DE2341563A1 - Continuous casting secondary cooling zone - in which bending and straightening rolls are positioned according to given formula - Google Patents

Abstract

Continuous casting machine has a mould and a sec. cooling zone, where bending rolls transfer the cast bar from a vertical position into an arc (operation I) and straightening rolls transfer the bar from the arc to a horizontal position (operation II). The rolls in both (I) and (II) are on a curve conforming with the differential equation: (where . '(xj) is a function of the changes in expansion which occur round the arc, first increasing, then decreasing RE is the radius of curvature at the end of (I) or (II); Xe is the vertical projection of (I) or the horizontal projection of (II); xj is a position co-ordinate in a cartesian system with origin at the beginning of the arc and the X-axis is a tangent on the outside of the arc during (I) and on the inside of the arc during (II)). The max. permissible expansion D is pref. 50d/RE (where d is the thickness of the cast bar). Reduces the risk of the partly solidified bar brusting open at casting speeds over 1.5t/min.

Description

Patent attorney

16. Α · .'π. ί37

United Austrian Iron and Steel Works - Alpine Montan Joint stock company in Vienna

Continuous caster

The invention relates to a continuous caster with a secondary cooling zone and downstream of the mold with rollers for guiding, bending and / or straightening the strand, the bending rollers along a transition curve from the vertical to the arc and the straightening rollers along a transition curve from the arc to the horizontal are arranged.

Such continuous casting plants, in which the strand is bent in the horizontal, have vertical plants compared to a lower overall height. If you don't want to use a curved mold, but a straight one, what has metallurgical advantages, it must be between the mold or one of the mold following short vertical Guide part and the circular arc-shaped guide section, for example with a diameter of 8 to 10 m, has an intermediate section curved according to a transition curve.

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piece are provided, so that sudden strains on the outside of the strand, which still has a liquid core, can be avoided. Therefore from several sides, cf. B. U.S. Patent No. 3,290,741, Austrian Patent No. 231,629, and Austrian patent specification No. 244 522 proposed have been to form the transition curve with a gradually or step-wise increasing radius of curvature, for example according to Art a hyperbola, parabola, ellipse or clothoid.

Also the straightening zone at the transition from the arc-shaped one Part of the secondary cooling section in the horizontal part of the conveyor section should be designed according to a transition curve to avoid excessive expansion on the Avoid the inside of the strand.

Despite the known proposals in this area, it has not yet been possible to eliminate the undesired points of discontinuity, to avoid, because with all curves of the second order, such as circle, ellipse, hyperbola, parabola, occurs at Transition from a tangent (infinite radius of curvature) to a point on the curve (finite radius of curvature) necessarily a sudden change in the radius of curvature. Also have the familiar suggestions for training of the transition bend to the respective change in strain Z \ d, d. i. the derivation of the elongation, no consideration is given. It is the importance of adhering to a maximum allowable Changes in strain have not yet been recognized.

The invention is based on the object of designing the transition curve in the bending and / or straightening zone in which the bending or straightening rollers are arranged so that a certain permissible change in strain on the outside of the strand or at a certain point between the Outside of the strand and the neutral fiber, i.e. along a selectable line in this area, during bending and a certain permissible elongation

5098H / CU1 9

-. "5 _

change on the inside of the strand or at a certain point between the inside of the strand and the neutral fiber is not exceeded at any time during straightening, and furthermore that the end radius at the end of the bending zone and the starting radius at the beginning of the straightening zone with the radius of curvature of the arcuate guide part between the bending and straightening zones is absolutely the same.

This goal is achieved according to the invention in a system of the type mentioned in that the Biegebzw. Straightening rollers are arranged along a curve, the differential equation

¹ (Xj) dx

corresponds, where f * (χ.) is a function of the strain change, which over the extension of the bending or straightening zone has an initially rising, then reaching the maximum of the permissible strain change and then falling again, R equals the circular arc radius at the end of the Bending or straightening zone and X "the vertical projection of the bending zone or the

Et

horizontal projection of the straightening zone, and x. a position coordinate in a Cartesian coordinate system whose origin is located at the beginning of the transition curve and whose X-axis represents a tangent to the transition curve to the outside of the strand when bending and to the inside of the strand when straightening. The invention is therefore based on the knowledge that it depends on the strain change φ ¹ (χ.), Which is derived from φ (χ.), A function that is proportional to the expansion. Since the deformation resistance of steel in the liquid-solid transition phase depends on the deformation speed, only changes in the elongation cause stresses and only this change is decisive for the risk of cracking. If the derivative of the strain φ ¹ (χ.) exceeds a limit value, cracks appear at the relevant point; the course of <p * (x ·) must therefore take place in such a way that

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this limit value is not exceeded during bending or straightening will.

The maximum elongation D is advantageous with -—

Assume E, where d represents the thickness of the strand and R _{E is} as defined above.

According to the invention, the rollers for bending and straightening the strand are arranged at points that result from a course of the function of the change in strain (0 '(χ.),

^J J preferably result from a polygonal, in particular trapezoidal, running, arcuate, parabolic or similar course.

The invention is based on exemplary embodiments and the accompanying drawing.

FIGS. 1, 2, 3 and 4 relate to a first exemplary embodiment; Fig. 1 is a side view of one of the present invention Bending device in a schematic representation, not to scale; Fig. 2 illustrates those cast on one Bending and supporting forces acting on the strand; 3 is a diagram that corresponds to a normalized course of the fictitious torque line or the fictitious change in strain on the strand outer shell or the fictitious third derivative y "'(x.), respectively referred to on the X-axis of a coordinate system, the origin of which is at the beginning of the bending device and on the outer shell of the strand and where y (x.) is the function for the geometric course of the curved strand shell; Fig. 4 is a diagram showing the shows the effective course of the elongation and the change in elongation of the strand outer shell, again based on the aforementioned Coordinate system.

FIGS. 5, 6, 7 and 8 relate to a second embodiment according to the invention, with FIGS. 5, 6 being similar Representations are like FIGS. 1 and 2 and FIGS. 7 and 8 correspond to FIGS. 3 and 4.

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9, ΊΟ and 11 .are similar representations as 3 and 7, but for different cases of stress on a strand of bending in the bending device according to the invention.

Figures 12, 13, 14 and 15 are similar illustrations as FIGS. 4 and 8 and relate to the prior art, FIG. 12 showing the geometric course of the curved strand shell after a circle, FIG. 13 after an ellipse, FIG. 14 after a general parabola and Fig. 15 corresponds to a clothoid.

Figures 16, 17, 18 and 19 relate to a third Embodiment according to the invention, namely on a straightening device, FIGS. 16, 17 being similar representations are like FIGS. 5 and 6 and FIGS. 18 and 19 are similar to FIGS Figures 7 and 8 are.

20 is a side view of a strand which is first bent in a bending device according to the invention and then bent is straightened in a straightening device according to the invention, and serves to illustrate the position of the coordinate system in the bending device or in the straightening device.

In FIGS. 1 and 2, the straight strand entering a bending device according to the invention is denoted by 1. It is a cast steel strand pulled out of a water-cooled mold with a rectangular cross-section and a thickness .d = 200 mm, which has a surface temperature after leaving the mold of about 1400 ° C and a strand shell thickness of about 30 mm. Below the mold, not shown, is a vertical, straight roller guide with opposite pairs Rollers are provided for supporting and guiding the strand 1, the last pair of rollers of this straight strand guide being dashed is shown and denoted by 2, 3.

The bending device according to the invention comprises nine non-driven pairs of rollers, the rollers 4, 7, 9, 13,

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17, 19, 20 for the bending of the strand 1 causing device belong, while the rollers 5, 6, 8, 10, 11, 12, 14, 15, 16, 18, 21 only have a support function, i. H. to counteract any bulging of the strand as a result of the ferrostatic pressure; all roles are 4 through 21 not driven and freely rotatable. The strand 1 leaves the bending device with a radius R "= 8000 mm and runs

-Egg

in the direction of the arrow in an arc-shaped strand guide, which also consists of pairs of rollers, the first of which is shown in dashed lines and denoted by 22 and 23.

The bending rollers belonging to the actual bending device are rollers 7, 9, 13, 17, 19, while the support rollers absorbing the reaction forces are rollers 4, 20; the center points or the axes of these rollers are each denoted by 7 ", 9", 13 ", 17", 19 "and the points of contact or generators of the outer surface of these rollers that touch the strand shell are denoted by 7 ¹ , 9 ¹ , 13 ', 17 ", 19'. The remaining rollers, which only absorb the ferrostatic pressure, touch the strand shell at points or lines 5 ¹ , 6 ¹ , 8 ¹ , 10 ', II ¹ , 12 ·, 14', 15 ', 16 ", 18' 21 'and their center points or axes are denoted by 5 ", 6", 8 ", 10", 11 ", 12", 14 ", 15", 16 ", 18", 21 ".

All rollers 4 to 21 are - like the rollers 2, 3 and 22, 23 - arranged equidistantly, and the points of contact 4 ', 5 ¹ ... to 20', 21 'lie on cam tracks 24, 25, which correspond to the geometric The course of the outer and inner strand shell correspond. The curve 24 corresponds to a function y (x.), The coordinates of which are to be determined, the origin of the coordinate system x, y being at point 4 ¹ ; the Y-axis is denoted by 26 and marks the beginning of the transition zone; the X-axis is denoted by 27 and is a tangent to curve 24 at point 4 ¹ , where

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the direction of the positive X-axis is in the direction of movement of the strand, while the direction of the positive Y-axis 26 is perpendicular to the interior of the strand. 26 therefore also designates the plane through the roller axes 4 ", 5" and through the contact points 4 ¹ , 5 'or the normal to the tangent in the contact points 4', 5 'of the curves 24, 25. The corresponding planes are analogous or normals designated by the subsequent pairs of rollers with 28, 29, 30, 31, 32, 33, 34, 35. In the touch

point 4 ¹ , the curve 24 has a radius of curvature R. = R ₀₀ / and the radii of curvature in the subsequent contact points 6 ¹ , 8 ¹ ... to 20 'are analogous to R _fi , R _{R /} Ri _O / R ₁₂ , R, " ^R i6 'denotes ^R i8 ^{and R} 20, where R" = R ^ = 8000 mm. The angles of inclination of the planes or normals 28 to 35 through the points of contact 6 ', 8 ¹ ... to 20' to the Y-axis 26 are 0C ₅ , c £ _Q , ^a: ₁₀ ' ⁰ ^ ₁₂ ' ⁰⁶ IA ' ° S.6 '^ 18 and ^ q and must also be determined for the bending device according to the invention.

The following are given for the construction: the x-coordinates of the contact points 6 ', 8 ¹ , 12', 16 ", 18", 20 'or the distances between these points: let the distance A be 200 mm; Thus, the total length of the curve 24 X = 1600 mm projected into the X-axis 27 - in the direction of the Y-axis 26 - and drawn exaggerated in FIGS 'or 16 ¹ , 18 "and .20" are the same size, namely A = mm in each case, and the distances between the contact points 8 ¹ , 12' and 16 'are twice as large, namely 2A = 400 mm in each case.

In Fig. 2, the vectors of the bending forces acting on the inside of the strand P ^, P _g , ^ ₁₃ / P ₁₇ , P _iq and the corresponding supporting forces (reaction forces) P, P ₃₀ are shown schematically; the lines of action of these vectors lie in the planes or normals 28, 29, 31, 33, 34, or 26, 35. In FIG.

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bene, through the point 5 'extending tangent 27' is shown for the curve 25th

In Fig. 3, the x-coordinates of the points 4 ', 6', 8 ', 12', 16 ', 18', 20 'are plotted on the X-axis; they have the designations χ ., χ ,, x “, χ .., χ ,,, x, g, ^χ ? ο * On the Y-axis, three dimensions 1,000, 0.667 and 0.375 are plotted on a freely selected scale , which represent the default values and - in this special case y-coordinates for the points χ _Ί ~ or x _o , χ _{Ί r} or x _r , X _1o

LZ ο Ib D Xo

to form a mirror-inverted symmetrical curve 42 with points 4 ", 39, 37, 36, 38, 40, 41, the axis of symmetry passing through points 36 and x, ₂ ; curve 42 is dashed and that between it and the area 43 enclosed by the X-axis is shown hatched.

The course of curve 42 has the following three different meanings:

The course of curve 42, which corresponds to a polygon in this exemplary embodiment, is similar to that Course of a moment line, which is determined by the load case shown in Fig., Which is statically determined, would result. Furthermore, the course of the curve 42 is similar to the course of a curve, the change in strain of a Line element of the strand outer shell - expressed in% / mm, measured along the X axis 27 - corresponds. Third, the course of curve 42 is similar to the course of a curve, that of the change in curvature of curve 24 or the third The derivative y "'(x.) Corresponds to the function y (x.).

The following characteristic is essential to the invention of curve 42:

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It has a first real zero at the origin of the coordinate system 4 ^: or x,.; it rises relatively sharply at first, then gradually flattens out to ground up to a maximum value of 36; the second part of the curve from the maximum value 36 to the second real zero at point 41 is - in this exemplary embodiment - a mirror image; after reaching its maximum value, the curve initially descends relatively little, then gradually descends more sharply up to this second real zero; the presence of two real zeros 4 'and 41 at the beginning and at the end of the curve 42 or at the beginning and at the end of the bending zone extending within the lines 26, 35 - based on the X axis 27 - with an intermediate one. Maximum value 3 6 is the essential core of the invention, which is used to determine the geometric location of all contact points of the rollers or the force application points of the bending device and to construct the bending device according to the invention, the transition curve 24 from the straight line (vertical) to the The arc of a circle does not follow a curve known from the prior art in the manner of a circle, an ellipse, parabola, hyperbola or KIothoide or chain line. It is also essential that the points 39, 37, 36, 38, 40 - in this embodiment, where several individual forces P ₇ , P, P, ^ '- ^ i 7' ^ ig ^ ^as bending - probably kinks, but there are no jumps in curve 42.

The area 43 - expressed in mm - is a

Auxiliary quantity FLE ₁ , which is required for further calculation. In order to obtain the course of the curve for the change in strain i- ¹ (x.), Which is denoted by 42 'in FIG. 4 and shown to scale, the curve 42 of the following is used. 3, which is designated as ψ ^% (χ ·), compressed, ie converted with the compression factor k ". The following equations apply:

5098U / 0419 OfciGINÄL INSPECTED

χ =

(Equation 1)

k ".4" (χ.) = / _ '(χ.) (Equation 2)

^k " ⁼ (equation 3)

^k ' ⁼ R- (equation 4)

k ¹ is another compression factor that is used later for the calculation of:
is used.

Calculation of the curve 24, which follows the function y (x.),

The ordinate values of the curve 42 'or the points 39', 37 ', 36 ", 38', 40 'are obtained by the y-values of the Curve 42 is multiplied by the compression factor k ".

By integrating der.Kurve 42 ″ to dx to curve 44 in FIG. 4, which corresponds to the elongation of a line element of the strand outer shell - expressed in% and is drawn to scale; the% scale is indicated in Fig. 4 on the ordinate on the right, while the left The scale shows the change in elongation - expressed in 10% / mm.

The mathematical relationship described between curves 42 * and 44 shows that there, where the curve 42 'has its real zeros 4', 41, extreme values are present and with the X-axis or parallel to these running tangents to curve 44 are present; the course of the curve 44 to the left of the extreme value 4 'is with 44 'and the course to the right of the extreme value 46 is denoted by 44 ", one tangent coinciding with the X axis 27 and the other tangent being designated by 27 ″. At the point where curve 42 'has its maximum value 36', a turning point 45 is present in curve 44.

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In detail it should be noted about the calculation:

For the curvature of y (x.), The geometrical location of the outer strand shell that is stressed by elongation in the bending device / applies

\ i = ~ (equation 5),

^R j

v / obei R. is the respective radius of curvature. For the percentage elongation of a line element of the outer strand shell - In the bending device - or the inner strand shell - which is stretched in the straightening device - applies

X (x.) = (Equation 6),

3 ^R j

where d is the thickness of the strand in mm; in this exemplary embodiment, d = 200 mm. From equations 5 and 6 it follows that the curvature K. is proportional to the elongation Έ. (x.). You can also - without a consideration

\ r ■ *

worthy of making a mistake - the curvature H. of the second derivative y "(x.), i.e. it holds

K = y "(x.) (Equation 7). ·

Similarly, the change in curvature fC ¹ is also proportional to the change in strain Σ ¹ (x.), Ie it applies

= k ¹ . f ^l (x.) (Equation 8),

/ 0 = y ¹¹¹ (x.) (Equation 9),

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d. H. the change in curvature is also proportional to the third Derivation of y (x.). These differential equations 1 to 9 are generally valid for the calculation of y (x.) or the bending device.

In order to obtain the numerical values for the present exemplary embodiment, equation 4 must first be assumed will. It applies

y "'(x.) = k ^1. ψ' (x.) (Equation 10),

with which an easily solvable third order differential equation for y (x.) is obtained. Next is through Integrate y "is obtained (equation 7), and by integrating again becomes

y ¹ (x.) (Equation 11)

obtained, y ¹ (x.) gives the slope of the puncture y (x.), expressed as the tangent of 06., so that the size of the angle

C ^ g, c £ -, Q / ··· to ⁰ ^ ₂ O ( ^F: * -9 · 2) can be calculated because - as mentioned - the lines 28, 29, 30 ... to 35 are normal to the The points of contact 6 ', 8', 10 '... to 20', which are on the curve 24 or y (x.).

By further integrating equation 11, one finally arrives at the function we are looking for

y (x.) (Equation 12).

In all integration steps, from x = 0, the origin of the coordinate system, to the current point x = x. integrated; the last point x. is X ",

3 3 k

d. H. in the exemplary embodiment 1 X "= 1600 mm or x ~~.

tj TO

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In the present exemplary embodiment, all rollers have the same radius r = 50 mm, and calculate it the roller centers 4 ", 6", 8 "... to 20" of the rollers 4, 6, 8, ... to 20 on the strand outer shell or of the curve 24 from the coordinates χ and y:

r ^J r

x = x. + r. sin oC. (Equation 13), y = y. - r. cos ex. (Equation 14).

The roller center points 5 ", 7", 9 "... to 21" of the rollers 5, 7, 9 ... to 21 on the strand inner shell or curve 25 can be determined analogously from the coordinates χ 'and y':

χ '= x. - (d "+ r). sin Di '. - (Equation 15), y' = y. + (d + r). cos cA. (Equation 16).

The coordinates of the curve 25, the dem-geometrical Location of the strand inner shell can be calculated from the following equations:

x = x. - d. sin (X. (Equation 17), y = y. + d. cos oc. (Equation 18).

The coordinates'χ, y _M for the geometric location

the centers of curvature of curves 24 and 25 are calculated from:

χ = x. - R.. sin Pc ^. (Equation 19),

y = y. + R. . cosi} £ ·. (Equation 20).

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The result of the numerical calculation for the present embodiment is in the following tables of numbers summarized:

Table 1 shows the values for the change in elongation and total elongation on the outer shell of the strand, which correspond to the Curves 42 "and 44 in Fig. 4 correspond, as well as the radius of curvature Usually included.

In table 2, the coordinates for curve 24 are in the first two columns according to the function y (x.) and the slope of this curve - expressed as y '(x.) and tangent OC, respectively. - contained in the third column;

the angles o £ ', ö ^ _Q , ... to <& are directly from the b ο ZU

Numerical values in column 3 can be calculated.

In table 3, the coordinates of the rollers 4, 6, 8 ... to 20 are in the upper part according to the equations 13, 14 and in the lower part the coordinates of the opposite rollers on the inside of the strand 1 accordingly contain equations 15, 16; the expression "roller axis" is identical to "roll center".

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Table 1: bending zone (Fig. 1-4)

• (= ^X 4> Elongation
modification 5 j Total elongation 0 Radius R.
τητη 901 j 10 ³ % / mm Ό 0.00310 J.IU.LI 810! 0 0.01241 164 ! Distance on
. the X-axis 0.124 0.02792 3 222 489 • mm
I. (= 0.248 0.04963 865 123 y i
i 0 0.372 0.07685 358 836 ^j 50 0.496 0.10888 201 614 j 100 0.593 0.14574 130 360 i 150 /
\ ~ " ^X 8 ^} 0.689 0.18740 ' 91 948 j 200 0.785 0.23284 68 588 I. 250 0.881 0.28099 53 138 j 300 0.936 0.33188 42 942 j 350 0.990 0.38547 35 635! 400 1.045 0.44179 30th 968 450 1,099 0.50081 25th 777 ■ 500 1.153 0.56254 22nd 950 I 550 ^X 12 ⁾ .1,208 0.62696 19th 464 j 600 1.262 0.69135 17th 281 ι 650 1,316 0.75296 15th 318 ι 700 1.2599 0.81179 14th 522 I 750 1.2044 0.86787 13th 856 800 1.1491 0.92118 . 12th 291 ; 850 1.0938 0.97173 11 808 900 I 1.038 1.0195 10 393 950 (= ^x l6 ^} 0.984 1.0646 10 043 1000 0.928 1.1059 9 754 : 1050 0.874 1.1424 9 516 1100 0.778 1.1740 9 327 : 1150 (= ^X 18 ^} 0.682
i i 1.2009 8th 181 i 1200 0.586 !
I. 1.2224 8th 079 ; 1250 0.490 1.2010 8th 019 ; 1300 0.368 1.2469 8th 000 1350 / - ^X 20> '0.245 1.2500 8th 1400 0.123 U / 0419 8th 1450 0 8th 1500 1550 1600 OJ 38

Table 2: bending zone (Fig. 1-4)

Distance on
the X-axis
min

mm

ο (■■

5O
100
150
(=
250
300
50

400 (= X ₁₂ ) 450 500 550 600 650 700 7 50 800 (= χ) 850 900 950 1000 (= χ) 1050 1100 1150 1200 (—Ν \ —Υ 125Ο 1300 1350 1400 1450 1500 1550 1600

_ 0.000065 0.001034 0.005236 0.016546 0.040379 0.083525 0.15399 0.26099 0.41493 0.62713 0.90964 1.275 1.737 2.310 3.007 3.845 4.841 6.009 7.364 8.924

10.699

12,706

14.955

17,459

20.229

23.275

26.607

30.232

34.157 38.388 42.928 47.779 = Y,

Ο, ΟΟΟΟΟ5 0.0000414 0.0001396 0.000331 0.000645 0.0011074 Ο, ΟΟ1742 0.002573 0.003622 0.004906 0.006437 0.008229 Ο, Ο1Ο296 0.012651 0.015309 0.018281 0.021578 0.025190 Ο, Ο291Ο3 0.033039 0.037777 0.042511 0.047490 0.052702 0.051296 0.06375

0.06954

0.07548

0.08155
0.0876?
0.09391
0.10015

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Table 3: bending zone (Fig. 1-4)

Location of X
r 1 3Γ Roller axles mm y mm a) on the outside t ' Role 4 0 ! -50! ^! Role 6 200.02 -49.9 8 ■■ j : Role 3 400.13 : -49.74 j Role 10 600.41 ; -48.72: Role 12 800.91 i -46.15; ■ Roll 14 1001.67 ^: -41.05 Role 16 1202.63 ; -32.47 j Roll 18 1403.76 : -19.63 Roll 20 ; 1604.93 - 1.97! i V ν ' • ^; . mm I mm f b) on the inside j I
i ί
i; Role 5 ^: o ! 250 ί Role 7 ; 199.92 ; 250.02 [ Role 9 ! 399.36 I 250.26; Role 11 ! 597.94 ■ 251.27 "! : Role 13 795.43 ■ 253.80 j Role 15 '991.68 ^; 258.78 j : Roll 17 : 1186.84 I 267.11 ί Roll 19 ', 1381.18 j 297.52 I. Roll 21 1575.09 •. 296.54 j

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5 to 8 is a modified version ung si orra of a continuous caster according to the invention explained. The straight strand entering the 3iegezone is marked miw 1; the dotted roles 2, 3 are the last rolls of a straight strand guide. The strand 1 again has a thickness, d of 200 mm and is in the direction of the arrow pulled out of the bending device and in a circular arc guide indicated by the pair of rollers 22, 23 continued, this circular arc guide has an outer radius R ^ of 8000 mm.

The bending device according to the invention comprises four rollers 47, 49, 50, 48, the rollers 49, 50 bending forces P / q / Ρ _ςη on the inside of the strand and the rollers 47,

48 Reaction _{forces P / rj} , P ,, -, generate (Fig. 6). Die Biegest / 'iO

rollers 49, 50 and the support rollers 47, 48 are not driven. Opposite the bending rollers 49, 50 there are guide rollers 51, 52 which do not take part in the strand bending itself, but instead counteract the ferrostatic pressure of the liquid strand core; the rollers 51, 52 can e.g. B. omitted if a completely solidified strand, z. B. a rail is bent. The corresponding points of contact of the rollers are denoted by 47 ', 48', etc., analogously to the exemplary embodiment according to FIGS. 1-4, as are the roller centers or roller axes with 47 ", 48", etc. 53 is the positive Y-axis and with 59 denotes the positive X-axis of a right-angled coordinate system for the curve 54, which is laid through the contact point 47 '. The curve 54 corresponds to the strand outer shell or the function y (x.), And the curve 55 corresponds to the equidistant strand inner shell. With 56, 57, 58 normals on the curve 54 at the contact points 51 ', 52 "and 48' are designated, and the associated radii of the curve 54 have the designations R ₁ - ,, ¹ Vo ' ^R 4ö ^{; the Nei} 9 ^'un € f ^{Swinke dor} l normal to the Y axis 53 are connected oC., oC and oC, respectively.

. B098U / 0A1 9

The distance between the point of contact 51 ′ projected onto the X axis 59 is denoted by B and amounts to 530 mm, the corresponding distance between points 51 'and 52' is C and is 180 mm and the distance between points 52 * and 48 'is D and is 570 mm; X_ is thus in this embodiment 1280 mm.

The calculation process and the equations to be used are the same as in the exemplary embodiment according to FIG Fig. 1-4.

The results are explained in more detail with reference to FIGS. 7 and 8 and the number tables 4, 5 and 6.

Corresponding to the assumed load case with two bending forces ^ ₄ Q / Pc _{0 there} is a trapezoidal course for the curves 63 and 63 ', ie there are two maximum values 60, 61 which form a "zone", namely the zone of the maximum value between X ₅ , and X ₅₂ - ' ^^ ^e corresponds to the maximum value of the change in strain. At 47 'and 62 there are real zeros again, and the hatched area 64 enclosed between the curve 63 and the X-axis is FLE, ie - as mentioned earlier - a computational auxiliary variable for determining the curve 63', which is drawn to scale; the corresponding numerical values for the change in elongation are contained in Table 4, and there are also the numerical values for the total elongation, on the basis of which curve 65 in FIG. 8 was drawn. The same mathematical relationship exists between the curves 63 'and 65 as in the exemplary embodiment according to FIGS. 3 and 4. The curve 65 consists of a straight section 65 ¹ which coincides with a tangent in the X-axis 59 at the point 47', a parabolic section up to point 66, a turning tangent 65 "'between points 66, 67, another parabolic section from point 67 up to the maximum value 68 and a straight section parallel to the X-axis 59 • 5098U / (H19

- 9Ω -

which together with a tangent 59 'at point 68

Table 5 contains numerical values for curve 54 and its slope - expressed as the tangent of oi; the curve 54 represents the geometric location of the bent outer strand shell in the bending zone; at their beginning or at their end the supporting forces P. _, P. _o

4 / 4o

while the bending forces P ₄₀ / Pr _{0 act} on the equidistant curve 55. The respective radius of curvature of curve 54 can be found in column 3 of table 4, and table 6 contains the coordinates χ ", y" of the roller centers of the rollers 47, 51, 52, 48 on the strand outer shell and the coordinates χ "', y "'of the two bending rollers 49, 50 on the inside of the strand.

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Table 4: Bending zone (Fig. 5-8)

Distance on
the X-axis
mm (= x) Elongation
modification
10 % / mm 0 0 50 0.16 100 0.33 150 0.49 i 200 (= 0.65 250 0.81 300 0.97; 350 1.14 400 1.30; 450 1.46 ■ 500 X ₅₁ ) 1.62 \ 530 1.71 550 1.71; 600 1.71 ": 650 1.71; 700 X ₅₂ ) 1.71 710 (= 1.71 750 1.59 800 1.44 I. 850 1.29 y 900 1.14 950 0.99 1000 0.84 1050 0.69 1100 0.54 1150 0.39 1200 0.24 12Ü0 ^X 48 ⁾ 0.08 1280 ο

Radius R.; mm - * ^:

0.00406 0.01625 0.03657 0.06500 0.10155 0.14620 0.19894 0.25976 0.32864 0.40557 0.45558 0.48988 0.57558 0.66120 0.74675 0.76385 0.82983 0.90550 0.9736 1.034 1.087 1.133 1.171 1.202 1.225 1.240 1.248 1.250

2,460 679 615 212 273 456 153 841 98 476 68 402 50 267 38 498 30th 428 24 657 21 9 50 20th 413 17th 373 15th 124 13th 391 13th 091 12th 051 11 043 10 278 '9 669 9 197 8th 827 8th 540 8th 322 8th 165 8th 062 8th 009 8th 000

5098U / CU1 9

Table 5: Bending zone (Fig. 5-8)

Distance on the X axis mm

ν

mm

50

100 150 200 250 300 350 400 450 5OO (= X ₅₁ )

550 600 650 700 (= X ₅₂ )

50 800 850 900

950 1000 1050 1100 1150 1200 1250 (= x _AO ):

0.000085

0.00135

0.00686

0.02167

0.05291

0.10969

0.20320

0.34661

0.55513

0.84597

1.06791

1.238

1.753

2,412

3.236

3.423

4,247

5.465

6,909

8,597

10,542

12.7

15.261

18.054

21,147

24,546

28.256

30.632 = Y

0.000007 0.000054 0.000183 0.000433 0.000846 0.001462 0.002322 0.003465 0.004933 O, OO6765 0.008056 0.009001 0.01166 0.01475 0.01828 0.019032 0.02222 0.02656 0.03126 0.03628 0.04159 0.04714 0.05291 0.05884 0.06491 0.07108 0.07730 0.08105

5Q98U / 041

Table 6: Bending zone (Fig. 5-8)

: Location of
■
Roller axles χ "
r
mm y.
mm
■ 251.06
253.24 a) on the outside :
j Roll 47
Roll 51
Roll 52
Role 48 0
530.40
710.95
1284.04 -50.!
-48.93;
-46.57
-19.20
■
*
i χ "·
r
mm ■ v * "'ί
^r I
mm ι j
b) on the inside ;
t
i Roll 49
Roll 50 527.99
705.24

S098U / 0419

9, 10, 11 are further examples characterizing the invention for the freely selectable Course of the normalized torque line, corresponding to different load cases of the strand in the invention Bending device, shown:

According to FIG. 9 engage in the area of points X ₃₁ / ^X 32 ^{/ X} 33 ^'X 34 ^{v i} - ^he bending forces to the strand inside of; the corresponding support or reaction forces act on points χ, ^x r> c ^au f ^ ^he strand outside, and it results in a by a polygon 69 "designated by dashed lines drawn curve with a maximum value at the point 169 or at x," if the magnitude of the bending forces is chosen so that the resultant lies in this range. The solid curve 69 corresponds to the ideal case from the point of view of the bending stress on the strand, ie when there is a constant load (uniform stress) on the inside of the strand, which is when used In order to keep the friction between the strand and the support elements as small as possible, the maximum 169 is placed in the area of the last third of the entire bending zone: x__ is therefore about 2/3 of X _35. Points 70, 71, 72 of curve 69 'are kink points, but not jump points.

According to FIG. 10, only a single bending force acts at X ₄ , and the supporting or reaction forces act symmetrically thereto at x. _n and x. ~ , so that a triangular, approximated curve 73 'with a maximum value 74 results. In the case of a uniformly distributed load for bending the strand, on the other hand, a symmetrical parabola 73 results, the apex of which is at the same time the maximum value and lies at 74.

5098U / 0A19

After Pig. 11, the maximum of a traverse marked 75 'is characterized by a zone between points 78, 7S and 79, which corresponds to the maximum value, while points 77, 80 are kinks, but no jumps. This is the ideal case of the construction of a bending device according to the invention using rollers to transfer the bending forces, which tap into points X ₅ -. * Xr ₂ / ^X 53 ' ^χ ς4' ^X 55, while the 'support or _{Reaction forces} attack at X ₁ - and X 56. If, on the other hand, a uniform bending load is assumed, the result is an arcuate course of the curve 75 for the change in strain or the course of the moment line or the course of the curve corresponding to the third derivative y "'(x.). The flat one over a large longitudinal extension Curve 75 'or 75 running (long bending zone) for the change in elongation characterizes a kind of mild stress on the strand, even if greater friction is accepted as a result of the great length of the bending zone

got to. In contrast, according to Fig. 10, the bending zone is relatively short and the friction is less, but the strand is in "one very short section curved, d. H. its stress is relatively strong and limited to a short zone.

For a better understanding of the invention compared to the prior art, the following FIGS. 12 to 15 are shown certainly.

According to the state of the art, e.g. B. the Austrian In U.S. Patent No. 231,629, it is known as a transition curve from a straight line to an arc of a circle or vice versa, curves to use the circular arcs with gradually graduated radii of an ellipse, parabola, hyperbola, clothoid or Catenary match.

• B098U / -04 19

In a representation analogous to that in FIGS. 4 and 8, but on the assumption that the transition curve (the geometric Location of the outer shell of the strand) Arcs of an ellipse, parabola or clothoid result in the Fig. 12 to 15:

In Fig. 12, the curve of the strain change Σ is fully drawn with 81. '(χ.) entered, which at the beginning of the bending zone at x, _n a jump point from co to zero - marked by the curve 81' - and at the end of the bending zone at x ,, a jump point from zero to <= - o - marked by the curve 81 "; in practice this means that in an infinitely small zone at x _{ßQ there is} a sudden, sudden, infinitely large change in strain, while along the bending zone the change in strain is constantly zero and at the end at χ, again a sudden, infinitely large change in strain occurs in an infinitely small zone at the transition to the subsequent circular arc. Curve 82, which is drawn in dashed lines and corresponds to the permanent strain Σ (χ.), runs analogously: at χ ,,, there is a jump point marked 83,

YOU

ie the elongation suddenly increases from zero to the value 83, then remains constant until x _g - only to suddenly increase further to the end value 85 (maximum value) at point 84; Fig. 12 thus also illustrates that by dividing circular arcs to form a transition curve, as has been proposed several times so far, you get a stepped course for the elongation, ie an extremely unfavorable, sudden stress on the strand at every transition point from the straight line to the first circular arc or between the individual circular arcs, as well as at the end of the transition curve at the transition to the circular arc-shaped strand guide.

5098U / 0419

13 is an analogous representation when the transition curve follows an ellipse: the curve 86 for the change in strain increases _{very slowly at the beginning of the bending zone (^ 70} ), i.e. at first almost linearly, and then in the last part very strongly in the manner of a parabola to a maximum value 87 and from there suddenly drops to zero after curve part 86 ″; at x ″, there is again a jump point which is undesirable the curve 88 runs for the elongation: at X _{70 there} is a jump point from zero to a finite value 89, from which the curve 88, similar to the curve 86, then runs up to a maximum value 90, where a kink is present The strand is loaded suddenly _{at X 70 and suddenly relieved at X 71.} The use of an ellipse as a transition curve results in better conditions than the use of circular arcs, but optimal bending conditions cannot be achieved.

14 is an analogous representation for the use of a general parabola of a higher order as a transition curve: the curve 91 for the change in strain starts from a zero value at χ _β _, rises very sharply at first, and then - gradually becoming flatter - up to a Maximum value 92 to rise where there is a jump point from which a sudden drop to zero (χ _ΟΊ ) occurs.

oil

The curve 93 for the elongation _{gradually increases from x 8Q} to Xg ₁ to the maximum value where there is a kink.

Finally, illustrates 15 the conditions when using a clothoid as transition curve:. ', The curve 94 for the change in strain has in x_ _{Q is} a jump point from zero to a finite value 95 and end at x _g, a maximum value 96 where a second discontinuity exists is where the curve drops to zero. The curve 97 for the elongation starts _{from zero at x QQ} and increases very quickly and fairly

5098U / 0419

borrowed evenly up to a maximum where again one There is a kink. The clothoid as a transition curve is thus comparable to an ellipse and also results unfavorable conditions for a strand to bend.

The hyperbola and chain line have finite radii of curvature at the transition from the straight line to the bending zone; there are also discontinuities or jumps

16 and 17 show a straightening device according to the invention, the strand 1 entering the straightening device with the inner radius R = 7800 mm and the thickness d = 200 mm, being stretched on the inside of the strand and compressed on the outside of the strand and thus straightened will; the strand 1 runs out in the direction of the arrow with the radius R'_ = R ' _M. The straightening device consists of the straightening rollers 100 and the rollers 98, 99 which absorb the reaction or supporting forces; the directional forces are _{denoted by P 100} ' ^P ioi in FIG. 17 and the bearing forces by A ₁ , B 1. 98 'i ^ t denotes the point of contact of the roller 9 8 on the inside of the strand, which forms the zero point of a coordinate system whose positive Y-axis is denoted by 102 and whose positive X-axis is denoted by 103 (the X-axis 103 is a tangent to curve 111 (y (x.)) at point 98 '). The center of curvature M of the circular strand guide with the inner radius R lies on the Y-axis 102, which at the same time represents the normal through the point 98 '. 104, 105, 106 also denote normals in which the lines of action of the bearing force B or the directional forces Ρ ·, _ηη / P _in1 lie. 107 ', 108' are points of intersection of the normal 102 with the outer transition ^{curve 112, which is equidistant to the inner transition curve 111, and 109 'and HO 1} are analogous points of intersection on the curve 111. The distance a of the point of intersection

5098U / 0A19

109 'on the X-axis 103 is specified and is 530 mm. The distance b of the point of intersection 110 'from the point of intersection 109' on the X-axis 103 is also specified and is mm, and c, the distance between the point of contact 99 'of the roller 99 and the point of intersection HO ¹ , is 570 mm; thus the length of the straightening zone X '= 1280 mm. We are looking for Y 'who

Γι E

Course of the curve 111 according to the function y (x.) And the course of the equidistant curve 112 'as well as the angles of inclination ot ^ ~ n , <= £ -, -, _n , oCc η of the normals 105, 106, 104 to the Y-axis ίο y hü yy

102, which are important for the construction of the straightening device.

FIGS. 18 and 19 are analogous representations to FIGS. 7 and 8. To calculate the curves for the Strain change, strain can be the equations 2, 5, 6, 7, 8, 9, 19 and 20 and the modified further equations be used:

FLE = / f ¹ (x.) Dx (equation la).

x = 0

^k "l = = (equation 3a)

^k 'l ^{= =} . (Equation 4a)

y " ¹ (x.) = k ' _x j>' (x.) (Equation 10a)

.) dx (equation 10b)

) dxj. dx (equals Ha)

5098U / CU1 9

X = X. X = X., X = X.

J / (i ~ " ^k 'i / 5 ^{? I (x} j ^{) dx} ) * ^dx * ^dx

χ = O χ = 0 x = 0 (equation 12a)

χ _± "= x. - r sin (oC.) (Equation 13a)

y. "= y. + r cos (χ.) (Equation 14a)

χ, "= χ. + (d + r). sin {06.) (Equation 15a)

Y ₁ "= y · - (d + r). Cos (o6.) (Equation 16a)

x ¹ = x. + d sin O ^) (Equation 17a)

y ¹ = y. - d cos (o £.) (Equation 18a)

• J «J

Equations 13a, 14a relate to the inside of the strand, and equations 15a, 16a, 17a, 18a to the outside of the strand. The calculation process is basically the same as for the calculation of a bending system. The characteristics of the straightening device result from the aforementioned Figs change ψ ^χ (χ.) is similar; the curve 113 given by the points 98 '( ^χ ₂ ^ 114, 115, 116 (x_) includes the surface 117 with the X-axis 103; this surface 117 is FLE. The compressed curve drawn to scale for the change in strain Σ . ' (x ·) is designated 113 "in FIG. 19; it has two real zeros at points 98', 116 and two maximum values 114 ', 115'. The associated curve 118 for the expansion ^ (x.) is from a horizontal branch

509814/0419

118 'via a first turning point 119 into a turning tangent 118 '' 'and a second point of inflection 120 as well as a maximum value 121, which corresponds to the maximum elongation, into one second horizontal branch 118 ". across. With 103 'there is one with this branch 118 "coinciding with the X-axis 103 parallel Tangent to the point 121 denotes what - as mentioned a characteristic of the course of the curve 118 for the Stretching is.

As shown in FIG. 16, further pairs of rollers 122 for guiding and supporting the strand shell can be arranged in the straightening device if this straightening device is used in a continuous casting plant for straightening a cast strand which has a still liquid core. The roller pairs 122 can then be arranged in a "floating" manner, ie they are mounted so that they can move freely while maintaining their relative spacing d in the direction of the normal through the roller centers. Further guide rollers are designated 107, 108, 109, 110; like the roller pairs 122, they do not take part in the actual straightening of the strand. The same applies mutatis mutandis to the stationary roller pairs of the circular arc-shaped strand guide, denoted by 123, and to the stationary roller pairs, denoted by 124, of the horizontal strand guide with the radius R ' _E = R ¹ Oo.

The results of the numerical calculation are contained in tables Ί, 8, 9, with table 7 containing numerical values for curve 113 '(change in strain) and 118 (total strain) as well as for the current radius R. of curve 111. Table 8 shows the numerical values for y. for curve 111 and its slope y ¹ . - again expressed as the tangent of oC. ~ included so that the points of contact of the rollers on the inside of the strand and the angle of inclination iX! and 0C ₉₉ result immediately. Table 9

5098U / 0A19

holds the coordinates x_. ", y." of rolls 98, 109, 110, 99 on the inside of the strand and the coordinates x. ", Y." of the two straightening rollers 100 and 101 on the outside of the strand.

509814/0419

Table 7: Straightening zone (? Ig. 16 - 19)

^{Ab3 2} cc. &Quot; d on
the X-axis

Warning annoyance Stretching

S / mm

xaaius k_. 7th 800 min 7th 825 7th 903 8th 03 5 3 228 8th 490 3 833 9 277 9 845 10 583 11 547 12th 274 12th 828 14th 458 16 550 19th 376 20th 058 23 207 28 305 35 283 45 193 53 7 49 83 279 123 447 201 581 ObO 487 1 020 465 7 243 851

0 (= x ₂ ); 0 50 0.169 100 : 0.338 150 0.506 200 0.675 250 0.844 300 1.012 3 50 1.178 400 1,345 450 1, 512 500 χ, ο ο Jl 530 1.73 550 1.73 500 1.78 6 50 1.78 700 1.73 710 (= X ₁₄ ) ^ 1.78 750 1.65 CCO 1.49 CS OO 1.34 £ 00 1.13 950 0.994 1000 0.859 1050 0.714 1100 0.553 1150 0.403 12C0 0.243 1250 0.093 123O i =: ■ :-) 0

0.00417 0.01657 0.03751 0.06668 0.10416 0.14997 0.20406 0.26544 0.33710 0.41602 0.46731 0.50250 0.59039 0.57821 0.76595 0.78349 0.35116 0.92375 0.99863 1.0608

1.12-5

1.162

1.201

1.232

1.255

1.272

1.281

1.232

6098U / 0419

Taballa 8: target zone (? Ig. 16 - 19)

Distance, on
the X-axis
R.A.M.

y ¹ .

R.A.M

ο (= x ₂ )

50
1OO
150
200
250
300

4C0

500

(= X ₁₃ )

550

600

65Ο

700

(= χ ,,)

750

ο 00

850

900

950

1100

12CO
1250
(=

0.1602

0.6396

1.4353

2.5418

3.9521

5.6567

7.644

9, SOl 12.411 15.153 16.911 13.121 21.278 24.6Ο9 28.091 2ο, -303 31.701 3 5.420 39.227 43.105 47.039 51.014 55.020 59.046 63,084 57,129 71,177 73,606 - Y "

0.0064 Ο, Ο128 0.0190 0.0252 0.0312 0.0369 0.0424 Ο, Ο477 0.0525 0.0572 0.0597 0.0613 0.0649 0.0682 0.0710 0.0715 0.073 4 0.0753 0.0769 0.0782 0.0791 0.0798 0.0803 0.0807 0.0808 ■ 0.0809 0.0310 0.0810

5098U / 041

BATH ORIGINAL

Table 9: Straightening zone (Fig. 16 - 19)

j a) on the: inside

RoI-Le So role 109 role 110 role 99

b) on the outside

Roll 100 roll 101

527.02

706.43

1275.96

mm

544.89 727.33

66.82

78.67

123.44

-232.64 -220.56

5098U / 0A19

Pig. 20 is a in a overview drawing for a bending device according to FIG. 5 and 6 and a straightening device according to can rig. 15 and 17, which are provided in a continuous steel casting plant, with a kraisbogenförrüiga strand guide being present between the biage device and the straightening device, which has an outer radius R ^ of SOOO-mm and an inner radius R 'of 7SCO πγλ; the strand thickness d is equal to 200 mm, -CTia the Lwümraungsraittelpunkt is denoted by M. Auo rig. 20 the position of the coordinate systems can be seen: the coordinate system, x, y with axes 59, 53 has its origin on the outside at the beginning of the bending zone at point 47 '; the coordinate system x, y with the axis. _: i 103, 102 has its origin on the inside at the beginning of the straightening zone at point 9S ¹ . The inside of the strand is compressed in the bending zone and the outside of the strand in the straightening zone.

A further calculation variable for the construction of a continuous casting machine according to FIG. 20, in which the strand gradually from the vertical into an arc of a circle and from this gradually deflected or bent into a horizontal line and is judged, cc oC is calculated from the

k k

relationship

<*, = 90 ° - oC - ^ _OQ (equation 21),

. wherein the angle a ^ _A o ^u nd ^ n ^ _g ^{of s} are given in Fig 5 and 17; It is therefore the angle of inclination of the normal 5S at the end of the bending device to the horizontal or Y-axis 53 and the angle of inclination of the normal 102 to the vertical at the beginning of the straightening device, which is identical to the angle of inclination of the normal 104 to the Y-axis 102 ..

5098U / CU19

It is advantageous that when bending continuously cast steel strands with a liquid core and of a solidified strand shell, the maximum value of the change in elongation does not exceed 0.0025% / mm; when judging, Where the strand shell is naturally thicker and somewhat colder, the maximum value of the change in elongation should be 0.0030% / mm do not exceed.

It is also useful that the longitudinal extension X_, the bending zone or X 'of the straightening zone - measured

Ü E

in each case in the direction of the associated X-axis - 1/7 to 1/5 of the radius of curvature R ^ or R of the circular arc.

It is also advantageous that the angle of inclination CiC ₀ Q, cC ^ Q of the normal 35, 58 at the end of the bending zone at the transition point 20 ", 48 'to the arc of the Y-axis 25, 53 3 to 10 °, preferably 5 to 7 The same applies to the inclination of the normal 104 at the transition point 99 'from the straightening zone to the horizontal to the Y-axis 102.

A particularly advantageous embodiment of the invention in a steel continuous casting plant consists in that all support and bending forces both within the bending device and the straightening device by means of preferably Driveless roles are transferred to the strand, with adjustment to different strand thicknesses d at least the rollers on the inside of the strand in the direction of the normal to the points of application of the bending forces - in the bending device - and the bearing forces - in the straightening device - shifted parallel to the strand shell will.

The main technical advantage of the invention is that the probability of occurrence of cracks caused by the dynamic change in shape of the strand is kept to a minimum, especially in the case of so-called rapid

509814/041 9

casting plants with an output of over 1.5 t / min. As from the. Curves can be seen, v / ird the change in elongation of the Strand (on the strand side when bending, on the Sürang inside when straightening) after a curve, which runs steadily from zero to a maximum value and from there steadily to zero at the end of the bending or straightening zone u; nowhere are there any jumps or discontinuities, which are a characteristic of all previously known, prior art facilities and the strand suddenly stress within an extremely small zone, causing these aforementioned cracks within the strand or can be triggered on the surface. Through the inventive arrangement of the elements (rollers) for bending or straightening a strand on transition curves that of 'The well-known transition curves can differ significantly, even a strand with a very thin and sensitive Strand shell be bent or straightened in a relatively short zone, and it can thereby increase the overall height of such Continuous casters are kept extremely low.

As can be understood by those skilled in the art from the foregoing description, the invention can also be used if the strand is only to be straightened, for example in the case of an arc-shaped mold is used, from which the strand emerges curved in a circular arc, then cooled and finally in the horizontal is steered. Furthermore, the invention can also be used outside the S-crano casting technology is used for solidified strands will. The term "strand" is also intended to include plates, profiles, rails and rolled products made of iron and non-ferrous metals include.

5098U / CU19

Claims (6)

Patent claims: Continuous caster with a secondary cooling zone downstream of the mold and with rollers for guiding, bending and / or straightening the strand _t whereby the bending rollers are arranged along a transition curve from the vertical to the circular arc and the straightening rollers are arranged along a transition curve from the circular arc to the horizontal, characterized that the bending or straightening rollers are arranged along a curve, that of the differential equation (χ) Bg / n corresponds to, where g? ^x (x.) is a function of the strain change, which over the extension of the bending or straightening zone has an initially rising, then the maximum of the permissible strain change and then falling again, Rp, equal to the circular arc radius at the end of the bending or . Straightening zone and X "the vertical projection of the bending zone or the horizontal projection. the straightening zone, and x. a position coordinate in a 'Kar- ■ cesian coordinate system, the origin of which is at the beginning of the transition curve and whose X-axis represents a tangent to the transition curve to the outside of the strand when bending and to the inside of the strand when straightening. 509814/0419 "OO C. HO - 2. S -z ~ s anggießanlaga according to claim I, characterized / that the maximum allowable elongation D is the same ■ ^ r- ^ t where d represents the thickness of the strand and R_ \ -rle above de ~ ir.ier-c. is. 3. S-ranggießanlage according to claim 1, characterized in that the rollers for bending and straightening the strand ar. Points are arranged, which result from a jump point-free course of the puncture of the strain change '■''{::.), Preferably from a polygon-shaped, in particular trapezoidal, running, circular arc-shaped, parabolic or similar course. 4. Suranggieüanlage according to claims 1 to 3, characterized in / that the rollers are arranged for bending or straightening of the strand at points that are determined in the following T \ ^T else: a) according to the number of bending or straightening rolls, a jump point-free expansion change function 4 ⁷¹ (x.) is specified, b) this function is integrated into the function ^ f (x.) within the limits of O biü X _E , then c) by multiplying the integrated value by ^ -. "" jE the compression factor rz - = determined, J O H ψ (x.) Dx ^J 3 d) by multiplying by the compression factor, the strain change curve y "'determines what e) by integrating y ", the reciprocal of the radius of curvature, d. H. the curvature, then B098U / 0419 BAD ORIGINAL λ ο or ········ c - _a s · ι - 41 - f) through, further integrating the slope and finally g) the position of the coordinate is determined by further integration. 5. S-cranggießanlage according to claim 1, characterized in that that the longitudinal extension X of the bending zone or X ' the straightening zone - measured in the direction of the associated X-axis - 1/7 to 1/5 of the radius of curvature R ^ or R of the arc. 6. Continuous caster according to claim 1, characterized in that the angle of inclination ⁰ ^ ₂₀ ' ⁰ Sa ^ ^{he Norma} l ^en 35, 53 at the end of the bending zone in the transition point 20', 48 'to the arc of the y-axis 26, 53 or the Normal 104 at the transition point 99 'from the straightening zone to the horizontal to the y-axis 102 is 3 to 10, preferably 5 to 7 °. 509814/0419