basalA comparison of two t-up generation systems for cold rolling mills
Henrique C. Ferreira1, Carlos T. A. Pires2, Daniel Uehara1, Roberto M. Sales1
1. INTRODUCTION
Set-up generation is an important aspect in the operation of tandem cold mills. It defines speeds and powers for the drives, stand reductions, roll forces and interstand tensions for the tandem cold mill control system. Set-up optimization should lead to improved thickness regularity, surface finish and shape performance of the strip. The importance of such optimization first appeared in (1) and it has been object of veral works (2, 3, 4, 5).
In ca of malfunction of the main processing unit responsible to execute the t-up generation system at Cosipa tandem cold mill, a brazilian steel industry, the normal procedure for the operation is interrupted, being necessary to u an emergency operation mode. As the process unit has low failure rate, the high cost of a redundancy implementation is not justified. This is the main reason for the development of an alternative simpler system for t-up generation, as prented in this work.
The propod system is bad on a cost function that evaluates the mill quality and productivity. The c
ost function is minimized using the Nelder and Mead simplex method (6), and the process variable are evaluated by the cold rolling model propod by Bryant (1).
2. PLANT DESCRIPTION
The propod t-up generation system was developed to be ud at Cosipa tandem cold mill, a coil to coil, four high, four stand mill, in which each stand is driven by two twin independent dc motors. Two hydraulics actuators, installed at the top of each stand, complete the t of the stands. Table 1 prents the main electrical and mechanical characteristics of the tandem cold mill.
Table 1: Electrical and mechanical characteristics
pdcAnnual production (tons) 1.248.000
Maximum speed (m/min) 1080
Work rolls diameter (mm) 490 to 575
Back up rolls diameter (mm) 1270 a 1422
liberalartsStand 1 2 3 4
Power (kW) 2 x 1800 2 x 1800 2 x 1800 2 x 1482
Motors
Speed (rpm) 433 to 1046433 to 1046433 to 1046 200 to 485
(V) 900 900 900 700
Voltage
Steel
Material Carbon
Entry thickness (mm) 2.00 to 4.75
谈谈美食
Exit thickness (mm) 0.38 to 3.00
Coil width (mm) 650 to 1575
Coil internal diameter (mm) 610
Coil external diameter (mm) 1930
3. THE PROCESS MODEL
Cold rolling mill process models have been developed for more than half a century. The most classic cold mill process model, propod by Bland and Ford (7), is compod by algebraic and integrals equations for forces and torques calculation. Bryant (1), through model simplifications, developed a cold mill model compod only by algebraic equations. This simple model demands low computational effort and shows satisfactory results. The t-up generation system here considered us the Bryant cold mill model.
1 (University of São Paulo, Department of Telecommunication and Control Engineering), Brazil
2 (COSIPA Companhia Siderúrgica Paulista, Cubatão), Brazil
Prior to rolling, t-up is calculated bad on expected steady-state mill behaviour. The threading process, where the strip must be successively introduced into the mill stands, is accomplished at low speed. After the threading of the last stand, the mill is then accelerated to the desired operating speed. At the end of the coil, the mill is decelerated to a low speed for the dethreading process and simultaneously it must already be t-up for the next coil.
The rolling force P is a nonlinear function of the entry thickness h in , the exit thickness h out , the entry tension σin , the exit tension σout , the entry yield stress k in , the exit yield stress k out , the coefficient of friction µ and the work roll radius R
()R µ,,k ,k ,σ,σ,h ,h F P out in out in out in P =
The entry yield stress k in and the exit yield stress k out are expresd by
()
()out 0k out in 0k in h ,h F k h ,h F k ==
The roll torque G is expresd by
()R P,µ,,k ,k ,σ,σ,h ,h F G out in out in out in G ′=
The deformed work roll radius R’ is expresd by
()trampoline
()⎥⎥⎦⎤⎢⎢⎣⎡−+=in out R R h h E πν2-14P 1R R' where νR and E R are the Poisson's Ratio and the You
ng's modulus for the work roll, respectively.
Through the stand the mass flow must balance, hence if the strip width remains constant
out out in in h V h V =
where V in is the strip entry speed and V out the exit strip speed. The exit speed depends on the forward slip f and the work roll speed V
()f 1V V out +=
()R µ,,k ,k ,σ,σ,h ,h F f out in out in out in f ′= The motor power is expresd by
R
ηηV GW W G R S = where W S is the strip width, ηR is the motor efficiency and ηG the gear efficiency.
4. COST FUNCTION AND MINIMIZATION METHOD
The cost function ud in the propod t-up generation system considers power drives, rolling forc
es and tensions as the most important variables associated to quality and productivity. The cost function is given by ()()(
)()∑∑=−=++=N 1i 1
N 1j j T i F i P J J J J where J is the total cost, J P and J F are stand i cost functions for power drives and rolling forces respectively, and N is the number of stands. J T is the cost tension function of zone j between adjacent stands.
For each pattern of thickness and tensions between stands, powers and forces are evaluated using the process model and the cost function is then calculated. The magnitudes of J P , J F and J T quickly increa when power, force and tension are out of ranges considered ideal by process engineers. The structure for J P is given by
()()()()()()()()i P n i min i max i min i max i i P i P 2P P 2P P P k J ⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛−+−=
伦敦大火The same structure is assumed for J F and J T .
There are veral methods for functions minimization applied to cold mills optimum t-up calculation. In (2) nonlinear programming is ud and in (3) a genetic algorithm is considered. Like in
(4), this work us the simplex method propod by Nelder and Mead (6).
Reductions, tensions, rolling forces, powers drives and speeds associated to the minimum of the cost function are taken as the optimum t-up for the tandem cold rolling mill.
5. RESULTS
The t-up generation system employed during normal operation conditions us the process model propod by Bland and Ford (7). Table 2 prents, for 20 coils, the mean percent error between the values of the process variables, calculated by the Bland and Ford t-up generation system and the values of the measured process variables, the later being the ba for the computation.
Table 2: Mean percent error between values calculated using the t-up generation system bad on Bland e Ford
model and corresponding measured process variables. Thickness Tension Force Speed Power
Zone 1 Fixed Fixed 8.06±32.04
Stand 1 1.39±5.52 13.45±32.43
Zone 2 0.11±0.46 -9.25±1.48 6.03±29.74
Stand 2 5.63±6.65 7.96±30.81
Zone 3 -1.34±1.13 -8.26±2.98 8.33±30.51
Stand 3 5.12±5.57 8.61±29.14
Zone 4 2.00±1.54 -6.10±8.23 4.60±28.63
Stand 4 0.04±2.28 5.39±37.57
Zone 5 0.42±1.24 Fixed 4.77±28.60
The results shows that the mill references generated by the Bland e Ford model are very clo to the data measure during the rolling of the coils, mainly for tension and force. However, differences a few percent greater can be obrved for values of stand speed and motor power. For the variables, the measured values during the rolling of the coils are bigger than the ones calculated by the system.
The propod t-up generation system was carried out in Matlab using the rolling mill process model propod by Bryant (1). To asss the performance of the propod system, values of the t-up calculated by the main system, for the same 20 arbitrarily chon coils referred in the last ction, were compared to the corresponding values calculated by the propod system. Table 3 prents the average deviation, in percent, between the two systems, taking the main system as the ba system. Table 3: Average deviation in percent between t-up calculated by two systems.
Thickness Tension Force Speed Power
Zone 1 Fixed Fixed 8.54±6.99
Stand 1 -5.52±4.78 3.45±2.61
Zone 2 -0.27±1.15 -0.85±6.76 8.83±6.61
Stand 2 1.21±5.74 4.09±2.48
Zone 3 2.31±2.54 5.00±7.04 6.13±6.58
Stand 3 1.15±7.15 3.76±3.29
Zone 4 2.38±1.12 4.45±9.04 6.01±6.40
Stand 4 3.23±7.50 9.06±12.58retarded
Zone 5 Fixed Fixed 8.54±6.99
While thickness, tension and force deviations may be accepted in the ranges shown in Table 3, that is, strip quality and process curity specifications are maintained for the ranges, some special considerations must be made with respect to speed and power.
In fact, it was obrved that the difference between the torque models for the propod and the main system is the reason for higher speed and power values in the propod system. In practice, this implies that some caution should be taken if the total power is exceeded, but since there is some power rerve in the ca of the main system calculations, no additional action was necessary for the deviations in Table 3.
6. CONCLUSION
The t-up generation system propod in this work, despite to be simpler than usual t-up generation systems, is suitable to be ud in emergency operation mode, becau it is quick, safe a
nd sufficiently accurate. Further studies have been made in order to extend the t-up generation system to the threading and tail out phas of the cold rolling mill process.
REFERENCES
Bryant
迈克尔杰克逊经典歌曲1. G.F.
“Automation of Tandem Mills”, The Iron and Steel Institute, London, 1973.
2. I.C. Ozsoy, G.E. Ruddle, A.F. Crawley
“Optimum Scheduling of a Hot Rolling Process by Nonlinear Programming”, Canadian Metallurgical Quartely, 3, 31, 1991.太原培训学校
3. D.D. Wang, A.K. Tieu, F.G. de Boer, B. Ma, W.Y.D. Yuen
“Toward a Heuristic Optimum Design of Rolling Schedules for Tandem Rolling Mills”, Engineering Applications of Artificial Intelligence, 13, 2000.
4. E. Fiebig, H. Zander
“Automation of Tandem Cold Rolling Mills”, Metallurgical Plant and Tecnology, 3, 5, 1982.
et al.
便宜英文5. K.
Sekiguchi
“The Advanced Set-Up and Control System for Dofasco’s Tandem Cold Mill”, IEEE Transactions on Industry Applications, 3, 32, 1996.
6. J.A. Nelder, R. Mead
“A Simplex Method for Function Minimization”, Computer Journal, 7, 1965.
7. D.R. Bland, H. Ford
“The Calculation of Roll Force and Torque in Cold Strip Rolling with Tensions”, Proc. Inst. Mech. Eng., 168, 1954.
