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23. - 25. 5. 2012, Brno , Czech Republic, EU THE INV E STIGATION OF THE UNINTERRUPTEDL Y - CASTED BILLETS OF SMALL CROSS - SECTION WITH THE SHAPE DEFECT « RHOMBOIDITY » DEFORMATION PROCESS IN BOX PASSES Aleksandr MINAYEV a , Yevgeny SMIRNOV b , Sergey SNITKO c , Sergey KRASENKOV d a Department of Metal Forming, Donetsk national technical university, 58, Artyom Street, 83001 Donetsk, Ukraine, omd@fizmet.dgtu.donetsk.ua, b Department of Metal Forming, Donetsk national technical university, 58, Artyom Street, 83001 Donetsk, Ukraine, omd@fizmet.dgtu.donetsk.ua, c Depa rtment of Metal Forming, Donetsk national technical university, 58, Artyom Street, 83001 Donetsk, Ukraine, snitko_sa@mail.ru, d Department of Metal Forming, Donetsk national technical university, 58, Artyom Street, 83001 Donetsk, Ukraine, s.krasenkov@hotm ail.com Abstract Uninterruptedly - casted billets shape defects are consequence of technological regulation failure of continuous caster machine. From the position of their stability during the subsequent billets rolling with shape defects, the majority of p roblm ari whn bill hav ignifican diffrnc of diagonal («rhomboidiy»). Th abolu valu of «rhomboidiy» prdrmin: h poibiliy in principl of hir ady rolling in breakdown mill passes with guaranteed obtaining of required shap e and dimensions of semi - finished rolled products for preleader passes; the necessary volume of deformation regimes adjustment and rolling schemes. In hi papr h mahmaical imulaion of quar bill 135×135 mm wih «rhomboidiy» rolling proc in box passes with different jamming degree (a) and elongation ratio ( μ ) is performed. The simulation results howd ha condiion whn uppr and lowr bill fac arn‱ paralll o h ba of a groov, lad o significant irregularity of reduction alon g billet width and elongation ratio along cross - section. This leads to a coiling relatively to the longitudinal axis of feed . Stated, that the creation of rolling conditions, when billet with «rhomboidiy» self - centered in pass allows to avoid longitudinal coiling of feed and makes prerequisites for obtaining required shape of semi - finished rolled produc from bill wih gra «rhomboidiy». Shown, ha h b correction ffc of «rhomboidiy» achieved by deformation in passes with a=1,04 and maximum values of μ1,32. Eablihd, ha «diagonal crack» accompanying h «rhomboidiy» in mo ca, wihou limiing bill urfac, ar dcrad in lngh wih growh of rducion (h «rhomboidiy» valu). Th locaion dph of h crack dcra a w ell. Keywords: BOX PASS, «RHOMBOIDITY», «DIAGONAL CRACKS», BILLET, IRREGULARITY OF REDUCTION 1. INTRODUCTION Uninterruptedly - casted billet s shape defect s of cross - section are the consequence of conditions failure of a metal solidification in casting mold and of subsequent secondary coo ling in processing line of continuous - casting machine (CCM). During subsequent rolling of such billets, the majority of problems arise in cases they have significant difference of cross - section diagonals size ( Δd). In addition to that, from one side, the absolute valu of h Δd is the size, which ch aracterizes the uninterruptedly - casted billets shape defects of cross - section ‬ «rhomboidiy», and from the other side ‬ predetermine s the possibility in principle o f their 23. - 25. 5. 2012, Brno , Czech Republic, EU steady rolling in box passes of breakdown mill s with guaranteed obtaining of required shape and dimension s of the semi - finished rolled products for preleader passes . The data analysis of available industrial experience of rolling uninterruptedly - ca sted billets with the shape dfc «rhomboidiy» has shown that the value of the «rhomboidiy» , greater than 15 mm , causes the problems , relating to providing stable conditions during the initial stage of rolling process ‬ the initial biting ( roll bi te ) . A lso observed shape distortion of the semi - finished rolled products after the first pass. It makes impossible its further rolling. Moreover , the special attention is deserved by a question, which is related to behavioral research of «diagonal crack» durin g rolling. As it has been stated in the works [1, 2] namely the «diagonal crack» in bill cro - section are accompanied by the shape defects «rhomboidiy» in mo cases . In the existing industrial practice of uninterruptedly - casted billets with great va lu of Δd they are subjected to the preparation operation of the flame peeling with the purpose of partial correction of cross - section shape. It leads to additional metal loss (burn - off loss and clipping) and it also leads to the unplanned expenditure for operation performance of flame correction of billets cross - section shape . The purpose of the present investigation is technological capability eval uation of obtaining of high quality semi - finished rolled products from unint erruptedly - casted billets with gr eat valu of h «rhomboidiy». 2. EXPERIMENTAL SETUP The finite element method (FEM) is used as a method of investigation . The mathematical model realization is executed using the software DEFORM 3D, developed by Scientific Forming Technologies Corporati on and provided for a temporary license by company TESIS. The validation of the finite element model is executed according to the actual data of metal forming of uninterruptedly - casted billets with cross - cion 135×135 mm in brakdown mill of linar mdiu m - section mill with diameter of forming rolls 500 ‬ 600 mm according to the acting strain - rate and temperature technological regulations. B ill wih diffrn valu of h iniial «rhomboidiy» ( Δd) wr rolld in the course of the experimental - industrial rolling . During the execution of calculated investigation with the help of the developed mathematical model, two variants of the deformation schemes were examined . The first variant is based on t he scheme of rolling on the flat body of forming rol ls, idea of which is expounded in the paper [3]. However, as opposed to the expounded approach, instead of rolling on the flat body , rolls were used, in which box passes were grooved. The main idea of suc h deformation scheme consist s in the insertion of box pass in the initial stage of deformation process (initial biting of rolls) , it prevent s the loss of billet stability (dumping) at the expense of fixation (clamping) only in the corners of the pass (the corners between the base of a groove and outlet of pass) and limitation absence of the transverse flow of metal a=b billet /b groove 0,95 (b billet - width of billet, b groove - width of base of a groove). Coefficient of longitudinal strain (elongation ratio) i s µ1,13. Taking ino accoun peculiarities of accepted deformation scheme , it is executed experimental setup of billets rolling with the valu of h «rhomboidiy» Δd =20 mm in box passes , under given conditions: - the initial rotation along the longitudinal axis of the billet at an angle αп from 0 to 6 о during the rolling process; - with limit ation of billet rotation along the longitudinal axis during the rolling process ; - without limitation of billet rotation along the longitudinal axis during the rolling process . According to the second variant the mathematical simulation of uninterruptedly - casted billets rolling process with great valu of h iniial «rhomboidiy» Δ d i s executed according to the operating system of conjugated box pa wih cofficin of longiudinal rain (longaion raio) i µ1,32 and wih h valu of limiaion of transverse metal flow is a = 1,04 in breakdown mill. The simulation is executed f or the following conditions: - thermal conditions of billet ‬ non - stationary; 23. - 25. 5. 2012, Brno , Czech Republic, EU - the surface temperature of forming rolls is taken equal to 300  C and remained unchanged in the course of deformation; - the heating temperature of billet (specimen) for rolling ‬ 118 0 ‬ 1230  С ; - the transportation time of billet from the furnace to the rolling mill 10 seconds; - the rolling rate ‬ 3 m/s ; - the model of billets material ‬ rigid - plastic; - the model of forming rolls ‬ rigid. The behavior of billet material in the course of so lution process is described by means of diagram effective stress - effective strain . The rheology of metal is determined by flow curve in accordance with given dependence of flow stress ( ) from degree of strain ( ), strain rate ( ) and temperature ( ): (1) During the simulation the conception of flow stres s is used, according to which the material is plastically defor med and the amount of stresses is determined by the flow curve depending on the amount of incremental strain . Rheological curves for billet marial (%C  0,42…0,50; %Mn 0,17…0,37; %Si 0,50…0 ,80; %Cr0,25) in the temperature range 900 ‬ 1250  С are accepted in accordance with the recommendations of the work [4], and thermophysical properties of steel ‬ in accordance with the recommendations of the work [5]. Th dimnion of h «diagonal crack» (for an angl >90 º the crack length (L) is equal to 12 mm, the location depth from the surface (S) ‬ 3 mm; for an angle 90 º L = 3 mm, S = 3 mm) are accepted on the basis of an average statistical data of the template cross - section analysis, obtained from the billets of current production, casted in the conditions of high - speed section CCM (Fig. 1). a b Fig. 1 ‬ External view of uninterruptedly - casted billet with the shape defect «rhomboidiy» ( Δ d = 20 mm): a ‬ template cross - section of uninte rruptedly - casted billet , b ‬ solid model of the billet with the «diagonal crack» S hearing friction model is accepted a s a model of contact friction: (2) where ‬ friction stress; ‬ friction factor ; ‬ shear yield point of material. For co nditions of interaction between forming rolls and billet with a considerable quantity of scale on the contact surface and in absence of lubrication it is accepted a value of is equal to 0,7 . 23. - 25. 5. 2012, Brno , Czech Republic, EU The finite - element mesh with four - nodal tet rahedrons is used for correct definition of the billet geometry in the simulation. The maximum size of a f inite element does n‱ t exceed 6 mm. In addition, calculations of metal flow in the simulation are executed on basis of the principle of minimum deforma tion work. 3. SIMULATION RESULTS AND DISCUSSION The results of numerical experimental investigation with using developed simulation has shown , that the obtaining of high - quality semi - finished rolled products in the course of uninterruptedly - caste d billet s rolling with value of iniial «rhomboidiy» up to 14 mm (Fig. 2 a ) is t e chnological l y feasible. In this case, the shape disto rtion of the deformed billet is n‱ t significant (Fig. 2 b ). Given conclusion correlate s well with practical data, obtained in condit ions of operating production. Δd =14 mm Δd =20 mm , α p =6 ° Δd =20 mm , α p =0 ° a c e b d f Fig. 2 ‬ The results of numerical simulation of the uninterruptedly - casted billet rolling process with the shape dfc «rhom boidiy» in h box pa wih µ1,32 and a =1,04 (operating technology): a ‬ the initial stage o f rolling (biting) ; b ‬ the final stage of rolling process ( outlet of billet from the rolls ) ; c ‬ the ini tial stage of rolling , the possibility of billet rotation along the longitudinal axis is limited; d ‬ the final stage of rolling process , possibility of billet rotation along the longi tudinal axis is limited; e ‬ the ini tial stage of rolling , the possibility of billet rotation along the longitudinal axis is n‱ limited ; f ‬ the f inal stage of rolling process , poibiliy of bill roaion along h longiudinal axi in‱ limid As a re sult of the calculated experiment implementation , in which the upper and lower billet faces arn‱ t parallel to the base of a groove (Fig. 2c), and the possibility of billet rotation along the longitudinal axis is limited , has shown , that in this case the s ignificant irregularity of reduction along billet occurs. It is conducive to longitudinal strain (elongation) irregularity of the shape cross - section and it cause s coiling relatively to the longitudinal axis of billet (Fig. 2d). Data about angles sizes of semi - finished rolled products coiling ( α  - an average value of two angles of coiling from the upper and lower billet faces ) are shown in the table 1. On the basis of mentioned data is seen, that closest shape of semi - finished rolled products to the regulated regimes of deformation and roll pas  dign i obaind in h cour of rolling wih а1,04 and µ1,32 . Therefore, the next sta ge of research associated with udy of h «diagonal crack» bhavior during h dformaion, i use d the given variant of the technological scheme of deformation . 23. - 25. 5. 2012, Brno , Czech Republic, EU Tab . 1 ‬ The angles of longitudinal coiling of billet after the first pass The possibility of billet rotation along the longitudinal axis α  a < 0,95; µ  1,13 a  1,04; µ  1,32 α p = 0  limited 4,860  3,515  not limited 4,188  3,365  α p = 2,5  l imited 6,462  3,702  not limited 4,106  3,326  α p = 6  limited 9,195  3,779  not limited 3,912  3,429  During the numerical investigation of uninterruptedly - cased billet rolling process with the shape defect «rhomboidiy» and h dfc of macroruc ur «diagonal crack» in addition the cooling of billet as a result of transportation from the furnace to the first mill stand and its heating due to the thermal effect of plastic deformation is take n into consideration . The simulation results are represen ted in f igure 3. a b Fig. 3 ‬ The distribution of equivalent (effective) strain ( a ) and temperature ( b ) of cross - section feed after the first pass ( billet temperature at the outlet of the furnace ‬ 1180  С ; a1,04, µ1,32) The analysis of the received data shows, that in the area of angles � 90  with increasing Δ d, other conditions being equal, the lengt h of the defects decreases : with Δ d = 0 mm ‬ 23, 6 %; with Δ d = 10 mm ‬ 28, 3 %; with Δ d = 20 mm ‬ 30, 6 % . The location depth of the defects decreases as well : for Δd  0 mm ‬ 40, 3 %; wih Δd  10 mm ‬ 32% ; wih Δd  20 mm ‬ 29, 7% (Fig. 4). In all examined cases , the required shape of semi - finihd rolld produc i obaind and h «diagonal crack» of uninrrupdly - casted billet are minimized. The cases of their appear on the surface of feed are absent. The calculations has also shown, that an additional ins tallation of a pushing advice (pusher) with a horizontal force of ~ 700 kN for implementation of such technological scheme is required, which provides conditions for the dynamic biting without fixation of billet along the longitudinal axis. 23. - 25. 5. 2012, Brno , Czech Republic, EU Fig. 4 ‬ Forming of the diagonal cracks after the first pass: a ‬ the change of length of the crack; b - the change of location depth of the cracks A imilar bhavior of «diagonal crack» a a rul of rolling in h ara of acu angl of h bill, in which gr eater strain and starts earlier than in the area of obtuse angles is observed (Figure 3 a ). This character of strain distribution in conjunction with the high rolling temperature creates prerequisites for welding of cracks a relatively short length (less th an 3 mm). Grounded on the results of research in the paper [6], it is established that for implementation of the rolling rgim, in which rquird hap of fd a a rul of rolling in fir pa will b obaind and h «diagonal crack» of uninrrup dly - cad bill will b wldd parly, wihou limiing fd urfac (crack won‱ rach to the surface of feed). For this purpose it is necessary to create the following conditions: the heating temperature of uninterruptedly - casted billet before rolling must be increased additionally by 50  C (from 1180 to 1230  C); rolling in the first pass must be conducted with a reduction  25,2%; the rolling rate must be reduced up to 8 ‬ 10 times. Besides that, in the first pass the biting is the most problematic process from the point of view of biting ability of uninterruptedly - casted billets with small radius of the corners rounding. Thus, increasing the heating temperature of billets will improve the conditions of roll bite in the first pass. CONCLUSION The si mulation results based on the FEM of rolling uninterruptedly - casted billet s 135  135 mm with value of «rhomboidiy» Δd = 20 mm in box passes with limitation absence of the transverse flow of metal (free longitudinal strain) and initial interaction of billet with pass (only in the corners of the pass), are showed : creation conditions, in which incoming billet can be self - centered in pass, provid ing more regular reduction along the strip width with its upper and lower faces. It allows to avoid longitudinal coi ling and makes prrquii for obaining rquird hap of fd from h bill wih gra «rhomboidiy». Th b corrcion ffc of hap dfc «rhomboidiy» is achieved with the limitation of the transverse flow of metal (limited longitudinal stra in a = 1,04) and with greater value of longiudinal rain (longaion raio µ =1,32). It is s hown, ha in hi ca h dimnion and h locaion dph of h «diagonal crack» in h area of billet angles �90 º , other conditions being equal , decreases. The conditions of dynamic biting of uninterruptedly - casted billet with a horizontal force of ~ 700 k N without fixation of billet rotation along the longitudinal axis are necessary for implementation . To achieve the effect of partial welding of cracks it i s necessary to increase additionally the heating temperature of uninterruptedly - casted billet before rolling from 1180 to 1230  C, and the deformation process in the first pass must be implement ed with reduction  25,2%, with simultaneous maximum possible r educe rolling rate ( proceeding from durability to the flame erosion of the surface of grooves ) . 23. - 25. 5. 2012, Brno , Czech Republic, EU LITERATURE [1] БОТНИКОВ С.А. 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A study of pore closure and welding in hot rolling process / A.Wang, P.F.Thomson, P.D. Hodgson // Journal of Materials Processing Technology. 1996. ‬ Vol. 60. ‬ p. 95 - 102.