APPLICATION OF COMPUTER PROGRAMMING IN OPTIMIZATION OF TECHNOLOGICAL OBJECTIVES OF COLD ROLLING

Transcription

1 Journal Journal of Chemcal of Chemcal Technology and and Metallurgy, 50, 6, 50, 2015, 6, APPLICATION OF COMPUTER PROGRAMMING IN OPTIMIZATION OF TECHNOLOGICAL OBJECTIVES OF COLD ROLLING Abdrakhman Nazabekov 1, Vtaly Talmazan 2, Sergey Lezhnev 2, Zhuman Amanzholov 2, Аlmas Erzhanov 2 1 Rudny Industral Insttute, Rudny, Kazakhstan E-mal: nfo@r.kz 2 Karaganda State Industral Unversty, Receved 19 February 2015 Accepted 30 July 2015 Temrtau, Kazakhstan Republc avenue 30, , Temrtau, Kazakhstan E-mal: sergey_legnev@mal.ru ABSTRACT Ths artcle s devoted of optmzaton of force and power parameters of cold rollng process. Anoptmzaton of cold rollng wth the use of computer programmng to reduce defects ofcold rolled metalwas carred out. For ths purpose a computer program for calculatons of optmal modes of rollng of strp wth surface defect was developed. It allows one to calculate power parameters for a gven mode of rollng, the degree of use of the resource of plastcty of metal strps wth defect and determnaton of optmal rollng modes. In the result were obtaned graphs of curves wth optmzed values of rollng force, power and also degree of usng of plastcty resource n compare wth workshop mode. Keywords: computer programmng, optmzaton, cold rollng, surface defects. INTRODUCTION Rollng process conssts of a seres of connected unt operatons, each of whch represents a converson nto a fnshed workpece profle. It s necessary to ratonally desgn process chan, thus, durng operaton to manage to get the hghest possble qualty of the fnshed products. Contnuous rollng process has a number of features whch complcate and mpede the development of optmal processes. One of the dffcultes s that the resultng optmzaton problem requres consderaton of many factors related to each other. In ths mode, contnuous rollng largely determnes the qualty of rolled metal. Durng rollng of the strp t s very mportant to fnd the optmal regmes of rollng to produce qualty steel [1]. The essence of optmzaton from a mathematcal pont of vew s the followng: t s requred to fnd such process control functons to mplement under gven constrants extremum of so-called objectve functon. The essence of optmzaton from a technologcal pont of vew s the followng: t s requred to fnd a mode of rollng process that for gven technologcal constrants to acheve the best results. By optmzng we understand some common problem wth a common goal, and also assume the formulaton of the objectve functon and the study of solutons provdng the extremum of the objectve functon. There are many methods for optmal control of technologcal processes. Optmzaton problem s solved by methods of rollng process of lnear and nonlnear programmng, as well as by means of dynamc programmng. The most unversal method for optmal control n relaton to producton problems s the method of dynamc programmng [2]. Dynamc programmng s a mathematcal tool that allows mplementng the optmal schedulng of multstage control processes and the processes that depend on tme. When solvng complex optmzaton problems t s often useful to make a decson mmedately, but gradually, step by step, so that the decson s dvded nto several stages. The fundamental bass of dynamc 638

2 Abdrakhman Nazabekov, Vtaly Talmazan, Sergey Lezhnev, Zhuman Amanzholov, Аlmas Erzhanov programmng s the prncple of optmalty, whch conssts n fndng the condtonal optmal controls from each state at ths stage n the fnal state. Usng the prncple of optmalty s to guarantee that the soluton that combnes the best decsons at certan stages would be the best when consderng the whole process [3]. Dynamc programmng method s characterzed by the followng: 1) step or gradual movement (complex problem s reduced to the successve soluton of the set of smpler problems);2) to apply dynamc programmng method t s necessary to obtan a recurrence relaton so that a new state at the end of phase unquely calculated on the bass of the state n the early stage and management at ths stage, regardless of how soluton s found; 3) the selected optmalty crteron must have the property of addtvty,.e., for the entre process, t must consst of values obtaned at varous stages (ths condton greatly restrcts the possblty of usng dynamc programmng or can lead to consderable complcaton of the problem when tryng t for addtvty). When used correctly, the method of dynamc programmng allows vewng all the necessary control channels and fndng the true optmal soluton. The method features wth a specfc targeted search, rejectng unwanted control path, whch saves computaton tme compared to blnd search. However, the complexty of the dynamc programmng method s to obtan recurrence relatons, whch would satsfy the condtons of the problem and lead to the desred result. The optmzaton problem s solved under certan constrants defned by the desgn parameters of the rollng mll and rollng technology. These are vald values of force and moment of rollng, the lmt values of rollng power and other lmts of the passages at the relatve compresson, the rato of specfc tenson to the yeld stress of the materal, the coeffcent of frcton and other. Deformaton zone durng rollng s characterzed by the presence of forward slp and backward slp zones. For backward slp zones n the deformaton zone s characterzed as follows: the vector of lnear speed of the roll s greater than the velocty vector of the strp; so n backward slp zones stress frcton facng forward n the course of rollng. In the forward slp zone stress frcton s drected aganst a course of rollng. In ths regard, the forward slp zone of the deformaton zone can be a process of defect formaton due to frcton force drected aganst rollng stroke caused by the velocty ncrease of the metal relatve to the speed of rollng rolls. Ths phenomenon s partcularly mportant durng rollng n the last rollng stands, n whch the fnal formaton of the strp surface occurs [4]. EXPERIMENTAL To reduce the defect formaton for the optmzaton parameter we adopted the total length of the forward slp zone for the whole rollng cycle. The whole rollng cycle s dvded nto fve stages (smlar to contnuous fve stand cold rollng mll 1700 at JSC ArcelorMttal Temrtau ). The program s structured so that the endponts of each of the prevous stand are the ntal parameters of each subsequent. Surface defects are a knd of stress concentrators n the places of whch occurrence, durng rollng an open tearcan be formed, and, as a consequence, ths can lead to the strp break, as well as the ntegrty of the workng surface of rolls barrel. Control of the degree of use of the resource of plastcty of metal n the zone of surface defects wll ncrease ther rollng out, reduce strp burst durng rollng, and as a consequence, mprove the qualty of steel products. As objectve functon durng optmzaton of rollng total length of the forward slp zone for all the passages of deformaton under the exstng restrctonscan be consdered : { ( n) } n l2 = mn l l (1) 2 mn = 1 An mportant condton s consdered to be preventon of excess of plastcty resource usng degree 1.0 [5]. In vew of ths system major lmtatons look as follows (consderng [6, 7]): [ ] [ ] a C µ, P < P, N < N, 0, 02 µ 0,15, 0, 2R0.2 q 0 1 0,5 R0.2, hmn h hmax, W > 0, q1 n 0,1 R0.2 n, ψ < 1, 0. (2) where: α С - capture angle, rad; [P], [N] - maxmum allowable value of force and power durng rollng correspondngly, kn, kw; μ - frcton coeffcent; q 1 - forward specfc tenson, MPa; R yeld strength of the metal, MPa; h - strp thckness, mm; ψ Σ - total plastcty resource utlzaton degree; 639

3 Journal of Chemcal Technology and Metallurgy, 50, 6, 2015 W - plastcty resource stocks; - passage number; n - quantty of passages. In general, the man functons can be wrtten as follows: P = µ ( pave, R0.2, ε, ldc, q0, q1, µ, R), N = µ ( M, υ, R), (3) W = µλψ (,, δ h, I δ,) where: P- rollng force, kn; N - rollng power, kw; M-rollng moment, kn m; pave- average specfc pressure, MPa; ε - relatve reducton, %; R - radus of the rolls, mm; υ - rollng speed, ms -1 ; λ - draw; ψ - plastcty resource utlzaton degree; δ /h - relatve depth of the surface defect; I δ - ntensty of rollng out of surface defect. Wth the use of [8-9] we developed a computer program for calculatng the optmal regmes of rollng strp wth surface defects. The program s wrtten n the programmng language «Delph». The program allows performng the followng tasks: calculaton of power parameters for a gven rollng mode; calculaton of the degree of use of the resource of plastcty of metal strps wth defect; determnaton of optmal rollng modes, provdng mproved surface fnsh and ncrease rollng out of strp surface defects, and consequently decrease burst of strps durng rollng. Problems are solved under certan constrants: desgn parameters of the rollng mll and rollng technology requrements. These are vald values of forces and power of rollng, capture angle relatons of front and rear specfc tensons to the yeld pont of the materal, based on the condtons for the effcent constructon of the mll. Also lmts on the values of the coeffcent of frcton, the front and rear specfc tensons, relatve reducton per passareset. The program has three control parameters, wth whose help there s a focused sortng of dfferent process states. Control parameters are compresson, frcton and front resstvty tenson. After nput of ntaldata there occurs avaraton ofcontrol parameterswthsmultaneous calculaton of DURPandpower parameters ofrollng. As 640 the three control parameters are accepted:μ frcton coeffcent; q 1 front tenson (MPa); h strp thckness (mm). Before the start of varaton process defne the boundares of varaton of selected parameters control. Varaton boundares are defned on the bass of the normal condtons of the rollng process and consttute: 1) 0.02 μ 0.15 wth teratonstep 0.01; 2) 0.2 R 0.20 q R 0.2 wth teraton step 1; 3) 0.97 h -1 h 0.6 h -1 wth teraton step A smplfed block dagram of the program s shown n Fg. 1. The varaton conssts of the followng: 1) at the begnnng control parameters are assgned to the ntal boundares of varaton and calculaton occurs; 2) further the value of one of the control parameters s changed to the teraton step, the values of the other two control parameters are not changed (control parameter changng occurs untl t reaches a fnal value lmt); 3) after the entre boundary has been calculated, there s a change of the next control parameter values on the step teraton (ths happens as long asall the borders of all control settngs calculated). Fg. 1. A smplfed block dagram of the rollng optmzaton program.

4 Abdrakhman Nazabekov, Vtaly Talmazan, Sergey Lezhnev, Zhuman Amanzholov, Аlmas Erzhanov In the forward slp zone of the deformaton zone could occur a process of defect formaton due to frcton forces drected aganst the rollng stroke and caused by an ncrease of the speed of the metal relatve to the speed of rolls. The system of constrants s necessary to ensure the normal rollng process and represents a lmtaton of the capture ablty, lmtatonson strength, power of the motor, and a lmt on the degree of use of the resource of plastcty. It s mportant that the total degree ofthe use of the resource of plastcty of metal does not exceed unty. Lmtatons system elmnates optons that exceed the permssble requrements. Next, when the entre set of solutons obtaned, the program selects a mode of rollng, whch provdes the smallest total length of the forward slp zone n the deformaton zone n the last stand for the entre rollng perod. Wth the results of regresson analyss of the data we obtaned a relatonshp equaton of compresson, tenson and frcton coeffcent (at R2 = 0.99): q ε a a = + + a µ q0, (4) where: a 0, a 1, a 2 - constants dependng on the rolled metal and shapes; q 0 - specfc back tenson, MPa; q 1 - specfc front tenson, MPa; μ - contact frcton coeffcent; -stand number. Appontment of rollng mode accordng to equaton (4) provdes a rollng process wthout exceedng the allowable values of energy-power parameters and degree of use of the resource of metal plastcty, and also reduces probablty of defect formaton n the deformaton zone. forward slp zone length to the fnal stand, t s because n ths stand the fnal formaton of the strp surfaceoccurs. Power parameters of rollng optmzed mode do not exceed the maxmum permssble values. Comparson of workshop and optmzed modes s shown n Fgs Tenson durng rollng on workshop mode s n the range of 0.2 R 0.2, ncreasng the tenson to 0,275 R 0.2 causes a slght lowerng of the rollng force (Fg. 2). Fg. 2. Rollng force. Fg. 3. Rollng power. RESULTS AND DISCUSSION In condtons of JSC ArcelorMttal Temrtau most often surface defects occur on a thn profle wth a thckness of 0.7 mm. Usng developed program has completed the calculaton of compresson optmzaton modes at mll 1700 of JSC ArcelorMttal Temrtau of profle mm made of steel AISI The results obtaned by computng are optmzed versons of compresson and tenson modes, provdng specfed profle rollng and satsfy gven constrants. Optmzaton of rollng s calculated consderng the mnmzaton of Fg. 4. Summary of the degree of use of the resource of plastcty. 641

5 Journal of Chemcal Technology and Metallurgy, 50, 6, 2015 Redstrbuton of compresson n stands leads to some ncrease of the rollng power n the thrd stand (Fg. 3). Optmzed rollng mode characterzng by more ntensve use of the resource of plastcty, whle there s no complete exhauston of t (Fg. 4). More ntensve use of plastcty resource, on the one hand postvely affects rollng out of surface defects, on the other hand there s the danger of the plastcty resource exhauston, whch can lead to the destructon of the strp n the deformaton. At last stand the fnal formaton of the strp surface occurs, hence, reducng the length of forward slp zone has a postve mpact on reducng the defect formaton durng rollng (Fg. 5). CONCLUSIONS Fg. 5. Forward slp zone length. After optmzaton of crteron selectng, determnng the technologcal and mathematcal formulaton of the optmzaton problem and the formulaton of restrctons we proposed an optmzaton program of cold rollng. An equaton of the relatonshp of compresson, tenson and frcton coeffcent was obtaned. From the resultng equaton t s mpled that an ncrease n the total relatve reducton ε frcton coeffcent and front specfc tenson q 1 current relatve depth of defect δ / h s reducng,.е. defect f rollng out. Reverse effect on δ / h provdng back tenson q 0. The ncrease of the ntal relatve depth of the defect δ 0 / h0 naturally ncreases δ / h, thus the rsk of defect development on tear rses. The purpose of the rollng mode accordng to the obtaned equaton provdes the rollng process wthout exceedng the allowable values of the power param- eters and the degree of use of the resource of plastcty. An optmzaton of modes of cold rollng mll 1700 was conducted. Optmzaton of the rollng mode was calculated by mnmzng the length of the forward slp zone of the last stand, ths s due to the fact that n ths stand the fnal formaton of the strp surface occurs. Comparson of workshop and optmzed modes showed that the power parameters of the rollng do not exceed the maxmum permssble values. Reducng the length of the forward slp zone of the last stand has a postve effect on reducng the defects formaton, because durng fnal formaton of the strp surface n ths zone stress of frcton s drected aganst the course of rollng, so the removal from the deformaton zone of the products of decomposton and deteroraton s dffcult. The results of the optmzaton calculatons showed that ncreasng the front tenson and relatve compresson sgnfcantly reduce rollng force and rollng power, except for stand No. 3.It should be noted that DURP ncreases. In the fourth and ffth stands and workshop and optmzed modes DURP do not reach the crtcal value of 1.0. Wth regard to the target functon, accordng to optmzed mode the length of the forward slp zone l 2 n the frst two stands s hgher than the workshop varant (for the frst stand: shop opt l 2 = 6.7 mm and l 2 = 7.37 mm; for the second shop opt stand: l 2 = 4.37 mm and l 2 = 4.79 mm), n the subsequent thrd and fourth stands close by value (4.4 mm and 4.5 mm). The most mportant pont n the optmzaton of the rollng mode s consdered a sharp decrease of the length of the forward slp zone n the ffth stand up to the value of mm (at workshop mode the value of the forward slp zone n the ffth stand s 5.29 mm). Thus, t s possble to consder that optmzaton of the rollng mode s to reduce the defect formaton durng rollng approprate. REFERENCES 1. А.N. Skorohodov, P.I. Poluhn, B.M. Ilyukovch, B.Е.Haykn, N.Е. Skorohodov, Optmzaton of rollng producton, Metallurgy, 1983, p. 432, (n Russan). 2. G.L. Hmch, М.B.Tsalyuk, Optmzaton of modes of cold rollng on a dgtal computer, Metallurgy, 1973, p. 256, (n Russan). 642

6 Abdrakhman Nazabekov, Vtaly Talmazan, Sergey Lezhnev, Zhuman Amanzholov, Аlmas Erzhanov 3. S. Roberts, Dynamc programmng n the processes of chemcal technology and management methods, Mr, 1965, p. 488, (n Russan). 4. E.А. Garber, E.N. Shebants, Е.V. Dlgensky, О.А. Pobegalo, N.P. Medvedev, Optmzaton of the structure of the deformaton zone on the mll 1700, Steel, 2007, 1, 48-50, (n Russan). 5. А.А. Bogatov,The mechancal propertes and fracture models of metals, SEIHPEUSТU-UPI, 2002, p. 329, (n Russan). 6. А.P. Grudev, Theory of rollng, Intermet engneerng, 2001, p. 280, (n Russan). 7. А.А. Korolev, Desgn and calculaton of the rollng mlls machnery, Metallurgy, 1985, p. 376, (n Russan). 8. Yu.N. Kuznetsov, V.I. Kuzubov, А.B. Voloschenko, Mathematcal programmng, Hghschool, 1980, p. 300, (n Russan). 9. I.L. Akulch, Mathematcal programmng n examples and problems, Hghschool, 1986, p. 319, (n Russan). 643