This work shows the results of theoretical analysis of asymmetric rolling process of plates in the finishing mill of plate rolling. Its aim was to determine the influence of asymmetry velocity of working rolls on decrease of unit pressure of metal on the rolls. The lower value of the unit pressure will reduce the elastic deflection of the finishing stand and improve the cross-section shape of plate. Three-dimensional simulation of asymmetric hot rolling of S355J2G3 steel plates was done with the aid of FORGE 2008® software. The tensor polynomial interpolation was used for comparing the values of the unit pressure obtaining from symmetric and asymmetric rolling.Rad daje rezultate teorijske analize asimetričnog valjanja platine u završnom stanu. Cilj je odrediti utjecaj asimetrične brzine radnih valjaka na umanjenje jediničnog pritiska metala na valjke. Niža vrijednost jediničnog pritiska smanjiti će elastičnu deformaciju završnog stana. i poboljšati oblik presjeka platine. Trodimenzionalna simulacija asimetričnog vrućeg valjanja S355J2G3 čeličnih platina izvedena je pomoću FORGE 2008® softvera. Polinomni tenzor interpolacije rabljen je za usporedbu vrijednosti jediničnog pritiska dobijenog sa simetričnim I nesimetričnim valjanjem

A. Kawalek

H. Dyja

M. Knapinski

S. Mroz

English

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A. KAWALEK, H. DYJA, S. MROZ, M. KNAPINSKIEFFECT OF PLATE ASYMMETRIC ROLLING PARAMETERSON THE CHANGE OF THE TOTAL UNIT PRESSURE OF ROLLReceived – Prispjelo: 2010-05-26Accepted – Prihva}eno: 2010-11-24Original scientific paper – Izvorni znanstveni radINTRODUCTIONPlate purchasers constantly increase their demandson the mechanical and plastic properties and the dimen-sional deviations of plates. In order to enhance the qual-ity of plates, various solutions are implemented, includ-ing normalizing rolling, rolling with accelerated coolingfollowing the rolling process, as well as new roll gapcontrol systems (such as hydraulic rolls positioning, orthe working roll bending system). The implementationof those systems takes place at the cost of increasedloads being applied to rolling stands and working tools.Another competitive solution is the implementation ofasymmetric rolling which involves making an inten-tional change to the stress and strain state in the roll gapand, unlike the former systems, does not increase loadson the drives, but quite the opposite – it causes a reduc-tion of the total roll separating forces 1-4.INITIAL CONDITIONS USED FORNUMERICAL MODELLINGThe material used for tests was steel of theS355J2G3 grade, whose chemical composition is givenin Table 1.Table 1 Chemical composition of the steel S355J2G3 /mas. %C Mn Si P S0,15 1,36 0,33 0,017 0,03Cr Ni Mo Cu Al0,05 0,089 0,03 0,23 0,030To determine the actual work-hardening curves forthis steel for the conditions of preset deformations andtemperatures used in the actual plate rolling process,tests were carried out using the Gleeble 3800 device.Then, the work-hardening curves determined for thissteel grade were implemented into the material databaseof the FORGE 2008 program 5.1000 mm-diameter working rolls and a constantlower working roll rotational speed of n = 50 rpm wereassumed for the tests. The asymmetric rolling processwas introduced by changing the rotational speed of theupper roll, vg, to be less than that of the lower roll, vd.The range of variation of the roll rotational speed factor,av = vd/vg, was 1,01 ÷ 1,15. A strip shape factor of h0/D= 0,05 ÷ 0,014 was assumed. The range of rolling reduc-tions applied was  = 0,08 ÷ 0,50.The rolled strip temperature was changed, depend-ing on the initial height, h0:h0=50 mm, the rolling temperature T=950 °C,METALURGIJA 50 (2011) 3, 163-166 163This work shows the results of theoretical analysis of asymmetric rolling process of plates in the finishing mill ofplate rolling. Its aim was to determine the influence of asymmetry velocity of working rolls on decrease of unitpressure of metal on the rolls. The lower value of the unit pressure will reduce the elastic deflection of the fini-shing stand and improve the cross-section shape of plate. Three-dimensional simulation of asymmetric hot rol-ling of S355J2G3 steel plates was done with the aid of FORGE 2008® software. The tensor polynomialinterpolation was used for comparing the values of the unit pressure obtaining from symmetric and asymme-tric rolling.Key words: numerical modelling plate, asymmetric rolling, pressure of rollU~inak parametara asimetri~nog valjanja platine na promjene ukupnog pritiska valjka. Rad dajerezultate teorijske analize asimetri~nog valjanja platine u zavr{nom stanu. Cilj je odrediti utjecaj asimetri~nebrzine radnih valjaka na umanjenje jedini~nog pritiska metala na valjke. Ni`a vrijednost jedini~nog pritiskasmanjiti }e elasti~nu deformaciju zavr{nog stana. i pobolj{ati oblik presjeka platine. Trodimenzionalna simula-cija asimetri~nog vru}eg valjanja S355J2G3 ~eli~nih platina izvedena je pomo}u FORGE 2008® softvera. Poli-nomni tenzor interpolacije rabljen je za usporedbu vrijednosti jedini~nog pritiska dobijenog sa simetri~nim inesimetri~nim valjanjem.Klju~ne rije~i: numeri~ko modeliranje platina,asimetri~no valjanje, pritisak valjkaISSN 0543-5846METABK 50(3) 163-167 (2011)UDC – UDK 621.771:519.61/.64=111A. Kawalek, H. Dyja, S. Mroz, M. Knapinski, Faculty of Materials Pro-cessing Technology and Applied Physics, Czestochowa University ofTechnology, Czestochowa, Polandh0=35 mm, the rolling temperature T=900 °C,h0=27 mm, the rolling temperature T=950 °C,h0=22 mm, the rolling temperature T=890 °C,h0=18 mm, the rolling temperature T=880 °C,h0=16 mm, the rolling temperature T=860 °C,h0=14 mm, the rolling temperature T=850 °C,in the temperature intervals applicable to normalizingrolling.RESULTS AND DISSCUSIONFigures 1÷3 show sample results of the tests of theeffect of the working roll peripheral speed asymmetryfactor av, being variable in the range of 1,01 ÷ 1,15, andthe relative rolling reduction  = 0,08 ÷ 0,50, for the in-vestigated feedstock thickness range (h0/D = 0,05 ÷0,014), on the magnitude of unit pressures, pm, kN/mm.The data in Figures 1÷3 indicate that for the values ofthe strip shape factor h0/D and the applied rolling reduc-tion , investigated in this work, the effect of the appliedworking roll peripheral speed asymmetry factor on thevariation in the magnitude of unit pressures (as com-puted per unit width of rolled strip) is different and de-pends on the remaining parameters: the feedstock thick-ness and the relative deformation used.For feedstock of a thickness of h0 = 35 mm (h0/D =0,35), no decrease in unit pressure values occurred forthe entire range of av factors tested, when a rolling re-duction of  = 0,08 was used; the same was true for roll-ing reductions of  = 0,15 ÷ 0,30 and for small presetvalues of av = 1,01 ÷ 1,03 (Figure 1). However, alreadyfor this deformation range, introducing greater rollingprocess asymmetry (av > 1,08) resulted in a fairly large(approx. 7 ÷ 10 %) decrease in unit pressures.When using the asymmetric process during the rollingof feedstock of a thickness of h0 = 22 mm (h0/D = 0,022),practically for the entire range of relative rolling reduc-tions and speed asymmetry factors applied (with few ex-ceptions, where av < 1,03 and  = 0,20 ÷ 0,25), a decreasein the unit pressures pœr was noted, as large as by approx.20 % for  = 0,15 and av = 115 (Figure 2). Even larger de-creases in pressure force values – exceeding 27 % (for  =0,15 and av = 1,15) – were observed for the asymmetricrolling of 16 mm-thick feedstock (h0/D = 0,016). For thisfeedstock, only when applying the least rolling reductionof  = 0,08 and the least speed asymmetry factors (av =1,01 ÷ 1,03), were not any changes (decrease) in pressureforce observed (Figure 3). The greatest drops in pressureforce value occurred upon introducing asymmetry, whenthe value of av > 1,05.For the determination of the roll separating forcevariation as against the symmetric process for thefeedstock thickness range investigated, tensor polyno-mial interpolation was used 6.The idea behind this method is to search for the coef-ficients of a multi-variable interpo-lating polynomial ofthe grade depending on the number of variables and thenumber of interpolated points. The tensor polynomialinterpolation method yields only one solution for a se-lected space of measurement points. It has been foundfrom the investigation that the following parametershave the greatest influ-ence on the roll separating forcein the asym-metric rolling process: relative rollingredu-ction, the working roll rotational speed asym-metry factor, and the strip shape ratio. Therefore, thetensor polynomial interpolation of strip curvature, oc-curring as the result of the applied rolling process asym-metry, was performed for three independent variables.For the three-variable case considered in the work:– X1 = h0/D (strip shape factor),164 METALURGIJA 50 (2011) 3, 163-166A. KAWALEK et al.: EFFECT OF PLATE ASYMMETRIC ROLLING PARAMETERS ON THE CHANGE OF THE TOTAL...Figure 1 Effect of the asymmetry factor av on the magni-tude of the average pressure force pm for diffe-rent relative rolling reduction values  and aconstant strip shape factor of h0/D = 0,035Figure 2 Effect of the asymmetry factor av on the magni-tude of the average pressure force pm for diffe-rent relative rolling reduction values  and aconstant strip shape factor of h0/D = 0,022Figure 3 Effect of the asymmetry factor av on the magni-tude of the average pressure force pm for diffe-rent relative rolling reduction values  and aconstant strip shape factor of h0/D = 0,016– X2 = av (working roll peripheral speed asymmetryfactor),– X3 =  (relative rolling reduction),in the following ranges:X10 = 0,014; X11 = 0,016; X12 = 0,018; X13 = 0,022;X14 = 0,027; X15 = 0,035; X16 = 0,050,for the shape ratio;X20 = 1,01; X21 = 1,02; X22 = 1,03; X23 = 1,05; X24= 1,08; X25 = 1,10; X26 = 1,15,for the working roll peripheral speed asymmetry factor;and X30 = 0,08; X31 = 0,15; X32 = 0,20; X33 = 0,25;X34 = 0,30; X35 = 0,40; X36 = 0,50,for the relative rolling reduction.The interpolation polynomial for the relative changeof roll separating force as against the symmetric processhas the following form: = W(X1, X2, X3) = a000 + a100X1 + +a010X2 + + a001X3+………….+ a666X16X26X36where: the coefficients a000, a100, a010, a001,..a666 dependboth on the measured values w000, w100, w010, w001,...w666of roll separating force, and on the values X10,..X36 ofthe assumed ranges.Sample computation results are shown in Figures4÷6.The data shown in Figures 4 ÷ 6 indicate that thegreatest decrease in the roll separating force occurredfor the strip with the initial thickness of h0 = 14 ÷ 22 mmfor rolling reductions from 8 to 30 % and asymmetryfactors of 1,10 and 1,15, and amounted to 27 % max.For strips with a thickness from 27 to 35 mm, this de-crease was slightly smaller for rolling reductions from15 to 40 % and asymmetry factors of 1,10 and 1,15, andwas approx 12 %.SUMMARY AND CONCLUSIONSFrom the theoretical studies carried out, the follow-ing conclusions have been drawn:– by introducing the asymmetric plate rolling pro-cess through differentiating working roll periph-eral speeds, depending on the asymmetry factorused, the magnitude of the total roll separatingforce can be reduced by up to 27 %;– the reduction of the total roll separating forces de-creases the elastic deflection of the rolling standparts, which in turn may contribute to a reductionof the required magnitudes of working roll bend-ing forces;– owing to the reduced elastic deflection of theworking rolls and the action of the complementarytension and back tension stresses in the roll gap,finished plate with smaller dimensional deviationson its width and length can be obtained at lowermagnitudes of the total roll separating forces dur-ing the normalizing rolling of plates.REFERENCES1 Dyja H., Sa³ganik A. M., Piesin A. M., Kawa³ek A.,Asymetryczne walcowanie blach cienkich Teoria, technolo-gia i nowe rozwi¹zania, Wydawnictwo Politechniki Czêsto-chowskiej, Seria Monografie nr 137 (2008).METALURGIJA 50 (2011) 3, 163-166 165A. KAWALEK et al.: EFFECT OF PLATE ASYMMETRIC ROLLING PARAMETERS ON THE CHANGE OF THE TOTAL...Figure 4 Relative change of roll separating force compa-red to the symmetric rolling process as a fun-ction of rolling reduction and the asymmetryfactor for the initial thickness of h0 = 35 mm, asdetermined from the interpolation of the testFigure 5 Relative change of roll separating force compa-red to the symmetric rolling process as a fun-ction of rolling reduction and the asymmetryfactor for the initial thickness of h0 = 22 mm, asdetermined from the interpolation of the testresultsFigure 6 Relative change of roll separating force compa-red to the symmetric rolling process as a fun-ction of rolling reduction and the asymmetryfactor for the initial thickness of h0 = 16 mm, asdetermined from the interpolation of the test2 Kawa³ek A., Hutnik Wiadomoœci Hutnicze, 6 (2006),p. 266-270.3 Tian Y., Guo Y., Wang Z, Wang G., Journal of Iron andSteel Research International 16 (4), (2009), p. 22-26.4 Farè S., Vedani M., Angella, G, Materials Science Forum604-605, (2009) p. 77-85.5 Forge3® Reference Guide Release 6.2, Sophia-Antipolis,November 2002.6 Biernat G., Ciekot A., Prace Naukowe Instytutu Matemat-yki i Informatyki Politechniki Czêstochowskiej, Czêstocho-wa (2008), p. 5 – 9.Note: The responsible translator for English language is Czes³awGrochowina, Czestochowa, Poland.166 METALURGIJA 50 (2011) 3, 163-166A. KAWALEK et al.: EFFECT OF PLATE ASYMMETRIC ROLLING PARAMETERS ON THE CHANGE OF THE TOTAL...

Učinak parametara asimetričnog valjanja platine na promjene ukupnog pritiska valjka

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