MATHEMATICAL SIMULATION OF THE PROCESS OF ROLLING IN THE BACK TAPER ROLLS. Eldar AZBANBAYEV, Aristotel ISAGULOV, Zhasulan ASHKEYEV

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1 MATHEMATICAL SIMULATION OF THE PROCESS OF ROLLING IN THE BACK TAPER ROLLS Eldar AZBANBAYEV, Aristotel ISAGULOV, Zhasulan ASHKEYEV Karaganda State Technical University, Karaganda, Kazakhstan, Abstract The research is fully devoted to mathematical description and modeling of newly developed rolling process in the back taper rolls. The results show that employing of the asymmetrical scheme of deformation during rolling in the back taper rolls (inverse coning) allows to reduce total rolling force in comparison with the traditional rolling and show more intensive shear strains to appear across the thickness of the billet. Keywords: Asymmetric rolling, back taper rolls, mathematical simulation, computer modeling, shear strain. 1. INTRODUCTION Rolling technology is the most attractive technology allowing billets production of considerable size of more than 1 m in a continuous cycle of deformation (Fig. 1). Fig. 1 Rolling process The combination of N number of deformation passes of the billet of unlimited length between the rolls not only changes the shape and size of the billet, but also mechanical properties. Thus, during conventional rolling there s improvement of strength with reducing of ductility due to the nature of the deformation of metal when grains stretching (elongation) in the rolling (deformation) direction and the formation of texture, which causes anisotropy of properties. In order to eliminate the negative effects of rolling (mostly cold) heat treatment is applied, such as annealing, which increases the cost of electricity and fuel used for heating furnaces, and also increases the overall production cycle, and more importantly, does not preserve the environment of pollution. In this sense, the most attractive is the technology of asymmetric rolling, where the key is to promote the role of shear straining by the asymmetry of the material flow velocity in the deformation zone. At the moment, the well-known types of asymmetric rolling: with the difference of the rolls speed, difference of the rolls diameters, on a fixed block (Fig. 2) [1].

2 а b c Fig. 2 - Asymmetric rolling: a - with different peripheral speeds of rolls; b - rolls with different diameters, c - on a fixed block The closest in principle and design parameters is the asymmetric rolling of metals and alloys, which makes it possible to induce higher shear strain in the billets of considerable size by the difference in diameters of the rolls. Fig. 3 [2] illustrates the principle of asymmetric rolling due to the speed difference between the work rolls, which allows emerging shear strain (shears are shown with inclined lines on the side of the strip at the exit of the rolls). V 1 >V 2 V 3 <V 4 V 5 >V 6 V 7 <V 8 Fig. 3 - Asymmetric rolling; t 0 - initial thickness of the billet, t 1 - the thickness after passing the deformation zone, θ shear angle Authors [3] used the asymmetric rolling as an alternative to traditional methods of severe plastic deformation in order to fine grain in pure aluminum. The disadvantage of these types of asymmetric rolling is the need to alternate the change of speed and rolls diameter from stand (pass) to stand in order to obtain equiaxed microstructure, also requires significant reconstruction of rolling mill with the introduction of each individual motor, gearbox and speed controllers of

3 the rolls in the case of speed asymmetry. Also the downside is the billet bending at the exit of the rolls, which complicates the process of rolling, and can destabilize it. 1.1 Rolling in back taper rolls. One of the effective solutions of these problems is the asymmetric rolling in back taper rolls (Fig. 4). Fig. 4 - Rolling in back taper rolls: 1 - Top semi-coned roll, 2 - billet, 3 - lower semi-coned roll The essence of the process of asymmetric rolling in back taper rolls is to use the principle of difference between the diameters D and d in the entire range of length L of rolls so that each part will have different ratio of the rolls diameters. This difference leads to a shear in the entire volume of the billet. Fig. 5 shows the patterns of movement along the billet under asymmetric rolling in back taper rolls. Fig. 5 - Diagram of movements along the billet in asymmetric rolling in back taper rolls As can be seen from the diagram of Fig. 5 displacement along the billet in the transverse cross section is complex. In longitudinal section the billet is divided into two areas: backward on the part of smaller diameter and forward slip on the part of a larger diameter, respectively, and along the width of the deformation zone at the central point we have movements conformity as in the case of equality of rolls diameter at the bottom and the top sides as in the traditional rolling, on the opposite side of the backward slip is replaced with forward slip. If in the case of asymmetric rolling rolls are of constant diameter the backward and forward slip maintains its position across the width of the billet, in our case it is replaced in a central section, where the rolls diameter is equal. Such character of strain distribution results from the intersection of shears in a central point. 2. MATHEMATICAL SIMULATION AND COMPUTER MODELING The results of investigation of stress state of the metal by the slip lines method in the rolling billet in back taper rolls with relative difference of rolls diameter d/d = 0,846, angle of taper (D d)/2l = 0,1 and with

4 reduction ε = 30% are shown below. These values are chosen from the condition that, as the tapering (over ) it s hard to hold and set the billet in the roll gap and the value of ε = 30% is the maximum limit. To study the stress-strain state slip-line field and the corresponding velocity field, both from the upper and lower roll (Fig. 6) are built due to the asymmetry of the rolling process in the back taper rolls. Analysis of results of investigation shows that during rolling in back taper rolls tension stress σ х0.0 reaches minimum value (0,054k), i.e. prevents initiation of the most dangerous tension axial stress and excludes materials loosening in this region. Velocity difference in the entering side into the deformation zone as follows: V L /V U =0,885 and in the exit side V 1L /V 1U =1,065, i.e. in the exit of the deformation zone the velocity of the material on the larger roll side is higher than on the smaller roll side. Difference of the velocity of the material initiates favorable conditions for internal defects removal (especially casting defects). Fig.6 Slip lines method with velocity hodographs in rolling in back taper rolls Comparison between results of theoretical investigation and mathematical model of stress state during asymmetric rolling in back taper rolls shows the shape of deformation zone (Fig. 7). Fig. 7 Effective strain distribution across the longitudinal section of the billet during asymmetric rolling in back taper rolling

5 Effective strain distribution across the cross section of the billet is shown on Fig. 8. а b Fig. 8 Effective strain distribution across the cross section of the billet during: a - asymmetric rolling in back taper rolls; b conventional rolling in cylindrical rolls When rolling in back taper rolls the distribution of the equivalent strain in the cross section of the billet is asymmetric, and the distribution of strain occurs diagonally. In the case of rolling in cylindrical rolls strain is concentrated in the peripheral parts of the billet, much of the central region has a lower value of effective strain. Also, the incremental values of equivalent strain in the case of the rolling in back taper rolls are much higher than when rolling in cylindrical rolls. Thus, with the conventional rolling mean effective strain in the cross section of the strip 1,05-1,1, and with the rolling in back taper rolls 2-2,5, that is twice higher than in conventional rolling. Mean stress distribution across the cross section of the billet is shown in Fig. 9. a b Fig. 9 Mean stress distribution across the cross section of the billet: a rolling in back taper rolls; b rolling in cylindrical rolls

6 During rolling in cylindrical rolls mean stress has positive value in central part of the billet (Fig. 9b), it means that there s constitutive tension stress proving our above mentioned conclusions of theoretical investigation. During rolling in back taper rolls the region of the billet on the larger roll side is deformed more severely than on the smaller roll side, this leads to initiation of considerable compression stress from the center to periphery. It should be noted that the velocity of metal entering the roll gap is not distributed symmetrically. In view of the difference in speeds of the rolls in the central region the metal has compressing stress. When rolling in cylindrical rolls mean stresses have the positive value in the center of the billet, which indicates the presence of significant tension stresses. 3. EXPERIMENTAL PART Laboratory testing of lead billets in mill DUO 120 were conducted to investigate the shape of the deformation zone and the deformation of grid mesh with a relative reduction per pass 25% and input data taken from theoretical investigation presented above (Fig. 10). Fig. 10 Lead billets with grid mesh printed on the side of the billets: h b l = mm, grid size 5 5 mm а b Fig The results of the deformation of the grid when rolling in back taper rolls: a, b on both sides of the billet As seen in Fig. 11a, b, during rolling in the back taper rolls severe shear strain occurs throughout the thickness of the billet shear angle γ 33, that the front and rear part has a wavy shape with "influx" of the metal in the periphery of the larger diameter rolls, which indicates a greater speed of movement of these areas compared with those from the smaller diameter.

7 4. CONCLUSIONS Full-scaled research of the new method of rolling in back taper rolls has been conducted. Theoretical investigation with slip-lines method showed significant asymmetry in velocity hodograph with prevalent material speed on the upper side roll with larger diameter that corresponds with calculated stresses which comprises considerable compression components at the central parts of the rolled billet. In comparison with the rolling in cylindrical rolls where significant tensile stresses tend to appear in the centre of the billet. Experimental procedures with lead samples consisted of study distribution of shear strain across the thickness of the billet and results showed intense shear strain with mean value γ 33 on both sides with only distinction of the direction of that shear. LITERATURE [1] FABIO J. PEREIRA SIMOES. Asymmetrical rolling of an aluminum alloy 1050: Diss. submitted as the fulfillment of the necessary requirements for obtaining the PhD degree / Fabio Jorge Pereira Simoes. Spain, p. [2] JOSE J. DE ALMEIDA GRACIO. Pat A1 USA 148/500. Grain refinement of metallic components by controlled strain path change/jose Joaquim De Almeida Gracio et.al. - 12/995,159; app , publ p. [3] CUI Q., OHORI K. Grain refinement of high purity aluminium by asymmetric rolling, Materials Science and Technology, vol. 16, 10, pp