Научная статья на тему 'Analysis of variations in roll separating forces and rolling moments in the asymmetrical rolling process of flat products'

Analysis of variations in roll separating forces and rolling moments in the asymmetrical rolling process of flat products Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

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Ключевые слова
NUMERICAL MODELLING / ASYMMETRICAL ROLLING / ROLL ROTATIONAL SPEED ASYMMETRY FACTOR

Аннотация научной статьи по электротехнике, электронной технике, информационным технологиям, автор научной работы — Kawałek Anna, Dyja Henrik

The paper presents the results of investigation into the effect of roll peripheral speed asymmetry on the force and energy parameters of the process for the conditions of normalizing rolling of plates in the finishing rolling stand.

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Текст научной работы на тему «Analysis of variations in roll separating forces and rolling moments in the asymmetrical rolling process of flat products»

Scientific School of Asymmetric Rolling in Magnitogorsk

Fig.7. Field of strain rate in asymmetric and symmetric rolling

References

Pesin A.M. Modelirovanie i razvtie processov asimmetrichnogo deformirovanja dlja povyshenija jeffektivnosti listovoj prokatki. Dokt. Diss. [Modeling and development of the processes of asymmetric deformation to improve sheet rolling: thesis]. Magnitogorsk, 2003. 395 p. Salganik V.M., Pesin A.M. Asimmetrichnaja tonkolistovaja prokatka razvtie teorii, tehnologii i novye reshenija [Asymmetric rolling of thin sheet the development of theory, technology and new solutions]. Moscow MISIS, 1997. 192 p.

Pesin A.M. New technological solutions based on the modeling of asymmetric rolling. Steel, 2003, no. 2, pp. 66-68. Dyja H., Pesin A.M., Salganik W.M., Kawalek A. Asymetriczne walcowanie blacli cienkicli: teoria, teclinologia i nowe rozwiazania: Seria Monografie nr 137. Wydawnictwo Politechniki Czestochowskiej. Czestochowa, 2008, 345 p.

Pesin A., Salganik V., Trahtengertz E., Drigun E. Development of the asymmetric rolling theory and technology / Proceedings of the 8-th International Conference on Metal Forming. Krakow / Poland / 3-7 September, 2000. Metal Forming 2000. Balkema / Potterdam / Brookfield / 2000. pp. 311-314.

Pesin A.M., Salganik V.M., E.M. Drigun, Chikishev D.N. Ustrojstvo dlja asimmetrichnoj prokatki tolstolistovogo metalla. [Device for asymmetrical rolling metal plate]. Patent RF, no. 38646, 2004. Pesin A.M., Salganik V.M., E.M. Drigun, Chikishev D.N. Ustrojstvo dlja asimmetrichnoj prokatki tolstolistovogo metalla. [Device for asymmetrical rolling metal plate]. Patent RF, no. 2254943, 2005.

8. Pesin A., Salganik V., Sverdlik M., Pustovoytov D., Chikishev D. Theoretical Basis and Technology Development of the Combined Process of Asymmetric Rolling and Plastic Bending. Proceedings of the 2011 International Conference on Mechanical Engineering and Technology UK ICMET 2011, ASME Press, 2011, USA, pp. 95-98.

9. Pesin A.M., Salganik V.M., Chikishev D.N. Improvement of production technology of large parts of bodies of revolution on the basis of mathematical modeling. Proizvodstvoprokata. [Production of rolled]. 2007, no. 3, pp. 34-40.

10. Pesin A.M., Salganik V.M., Dyja H., Chikishev D.N., Pustovoitov D.O., Kawalek A. Asymmetric rolling: Theory and Technology. HUTNIK-WIADOMOSCI HUTNICZE. 2012, no 5, pp. 358-363.

11. Pesin A.M., Salganik V.M., Chikishev D.N., Drigun E.M. Razvitie teorii i tehnologii poluchenija detalej krupnogabaritnyh tel vrashhenija: monografija. [The development of the theory and technology of parts of large bodies of revolution: monograph]. Magnitogorsk: «NMSTU», 2010, 102 p.

12. Salganik V.M., Pesin A.M., Chikishev D.N., Lokotunina N.M., Pustovoitov D.O. Prilozhenija teorii plastichnosti k razrabotke i analizu tehnologicheskih processov [Applications of the theory of plasticity in the design and analysis process]. Magnitogorsk: «NMSTU», 2012, 251 p.

13. Pesin A.M., Pustovoytov D.O., Perehogih A.A., Sverdlik M.K. Simulation of shear strain in the extreme case of asymmetric sheet rolling. Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical University]. 2013. no 1, pp. 65-68.

Kawalek A., Dyja H.

ANALYSIS OF VARIATIONS IN ROLL SEPARATING FORCES AND ROLLING MOMENTS IN THE ASYMMETRICAL ROLLING PROCESS OF FLAT PRODUCTS

Abstract. The paper presents the results of investigation into the effect of roll peripheral speed asymmetry on the force and energy parameters of the process for the conditions of normalizing rolling of plates in the finishing rolling stand. Keywords: numerical modelling; asymmetrical rolling; roll rotational speed asymmetry factor.

1. Introduction

An important problem that drives the upgrading of plate rolling mills are increasing demands on the geometrical dimensions of finished products. These demands force the manufacturers to implement roll gap control systems that helps to maintain stability and improve the geometrical parameters of rolled strip.

Works [1-4] have demonstrated that by using asymmetrical plate rolling process, improvement in the quality of plate geometry can be achieved. The idea behind the asymmetrical rolling technology consists in taking ad-

vantage of the positive effects of the asymmetrical deformation zone, which include primarily the reduction of the total roll separating force and the enhancement of the product service properties.

The asymmetrical rolling system relies chiefly on a direct action being exerted on the strip in the deformation zone, in which, owing to an asymmetry introduced to the working roll peripheral speed, longitudinal tensile stresses occur, whose effect is analogous to that of tension and back tension in continuous rolling mills. These stresses have the effect of reducing the magnitude of unit pressure in the roll gap and enhancing the equalization of the non-

uniform distribution of rolled strip thickness, at the cost of the elastic properties of the rolling stand itself. At the same time, the regulation of the distribution of thickness over the strip length, flatness and the cross-sectional strip shape occurs at a reduced total roll separating force [5-7].

Reducing the total roll separating force has a direct effect of decreasing the elastic deflection of the mill housing and rolls, and an indirect effect on the roll gap shape that determines the cross-sectional shape of rolled flat products.

2. Selection of the kinetic and initial parameters of the plate hot rolling process

The material used for tests was steel of the S355J2G3 grade. Working rolls of D = 1000 mm diameter and a constant lower working roll rotational speed equal to n = 50 rpm were assumed for the tests. The asymmetrical rolling process was run by varying the rotational speed of the upper roll, which was lower than that of the lower roll. The range of variation of the roll rotational speed factor, av =vl/vu (where v u vu - the rotational speed of the lower roll and the upper roll, respectively) was 1.01-1.15. A strip shape factor of h0ID = 0.05-0.018 was assumed. The range of relative rolling reductions applied was e = 0.08-0.50.

Moreover, the following input data were taken for simulation: tool temperature, 60°C; ambient temperature, 20°C; friction coefficient, 0.3; friction factor, 0.7; the contact thermal conductivity, atooi = 3000 [W/Km2]; and the heat transfer coefficient, a!uulface = 100 [W/Km2].

The temperature of the rolled strip was varied depending on the initial height h0 within the temperature ranges for normalizing rolling:

h0 = 50 mm, the rolling temperature T = 950°C, h0 = 27 mm, the rolling temperature T = 900°C, h0 = 18 mm, the rolling temperature T = 880°C.

The parameters describing the physical features of steel were adopted based on the material database enclosed to the Forge2008® program [8], and were as follows: thermal conductivity, 35.5 W/(mK); specific heat, 778 J/(kgK); steel density, 7 850 kg/m3; emissivity, 0.88.

In order to implement asymmetrical rolling in the conditions of existing Rolling Mill it is necessary to consider conditions prevailing in that Rolling Mill and apply one of the newest, proven numerical methods for analysis.

On the date base given from industrial conditions said, then in the finishing mill of the Rolling Mill 3600 uneven loading of the driving motors is used. "Rough" wire rod (i.e. the strip obtained in the break-down stand) in the first two passes is deformed with relative rolling reductions as high as

above 40%, whereas in the last passes the strip deformation is only at a level of a few percent. The rolling moments in the first roll passes exceed the nominal moment value. The driving motors are exposed to overheating. The use of driving motor power in the subsequent roll passes is lower from nominal, which allows the introduction of a difference in the rotational speeds of individual working rolls in the range of 4-9% in the intermediate roll passes and above 15% in the end roll passes.

Therefore, by introducing the asymmetric rolling system in the finishing mill of the Rolling Mill 3600 the achieving of favourable technical and economic effects (a reduction of thickness deviations over the band length and an improvement in the flatness of finished plate) should be fully ensured, despite the non-stationary temperature distribution in the deformed strip, which occurs under actual conditions [9].

3. Investigation results and their analysis

Figures 1-8 illustrate the effects of the working roll peripheral speed asymmetry factor, av, being variable in the range 1.01-1.15, and of the relative reduction s =0.08-0.50, for the feedstock thickness range under investigation (h(/D = 0.050-0.018), on the magnitude of unit pressures pm [kN/mm]. As shown by data in Figs. 1, 4 and 5, for the feedstock of the greatest thickness, i.e. h0=50 mm (h0/D = 0.050), rolled asymmetrically with asymmetry factors from the range of av=1.01-1.15, no decrease in the unit pressure, pm, was observed; just the opposite, even a slight increase in its magnitude occurred. This was caused by the non-uniform deformation over the strip height and by the different lengths of the contact arc, ld, as a result of the large bending of the strip on exit from the deformation zone. The application of rolling reductions of e>0.15 resulted in a reduction of unit pressure magnitudes from a few percent (for e=0.20) up to approx. 8% for the larges values of the asymmetry factor, (Figs.1, 6-8).

E Si

100

90

80

70

60

50

40

30

20

10

1-1-1-1-1-1-1-1-1-1-1—

S=0.08 s=0.15 s=0.20 -W- s=0.25 -A- s=0.30 s=0.40 s=0.50

——< i —— >

i-< )— -< >

s-* ( ) (

-*

1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15

Fig. 1. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different relative rolling reduction values and a constant strip shape factor of ho/D = 0.050

a

v

For the h0=27 mm thick (h/D=0.027) feedstock rolled asymmetrically, using the least rolling reductions of e=0.08-0.10, no decrease in the unit pressure magnitude was observed for the entire asymmetry factor range of av=1.01^1.15 as a result of introducing asymmetric rolling; quite the opposite, a slight increase in the value of pm occurred (Figs. 2 and 4). For rolling reductions e>0.10, a drop in the unit pressure magnitudes by as much as ap-prox. 11% was found for e=0.15 and av=1.15 upon introducing asymmetric rolling (Figs. 2 and 5).

The application of asymmetric rolling for the h0=18 mm

thick (h0/D=0.018) feedstock and asymmetry factors of av>1.01 resulted in a decrease in the average pressure magnitude by approx. 8% (for av=1.15) already for the lowest rolling reductions used, i.e. e=0.08. After applying rolling reductions from the range of e=0,15-0.30 with av=1.15, the pressure decrease was even greater, reaching nearly 22% (Figs. 3, 5 and 6). For rolling reductions of e=0.40-0.50 and with small asymmetry factor values of av=1.01-1.03, no pressure force decrease was found, whereas for av>1.05 a pressure force reduction occurred, which was greater than 12% (for e=0.40), Figs. 3, 7 and 8.

70

60 - —

50

40

30

20

10

—1-1-1-1-1-1-1-1-1-1-1— -♦-s=0.08 -"-s=0.15 -A-s=0.30 -•-s=0.40 -«-s=0.50

1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15

av

Fig. 2. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different relative rolling reduction values and a constant strip shape factor of h(/D = 0.027

1 1 1 1 1 1 1 1 1 1 1 1

-♦-s=0.08 -»-s=0.15 -£-s=0.30 -*-s=0.40 -»-s=0.50

1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15

av

Fig. 3. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different relative rolling reduction values and a constant strip shape factor of h0/D = 0.018

1 1 1 1 1 1 1 1 1 1 1 1 1 1

-»-Ho/D=0.05 -*-Ho/D=0.027 -"-Ho/D=0.018

1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15

av

Fig. 4. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different shape factor of h(/D and relative rolling reduction s = 0.08

0

70

60

50

40

E 30

20

10

0

50

45

40

i= 35

>-

30

25

E 20

15

10

5

1 1 1 1 1 1 1 1 1 1 1 1 1

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-*-Ho/D=0.05 -*-Ho/D=0.027 -"-Ho/D=0.018

1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15

av

Fig. 5. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different shape factor of h(/D and relative rolling reduction s = 0.15

60

55

50

f= 45

t 40

35

30

25

20

15

-Ho/D=0.05

-Ho/D=0.027

-Ho/D=0.018

1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15

av

Fig. 6. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different shape factor of h(/D and relative rolling reduction s = 0.30

-»-Ho/D=0.05 -*-Ho/D=0.027 -"-Ho/D=0.018

1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15

Fig. 7. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different shape factor of h(/D and relative rolling reduction s = 0.40

-1-1-1-1-1-1-1-1-1-1-1-1- -«-Ho/D=0,05 -*-Ho/D=0,027 -e-Ho/D=0,018

1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15

av

Fig. 8. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different shape factor of h(/D and relative rolling reduction s = 0.50

80

70

60

30

20

a

95

85

75

65

55

45

35

The data in figures 1-8 indicate that for the h0/D strip shape factor values investigated in this work, the effect of the applied working roll peripheral speed asymmetry factor on the variation of the unit pressure magnitudes (as computed per unit width of rolled strip) is different and depends on the remaining process parameters, namely the feedstock thickness and the relative deformation used.

The effect of the asymmetric rolling process on the magnitudes and variations of rolling moments for particular working rolls and the total rolling moment is illustrated in Figs. 9-10.

3.00 2.75 2.50

2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 -1.00

„ X« C -

> / <

'S r"*

✓ s

✓ " >

g

M1, M2, av=1.00 M1, av=1.01

-K-M2, av=1.01

-M1, av=1.02

-M1, av=1.03

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

8

Fig. 9. Effect of the relative rolling reduction s on the magnitude of rolling moments for a constant strip shape factor of h(/D = 0.05

1.50

1.25

1.00

0.75

0.50

E E E

I 0.25

0.00

-0.25

-0.50

-0.75

-1.00

—■ i ---

•i 1- _ . ___i r* "

■ < j

^ j

It can be found from the moment magnitude distributions shown in these figures that the moment on the roll with higher peripheral speed (the lower roll) is always positive. This roll is always a driving roll. The rolling moment on the roll with lower peripheral speed (the upper roll) may either be negative (then it becomes a driven roll), have a zero value, or be positive. The introduced asymmetry of roll peripheral velocities has a substantial influence on the value of the rolling moments Mi and M2. The greater feedstock thickness ho, the greater moment is required for carrying out the rolling process. This is due to the greater absolute rolling reduction Ah in the case of rolling thicker strips, at the same magnitude of relative rolling reductions in particular passes. Depending on the magnitude of the asymmetry factor av, at the same magnitude of the relative rolling reduction e, the magnitudes of Mi and M2 change. The presented results of the investigation of the effect of asymmetric rolling process parameters on the magnitudes of total roll separating forces (the average pressure per unit strip width) and the rolling moment distributions on particular working rolls were obtained on assuming a constant rotational (peripheral) speed of the lower roll and a reduced rotational (peripheral) speed of the upper roll. Such a method of asymmetric rolling cannot be used under the actual conditions of finishing mill operation, as the continual overloading of the main rolling mill motor driving the lower roll would result in its overheating (especially during summer months, at relatively high ambient temperature in the drives hall) and shutting it down.

Therefore, the rolling process asymmetry should be introduced alternately by applying a higher rotational speed of the lower and the upper rolls in successive passes, which will cause the rolls to be alternately driving and driven rolls, whereby their excessive overloading will be prevented.

-X-M2, av=1.03

-M1, av=1.05

-M1, av=1.08

-M1, av=1.10

-M1, av=1.15

-M1=M2, av=1,00 -M1, av=1.01

■ M2, av=1.01 -M1, av=1.02

--M2, av=1.02

-*-M1, av=1.03 -X-M2, av=1.03 —«—M1, av=1.05 —* - M2, av=1.05 —s— M1, av=1.08 -•-M2, av=1.08

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Fig. 10. Effect of the relative rolling reduction s on the magnitude of rolling moments for a constant strip shape factor of ho/D = 0.018

4. Summary and conclusions

From the investigation carried out, the following conclusions have been drawn:

- by introducing the asymmetric plate rolling process through differentiating working roll peripheral speeds, depending on the asymmetry factor used, the magnitude of the total roll separating force can be reduced and, at the same time, a smaller elastic deflection of rolling stand elements can be achieved;

- thanks to the smaller elastic deflection of the working rolls, finished plate with smaller dimensional deviations across its width and length can be obtained;

- the asymmetry of the rolling process should be introduced alternately by applying

-1.25

a higher rotational speed of the lower and the upper rolls in successive passes, which will cause the rolls to be alternately driving and driven rolls, whereby their excessive overloading will be prevented.

References

1. Dyja H., Satganik A. M., Piesin A. M., Kawatek A. Asymetryczne walcowanie blach cienkich Teoria, technologia i nowe rozwi^zania [M]. Wydawnictwo Politechniki Czçstochowskiej, (Poland), 2008. 345.

2. Kawatek A., Dyja H., Knapinski M. Wptyw asymetrycznego walcowania na poprawç wskaznikôw techniczno-ekonomicznych procesu walcowania blach na gor^co [J]. Hutnik Wiadomosci Hutnicze. 2008, 6: 266-270 (in Polish).

3. Markowski J., Dyja H., Knapinski M., Kawatek A. Theoretical analysis of

the asymmetric rolling of sheets on leader and finishing stands [J]. Journal of Materials Processing Technology, 2003, 183-188.

4. Sinicyn V.G. Nesimmetrichnaja prokatka listov i lent [M]. Metallurgy, Moskva, 1984, 165 (in Russian).

5. Kawatek A. Analiza pol pr^dkosci i pr^dkosci odksztatcenia w asymetrycznej kotlinie walcowniczej [J]. Hutnik Wiadomosci Hutnicze. 2002, 12: 485-488, (in Polish).

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6. Dyja H., Wilk K. Asymetryczne walcowanie blach i tasm [M]. Wydawnictwo WMilM Politechniki Cz^stochowskiej, (Poland), 1998. 268.

7. Gorelik V.S., Nalcha G.I., Rudnev A.E., Klimenko I.V., Feofilaktov A.V. Uluchshenie sluzhebnykh svojstv tolstykh listov putem osvoenija tekhnologii asimmetrichnoj prokatki [J]. Stal', 11, 1991, 41-44 (in Russian).

8. Forge3® Reference Guide Release 6.2, Sophia-Antipolis, 2002.

9. Kawatek A. Asymetryczne walcowanie blach grubych w walcarce wykanczajqcej [J]. Hutnik Wiadomosci Hutnicze, 2006, 6: 266-270, (in Polish).

Chukin M.V., Korchunov A.G., Gun G.S., Polyakova M.A., Koptseva N.V.

NANODIMENTIONAL STRUCTURAL PART FORMATION IN HIGH CARBON STEEL BY THERMAL AND DEFORMATION PROCESSING

Abstract. On the example of high carbon steel of grade 80, updated by boron, the ability of forming nanodimensional structural constituents has been proved. Special types of thermal and deformation processing are used. The thin- plate pearlite structure, obtained in this way, according to modern material science concept is considered to be a nanomaterial where interlamellar spacing in a ferrite-carbide mixture is a nanodimensional element. It is experimentally proved that interlamellar spacing decreasing takes place in steel, being investigated after heat treatment and further cold plastic deformation. The rate of interlamellar spacing, after heat treatment, and cold plastic deformation is 1,66, the rate of billet geometrical dimensions, before and after deformation, is 1,6. The results obtained are used to achieve desired properties of high-tensile reinforcing bars of 9,6 mm in diameter for the new generation of concrete sleepers.

Keywords: Nanodimensional structural constituents, high carbon steel, pearlite structure, interlamellar spacing, thermal processing, deformation processing

Achievement of high quality and field reliability of metallic constructions is possible on the basis of knowledge-intensive technologies of getting materials with a new unique property package. Nowadays such technologies are those, which allow obtaining ultrafine and nanostructures, which considerably affect metal and alloy mechanical properties during the production of hardware items of different purpose [1]. This investigation actuality is stipulated by searching of an effective complex of impacts on billet microstructure with major diameters (more than 10,0 mm) made from high carbon steel to get the highest strength and ductility.

The aim of this work is to study peculiarities of getting nanodimensional structural constituents in the billet from high carbon eutectoid steel of grade 80, updated by boron, after special types of thermal and deformation processing. The thin- plate pearlite structure, obtained in this way, according to modern material science concept is considered to be a nanomaterial with structural constituents of plate form. Interlamellar spacing in a ferrite-carbide mixture is a nanodimensional element of steel structure.

The subject matter of the chosen thermal processing lies in heating and isothermal holding in the field of minimal stability of overcooled austenite with further cooling in lead hot melt. The thermal processing task is formed, in major diameter billets, steel structure, providing the capability of the highest hardening during the following deformation effect with large total deformation degrees.

The history of steel structural constituent fine crushing is known to be determined mainly by accumulation of sharing deformation in processing. Considerable steel structure fine crushing is achieved by large degrees of plastic deformation close to 1. To provide such processing conditions, repetitive cold plastic deformation was used. The differential characteristic of offered deformation effect is that operation modes are appointed in such a way, that each deformation cycle initiates active dislocations sliding and it provides additional fragmentation of microstructure and the highest hardening of thermally processed steel.

The billet of diameter 16,0 mm from high carbon steel with carbon content of 0.8 % was used to carry out the experiments. Thermal processing was realized with the following parameters: reheat temperature range was 930°C to 970°C; isothermal holding temperature range was 4700°C to 550°C. Ageing time was chosen that way to provide finishing diffusional decay of overcooled aus-tenite in the preset temperature. Cold plastic deformation was carried out with total deformation degree up to 60%. Herewith the billet diameter decreased from 16,0 mm to 10,0 mm. Scanning electron-microscope analysis of the bars was done on the electron microscope JEOL JSM-6490 LV with accelerating voltage 30 kW in modes of secondary and temporary reflected electrons in conditions of Nano Steel Research Studies Institute of Nosov Magnitogorsk State Technical University. Quality and quantity microanalysis was carried out on the metallographic mi-

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