolling´, ISIJ, vol. 7 Y. Okamura et al., (1997). ³State feedback control of the strip steering for aluminium hot rolling mills´, Control Eng, vol. 5, pp. 1035-1042
439
Estimation of Camber Generation in Rough Rolling Process Youngil Kang *, Yong-Joon Choi**, Gijang Oh***, Sangchul Won**** *Graduate Institute of Ferrous Technology, POSTECH, Pohang, Korea (Tel: +82-54-279-9278; e-mail: [email protected]). **Technical Research Laboratories, POSCO, Pohang, Korea (e-mail:[email protected]) **Technical Research Laboratories, POSCO, Pohang, Korea (e-mail:[email protected]) *** Department of Electrical Engineering, POSTECH, Pohang, Korea (e-mail: [email protected])} Abstract: In this paper, a method predicting camber generation during rough rolling process is proposed. Using previous studies on mathematical model of camber in roughing mill process, mechanisms of camber generation is presented using Frenet formula. Curvature of the strip is obtained using least square curve fitting method to centerline of the strip. Previous mathematical relation of strip curvature before rolling and after rolling is introduced and verified using FEM simulator describing rough rolling process. The FEM (Finite Element Method) simulator is composed of commercial FEM software DEFORM 3D combined with MATLAB. Assuming that initial tangent vector of the strip after rolling is measured; shape of the strip is estimated using Frenet formula. Simulational results where reasonable parameters are applied show that proposed mathematical relation of camber generation is appropriate. Keywords: Roughing Mill Process, Camber, FEM, Lateral motion, Frenet formula
1. INTRODUCTION Hot rolling process is one of the main processes among steel making process. Its role is making thin strip from thick strip while maintaining pre-determinate temperature during rolling. Since quality of final steel product is strongly related with uniformity of strip thickness, most control algorithm in hot rolling process is focused mainly on regulating thickness of strip to desired value. Meanwhile, there are several abnormal behaviours during hot rolling process such as lateral motion or steering of strip. Due to these abnormal behaviours, suspension of rolling process could be happen which is related with deterioration of productivity. Also, continuous lateral motion or steering of strip could be one of the reasons of frequent substitution of main equipment such as work rolls. Since all these things are directly connected with conductivity of hot rolling process, prevention of lateral motion and steering of strip is good topic for study.
This paper consists of several chapters. At first, mathematical relation of camber and factors of camber is studied on chapter 2. Simulational results from the FEM simulator is shown on chapter 3. On Chapter 4, conclusion of this paper is mentioned. 2. Mechanism of Camber Generation Camber and lateral motion of the strip is well known behaviours which are shown during hot rolling process. Fig. 1 shows what is camber and lateral motion of strip. The concept of camber is steering of strip during rolling process. Difference of mass flow between work-side and drive-side of process is direct reason of camber generation. Quantification of camber is mainly defined as using curvature concept along a point on centerline of strip. On the other hand, lateral motion of the strip is defined as distance between center of roll and centerline of strip.
Although a lot of researches have been conducted to study the reason of those behaviours, it is not yet investigated how those factors work and as a result lateral motion and steering of strip are generated. Asymmetric properties of rolling process such as difference of temperature distribution, thickness deviation of strip, roll gap, rolling force, and stiffness of roll between work side and drive side of process are considered as factors bringing such abnormal behaviours.
Camber and lateral motion of the strip is related with each other. That means, lateral motion is one of the most important factors intensifying camber generation and the reverse is also
This paper studies how steering of strip (or camber) is generated. Mathematical model of camber generation due to 978-3-902823-42-7/2013 © IFAC
lateral motion, entry strip thickness deviation, and roll gap difference is induced from previous studies of rolling process. Mathematical representation of camber generation is verified by using FEM simulator combined with MATLAB. From simulational results, proposed mathematical relation between camber and factors of camber is confirmed as useful and shape of the strip after rolling could be estimated using Frenet formula as well.
436
10.3182/20130825-4-US-2038.00076
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
437
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
rolling could be also possible. Fig. 4 shows comparison between estimated curvature and actual curvature after rolling in the case of equation (2) and (3). It is clear that equation (3) is more precise mathematical model then equation (2).
elasticity. Shape of strip is shown as follows. Entry thickness deviation follows sine function with magnitude 5mm. Specification of strip and roll is listed in table 1.
-5
equation (2)
x 10 curvature(mm-1)
5
estimation actual
0
-5
0
20
40
60
80 step equation (3)
-5
x 10
(a) FEM Simulator on DEFORM 3d
100
curvature(mm-1)
5
120
140
estimation actual
0
-5
0
20
40
60
80
100
120
140
step
(b) Shape of Strip
Fig 4. Comparison between equation (2) and (3)
Fig 2. FEM simulator
Shape of strip after rolling 60
Table 1. Dimension of rolling process 40
Value 1100 9200 107 87 650 2080 1200
Temperature of strip( ) Max. Magnitude of wedge(mm)
20 y direction(mm)
Specification Width(mm) Length(mm) Entry strip thickness(mm) Exit strip thickness(mm) Roll Radius(mm) Length of roll(mm)
-20
-40
5
-60
-80 2000 -5
curvature(mm-1)
2
curvature of strip before rolling
x 10
0
6000
8000 10000 x direction(mm)
12000
14000
16000
Using Frenet formula of equation (1), shape of strip could be estimated assuming that initial tangent vector of strip after rolling is measured. Fig. 5 shows proposed method is useful for estimating shape of curve after rolling.
-1
0
20
40
60
80 100 step wedge of strip before rolling
120
140
4 wedge(mm)
4000
Fig 5. Shape of strip after rolling
1
-2
estimation actual
0
4. Conclusion
2
In this paper, mechanism of camber generation is studied. Based on previous researches on lateral motion and camber, two mathematical model of curvature after rolling is introduced. FEM simulator for hot rolling process is used to verify which model is more appropriate.
0 -2 -4
0
20
40
60
80
100
120
140
step
REFERENCES
Fig 3. Curvature and wedge of strip before rolling
K. Nakajima, T. Kajiwara, and H. Matsumoto, (1980). ³Automatic side-walk control in hot strip mill´, Proc. of Japanese Spring Conference for the Technology of Plasticity,vol. 116, pp. 61-64
Based on the fitted curve of centerline of the strip, curvature and wedge of strip before rolling is derived as depicted in Fig 3. After FEM simulation, wedge of strip after rolling could be obtained using same way. Since wedge profile of strip before and after rolling is known, estimation of curvature after 438
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
M. Okada et al., (2005). ³VSS control of strip steering for hot rolling mills´, IFAC World Congress T. Ishikawa et al., (1988). ³Fundamental study on snaking in strip rolling´, ISIJ, vol. 28 T. Shiraishi, H. Ibata, A. Mituza, et al., (1991). ³Relation between camber and wedge in flat rolling under restrictions of lateral movement´, ISIJ, vol. 31, pp. 583587 Y.J. Choi et al., (2009). ³PID sliding model control for steering of lateral moving strip in hot strip rolling´, ISIJ, vol. 7 Y. Okamura et al., (1997). ³State feedback control of the strip steering for aluminium hot rolling mills´, Control Eng, vol. 5, pp. 1035-1042
439