U.S. patent application number 10/490538 was filed with the patent office on 2004-12-09 for continous casting mould.
Invention is credited to Flick, Andreas, Lettmayr, Gernot, Shan, Guoxin, Wimmer, Franz.
Application Number | 20040244938 10/490538 |
Document ID | / |
Family ID | 3688332 |
Filed Date | 2004-12-09 |
United States Patent
Application |
20040244938 |
Kind Code |
A1 |
Flick, Andreas ; et
al. |
December 9, 2004 |
Continous casting mould
Abstract
An open-ended mold for casting metal strands with a thin slab
cross section, the mold having broad-side walls which form a
central widening region which extends from the mold inlet edge to
the mold outlet edge and at the outlet edge opens out in a
rectangular outlet cross section. To prevent to a great extent the
strand from coming away from the broad-side walls, the contour of
the mold cavity in the widening region is formed, as seen in
sectional planes taken at right angles to the longitudinal axis of
the mold, by curves which at least in partial regions form
clothoids or clothoidal curves, within which sudden changes in
curvature (.DELTA.k) are minimized or reduced to zero. The
curvature reduces to flat at the mold outlet edge. Other cavity
surface features are disclosed.
Inventors: |
Flick, Andreas; (Linz,
AT) ; Lettmayr, Gernot; (St Florian, AT) ;
Wimmer, Franz; (Riedau, AT) ; Shan, Guoxin;
(Linz, AT) |
Correspondence
Address: |
OSTROLENK FABER GERB & SOFFEN
1180 AVENUE OF THE AMERICAS
NEW YORK
NY
100368403
|
Family ID: |
3688332 |
Appl. No.: |
10/490538 |
Filed: |
March 24, 2004 |
PCT Filed: |
September 2, 2002 |
PCT NO: |
PCT/EP02/09765 |
Current U.S.
Class: |
164/418 ;
164/459 |
Current CPC
Class: |
B22D 11/0408
20130101 |
Class at
Publication: |
164/418 ;
164/459 |
International
Class: |
B22D 011/00 |
Foreign Application Data
Date |
Code |
Application Number |
Sep 28, 2001 |
AT |
A 1541/2001 |
Claims
1. An open-ended casting mold for a continuous casting installation
for casting a metal strand with a thin slab cross section the mold
comprising: a mold cavity formed by mutually opposing, spaced
apart, cooled broad-side walls and of mutually opposing, spaced
apart, narrow-side walls between the broad-side walls, the mold
having a mold inlet edge and a mold outlet edge; the mutually
opposing broad-side walls forming a central widening region between
the broad-side walls, and which extends from the mold inlet edge to
the mold outlet edge and the widening region ending at the mold
outlet edge in a rectangular outlet cross section of the open-ended
mold; the widening region extending in the directions toward and
narrowing toward the mutually opposing narrow-side walls and
merging into laterally adjoining narrow-side adjusting regions
where the broad-side walls are closer together than in the widening
region; the contour of the mold cavity in the widening region is
formed, as seen in sectional planes taken at right angles to the
longitudinal axis of the mold, by curves which at least in first
partial regions form clothoids or clothoidal curves such that
within the clothoids or clothoidal curves, the sudden changes in
curvature are minimized or reduced to zero.
2. The open-ended mold as claimed in claim 1, wherein the curves
include second partial regions between successive first partial
regions, and the second partial regions are either formed
approximately or exactly by arcs of a circle or straight lines and
are joined by the first partial regions of the curves, whereby
sudden changes in curvature (.DELTA.k) of these curve portions at
their transitional points are minimized or reduced to zero.
3. The open-ended mold as claimed in claim 1, wherein the contour
of the mold cavity in the widening region is formed in sectional
planes, taken at right angles to the longitudinal axis of the mold,
and the curves run symmetrically in relation to the narrow-side
walls with a convex-concave profile, the profile starting from the
center of the mold cavity contour with only a small curvature or no
curvature, and going over into a region with constantly increasing
curvature.
4. The open-ended mold as claimed in claim 3, wherein the curvature
(k) in the center of the mold cavity contour meets the
conditionk.ltoreq.0.3*(4H- )/(H.sup.2+L.sup.2),where k=curvature
(mm) H=half the mold cavity widening (mm) L=half the width of the
widening region B.sub.1 (mm).
5. The open-ended mold as claimed in claim 1, further comprising
transitions between the central region and the narrow-side
adjusting regions, wherein sudden changes in curvature at the
transitions from the central widening region to the narrow-side
adjusting regions and at locations of inflectional tangents in the
curve profile are minimized to tend toward zero.
6. The open-ended mold as claimed in claim 5, wherein the sudden
changes in curvature (.DELTA.k) at the transition from the central
widening region to the narrow-side adjusting regions meet the
condition.DELTA.k.ltoreq.0.5*(4H)/(H.sup.2+L.sup.2)where
k=curvature (mm) H=half the mold cavity widening (mm) L=half the
width of the widening region B.sup.1 (mm).
7. The open-ended mold as claimed in claim 5, wherein the sudden
changes in curvature (.DELTA.k) at the locations of the
inflectional tangents meet the
condition.DELTA.k.ltoreq.0.4*(8H)(H.sup.2+L.sup.2)where k=curvature
(mm) H=half the mold cavity widening (mm) L=half the width of the
widening region B.sub.1 (mm).
8. The open-ended mold as claimed in claim 1, wherein the mold
cavity in the widening region has the contour thereof, as seen
formed in sectional planes taken parallel to the longitudinal axis
of the mold and the contour of the narrow-side walls, by straight
lines between the mold inlet edge and the mold outlet edge.
9. The open-ended mold as claimed in claim 1, further comprising
transitions from the central widening region to the laterally
adjoining narrow-side adjusting region regions, the transitions are
formed by a straight line which, in a sectional plane, taken
parallel to the longitudinal axis of the mold and the narrow-side
walls, joins the mold inlet edge and the mold outlet edge.
10. The open-ended mold as claimed in claim 5, wherein in the
contour of the mold cavity, in sectional planes taken at right
angles to the longitudinal axis of the mold, the locations of the
inflectional tangents form straight lines between the mold inlet
edge and the mold outlet edge and the straight lines lie in a
sectional plane taken parallel to the longitudinal axis of the
mold.
11. The open-ended mold as claimed in claim 8, wherein the straight
lines are arranged inclined by the extent of strand shrinkage of
the strand being molded.
12. The open-ended mold as claimed in claim 1, wherein in sectional
planes taken parallel to the longitudinal axis of the mold and the
narrow-side walls, the contour of the mold cavity in the widening
region has a curved profile between the mold inlet edge and the
mold outlet edge which is dependent on the solidifying conditions
of the metal to be cast.
13. The open-ended mold as claimed in claim 12, further comprising
transitions between the central widening region and the laterally
adjoining narrow-side adjusting region are formed by a curve with
an essentially parabolic profile and, in a sectional plane parallel
to the longitudinal axis of the mold and the narrow-side walls,
that curve joins the mold inlet edge and the mold outlet edge.
14. The open-ended mold as claimed in claim 12, wherein in
sectional planes taken at right angles to the longitudinal axis of
the mold, the mold has inflectional tangents at locations in the
contour of the mold cavity which form curves having an essentially
parabolic profile between the mold inlet edge and the mold outlet
edge, and the curves lie in a sectional plane parallel to the
longitudinal axis of the mold.
15. The open-ended mold as claimed in claim 14, wherein the curves
with the essentially parabolic profile are arranged inclined by the
extent of strand shrinkage.
16. The open-ended mold as claimed in claim 1, wherein in the
widening region, in sectional planes taken at right angles to the
longitudinal axis of the mold, the radii of curvature of the
contour of the mold cavity become greater between the mold inlet
edge and the mold outlet edge in the direction of the mold outlet
edge until they are infinite at the outlet edge.
17. The open-ended mold as claimed claim 1, wherein the broad-side
walls are essentially parallel to one another in the narrow-side
adjusting regions laterally of the central regions.
18. The open-ended mold as claimed in claim 1, wherein the
narrow-side walls are convexly formed with respect to the cavity in
dependence on the shrinking behavior of a respective metal to be
cast.
19. The open-ended mold as claimed in claim 1, wherein the mold is
shaped for casting a metal strand with a maximum thickness of 150
mm.
20. The open-ended mold as claimed in claim 12, wherein the contour
of the mold cavity in the widening region has a curved parabolic
profile.
Description
[0001] The invention relates to an open-ended mold for a continuous
casting installation, in particular an open-ended steel casting
mold, for casting a metal strand with a thin slab cross section
with a maximum thickness of 150 mm, with a mold cavity formed by
cooled broad-side walls and narrow-side walls, the mutually
opposing broad-side walls forming a central widening region, which
extends from the mold inlet edge to the mold outlet edge and ends
there in a rectangular outlet cross section of the open-ended mold
and which goes over in the direction of the mutually opposing
narrow-side walls into narrow-side adjusting regions.
[0002] Open-ended molds of this type are referred to in practice as
"funnel molds" and are described with various configurations of the
funnel-shaped widening region in the literature. The many
embodiments that have been derived from the original Rossi mold
(DE-C 887 990) and the first trial mold with a funnel-shaped
widening region (EP-B 149 734) reflect the problems in the forming
of the strand shell and the shaping of this strand shell in the
spatially curved widening region.
[0003] On the inlet side, the known open-ended molds have in the
region of the meniscus a spindle-shaped cavity cross section, which
is constricted continuously in the direction of the narrow-side
walls to the size of the strand to be cast and is made to revert to
the size of the desired strand thickness in the strand drawing-out
direction or casting direction, either still within the length of
the mold or directly in the outlet cross section or in the
downstream backup and guiding roll stand of the continuous casting
installation.
[0004] By this configuration it is possible to produce in such a
mold steel strands which, with customary slab widths, have strand
thicknesses of less than 150 mm, preferably however 30 to 100 mm,
and at the same time to introduce melt into the open-ended mold
with submerged casting nozzles which are thicker than the target
thickness for the cast strand.
[0005] EP-A 1 002 599, DE-A 39 07 351 and EP-A 552 501 already
disclose open-ended molds in which the funnel-shaped widening
region is formed in sectional planes taken at right angles to the
longitudinal axis of the mold by arc portions which replicate the
concave-convex-curved spindle form. In particular at the points of
inflection at which arcs of a circle with radii deviating from one
another merge in line with one another, there are great sudden
changes in radius and curvature. At these points of discontinuity,
the strand shell comes away from the mold wall, whereby
inhomogeneous temperature conditions occur in the strand shell and,
as a result, there is uneven strand shell development. As a further
consequence, this leads to thermal stresses between neighboring
strand zone and increased loads, and also under some circumstances
to damage of the strand shell.
[0006] EP-A 552 501, EP-A 909 597 and DE-A 39 07 351 disclose for
example open-ended molds in which the contour of the funnel-shaped
widening region change in the longitudinal direction, i.e. along
sectional planes parallel to the longitudinal axis of the mold,
abruptly or with a great change in curvature. This usually applies
to molds in which the funnel-shaped widening region already ends at
a relatively great distance from the mold outlet edge. Apart from
the disadvantages already described above of sudden or great
changes in radius and curvature of the curves describing the
widening region, additional loads on the strand shell are produced
by the oscillation of the mold. The locally intensified knocking of
the mold on the funnel-shaped taper of the strand brings about
additional impairment of the strand shell in this region.
[0007] An open-ended mold of the type described at the beginning,
with a widening region which extends from the mold inlet edge over
the entire length of the mold and is only made to revert to the
rectangular cross section of the strand to be cast in the mold
outlet cross section is already known from DE-C 35 01 422. It is
also the case with this mold that the contour of the widening
region is formed in sectional planes taken at right angles to the
longitudinal axis of the mold by arcs of a circle adjoining one
another in line and likewise has the disadvantages described above.
The shortening of the circumferential length of the strand
inevitably occurring as a result of the reversion of the widening
region is counteracted by a corresponding adjustment of the
narrow-side walls and a distortion of the strand shell is already
avoided in this way.
[0008] The object of the present invention is therefore to avoid
the described disadvantages of the known prior art and to propose
an open-ended mold with which the contour of the mold cavity is
optimized in such a way that coming away of the strand from the
mold wall is to a great extent prevented from the meniscus to the
mold outlet edge, and consequently homogeneous forming of the
strand shell in the mold is ensured.
[0009] This object is achieved according to the invention by the
contour of the mold cavity in the widening region being formed in
sectional planes taken at right angles to the longitudinal axis of
the mold by curves which at least in partial regions form clothoids
or clothoidal curves, within which the sudden changes in curvature
are minimized or reduced to zero. Extensive avoidance of sudden
changes in curvature creates the best conditions for optimum
forming of the strand shell.
[0010] The described advantage of avoiding the strand shell coming
away is equally obtained if curve portions formed approximately or
exactly by arcs of a circle or straight lines are joined by curve
portions formed by clothoids or clothoidal curves and sudden
changes in curvature of these curve portions at their transitional
points are minimized or reduced to zero.
[0011] A preferred configuration in the central region of the
widening region is obtained if the contour of the mold cavity in
the widening region is formed in sectional planes taken at right
angles to the longitudinal axis of the mold by curves running
symmetrically in relation to the narrow-side walls with a
convex-concave profile, which, starting from the center of the mold
cavity contour with only a small or no curvature, go over into a
region with constantly increasing curvature. This effectively
counteracts tendencies of the strand shell to come away in the
central region.
[0012] Favorable conditions are obtained thereby if the curvature
(k) in the center of the mold cavity contour meets the
condition
k.ltoreq.0.3*(4H)/(H.sup.2+L.sup.2),
[0013] where k=curvature (mm)
[0014] H=half the maximum mold cavity widening (mm)
[0015] L=half the width of the widening region B.sub.1 (mm)
[0016] An improvement in the forming of the strand shell and
guiding of the strand shell along the broad-side walls is obtained
if the sudden changes in curvature at the transition from the
central widening region to the narrow-side adjusting regions and at
the location of the inflectional tangents in the curve profile are
minimized, preferably tend toward zero. This produces favorable
conditions if the sudden changes in curvature (.DELTA.k) at the
transition from the central widening region (11) to the narrow-side
adjusting regions (12, 13) meet the condition
.DELTA.k.ltoreq.0.5*(4H)/(H.sup.2+L.sup.2), or if the sudden
changes in curvature (.DELTA.k) at the location of the inflectional
tangents (25) meet the condition
.DELTA.k.ltoreq.0.4*(8H)/(H.sup.2+L.sup.2).
[0017] The coming away of the strand shell from the broad-side wall
of the mold is to a great extent avoided if the contour of the mold
cavity in the widening region is formed in sectional planes taken
parallel to the longitudinal axis of the mold and the narrow-side
walls by straight lines between the mold inlet edge and the mold
outlet edge. This linear formation of the central widening region
in the longitudinal direction of the mold has the effect that a
change in curvature conducive to the strand shell coming away only
occurs at the mold outlet. There, however, no adverse effect caused
by an inhomogeneous temperature distribution is to be expected,
since in this region the effect of the direct spray cooling on the
cast strand commences.
[0018] Critical regions with regard to the coming away of the
strand shell from the broad-side wall of the mold are formed by the
maximum widening, the transition from the central widening region
to the adjoining narrow-side adjusting regions and the regions of
the mold cavity that have points of inflection. Here, minimizing of
the coming away of the strand shell is achieved on the one hand by
the transition from the central widening region and the narrow-side
adjusting region laterally adjoining the latter being formed by a
straight line which, in a sectional plane taken parallel to the
longitudinal axis of the mold and the narrow-side walls, joins the
mold inlet edge and the mold outlet edge, on the other hand by the
locations of the inflectional tangents in the contour of the mold
cavity with sectional planes taken at right angles to the
longitudinal axis of the mold forming straight lines between the
mold inlet edge and the mold outlet edge which lie in a sectional
plane taken parallel to the longitudinal axis of the mold.
[0019] In keeping with operational practice, it is advantageous if
the straight lines are arranged inclined by the extent of strand
shrinkage. The inclination corresponds in its spatial orientation
and order of magnitude to the values customary for a taper setting
of the narrow sides. This measure is intended to avoid the strand
shell having to run through a transition from a parallel wall
region into the widening region in the strand drawing-off
direction.
[0020] In order to meet special solidifying and shrinking
conditions of particular grades of steel, it is expedient if the
contour of the mold cavity in the widening region has in sectional
planes taken parallel to the longitudinal axis of the mold and the
narrow-side walls a curved, preferably parabolic, profile between
the mold inlet edge and the mold outlet edge, in dependence on the
solidifying conditions of the metal to be cast. This also applies
especially to the regions of the transition from the central
widening region to the adjoining narrow-side adjusting regions and
the locations of the points of inflection or inflectional tangents,
if appropriate with allowance for a shrinkage-dependent
inclination.
[0021] Further favorable influences on the quality of the strand to
be cast are obtained if the radii of curvature of the contour of
the mold cavity in the widening region in sectional planes taken at
right angles to the longitudinal axis of the mold become greater
between the mold inlet edge and the mold outlet edge in the
direction of the mold outlet edge and are infinite at the outlet
edge. With an overall mold concept in mind, it is expedient if the
broad-side walls in the narrow-side adjusting regions are arranged
essentially parallel to one another and the narrow-side walls are
convexly formed in dependence on the shrinking behavior of the
metal respectively to be cast.
[0022] Further details, features and advantages emerge from the
explanations and representations which follow of an exemplary
embodiment not restricting the extent of protection.
[0023] In the drawings:
[0024] FIGS. 1a, 1b, 1c show a schematic representation of the
open-ended mold according to the invention in a plan view (view Z),
front view and side view (section A-A) according to one possible
embodiment of the invention,
[0025] FIG. 1d shows a further embodiment of the open-ended mold
according to the invention in side view (analogous to section A-A
in FIG. 1c),
[0026] FIG. 2 shows the open-ended mold according to the invention
in a longitudinal section with submerged casting nozzle and cast
strand,
[0027] FIG. 3 shows the coming-away behavior of the strand from the
broad-side wall when there are great changes in curvature in a
central widening region of a rectangular shape in a continuous
casting mold according to the prior art,
[0028] FIG. 4 shows the coming-away behavior of the strand from the
broad-side wall when there are great changes in curvature in a
central widening region of a trapezoidal shape in a continuous
casting mold according to the prior art,
[0029] FIG. 5 shows the coming-away behavior of the strand from the
broad-side wall when there are minimized changes in curvature in a
central widening region of a rectangular shape in a continuous
casting mold according to the invention,
[0030] FIG. 6 shows a comparison of the contour of the central
widening region and the associated curvature profiles in the case
of the mold according to the invention and a mold according to the
prior art.
[0031] An open-ended mold of the type according to the invention is
represented in FIGS. 1a to 1c in a schematic representations. It
comprises two mutually opposing broad-side walls 1, 2 and two
likewise mutually opposing narrow-side walls 3, 4, which can be
adjusted between two positions B, B1 in the sense of a format
adjustment. Bounded by the broad-side walls 1, 2 and the
narrow-side walls 3, 4, between the mold inlet edges 5 and the mold
outlet edges 6, is the mold cavity 7 of the open-ended mold, in
which a cast strand, comprising a strand shell 9 and a liquid core
10, is formed between a meniscus (liquid metal level) 8 and the
mold outlet edge 6, as illustrated in FIG. 2.
[0032] The broad-side walls 1, 2 have a central widening region 11,
which is bounded essentially by the narrowest adjusting region B1
of the narrow-side walls 3, 4 and goes over on both sides into the
narrow-side adjusting regions 12, 13. These narrow-side adjusting
regions are formed by mutually plane-parallel wall parts of the
broad-side walls 1, 2 and extend from the mold inlet edge 5 to the
mold outlet edge 6. As a departure from this embodiment, it is
quite possible for the broad-side walls to form planar surface
areas arranged such that they converge in the strand drawing-off
direction or the direction of the narrow-side walls in the region
of the narrow-side adjusting regions.
[0033] The central widening region 11 has at the mold inlet edges 5
a cross section which narrows in the form of a spindle to the
narrow-side adjusting regions 12, 13. It is provided in its central
region with a width adequate for receiving a submerged casting
nozzle 14 and is reduced toward the narrow-side adjusting regions
12, 13 to the thickness D of the metal strand to be cast by curves
15 with a curvature profile that is to a great extent free of any
sudden changes. These curves 15 comprise for example arcs of a
circle 16, 17, which are joined in line by clothoids 18, 19, 20, 21
or clothoidal curves and the curvature profile of which runs
without any abrupt changes or with abrupt changes minimized.
[0034] The central widening region 11 is continuously constricted
between the mold inlet edge 5 and the mold outlet edge 6 and is
reduced at the mold outlet edge 6 to the size of a rectangular
outlet cross section 22, which corresponds to the desired casting
cross section. The contour profile of the central widening region
11 between the mold inlet edge 5 and the mold outlet edge 6 is
formed, in relation to a sectional plane which is taken parallel to
the longitudinal axis 23 of the mold and parallel to the
narrow-side walls 3, 4, by straight lines 24a, 24b, . . . 24n. This
linear configuration of the central widening region in the casting
direction ensures freedom from deformation in the vertical strand
drawing-off direction. This definition of the sectional plane is
based on the assumption that the narrow-side walls 3, 4 are
arranged plane-parallel to one another and there is therefore no
taper adjustment.
[0035] Consequently, the end faces of the planar narrow-side walls
are oriented parallel to the longitudinal axis of the mold. A taper
adjustment of the narrow-side walls that is provided in practice
therefore does nothing to change the orientation of the straight
lines described. The central widening region 11 can also be
constricted between the mold inlet edge 5 and the mold outlet edge
6 by a curve with a parabolic profile 26. (FIG. 1d)
[0036] FIG. 3 illustrates results of numerical investigations on a
finite-element basis in a half-section of a broad-side wall between
the meniscus and the mold outlet edge by an example of an
open-ended mold according to the prior art with a central widening
region which is of a rectangular shape in an end-on view and
extends in the transverse direction between the line I, which
corresponds to the longitudinal axis (23) of the mold in FIG. 1a,
and the narrow-side adjusting region, and in the longitudinal
direction between the meniscus and the line A. The light areas show
regions at which the coming away of the strand shell from the
broad-side wall is particularly pronounced. In these regions, a
great change in curvature occurs in the contour of the central
widening region. At these points, inhomogeneous temperature
conditions and reduced strand shell development are to be expected.
A distinction can be made here between essentially three regions in
the transverse direction, indicated by the vertical lines I, II,
III, and a region in the longitudinal direction, indicated by the
horizontal line A. Particularly at risk is the region with the
greatest widening in the mold (line I), followed by two regions
(lines II, III) at the curve transitions toward the edge of the
mold. In the longitudinal direction there follows at the end of the
funnel an extended region (line A) with diminishing contact of the
strand shell with respect to the broad-side wall. This may be
regarded as a serious disadvantage of funnel molds in which the
funnel ends inside the mold.
[0037] FIG. 4 shows analogous results with respect to a funnel mold
with a V-shaped constriction of the widening region between the
meniscus and the mold outlet edge, as is likewise known from the
prior art. The structural composition of the representation
corresponds to FIG. 3. In the case of this type of mold too, great
regions with disturbed contact between the strand shell and the
mold wall occur. This is attributable to the V-shaped funnel edge
(line V), which lies obliquely in relation to the casting direction
and which the strand/strand shell must pass. The associated changes
in curvature in the longitudinal direction cause these disturbances
of the contact behavior.
[0038] FIG. 5 shows the results of the numerical investigation on a
finite-element basis with reference to an open-ended mold according
to the invention. The structural composition of this representation
corresponds in turn to that of FIG. 3. As a result of the
optimization according to the invention of the contour of the mold
cavity of the mold, light regions with disturbed contact between
the strand shell and the broad-side wall now occur in the direct
vicinity of the mold outlet edge, where no adverse effects on the
forming of the strand shell occur any longer.
[0039] A comparison of the contours of the mold cavity in the
widening region in the case of a funnel mold according to the prior
art and a mold according to the invention in a sectional plane
taken at right angles to the longitudinal axis of the mold is
represented in FIG. 6. Represented in the upper half of the figure
is the contour profile of the mold width, starting from the center
of the mold (longitudinal axis of the mold), and the lower half of
the figure shows the assigned curvature profile over the mold
width. The contour profile according to the prior art, represented
by dotted lines, is formed by two arc portions merging one into the
other and ends in a straight line which identifies the narrow-side
adjusting region. The associated curvature profile, represented by
a dotted line, jumps at the contact point of the two arc portions
(point of inflection 25') from an until then constant negative
value to a constant positive value. Occurring here is the massive
point of discontinuity in the curvature profile that was described
as disadvantageous and contributes significantly to the coming away
of the strand shell. Conditions with the same effect occur at the
transition from the arc to the straight line at the transition to
the narrow-side adjusting region. Here, the curvature jumps at a
point of discontinuity back to the value zero. In comparison with
this, represented by the solid line is the contour profile
according to an embodiment of the invention, which, starting from
the center of the mold, is formed by a clothoid 18 or clothoidal
curve with a constantly increasing curvature, which is adjoined by
an arc portion 16 with a constant curvature. This is adjoined by a
transitional portion which is formed by two clothoids 19, 20 or
clothoidal curves and in the profile of which the curvature is
changed continuously from a negative maximum value to a positive
maximum value as it passes through a point of inflection 25. There
further adjoins an arc portion 17 with a positive curvature value,
which is then transformed by a clothoid 21 or clothoidal transition
curve to the curvature value zero of a straight line. The avoidance
of sudden changes in curvature is provided by this contour
profile.
[0040] Instead of the arc portions in the contour profile that are
specified in this exemplary embodiment, curve portions formed to
approximate arcs of a circle may also be used. In the region of
maximum widening in the widening region, a curve portion formed by
a straight line or approximately by a straight line may be
provided. All these modifications are within the extent of
protection of the invention.
* * * * *