- Email: [email protected]
Optimization of Short Stroke Control Preset for Automatic Width Control of Hot Rolling Mill
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ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2010, 17(6): 16-20
Optimization of Short Stroke Control Preset for Automatic Width Control of Hot Rolling Mill DU Xiao-zhong':" ,
YANG Quan' ,
LU Cheng' ,
WANG Ai-li l
,
Tieu A Kiet"
(1. National Engineering Research Center for Advanced Rolling Technology, University of Science and Technology
2. School of Materials Science and Engineering, Taiyuan University of Beijing, Beijing 100083, China; 3. School of Mechanical, Materials and Science and Technology, Taiyuan 030024, Shanxi, China; Mechatronic Engineering, University of Wollongong, Wollongong, NSW 2522, Australia) Abstract, Automatic width control is a key issue in hot strip rolling process. The edge rolling has been widely used in the roughing stand of hot strip mill to control the width of the slab. However, the edge rolling and consequent horizontal rolling will cause a significant width change in the head part and tail part of the slab, which have to be trimmed before the finishing stands. Based on the width reduction deformation curve of the head and tail along the longitudinal direction of slab, the short stroke control (SSC) technology has been developed to overcome this problem. The finite element method has been used to simulate the unsteady edge rolling process. Three short stroke control curves have been compared in order to obtain the best width control result. The optimized short stroke control curve has been applied to the automatic width control system of industrial hot rolling mill, and good performance is obtained. Key words: unsteady rolling; edge rolling; short stroke control; automatic width control; L5-0YNA
Automatic width control is a key issue in hot strip rolling. The finished product quality is influenced significantly by the width control precision. The slab edge rolling has been widely used in the roughing stand of hot strip mill to control the width of the slab. A number of researches on the edge rolling have been conducted, most of which focused on the steady rolling processing-Y". The unsteady edge rolling process has also been numerically and experimentally studied[4-5]. However, the detailed investigations on the short stroke control process and the optimization of the control curves have not been reported. In this paper, the finite element method (FEM) has been used to simulate the unsteady edge rolling process. Three short stroke control curves have been compared in order to obtain the best width control result. The optimal schedules preset parameters have been applied to the automatic width control system of 1500 mm hot continuous rolling mills. The industrial application has shown
that the shape of the head and tail can be improved significantly.
1
Principle of Short Stroke Control
Application of the slab edge rolling decreases the online adj usting range of the continuous casting process and reduces the specifications of the as-casted products. However, the slab edge rolling and consequent horizontal rolling will cause a significant width change in the head part and tail part of the slab (as shown in Fig. 1), which have to be cut before the finishing stands. To overcome this problem, the short stroke control technology has been developed. The short stroke control technology utilizes a dynamic gap between two vertical rolls to compensate the width reduction during the head part and the tail part of the slab as shown in Fig. 1. The short stroke control curve is normally simplified into two or three continuous straight lines.
Foundation Item, Item Sponsored by National Science and Technology Support Program for 11th Five-Year Plan of China (2006BAE03A13) ; International Cooperation Research Project of Shanxi Province (2009081013) E-mail: [email protected]; Received Date: June 10. 2009 Biography,DU Xiao-zhong0974-). Male. Doctor. Associate Professor;
Issue 6
,
statement of the principle of virtual work,
- Widthcurve of slab without sse ---- Setup curve for sse ••._.Widthcurve of slab with sse -,
....'"
sse
sse
x'i8xi dv=
f~li8xidv+ Is!
1.
e.
t i8x i ds -
LGij8Xi,jdv
~
(6)
The simulation body can be modeled by many elements. The geometry of the element is represented by Lagrangian description that is in terms of shape function. After assembly, the elemental mass is lumped at the nodes.
.1
Length of slab
Fig. 1
f~
,.,-
?~ .'
I.
Diagram of short stroke control principle
2.2
2
• 17 •
Optimization of Short Stroke Control Preset for Automatic Width Control of Hot Rolling Mill
Analysis of Finite Element Method
Equation solving algorithm
An iteration algorithm is used to solve Eqn. (6). At time step i 1, the stress is calculated using the strain determined at time step i, Based on the boundary condition t, at 51 and the known body force Ii' all the items on the right side of Eqn. (6) can be
+
To analyze the effect of edge rolling on the head part and the tail part of the slab, the explicit dynamic finite element method code has been developed. The explicit dynamic finite element method theory is described as follow.
2. 1
Governing equation For a point in a body (V), the time-dependent deformation can be found by seeking a solution to the momentum equation:
+
Gij ,j p • II = P x· i where, G is Cauchy stress; p is density;
0)
I
is body
x
force density; x is displacement; and is acceleration. Eqn. (1) satisfies the traction boundary conditions Gij • n, =t i (2) On boundary 51, the displacement boundary conditions (3) xi=D i On boundary 52' the contact discontinuity (Gt -Gij) • n, =0 (4) Along an interior boundary 53' where, t is traction stress; ni is a unit outward normal to the boundary; D, is boundary displacement. From Eqn, (1) to Eqn. (4), the following can be obtained
f
v
(p x'i-Gij,j-pl,)8xi dv+
t i)8xids+
f
f
~
2. 3
Time step control
The time step size plays an important role on the accuracy and efficiency of the explicit dynamic FEM. In this study the time step size is determined by taking the minimum value over all the elements. ~ti+ I = a • min {~tl ,~t2 ,~t3 , ... , ~tN } (7) where, ~t is the time step size; N is the number of elements. For stability reasons the scale factor a is typically set to a value of O. 9 or some smaller value. A critical time step ~tc is computed for each elements from
~tc= Q+(QI;:h 2 ) 1/ 2
(8)
where, Q is a function of the bulk viscosity coefficient Co and CI ; L, is a characteristic length; and c is the adiabatic sound speed. CI • c+C~ • i; IEkk I for (9) for
Q={
L=~ e A
(0)
emax
where, V e is the element volume; A emax is the area of the largest side.
(Gijni-
(Gt -Gij )n i8xi ds=0
x
obtained, and then the acceleration can be calculated by Eqn, (6). Finally the velocity and displacement of each element are determined.
(5)
3
Finite Element Method Model
53
where 8Xi is the kinematically admissible virtual displacement field, which is infinitesimal and completely arbitrary except that it must obey the boundary conditions on displacement. By using the divergence theory it can lead to a
The explicit elastic-plastic FEM model has been developed to simulate the vertical-horizontal rolling process of a 1500 mm hot strip mill. Bilinear kinematic hardening elastic-plastic material was chosen to be the slab material in the simulation, while the
Journal of Iron and Steel Research. International
• 18 •
roll is rigid. The hexahedral eight-nodes element was used for both roll and slab. The Coulomb friction law was applied to the interface of rolls and slab. Due to symmetry. half of the whole model was simulated in order to reduce the calculating time. as shown in Fig. 2. During the simulation. the slab moved to the vertical roll gap with an initial certain speed. and then it encountered the edge rolling by the vertical rolls and the horizontal rolling by the horizontal rolls. The simulation parameters are shown as following: length of vertical roll is 675 mm , diameter of vertical roll is 1090 mm , length of horizontal roll is 1500 mm , diameter of horizontal roll is 950 mm , thickness of slab are 160 and 240 mm , width of slab are 750 and 1400 mrn , thickness reduction is 0, 20 and 40 mm , width reduction is 0, 25 and 50 mm , length of slab is 3000 mm , rolling speed is 2. 0 m/ s.
Fig. 2
4
FEM model for roll and slab
Results and Discussion
The deformations of the slab head and tail without short stroke control is simulated firstly. The width reduction is 0, 25 and 50 mm during the edge rolling, respectively. The thickness reduction varies from 0 to 40 mm during the horizontal rolling. Fig. 3 (a) shows the width change along the slab length for various width reductions and constant thickness reduction of 40 mm, It can be found that the width remains constant in the middle part of the slab, while it varies during the unsteady rolling process, namely the head and the tail part. The head and tail parts of the slab without width reduction
Vol. 17
have been widened along the width, which is consistent with the industrial observation. When the width reduction is applied, the width during the unsteady rolling process becomes narrow. It can be seen from Fig. 3 (a) that the width loss increases with the width reduction. Fig.3 (b) shows the width change along the slab length for various thickness reductions and constant width reduction of 40 mm. It can be seen that the width loss in the slab head part is larger than that in the slab tail part. This is due to the deformation in slab tail is different with the deformation of slab head. With increasing horizontal reduction, the width loss has been improved. The effect of the entry slab thickness on the width change is shown in Fig. 3 (c). Two cases with different entry slab thickness (160 mm and 240 mrn) have been simulated. The curves of the width loss exhibit similar pattern for two cases. As the entry slab thickness increases, the width loss increases. Fig. 3 (d) depicts the width change for different slab widths. The slab widths are 750 mm and 1400 rnm , respectively. The width reduction is 50 mm , the thickness reductions is 40 mm and the entry slab thickness is 160 mm, Fig. 3 (d) indicates that as the slab width increases, the width loss in both the head and tail part increases. The developed FEM model has also been applied to simulate the vertical-horizontal rolling with short stroke control. Three short stroke control curves have been designed and setup values of curves have been given. The details are shown in Table 1. The process parameters are shown as following: setting value for horizontal roll gap is 170. 29 mm , slab thickness in horizontal roll entrance is 213. 15 mm , slab thickness in horizontal roll exit is 170.51 mrn , setting value for edge roll gap is 1086.46 mm , slab width in exit of horizontal roll is 1105.81 mm , slab width in exit of edge roll is 1088. 76 mrn , slab width in entrance of edge roll is 1088.76 mm , length of slab is 10. 02 m. The simulation results are depicted in Fig. 4. It is clear that three application of all the short stroke control curves have improved the width loss. The short stroke control result of curve A has a slight improvement, while the result of curve C generates an over control. It can be concluded that the short stroke control result of curve B exhibits the best width control capability.
Issue 6
Optimization of Short Stroke Control Preset for Automatic Width Control of Hot Rolling Mill
0.02
0.02
(a)
• 19 •
(b)
0 0 -0.02
• Rv=Onun • Rv=25 nun .. Rv=50nun
-0.02
~
W=1 400 nun, H=160 nun, Rh=40 nun
W=1 400 nun, H=160 nun, Rv=50 nun
-0.06
.tj
.g
• Rh=Omm • Rh=20nun .. Rh=40nun
-0.04
-0.04
e
0 (c)
~
(d)
0
~
-0.01
-0.02
• H=I60nun • H=240nun
• W=1400nun • W=750nun
-0.02
-0.04
W=1400 nun, Rh=40 nun, Rv=50 nun
H=160 nun, Rh=40 nun, Rv=50 nun
-0.03
-0.06
-0.04 0
0.5
1.5
1.0
2.0
0
0.5
1.0
1.5
2.0
Length of slab/m
Fig. 3
Width change of slab for different width reductions, thickness reductions, entry slab thickness and slab width
Table 1
Short stroke control curve setup values
Setup values for curve A/mm
Setup values for curve B/mm
Setup values for curve C/mm
20.0
30.0
50.0
8 16
20.0
30.0
50.0
10.0
20.0
30.0
30
0
0
0
50 85 90
0 10.0 20.0
0 20.0 30.0
0 30.0 50.0
95
20.0
30.0
50.0
Relative time/%
0.02 , . . . . - - - - - - - - - - - - - - - - ,
5
The optimized short stroke control curve has been applied to automatic width control system of an industrial rolling mill. The statistical results of field show excellent control performance, for example, the error of gauge control system in the range of 50 p'm is more than 96 %, and more than 97 % of the error of width control system is less than 7 mm. The qualified rate of production is more than 96 %, and the full automatic running rate is more than 98%[6J. It shows that the width loss of head and tail can be significantly improved by short stroke control.
6
~0 'l:l .g'"
0
~
-0.02
~
• Without SSC • SSC curve A .. SSC curveB • SSC curveC
~ -0.04 0
0.5
1.0
1.5
Length of slab/m
Fig. 4
Width reduction of slab by different short stroke control models
2.0
Application
Conclusions
1) An explicit elastic-plastic FEM model has been developed to simulate the edge rolling process in the roughing stands of hot strip mill. It has been found that the process parameters significantly affect the width change in the head part and tail part of the slab. The width loss increases as the width reduction, the thickness reduction, the entry slab thickness and the slab width increases. 2) The short stroke control technology has been used to reduce the width loss in the head and tail
• 20 •
Journal of Iron and Steel Research, International
part of the slab. Three cases with different short stroke control curves have been simulated. It has been found that the sse curve B provides the best width control result. 3) This curve has been applied in an industrial rolling mill. Its width control ability has been confirmed by the on-line width measurement.
[3J
[4J
[2J
Gerlinde D, Reinhold F. Edging in Hot Strip Mills Design, Technology and Product Improvements [JJ. AISE Steel Technology, 2003, 80(6): 78.
[MJ. New York: Marcel Dekker, 1989. Xiong S W, Liu X H. Slab Width Reduction Technology in Roughing Trains of Hot Strip Mills and Methods for Improvement of Crop Loss [JJ. Iron and Steel, 1994, 29(12): 75 (in Chinese). Nikaido H, Naoi T. FEM Simulation of Nonsteady Deformation in Edge Rolling [JJ. Journal of the Japan Society for Technology of Plasticity, 1983, 24(2): 486.
[5J
Xiong S W, Lu C. Simulation of Unsteady-State Edging
[6J
Process by Full Three-Dimensional Rigid-Plastic Finite Element Method [JJ. Journal of Northeastern University, 1999, 20(6): 647 (in Chinese). Guo Q, Wang J. Automation Control System of Rizhao 1580
References: [IJ
Vol. 17
Hot Strip Mill [JJ. Journal of University of Science and Technology Beijing, 2007, 29(12): 178 (in Chinese).
Ginzburg V B. Steel Rolling Technology: Theory and Practice
-----_.~--~---~
(Continued From Page 15) References: [IJ
[2J
Wickert J A, Mote C D. Classical Vibration Analysis of Axially Moving Continua [JJ. ASME Journal of Applied Mechanics, 1990,57(3): 738. OZ H R, Pakdemirli M, Boyaci H. Non-Linear Vibrations and Stability of an Axially Moving Beam With Time-Dependent Ve-
[6J
During the Rolling Mill Operation []]. Journal of Materials Processing Technology, 2005, 162(spec iss): 464. [7J
[8J
Bar A, Swiatoniowski A. Interdependence Between the Rolling Speed and Non-Linear Vibrations of the Mill System [JJ. Journal of Materials Processing Technology, 2004, 155(1): 2116. Kim C H, Perkins N C, Lee C W. Parametric Resonance of
[9J
Plates in a Sheet Metal Coating Process [JJ. Journal of Sound and Vibration, 2003, 268(4): 679. TANG Hua-ping , DING Rui, WU Yun-xin, Investigation for
locity [] J. International Journal of Non-Linear Mechanics, 2001, 360): 107. [3J
[4J
CHEN Li-qun , YANG Xiao-dong. Steady-State Response of Axially Moving Viscoelastic Beams With Pulsating Speed: Comparison of Two Nonlinear Models [JJ. Internal Journal of Solids and Structures, 2005, 42(1): 37. ZHANG Hong-xing , ZHANG Wei, YAO Ming-hui, Experi-
Parametric Vibration of Rolling Mill []J. Trans Nonferrous Met Soc China, 2002, 12(3): 485.
mental Research on Nonlinear Vibration of an Axially Moving Viscoelastic Belt [j]. Journal of Dynamics and Control, 2007, 5(4): 361. [5J
Swiatoniowski A, Bar A. Parametrical Excitement Vibration in
Tandem Mills, Mathematical Model and Its Analysis []J. Journal of Materials Processing Technology, 2003, 134 (2): 214. Bar A, Bar O. Types of Mid-Frequency Vibrations Appearing
[10J
Kong L, Parker R G. Approximate Eigensolutions of Axially Moving Beam With Small Flexural Stiffness [J]. Journal of Sound and Vibration, 2004, 276(1): 459.
ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2010, 17(6): 16-20
Optimization of Short Stroke Control Preset for Automatic Width Control of Hot Rolling Mill DU Xiao-zhong':" ,
YANG Quan' ,
LU Cheng' ,
WANG Ai-li l
,
Tieu A Kiet"
(1. National Engineering Research Center for Advanced Rolling Technology, University of Science and Technology
2. School of Materials Science and Engineering, Taiyuan University of Beijing, Beijing 100083, China; 3. School of Mechanical, Materials and Science and Technology, Taiyuan 030024, Shanxi, China; Mechatronic Engineering, University of Wollongong, Wollongong, NSW 2522, Australia) Abstract, Automatic width control is a key issue in hot strip rolling process. The edge rolling has been widely used in the roughing stand of hot strip mill to control the width of the slab. However, the edge rolling and consequent horizontal rolling will cause a significant width change in the head part and tail part of the slab, which have to be trimmed before the finishing stands. Based on the width reduction deformation curve of the head and tail along the longitudinal direction of slab, the short stroke control (SSC) technology has been developed to overcome this problem. The finite element method has been used to simulate the unsteady edge rolling process. Three short stroke control curves have been compared in order to obtain the best width control result. The optimized short stroke control curve has been applied to the automatic width control system of industrial hot rolling mill, and good performance is obtained. Key words: unsteady rolling; edge rolling; short stroke control; automatic width control; L5-0YNA
Automatic width control is a key issue in hot strip rolling. The finished product quality is influenced significantly by the width control precision. The slab edge rolling has been widely used in the roughing stand of hot strip mill to control the width of the slab. A number of researches on the edge rolling have been conducted, most of which focused on the steady rolling processing-Y". The unsteady edge rolling process has also been numerically and experimentally studied[4-5]. However, the detailed investigations on the short stroke control process and the optimization of the control curves have not been reported. In this paper, the finite element method (FEM) has been used to simulate the unsteady edge rolling process. Three short stroke control curves have been compared in order to obtain the best width control result. The optimal schedules preset parameters have been applied to the automatic width control system of 1500 mm hot continuous rolling mills. The industrial application has shown
that the shape of the head and tail can be improved significantly.
1
Principle of Short Stroke Control
Application of the slab edge rolling decreases the online adj usting range of the continuous casting process and reduces the specifications of the as-casted products. However, the slab edge rolling and consequent horizontal rolling will cause a significant width change in the head part and tail part of the slab (as shown in Fig. 1), which have to be cut before the finishing stands. To overcome this problem, the short stroke control technology has been developed. The short stroke control technology utilizes a dynamic gap between two vertical rolls to compensate the width reduction during the head part and the tail part of the slab as shown in Fig. 1. The short stroke control curve is normally simplified into two or three continuous straight lines.
Foundation Item, Item Sponsored by National Science and Technology Support Program for 11th Five-Year Plan of China (2006BAE03A13) ; International Cooperation Research Project of Shanxi Province (2009081013) E-mail: [email protected]; Received Date: June 10. 2009 Biography,DU Xiao-zhong0974-). Male. Doctor. Associate Professor;
Issue 6
,
statement of the principle of virtual work,
- Widthcurve of slab without sse ---- Setup curve for sse ••._.Widthcurve of slab with sse -,
....'"
sse
sse
x'i8xi dv=
f~li8xidv+ Is!
1.
e.
t i8x i ds -
LGij8Xi,jdv
~
(6)
The simulation body can be modeled by many elements. The geometry of the element is represented by Lagrangian description that is in terms of shape function. After assembly, the elemental mass is lumped at the nodes.
.1
Length of slab
Fig. 1
f~
,.,-
?~ .'
I.
Diagram of short stroke control principle
2.2
2
• 17 •
Optimization of Short Stroke Control Preset for Automatic Width Control of Hot Rolling Mill
Analysis of Finite Element Method
Equation solving algorithm
An iteration algorithm is used to solve Eqn. (6). At time step i 1, the stress is calculated using the strain determined at time step i, Based on the boundary condition t, at 51 and the known body force Ii' all the items on the right side of Eqn. (6) can be
+
To analyze the effect of edge rolling on the head part and the tail part of the slab, the explicit dynamic finite element method code has been developed. The explicit dynamic finite element method theory is described as follow.
2. 1
Governing equation For a point in a body (V), the time-dependent deformation can be found by seeking a solution to the momentum equation:
+
Gij ,j p • II = P x· i where, G is Cauchy stress; p is density;
0)
I
is body
x
force density; x is displacement; and is acceleration. Eqn. (1) satisfies the traction boundary conditions Gij • n, =t i (2) On boundary 51, the displacement boundary conditions (3) xi=D i On boundary 52' the contact discontinuity (Gt -Gij) • n, =0 (4) Along an interior boundary 53' where, t is traction stress; ni is a unit outward normal to the boundary; D, is boundary displacement. From Eqn, (1) to Eqn. (4), the following can be obtained
f
v
(p x'i-Gij,j-pl,)8xi dv+
t i)8xids+
f
f
~
2. 3
Time step control
The time step size plays an important role on the accuracy and efficiency of the explicit dynamic FEM. In this study the time step size is determined by taking the minimum value over all the elements. ~ti+ I = a • min {~tl ,~t2 ,~t3 , ... , ~tN } (7) where, ~t is the time step size; N is the number of elements. For stability reasons the scale factor a is typically set to a value of O. 9 or some smaller value. A critical time step ~tc is computed for each elements from
~tc= Q+(QI;:h 2 ) 1/ 2
(8)
where, Q is a function of the bulk viscosity coefficient Co and CI ; L, is a characteristic length; and c is the adiabatic sound speed. CI • c+C~ • i; IEkk I for (9) for
Q={
L=~ e A
(0)
emax
where, V e is the element volume; A emax is the area of the largest side.
(Gijni-
(Gt -Gij )n i8xi ds=0
x
obtained, and then the acceleration can be calculated by Eqn, (6). Finally the velocity and displacement of each element are determined.
(5)
3
Finite Element Method Model
53
where 8Xi is the kinematically admissible virtual displacement field, which is infinitesimal and completely arbitrary except that it must obey the boundary conditions on displacement. By using the divergence theory it can lead to a
The explicit elastic-plastic FEM model has been developed to simulate the vertical-horizontal rolling process of a 1500 mm hot strip mill. Bilinear kinematic hardening elastic-plastic material was chosen to be the slab material in the simulation, while the
Journal of Iron and Steel Research. International
• 18 •
roll is rigid. The hexahedral eight-nodes element was used for both roll and slab. The Coulomb friction law was applied to the interface of rolls and slab. Due to symmetry. half of the whole model was simulated in order to reduce the calculating time. as shown in Fig. 2. During the simulation. the slab moved to the vertical roll gap with an initial certain speed. and then it encountered the edge rolling by the vertical rolls and the horizontal rolling by the horizontal rolls. The simulation parameters are shown as following: length of vertical roll is 675 mm , diameter of vertical roll is 1090 mm , length of horizontal roll is 1500 mm , diameter of horizontal roll is 950 mm , thickness of slab are 160 and 240 mm , width of slab are 750 and 1400 mrn , thickness reduction is 0, 20 and 40 mm , width reduction is 0, 25 and 50 mm , length of slab is 3000 mm , rolling speed is 2. 0 m/ s.
Fig. 2
4
FEM model for roll and slab
Results and Discussion
The deformations of the slab head and tail without short stroke control is simulated firstly. The width reduction is 0, 25 and 50 mm during the edge rolling, respectively. The thickness reduction varies from 0 to 40 mm during the horizontal rolling. Fig. 3 (a) shows the width change along the slab length for various width reductions and constant thickness reduction of 40 mm, It can be found that the width remains constant in the middle part of the slab, while it varies during the unsteady rolling process, namely the head and the tail part. The head and tail parts of the slab without width reduction
Vol. 17
have been widened along the width, which is consistent with the industrial observation. When the width reduction is applied, the width during the unsteady rolling process becomes narrow. It can be seen from Fig. 3 (a) that the width loss increases with the width reduction. Fig.3 (b) shows the width change along the slab length for various thickness reductions and constant width reduction of 40 mm. It can be seen that the width loss in the slab head part is larger than that in the slab tail part. This is due to the deformation in slab tail is different with the deformation of slab head. With increasing horizontal reduction, the width loss has been improved. The effect of the entry slab thickness on the width change is shown in Fig. 3 (c). Two cases with different entry slab thickness (160 mm and 240 mrn) have been simulated. The curves of the width loss exhibit similar pattern for two cases. As the entry slab thickness increases, the width loss increases. Fig. 3 (d) depicts the width change for different slab widths. The slab widths are 750 mm and 1400 rnm , respectively. The width reduction is 50 mm , the thickness reductions is 40 mm and the entry slab thickness is 160 mm, Fig. 3 (d) indicates that as the slab width increases, the width loss in both the head and tail part increases. The developed FEM model has also been applied to simulate the vertical-horizontal rolling with short stroke control. Three short stroke control curves have been designed and setup values of curves have been given. The details are shown in Table 1. The process parameters are shown as following: setting value for horizontal roll gap is 170. 29 mm , slab thickness in horizontal roll entrance is 213. 15 mm , slab thickness in horizontal roll exit is 170.51 mrn , setting value for edge roll gap is 1086.46 mm , slab width in exit of horizontal roll is 1105.81 mm , slab width in exit of edge roll is 1088. 76 mrn , slab width in entrance of edge roll is 1088.76 mm , length of slab is 10. 02 m. The simulation results are depicted in Fig. 4. It is clear that three application of all the short stroke control curves have improved the width loss. The short stroke control result of curve A has a slight improvement, while the result of curve C generates an over control. It can be concluded that the short stroke control result of curve B exhibits the best width control capability.
Issue 6
Optimization of Short Stroke Control Preset for Automatic Width Control of Hot Rolling Mill
0.02
0.02
(a)
• 19 •
(b)
0 0 -0.02
• Rv=Onun • Rv=25 nun .. Rv=50nun
-0.02
~
W=1 400 nun, H=160 nun, Rh=40 nun
W=1 400 nun, H=160 nun, Rv=50 nun
-0.06
.tj
.g
• Rh=Omm • Rh=20nun .. Rh=40nun
-0.04
-0.04
e
0 (c)
~
(d)
0
~
-0.01
-0.02
• H=I60nun • H=240nun
• W=1400nun • W=750nun
-0.02
-0.04
W=1400 nun, Rh=40 nun, Rv=50 nun
H=160 nun, Rh=40 nun, Rv=50 nun
-0.03
-0.06
-0.04 0
0.5
1.5
1.0
2.0
0
0.5
1.0
1.5
2.0
Length of slab/m
Fig. 3
Width change of slab for different width reductions, thickness reductions, entry slab thickness and slab width
Table 1
Short stroke control curve setup values
Setup values for curve A/mm
Setup values for curve B/mm
Setup values for curve C/mm
20.0
30.0
50.0
8 16
20.0
30.0
50.0
10.0
20.0
30.0
30
0
0
0
50 85 90
0 10.0 20.0
0 20.0 30.0
0 30.0 50.0
95
20.0
30.0
50.0
Relative time/%
0.02 , . . . . - - - - - - - - - - - - - - - - ,
5
The optimized short stroke control curve has been applied to automatic width control system of an industrial rolling mill. The statistical results of field show excellent control performance, for example, the error of gauge control system in the range of 50 p'm is more than 96 %, and more than 97 % of the error of width control system is less than 7 mm. The qualified rate of production is more than 96 %, and the full automatic running rate is more than 98%[6J. It shows that the width loss of head and tail can be significantly improved by short stroke control.
6
~0 'l:l .g'"
0
~
-0.02
~
• Without SSC • SSC curve A .. SSC curveB • SSC curveC
~ -0.04 0
0.5
1.0
1.5
Length of slab/m
Fig. 4
Width reduction of slab by different short stroke control models
2.0
Application
Conclusions
1) An explicit elastic-plastic FEM model has been developed to simulate the edge rolling process in the roughing stands of hot strip mill. It has been found that the process parameters significantly affect the width change in the head part and tail part of the slab. The width loss increases as the width reduction, the thickness reduction, the entry slab thickness and the slab width increases. 2) The short stroke control technology has been used to reduce the width loss in the head and tail
• 20 •
Journal of Iron and Steel Research, International
part of the slab. Three cases with different short stroke control curves have been simulated. It has been found that the sse curve B provides the best width control result. 3) This curve has been applied in an industrial rolling mill. Its width control ability has been confirmed by the on-line width measurement.
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