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STUDY OF THICKNESS CONTROL OF STRIP HEAD SECTION USING MATHEMATICAL SIMULATION METHODS
V.R. Khramshin, Magnitogorsk State Technical University (Magnitogorsk,
Russian Federation)
A.S. Karandaev, South Ural State University (Chelyabinsk, Russian Federation)
A.A. Radionov, South Ural State University (Chelyabinsk, Russian Federation)
R.R. Khramshin, Magnitogorsk State Technical University (Magnitogorsk,
Russian Federation)
The authors participated in the modernization of the automatic strip thickness control system of OJSC “Magnitogorsk Iron and Steel Works” 2000 hot rolling mill (OJSC “MMK”). The article offers a brief description of the implemented automatic strip thickness control system developed on the basis of hydraulic screw-down mechanisms. Industrial trials found significant thickness deviation of up to 10% in the strip head section. As a result the length of strip head section with thickness deviation can achieve 40-50 m after the last finishing rolling stand of the mill. The authors offer a new way of strip head thickness control by means of roll gap increase before the strip grip and its further decrease to the required gauge by hydraulic screwdown adjustment during rolling. They also studied the algorithm of roll gap control and factors influencing its adjustment. The research group developed mathematical model of the electromechanical system “stand electric drive - hydraulic screwdown mechanism” taking into account the interrelation of their drives through the rolled metal. The mathematical model of the stand electric drive is developed in the system of two-region speed control. The hydraulic screwdown mechanism can be described by linearized differential equations of fluid flow rate, servo valve for small coordinate increment and forces relationship in the rolling stand. The model consists of a system of differential equations describing the rolled strip as a control object and mathematical description of automatic screwdown mechanism control. The validity of the developed mathematical model was also proved. The authors studied dynamic modes for various parameters of roll gap control and determined the optimum control parameters providing the minimum thickness deviation of the strip head section. The results of the first strips rolling proved that the developed method is quite effective and can be recommended for advanced automatic strip thickness control.
Keywords: mathematical model, hot rolling mill, control system, strip, control system, thickness deviation.
The revamping of the automatic process control system of the finishing train of OJSC “MMK” 2000 hot rolling mill included modernization of the automatic strip thickness control system [1-3]. The new system is based on the multiprocessor digital controller. Controller enhancement made it possible to develop the advanced digital algorithms of strip thickness control. In order to study the accuracy of strip thickness control and to estimate dynamic parameters of electric drives at the stages of feasibility study and project implementation, it was necessary to develop the dynamic mathematical model of the electromechanical system “stand electric drive - hydraulic screwdown mechanism” taking into account their interrelation through the rolled metal [4-7].
The complex of the automatic strip thickness control system of the finishing train of 2000 hot rolling mill consists of hydraulic screwdown mechanisms, Davy McKee automatic strip thickness control system, work roll bending (system) of rolling stands №10-13 [8-9]. Hydraulic screwdown mechanisms are the main final control actuating link for final thickness control. Electromechanic adjusting screws are applied only for roll gap adjustment during the mill reconstruction. The main adjuster of the automatic strip thickness control system was designed on the principle of indirect thickness measuring in the rolling stand. Exit thick-
ness gauge adjustment is used as the main control method [10-11].
Pilot research carried out on the rolling mill [4, 12] showed significant thickness deviations of the strip head section up to 5-10 % while the standard tolerances are +3,5 %. The rolling time of the uneven section of the strip is 10-20 s, corresponding to 40-80 m of the strip length on the mill exit. This kind of thickness deviation is characteristic for all the product range of the 2000 rolling mill irrespective of the strip thickness. The analysis of the operating schedule showed that the thickness deviation of the strip head section results from its higher temperature and this deviation along the strip length is mainly characteristic for thin strip rolling.
The research group offers a new way of strip head thickness control by means of roll gap increase before the strip grip and its further decrease to the required gauge by hydraulic screwdown adjustment during rolling [13-18]. Thickness adjustment is carried out according to the diagram given in fig. 1.
The following parameters are depicted in fig. 1: Sc - additional correction value; Ati - time of constant correction value; At2 - time of correction decrease to zero. Colour background shows logic signal of metal presence in the stand.
Fig. 1. Diagram of thickness adjustment of strip head section
In order to adjust the parameters of roll gap change of the rolling mill, the authors carried out a number of experiments where they studied rolling of strips with different correction parameters in each stand [9, 13, 15]. The parameters were selected empirically and input to the controller of the automatic process control system. Oscillograph records of strip thickness obtained at different rolling parameters are given in fig. 2.
The first strip (fig. 2, a) was rolled without any additional thickness adjustment of the strip head section. Higher temperature of the strip head section results in - 2,9 % strip thickness deviation. During rolling the temperature of the strip head decreases and consequently the strip thickness increases on the stand exit even though the roll gap does not change. Thickness deviation along the length of the strip head section is 5,6%. In the process of the following strips rolling (fig. 2, b - e) the authors applied method of automatic strip thickness control for the strip head section. Additional correction values (Sc), time of constant correction value (A/j) and time of correction decrease to zero (At2) were adjusted in accordance with the values given in fig. 2.
The analysis of findings allowed the authors to make a conclusion that the thickness deviation of the strip head section depends directly on the temperature of the processed strip, initial settings of the roll gap and the value of additional correction Sc.
Changing the value of Sc one can obtain favourable settings for a well defined range of processed strips thus the problem of initial thickness deviation of the strip head section is substantially solved (fig. 2, c). To eliminate the above mentioned thickness deviation along the length of the strip head section due to the temperature difference it is necessary to select the optimal time of constant correction value (A/1) and time of correction decrease to zero (At2).
The experiments prove that it is necessary to study rolling processes with different parameters of the strip head section adjustment. Such trials at an operating plant are fraught with emergency stops of the rolling mill. So the authors believe it is necessary to develop the dynamic mathematical model of the system “stand electric drive - hydraulic screwdown mechanism” taking into account their interrelation through the rolled metal. The model structure should include mathematical description of the automatic strip thickness control system algorithms and the sys-
tem of two-region speed control of the main electric drive [19-21].
The mathematical model of a stand electric drive can be described by the system of equations including equations of the anchor chain and equations taking into account changes of the motor magnetic flux:
Kfc i
Ed i =
Тц ,P +1
Ed i = E + Req. i1 i (Teq. ip + 1);
Mt = Щ1 г;
Е i = Щ ®i;
Mi -Ms. i = гР^г;
L
kt
Т
1 с.ел. ц ex. гр + 1
1+Tk iP
ex. i + Tk i )p]
U
Rex. i [1 + (Te.
®k i = f (Iex. i )
where xt.c. and T^ are the amplification factor and the
response time of the thyristor converter;
uc, is the gate voltage of the thyristor converter; Req. and Teq. are the active resistance equivalent and the response time equivalent of the anchor chain;
M and Ms are the motor torque and static resistance;
JE is the total mass moment of inertia of the rolling stand drive;
Uc.x and Ux are the gate voltage and output voltage of the thyristor actuator;
Rex. is the active resistance of the excitation circuit;
Tx and Tk are the response time of the excitation circuit and the eddy current circuit;
p = -d is the time differentiation operator (Laplace operator).
The hydraulic screwdown mechanism as a control object can be described by three linearized differential equations [22].
1. Equation of fluid flow rate in the hydraulic screwdown mechanism for small coordinate increment:
Q = S
dS,
h.c.
p.t. + Vp.t. dPhc
- + rPh
h.c.
dt E dt where Q is the flow rate of the fluid incoming to the head end of the hydraulic cylinder;
S„L is the position of the hydraulic cylinder pis-
ton;
Shc is the area of the hydraulic cylinder piston;
Vp± is the piston displacement in the initial position;
E is the volumetric modulus of elasticity of the hydraulic fluid;
Phc is the pressure in the head end;
r is the leakage factor provided the flow rate due to leakage is proportional to the pressure in the head end.
u
146 Вестник ЮУрГУ. Серия «Энергетика»
Set the position of the left HPD, stand №9 (mm) - V
■ Set the position of the left HPD, stand №8 (mm)- 2
■ Set the position of the left HPD, stand №7 (mm)- 3
• Enable signal of the automatic thickness control - 4
■ Resolution lifting the head - 5 I
Fig. 2. Oscillograms when dealing with the correction of the head section thickness by rolling strips of 2 mm
Электромеханические системы
2. Equation describing forces relationship in the rolling stand:
d 2 S,
p.t.
+ b-
dS
p.t.
dt2 dt
where P is the total rolling pressure;
m is the weight of mechanical parts of the rolling stand moving with the hydraulic cylinder as well as the weight of the fluid in the pipe line from the battery to the hydraulic cylinder modified to the piston area;
b is the viscous friction factor determining the friction magnitude proportional to the displacement rate of the hydraulic screwdown mechanism and arising in the points of contact between the roll carriages and the bed shear of the rolling stand as well as between the hydraulic cylinder walls and the piston.
3. Linearized equation of the servo valve for small coordinate increment:
Ts.v. -Q + Q = ks.vUs.v. - kf c.P,
where Tsv is the response time of the servo valve;
u sv is the control voltage (voltage on the input of the amplifier determining the control current in the electromagnetic coil of the servo valve);
dQ is the flow rate factor of the servo
ks.v =
du„
valve constant almost in any voltage variation range; kf =| — | is the rigidity rate of the servo
dm
valve flow characteristic when the initial pressure in the head end is P0.
The position control system of the hydraulic screwdown mechanism is equipped with a proportional action regulator. The hydraulic screwdown mechanisms are controlled by means of the automatic strip thickness control system developed on the principle of indirect thickness control on the basis of Go-lovin-Sims equation:
P,
Hi+i - di+i +
K
i +1
where -i+1 is the value of roll gap;
Pi+1 is metal pressure on the rolls;
Ki+1 is the modulus of rigidity of the rolling stand.
The processed strip as a control object can be described by the following equations [23]:
E
^ = “f V i+i - Vst i + V, i) + CT0 i;
PL
Vi - K.i(1+So i + к i °i);
Vi+1 - Vr. i+1(1 + S0 i+1 + Ks i+1 CTi) '
H,
i+1 .
H
V. ,■ -■
2r,
1. i
L
-rni sin2pi
where ai is the specific tension of rolled metal in the i-th interstand space;
Est is the elastic modulus of rolled metal;
Vst i is the strip delivery speed from the previous rolling stand of the i-th interstand space;
V’st. i+1 is the strip entrance speed into the successive rolling stand of the i-th interstand space;
a0 i is the initial value of specific tension of rolled metal in the i-th interstand space;
Vr. i, Vr, i+1 are linear speeds of roll rotation of the i-th and (i+1)-th rolling stand respectively;
ks i is the interaction factor between the values of forward creep and front specific tension for the i-th rolling stand;
ks i+1 is the interaction factor between the values of forward creep and back specific tension for the (i+1)-th rolling stand;
S0 i, S0 i+1 are the values of forward creep for the i-th and the (i+1)-th rolling stands respectively;
H, Hi+1 is the thickness of rolled metal at the outlet of the i-th and the (i+1)- th rolling stand respectively;
Vl. i is the linear speed of the roll movement of the i-th looper.
Dresden formula is used to calculate the forward creep during rolling in the stand rolls, it can be expressed as:
S -1 So i+1 - 4
V
--1
i+1
i i+1
i 2D+1
В (стг+1 -CTi) 2pl+1M
^2
The equation offered by academician A.I. Tseli-kov can be used to calculate metal pressure on rolls [23]:
P - bx,h,-1
2Мг
where фг -
1
Фг
H
X
\ф,-
i-1
V Xi У
X
i-1
X
-1
1
фг
Ht-1 + нг
Хг-! - 1,15СТ^ j-1 -аг-! :
Xi = 1,15°s i -°i ;
i-1, crs i are yield points of metal strip before and after reduction in the stand;
|a,- is the friction factor between the working face of rolls and rolled metal;
2^ h
Hi-1 + H
- factor.
As a result of mathematical description of the electromechanical system “stand electric drive - hydraulic screwdown mechanism” the research group developed a structural diagram given in fig. 3.
The validity of the developed mathematical model was proved by comparison of transient processes of the main electric drive coordinates in the mode of roll gap decrease on the strip obtained by modeling and by oscillographic testing on the mill. Percentage error of the compared figures in the representative points does not exceed 7 %, which is quite acceptable for complex system modeling.
The developed mathematical model was used to study the main dynamic modes of electromechanical systems of seven rolling mills of the finishing train of 2000 rolling mill for measuring of the following parameters:
- additional correction value on the strip head section Sc;
- time of constant correction value At1;
- time of correction decrease to zero At2.
+
e ' -
2
Fig. 3. Structural diagram of the mathematical model “stand electric drive - hydraulic screwdown mechanism”
Real variables of various strips were used as source data.
Calculated curves of thickness change AHi with the change of roll gap (time At2) are given in fig. 4 as an example.
Simulation data made it possible to determine the optimal control parameters on the strip head section (assumption 4 fig. 4) providing the least strip thickness deviation AHi=0,6 %. Besides, the analysis of fig. 4 shows that selection of wrong adjustment parameters on the strip head section may result in thickness deviation (curve 6 fig. 4) comparable with deviations that would result if no adjustments were made (curve 1 fig. 4).
The results of investigations on the basis of the mathematical model allowed the authors to determine the control parameters of the roll gap providing the least thickness deviation of the strip head section. The varia bles for stands № 7-10 are given in the table 1. The minimum thickness deviation is less than 1 % (tolerances +3,5 %).
The result of rolling of the first strips in the rolling mill proved that the selected parameters of roll gap adjustment can be considered optimum ones and can be recommended for advanced automatic strip thickness control of the mill [24-25]. Implementation of thickness control algorithm with the calculated optimum parameters of roll gap adjustment results in reduction of thickness deviation.
Table 1
Correction parameters thickness of the cerebral part of the band
Stand The thickness/ the correction > 2 mm 2-4 mm 4-8 mm 8-12 mm > 12 mm
№7 Sc, mm 0,6 0,5 0,9 0,75 0,4
Atb s 4 5 4 9 7
At2, s 6 3 5 8 8
№8 Sc, mm 0,4 0,4 0,7 0,5 0,3
Ati, s 3 4 3 9 7
At2, s 6 5 5 8 8
№9 Sc, mm 0,2 0,4 0,5 0,3 0,3
At1, s 2 4 2,5 9 7
At2, s 6 5 5 8 8
№10 Sc, mm 0,15 0,2 0,3 0,2 0,3
At1, s 1 3 4 9 6
At2, s 6 5 5 8 8
№11 Sc, mm 0,1 0,1 0,2 0,1 0,2
At1, s 2 3 4 9 6
At2, s 5 5 5 8 9
Conclusions
1. The authors proved that it is necessary to study the rolling process with various control parameters of the strip head section and this study should be carried out using mathematical simulation methods.
2. The developed dynamic mathematical model of the system “stand electric drive - hydraulic screwdown mechanism” makes it possible to apply the suggested method of thickness control for the strip head section.
3. As a result of the research work the authors determined the optimum roll gap control parameters for the strip head section rolling and proved that these parameters provided the minimum thickness deviation.
4. The dynamic mathematical model can be used to analyze dynamic modes and to set the rolling stand automatic electric drives as well as hydraulic screw-down mechanisms thus contributing to improvement of final product quality of wide strip rolling mills.
References
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УДК 621.313.2
ИССЛЕДОВАНИЕ СИСТЕМЫ АВТОМАТИЧЕСКОЙ КОРРЕКЦИИ ТОЛЩИНЫ ПОЛОСЫ НА ШИРОКОПОЛОСНОМ СТАНЕ ГОРЯЧЕЙ ПРОКАТКИ
В.Р. Храмшин, А.С. Карандаев, А.А. Радионов, Р.Р. Храмшин
Выполнена модернизация системы автоматического регулирования толщины (САРТ) стана 2000 ОАО «Магнитогорский металлургический комбинат» (ОАО «ММК»). Дано краткое описание внедренной САРТ, выполненной на базе гидравлических нажимных устройств (НУ). Проведенные экспериментальные исследования выявили недопустимые отклонения толщины на головном участке полосы, достигающие 10 % в сторону уменьшения. Это приводит к возникновению разнотолщинного головного участка полосы длиной 40-50 м на выходе стана. Предложен способ коррекции толщины головного участка, осуществляемый за счет разведения валков клетей перед захватом полосы и последующего их сведения до заданного положения за счет перемещения гидравлических НУ во время прокатки. Рассмотрен алгоритм изменения межвалкового зазора. Обоснована необходимость оптимальной настройки времени удержания максимального разведения валков и времени уменьшения коррекции до нуля. Разработана математическая модель системы «электропривод клети - гидравлический привод нажимных устройств» с учетом взаимосвязи названных приводов через прокатываемый металл. Математическая модель электропривода клети построена в системе двухзонного регулирования скорости. Гидравлические НУ описываются линеаризованными дифференциальными уравнениями расхода жидкости, сервоклапана для малых приращений координат и соотношения усилий в прокатной клети. Модель включает систему дифференциальных уравнений, описывающих прокатываемую полосу как объект управления, а также математическое описание системы автоматического регулирования положения НУ. Дано подтверждение адекватности разработанной модели исследуемому объекту. Выполнено исследование динамических режимов при изменениях параметров коррекции межвалкового зазора. Определены оптимальные параметры коррекции, при которых обеспечивается наименьшее отклонение толщины головного участка. Прокатка на стане первых партий полос подтвердила эффективность разработанного способа компенсации разнотолщинности головного участка.
Ключевые слова: стан горячей прокатки, толщина полосы, отклонения, система регулирования, математическая модель, исследование, эксперимент.
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Храмшин Вадим Рифхатович, кандидат технических наук, доцент, доцент кафедры электротехники и электротехнических систем, МГТУ им. Г.И. Носова, г. Магнитогорск, тел. 8 (3519) 29-84-16, E-mail: hvr_mgn@mail.ru
Карандаев Александр Сергеевич, главный научный сотрудник кафедры теоретических основ электротехники, Южно-Уральский государственный университет, г. Челябинск, доктор технических наук, профессор, тел. 8 (3519) 29-84-16; E-mail: askaran@mail.ru
Радионов Андрей Александрович, доктор технических наук, профессор, декан энергетического факультета, заведующий кафедрой теоретических основ электротехники, Южно-Уральский государственный университет, г. Челябинск, тел. 8 (351) 272-31-41, E-mail: radionovaa@susu.ac.ru
Храмшин Рифхат Рамазанович, доцент кафедры электротехники и электротехнических систем МГТУ им. Г.И. Носова, г. Магнитогорск, кандидат технических наук, доцент, тел. 8 (3519) 29-84-16, E-mail: hramshinrr@mail.ru
Поступила в редакцию 20.03.2013 г.
