CC BY
1UDC 621.77.014
PhD Korobko T.B, Senior lecturer Tokarev A. V. (DonSTU, Alchevsk, LPR)
DETERMINING SHIFT RESISTANCE OF METAL CONSIDERING TEMPERATURE-AND-RATE CONDITIONS OF COLD ROLLING
In the paper it has been analyzed the mathematical models of double shear resistance of metal at cold thin sheet rolling. On the basis of the analysis there has been shown that it is reasonable to account the impact of temperature-rate conditions of strain in the presented models. The improved by the authors a numeric mathematical model allows specifying the calculation of doubled shear resistance of metal considering temperature and rate of cold thin sheet rolling as well as real character of distributions along the deformation zone of its dimensional parameters and indicators of external contact friction.
Key words: cold rolling, elasticity stress, double shear resistance, temperature-rate conditions, deformation zone, mathematic simulation.
ISSN 2077-1738. CGopmiK HuynHbix mpydoe flottTTy. 2015. № 2
ME T AJ1 Jiy Prim
The problem and its connection with scientific and practical tasks.
New techniques for cold rolled bars production supplying the operation of automated control systems in technological process prove the need of increasing the accuracy of applied mathematical models.
In particular, the accurate determination of the calculated values of double shear resistance of deformable metal significantly affects the prediction accuracy of power parameters of rolling [1].
Author [2] believes that the definition of computed values of yield stress aT and hence double shear resistance 2K of the metal should be implemented only as a function of compression exponent of rolled strips. In [3, 4] it is shown that neglecting the influence of temperature-rate deformation conditions leads to substantial errors in the calculation of quantities and values aT and 2K. To determine the yield stress and double shear resistance for bars depending on the rate of cold rolling B. Roberts [5] developed a mathematical model that does not consider the effect of the strain temperature. More capable method of computation is proposed by A.P. Grudev and Y.B. Sigalov and is described in [6]. However, this method does not take into account the effect of the preliminary
deformation of the rolled metal. Mathematical model the authors [4] does not have these shortcomings. Herewith, applied numerical approach to the computation of normal contact stresses defining the strip temperature, has a number of assumptions, the most important of which are the constancy of the friction coefficient along the length of the strained zone, the application of the friction law of Coulomb-Amonton and idealization of the actual shape of the contact surface of the work rolls. Mathematical model [7] excludes the adoption of these assumptions, and so it is interesting to update on its basis the method [4] of quantify assessment of local and integral quantities and values aT and 2K .
Setting the problem.
Refinement of mathematical model for calculation of doubled shift resistance of metal considering temperature-and-rate conditions of cold rolling is an aim of the paper.
Presentation of the material and its results.
To determine the contact stresses they used mathematical model [7]. Deformation zone (fig. 1, a), consisting of zones of plastic forming length Lpi and elastic recovery length Ld
broke into augment Ax to form a finite set of n-number z'-th elementary volumes (fig. l,b), which position of the boundary sections (sec-
МЕТАЛЛУРГИЯ
tion ae and cd in fig. 1, b) was defined by coordinates Xj\ and Xj2Heights hxi\.
For calculation of contact stress a mathematical model has been used [7]. Deformation zone (fig. 1, a), which consists of plastic forming areas Lpi and elastic recovery Ld,
was broken with A x augment into a finite set of n z-th elementary volumes (fig. 1, 6), which location of boundary sections (sections ae and cd at fig. 1, 6) has been determined by Xj\ and Xj2 coordinates. Heights hxilandhxi2of
these sections were calculated basing the approach of I.Ya.Shtaerman [8], and rates VxilandVxi2 (fig. 1, 6) of metal particles motion were on the basis of sliding hypothesis [1]. Herewith a plastic forming area (fig. 1, a) has been divided into delay zone Lbac and outrunning zone, which length Ladv and depth hn of a bar in neutral section they determine considering stress of back aQ and frontal c?! tension, radial rate of rolls Vr, as well as rolling depth before hQ and after h\ passing. To calculate contact shear stress rxi\ and zxi2 (fig. 1, 6) one have used A.N. Levanov's principle, and to calculate normal contact (pxi\ and pxl2) and normal axial (crxi\ and axi2) stress they used principles of
Doubled shear resistance of metal considering temperature-rate influence the conditions of thin sheet cold rolling has been determined as follows [3,4]:
2Ktllxi2 = 2_Ksn'2 . ktxi2 -kuxj2, (1)
where 2K^- current value of double
shear metal resistance index, determined considering strengthening effect;
ktxi2.kuxi 2 - current values of indexes considering impact of strain temperature and rate accordingly;
number 2 in the index of variables indicates a finite boundary section (section ae at fig. 1, 6) of marked 7-th elementary volume.
For analytical description of changing the values of polynomials of the 3rd level
have been used [7, 8]:
2Ksxi2 = u55(°To +a\£xi2 +a2£xi2 +«3^2) (2)
where aTo - elasticity stress of metal in initial (annealed) state;
£xi2={H0-hxi2)/H0- current values of total extent of metal compression (H0 - depth of hot-rolled billet; hxi2 - current value of bar depth in deformation zone);
Figure 1 - Calculating schemes for deformation zone (a) and z-th elementary volume (6): o, - normal axial stress effective within the boundary of plastic forming and elastic recovery; axi - contact angle of
z-th elementary volume with rols
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indexes, which depend on chemical content of metal [8].
Values ktxi2, kuxi2 were calculated by parity of reasoning with authors [3, 4]:
Kxii ~ ao + a\
xi2 cm
+
V ПЛ J
(3)
+a.
t ., -t
xi 2 cm
V ПЛ J
t., -t
xi 2 cm
V пл J
7682,4
uxil = 1+-X
2KEXi2 ■ ktxi2
/('„:+273) (4)
In Ah/Av,
0,14
5 • 1011 -60,842
where - indexes, which depend
on chemical content of metal [3];
txi2 - current temperature values of a bar
in deformation zone;
tcT = 20° C - metal temperature at static tests; tpi - melting temperature of metal;
uxi2 = 2Ah Г{1ц [xi2 / Lnn)/ hi
xil пл
- current
value of strain rate (Fj -rolling rate;A/? = /?0 -hi - absolute compression after skip);
X - Boltzmann constant (0,862-KT4, ev/K).
Considering author's recommendations [3] to determine value txi2 algorithm consequence has been used of a such type:
Axxi2 =
ЧвыхРпл Axi2 Умсм
[l -{ха! ^ пл Л
txi2= Vi[ho + hxi2) '
(5)
(6)
хехр
умсм{К+Кп)
(7)
where txi2 - current value along length
Lpi (fog. 1, a) of temperature increment of a
bar due to heat, which is released at plastic deformation;
ppi - average pressure of metal onto rolls
in the zone of plastic forming, determined considering the results of calculations of normal contact stresses pxi\ и pxi2;
цvyh ~ index of heat release at plastic deformation equal to 0,84 - 0,94 [3];
Xxi2 = /?o / hxi2 - current values of compression index;
yM,cM - accordingly specific gravity and heat capacity of metal;
txi2 - current value of contact period of
particles with a roll along the area of plastic forming;
A = /?0//?| - index of bar compression during a skip;
to - bar's temperature at entering into strain area;
tv - average temperature of operating rolls;
ув,св,Яв - accordingly specific gravity, heat capacity and index of heat conductivity of operating rolls material.
As a result of numeric implementation of mathematical model (formulas (l)-(7)) have received calculated distributions along Lpi the
values of compression level sxi2, temperature
txi2 and rate uxi2 of deformation (fig. 2), as
well as values of double shear resistance of metal 2Ki:xii and 2КШХ11 (fig. 3). Mathematical
modeling has been made for the first cage of cold thin sheet rolling of PC MISW of Ilyich.
Herewith, for initial data it was used: rolled bar grade - steel 08кп; bar depth before skip /?0 = 2 mm; bar width B= 1260 mm; compression level value during a skip s =0,3; rare tension stressHa <tq = 0 MPa; front tension stress a\ = 100 MPa; bar's output rate from the deformation zone V\ = 5 м/с; friction index / = 0,12.
МЕТАЛЛУРГИЯ
Analysis of the results obtained during mathematical simulation has shown that temperature and strain rate variation along the deformation forming zone has got a complex character (fig. 2).
Wherein, accounting the impact of temperature-rate conditions of cold thin sheet
rolling lead to redistribution of values of double shear resistance of metal (fig. 3).
In separate cases difference in values 2Ksxi2 and 2Ktuxil can be 20% and more that
has been valuable and should be considered at predicting of metal pressure onto rolls as well as power and capacity of cold rolling of thin bars.
С * tKp. С S
100 0,35
£1 175
15Г»
125
100
75
50
Я E _
90 SO
0.30 0J5
70 - 0.20
GO- 0.15
50 0,10
-10 0.05
30 4 0. 0
A * s '
■4 s ->
A > X
t / \ \ 1 V
/ / s i \\
/ \
xi2
oj
0,J
0,6
OS
I L
ПЯ
Figure 2 - Calculated distributions of values for compression level sX[2 (1), strain temperature lxP (2) and rate u xi2 (3) along the length of plastic forming zone of deformation zone
600 ¿50 500 450 400 350 300 250
2Kni2;2Kteil,MIIa
/ ? ■os.
/ / 4 \ v
/ ] J \\ \ n
=42
0,2 0,4 0,6 0,S
1 ^-пл
Figure 3 - Calculated distributions of values of double shear resistance of metal at cold thin sheet rolling along the length of plastic forming zone determined when considering the influence of only strengthening 2Kexi2 (1) and temperature-rate conditions of strain 2Kluul (2)
ISSN 2077-1738. Сборник научных трудов ДонГТУ. 2015. № 2
МЕТАЛЛУРГИЯ
Conclusions and directions for further research.
As a result of the fulfilled researches there was refined a mathematical model for calculation of doubled shift resistance of metal considering temperature-and-rate conditions of deformation mainly meeting the real production conditions of cold rolled bars at industrial roll mills.
Bibliographic list
On the results of numeric implementation of developed model it has been found out that if impact of temperature and rate of cold thin
sheet rolling onto the values °T and 2A" js excluded , the assumed mistake is about 20% and more, that approves the reasonability of the problem being solved in the paper.
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2. Garber Je. A. Stany holodnoj prokatki. (Teorija, oborudovanie, tehnologija) / Je. A. Garber. — M. : ОАО «Chermetinformacija»; Cherepovec : GOU VPO ChGU, 2004. — 416 s.
3. Vasilev Ja. D. Inzhenernye modeli i algoritmy rascheta parametrov holodnoj prokatki / Ja .D. Vasilev. — M. : Metallurgija, 1995. —368 s.
4. Mazur V. L. Teorija i tehnologija tonkolistovoj prokatki (chislennyj analiz i tehnicheskie priloz-henija) / V. L. Mazur, A. V. Nogovicyn. —Dnepropetrovsk : RVA «Dnipro-VAL», 2010. — 500 s.
5. Roberts V. Holodnaja prokatka stali / V. Roberts; pod. red. P. I. Poluhina, V. P. Poluhina // Cold rolling of steel; per. s angl. — M. : Metallurgija, 1982. — 544 s.
6. Kaplanov V.I. Dinamika i tribonika \ysokoskorostnoj tonkolistovoj prokatki. Mirovaja tendencija iperspektiva : monografija / V.I. Kaplanov. - Mariupol': Renata, 2008. - 456 s.
7. Satonin A. V. Razvitie chislennyh odnomernyh matematicheskih modelej naprjazhenno-deformirovannogo sostojanija metalla pri holodnoj prokatke otnositel'no tonkili polos / A. V. Satonin, A. G. Prisjazhnyj, A. M. Spaskaja, A. S. Churunakov // Obrabotka metallov davleniem : sb. nauch. tr. — Kramatorsk: DGMA, 2012. —№ 2(31). — S. 62-68.
8. Fedorinov V. A. Matematicheskoe modelirovanie naprjazhenij, deformacij i osnovnyh pokazatelej kachestva pri prokatke otnositel'no shirokih listov i polos : monografija / V. A. Fedorinov, A. V. Satonin, Je. P. Gribkov //Donbas. gos. mashinostroit. akad. —Kramatorsk, 2010. —243 s.
Recommended to printing by Doctor of Engineering Science, Prof. DonSTU Novokhatskiy A.M.,
Head of section rolling mill PJSC «AISW» Klepach E.N.
The date of submission 23.11.15.
k.t.h. Коробко Т.Б., Токарев A.B. (ДонГТУ, г. Алчевск, JIHP)
ОПРЕДЕЛЕНИЕ УДВОЕННОГО СОПРОТИВЛЕНИЯ МЕТАЛЛА СДВИГУ С УЧЕТОМ ТЕМПЕРАТУРНО-СКОРОСТНЫХ УСЛОВИЙ ХОЛОДНОЙ ТОНКОЛИСТОВОЙ ПРОКАТКИ
В статье проанализированы математические модели удвоенного сопротивления металла сдвигу при холодной тонколистовой прокатке. На основе выполненного анализа показана целесообразность учета в указанных моделях влияния температурно-скоростных условий процесса деформации. Усовершенствованная авторами статьи численная математическая модель позволила уточнить расчет удвоенного сопротивления металла сдвигу с учетом температуры и скорости холодной тонколистовой прокатки, а также реапьного характера распределений по длине очага деформации его геометрических параметров и показателей внешнего контактного трения.
Ключевые слова: холодная прокатка, напряжение текучести, удвоенное сопротивление сдвигу, температурно-скоростные условия, очаг деформации, математическое моделирование.
ЖЫ 2077-1738. Сборник научных трудов ДонГТУ. 2015. № 2
МЕТАЛЛУРГИЯ
к.т.н. Коробко Т.Б., Токарев О.В. (ДонДТУ, м. Алчевськ, ЛНР)
визнАЧЕНия подвоеного ОПОРУ ЗРУШЕННЮ ДЕФОРМОВАНОГО МЕТАЛУ 3 УРАХУВАННЯМ ВПЛИВУ ТЕМПЕРАТУРНО-ШВИДК1СНИХ умов холодно! Т0НК0ЛИСТ0В01 ПРОКАТКИ
У статпи проаналгзоват математичт моделг напруги текучоат г подвоеного опору металу зруьиенню при холоднш тонколыстовш прокатщ. На основ! виконаного аналгзу показана дощлъ-тстъ облгку у вказаних моделях вплыву температурно-швидтсних умов процесу деформаци. Вдосконалена авторами статпи чисельна математична модель дозволила уточнити розраху-нок подвоеного опору металу зруьиенню з врахуванням температуры г швидкоат холодног тон-колистовог прокатки, а також реального характеру розподшу по довжит осередку деформаци геометричних параметров г показниюв зовтшнъого контактного тертя.
Ключосп слова: холодна прокатка, напруга плинноат, подвоений отр зруьиенню, температу-рно-ьивидюст умови, осередок деформаци, математычне моделювання.
