WO2003035298A1

WO2003035298A1 - A die for simultaneous deep drawing and ironing processes, a product produced by use of such die and a method for producing such product

Info

Publication number: WO2003035298A1
Application number: PCT/DK2002/000715
Authority: WO
Inventors: Joachim Danckert
Original assignee: Aalborg Universitet
Priority date: 2001-10-26
Filing date: 2002-10-28
Publication date: 2003-05-01

Abstract

The invention relates to a die design having a non-circular die land, e.g. a circular die land. With the new design, a possible small tilt of the die only gives rise to minor changes in the contact between cup and die. With the new design, great improvements can be obtained, especially: 1) A small tilt will only give rise to very minor differences or variations in cup height, 2) The die does not drift, which means that a cup with more even wall thickness in the height direction will be produced, 3) As the cup quality is nearly unaffected by small changes in the tilt angle, it will be much easier to keep the production under control, and 4) The die is easier to manufacture.

Description

A DIE FOR SIMULTANEOUS DEEP DRAWING AND IRONING PROCESSES, A PRODUCT PRODUCED BY USE OF SUCH DIE AND A METHOD FOR PRODUCING SUCH PRODUCT

FIELD AND BACKGROUND OF THE INVENTION

The present invention relates to a die and a product of deep drawing processes.

Thin walled cans can be made from sheet material by deep drawing a cup. After the deep drawing the cup wall thickness is reduced in one or more ironing stages. In some cases deep drawing and ironing is combined in the first stage. However, known dies all have cylindrical die land for the ironing of the cup being deep drawn. This involves some disadvantages. Even a small tilt of the die in relation to the punch, or a small tilt of the punch in relation to the die, will lead to a radially uneven wall thickness of the cup being shaped. A mutual tilt between the die and the punch can easily occur, perhaps if the die is inaccurately produced, if the die is inaccurately mounted in the press or during elastic deflection of either the shaping tools or of the press during the shaping process leading to inaccuracies in the relationship between die and punch.

SUMMARY OF THE INVENTION

It is an object of the present invention to remedy the said disadvantages by providing a die eliminating or at least reducing the effect of the above-mentioned inaccuracies, i.e. a finally shaped cup having an uneven wall thickness and/or having other defects, but realising that the said inaccuracies cannot be totally avoided.

This object is obtained by a die where the die is annularly shaped and has an inlet and an outlet, and where between the inlet and the outlet an annular shaped die land is formed running along an inner surface of the die and extending from a die land start to a die land end along a die land trajectory, and where the die land trajectory is non-cylindrical.

By providing a die having the feature of a non-cylindrical die land several advantages are obtained. Firstly, even only a slight tilt of the the die in relation to the punch, or a tilt of the punch in relation to the die, lead to only very small changes in contact conditions between the cup to be drawn and the inner surface of the die, and thus the trajectory of the die land. The only small changes in the contact conditions has the effect that the cup being drawn only exhibits small changes in cup wall thickness, changes which may be tolerated. Secondly, contrary to dies having a cylindrical die land, a die with a non- cylindrical die land may be shaped so that the die floats only very little even if the die tilts a bit. Thirdly, a die with a non-cylindrical die land is much more self-centering than a die with a cylindrical die land. Fourthly, by utilising a die with a non-cylindrical die land it much easier to control the process of deep drawing and wall thickness reduction. Finally, the time spent for setting up and the time spent adjusting may be reduced because a die with a non-cylindrical die land can be made self-centering even if the die tilts a bit. 5

Depending on the deep drawing process in question, i.e. taking into account different factors such as the material being deep drawn, the choice of lubricant, the number of steps and the height increase and wall thickness reduction in each step, and the dimension of the initial blank together with the final height, diameter and wall thickness of the cup being 10 manufactured, different dies having die lands with different trajectories may be employed. The trajectory of the die land may be partly circular, partly elliptic, may be part of a tractrix or may have any other non-linear, i.e. non-straight, extension.

Preferably, the die according to the invention has a die corner radius (Rdie) between 1 and 15 20 times, as example 2.8 times, an initial blank thickness of a product to be produced. Also preferably, the die according to the invention has a length (I) of the die land between 0.1 and 30 times, as example 3.44 times, the initial blank thickness of a product to be produced. As commonly known, the dimension of a die is determined also by the initial blank used when producing the product. Thus, the dimensions mentioned, i.e the die 20 corner radius and the die length will be dimensioned in relation to the blank. According to the invention, the ratios mentioned are now possible based on the invention having a non- cylindrical die land trajectory. Formerly, such ratios were not possible due to the problems mentioned above and discussed below, i.e. tilting and/or off-centring of the die and/the punch. 25

The product produced utilising the die according to the invention may be any cup having a circular cylindrical cross-section or having a polygonal cylindrical cross-section. Thus, the die according to the invention is equally well suited for any of these types of products.

30 The product produced may exhibit a deep drawing ratio being as high as up to 3.0, as example 1.67. Furthermore, either in addition to the relatively high deep drawing ratio mentioned or at much lower deep drawing ratios, the nominal thickness reduction of the blank may be as high as between 1% and 30%, as example 8.75%. Thus, because of the new die design, much greater deep drawing ratios and much greater thickness reductions,

35 either separate of each other or in combination, may be obtained without difficulty.

DETAILED DESCRIPTION OF THE INVENTION

In the following the invention will be further described with reference to the figures. In fig. 1 is shown a sketch of the tooling for the combined deep drawing and ironing stage. In the press, the die and the punch are fixed. This in contrast to some of the later ironing stages, where the die is floating, allowing the die to be displaced radially to the punch during the ironing processes.

It is of major importance for the subsequent ironing stages that the cup produced in the combined deep drawing and ironing stage has a very even cup height. An uneven cup height indicates that the cup wall thickness varies in the circumfrerential direction. A varying cup wall thickness in the circumferential direction will inevitably create problems in the subsequent ironing stages (e.g. wrinkles in the ironed cup wall, fracture in the cup wall, unacceptable variations in the cup wall thickness).

From time to time, an industrial company has found it very difficult to produce a satisfactory cup in the deep drawing- ironing stage. It is not understood what causes the problems, and problems are mainly solved on a trail and error basis. The main parameters in the deep drawing and ironing stage are:

- deep drawing ratio: 1.67

- die corner radius (Rdie): 2.8 * initial blank thickness

- length of die land (I): 3.44 * initial blank thickness - nominal thickness reduction in the ironing process: 8.75 %

The purpose of the following is to see if is possible from measurement of cup wall thickness and cup heights on two cups with unacceptable variations in the cup height to arrive at sensible conclusions why cups with uneven cup height are produced.

Measuring procedure

The cup height and the cup wall thickness were measured on a coordinate measuring machine. Two cups were measured (these cups are in the following denoted cup 1-5 and cup 2-5). In fig. 2 a sketch of the cup is shown. The thickness of the cup wall was measured in 0, 45, 90, 135, 180, 225, 270 and 315 degrees (as indicated in fig. 2) from a height = 2 mm to height = 14 mm in steps of 1 mm. The height of the cup rim was measured by probing 50 evenly spaced point on the cup rim. The height datum for all the measurements was the inside bottom of the cup as indicated on fig. 2.

Results

In fig. 3 the measured cup height is shown as function of the angle of the two cups. From fig. 3 it can be seen that the maximum difference in cup height is approximately 1.2 mm for both cups. It can also be seen that the two cups have almost identical variations in the cup height. This is important, because this suggests that the deep drawing and ironing process (and the press used) is able to produce nearly identical cups with regard to cup height (despite the fact, that the two cups measured have an unacceptable height variation).

In fig. 4 is shown the measured cup wall thickness as function of cup height at the different angles. The figures to the left are for cup 1-5 and the figures to the right for cup 2-5. By comparing the thickness distributions for cup 1-5 and cup 2-5 it can be seen that there is a very similar thickness distribution in the two cups. For both cups, there is a strange king in the thickness variation near the bottom of the cup (from a cup height of 2 mm to a cup height of 3 mm). A likely reason for this strange looking variation will be given later.

It can also be seen, that there is a large thickness variation in the height direction This variation is due to elastic deformation of the tools. This thickness variation can not be removed completely in the subsequent ironing stages, so with the prior art tool design commonly used in the deep drawing and ironing stage it will not be possible to manufacture long thin walled cups with no variation in the cup wall thickness. It is shown in /l/ that the radial force on the die is heavily influenced by the semi-die angle and the length of the die land. The tool design should be made in such a way, that the elastic deformation of the tools is minimized. This will enable the manufacture of cups with a lower thickness variation in the height direction.

In fig. 5 is shown the measured cup wall thickness in the different directions with the cup height as parameter. By comparing the thickness as function of the angle for cup 1-5 and cup 2-5, it can be seen that the thickness distributions are indeed very similar; only very small differences are present.

It can also be seen, that the variation in thickness at 2 mm cup height is very much different from the variation at 3 mm cup height. At 2 mm cup height, the smallest cup wall thickness is found around 180 degree, whereas at 3 mm height up to 12 mm cup height the smallest cup wall thickness is in zero degree. At 14 mm cup height, the thickness distribution changes again, so that the smallest cup wall thickness is measured at 180 degree.

A likely explanation for this variation in thickness distribution may be: 2 mm cup height. On the press used, the punch can be displaced horizontally relative to the die. That is, the punch can be positioned slightly off-centre. A likely explanation why the cup wall in 2 mm cup height is thicker at 0 degree than at 180 degree is that the punch has been aligned slightly off-centre (this off-centre alignment may have been made intentionally by the press operator in an attempt to produce a cup with an even height of the cup rim and or an even thickness of the cup wall at the cup rim (in other word an attempt from the operator to counteract, that the cup rim is too high in 0 degree (see fig. 3).

- The relative larger increase in cup wall thickness in 180 degree compared to 0 degree from a cup height of 2 mm to 12 mm.

In the following it is assumed, that cylindricity of the punch has been very little and that the punch has been mounted in the press in such a way that the punch axis was parallel to the direction in which the punch was moved; if the punch employed was not straight and or was mounted so that the punch axis did not coincide with the direction of movement, this might explain the variation in cup wall thickness as function of cup height and angle. The reason for variations in cup wall thickness can be that the ironing process has not been stable. That is, the ironing process has been carried out close to the critical reduction ratio (for a more detailed explanation regarding critical reduction ratio, see /l/) or because the die land has been slightly tilted (the die land has not been parallel to the punch). A tilt of the die land could be caused by a) inaccurate machining, b) inaccurate mounting in the press or c) elastic deformation of press during the deep drawing and ironing process.

The critical reduction ratio has not been determined for the die geometry and the cup material used. The determination of the critical reduction ratio may be a topic for future research.

The reduction ratio in the ironing stage is small (nominal thickness reduction ratio = 8.75%), and with the die radius used, the semi-die angle (which of course varies because the die radius is circular) is also small (around 12 degree at the entry point). According to /l/ the critical reduction ratio for a "normal" die is around 25% with a semi-die angle of 10 degree and a die land = 3 * initial wall thickness. The most likely reason for the instability in the ironing process is thus that the die land has been slightly tilted during the ironing.

If instability is the reason for the varying cup wall thickness in the circumferential direction, then one important lesson can be learned from looking at the thickness distribution in the before-mentioned figures. Even if the cup height does not vary, this does not guarantee that there is no variation in the cup wall thickness in the circumferential direction. One might obtain a cup with very small variations in cup height by off-setting the punch, but off-setting the punch will inevitably lead to variations in the cup wall thickness in circumferential direction. Or in other words, if it is necessary to off- set the punch in order to obtain a cup with small variations in cup height, the ironing process is unstable and will produce cups with thickness variations in the circumferential direction.

An explanation why a slight tilt of the die land may have such a huge effect

In fig. 6 is shown the die slightly tilted. The effect of even a very slight tilt of the die land is, that the "effective" length of the die land on one side reduces to zero (the right side at fig. 6). On the opposite side, the "effective" length of the die land remains nearly unchanged (if the tools can be regarded as rigid and the elastic strains in the cup wall can be neglected, the required tilt angle to force the change approaches zero). As shown in /l/ the length of the die land has a significant influence on the radial force on the die; a slight tilt will thus increase the reduction ratio on one side and decreases the reduction ratio on the other side in order to maintain force balance in the radial direction.

FEM-simulations

A few simple FEM-simulations have been carried out in order to qualitatively investigate the effect of a slightly tilted die. The simulations have been carried out using the FEM-code Nike2d assuming plane strain. Of course, a plane strain model can not show exactly what is going to happen in the real ironing process, which is a 3 dimensional process. However, it is believed that there will be qualitative agreement between the results obtained with the plane strain model and corresponding 3D-model. This ought to be checked, but a real 3D- simulation has not yet been carried out of the ironing process.

Ironing with a floating die with straight die land

In fig. 7 is shown the FEM-model. The die, which has a straight die land, has been slightly tilted (0.2 degree). The die has also been slightly off-set to the left; when the punch is moved down, the cup meet the right half of the die first. The die is floating (it can freely move in horizontal direction).

In fig. 8 are shown different stages during the ironing. The pictures have been scaled in the horizontal direction in order to make it easier to see what happens during the ironing process. The slight tilt of the die (tilt angle = 0.2 degree) has the effect, that the

"effective" length of the die land on the right die part in fig. 8 reduces to zero, whereas the "effective" length of the die land on the die part to the left remains nearly unchanged. The die is floating, which means that the die will move horizontally until the radial force on the left part of the die balances the radial forces on the right part of the die. From fig. 8 it can bee seen that a slight tilt of the die will force the die to move to the left leading to an increasing cup wall thickness on the left half and a decreasing cup wall thickness to the right.

Ironing with a constrained die with straight die land

In fig. 9 is shown the FEM-model of the ironing with a die with a straight die land. The die (both the left half and the right half of the die) is constrained in horizontal direction, because they are attached to a spring, which is constrained not to move on its left side. The simulation is carried out as plane strain. The nominal reduction ratio is 8.75 % and the length of the die land is equal to 2.75 times the initial cup wall thickness. The die has been slightly tilted (tilt angle = - 0.2 degree), with the effect, that the "effective" length of the die land on the left die half is zero, whereas the "effective" length of the die land on the right die half remains nearly unchanged. The die has been shifted slightly to the left in order to have initially a larger reduction ratio on the right half (this shift to "simulate" the off-centre punch setting, which has been used when producing the two measured cups)

In fig. 10 the different stages during the ironing process are shown (the pictures have been scaled in horizontal direction in order to make it easier to see what happens). To start with, (upper left figure) the reduction ratio is larger on the right side than on the left side, due to the off-centre placement of the die. The tilt of the die will try to force the die to the right, increasing the reduction ratio on the right and decreasing the reduction ratio to the right. As can be seen from upper right figure, the spring has not been stiff enough to avoid the shift of the die. The initial off-centre placement of the die has reduced the difference in height, but has increased the variation in cup wall thickness as function of cup height. At the very end of the ironing process, lower left figure, the radial forces on the die decreases, and the spring force is large enough to squeeze the upper part of the right cup wall. On the left side, the cup wall thickness increases towards the very end (these two areas are indicated with arrows on the lower right figure). The change in the cup wall thickness towards the end of the ironing process is in very good qualitative agreement with the thickness measured on the real cups, see fig. 4.

The total thickness distribution in the left and right cup wall is in very good qualitative agreement with the measured thickness distribution on the real cups, see fig. 5.

The FEM simulation thus suggest, that a slight tilt of the die land can explain the measured variation in cup height and the measured variation in cup wall thickness Comments regarding the use of a die with a linear, i.e. straight, die land

Currently the most used die design in the combined deep drawing and ironing stage is a die with a straight, limear die land as shown in fig. 11. As shown in /l/, the length of the die land has a significant influence on both the critical reduction ratio and on the total radial force on the die during ironing. A slight tilt of the die land has a significant influence on the ironing process; a very slight tilt will reduce the "effective" length on the die land on one side, whereas the "effective" length on the opposite side remains nearly unchanged. A slight tilt will thus increase the reduction ratio on one side (where the "effective" length of the die land is zero) and decrease the reduction ratio on the opposite site.

From a practical point of view it is very difficult to avoid a small tilt, and thus very difficult to produce cups with an even cup height and even cup wall thickness in circumferential direction. A small tilt may be cause by inaccurate machining - polishing, inaccurate mounting of the die, elastic deformation during the ironing process.

It is quite surprising that this has not been the subject of many investigations. It is of outmost importance that the cup produced in the deep drawing and ironing stage has a very even cup wall thickness in circumferential direction, because an uneven cup wall thickness can not be completely removed in subsequent ironing stages.

Not any literature has been found discussing what effect the length of the die land has or articles discussing the effect of a slight tilt of the die. The use of a die with a straight die land is bound to cause problems (it is difficult to produce a cup with an even thickness in the circumferential direction, and it is difficult to keep the production under control). So the conclusion is, that the die with a straight die land is far from being optimal. The problem is thus: How should the die design be in order to avoid or reduce the effect from a slightly tilted die. The suggestion according to the invention is to use a die design as shown in fig. 12, where the straight die land has been replaced with a non-straight die land (e.g. a circular die land as shown in the figure). Using this design, a slight tilt of the die will only change the contact condition in the cup - die interface slightly, and a slight tilt will thus have a much smaller effect on the cup height and the cup wall thickness.

The die radius at the inlet (R-deep drawing) should be chosen with regard to the deep drawing process, whereas the radius, where ironing takes place (R - ironing) should be chosen with regard to the ironing process. The radius R-ironing should among other things be chosen with regard to: - critical reduction ratio

- change of contact condition as function of tilt

- elastic deformation of the die

- wear

The effect of using a die with a circular die land in place of a straight die land is demonstrated below using plane strain FEM-simulations. In fig. 13 the two FEM-models are shown, to the left with a straight die land and to the right with a circular die land. There are only minor differences between the profile of the die with the straight die land and the profile of the die with the circular die land. In fig. 14 the two profiles are shown together. Despite from the difference in die land profile, everything else is the same in the two FEM- models. Both dies are floating and both dies have been slightly tilted (tilt angle = 0.2 degree).

In fig. 15 the cups are shown towards the end of the process, to the left with the straight die land and to the right with the circular die land.

The difference in the two cups is remarkable. With the straight die land, the die is forced to the left, and the thickness of the cup wall to the left is steadily increasing, while the thickness of the cup wall to the right is steadily decreasing. With the circular die profile, there is also a shift of the die to the left, but the shift is much less than in the case of the die with the straight die land, and after the initial shift, the die remains in the same position, so that cup wall on the left respectively the right side is nearly constant in the height direction. With the die with the straight die land, there is a significant difference between the cup height in the left and right half. With the circular die land the difference between the cup height in the left and right half is significantly smaller. The effect of a slight tilt of the punch during a combined deep drawing and ironing stage has also been analysed using 3D-FEM simulations. Two different die geometries have been investigated:

a) a die with a circular die profile and a cylindrical die land b) a die with a circular die profile and a circular die land.

In fig. 16 the dies employed are shown. To the left the conventional die profile with a cylindrical die land and to the right with the circular die land. To the right is the profile of die with cylindrical die land also shown as a dashed line. In the FEM-simulations, the punch was slightly tilted (approximately 0.4 degree). All rotations were constrained, but the punch could move freely horizontally. In fig. 17 and fig. 18 the cross section of the finished cup and the equivalent strain distribution in the cup are shown, when the conventional die profile with cylindrical die land was employed. In fig. 19 and fig. 20 are shown the cross section of the finished cup and the equivalent strain distribution in the cup when the die profile with the circular die land was employed.

When the conventional die with the cylindrical die land is used, a slight tilt of the punch will have the effect, that the cup height (and thus also the cup wall thickness) becomes very uneven. The variation is cup height is clearly visible in fig. 17 and fig. 18. When the die with the circular profiled die land is employed, a slight tilt of the punch has hardly any effect on the cup height and the cup wall thickness. Hardly any variations in the cup height can be noticed in fig. 19 and fig. 20.

Conclusions

Conclusions based on measured cup wall thickness and cup heights

The combined deep drawing and ironing process used (tools + press etc.) produces nearly identical cups. Hardly any difference in cup height could be detected and the variation in cup wall thickness in circumferential direction in the different cup heights is nearly identical for the two cups. The punch has been mounted off-centre. The off-centre mounting might have be done intentionally to counteract an uneven cup height variation.

The measurements (and the FEM-simulations) suggest that it may be possible to produce a cup with an even cup height without an even cup wall thickness in the circumferential direction. If this is the case, measurement of the cup height (or variation in the cup height) should not be used as a criterion to determine whether a cup is of sufficient quality or not. The measurements also suggest that the method of forcing the punch off-centre in order to produce a cup with an "acceptable variation" in cup height should be avoided. Off- setting the punch will inevitably produce a cup with variations in the cup wall thickness in the circumferential direction.

The elastic deformation of the tools (die + punch) is large during the ironing process. The elastic deformation has the effect, that there is a large variation in cup wall thickness from bottom to top. The die geometry should be optimized with regard to the elastic deformation, so that the cup produced has as small variation in cup wall thickness from bottom to top as possible. A variation in cup wall thickness can be reduced but not eliminated in the subsequent ironing stages. FEM-simulations

FEM-simulations have been carried out of the ironing process. The ironing process has been modelled as both plain strain and in 3D. The results obtained assumed that plain strain can not be directly transferred to the real 3-dimensional ironing process. It is however believed, that there is a quantitative agreement between the plane strain simulation and the corresponding three-dimensional simulation.

The FEM-simulations show that a slight tilt of the ironing die (this tilt may be either due to inaccurate machining-polishing, inaccurate mounting in the press, or elastic deformation during the deep drawing - ironing process) has a significant influence on the process. Even a very slight tilt will increase the reduction ratio on one side and decrease the reduction ratio on the opposite side. The effect is that the cup wall thickness will vary both in the circumferential direction and in the height direction and that the cup height will vary. A tilt may also cause fracture in the cup wall, if the reduction ratio on one side becomes too large. The FEM-simulation of the ironing with a constrained die suggest that off-setting the punch and tilting the die slightly may produce a cup with the same variation in the cup wall thickness as measured.

New die design

The used die design with a straight die land is very sensitive to a small tilt in the die, and the use of this die design is judged to make it difficult to keep the production under control. The new die design, where the straight die land is replaced with a non-circular die land, e.g. a circular die land, is proposed. With the new design, a small tilt of the die only gives rise to minor changes in the contact between cup and die. FEM-simulations carried out with a die with a circular die profile suggest that great improvement can be obtained with such a die design: 1) a small tilt will only give rise to very minor differences or variations in cup height, 2) the die does not drift, which means that a cup with more even wall thickness in the height direction will be produced, 3) as the cup quality is nearly unaffected by small changes in the tilt angle, it will be much easier to keep the production under control, 4) the die is easier to manufacture.

References /l/ Danckert, J. Ironing of thin walled cans with focus on stability problems. Department of Production, Aalborg University, 2001.

Claims

1. A die for simultaneous deep drawing and ironing processes, where the die is annularly shaped and has an inlet and an outlet, and where between the inlet and the outlet an annular shaped die land is formed running along an inner surface of the die and extending from a die land start to a die land end along a die land trajectory, and where the die land trajectory is non-cylindrical.

2. A die according to claim 1, where the ironing trajectory is partly circular.

3. A die according to claim 1, where the ironing trajectory is partly elliptic.

4. A die according to claim 1, where the ironing trajectory is part of a tractrix.

5. A die according to any of the preceding claims, where the die corner radius (Rdie) is between 1 and 20 times, as example 2.8 times, an initial blank thickness of a product to be produced.

6. A die according to any of the preceding claims, where a length (I) of the die land is between 0.1 and 30 times, as example 3.44 times, the initial blank thickness of a product to be produced.

7. A product produced by use of a die according to any of the preceding claims, said product being a final product, and said product constituting a cup with a bottom and side walls extending from the bottom, and said side walls already, after having been produced in a die according to any of the preceding claims, having a substantially equal height along an entire circumference of the side walls.

8. A product produced by use of a die according to any of the preceding claims, said product being an intermediate product, and said product constituting a cup with a bottom and side walls extending from the bottom, and said side walls already, after having been produced in a die according to any of the preceding claims, having a substantially equal height along an entire circumference of the side walls.

9. A product according to claim 7 or claim 8, where the cup has a circular cylindrical cross- section.

10. A product according to claim 7 or claim 8, where the cup has a polygonal cylindrical cross-section.

11. A product according to any of claims 7-10, where the deep drawing ratio is up to 3.0, as example 1.67.

12. A product according to any of claims 7-11, where the nominal thickness reduction is between 1% and 30%, as example 8.75%.

13. A method for producing a product according to any of claims 7-12 by utilising a die according to any of the claims 1-6, said method comprising implementation of a nominal thickness reduction ratio of a blank in the ironing stage of less than 25% such as 8.75%.

14. A method for producing a product according to any of claims 7-12 by utilising a die according to any of the claims 1-6, said method comprising utilising a die having a semi- angle less than 15 degrees, such as 12 degrees, at the entry point of the die.