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Energy analysis of a through-put radial forging machine
Journal of Materials Processing Technology 86 (1999) 291 – 299
Energy analysis of a through-put radial forging machine S.P. Bourkine a,*, N.A. Babailov b, Y.N. Loginov a, V.V. Shimov a a
b
Metallurgical Department, Ural State Technical Uni6ersity, 19 Mira Street, 620002 Ekaterinburg, Russia Institute of Engineering Science, Ural Branch of Russian Academy of Sciences, 91 Per6omaiskaia Street, GSP-207, 620219 Ekaterinburg, Russia Received 23 July 1997
Abstract The problem of a detailed study of the thermomechanical features of radial reduction is associated with the new technological processes of the direct combination of continuous casting and forming of metals and alloys. It is difficult to secure economical efficiency in small-tonnage metallurgical production by means of the employment of traditional technological schemes. If the heat of the casting operation is used for the following hot working, the production of metal products can be made economical for comparatively small volumes of production (20/50 thousand tons year − 1). Through-put forging is one of few processes that can be simply combined with both horizontal continuous casting and subsequent rolling. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Through-put radial forging; Thermomechanical; Metallurgical production
1. Introduction The problem of the manufacture of qualitative metal products from continuously cast billets is associated with producing large total strains to convert the cast structure of metal. The employment of deformation modes of combined loading, for example, radial reduction with transverse shear, makes it possible to obtain a good quality, hot-deformed semi-finished product from a continuously cast billet. Unlike traditional radial or rotary forging, the reduction in such a process is carried out for one stroke of the die up to the final section size. The contact surfaces of the dies constantly form a polygonal (from 3 to 8) closed contour in the gap during reduction. Fig. 1 presents a diagram of the scheme of through-put multi-die forging. The direct combination of continuous casting of billets with through-put radial reduction in a cast – deformation assembly complicates the stress state of the metal during the forging of the billet. Specifically, radial reduction is carried out during the action of additional axial stresses. Transverse shear stresses operating upon the billet during the reduction generate the twisting of the billet. * Corresponding author. [email protected],su
Fax:
+7
3432
743884;
e-mail:
There are numerous optimization parameters of the through-put radial forging process for the selection of rational technology since many variants of this process, utilized instead of billet rolling, can be obtained by the variation of pass numbers, reduction plans and single feeds. The influence of the radial reduction parameters on energy consumption during the execution of intensive deformation of cast billets is analysed in the present work. The proposed methods and results of the calculation of specific deformation situations enables a comparison of the productivity of the working process of the billet and allows a comparison of the energy consumption of radial forging and other breakdown operations such as extrusion, cogging rolling and reducing which are in principle admissible for combination with continuous casting and rolling.
2. Methods of calculation of the energy consumption for through-put radial forging Forming during multi-die radial forging is realised by a multi-sectional forging block. The calculation of forming was carried out within the framework of the hypothesis about the invariance of the billet diameter in the deformation domain up to the moment of the filling
0924-0136/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII S0924-0136(98)00319-7
S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299
292
+
Fig. 1. The scheme of the deformation of the billet by multi-die forging block. (a) The clamping and deformation up to the filling of the die space (1st stage). (b) The deformation when the gap between the dies is filled completely by metal (2nd stage); 1 is the deformable billet; 2 is the die of forging block.
of the gap between the dies by metal (deformation is realized without widening). This hypothesis is confirmed with experiments [1,2]. The process of deformation of a cylindrical billet by multi-die forging block can be divided conditionally into two stages: the first stage is the clamping and deformation up to the filling of the die space (Figs. 2 and 3(a) show the section of the billet); whilst the second stage is the deformation when the gap between the dies is filled in by metal completely (Figs. 2 and 3(b) show the section of the billet). A diagram of the work cycles of the three-sectional forging block is shown in Fig. 4. The solution of the problem of the determination of the contact stresses during radial forging by a four-dies forging block has been obtained by the analytical method of the solution of approximate equations of equilibrium and the state of plasticity. The analysis of the radial reduction by a multi-die forging block (with the number of dies not less than three) is presented [3,4]. The relative contact stress for the stage of the full filling of the die gaps by metal is determined by the equation:
p 1 A ah − =1+ ss sin (a)r 2 2 rlkl0
2A 2 0.58c lkl0 + 3 cos (a/2) 2r r lkl0
(1)
where lk is the length of the contact die surface with the billet; l0 is the relative feed, l0 = Lk0/RH; Lk0 is the feed of the billet into the dies of forging block; RH is the radius of the external surface of the billet before deformation; r is the current relative radius of the circumcircle of the billet cross-section, r=Ri /RH; h is the parameter that characterizes the action of the drawing device out of the continuous casting machine, h=s0/ss; s0 is the backing stress of the drawing device out of the continuous casting machine; A is the value determined as A= 3ha/8c sin(a/2) and c is the friction factor. The relative contact stress before the moment of the filling of the gap between the dies by metal for the mode ‘circle–square’ is expressed as:
p ph 1
3hp = 1+ − p −2(g − sin g) 2 16cr sin (g/2)lkl0 ss
4cr sin (g/2)
lkl0
3 [p− 2(g − sin g)] 2 3h 2p 2 + 2 2 128c r sin2(g/2)lkl0
+
(2)
where g= 2 arccos (Ri / 2RH); and for the mode ‘square–square’ with rotation of 45° is:
p h 1
3h = 1+ − ss 1−2(1− r)2 2 8 2c(1− r)lkl0 2 2c(1− r) 3h 2 lkl0 + + 64c 2(1−r)2lkl0
3 [1 − 2(1− r)2] 2
(3)
where r is the moving relative radius of the billet, r= Ri /BK. The relative contact length in the Nth forging block may be expressed as: {lk}N = {(lk)1}N {(lk)2}N
(4)
Fig. 2. The profile of the billet during deformation by a four-die forging block for the pass ‘circle – square’. (a) The first stage of deformation. (b) The second stage of deformation.
2.011 2.601 2.403
¥ 80– 50
50– 31
31– 20
I II III
0.375 0.380 0.355
Reduction (o)
1.25 1.27 1.18
Rate of strain (s−1)
The temperature of the billet is T0 = 1250°C, whilst the feed of the billet is LK0 =50 mm.
Extension (l)
Technological pass (mm)
No. of forging block 61.9 73.2 76.0
ss (MPa)
Table 1 Technological and power and force parameters of a billet forging with a multi-sectional forging block
1133 1068 1042
Temperature at entrance (°C)
1068 1042 1024
Temperature at exit (°C)
1.45 2.35 2.35
p/ss
451 694 429
Force of deformation (kN)
150 146 52
Power (kW)
S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299 293
2.011 2.601 2.403
¥ 80– 50
50– 31
31– 20
I II III
0.375 0.380 0.355
Reduction (o)
1.25 1.27 1.18
Rate of strain (s−1)
The temperature of the billet is T0 = 1200°C, whilst the feed of the billet is LK0 =50 mm.
Extension (l)
Technological pass (mm)
No. of forging block 67.9 78.6 80.6
ss (MPa)
Table 2 Technological and power and force parameters of billet forging with a multi-sectional forging block
1096 1040 1019
Temperature at entrance (°C)
1040 1019 1005
Temperature at exit (°C)
1.45 2.35 2.35
p/ss
495 745 455
Force of deformation (kN)
165 157 56
Power (kW)
294 S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299
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295
Fig. 3. The profile of the billet during deformation by a four-die forging block for the pass ‘square – square’ (with rotation of 90°). (a) The first stage of deformation. (b) The second stage of deformation.
where N= 1, 2, 3; {(lk)1}N is the relative contact length of the die with the billet during the first stage of deformation under the deformation according to modes ‘circle–square’ or ‘square – square’ in the Nth forging block, this length being determined in conformity with the recommendations of [3]; and {(lk)2}N is the relative contact length of the die with the billet during the second stage of deformation in the Nth forging block, this length being by Eq. (5). The value of {lk}N is the relative feed into the (N +1 )th forging block. The forming of the deformable billet was determined from the incompressibility condition [3]. The equation for the determination of the relative contact length during radial reduction for nth press of dies is expressed as: lkn =
n n n n
n
1 qn q 1 n − 1 qn − m + 1 + % m + 1− n ln 2 2 r m = 1 2 m!r r
+ 1−
qn − 1 A 1 −1 2 l0 r
n−2
qn − m A 1 ln m r m=1 2 m! rl0
+%
m
m
n
A 1 ln n−1 2 n!rl0 r
+
n
(5)
3. Results of the calculation of the specific work of forging The determination of power and force parameters for the forging of a continuously cast billet by a three-sectional block (when a continuous casting machine and a forging block are combined directly) requires the knowledge of the total change of billet temperature: DT = DT1 + DT2 + DT3 − DT4
where DT1 and DT2 are the decrease in the temperature of the billet owing to heat emission and convection, respectively (DT2 = 0), (°C); DT3 is the decrease in the temperature of the billet on account of thermal conductivity during the contact of the billet with dies, (°C); and DT4 is the increase in the temperature of the billet owing to the transformation of mechanical energy of deformation into heat, (°C). The change in the billet temperature during the period of forging in one forging block and the motion to the next block can be calculated on the basis of the method of Tselikov [5], accepting that Dt = DT1 −DT4. It is expressed as: Dt = T0 −
' 3
where qn is the numerical row, calculated from the equation qn + 1 =1− qn /2 (where q1 =0). The relative power of deformation for forging is determined from the equation: N( =
&
o1
pcp (o) do/t( 0 ss
(6)
where o is the relative reduction, o =1 −r; t( is the relative deformation time, t( =t/t0; and t0 is the deformation time when the forging assembly has maximum productivity. Fig. 5(a) and (b) shows the dependence of the relative power of deformation, N( , on the reduction, o according to the different values of the parameter h (for the stage of full filling of the gap between the dies by metal).
(7)
1000
0.0255 · II · t 1000 + v T0 + DT4 + 273
3
+273 (8)
where T0 is the temperature of the billet before entry into the forging block (°C); II is the perimeter of the cross-section of the billet after forging (mm); v is the area of the cross-section of the billet after forging (mm2); and t is the cooling time (s). The decrease in the temperature of the billet on account of thermal conductivity during the contact of the billet with the dies are given as follows [6]: DT3 =
4SK(T0 − TD )tKaK cG
(9)
where SK is the area of the contact of the die with the billet at the end of reduction (m2); TD is the die temperature (°C), (TD = 200°C); T0 is the billet temper-
S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299
296
Fig. 4. Diagram of the work cycles of a three-sectional forging block combined with a continuous casting machine.
ature (°C); tK is the time of contact (h); aK is the coefficient of heat rejection (aK =20 kW m − 2 K); c is the heat capacity of billet metal (kJ kg − 1 K); and G is the weight of the billet (kg). The temperature increase of the billet owing to the transformation of mechanical energy of deformation into heat is determined by Eq. (6) DT4 =0.183ss ln l
(10)
where ss is the flow stress of the metal of the billet determined by the method of thermo-mechanical coefficients [7], MPa; and l is the coefficient of elongation (extension). The results of the calculation of the energy consumption for forging by a three-sectional forging block combined with a continuous-casting machine are given in the Tables 1 and 2. The specific work of radial forging when the radial forging is combined with continuous casting was calculated according to the proposed method of calculation, and correlated with speeds comparable of section rolling. It may be presented by the following data (the coefficient of efficiency of the drive is not taken into consideration): for a reduction in a one-section forging block it is 100/125 MJ t − 1; for a two-section forging block it is 55/70 MJ t − 1; and for a three-section forging block it is 35/40 MJ t − 1. 4. Discussion It is interesting to carry out a comparative analysis of the energy consumption for known processes of metal forming. It is the analysis that gives the possibility of discussing the advantages and shortcomings of radial forging combined with continuous casting. The energy of section rolling depends on the system of grooves. The calculation of the energy consumption of section rolling is made on the basis of data of the pressure, the moment and the power of rolling. These values are determined according to known methods [8] during the calculation of grooving. The temperature regime of the rolling is also analysed.
If the power N and the speed of the rolling n (rev min − 1) are known, the work of the rolling of the bar of the length L1 is expressed by the equation: L1 V
A=N · t= N
(11)
where t is the rolling time; V= pnR/30 is the velocity, and R is the rolling radius of roll. For some products [6] the specific deformation work is transferred to the unit volume of the billet using the dimension J cm − 3. Let this value be AV, then: AV =
A 30N = VhM pRnF1hM
(12)
where hM is the coefficient of efficiency of the drive and F1 is the area of the cross-section of the bar. It is more convenient to use the deformation work referred to unit mass of the billet with metal of density g: Am =
30N pRnF1hMg
(13)
Consider the process of the rolling of a round billet made of mild steel on a continuous mill 200. The diameter of the billet is 45 mm before rolling and 20 mm after rolling. Calculated parameters of the forming as well as the power and the force parameters are given in Table 3. These values are utilized as initial data. The specific energy consumption for continuous rolling was determined by Eqs. (12) and (13) using the data of Table 3 and are presented in Table 4. It was assumed that hM is equal to unity everywhere. The data of Table 4 enables the estimation of the energy consumption of separate passes of rolling as well as the total energy consumption of continuous rolling. The example considered is the continuous rolling of a bar in the system of grooves ‘oval–oval rotated through 90°’. This grooving is very popular in section rolling, although it does not have high elongation ability. However, the comparison of the energy consumption for different groovings did not show essential distinctions of total energy consumption under the compared conditions of rolling.
S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299
297
Fig. 5. The dependence of the relative deformation power on the reduction during deformation with the feed l0 =1.0 when the friction factor on the contact surface is: (a) c =0.5 and (b) c= 0.8, where: 1 − h =1.0; t( = 1; 2 −h =0.8; t( =1; 3 −h =0.6; t( =1; 4 −h = 0.4; t( =1; 5 −h= 0.2; t( =1; 6− h= 0 and t( = 1.
Amongst known methods of forming for the continuous deformation of a continuously cast billet there is also extrusion [9]. Extrusion can defy competition with other methods for the processing of a continuously cast billet. The work of extrusion is estimated by the equation: A = PLn, where P is the force of extrusion and Ln is the length of the billet after extrusion. The specific work of extrusion may be expressed as follows: Am =
P PLn = VhMg FhMg
where F is the area of the cross-section of the container and hM is the efficiency coefficient of the extruder drive. The force of extrusion is determined by the known equation (14)
P= Rf + Tf + Tb +Tc
where Rf is the fraction of the force for deformation and Tf, Tb and Tc are the fraction of the force to
overcome the action of the force of friction in the die, in the sizing bush and the container, respectively (Tc = 0 for the indirect extrusion). The variables of Eq. (14) are calculated by the methods described in Ref. [10] and depend on the form of the deformation domain, the friction factor and the flow stress ss. The latter is approximated [11] by the equation: ss =
ao mu n exp (qt)
where a, m, n and q are empirical coefficients depending upon the deformable metal; o =ln (l) is the relative reduction and u is the strain rate u= 66l ln(l)tga/ (l l − 1)d (where 6 is the velocity of extrusion; d is the diameter of the billet after the extrusion; 2a is the angle of the die). The specific energy consumption for the extrusion of a steel bar with a diameter of 20 mm from a billet with a diameter of 45 mm at a temperature of 1200°C and a velocity at the exit of the die of 2.1 m s − 1 is calculated similarly to the previous example. The parameters for the determination of the specific energy consumption for the extrusion are l=5.06;
Table 3 Parameters of the rolling of a round bar to a diameter of 20 mm from a billet with a diameter of 45 mm, at a temperature of 1200°C Number of the pass
Shape and dimensions of the bar (mm)
Cross sectional area (mm2)
0 1 2
Circle 45 Oval 28.0×52.2 Oval (rotated through 90°) 41.0×32.8 Oval 22.0×45.7 Oval (rotated through 90°) 33.0×26.4 Oval 19.5×34.5 Circle 23.8 Oval 17.8×25.8 Circle 20.2
1590 1190 1012
1.34 1.174
800 650 555 444 368 314
3 4 5 6 7 8
Extension
Velocity (rev min−1)
Moment (kN m)
Power (kW)
42.4 51.3
6.63 2.11
29.5 11.4
1.264 1.234
62.2 78.6
3.57 2.52
23.2 20.7
1.174 1.25 1.21 1.17
89.3 142.7 169.3 200
1.87 1.76 1.70 0.89
17.5 26.3 30.2 18.7
298
S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299
Table 4 The specific energy consumption of the rolling process Number of the pass
1 2 3 4 5 6 7 8
Specific energy consumption
Cumulative total of the specific energy consumption
(J cm−3)
(kW · h t−1)
(MJ t−1)
(J cm−3)
(kW · h t−1)
(MJ t−1)
55.8 21.0 44.5 38.7 33.7 39.6 46.3 28.4
1.98 0.74 1.58 1.37 1.20 1.41 1.64 1.01
7.13 2.66 5.69 4.93 4.32 5.08 5.90 3.64
55.8 76.8 121.3 160.0 193.7 233.4 279.7 308.1
1.98 2.73 4.32 5.70 6.90 8.31 9.96 10.97
7.13 9.79 15.55 20.52 24.84 29.92 35.86 39.49
6 = 0.415 m s − 1; u= 170 s − 1; and o = 0.80. The flow stress of the metal at the exit of die is ss =120.8 MPa for a= 1250 MPa; m =0.25; n =0.14 and q = 0.0025. The volume average value of the flow stress is s¯ s = 96.64 MPa. Under these parameters, the force of the extrusion is P= 392.8 kN and the specific energy consumption is Am =31.7 MJ t − 1 = 8.80 kW · h t − 1. The calculation was carried out for the indirect extrusion. As to the direct extrusion, the specific energy consumption increases by 20/25%. Hence, it follows that direct extrusion is inferior to section rolling as to specific energy consumption. Indirect extrusion gains advantage, but unfortunately is rarely used. A similar calculation of the specific energy consumption for radial forging combined with continuous casting was accomplish for comparable conditions. The forging of the bar of square section 17.72 × 17.72 mm from a billet with the diameter of 45 mm at a temperature of 1200°C and the velocity of forged bar 2.1 m s − 1 at exit was considered. The following modes of the radial forging of the billet were considered (all modes were transferred to comparable values of the capacity of rolling and extrusion): 1. Forging by the scheme: a circle with a diameter 45 mm to a square of sides 17.72 mm in a one-section forging block with a feed of 22.5 mm (the time of one stroke of the die is t= 0.0054 s); ss =62.6 MPa. 2. Forging by the scheme: a circle with a diameter of 45 mm to a square of sides 29 mm and then to a square of sides 17.72 mm in a two-section forging block with a feed of 22.5 mm; two strokes of the second section fit one stroke of the first section; t =0.018 s; ss = 82 MPa. 3. Forging by the scheme: a circle with a diameter of 45 mm to a square of sides 33 mm, further to the square of sides 24 mm, then to the square of sides 17.72 mm in a three-section forging block with a feed of 22.5 mm; two strokes of the second section .
and four strokes of the third section fit one stroke of the first section; t = 0.008 s; ss = 98 MPa. The specific energy consumptions are: for the one-section forging block Am = 46.5 MJ t − 1 = 20.8 kW · h t − 1; for the two-sectional one Am = 35.6 MJ t − 1 = 14.3 kW · h t − 1; for the three-sectional one Am = 29.3 MJ t − 1 = 11.3 kW · h t − 1. The analysis shows that the through-put radial forging has the greatest energy consumption. The energy consumption of through-put radial forging remains quite high, even after significant subdivision of the deformation between sections of the multi-die forging block. The further sub-division of deformation is able to provide efficiency of forging in comparison with continuous rolling and direct extrusion, but it is not reasonable in all respects.
5. Conclusions Presently, the through-put radial forging is considered, especially in combination with continuous casting, as a pertinent method for the intensive reduction of metal. However the forging leads to overconsumption of energy. The best course would be to decrease the single reductions, i.e. to use multi-sectional blocks. The design of such forging blocks is complicated and operation and automation are made difficult. However, as can be seen from the results of the analysis, throughput radial forging can compete with the other methods of forming in energy consumption. On the other hand, forging compares favourably with rolling and especially extrusion by the short duration of the contact between the deformable metal and the die. Heat loss is insignificant during forging. There was no possibility, when the analysis was being realized, to take into consideration the real change of metal temperature. This circumstance may appear important for the selection of the processing technology of metals and alloys having inadequate workability.
S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299
Through-put radial forging is the most suitable method for the formation of continuous cast billets. Insufficient ductility of the cast metal and a temperature gradient in the section do not affect the success of plastic working.
[4]
[5] [6]
References [7] [1] S.P. Bourkine, V.P. Tatarchenkov, E.A. Andrukova, The powerenergy parameters of radial forging with shear, Dep. VNIITEMR 09.11.88 N 409-MIII88 (in Russian). [2] E.A. Andrukova, S.P. Bourkine, O.V. Perepliotchikova, et al., The kinematic parameters of the deformation zone during radial reduction with shear, Dep. VNIITEMR 09.11.88 N 408-MIII88 (in Russian). [3] S.P. Bourkine, N.A. Babailov, The analysis of radial reduction
[8] [9] [10] [11]
of axisymmetric billets by the multi-die block, Dep. VNIITEMR 12.05.93, No. 31-MIII93 (in Russian). V.L. Kolmogorov, S.P. Burkin, N.A. Babailov, Automated forging center as renaissance of hammer forging in heavy industry, J. Mater. Proc. Technol. 56 (1 – 4) (1996) 631 – 642. A.I. Tselikov, The theory of account of efforts in rolling mills, Metallurgizdat (1954) (in Russian). A. Hensel, T. Spittel, Account of power-energy parameters during processing of metal forming, Metallurgy (1982) (in Russian). A.I. Tselikov, A.D. Tomlenov, V.I. Zuzin, et al., The rolling theory, Metallurgy (1982) (in Russian). V.K. Smirnov, V.A. Shilov, Y.V. Inatovich, Roll surface grooving, Metallurgy (1987) (in Russian). Forming of light and special alloys, VILS (1996) (in Russian). I.L. Perlin, L.H. Raytbarg, Theory of metal extrusion, Metallurgy (1975) (in Russian). V.I. Zuzin, A.V. Tretiakov, The mechanical properties of metals and alloys during metal forming, Metal (1993) (in Russian).
.
.
299
Energy analysis of a through-put radial forging machine S.P. Bourkine a,*, N.A. Babailov b, Y.N. Loginov a, V.V. Shimov a a
b
Metallurgical Department, Ural State Technical Uni6ersity, 19 Mira Street, 620002 Ekaterinburg, Russia Institute of Engineering Science, Ural Branch of Russian Academy of Sciences, 91 Per6omaiskaia Street, GSP-207, 620219 Ekaterinburg, Russia Received 23 July 1997
Abstract The problem of a detailed study of the thermomechanical features of radial reduction is associated with the new technological processes of the direct combination of continuous casting and forming of metals and alloys. It is difficult to secure economical efficiency in small-tonnage metallurgical production by means of the employment of traditional technological schemes. If the heat of the casting operation is used for the following hot working, the production of metal products can be made economical for comparatively small volumes of production (20/50 thousand tons year − 1). Through-put forging is one of few processes that can be simply combined with both horizontal continuous casting and subsequent rolling. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Through-put radial forging; Thermomechanical; Metallurgical production
1. Introduction The problem of the manufacture of qualitative metal products from continuously cast billets is associated with producing large total strains to convert the cast structure of metal. The employment of deformation modes of combined loading, for example, radial reduction with transverse shear, makes it possible to obtain a good quality, hot-deformed semi-finished product from a continuously cast billet. Unlike traditional radial or rotary forging, the reduction in such a process is carried out for one stroke of the die up to the final section size. The contact surfaces of the dies constantly form a polygonal (from 3 to 8) closed contour in the gap during reduction. Fig. 1 presents a diagram of the scheme of through-put multi-die forging. The direct combination of continuous casting of billets with through-put radial reduction in a cast – deformation assembly complicates the stress state of the metal during the forging of the billet. Specifically, radial reduction is carried out during the action of additional axial stresses. Transverse shear stresses operating upon the billet during the reduction generate the twisting of the billet. * Corresponding author. [email protected],su
Fax:
+7
3432
743884;
e-mail:
There are numerous optimization parameters of the through-put radial forging process for the selection of rational technology since many variants of this process, utilized instead of billet rolling, can be obtained by the variation of pass numbers, reduction plans and single feeds. The influence of the radial reduction parameters on energy consumption during the execution of intensive deformation of cast billets is analysed in the present work. The proposed methods and results of the calculation of specific deformation situations enables a comparison of the productivity of the working process of the billet and allows a comparison of the energy consumption of radial forging and other breakdown operations such as extrusion, cogging rolling and reducing which are in principle admissible for combination with continuous casting and rolling.
2. Methods of calculation of the energy consumption for through-put radial forging Forming during multi-die radial forging is realised by a multi-sectional forging block. The calculation of forming was carried out within the framework of the hypothesis about the invariance of the billet diameter in the deformation domain up to the moment of the filling
0924-0136/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII S0924-0136(98)00319-7
S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299
292
+
Fig. 1. The scheme of the deformation of the billet by multi-die forging block. (a) The clamping and deformation up to the filling of the die space (1st stage). (b) The deformation when the gap between the dies is filled completely by metal (2nd stage); 1 is the deformable billet; 2 is the die of forging block.
of the gap between the dies by metal (deformation is realized without widening). This hypothesis is confirmed with experiments [1,2]. The process of deformation of a cylindrical billet by multi-die forging block can be divided conditionally into two stages: the first stage is the clamping and deformation up to the filling of the die space (Figs. 2 and 3(a) show the section of the billet); whilst the second stage is the deformation when the gap between the dies is filled in by metal completely (Figs. 2 and 3(b) show the section of the billet). A diagram of the work cycles of the three-sectional forging block is shown in Fig. 4. The solution of the problem of the determination of the contact stresses during radial forging by a four-dies forging block has been obtained by the analytical method of the solution of approximate equations of equilibrium and the state of plasticity. The analysis of the radial reduction by a multi-die forging block (with the number of dies not less than three) is presented [3,4]. The relative contact stress for the stage of the full filling of the die gaps by metal is determined by the equation:
p 1 A ah − =1+ ss sin (a)r 2 2 rlkl0
2A 2 0.58c lkl0 + 3 cos (a/2) 2r r lkl0
(1)
where lk is the length of the contact die surface with the billet; l0 is the relative feed, l0 = Lk0/RH; Lk0 is the feed of the billet into the dies of forging block; RH is the radius of the external surface of the billet before deformation; r is the current relative radius of the circumcircle of the billet cross-section, r=Ri /RH; h is the parameter that characterizes the action of the drawing device out of the continuous casting machine, h=s0/ss; s0 is the backing stress of the drawing device out of the continuous casting machine; A is the value determined as A= 3ha/8c sin(a/2) and c is the friction factor. The relative contact stress before the moment of the filling of the gap between the dies by metal for the mode ‘circle–square’ is expressed as:
p ph 1
3hp = 1+ − p −2(g − sin g) 2 16cr sin (g/2)lkl0 ss
4cr sin (g/2)
lkl0
3 [p− 2(g − sin g)] 2 3h 2p 2 + 2 2 128c r sin2(g/2)lkl0
+
(2)
where g= 2 arccos (Ri / 2RH); and for the mode ‘square–square’ with rotation of 45° is:
p h 1
3h = 1+ − ss 1−2(1− r)2 2 8 2c(1− r)lkl0 2 2c(1− r) 3h 2 lkl0 + + 64c 2(1−r)2lkl0
3 [1 − 2(1− r)2] 2
(3)
where r is the moving relative radius of the billet, r= Ri /BK. The relative contact length in the Nth forging block may be expressed as: {lk}N = {(lk)1}N {(lk)2}N
(4)
Fig. 2. The profile of the billet during deformation by a four-die forging block for the pass ‘circle – square’. (a) The first stage of deformation. (b) The second stage of deformation.
2.011 2.601 2.403
¥ 80– 50
50– 31
31– 20
I II III
0.375 0.380 0.355
Reduction (o)
1.25 1.27 1.18
Rate of strain (s−1)
The temperature of the billet is T0 = 1250°C, whilst the feed of the billet is LK0 =50 mm.
Extension (l)
Technological pass (mm)
No. of forging block 61.9 73.2 76.0
ss (MPa)
Table 1 Technological and power and force parameters of a billet forging with a multi-sectional forging block
1133 1068 1042
Temperature at entrance (°C)
1068 1042 1024
Temperature at exit (°C)
1.45 2.35 2.35
p/ss
451 694 429
Force of deformation (kN)
150 146 52
Power (kW)
S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299 293
2.011 2.601 2.403
¥ 80– 50
50– 31
31– 20
I II III
0.375 0.380 0.355
Reduction (o)
1.25 1.27 1.18
Rate of strain (s−1)
The temperature of the billet is T0 = 1200°C, whilst the feed of the billet is LK0 =50 mm.
Extension (l)
Technological pass (mm)
No. of forging block 67.9 78.6 80.6
ss (MPa)
Table 2 Technological and power and force parameters of billet forging with a multi-sectional forging block
1096 1040 1019
Temperature at entrance (°C)
1040 1019 1005
Temperature at exit (°C)
1.45 2.35 2.35
p/ss
495 745 455
Force of deformation (kN)
165 157 56
Power (kW)
294 S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299
S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299
295
Fig. 3. The profile of the billet during deformation by a four-die forging block for the pass ‘square – square’ (with rotation of 90°). (a) The first stage of deformation. (b) The second stage of deformation.
where N= 1, 2, 3; {(lk)1}N is the relative contact length of the die with the billet during the first stage of deformation under the deformation according to modes ‘circle–square’ or ‘square – square’ in the Nth forging block, this length being determined in conformity with the recommendations of [3]; and {(lk)2}N is the relative contact length of the die with the billet during the second stage of deformation in the Nth forging block, this length being by Eq. (5). The value of {lk}N is the relative feed into the (N +1 )th forging block. The forming of the deformable billet was determined from the incompressibility condition [3]. The equation for the determination of the relative contact length during radial reduction for nth press of dies is expressed as: lkn =
n n n n
n
1 qn q 1 n − 1 qn − m + 1 + % m + 1− n ln 2 2 r m = 1 2 m!r r
+ 1−
qn − 1 A 1 −1 2 l0 r
n−2
qn − m A 1 ln m r m=1 2 m! rl0
+%
m
m
n
A 1 ln n−1 2 n!rl0 r
+
n
(5)
3. Results of the calculation of the specific work of forging The determination of power and force parameters for the forging of a continuously cast billet by a three-sectional block (when a continuous casting machine and a forging block are combined directly) requires the knowledge of the total change of billet temperature: DT = DT1 + DT2 + DT3 − DT4
where DT1 and DT2 are the decrease in the temperature of the billet owing to heat emission and convection, respectively (DT2 = 0), (°C); DT3 is the decrease in the temperature of the billet on account of thermal conductivity during the contact of the billet with dies, (°C); and DT4 is the increase in the temperature of the billet owing to the transformation of mechanical energy of deformation into heat, (°C). The change in the billet temperature during the period of forging in one forging block and the motion to the next block can be calculated on the basis of the method of Tselikov [5], accepting that Dt = DT1 −DT4. It is expressed as: Dt = T0 −
' 3
where qn is the numerical row, calculated from the equation qn + 1 =1− qn /2 (where q1 =0). The relative power of deformation for forging is determined from the equation: N( =
&
o1
pcp (o) do/t( 0 ss
(6)
where o is the relative reduction, o =1 −r; t( is the relative deformation time, t( =t/t0; and t0 is the deformation time when the forging assembly has maximum productivity. Fig. 5(a) and (b) shows the dependence of the relative power of deformation, N( , on the reduction, o according to the different values of the parameter h (for the stage of full filling of the gap between the dies by metal).
(7)
1000
0.0255 · II · t 1000 + v T0 + DT4 + 273
3
+273 (8)
where T0 is the temperature of the billet before entry into the forging block (°C); II is the perimeter of the cross-section of the billet after forging (mm); v is the area of the cross-section of the billet after forging (mm2); and t is the cooling time (s). The decrease in the temperature of the billet on account of thermal conductivity during the contact of the billet with the dies are given as follows [6]: DT3 =
4SK(T0 − TD )tKaK cG
(9)
where SK is the area of the contact of the die with the billet at the end of reduction (m2); TD is the die temperature (°C), (TD = 200°C); T0 is the billet temper-
S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299
296
Fig. 4. Diagram of the work cycles of a three-sectional forging block combined with a continuous casting machine.
ature (°C); tK is the time of contact (h); aK is the coefficient of heat rejection (aK =20 kW m − 2 K); c is the heat capacity of billet metal (kJ kg − 1 K); and G is the weight of the billet (kg). The temperature increase of the billet owing to the transformation of mechanical energy of deformation into heat is determined by Eq. (6) DT4 =0.183ss ln l
(10)
where ss is the flow stress of the metal of the billet determined by the method of thermo-mechanical coefficients [7], MPa; and l is the coefficient of elongation (extension). The results of the calculation of the energy consumption for forging by a three-sectional forging block combined with a continuous-casting machine are given in the Tables 1 and 2. The specific work of radial forging when the radial forging is combined with continuous casting was calculated according to the proposed method of calculation, and correlated with speeds comparable of section rolling. It may be presented by the following data (the coefficient of efficiency of the drive is not taken into consideration): for a reduction in a one-section forging block it is 100/125 MJ t − 1; for a two-section forging block it is 55/70 MJ t − 1; and for a three-section forging block it is 35/40 MJ t − 1. 4. Discussion It is interesting to carry out a comparative analysis of the energy consumption for known processes of metal forming. It is the analysis that gives the possibility of discussing the advantages and shortcomings of radial forging combined with continuous casting. The energy of section rolling depends on the system of grooves. The calculation of the energy consumption of section rolling is made on the basis of data of the pressure, the moment and the power of rolling. These values are determined according to known methods [8] during the calculation of grooving. The temperature regime of the rolling is also analysed.
If the power N and the speed of the rolling n (rev min − 1) are known, the work of the rolling of the bar of the length L1 is expressed by the equation: L1 V
A=N · t= N
(11)
where t is the rolling time; V= pnR/30 is the velocity, and R is the rolling radius of roll. For some products [6] the specific deformation work is transferred to the unit volume of the billet using the dimension J cm − 3. Let this value be AV, then: AV =
A 30N = VhM pRnF1hM
(12)
where hM is the coefficient of efficiency of the drive and F1 is the area of the cross-section of the bar. It is more convenient to use the deformation work referred to unit mass of the billet with metal of density g: Am =
30N pRnF1hMg
(13)
Consider the process of the rolling of a round billet made of mild steel on a continuous mill 200. The diameter of the billet is 45 mm before rolling and 20 mm after rolling. Calculated parameters of the forming as well as the power and the force parameters are given in Table 3. These values are utilized as initial data. The specific energy consumption for continuous rolling was determined by Eqs. (12) and (13) using the data of Table 3 and are presented in Table 4. It was assumed that hM is equal to unity everywhere. The data of Table 4 enables the estimation of the energy consumption of separate passes of rolling as well as the total energy consumption of continuous rolling. The example considered is the continuous rolling of a bar in the system of grooves ‘oval–oval rotated through 90°’. This grooving is very popular in section rolling, although it does not have high elongation ability. However, the comparison of the energy consumption for different groovings did not show essential distinctions of total energy consumption under the compared conditions of rolling.
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297
Fig. 5. The dependence of the relative deformation power on the reduction during deformation with the feed l0 =1.0 when the friction factor on the contact surface is: (a) c =0.5 and (b) c= 0.8, where: 1 − h =1.0; t( = 1; 2 −h =0.8; t( =1; 3 −h =0.6; t( =1; 4 −h = 0.4; t( =1; 5 −h= 0.2; t( =1; 6− h= 0 and t( = 1.
Amongst known methods of forming for the continuous deformation of a continuously cast billet there is also extrusion [9]. Extrusion can defy competition with other methods for the processing of a continuously cast billet. The work of extrusion is estimated by the equation: A = PLn, where P is the force of extrusion and Ln is the length of the billet after extrusion. The specific work of extrusion may be expressed as follows: Am =
P PLn = VhMg FhMg
where F is the area of the cross-section of the container and hM is the efficiency coefficient of the extruder drive. The force of extrusion is determined by the known equation (14)
P= Rf + Tf + Tb +Tc
where Rf is the fraction of the force for deformation and Tf, Tb and Tc are the fraction of the force to
overcome the action of the force of friction in the die, in the sizing bush and the container, respectively (Tc = 0 for the indirect extrusion). The variables of Eq. (14) are calculated by the methods described in Ref. [10] and depend on the form of the deformation domain, the friction factor and the flow stress ss. The latter is approximated [11] by the equation: ss =
ao mu n exp (qt)
where a, m, n and q are empirical coefficients depending upon the deformable metal; o =ln (l) is the relative reduction and u is the strain rate u= 66l ln(l)tga/ (l l − 1)d (where 6 is the velocity of extrusion; d is the diameter of the billet after the extrusion; 2a is the angle of the die). The specific energy consumption for the extrusion of a steel bar with a diameter of 20 mm from a billet with a diameter of 45 mm at a temperature of 1200°C and a velocity at the exit of the die of 2.1 m s − 1 is calculated similarly to the previous example. The parameters for the determination of the specific energy consumption for the extrusion are l=5.06;
Table 3 Parameters of the rolling of a round bar to a diameter of 20 mm from a billet with a diameter of 45 mm, at a temperature of 1200°C Number of the pass
Shape and dimensions of the bar (mm)
Cross sectional area (mm2)
0 1 2
Circle 45 Oval 28.0×52.2 Oval (rotated through 90°) 41.0×32.8 Oval 22.0×45.7 Oval (rotated through 90°) 33.0×26.4 Oval 19.5×34.5 Circle 23.8 Oval 17.8×25.8 Circle 20.2
1590 1190 1012
1.34 1.174
800 650 555 444 368 314
3 4 5 6 7 8
Extension
Velocity (rev min−1)
Moment (kN m)
Power (kW)
42.4 51.3
6.63 2.11
29.5 11.4
1.264 1.234
62.2 78.6
3.57 2.52
23.2 20.7
1.174 1.25 1.21 1.17
89.3 142.7 169.3 200
1.87 1.76 1.70 0.89
17.5 26.3 30.2 18.7
298
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Table 4 The specific energy consumption of the rolling process Number of the pass
1 2 3 4 5 6 7 8
Specific energy consumption
Cumulative total of the specific energy consumption
(J cm−3)
(kW · h t−1)
(MJ t−1)
(J cm−3)
(kW · h t−1)
(MJ t−1)
55.8 21.0 44.5 38.7 33.7 39.6 46.3 28.4
1.98 0.74 1.58 1.37 1.20 1.41 1.64 1.01
7.13 2.66 5.69 4.93 4.32 5.08 5.90 3.64
55.8 76.8 121.3 160.0 193.7 233.4 279.7 308.1
1.98 2.73 4.32 5.70 6.90 8.31 9.96 10.97
7.13 9.79 15.55 20.52 24.84 29.92 35.86 39.49
6 = 0.415 m s − 1; u= 170 s − 1; and o = 0.80. The flow stress of the metal at the exit of die is ss =120.8 MPa for a= 1250 MPa; m =0.25; n =0.14 and q = 0.0025. The volume average value of the flow stress is s¯ s = 96.64 MPa. Under these parameters, the force of the extrusion is P= 392.8 kN and the specific energy consumption is Am =31.7 MJ t − 1 = 8.80 kW · h t − 1. The calculation was carried out for the indirect extrusion. As to the direct extrusion, the specific energy consumption increases by 20/25%. Hence, it follows that direct extrusion is inferior to section rolling as to specific energy consumption. Indirect extrusion gains advantage, but unfortunately is rarely used. A similar calculation of the specific energy consumption for radial forging combined with continuous casting was accomplish for comparable conditions. The forging of the bar of square section 17.72 × 17.72 mm from a billet with the diameter of 45 mm at a temperature of 1200°C and the velocity of forged bar 2.1 m s − 1 at exit was considered. The following modes of the radial forging of the billet were considered (all modes were transferred to comparable values of the capacity of rolling and extrusion): 1. Forging by the scheme: a circle with a diameter 45 mm to a square of sides 17.72 mm in a one-section forging block with a feed of 22.5 mm (the time of one stroke of the die is t= 0.0054 s); ss =62.6 MPa. 2. Forging by the scheme: a circle with a diameter of 45 mm to a square of sides 29 mm and then to a square of sides 17.72 mm in a two-section forging block with a feed of 22.5 mm; two strokes of the second section fit one stroke of the first section; t =0.018 s; ss = 82 MPa. 3. Forging by the scheme: a circle with a diameter of 45 mm to a square of sides 33 mm, further to the square of sides 24 mm, then to the square of sides 17.72 mm in a three-section forging block with a feed of 22.5 mm; two strokes of the second section .
and four strokes of the third section fit one stroke of the first section; t = 0.008 s; ss = 98 MPa. The specific energy consumptions are: for the one-section forging block Am = 46.5 MJ t − 1 = 20.8 kW · h t − 1; for the two-sectional one Am = 35.6 MJ t − 1 = 14.3 kW · h t − 1; for the three-sectional one Am = 29.3 MJ t − 1 = 11.3 kW · h t − 1. The analysis shows that the through-put radial forging has the greatest energy consumption. The energy consumption of through-put radial forging remains quite high, even after significant subdivision of the deformation between sections of the multi-die forging block. The further sub-division of deformation is able to provide efficiency of forging in comparison with continuous rolling and direct extrusion, but it is not reasonable in all respects.
5. Conclusions Presently, the through-put radial forging is considered, especially in combination with continuous casting, as a pertinent method for the intensive reduction of metal. However the forging leads to overconsumption of energy. The best course would be to decrease the single reductions, i.e. to use multi-sectional blocks. The design of such forging blocks is complicated and operation and automation are made difficult. However, as can be seen from the results of the analysis, throughput radial forging can compete with the other methods of forming in energy consumption. On the other hand, forging compares favourably with rolling and especially extrusion by the short duration of the contact between the deformable metal and the die. Heat loss is insignificant during forging. There was no possibility, when the analysis was being realized, to take into consideration the real change of metal temperature. This circumstance may appear important for the selection of the processing technology of metals and alloys having inadequate workability.
S.P. Bourkine et al. / Journal of Materials Processing Technology 86 (1999) 291–299
Through-put radial forging is the most suitable method for the formation of continuous cast billets. Insufficient ductility of the cast metal and a temperature gradient in the section do not affect the success of plastic working.
[4]
[5] [6]
References [7] [1] S.P. Bourkine, V.P. Tatarchenkov, E.A. Andrukova, The powerenergy parameters of radial forging with shear, Dep. VNIITEMR 09.11.88 N 409-MIII88 (in Russian). [2] E.A. Andrukova, S.P. Bourkine, O.V. Perepliotchikova, et al., The kinematic parameters of the deformation zone during radial reduction with shear, Dep. VNIITEMR 09.11.88 N 408-MIII88 (in Russian). [3] S.P. Bourkine, N.A. Babailov, The analysis of radial reduction
[8] [9] [10] [11]
of axisymmetric billets by the multi-die block, Dep. VNIITEMR 12.05.93, No. 31-MIII93 (in Russian). V.L. Kolmogorov, S.P. Burkin, N.A. Babailov, Automated forging center as renaissance of hammer forging in heavy industry, J. Mater. Proc. Technol. 56 (1 – 4) (1996) 631 – 642. A.I. Tselikov, The theory of account of efforts in rolling mills, Metallurgizdat (1954) (in Russian). A. Hensel, T. Spittel, Account of power-energy parameters during processing of metal forming, Metallurgy (1982) (in Russian). A.I. Tselikov, A.D. Tomlenov, V.I. Zuzin, et al., The rolling theory, Metallurgy (1982) (in Russian). V.K. Smirnov, V.A. Shilov, Y.V. Inatovich, Roll surface grooving, Metallurgy (1987) (in Russian). Forming of light and special alloys, VILS (1996) (in Russian). I.L. Perlin, L.H. Raytbarg, Theory of metal extrusion, Metallurgy (1975) (in Russian). V.I. Zuzin, A.V. Tretiakov, The mechanical properties of metals and alloys during metal forming, Metal (1993) (in Russian).
.
.
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