ISSN 09670912, Steel in Translation, 2011, Vol. 41, No. 1, pp. 41–47. © Allerton Press, Inc., 2011. Original Russian Text © G.N. Elanskii, I.F. Goncharevich, 2011, published in “Stal’,” 2011, No. 1, pp. 14–21.
Improving Mold Operation in ContinuousCasting Machines G. N. Elanskiia and I. F. Goncharevichb a
Moscow State Evening Metallurgical Institute, Moscow, Russia b Russian Engineering Academy, Moscow, Russian
Abstract—Mold operation with spring suspension and a programmable hydraulic drive is considered. Com puter methods of investigating the mold–billet interaction are developed. A new mold with longitudinal– transverse vibration and dynamic stabilization has been developed for continuouscasting machines. DOI: 10.3103/S0967091211010049
The mold in a continuouscasting machine is a complex multifunctional system. This system includes the mold itself, which is primarily a thermal unit, con trolling the heat transfer from the steel melt that will form the continuouscast billet; a suspension system, which ensures specified billet trajectory and, if it is elastic (usually a spring system), also somewhat com pensates the dynamic loads; a drive ensuring specified vibration of the mold; and a supply system for the slag forming mixture. On melting in the gaps between the casing of the continuouscast billet and the mold walls, the slagforming mixture performs a series of functions, such as control of the thermal processes; lubrication with reduced drag on the billet as it moves through the mold; and removal of nonmetallic inclu sions from the melt. Note the important role of the lubricant in transforming frictional forces that do not depend on the speed (dry friction) into viscous fric tion. Viscous friction between the mold and the billet is essential for effective asymmetric vibration. Effec tive operation of the mold system depends on smooth interaction of all the subsystems, which must perform their assigned functions. When continuous casting was first introduced, the mold was motionless. However, it was quickly estab lished that this process is problematic. Then recipro cating motion (rocking) of the mold along the cast bil let was induced, with significant improvement in the process. The benefits of reciprocating motion are largely due to the replacement of static friction between the casing of the continuouscast billet and the mold walls by dynamic friction, which is less pro nounced and more stable. When using large rocking speeds (higher than the billet’s extrusion rate), the interaction between the casing of the continuouscast billet and the mold walls is fundamentally changed. In some stages of motion, the mold walls outpace the billet, which was not previ ously the case. The exclusively tensile force on the cas ing of the continuouscast billet in the stationary mold is replaced by compressive force in some stages of mold motion. It is also found that the damage to the
billet casing that sometimes appears when the mold outpaces the billet (when its speed exceeds the billet’s extrusion rate) will be partially or completely elimi nated. This is a fundamental benefit of a rocking mold over a stationary mold. Detailed study of defect amelioration permits the development of special rocking conditions to maxi mize this effect. To this end, very complex suspension mechanisms and drives are required. In practice, how ever, many of these systems are unwieldy and difficult to maintain; in other words, their operational effi ciency is poor. Special rocking conditions with unsmooth motion and dramatic changes in mold speed create considerable dynamic loads in the drive mechanisms, on account of the associated accelera tion. Therefore, in industry, molds with ball–lever sus pension operate predominantly in smooth slow har monic processes characterized by low frequency and large amplitude, which are more stable and less dynamic. When steel plants began to increase the billet’s extrusion rate so as to improve productivity, it was nec essary to increase the mold’s rocking speed. This required increasing the rocking frequency (to which the rocking speed is proportional), because the rock ing amplitude could not be increased without impair ing the billet surface. As a result, the acceleration sharply increased (in proportion to the square of the rocking frequency) and hence the dynamic load increased. In many hinges with fixed technological gaps, impact loads arose, breaking the suspension [1]. In those conditions, hingedlever suspension systems proved impracticable and were replaced by deformable elastic suspensions (specifically, spring suspensions), which had long been used in vibrational engineering. Thanks to the lack of free play, such suspensions per mit the mold to precisely track the specified billet con figuration (linear or curvilinear). Elastic spring sus pensions proved extremely effective in practice, both in technological terms and in terms of simplifying the design of the continuouscasting machine and reduc ing its cost. 41
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To improve the billet produced by traditional con tinuouscasting machines, we need to investigate the factors responsible for unsatisfactory product quality. Industrial experience indicates that, in outdated con tinuouscasting machines, the main factor reducing billet quality is imperfection of the mold’s hinged lever suspension. However, analysis shows that such suspensions cannot be replaced by spring suspensions without changing many auxiliary systems. In particu lar, old and new continuouscasting machines differ fundamentally in design. Therefore, replacing any sin gle component of an old system by new mechanisms unavoidably entails the installation of appropriate auxiliary equipment, at great cost. Accordingly, a lowcost option is not to replace the entire suspension but to use elastic hinges, which have been satisfactorily employed in cyclic systems [1]. As well as the equipment, continuouscasting tech nology has been radically changed. In new molds with elastic suspension that are switched to highfrequency operation with low amplitude, asymmetric vibration proves more effective in technological terms. To ensure reliable maintenance of complex nonharmonic mold oscillation, programmable electrohydraulic drives are employed. Thus, there is a qualitative shift from traditional molds with rigid kinematic elements and undeform able eccentric drives to machines with deformable links and nonrigid hydraulic drives and from harmonic vibration to spectrally more complex nonharmonic vibration. Whereas the rocking conditions are rigidly specified in molds with eccentric drives (provided there are no gaps in the hinges), the presence of elastic links in the new molds means that their motion is determined not only by the drive but also, to some extent, by the dynamic properties of the whole system consisting of the billet, the mold, and the continuous casting machine’s drive mechanisms. In developing new casting processes, designers must take full account of these design changes and the new scope for the operation of continuouscasting machines. Special research is required to make sense of the wide range of parameters for the new molds, to clarify the diverse criteria for the assessment of casting efficiency, and to reconcile the sometimes contradic tory technological and dynamic requirements. Thus, new approaches are required in view of the radical changes in design principles for the new molds and the powerful and continuous dynamic relation between the process and the operating conditions of the equip ment. The further development of continuouscasting technology requires the consideration of the whole complex machine–load system. Note that the con tinuing increase in casting speed entails appropriate increase in amplitude of the rocking speed in any con ditions (including harmonic conditions, which still predominate). On account of technological consider
ations, this entails increasing the carrier frequency of the vibrations, with considerable increase in dynamic loads in all the components of the system and in the mold drive. If we use special asymmetric nonharmonic vibra tions (containing higher harmonics), which are techno logically more effective, the mold acceleration and the corresponding inertial forces increase considerably. This increase in inertial forces is even greater than in harmonic conditions, since it is proportional to the square of the oscillation frequencies in the nonhar monic motion (including the higher harmonics). Accordingly, methods of reducing the dynamic load on the continuouscasting machines must be developed. The dynamic loads may be reduced if the inertial forces of the rocking masses are compensated by the elastic forces of the spring suspension. The inertial forces are completely balanced when the eigenfre quency of the mold (determined by the rigidity/mass ratio of the spring suspension) matches the drive fre quency (in resonant conditions). Reduction in the dynamic load of drives in contin uouscasting machines by ensuring resonant condi tions with asymmetric rocking is complicated that the system only has only operating frequency, whereas asymmetric rocking of the mold is a polyfrequency process. Another difficulty is that the eigenfrequencies of existing molds are constant, specified in the design process (by the mold mass and the rigidity of the spring suspension), and cannot be adjusted during mold operation, whereas the oscillation frequency is deter mined by the selected technological conditions and varies widely in the course of operation Therefore, the eigenfrequency of the mold must be established by optimal design with inconsistent quality criteria [2, 3]. Partial dynamic balancing of the mechanisms of con tinuouscasting machines that operate in asymmetric polyharmonic conditions has been developed. Meth ods that permit maximum possible reduction in dynamic load by selecting optimal parameters of the spring suspension have also been formulated. It has been shown that continuous variation in oscillation frequency of the drive within each cycle imposes fun damental constraints that prevent the complete bal ancing of dynamic loads within the vibrating parts of the continuouscasting machine. Thus, in switching newgeneration molds of con tinuouscasting machines to effective nonharmonic operation, it is important to develop an optimal design method for continuous casting such that the dynamic complications may be reconciled. At present, progress is being made in that area—in particular, thanks to introduction of special biharmonic mold vibrations. We will now focus attention on the optimal combination of effective operation and dynamic bal ancing of the continuouscasting machine. STEEL IN TRANSLATION
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The measures considered next facilitate the use of highly efficient nonharmonic vibration and simultaneous reduction in dynamic loads within the mold’s drive. INTERACTION OF THE CONTINUOUSCAST BILLET WITH THE MOLD’S WALLS The interaction of the continuouscast billet with the mold’s walls is affected not only by the conditions of mold vibration but also by the supply of slagform ing mixture and its properties. According to current concepts, the slagforming mixture dissolves in the melt within the mold and mixes with the solid particles to form a coating with lubricant properties. Close to the meniscus, it acts as a viscous lubricant, and mea surements show that viscousfriction forces predomi nate in this region. These forces are proportional to the relative velocity of the frictional pair (the billet and the mold wall). On moving away from the meniscus, viscoplastic friction (viscous–dry friction) is observed; this force depends less on the relative speed of the billet and mold and begins to depend on the pressure of the billet casing at the wall. As the billet moves toward the mold exit, the proportion of viscousfriction forces declines, and the proportion of dryfriction forces increases. Specialists assert that dry friction largely acts when the billet leaves the mold; its magnitude depends on the force pressing the continuouscast billet against the mold wall. We may also assume that this effect is due to the maximum ferrostatic pressure on the billet casing at its exit from the mold. Thus, in model research, these experimental laws should be reproduced. Note that these processes are also accompanied by increase in thickness of the billet casing. Accordingly, the stress in the casing declines on moving toward the mold’s exit, despite the increase in frictional forces. The casing usually breaks down in the meniscus region, especially on account of the increase in stress due to the unfavorable balance of the forces acting and the strength of the casing. Study of the formation of drag on the billet in the mold is important not only to develop preventive mea sures, but also so as to reduce the extrusion forces of the blank and reduce the load in the tractional mech anism. This requires appropriate selection of the com position of the slagforming mixture, its delivery con ditions, and the rocking parameters of the mold. In addition, it is important to formulate rocking condi tions corresponding to sufficient lubricant supply, specified billet motion, and reduced frictional forces. The interaction of the billet with the mold walls depends primarily on their relative speed, which deter mines the viscous–dry frictional forces. When their relative speed is reversed, the direction of action of the frictional forces changes. The efficiency of mold oper ation is characterized by the ratio of the times of mold operation in the same direction as the billet and the STEEL IN TRANSLATION
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opposite direction. For mold motion in the same direction at a speed exceeding the extrusion rate, the mold walls outpace the billet, and the frictional force between them becomes a motive force, with corre sponding decrease in mean drag forces over the cycle. According to the available data, the compressive stress in the casing is associated with 20–30% decrease in the defects arising at the billet surface in the case of opposite motion of the mold and billet, when tensile forces act in the billet casing. With increase in the ratio between the times of mold operation in the same direction as the billet (positive motion) and the oppo site direction (negative motion), mold rocking becomes more effective, in technological terms. Anal ysis shows the high efficiency of asymmetric rocking in newgeneration molds, especially when viscous drag predominates. Thus, with sufficiently asymmetric vibration, the speed may be significantly higher in the positive part of the cycle than in the negative part. The mean drag over the cycle also changes on account of mold rocking. The available data indicate relatively effi cient mold operation in asymmetric conditions, in terms of reduced mean drag (predominantly viscous drag, with a modest dryfriction component) on the bil let as it travels through the mold. Because of the greater efficiency with viscous drag, it is expedient to organize reliable lubrication in asymmetric vibration. Note that asymmetric conditions tend to increase the lubricant supply. In correctly selected conditions, the newgener ation molds more effectively reduce the mean drag on the billet in comparison with traditional molds. To assess the effectiveness of the rocking condi tions—in particular, to determine the stress in the bil let casing and the lubricant supply—phenomenologi cal inertial elastoviscoplastic models and correspond ing systems of nonlinear differential equations have been developed. The methods used in developing the models were outlined in [4–12]. These models may be used to select optimal rocking conditions—in terms of minimal internal stress of the billet casing—without impairment of the system’s dynamic properties. On that basis, there is a real possibility of selecting non harmonic rocking conditions while reducing the dynamic loads on the drives of the continuouscasting machine. Note that it is impossible to eliminate dynamic loads in the drives of the continuouscasting machine with asymmetric polyharmonic operation, because there is only a single operating frequency, whereas the asymmetric rocking of the mold is polyharmonic; within a single cycle, the drive frequency varies con tinuously, while the eigenfrequency of the existing mold systems is constant. At present, a possible approach to efficient rocking of the mold and reduction in the dynamic loads on the drive is to develop special biharmonic mold vibrations. As shown by computer experiments, this approach is relatively effective, both in technological terms and in
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ELANSKII, GONCHAREVICH (a) 5
20 Ps Ps Pν
Reduced load
Reduced force
40 0 –20 –40 –60 0
1
Reduced energy consumption
Reduced force
50
2 (b)
3
4
5
0
GΣ
–5 0
25 PΣ PΣ
DΣ
0
2 4 Phase angle φ of drive
6
Fig. 2. Uncompensated dynamic load G from the rocking load that acts on the continuouscasting machine’s drive when using hingedlever suspension and load D compen sated by the restoring forces of the spring suspension with biharmonic mold vibration.
–25 –50 –75 0
1
2 (c)
3
4
5
mold. In other words, we analyze the feasibility and expediency of combining the initial stage of reduction with casting. We briefly review the necessary precondi tions for such an approach.
100 Q Q
50
0
2
4 6 8 Phase angle φ of drive
10
Fig. 1. Forces transmitted from the mold to the billet in biharmonic vibration: (a) viscous force Pν and plastic force Ps; (b) total viscoplastic force; (c) energy consumption of model in overcoming the frictional forces on the continu ouscast billet.
reducing the dynamic loads in the continuouscasting machine. In Figs. 1 and 2, we compare some charac teristics of continuous casting for the proposed and traditional methods. In Fig. 1, we show the stress in the billet casing: (a) force due to dry friction; (b) force due to viscous friction; (c) total viscoplastic forces on the billet casing. In Fig. 2, we show the uncompen sated dynamic loads in the drive due to mold rocking with a hingedlever suspension and the load compen sated by the recovery forces of the elastic spring sus pension in biharmonic oscillation. NONTRADITIONAL ROCKING OF THE MOLD To ensure high billet quality in continuous casting, two basic methods are employed: casting through a rocking mold; and mild billet reduction on leaving the mold. In these processes, a reduction cell is used together with the mold. In the present section, we con sider the possibility of initial billet reduction within the
The operational efficiency of the mold is primarily determined by its rocking conditions along the billet axis. The reduction cell is pressed against the mold by transverse forces. Since rocking occurs along the billet axis, the frictional forces between the mold walls and the billet produce tension–compression stress in the billet casing. This will considerably affect the billet quality and the overall stability of the process. In longitudinal rocking, the frictional force at the mold–billet casing may only be regulated when the forces between them depend on their relative speed (that is, viscousfriction forces). In the presence of such forces, only the rocking speed or the extrusion rate of the billet need be adjusted. In the sections of billet–wall contact characterized predominantly by dry friction, which is unaffected by the relative speed, the frictional forces may vary only in direction; their magnitude is constant. In practice, as already noted, different combina tions of viscous and dry forces act on the billet at dif ferent points of the mold. This must be taken into account in formulating the rocking conditions. Noting that viscous friction predominates within a limited zone (mainly around the meniscus), we may conclude that the rocking conditions developed pri marily for viscous friction (in particular, highly effi cient asymmetric rocking, which is widely promoted) are of very limited value over the whole contact zone. At the same time, we know that the frictional force may be very effectively regulated by oscillations per pendicular to the relative velocity of the frictional sur faces. (Modern molds operate in conditions of high frequency vibration.) STEEL IN TRANSLATION
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In the present work, we will preliminarily address the possibility of combining this approach with the traditional approach in continuouscasting molds. Note that the use of oscillations perpendicular to the relative velocity of the frictional surfaces in the molds of continuouscasting machines poses considerable engineering difficulty and remains to be industrially adopted. However, at the Serp i Molot plant, specialists from Moscow State Evening Metallurgical Institute have undertaken some experiments on a 140 × 140 mm mold sleeve, using specially developed compact pneu matic inertial turbine vibrators of relatively high power. The experimenters took into account that the stress and strain in the billet casing depend on its tem perature, the type of steel, and other factors, but the most significant factor is the force on the billet casing at the mold wall. With considerable frictional forces, the billet casing in the mold is deformed and may even break, since its strength near the melting point is rela tively small. Such deformation may also result in seri ous disruptions of casting, such as tearing of the metal. In most cases, such damage appears at the mold exit but is initiated as a result of previous rupture of the bil let casing in the upper part of the mold. With practically any mold rocking in the direction of the billet’s longitudinal axis, alternating tensile– compressive stress appears in the billet under the action of frictional forces at the mold wall. Tensile stress is extremely undesirable in terms of stability of the casting process and the required billet quality. Therefore, various measures have been developed to reduce the tensile stress in the billet. One approach is to adopt special rocking conditions that minimize the tensile stress, especially at the weakest section, which is predisposed to failure. Research at the Serp i Molot plant has tested the hypothesis that tensile stress may be reduced by special mold vibration with transverse components. In mold design, particular attention must be paid to its oscillation in the premeniscus region, which may be characterized by adhesion of the billet casing to the mold wall. Capture of the billet is associated with extreme tension in its casing, followed by rupture; the escaping liquid solidifies, with partial patching of the tear. However, if the repair cannot withstand the force necessary to sever the adhesion, another tear will occur. Extrusion of the billet moves the tear toward the mold exit, where it may disrupt the normal casting process. Accordingly, it is of interest to consider vibration of a mold sleeve with four pneumatic vibrators at its faces, so as to ensure the most effective vibration of the sleeve’s upper part. Mild reduction is used to eliminate the defects at the billet casing on leaving the mold. The continuous cast billet solidifies with radial heat transfer. The extent of the liquid core depends on the blank’s cross STEEL IN TRANSLATION
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section and the casting rate. Even with small disrup tions of solidification and especially with the interrup tion of casting, displacement of the solidification front leads to the formation of crosslinks in the tip of the liq uid core. Isolated melt volumes solidify and shrink, with the formation of shrinkage cavities and axial porosity and the development of axial macroliquation. The quality of the axial zone declines with decrease in taper of the conical liquid core, which is typical of high casting rates for billets of large cross section. Macroliquation leads to nonuniform physicome chanical characteristics over the billet cross section. As shown by metallographic data, macroliquation is most effectively reduced by mild reduction of the blank, which compensates for the shrinkage on solidification and thereby prevents liquation stratification in the central part of the billet. Experiments at the Serp i Molot plant show that transverse vibration of the mold sleeve also reduces the macroliquation. Melt supply to the twophase zone is hindered when the degree of solidification is 30% and com pletely prevented at a degree of 70–95%, since the drag is too great. Correspondingly, when the solidifi cation at the center of the billet is 30%, compensation of the hindered supply must begin and extend practi cally to the tip of the liquid crater. We assume that starting mild reduction on exit from the mold permits more effective control of the shrinkage. At MGMVI, with the participation of spe cialists from the Russian Engineering Academy, mold designs with special vibrations of the sleeve have been developed for the casting of round and square billet with a small cross section. In these molds, billet for mation is combined with its mild reduction. For such molds, the formation of continuouscast billet is considered by means of phenomenological models. The lack of information on this topic calls for the development of procedures for computer experi ments. Experience shows that computer experiments are physically reliable. One benefit of computer exper iments is that they permit the analysis of any condi tions of mold vibration, no matter how expensive and laborious their actual experimental study would be. Although the application of longitudinal mold vibrations is unavoidable and will offer great benefit— especially as methods are always being improved—this approach cannot resolve all the problems of mold–bil let interaction. In themselves, longitudinal mold vibrations cannot eliminate tensile stress, which is the main source of casing damage. Relatively rapid analysis of this problem is possible by means of computer experiments based on the rhe ology of nonsteady processes (vibrorheology), with the development of phenomenological inertial models of melt–mold interaction, special computation software for nonlinear systems, and optimal multicriterial design. Inertial elastoviscoplastic models (the rheol ogy of nonsteady processes) may be useful here
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tem that tracks its configuration at all stages of the pro cess, with continuous adjustment of its structure and the parameters. Such selfconfiguring of the model permits physically more reliable reproduction of pro cesses of any complexity, at all stages. At the same time, the phenomenological models provide the base line in ensuring the required computational accuracy.
Force on casing
20 Fi
0 –20 –40 –60 –80 50
60 70 Phase angle ωti of drive
80
Fig. 3. Force exerted by mold wall with transverse vibration on billet casing.
because the melt, as it passes through a mold operating in highfrequency conditions, is subject to inertial loads comparable with the other forces acting. There fore, neglecting these loads may yield erroneous results. Note also that, in highfrequency conditions (vibrational and pulsed conditions), effects that are not seen at low frequency will be observed in the tech nological systems and in the corresponding machines: specifically, the appearance of an inertial field and the conversion of the gravitational forces, reduction of the dry and viscous friction and the limit of plastic defor mation, and acceleration of energy and mass transfer. Other effects may also be seen in continuous casting with highfrequency vibration. The structure of the billet will improve with sufficiently strong vibration in the solidifying metal. The methods developed take into account that, in practice, the interaction of the melt with the mold wall is accompanied by constant variation in frictional forces, billet length, and stress–strain state over the length of the mold. Since these changes depend on the unfolding of the casting process and are unknown in advance, the model of the melt includes a logical sys
The proposed methods permit analysis of the influ ence of mold vibration on the billet surface and the drag on the billet in the mold; optimal supply of slag forming mixture; and selection of the most effective rocking configuration and parameters. The corre sponding computer software provides representative uptodate and summary information regarding the process in tabular and graphical form. The kinematic and dynamic characteristics pro vided include the deformation and displacement and their first and second derivatives. The force character istics include the elastic, viscous, elastoviscous, and plastic stress (with and without hardening) and the normal and tangential forces on the mold walls. The energy characteristics include the energy costs in elas tic, ductile, and plastic deformation of the billet and its mechanical motion, the circulation of potential and kinetic energy in the billet during periodic deforma tion, and the energy consumption in overcoming all the drag components. Various specialized characteris tics may also be provided. As an example, we present some calculated charac teristics for the passage of billet through a mold sleeve performing transverse vibration. In Fig. 3, we show the force applied by the mold wall on the billet casing in asymmetric polyfrequency vibration. Such periodic treatment only reduces the billet, whereas longitudinal vibration creates compress–tensile stress, which results in mild reduction.
0.1 x'i (50x)i
Viscoplastic stress
Strain, strain rate
0.2
The state of the billet surface depends significantly on the conditions of casing formation in the mold. The continuing search for fundamentally new rocking conditions may be attributed to the need for better quality of the surface and the subsurface layer in the continuouscast billet (fewer scratches due to mold rocking, reduced height of the creases, elimination of cracks, etc.). The proposed rocking conditions may be preliminarily tested in computer experiments.
0
–0.1 –0.2 80
90 100 Phase angle ωti of drive
110
Fig. 4. Strain and strain rate of billet casing with transverse mold vibration.
100 F Σi 50 50
60 70 Phase angle ωti of drive
80
Fig. 5. Stress in billet casing due to ferrostatic pressure and reduction by mold wall. STEEL IN TRANSLATION
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It is evident in Fig. 4 how the casing is deformed, and at what rate. On account of the irreversible strain, cyclic deformation of the billet casing under the action of the transverse mold vibration leads to overall reduc tion of the billet, with some mean reduction in its cross section, and effective summation of the pressure at the wall. This results in pulsation of the billet casing under the action of the transverse mold vibration. The slight irreversible strain of the casing somewhat reduces its cross section, which reduces the mea pressure at the mold wall. (The ferrostatic pressure of the melt in this case is partially experienced by the compressed cas ing.) This leads to smaller mean pulsating pressure of the billet casing on the mold wall and consequently smaller frictional forces. The mold consumes some energy in casing reduction, but this is easily compen sated by the decrease in extrusion forces of the billet. In Fig. 5, we see the formation of the transverse elas toplastic stress (with irreversible components) in the billet casing due to the ferrostatic pressure (constant component) and the mold vibration (periodic compo nents). We may assume (as confirmed by computer calcu lations) that such highfrequency treatment of the bil let offers a number of benefits: in particular, the elim ination of casing–wall adhesion and hence reduction in the risk of tearing; simpler forward and backward motion of the mold thanks to the reduced mean (effective) frictional coefficient; probable improve ment in casing surface; and possible improvement in the state of the subsurface layer. In turn, experiments at the Serp i Molot plant regarding the influence of transverse vibration on the melt have proven effective in improving the billet structure.
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