A NEW MATHEMATICAL MODEL DETERMINATING THE FORMING FACTOR

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1 Acta Metallurgica Slovaca,, 6, 4 ( ) 477 A NEW MATHEMATICAL MODEL DETERMINATING THE FORMING FACTOR Rusz S., Schinler I., Kubina T., Bořuta J. VŠB Technical University of Ostrava, Institute of Moelling an Control of Foring Processes, 7. listopau 5, Ostrava, Czech Republic, stanislav.rusz.fi@vsb.cz, ivo.schinler@vsb.cz, toas.kubina@vsb.cz VÍTKOVICE Research an Developent Lt., Pohraniční 693/3, 76 Ostrava - Vítkovice, Czech Republic, josef.boruta@vitkovice.cz, NOVÝ MATEMATICKÝ MODEL URČUJÍCÍ TVÁŘECÍ FAKTOR Rusz S., Schinler I., Kubina T., Bořuta J. VŠB Technická univerzita Ostrava, Ústav oelování a řízení tvářecích procesů, 7. listopau 5, Ostrava, Česká republika, stanislav.rusz.fi@vsb.cz, ivo.schinler@vsb.cz, toas.kubina@vsb.cz VÍTKOVICE Výzku a vývoj, spol. s r.o., Pohraniční 693/3, 76 Ostrava - Vítkovice, Česká republika, josef.boruta@vitkovice.cz Abstrakt Tvářecí faktor Q Fv charakterizuje vliv střeního napětí působícího na stykové ploše ezi válcovaný kove a pracovníi válci v pásu eforace a ve sěru válcování na velikost válcovací síly. Tvářecí faktor Q Fv uožňuje převést honotu přirozeného eforačního oporu σ e, získanou napříkla poocí plastoetrického ěření, na válcovací sílu a preikovat zatížení při vlastní tváření. Všeobecně lze konstatovat, že honota Q Fv je závislá na tvaru a geoetrii provalku ve válcovací ezeře, na eforačních poínkách a poínkách tření ezi provalke a pracovníi válci. Třecí poínky ve válcovací ezeře jsou ovlivňovány rsností a tvrostí pracovních válců, povrche zokujeného povrchu provalku, teplotou provalku, rychlostí válcování a alšíi faktory. U vyhonocování pro konkrétní válcovací stolici přepoklááe, že honota součinitele tření µ vs je v průběhu válcování konstantní a lze ji zanést přío o honoty válcovacího faktoru Q Fv. Pro tento experient bylo nutné provést v plastoetrické laboratoři Výzkuu a vývoje, Vítkovice spol. s r. o. spojité krutové zkoušky a válcování plochých vzorků na laboratorní válcovací stolici TANDEM v Ústavu oelování a řízení tvářecích procesů. Srovnání takto získaných střeních eforačních oporů ohl být ovozen nový oel tvářecího faktoru na válcovací stolici s uvažování geoetrických paraetrů válcování. Byly zkouány vě uhlíkové oceli le nory ČSN 53, resp. 4 a vě korozivzorné oceli ČSN 7 5, resp Nový oel tvářecího faktoru byl ovozen v závislosti na široké rozsahu geoetrických poěrů l / h. Abstract The foring factor Q Fv highlights influence of the ean stress exerting on the contact surface between the rolle etal an work rolls in the roll bite an in the rolling irection on the roll force size. The foring factor Q Fv enables conversion of the equivalent stress σ e value, obtaine e.g. by eans of plastoetric easureents, to the roll force an preict loa in foring. Generally, the Q Fv value is influence by shape an geoetry of the rolling stock in the roll gap, eforation conitions an friction conitions between the rolling stock an work rolls. Friction conitions are affecte by roughness an harness of work rolls, scale surface of the

2 Acta Metallurgica Slovaca,, 6, 4 ( ) 478 rolling stock, teperature of the rolling stock, rolling spee an other factors. In evaluation for a particular ill stan we suppose that a value of the friction coefficient µ vs is constant in the course of the rolling process an ay be irectly integrate into the foring factor Q Fv. For eterination of the foring factor it was necessary to carry out continuous torsion tests in the plastoetric laboratory of Research an Developent of Vítkovice an rolling of flat saples in the laboratory rolling ill Tane in the Institute of Moelling an Controlling of Foring Processes. Coparing the obtaine values of ean stress, foring factor for the applie rolling ill coul be evelope as a function of geoetrical paraeters of rolling. The experient was carrie out with saples fro steel graes ČSN 53, 4, 7 53 an 7 5. A new oel for the foring factor was evelope in epenence on a wie range of values of aspect ratio l /. h Keywors: hot flat rolling, foring factor, torsion test, ean equivalent stress, rolling force. Introuction Deforation resistance is efine like internal resistance of the aterial, acting against effect of external forces which try to bring about a shape change of the given boy. The given stress can be oriente towars the contact surface in both noral an tangential irection. As this stress varies along the whole contact surface, so calle ean eforation resistance is eterine for power an force calculations. The ean eforation resistance σ [MPa] ay be expresse as a prouct of the ean equivalent stress σ e [MPa] an the foring factor Q F : σ = σ Q () e F The equivalent stress σ e is conventionally efine like resistance of the etal against its eforation in uniaxial tension state an onotonous strain. So for the given aterial it is a function of theroynaic factors [] ( T, ε, & ε ) σ e = f () where T [K] teperature, ε [-] strain size an ε& [s - ] strain rate, an further it epens on etallurgical factors (cheical coposition, structural state, grain size). During noral (conventional) foring operations - e.g. in rolling - the fore etal is efore by a variable reuction size with variable strain rate an often also with variable foring teperature which eans that various values of the local equivalent stress occur in each place of the contact surface. However, knowlege of the resulting effect, i.e. of ean equivalent stress, is require for obtaining force conitions. The ean equivalent stress is efine as follows: e σ e = σ e ( e) e (3) e The ean equivalent stress represents eforation behaviour uring the whole course of raught with size of e.

3 Acta Metallurgica Slovaca,, 6, 4 ( ) 479. Materials an experiental ethoics. eterination of equivalent stress by torsion test The hot torsion test belongs to ost use ethos of eterination of ean equivalent stress an forability of steels. Plastic properties of the aterial are euce fro a nuber of twists of the test bar leaing to rupture, echanical properties are euce fro the torque. The torsion test has avantages against other forability tests. It akes it possible to reach extree egrees of eforation, with exclusion of an influence of the external friction. A wie use of this test is also beneficial. Torsion test speciens have a cylinrical shape, one en is clape in a fixe jaw, the other in a rotating jaw. The torque is etecte fro the fixe jaw. The rotary jaw is in longituinal irection of testing either shiftable or firly grippe. Requireents for investigation of etallurgical/physical processes in plastic eforation or siulation of foring processes cause increase eans on accuracy an stability of testing paraeters an, above all, on control of processes in tie. The high sensitivity to plastic properties enables use of the torsion test also for steels with high forability, where tension, ipact or copression tests o not provie require results. The saple shape for the torsion test is illustrate in Fig.. Fig. Shape an iensions of saples use for hot torsion tests. In collaboration with the plastoetric laboratory at Vítkovice an original oel for escription of equivalent stress σ e [MPa] of steel in hot foring was erive, taking into consieration ynaic softening [, 3]. F e D B T σ e = A e exp B e& exp( G T ) (4) e p where e - true strain [-], e p - strain to peak [-], - strain rate [s e& - ], T - teperature [K], A, B, D, F, G - aterial constants. The ter e B represents harening, the exponential ter that inclues variables e an e p reflects ynaic softening processes (ost frequently recrystallization). The eforation teperature influences the eforation resistance value twice. The irect teperature effect is expresse in the ter exp(-gt). The T-value appears also in the strain rate ter because strain rate influences the s-value ore arkely at high teperatures. The experient was carrie out with saples fro steel graes ČSN 53, 4, 7 53 an 7 5, cheical coposition of which is given in Tab.. For each of these

4 Acta Metallurgica Slovaca,, 6, 4 ( ) 48 aterials a oel of equivalent stress in the expression accoring to relation (4) was erive, base on continuous torsion tests. Fro these torsion tests values of ean equivalent stress σ e-t ay be calculate by integration an then copare with values of ean eforation resistance σ -r, obtaine by rolling in analogous conitions. Table Cheical analysis of the investigate steels in wt. % ocel ČSN C Mn Si P S Cr Ni Mo V Cu Al 53,6,8,,5,4,6, - -,8,3 4,36,63,,9,6,5, - -,9, 7 53,5,4,79,3,5 4,87,,,6,7,4 7 5,,9,65,3, 9,98,4,37,5,5,4. Rolling in Tane ill Flat saples were rolle with a various reuction size at various foring teperatures. The initial height of iniviual saples varie in the range of 4-3. For reaching of a wie range of the aspect ratio l /h, height reuctions in the range of 5 % were realize, accoring to power possibilities of the laboratory ill TANDEM [4]. The aspect ratio l /h inclues roll geoetry an ajustent of the roll gap an ay be eterine as follows: l h R ( h h ) = (5) h + h where R - roll raius [], h - initial height [], h - height after rolling []. Each saple was easure (height h, with b ) an heate in an electric resistance furnace to a foring teperature (85 to C). Heate saples were ieiately after ischarging the furnace rolle in one pass in stan A of the laboratory ill Tane. Roll forces an the actual spee of roll rotation were coputer-registere. After each pass also iensions of the rolling stock were easure. In case of the carbon steel rolle at high teperatures a loss of scale was copensate by ecrease in initial size of the saple. For higher stress values the elastic flattening of work rolls has to be taken into account. This phenoenon results in the fact that the raius of roll on the contact surface will be enlarge fro R to R an the value of the length of contact l [] will be enlarge to l. In hot rolling the ipact of flattening is very high. For eterination of the roll raius the roll flattening was consiere accoring to forula [5] (,7 ) 6 R = R + π 7 b F ( ) v h h where F v roll force [N], R roll raius [], b ean with of the rolle stock. Base on obtaine ata the strain e h, ean strain rate e& an ean eforation resistance σ-r were calculate (7). Fv σ r = (7) l b (6)

5 Acta Metallurgica Slovaca,, 6, 4 ( ) 48.3 Deterination of the foring factor The ean equivalent stress σ e-t was calculate by subsequent integration accoring to the equation (3). The value of the foring factor Q Fv (8) for each saple was calculate by eans of the ean eforation resistance achieve fro roll forces σ -r (7) an ean equivalent stress σ e-t (3). Q Fv = σ σ r e t (8) By eans of non-linear regression the relationship of the experientally eterine foring factor in relation to the aspect ratio l / h was expresse: l,35 exp l,349 exp Q = +,87,67 (9) Fv h h In Fig. values of the foring factor relate to aspect ratio for particular types of steel are seen, as well as epenence of Q Fv base on the equation create by the authors of this paper for the ill stan A. 3. Conclusions We eterine values of the foring factor for ill stan A fro values easure in rolling of flat proucts fro steel graes ČSN 53 [6], 4, 7 5 an 7 53 in the laboratory rolling ill Tane an fro a oel escribing eforation behaviour of these steels on the basis of torsion tests. These values were relate to the aspect ratio l / h. The resulting equation escribes with goo accuracy the function Q Fv = f ( l / h ) in the whole range of applie teperatures an eforations, regarless of friction coefficient. QFv equation (9) l /h Fig. Graphic expression of the relationship between the foring factor of the stan A of laboratory ill Tane an aspect ratio l / h A new atheatical oel that inclues a wier range of aspect ratio l / h was create, up to values of l / h = 6. For values of l / h > 4 the experient was ipleente with

6 Acta Metallurgica Slovaca,, 6, 4 ( ) 48 stainless steel graes 75 an 753, naely for the reason of lesser extent of scaling of thinner saples. The newly erive equation (9) was copare with the equation () entione below, which ha been erive earlier [7] for the range of lower values of the aspect ratio l /. As it can be seen in Fig. 3 both equations give very siilar results for the range of l / h. to.4. Just this range of the geoetric factor (aspect ratio) we use for rolling of saples with grae-in-size thickness in the ill Tane. l h + QFv =,483 4,798 exp,84 exp, 475 h l 4 () This rolling serves for recalculation of roll forces to ean equivalent stress an their subsequent escription in epenence on eforation conitions [8]. It stans to reason that the oler oel () escribes the foring factor better for values of paraeter l / h <. On the other sie, its accuracy is aversely influence by values of Q Fv = f ( l / h ) eterine earlier uring rolling of thin saples fro carbon steel ČSN 4. In these cases influence of scaling of saples was pronounce relatively stronger than in rolling of saples with bigger thickness. Accuracy of escription of the relationship Q Fv = f ( l / h ) by one equation in such wie range is worse an therefore it is better to erive the equation for narrower ranges of the given geoetric factor, which correspon to specific conitions of the given rolling ill. h 6 5 equation () new equation (9) 4 Q Fv l /h Fig.3 Graphic coparison of two equations for eterination of the foring factor value for l / h < 6 Acknowlegeents This work cae into being uring solution of project 6/4/35 (finance by the Czech Science Founation), with use of the laboratory equipent evelope in the fraework of Research Plan MSM69895 (Ministry of Eucation of the Czech Republic). Literature

7 Acta Metallurgica Slovaca,, 6, 4 ( ) 483 [] Hajuk M., Konvičný J.: Silové poínky při válcování ocelí za tepla. Praha, 983. [] Schinler I., Bořuta J.: Utilization Potentialities of the Torsion Plastoeter. Katowice, 998. [3] Schinler I., Kliber J., Bořuta J.: Preikce eforačních oporů při vysokoreukční tváření. In: Metal 94, Ostrava 994, No. 3, pp [4] [5] Celikov A. I., Griškov A. I.: Teorija prokatki. Moskva, Metallurgizat, 97. [6] Kubina T., Schinler I., Bořuta J. Příspěvek k probleatice ateatického popisu tvářecího faktoru při válcování. In FORMING. Katowice,, pp. -6. [7] Rusz S., Schinler I. et al.: Experientální určení tvářecího faktoru a jeho vliv na preikované válcovací síly. In: FORM 4. Congress Centre Brno 4, pp [8] Rusz S., Schinler I. et al.: Hot eforation resistance oels base on the rolling forces easureent. Acta Metallurgica Slovaca, 5, Vol., No., pp