DE2501613A1 - Die built up of segments for metal forming - has curved segment contact interfaces ensuring favourable distribution of forces - Google Patents

Abstract

The die built up of segments is used in metal forming processes such as deep drawing, upsetting, pressing, punching and cutting. The segmented die is designed to withstand extremely high forces on working materials which impose such loads on the die. The segments (2) have interfaces (C) which do not run in a radial direction but at an angle alpha and the curved interface is designed on considering that the working force components act uniformly in all direction against the inner face of the die opening. This distribution of the force components on die segment connecting surfaces ensures that the die life is extended and its crumbling under excessive loads is prevented.

Description

Segment matrices This invention deals with segment matrices having resistive properties against loads that lead to rapid destruction in similar matrices of earlier design led (with crumbling, crack cone formation, decay and similar phenomena as Sequence), and manufacturing processes for such matrices and application methods for such matrices.

In the previous methods of die-controlled metalwork like pulling (in its various forms as pulling forward, pulling backward, Butt drawing, reduction drawing, etc.), upsetting, advising against, punching, cutting and Other metal forming work involved a wide variety of dies. These earlier matrices and the procedures in which they were used were but largely unsatisfactory not only due to the defective products, but also due to the short life of the dies themselves and the associated ones Costs. The transverse side walls of the segments of these conventional segment matrices, which in their interplay the rejuvenation of the die form, are flat surfaces and are arranged in relation to each other so that the angle between the plane through the central axis of the die opening and the curve that the planes Segmental areas along the inside of the die opening describe the ability the segments reduce, if not exclude, to harsh on each other and the Extend the life of the die in this way. Regardless of their size or The outer shape is formed by the contact surfaces between the flat segment surfaces Source of problems related to the long life and usefulness of the segments as Counteracting components of precisely adjusted matrices. The result is a relative rapid deterioration in quality and roughness, crumbling, fractures, crack cone formation and prevent decay.

This invention summarizes as an object and advantage matrices, their new design and construction brings resistance properties with sic, which the Machining and shaping of materials allows the extreme loads on the segments under extreme conditions. Address the other objects of the invention deq products that are manufactured under controlled conditions with new properties and the associated manufacturing process.

The patent also understands its objectives to be those of experts can be achieved by changing the state shown here without thereby deviating from the spirit and intent of this publication.

In conjunction with the following description, Figure 1A shows in elevation the segment die of the present invention with the shrink ring or a correspondingly suitable other housing is omitted and the segments appear in the matrix in its normal working position, in which it is the complete Forming a die opening with a free, round opening cross-section is shown in drawing 1B three-dimensionally represent a single segment of the die, the elevation of which is shown in drawing 1A can be seen, drawing 2A corresponds to drawing 1A except for the fact that in drawing 2A the opening cross-section is polygonal, drawing 2B corresponds to FIG Drawing 2A except for the fact that the inner working surface of the segment in this Drawing is flat, drawing 2C is a partial elevation of a segment die, the boundary surface of which is described by heterogeneous curves represents drawing 3 is a partial elevation of a segment die, the segment curves of which resemble Cc curves Represent pressure, represent FIGS. 4 and 5 special cases of cross-sectional curves shown in drawing 3, represents drawing 6 for simultaneous Compare a partial elevation of a segment matrix, the segments with curves of the Classes I, II and III - all with the same starting angle alpha - combined Drawing 7 shows a partial elevation of a segment die with a circular opening and a straight line Represents segment boundary curves, drawing 8 corresponds to drawing 7 except for The fact that the opening cross-section is hexagonal corresponds to drawing 9 of the drawing 8 except for the fact that the opening cross-section in the drawing is decagonal, Figure 10 shows a partial elevation of a segment die, the b ££ voltage cross-section is square and in which different types of segments with straight boundary surfaces are shown for comparison, drawing 11 corresponds to drawing 10 except for the fact that the opening cross-section is triangular in this drawing Drawing 12 is a partial elevation of a segment die with a segment boundary curve Class II, Figure 13 shows a partial elevation of a segment die hexagonal opening cross-section, its original logs curved and whose segment boundary curves belong to class II, drawing represents 14 is an elevation of a segment die with a circular opening and a curved reflection Represents segment boundary curves, the drawing 14A corresponds to the drawing 14 to to the fact that in this drawing the opening cross-section is square, Drawing 14B illustrates the mathematical derivation of the reflection of a segment boundary curve from drawing 6 on a straight line D-Dt, put the class III curves on the Drawings 15-19 boundary lines for the inter-segment contact surface cross-sections based on which the construction of the segments for this invention was made can be, Figs. 20 - 27 show curves used in determining the segment shape, There are also further elevations of segment matrices in drawings 28 - 31, which have the features according to the invention, a plan view can be seen in drawing 32 recognize a complete matrix structure including the shrink ring and the die holder, Figure 32A provides the corresponding elevation Of the structure of drawing 32, drawings 33, 34 and 35 constitute scale drawings of segment matrices, as detailed in Examples 2, 3 and 4 are, in Tables 36 and 36A, pairs of numbers for n and K are dependent on given values for Qmax and Alpha are given.

Accordingly, the present invention is based on segment matrices geared towards who are able to withstand maximum workloads under extreme conditions to endure as they can occur in material forming and processing. Generally speaking, the matrix used here is a segment matrix with a mathematical one derived structure, in particular a matrix with a group mathematically derived segment-shaped parts that, meaningfully connected to one another, form a desired die opening and, suitably held together, the shape of the keep the desired die. Any suitable structure and method can be used to hold the individual segments together in their working position. The invention does not extend to these structures and methods except to the extent that they are used in the The latter interacts with the die segments in the final die structure stick together.

The basic idea of the invention lies in the mathematically derived segment-shaped part or die opening segment, one of which is an X Multiplicity; properly assembled, form the die opening.

Each segment slides on the next in a predetermined order Segment along a mathematically determined curved surface. The main advantage The invention explained here is the mathematically determined geometric contact between the segments' which takes on the workload through controlled distribution the cohesion pressure on the segment contact surfaces. Those surfaces of the segment-shaped Parts that are planned for machining the workpieces form the die opening of desired shape, the curved transverse surfaces are in a number of Shapes are represented that depend on the type of cohesive pressure exerted by the segments exercise one another under given working conditions, in three special groups can be divided. The mode of action of the cohesive printing can be influenced by this diversity arbitrarily determined by die segment shapes and their mutual arrangement will. How this comes about will be shown in detail below.

Figures 1-A, 1B, 2A and 2B are representative of a theoretical one unlimited group of matrices that differ from each other a) by the Angle alpha of the slope of curves C at the starting point (where alpha is between more than Oo and less than 900), b) by the width t of the die wall, which, as will be shown, was subject to special restrictions in certain cases can be, c) by the shape of curve C, d) by the number of Segments m, which form the die, and e) by the shape of the opening cross-section the die, which can be curved or polygonally delimited as desired.

For the purposes of this invention, the segment boundary curves are designed in such a way that that the distribution of the cohesive pressures that the segments exert on one another is as follows can be arbitrarily controlled: I. The cohesive prints can essentially are evenly distributed over the entire length of the contact surfaces of the segments, when the working pressures are uniform and radial from the center of the die cross-section have an effect.

II. The cohesive pressures can be continuously, under the same working pressures, starting from the die opening outwards, decreasing; or you can more or less uniformly over the entire length of the contact surfaces of the Segments are distributed when the working pressures are radial but not homogeneous act over the entire circumference, for example with less force against the inner walls of the Segments than against points further out on the contact surfaces of the segments.

III. The cohesive prints can have a certain initial length the contact surfaces of the segments are made monotonously growing, if the working pressures are substantially radial and uniform from the center of the die cross-section act out; or they can be more or less uniform on the contact surfaces of the segments are distributed when the working pressures oppose radially with greater force the inner walls of the segments than against points further out on the contact surfaces of the segments work.

In addition, heterogeneous segment boundary curves can be created, by going about a certain initial length with a curvature of a curve above mentioned class begins and subsequently with curvatures according to the curves of others Classes continues.

In this way, the changes in the cohesive forces can be passed over a certain length between two points of the segment contact surfaces between certain, pre-selected limit values and in any direction. (See illustration 2C).

In Section IV, there are some important notes about the meaning of the angle alpha for the development of the segment matrices.

Section V will discuss some important pointers on your choice of Find number of segments m for developing segment matrices.

In Section VI some examples of the operation and the Development of segment matrices according to those explained in this publication Criteria given.

Representation 1A represents an elevation of a segment die the present invention without a shrink ring or any other, suitable Housing, with the segments of the die in their normal working position, the die opening shapes, which in this case are drawn circularly for the sake of simplicity is.

In this form, the die 1 is composed of a given number of segments 2 (here four individual segments) together, which are arranged in a suitable form form the die 1.

For this purpose, each segment 2 has four side walls, in cross section generally denoted by C, two of which are curved, in concrete their cases also flat, a side wall 3 is convex or flat and the wall 4 is concave or flat is (see drawing 1B). The curvature of the walls 3 and 4 match each other made so that they allow the segments to be joined together so that they have a form a complete die. As explained below, the curvatures can be of side walls 3 and 4 can be derived mathematically as required (see the examples 1 to 4 in Section VI as well as the corresponding places in the text).

Each segment also has an inner wall 5, the curvature of which in the in this case is shown in cross-section as a quarter circle, so that four such inner walls, As can be seen in the drawing, form a die opening 6, the cross section of which is circular. This opening is used to shape the material during the work process and can have the usual lead and end angles.

The fourth side wall of each segment can be a predetermined one Assume size and shape that are only possible through consideration and restrictions imposed in the Further to be discussed, and on the of the shrink ring or another suitable housing is restricted. This wall forms together with the walls of the remaining segments the outside of the die that of the shrink ring or another housing is included, wherein for a meaningful operation The size and shape of the ring or the corresponding housing must be complementary. The shrink ring or the housing can be of conventional construction or be manufactured according to a special process.

The top and bottom of the segments should be as smooth as possible although a different surface condition is also beneficial.

In addition, a rear cover plate or other device can be used be built into the housing of the die.

The representations 2A and 2B are similar to the representations 1A and 1B to on the shape of the inner wall 5 of each segment, which is indicated in the drawings 2A and Figure 2B shows a polygonal, especially a hexagonal W, cross-section of the die opening 6 result. On the sizes and the arrangement of the die segments in these representations also extends the mathematical derivation discussed in this patent method.

If the design of the die segments is based on those developed in this patent If the criteria are mathematically done, the segments can be produced in various ways will. Any suitable method available in the art can be used such as machine tool or powder metallurgical processes, 1- Cold rolling process or electrolytic processes. The segments can be made of materials as they were customary in the prior art, including Powder metals, plastics, metal-plastic compounds or injection-molded metals. The innovations in the design of the die segments could even include the use of Allow materials for their manufacture that were previously in such use were unknown.

The manufactured segments can be done in any satisfactory way be combined to form a die. One developed and manufactured for this purpose The shrink ring can be heated to the extent that the ring, which has been stretched by the heat, is also heated sufficient play around the composite segment matrix can be fitted and shrinks around the die on cooling according to the instructions. Any other suitable However, the housing can also be adapted to the assembled segment matrix.

I. The intention of the cohesive pressures between adjacent-segments the die on the entire contact surface of the segments as evenly as possible to distribute when the working pressures are substantially uniform and radial from the central axis of the die opening, leads to the segment boundary curves Class I. This type of curves may be called "equal pressure curves" and in elevation marked with Cc, as can be seen from the drawings 3, 4, 5, 6 and 32. It will be shown that Cc must be a member of a family of circles, where for Any given choice of alpha (the angle at which the curves Cc from the inner surface the Die opening start from) in each case and only one such circle exists.

The mathematical equation describing curve Cc is based on following assumptions: a) The cross-sectional components of the working pressures act uniformly in all directions against the inner surface of the die opening (in practice be some materials will not be uniform objects their work prints will but act uniformly enough, at least under favorable conditions, that these Assumption seems justified), in the case of circular die openings this applies Adoption for all operations of cold rolling, punching, advised against, cutting and similar; cold rolling is an exception for polygonal openings.

b) The pressure on a unit arc length is directly proportional to the sine of Beta (where Beta is the angle that the radial force component makes with the tangent to the limiting curve at a certain curve point r, as can be seen from drawing 3) and indirectly proportional to the distance thereof Curves, points from the center of the die opening: / r sin beta. The pressure is indirectly proportional to the distance r, because the total force is distributed over larger areas with increasing r, and is directly proportional to the sine of beta, since the sine causes only the normal components of the force to the curve to be considered.

Equation (4).

If one substitutes equation (4) in equation (2), then equation (5) follows: So that the pressure remains on the curve Cc independent of the respective position, P must be independent of @ Be O be. This immediately results in the differential equation. In polar coordinates, the curve Cc in illustration 3 can be represented by the generic equation r = f (@) equation (1). From what has just been said about the pressure, the following relationships result: sin beta sin beta P = H ------- or P = H -----, equation (2) r £ (e) where H is an experimental one represents determinable proportionality factor. As will be shown below, the formula for the segment curves r = f (@) can be derived without defining a value for H. Using the standard equation ft cot beta = ------- equation (3) f (e), equation (6) results for (ft (g)) 2 +)) 2 = c2, where c is a positive constant target.

The mathematical solution to this differential equation is £ (e) = c sin (e + alpha) = r equation (7), where alpha is the starting angle of the curve (see Drawings 3 and 4) and the constant c is subject to the condition: f (e) = 1 equation (8) or according to equation (7): c sin alpha = 1 equation (8a) so that the curve Cc starts at a point with r = 1 from the center (see drawings 3 and 4).

In right-angled X-coordinates we get for equation (7) with the boundary conditions (8) and (8a): Equation (9) where for c in this case: c = sin alpha v or c = csc alpha equation (9a).

Equations (9) or (9a) represent a family of circles with the center in cot alpha) and a radius csc alpha 2 It follows that that the centers of these circles lie on a straight line x = 2, which goes through exactly the middle runs between the center and the edge of the die opening. (Please refer Drawings 3 and 4).

It is best to start with the geometric representation of the curve Cc with the die opening (shown circular in drawing 4) and chooses arbitrarily the unit length is the distance from the center to the periphery of the die opening. The radius is therefore a unit of length. Through the point on the circumference under 60 °, which is marked with 1? Q1, should be vertical (x =).

The center R of the circular curve Cc must lie on this line (a a more detailed description of the character of this curve follows below). the Distance from R to point (1,0) should be the radius of the curve (radius L>.

eotAjPha, the angle alpha and the ordinate of R, cot alpha, are then mutually dependent.

Depending on the requirements of the cohesive prints and the size of the matrix the equation (9) the angle alpha values between more than 0 ° and accept less than 900. The smaller the angle alpha, the closer to each other the circular curves Cc straight lines and the more the cohesive pressures decrease (with the sinus from Alpha).

In this case, under workload, the segments become Des integration tend.

However, the inner edges are less prone to breakage, and the Width t of the wall compared to the die opening can be relatively large. The maximum width The Tmax of the wall belonging to this class of curves can be derived from is maximized in equation (7), r = c sin (e + alpha), and of the unit radius the die opening subtracts: T max = rmax -1 (a) dr = c (cos alpha) (cos O) - c (sin Alpha) (sin Q); (b) To get to the maximum of r, one sets c (cos Alpha) (cos ° max) - c (sin alpha) (sin Gmax) = ° (c) It follows that -ot gmax = tg alpha, or ° max + alpha = 900.

(d) If one now substitutes in equation (7): rmax - c sin (90 - alpha + Alpha) - c sin 90 = c (e) from equation (8): (c sin alpha) = 1 or c = csc alpha then follows: Tmax = c - 1 = csc alpha - 1 equation (10).

Therefore, as alpha approaches 0, Tmax approaches infinity.

Conversely, when alpha is large, the cohesive pressures are also between the die segments large. For maximum alpha, the cohesive pressure takes a value how it would occur if the die was made of concentric lamellas were. In this case the segments stick together very strongly, and the cohesive pressure increases evenly with an increase in the workforce. Since between the segments too If no opening occurs, material leakage into these openings remains complete locked out. However, the inner edges of the segments become thicker in this case Have points and are therefore more prone to crumbling than when Alpha is small. the Wall width t can never be greater than the radius of the circle Cc less that Length from the center of Cc to the inner surface of the die when the center is R the curve Cc is still within the inner surface of the die (see drawing 5), then the maximum wall width t can be calculated by taking the distance from the Inner surface with a negative sign subtracts from the radius of Cc, whereby this Length then added instead of subtracted.

Geometrically, the maximum wall thickness Tmax can be more easily reduced to the following Represent the way: you draw a straight line from the center of the matrix through the center R of curve Cc until it meets curve Cc with radius (csc Alpha / 2. T drawing 4 shows the case where R lies within the inner surface of the die. Drawing 5 shows the maximum die wall width TmaXs when the center point R is outside the The inner surface of the die lies. The maximum wall width Tmax approaches 0 when Alpha about 900 goes.

If one takes the same drawings 4 and 5 to express the maximum width of the die wall in polar coordinates, then the following relationships apply: rl = f (@ 1) equation (11) and according to equations (7) and (8) where 91 + alpha = 900.

Then the maximum width is Tmax = f (1) - 1 = r1 - 1: or Tmax = sin alpha - 1 = csc alpha - 1.

The 1 denotes the unit radius of the die opening. The last Equation is just another notation for equation (10); it clarifies but better that # 1 is the polar angle of the line through the center of the curve Cc is.

The maximum width Tmax can easily be calculated from equation (10); a few general examples are briefly given here: for. Alpha = 600, Tmax = 8% of the opening diameter; for Alpha = 450, Tmax - 20% of the opening diameter; for Alpha = 300, Tmax - 50% of the opening diameter; for Alpha = 150, Tmax = 143% the opening diameter.

Equation (9), from which it is particularly clear that the center of Cc is on the vertical x = 1 (as can be seen from drawings 4 and 5), clearly shows that if the midpoint were approximately at point Q (on a straight line through the origin, which forms an angle of 600 with the horizontal, the angle Alpha would take the value of 300; for larger alpha the midpoint would be below, for smaller alpha are above Q, when constructing a Segments proceed as follows: First, the curve Cc is determined from the Polar coordinate equation (7) according to all of the other instructions that go on were given above; determine the number of segments m in agreement with the instructions from section V.

After the first curve has been drawn from point (1,0), turn the construction, as can be seen in drawing 3, clockwise by 360 / m degrees and repeat the same curve Cc from the non-rotated point (1,0).

II. The second class deals with segment matrices that are under uniform radial working pressures the cohesive pressures between the segments more in Distribute towards the inner walls and, under working pressures, apply more to the inner walls than act on points further out along the interfaces of the segments that Distribute cohesive pressures evenly (see drawings 6, 7, 8, 9, 10, 11, 33 and 35).

In operations such as cold rolling, drawing and the like, the radial Print against the inner walls of a polygonal die, not uniformly in all of them Directions, but larger towards the middle of the pages than towards the corners. This sees best when workpieces are drawn from an original shape in the work process or be deformed into a new angled shape such as a blank that becomes the spark plug body is deformed. In this case the radial forces are in the direction of the bisector of the polygon must be larger than in the direction of the corners From drawing 2A, which is the hexagonal Cross-section shows, it can also be seen that the outer part of curve C of the corresponding Hexagon side is much more parallel than the inner part. The family of Circular curves will therefore no longer form a family of curves of equal pressure, but rather the cohesive pressure as a characteristic with increasing distance from the center increase (depending on the angle alpha, this increase can in certain cases remain restricted to a certain initial zone).

In the same way, in curved die openings (circular £ Urmigsenv elliptical, etc.) the working pressures are not uniform radially distributed, if workpieces with a different geometric shape are pulled through the die opening, cold worked or trimmed.

By modifying the circular die segment boundary curves Class I Cc, however, can form a new family of Class II curves whose members Cs (see drawing 6) have the property that, if the working pressures uniformly radially from the central axis of the die opening act, the cohesive pressures between the die segments starting from the inside remove the die opening along the contact surfaces towards the outside. Under Under the conditions just described, the new curves C5 prevent the tendency of the Die segments to gape apart at the inner edges and challenge them Way an even distribution of the cohesive pressures between the segments when the working pressures admittedly radially, but with less force against the inner walls than against points further act outside on the contact surfaces of the segments. Otherwise there would be a gap of the segments allow small parts to be deposited in the cavities, and with With each new work step, this attachment would mean clearing the segments apart still worsen.

For the same starting angle alpha, each class II curve differs from the corresponding class I curve in that it curves more slowly. For a given starting angle alpha, there are many class II curves, the class II curve starting with this angle, on the other hand, fulfills the condition (according to equation (5)): is an increasing (or not decreasing) function of @, if r = f (@) represents the curve equation as before. The first derivative must therefore be positive: 2f '(O) (f''() + f ())> O equation (12a).

Since fl (@) in most of the cases that are of interest here, is greater than O, it follows that they + r (e)> o equation (12b).

The number of formulas for curves that meet this condition is subject to no restrictions. Some should be mentioned here for illustration: 1. A lot of curves have the property that the cohesive pressure decreases with 1 / r, where r is the distance to the central axis of the matrix zen opening. Form these curves the group of logarithmic spirals with the polar equation: r = eO cot Alpha where alpha has the same meaning as before. These have logarithmic spirals further the property that the angle alpha between the radial vector and the tangent to the spiral is constant (see drawing 12). Choosing this Angle alpha not only defines the amount of cohesive pressure between the segments the die (the larger the angle alpha, the greater the cohesive pressure in the direction the inner wall), but also where the segment boundary curves encompass the perimeter of the die cut. If one denotes the polar angle of the curve with S and assumes that the wall thickness of the matrices is a multiple of the opening radius T, then T applies = e5 (cot alpha) - 1 equation (14a).

If SO and Alpha + 900, then it follows that T T0> O. If one wants to make the wall thickness of the die as a minimum multiple T1 of the die opening radius, then the relationship between S and Alpha can be expressed in terms of T1: Equation (14b).

Therefore, the larger the alpha, the larger S must be for a given one and the more the matrix tends towards the quasi-lamellar shape.

For certain operations for which the work pressures are extremely large this would constitute a notable advantage, although one for manufacturing reasons for S becomes a size smaller than preferred. For T1 = 1, alpha would therefore be smaller or equal to 770 34 °. On the other hand, if Alpha = 500 and S = 7v / 2, then T would be 2.75 according to equation (14a); Alpha would be smaller or S larger (but not be greater than -, then T would also be correspondingly greater; on the other hand would be alpha larger (but not larger than 77 ° 34 ') and S smaller (but not smaller than 0.83), then T would be correspondingly smaller (but not smaller than 1).

Of course you can change the values for the variables as required choose any according to equations (14a) and (14b). That way you don't get merely a class II curve showing the cohesive pressures between the segments in the direction of the inside of the die intensifies, but also gains control over the Starting angle alpha, the intersection of the segment boundary curves and the die perimeter and within desired limits across the thickness of the die wall.

2. If Alpha = 450, then equation (13a) becomes: r = e @, because cot 450 = 1 equation (13b).

3. Straight segment boundary curves also meet the criteria for Class II curves (see drawings (7, 8 and 9)). You can be in polar coordinates Express it as follows: r = f tG) = tg Alpha Equation (15).

cos ~ O tg Alpha - sin O In the event that the matrix cross-section is a regular m-corner, it should be remembered that the angle alpha (which the straight segment boundary curves enclose with the horizontal) should be selected according to the following criteria: (a) For m 48 (as in drawings 8, 10 and 11) for better i adhesion between the die segments and against outward rotation of the segments due to torsional forces, Alpha should be subject to the following restrictions: Equation (16a) Depending on the width of the die, a common polar angle for the end point of the first straight segment boundary curve and the starting point of the following can be rounded by a suitable choice of alpha (see drawing 8). In this way, not only is adequate adhesion between the die segments ensured, but in particular the edges of the inner walls are no longer exposed to breaking forces.

(b) In order to reduce the breakability of the segment inner wall corners for an m> 8 (such as in drawing 9), the following restriction should be observed when choosing alpha: Equation (16b).

As just mentioned, depending on the number of corners the die opening and die width find an angle alpha such that for one and the end point of a straight segment boundary curve with the same polar angle The starting point of the following matches (see drawing 9).

The cohesive force ratio between the inside of the die unt the outside is larger for straight segment boundary curves than for logarithmic ones, if the angle alpha is the same for both, as the spirals curve faster than straight lines. However, it is apparent for the same starting angle Alpha is the polar angle S that the curve between the start point and end point on the Periphery the die passes through, for logarithmic spirals to be larger than for straight lines. This enables the spiral curve matrices to produce larger working pressures resist than is conducive to straight segments. At the same time need the inner ones Corners of the segments not to be so pronounced. The advantage of the straight segments is of course their simplicity in construction.

4. To the ratio of the cohesive forces on the inside and on the To maximize the periphery of the die, limiting curves must be used, which wind clockwise instead of counterclockwise (as in the drawings 1X, 14a and 14b).

Those whose tangent at the point r = 1, @ 0 = O (or x = 1, y = O) is normal to the radius vector at the same point, give the best ratio, since in this case the angle beta from equation (23 is 900 and accordingly sin beta = 1. A family of such curves can be developed by the following equations: y2 + a (x - (1 + w)) 2 = d (x - (l + w)) + e equation (17a) j where for a90 is.

(a) For the case d = 0, a = 1> w2 = e one obtains a family of Circles whose center is at the point x = 1 + w, y = O, and whose radius is the same ~ is.

e (b) In the case d = O, w = - one obtains a family of ellipses, a of which The center is at the point x = w + 1, y = 0 and whose semi-axis lengths are w and #.

(c) A family of parabolas with the focus at the point ddx = 1 + -, y = 0 and the guideline x = 1 - - results from the 4 e 4 condition a = 0, = 0> e 0 and w = -d (d) If d = 0, a and e <0 and is) then we get a family of hyperbolas whose right focal point is at the point x = 1 + w (1- Ir1-a), y = 0, whose center is at the point x = 1 + w, y = 0, and whose vertex is lies at point x = 1, y = O.

By slightly changing equation (17a), conic sections can be developed whose tangent at the point r = 1, @ 0 = O 0 (x = 1, y = O) includes an angle Delta> 900 with the radius vector at the same point, where the modified equation takes the following form: (yz) 2+ a (x- (1 + w)) 2 = b (yz) (x- (l + w)) + c (yz) + d (x- (l + w)) + e equation (17b), where for a = 0, will, and for a # o, will.

It is easy to see that by reflection along a straight line D-D 'the counterclockwise curves of classes 1 and II and also those in the following Treated Class III curves are mirror-inverted clockwise curves (as in drawing 14b, for example). If the reflection line runs through the point r = -1, O = O (or x = 1, y = 0) and closes the angle gamma with the horizontal (49 °° for die openings with 8 or fewer corners and <450 for all others polygonal or curved openings), then the tangents of these close Curves at the same point with the horizontal an angle 1800 + Alpha - 2Gamma (as can be seen from drawing 14b).

From the number of possible mathematical transformations, one should be touched upon for illustration, which also leads to the desired result: x = r cos (2 Gamma - 8) + 2 sin2 Gamma y = r sin (2 Gamma - O) - sin (2 Gamma) Equation (17c) Equation (17d) where r 'and gut represent the coordinates of the reflected curves.

From equations (17c) and (17d) it is immediately apparent that the point at which the radius is vector of the curve coincides with the tangent at the same point, is that point at which the radial forces result in the lowest cohesive pressure and therefore the ratio of the cohesive pressures inside the die and at that point is greatest. In practice, this means that by using segments with the just described reflected segment boundary curves of classes I, II and III even under very high working pressures, which would otherwise try to push the segments far enough apart to cause complications (accumulation of small particles between the segments, breakage destruction the segment corners, etc.), cohesive prints can be produced on the inside of the segments, which are much higher than would be possible by using limiting curves in a clockwise direction.

To the mathematical derivation of the mirroring of the curves on a Straight lines D-D '(as shown in drawing 14b) are to be explained in more detail below Conversion tables (derived from equations (17c) and (17d)) given for a family of Class II curves described by equation (13a) (r = exp (@ cot Alpha)), where alpha and gamma are an independent pair of variables form..

Gamma 15 Alpha 40 r x X y r 1.1041 1 Dvvh 0.01525 1.1002 1.8363 ' 1.2189 2 1.2102 0.07225 1.2124 3.4164 '1.3457 3 1.33.10 0.11906 1.3376 4.7580 1.4857 4 '1.4694 0.15131 1.477 5.8796 1.64 () 3 5' 1.6206 0.19324 1.6321 6.7998 * 1.8110 6 ° 1.7884 0.23661 1.8040 7.5365 1.9995 7- 1.9745 0.28125 1.9944 8.1068§ 2.2075 8 '2.1807 0.32694 2.2051 8.5265-2.4372 9 '2.4093 0.37341 2.4380 8.8100 2.6908 10' 2.6625 0.42029 2.6954 8.9707 * 2.9707 I 2.9429 0.46718 2.9797 '9.0202. Gamma 30 Alpha 10 1.1040 1.0686 0.0803 1.0716 4.29X80 1.6404 5.1.4409 0.4777 1.5179 18.3413 '2.4372 9 ° 2.0338 1.0280 2.2788 26.8155-3.6211 13 * 2.9696 1.7823 3.4634 30.9711-5.9399 18 ° 4.9142 3.1085 5.8148 * 32.3136 ° Alpha 20 ° 1.0491 1 '1.0403 () .0332 1.0409 1.8304 ° 1.3333 6 ° 1.2837 0.2127 1.3012 9.4077 '1.6153 10. 1.5383 0.3714 1.5825 13.5725' 2.0529 15. 1.9517 0.5856 2.0376 16.7031 '2.8719 22 ° 2.7630 0.9020 2.9066 18.0805 ° * Gamma 30 ° Alpha 30 ° 1.0307 1 1.0308 0.0175 1.0310 0.09697-1.1989 6 ° 1.2047 0.1039 1.2092 4.928519 1.3945 II- 1.4187 0.1864 1.4271 7.50556 1.6220 16 ° + 1.6668 0.2607 1.6871 8.89061 1.8867 21 ° 1.9662 0.3213 1.9923 9.28097 ° * The radius vector by the point given by r "# coincides with the tangent to the curve in the same Point together, which is why the conditions explained above occur.

All of the above-mentioned reflected curves can be drawn up to an angle #L in which the condition of the corresponding radius vectors and tangents to the curves are fulfilled (see drawing 14b). This also sets the maximum die wall thickness for the corresponding curve. For example, in the case of circles with the center at the point r = w + 1, g = 0 and with the radius w (see equations (17a) - (17d)) for aL and t, the following values would be obtained It should be emphasized that curves made up to this point do not provide any cohesive pressure between the segments at the periphery of the die. This should be borne in mind when their use is in question, for example when drawing very thin wires.

III. The third class includes segment matrices in which the Condition uniform, radial acting working pressures the cohesive pressures between the segments over a certain initial length of the segment boundary curves Cf> starting from the inner wall of the die, increasing uniformly; do the Working pressures, on the other hand, are radial, but not uniform, but with more force in the direction of the inner wall of the die than against points Outside on the contact surfaces of the segments, these matrices then achieve a uniform distribution of cohesive prints (see drawings 6, 15> 16, 17, 18, 19, 34 and 35).

In operations in which the work prints unevenly or intermittently act, and therefore a certain degree of elastic adaptability of the die inner zone to prevent premature failure of the die, the die segments must be designed and built so that, by appropriate yielding on the inner wall the shocks can absorb what can best be achieved when the cohesive pressure between the segments over a certain initial length, starting from the inside of the die, increases evenly. This would e.g. with a workpiece with hot rolled irregular Cured surface occur in the work process under certain conditions can lead to bruises on the die and its earlier failure. Another Case would be the manufacture of parts from powder metals. As further examples Example 3 and curve C of Example 4 are given.

Another modification of the circles that comprise the Class I curves, gives rise to a new family of Class III curves, each of which has the property has that the cohesive pressures between the die segments along a certain Length, starting from the inner wall of the die, increase when the working pressures are even act radially from the central axis of the die opening. This characteristic of the cohesive pressure differential causes a shock-absorbing uprange effect. Every Curve of Class III differs from the corresponding one, Class I curve beginning with the same starting angle alpha in that they bends much faster in the initial phase.

Every curve of class III fulfills the condition (from equation (5)), that (f ()) 2 + (f (g)) 2 within the interval ° <max a decreasing Function of @, where as before r = f (9) represents the curve equation. This condition leads to the differential inequality: f (@) + ft) <O equation (18), which is also satisfied by all curves of the subgroup that - as shown will be - are characterized by equation (19).

The number of formulas that can be used for curves that meet this condition can be given is unlimited. Even the following equation (19) describes a doubly infinite family for different positive values of K and n (for However, this formula results in values of K that are too small and values of n less than 1.5 no class III curves (see equation (23)).

Some general considerations and selected examples should follow as an illustration: For a class of spirals that meet the above condition, the polar equation is: Equation (19), where K and n are independent, positive constants. In the following, information is given on how practical values for K and n can be found (see equations (24) and (25) and drawings 36 and 36A).

For each curve of this family of spirals (i.e. for a given K and n) there is a value Gmax which determines the point M on the curve (see drawings 15, 16, 17, 18 and 19), in which the maximum of the cohesive pressure of two adjacent, occurs in accordance with this equation of developed segments.

Starting from the inner wall of the die, the cohesive pressure between the segments of the die up to this point M.

Beyond the point M, the cohesive pressure slowly drops. One would like to however, change the rate of decay of cohesive pressure (either making it growing or keep constant 0), i.e. the cohesive pressure between the segments beyond the point M keep constant), then you can use curves of classes I and II from point M on instead the original curve (see drawing 2C).

Starting from equation (5) from Section I. for the cohesive pressure P between the segments, one can determine 0max: Obviously, (ft (g)) 2 + (f ((O)) must be a decreasing function of 9 in order for P to be an increasing function of 9. The first derivative 2ft () (f ″ () + f (9)) must therefore be negative, for the curve described by equation (19) is and 2ft (@) is always positive in the given case. It follows that f '' () + f (g), or must be negative within the interval 0 # 0 # From the definition of degree it naturally follows that for emax f '' (8) f + f (0) vanishes. In other words: (in radians) equation (20).

Solving equation (19) for an r corresponding to #max one obtains: Equation (21).

From equation (3) above f () cot beta = f '(#) it follows that in the case of beta = alpha (here alpha has the same meaning as in the rest of the text) for the curves described by equation (19) is applicable: (from equation (19)), it follows: Equation (22). From equations (20) and (22) it can be seen that for a given K and n the values for Gmax and alpha inevitably follow; on the other hand, for a given K and n, both max and alpha are uniquely determined as shown by the following equations (24) and (25-). To find practical values for K and n, it is worthwhile first To exclude extreme values for both: First, for large K alpha goes towards 0 (from lim cot alpha = oo), which is undesirable because the cohesive pressure becomes very small near the inner wall. Second, for large n, for the same reason (lim cot alpha = oa), alpha tends to zero. Practical values for K and n will therefore not be very large. On the other hand, curves with K and n around 1 do not qualify for Class III curves. Even K = 1.5 and n = 1.5 are not enough.

The dependence of K on n and vice versa can be derived from equation (20) for curves of equation (19), if one takes into account that ° max must be positive. It is therefore Equation (23).

From this it is immediately evident that for an n is only slightly larger than 1 K must assume values and vice versa.

Solving equations (20) and (22) for n as a function of alpha and emax, one obtains: Equation (24).

Here alpha is given in degrees and #max in rads.

As soon as n is determined by equation (24), K can also be passed through Express equation (22) as a function of alpha and ° max: K = (n cot alpha) ñ equation (25).

With n from equation (24); So that n from equation (24) is a real quantity is, the expression under the root must be positive. If you put this expression under the root zero and expanded for #maxs is then obtained regardless of the choice for n and K the largest possible value for ° max O '= 1 - sin Alpha1 equation (26).

max 2 cos Alpha For Alpha = 0 °, ° max takes the value 1 rad, or 28 ° 36 '. If p max 2 rad a, oer e Alpha1, however, goes towards 90 °, then O'max must go towards walk.

max Before the values for Alpha and Omax for a segment boundary curve of class III according to equation (19) are selected, the following general criteria should be considered: 1) Final state of the workpiece.

a) If the final state of the surface is extremely important, ° max should be chosen as close as possible to the inner wall; are you on the other hand, the resistance of the die to momentary shock from the workpiece here is the dominant decision-making factor, such as avoiding the loss of matrices, you will choose a ° max further away from the inner wall of the die. This transfer the point of maximum cohesive pressure to the outside allows the die segments to yield from the inner wall to point M (corresponding to Gmax and rmax) and therefore acts as a cushioning shock absorber. All other conditions described in the text are to be observed independently of this (see Sections IV and V, equations (5), (19), (20), (21), (24) and (25) and the accompanying text).

2) Early failure of the die as a result of splinters can be prevented are made by a practically defensible smallest choice of alpha. All other conditions of the text (as explained in the previous section l) b)) must be taken into account.

3) If not splintering is the dominant factor in the failure of the Represents a die, such as in the manufacture of parts from powder metals or malleable metals, with slight tapering or the like, then the Angle alpha take on larger values with the remaining conditions of the text and those just mentioned under l) b) are not in contradiction.

4) From a practical point of view, the angle should be alpha for polygonal die openings values between 100 and 700 anj to take and for round die openings those between 10 ° and 500.

5) As already stated in equation 26, Gmax must be between Oo and 28036T.

6) The thickness of the die wall at the point of maximum cohesive pressure between the segments is determined by the value of max (i.e. f (Omax)), which of course depends on Gmax itself, less on the unit radius of the die opening. It should be noted, however, that the solution curve for equation (19) can be extended beyond the angle max without changing the condition that it is a class III curve with increasing cohesive pressure between the segments in the interval O # 0 # For for certain types of dies, the industry typically prefers die wall thicknesses that are equal to the opening radius of the die. One can then solve equation (19) for a given n and K and a value r = 2 to obtain that angle &commat; g to be found, up to which one has to extend the segment boundary curve in order to obtain the appropriate wall thickness. In this case, however, alpha and max cannot be selected independently of one another. Alpha first determines the upper limit of alpha Equation (27), where S represents the polar angle in radians that the curve sweeps before it ends at the periphery of the die. For example, if the segment boundary curve starts at point r = 1, O = Oo and at point r = 2, &commat; 0 = 900 ends, then S is equal to ir / s or 1.5708 and is accordingly If equation (27) is represented graphically (as in curve representation 20) for S = T / 2 or for S = # / 3 (as in curve representation 22) as special examples, one finds every alpha that corresponds to a certain alpha. If one goes with the found value in equation (25) and develops for K and puts the found value for K in equation (20), then one obtains the upper limit of #max for each previously given value of alpha.

This relationship is shown in drawing 21, where a die wall thickness is assumed as the boundary condition for S = 7/2, which is equal to the die opening radius; the same relationship is shown in diagram 23 for the changed boundary condition of S = W6 / 3. In other words, this means that for each alpha one can only choose those values for #max which lie between 0 ° and the maximum value of Gmax determined by the curves and corresponding to that alpha. If one does not choose the exactly corresponding value for Gmax, then one obtains a correspondingly thicker die wall than just a wall thickness equal to the radius of the die opening. It should also be noted that the upper bound for alpha itself is determined by in the following equation: Equation (28) With the help of Newton's approximation method, this equation can be read relatively easily. You first determine the function Then one looks for a solution with the help of the experimental value for case g (nα * -) ao one corrects with a new approximate value n-α ** If the corrected approximate value still does not result in a g (n «+ *) = 0, you correct in successive steps until you get g (nα **) = 0 for a value n *.

Some examples: For S = T / 2, n # * = 2.06 and Alpha = 45040? follows max ° m Omax O ° (according to equation (27)). For S = 1r / 3 = 1.0472 (or 600), nα = 1.65 and alpha = 380551 (maximum alpha), it follows again ° max = 00.

If one wants to achieve a die wall thickness of a multiple T of the die opening radius, it is best to modify equation (27) as follows: Equation (29).

S has the same meaning as before and represents the angle e in rad (for r = T + 1; see equation (19)). Accordingly, equation (28) must also be changed slightly for the n &, which corresponds to the upper limit of alpha: Equation (30).

To get to the solutions for ny in equation (29) and n- in equation (30) Again, it is best to use Newton's approximation method, as already explained in connection with equation (28), in these cases, however with the term (T + 1) instead of the factor 2. Diagram 24 represents equation (29) for the values T = 0.5, S = t / 4 (450) degrees, the graph 26 for the values T = 0.5, S = / 3 (600). Correspondingly, the diagrams 25 and 27 represent the upper limit values of Gmax for rr represents a given alpha for T = 0.5, S = / 4 or T = 0.5, S = / 3.

From what has been said so far it follows that as soon as three of the four independent greats T, S, Alpha and max are determined, the fourth is determined by them as well. For example, if someone were interested in a special value of alpha and the corresponding value of degrees or vice versa, then not all graphical representations, as they have been explained so far, need to be carried out (as in diagrams 21, 23, 25 and 27) It is best to solve a) equation (29) for qA with the help of Newton's approximation method (as explained under equation (28)) if T, S and an alpha are given below its maximum value (see equations (30) and (29)), and then determines K from equation (25) and finally ° max from equation (20); b) the following equation according to n4 with the help of Newton's approximation method (as explained in connection with equation (28)), if T, S and a 0max (in rad) are given below its upper limit: Equation (31).

Then one solves equation (29) for alpha.

The advantage of being able to prescribe for a curve T and S becomes clear when you think of the relationship between the segments.

A curve can be laid out in such a way that the polar angle with which it ends is is larger, smaller or identical to the polar angle with which the limiting curve of the next segment begins.

The degree of overlap between each one that can be selected in this way Segments has the effect that, the later the previous curve in relation to the polar angle, with which the new one begins, ends, the greater the degree of overlap and the more greater the relationship between the die and the quasi-laminar form (as in the characters 28 - 30), for a number of work processes, such as reduction drawing with large diameters, the quasi-laminar shape would be a considerable advantage represent, while for the reduction drawing smaller diameter segment limitation4 will prefer curves whose overlap is such that the polar angle one end of the curve is smaller than that of the beginning of the following segment.

7) If multiple uses in the construction of the die is envisaged by changing the die inside diameter, then should the original rg (corresponding to max an @max as indicated by equations (20) and (21) is set) large enough to be chosen to be maximum for a point Provide cohesive pressure between the segments for all expected conditions suitable is. As soon as values for Alpha and Smax are fixed, one solves equation (24) for n and then equation (25) according to K. The values found for n and K are then given in equation (19) used. That way you finally get a specific equation for the desired segment delimitation curve, as shown in Figures 15, 16, 17, 18, 19 and 34 shown in polar coordinates and used as a production drawing can be.

Of the many other curves besides those described by equation (19), that meet the criteria for Class III curves is within range out of 6, which defines them as Class III curves, none that is not merely a minor one Represents change to that which, by suitable choice of n unQ K in equation (19) can be obtained.

In FIGS. 36 and 36A, for a better understanding, a Number table with representative values for n and K, each depending on one special 8 and starting angle alpha indicated. For the range of values T = 1, S = Xr / 3 is the Limitation --------- (4) provided; for T = 1, S = AD / 2 the limit -. -. -. (3); for T = 0.5, S = # / 4 the limitation .......... (2); and for T = 0.5, S = T / 3 the limit (1).

IV. Some remarks about the importance of the alpha angle for the Development of segment matrices: 1) Limits for alpha: For curves of the class I (circles Cc) \ or class III (curves Cf that curve faster than Cc (see illustration 6)) Alpha is restricted to values between greater than 0 ° and less than 90 ° For Class Ii curves (curves C5, which curve more slowly than curves Cc (see illustration 6)), or for straight lines the angle can assume alpha values that are greater than 900. For straight lines, the theoretical limit is an angle of less than 900 + 1800 / m (see Section II, 3 following). For the slower bending curves C5, alpha must be correspondingly smaller than this limit value according to the character of the curve present in each case (e.g. for the curve given by the equations (13a), (13b) and (14a)).

2) Some pointers for choosing alpha: the larger alpha chosen is, the greater the cohesive pressure between the segments towards the center.

For one and the same starting angle alpha, the wall thickness t is the Die for curves of class II (the curves Cs that are less quickly curve as the curves Cc (see Figure 6)), as shown by equations (13a), (13b) and (14a), or less restricted for straight lines than for curves class I (circles Cc).

There are basically no theoretical ones for straight segment boundary curves The limit for alpha and the thickness of the die wall can be of any size.

For class I curves (circles Cc), tmax becomes smaller the larger Alpha becomes in accordance with equation (10) (see the associated examples).

For one and the same starting angle alpha, r for curves max is the Class III (the curves C which bend faster than the circles Cc (see Figure 6)) smaller than for the corresponding circles Cc (see equation (21) and explanations to). However, the thickness of the die wall t can be adapted as required (see above).

3) Ratio of the cohesive pressure for different curves with an identical starting angle alpha: Mirror curves, as described by equations (17a) - (17d), result in the greatest cohesive pressure between the segments in the vicinity of the inner wall of the die for any given alpha (see Fig . 14 and 14A). Other Class II curves including straight lines with (see Fig. 6) have a smaller ratio of cohesive pressure on the inner wall to that on the periphery of the die than the mirrored spiral with the same starting angle alpha. And curves of class III have the smallest ratio of all in the interval 0 (8 <8max (see above). Basically, they would rather favor a greater cohesive pressure further away from the surroundings of the inner wall. The cohesive pressure remains for uniform, radial working pressures constant along the arc of a circular curve Cc: accordingly the ratio of the cohesive pressure on the inner wall to that on the periphery of the die is the same.

4) As already mentioned in the case of the circular curves Cc> they are pointed The larger the starting angle, the more pronounced the corners on the inside of the die Alpha and the more easily they split (compared to small angles alpha). this applies to all types of curves that have been covered so far, including the Straight lines.

As also mentioned earlier, the cohesive pressure is in the direction of the inner wall of the die becomes larger the larger the alpha.

Even if one takes into account the splintering property just mentioned pulls, the property of increasing cohesive pressure when machining can be certain Metals can be beneficial and also allows the number of segments in the die to increase compared to the number of sides of the die opening; in the case of a circular or otherwise curved die opening, the number of segments can of course can be chosen as large as desired. As a Brgebni you get accessible and good too waiting die inner walls 1 with less tendency to form grooves and breakage than the after. segment matrices developed using previous methods.

V. Some general references to the number of segments m for segment matrices: Some practical considerations, among other requirements, dictate the choice of Segment number m for both class I curves (Cc or circular, discussed in Section I) as well as for Class II curves (Cs or more slowly curving as circles, described in Section II) and Class III (Cr or faster curving as circles, treated in section III): 1. If one uses the segment boundary curves C only wants to start at the corners of a polygonal die opening, then the number of segments m is limited by the number of sides of the polygon. In selected cases, the number of segments can be reduced even further: for example three segments for a hexagonal die opening, four segments for an octagonal one Die opening and so on. Recommended for a three- or four-sided die opening it is up to you to let the number of segments agree with that of the sides.

In some cases of polygonal matrices, such as the one in FIG. 1 shown example of a hexagonal opening, the edge is not pronounced, but instead take the form of curves or straight lines (the latter case is shown in Fig. 13). Any q Segment can also change contribute to the geometry of the polygon of the die opening by adding the point where the inner wall of the die begins, at the beginning of the apex curve begins: the next one The segment then begins at the beginning of the next following apex curve (as in Fig. 13 shown). Such a change in the corners of the inner wall of the die has no effect on the other considerations such as the type of curve C, starting angle alpha, wall thickness t and other points discussed above.

In theory, the number of segments can be that of the sides of the polygon surpass. However, the length of curve C is used for starting points along the polygon sides longer than for starting points in the corners. The maximum thickness of the die wall max is therefore determined by the longest of these curves, which in turn is in the case of of the Class I curves (Cc or circles) are limited by the above circumstances are. If, on the other hand, the die opening is circular, elliptical or otherwise curved shape, then the number of segments can vary according to practical needs can be chosen at will. Leave even for irregular die openings as in Fig. 71 segments develop according to the criteria explained here. In such cases however, not all segments will have the same overall shape; although the segment boundary curves are all derived from the same equation, depending on the geometry of the Opening some longer than the other. This is also illustrated in Fig. 31, in which the straight part of the opening, for reasons of expediency, is -n segment is worn. In other cases, however, segment boundary curves can be used even Belong to different classes if the unequal distribution of work pressures against the inner wall of the die. This is in FIG. 35 and in Example 4 presented in Section VI. The most important aspect of this patent is the choice of the class of the curve according to the requirements of the intended use. From this point of view, all considerations regarding the number of segments, the starting angle alpha, the die wall thickness, etc. are the same as in the respective Sections of this patent specification.

2. The following rule of thumb can be used: if the metalworking process is too hard for the die and leads to its early failure, then this can occur tough working conditions are more likely to be met with a larger number of segments. In operations with extremely critical dimensions such as cold work or punch presses however, the service life will remain of secondary importance to the final tolerances and the number of segments, the starting angle alpha and the shape of the limiting curve are very critically linked.

The segments made in accordance with the present invention are summarized with one or more shrink rings, which in turn on conventional Way brought to their exact dimensions and in a die block and / or Containers are built in.

The die block or die holder or container forms one important point in harnessing assets and abilities one good die according to the claims of this patent. In practice one becomes a die block wall thickness request that is the same, or if the space requirements allow, greater than that Total diameter of the die body and the shrink ring (s) surrounding it. This is especially true in cases of high tolerances within o, o25 to o, o75 mm (o, oo32 "tis 0.0012 "), such as is required for non-cutting work or punch pressing are when the working pressure against the inner wall is momentary or discontinuous acts and, as soon as the material begins to flow, decreases rapidly. The general The objective of a good die and a good die housing is the tolerances to be able to keep critical for all dimensions of the workpiece, and despite one thing the cleanest possible production process to achieve a good service life of the die. By applying the teachings of this invention, one can achieve the objectives just mentioned Realize better than with a known die, When realizing the present In the invention, any material can be used to manufacture the die, as is currently the case for the production of matrices for, for example, strand and extrusion, hot and cold drawing, upsetting, trimming, punching, cutting and other metal and non-metal forming work (e.g. for various types plastic) in use. The die can therefore be made of suitable Metals and alloys such as tungsten carbide steel, tool steel, monel, ice, cobalt, Nickel, copper and other transition metals, especially If you are available in grain sizes smaller than 3 p.

Of the many materials that can be used with a die the current one Invention can be treated as workpieces, only a few are intended as examples the following are named: brass, stainless steel, chrome-nickel steel, tool steel, tungsten carbide in powder alloys, nylon, polyolefins such as polyethylene, polyurethane, phenol formaldehyde etc.

VI. Four examples of matrix applications and the corresponding matrix development for this according to the aspects explained in this patent, Example 1, Figure 32 shows a die for the production of ball-and-socket pins (with a device for the manufacture of the pin head is omitted). To find the most appropriate To arrive at the segment boundary curve, one first takes into account the known factors and requirements such as: workpiece material, intended reduction of the workpiece (in this example 28.5%) and later cold work in the manufacture of the pin head. The working pressures act almost uniformly radially on the inner wall of the die and it is best to choose a segment delimitation curve which gives the cohesive pressure evenly redistributed. The decision is therefore in favor of a curve of the class I.

The next step is to determine the die wall thickness as a function from the starting angle alpha according to equation (10). In the given case, the die wall thickness should be be at least 50% of the die opening diameter. This corresponds to a Starting angle alpha of 30 ° (see above) and guarantees good cohesive pressure distribution along the segment boundary curves, without the inner corners of the segments being too pronounced (see Section IV).

After alpha is determined, the next step is to equation (9) for the curve to solve. One then finds the point x = as its center 1 X = ctg 300/2 = o, 866, and for 2> Y = ctg = and their radius 1 unit (the The radius of the die opening cross section is assumed to be a unit of 1/2 300). The curve is shown in FIG.

Now the number of segments should be considered. The general information are set out in Section V and it is sufficient here to merely give six segments as a result to cite. We also know from above that the polar angle of the curve is for an alpha from 300 even sweeps an angle of 60 ° until it reaches the point tmax. This means that for six segments each curve begins with a polar angle, with which the previous curve ends. This enables the stencil to do better work prints to be able to resist than would be possible with segments that stop earlier.

The usual procedure for the calculation and development of the The shrink ring and die housing seems sufficient and does not require any modification.

Example 2 Figure 33 shows a hexagonal die. As above explained, the working prints in this case work more strongly against the middle of the page than against the corners of the inner wall of the die. To the slope the segment matrices, to gape apart at the corners under these given pressure conditions, to prevent, Class II curves should be chosen for this die. Under the given Working conditions are these curves for an even distribution of the cohesive pressures worry (see above).

Among the class II curves, you will choose straight lines and segments develop as in Fig. 8. However, assuming extreme work pressures on the Then the curves described by equation (13a) are suitable Family better: for a given S and T (see equation (14a)) they lead to less pronounced inner edges than they would occur for straight lines.

In addition, such a curve is created for one and the same starting angle Alpha sweeps over a larger polar angle over its entire length than one Would just do, which is why the die can withstand rather high working pressures.

For the same reasons as in Example I, S should have the value 1.0472 rad (or 600), and the die wall thickness should again be a unit. If you put all these values in equation (14a), you get for alpha = 560301.

Then you put the found value for alpha in calibration (13a) and draws the resulting curves in polar coordinates as in FIG. 33. All further steps in the development and manufacture of the segment die are the same As in example I.

Example 3 Figure 34 shows a die for the production of hexagonal Shells in the stamp press deep drawing process. The unevenly distributed forces of this In conventionally developed matrices, the process does not just cause something early Failure of the die but lead to frequent defects in the end product.

This example is not intended to be based on the best manufacturing method for segments for such working conditions, but it should be the Advantage underlined, the segment matrix zen, ßach in this patent criteria were developed compared to conventional segment matrices exhibit. Die failure as a result of material defects should therefore also be used here are excluded like the possible inability of the materizen material applied work prints suitable to pass on.

In order to prevent cupping cracking in the end product, a certain amount is required The amount of "yielding" of the die segments directly on the inner wall of the die is necessary. In this way, the die can instantly adapt to the deformation geometry of the Workpiece react. Curves are of course used for such a purpose of class III in question, which after a suitable choice by emax for each individual case Have property.

In our example, emax should be 50 or 0.087267 rad.

Several factors must be considered when determining the die wall thickness The following must be considered: the mechanical properties of the workpiece material, the quality of the matrix material, empirical experience, etc.

In the example given, T = 1.

The next step is to determine the polar angle S of the curve sweeps along their entire length. In the case of high loads, it seems to be desirable that S assumes a value of at least number of segments, so that the curves at least have a minimum of overlap. Under extreme working conditions should S will of course be larger, although S should be seen in relation to alpha not due to too small a choice of alpha insufficient cohesion of the segments at the To generate die opening. If in our example S = t / 3 = 1, o472 (or 600) is, alpha can have values up to 38055 '(see equation (28) and accompanying text).

As soon as three of the four independent variables are established, the fourth is determined. In our example T = 1, S 'is / 3 and emax = 50, so that according to diagram 23 or equations (31) and (29) alpha must be 370. This is an entirely acceptable value, since it has sufficient cohesion between the segments allowed and yet does not lead to excessively pronounced inner corners of the segments. If however, the first three variables resulted in an unacceptable value for alpha would have had one or more need to be changed.

The corresponding ones can now be found with the aid of FIGS. 36 and 36a Values for n and K: n = 1.835, K = 1.624.

These values for n and K are now inserted into equation (19) and drawn the resulting curve in polar coordinates, rotates the curve 60 ° and pulls the next curve and so on, until all segments are finished (see Fig. 34).

All further steps in the production of the die, the shrink ring (s) and the housing follow the previous standard procedures.

Example 4 FIG. 35 shows a die for producing an approximately D-shaped head on a drawn bolt that is not concentric with the head is. A closer examination of the working pressures against the inner wall of the die shows that the greatest forces act in the solid arrows shown in Fig. 35, less large in the direction of the dashed and the smallest forces in the direction of the dotted arrows are effective. Since now segment boundary curves in the four Start corners of the segment die opening, starting from a point smaller Radial forces should sweep over a range of increasing radial forces if they are curved be of class II. The segment boundary curves would however start at points; indicated by the solid arrows (see Fig. 35), then they would go from points of greatest radial pressure to points of decreasing radial pressure run, and. should therefore be class III curves in order to be close to the inner wall of the die to cause a slight "yield" of the segments ..

For the sake of simplicity, this example is a matrix shown with only three segments. However, the workprints should be larger as previously assumed here, then six segments should be considered. The rules of development. stay the same, of course.

In our example, the die opening is designed in polar coordinates. However, instead of moving its center to the origin, it became the center of the page of the straight part moved there.

For curves A and B, the smallest radius of the die opening was used taken as a unit length; for curve C, the smallest opening diameter became chosen as a unit length. It should be emphasized again that this. just one is an arbitrary convention to simplify drawing and does not have any influence on the actual mode of operation of the die.

Curves A and B in Fig. 35 belong to Class II out of those mentioned above Establish. They are both chosen from the family described by equation (13a) i. However, in order to be as large as possible Area of sufficient cohesive pressure to agree with the requirements regarding the characteristics of the inner edges. each curve sweeps a different polar angle S over its entire length. Ever The greater the die wall thickness, the greater the size S can be selected (see Equations (14a), (14b) and accompanying text). In our example we assume that The thickness of the die wall is equal to the smallest diameter of the die opening (indicated by the solid arrows in Fig. 35). For curve A, S should be 1.74533 rad or be lob0; for curve B, S = -.o, 69 & 13 or 400.

Since in our example, instead of the center of the die opening, the side center of the straight edge of the opening lies at the origin of the coordinate system, T in equation (14a) represents r5 - 1, where for curve A and rS = 4 for curve B.

One now develops equation (14a) according to alpha. For curve A is alpha = 67054 '; for curve-B, alpha = 260421. Alpha still represents the angle between the radius vector and the tangent to the curve at point e = 0 °; but off For the same reasons as in the previous section, alpha no longer represents the angle between the tangent to the curve and the force vector from the center of the die. But this has no influence on the shape of the curves.

In the present case, this value would have to be corrected by 459.

One would get 22054 'for curve A and 710421 for curve B.

This does not affect the representation of the curves in any way. Through this it should only be checked that the cohesion between the segments in the case of the inner wall of the matrix is sufficient since, according to equation (2), P = H sin Beta n, where Beta denotes corresponds to the corrected angles just given.

Then substitute the values for alpha for curves A. and B in equation (13a) and plots the resulting curve in polar coordinates as shown in FIG.

As already stated above, curve C belongs to class III and begins at the midpoint of the longest, curved side (see Fig. 35). For the sake of simplicity, the smallest diameter of the die opening is again as a unit length it follows that men, / T = 1. About the production of the segments To make it easier, it is best to leave the curve on the next following outer edge of the Die ends. S therefore becomes S = 1.25664 rad (or 720).

About the working pressure at the starting point of the curve on the inner wall of the die one chooses an emax 'O. For larger work prints, emax should be used accordingly be chosen larger.

From equation (31) one now determines ne according to the values max T = 1, S = 1.25664 and emax = o, o87267 rad (or 50). For ng one then gets max 2, oil. If you put this value in equation (29), you get one for alpha Value of 40so4 '. From equation (25) it follows for K = 1.543.

As before, put the values found for n and K in the equation (19) to arrive at the curve that can now be graphed in polar coordinates as shown in FIG. 35.

As in the previous examples, all others are carried out Steps in making the die, shrink ring and housing according to the usual standard procedures.

- patent claims -

Claims (1)

Claims 9 die for forming material, which by a Holder has segments held together, each part of the die opening limit, characterized in that the Segrein elements (2) each one non / radial running contact surface (C) and one opposite this, in the circumferential direction have offset, complementary contact surface (C), with ds they to the complementary Contact surfaces of adjacent segments. 2. die according to claim 1, characterized in that the contact surfaces (C) at the inner wall of the die opening with a beam from the center of the die opening an angle O; that is greater than Oo and less than 900. 3. Die according to claim 1 or 2, characterized in that the Contact surfaces (2) are flat. .1 die according to claim 1 or 2, characterized in that the Contact surfaces be formed by convex surfaces and correspondingly curved concave surfaces. .5. Die according to one of claims 1 to 4i characterized in that that the segments have a constant cross-section in the axial direction.-6. Die according to one of Claims 1, 2, 4, 5, characterized in that the cutting curves of the contact surfaces (C) with a plane perpendicular to the axis of the die Arcs are. 7 die according to one of claims 1, 2, 4, 5, characterized in that that the intersection curves of the contact surfaces (CY with a perpendicular to the axis of the Die are standing plane spirals. 8. Die according to one of claims 1 to 7, characterized in that that the enclosed between the contact surfaces and the inner wall of the die opening Angle and the curvature of the contact surface are chosen so that optionally one longitudinal the contact surface constant, decreasing or increasing cohesive force obtained will. 9. Die according to one of claims 1 to 8, characterized in that that at least three segments are arranged within a holder, each Have contact surfaces which correspond to the plane through the center point of the die opening and those. Is just spanned by the cut of the contact surface with the inner wall of the die opening create an angle lock in, for i) curved matrix opening cross sections values in the interval greater than than 00 and less than 900 ii) polygonal die opening cross-sections with more than eight side values in the interval from more than Oo to less than 900 - 1800 / m, where m corresponds to the exact number of pages, and less iii) polygonal die opening cross-sections with than eight sides in the interval from greater than 900 - 1800 / m to less than 900 + 1800 / m, where m again corresponds to the exact number of pages. 10. Die according to one of claims 1 to 9, characterized in that the cohesive pressure between the segments, expressed by the form where H represents an experimentally determinable proportionality factor and r = f (g) is the generation equation for the cross-sectional curve of the contact surfaces of the segments, is determined both by the working conditions and by the choice of the cross-sectional curves of the transverse surfaces from one of the groups, a) in the the cohesive pressure between the segments along the entire inter-segment contact surfaces feich and (f '+ (f (9)) 2 is constant; b) in which the cohesive pressure between the segments in the direction of the die opening is greater than in the direction of the die periphery and (f' ( O)) ² + (f (O)) 2 is an increasing function of 8: c) in which the cohesive pressure between the segments can be made increasing over a certain initial range OcBcBmax of the segment curves starting from the inner wall of the die and (f '(9)) 2 + (f (e)) 2 in the interval oe <e max is a decreasing function of 9; d) in which the cohesive pressure between the segments on the inner wall can be increased even further by mirroring the counterclockwise curves a), b) and c). is selected and the maximum wall thickness of the die wall T max a) equal to csc alpha - 1 for curves of class I b) equal to exp (S ctg alpha) - 1 for elliptical spirals of class II c) equal for Class III curves. 11. Die according to claim 10, characterized in that the cohesive prints is the same between the segments over the entire contact area of the segments as long as the working pressures act radially evenly from the workpiece, and as long as the cross-sectional curve of the contact surfaces of the segments through the equation in polar coordinates r = f (9) = sin O ctgs + ctg 9 is defined, where 9 is the angle that the radius vector with the horizontal. 12. Die according to claim 10, characterized in that the cohesive prints between the segments in the direction of the inner wall of the segments is greater than in the direction the die periphery as long as the working pressures act radially evenly, and as long as the cross-sectional curves of the contact surfaces of the segments by the equation is given in polar coordinates r = f (O) = eg ctgX. 13. Die according to claim 10, characterized in that the cohesive pressures between the segments increase over a certain range O 9 <9max over the segment contact surfaces as long as the cross-sectional curve of the transverse surfaces of the segments is given by the equation in polar coordinates is given, where n and K are positive, independent quantities that correspond to the inequality to obey. 14. Die according to one of claims 1 to 9, characterized in that the cohesive pressures between the segments are expressed by the formula are, where Ii represents an experimentally determinable proportionality factor and is the equation for describing the cross-sectional line of the flat contact surface of a segment, are larger in the direction of the die opening than in the direction of the periphery of the die, and (f '(9)) 2 + (f (9)) 2 is an increasing function of 9 is. 15. Die according to claim 10, characterized in that the cohesive prints between the segments are greater in the vicinity of the segment inner walls and that the cross-sectional curves of their transverse surfaces reflections of the respective curves according to claim 11, 12 or 13 are mirrored along a straight line passing through the starting point of the cross-sectional curve of the transverse surface on the inner wall of the die runs and with a straight line through the same point and the center of the corresponding Die opening encloses a certain, positive angle gamma. These reflected curves are defined by the following four equations: x = r cos (2 gamma - 9) + 2 sin2 gamma y = r sin (2 gamma - 9) + sin (2 gamma) r = x2 + y2 where gamma is defined as above, and r = f (g) represents the equation of origin of the respective unreflected curve. : 16. Die according to Claim 10, characterized in that the cross-sectional curve of the flat transverse surfaces of the segments is given by the following equation in polar coordinates where alpha is the angle enclosed by the curve described by the equation with the straight line that passes through the starting point of the same curve on the inner wall of the die and through the midpoint of the same die opening, and i) values between more than 0 for curved die opening cross-sections ° and less than 9o0, ii) ore for polygonal die opening cross-sections with more than eight sides values between more than 0 ° and less than 900 - 18o0 / m, where m corresponds to the exact number of sides of the die opening, and iii) for polygonal die opening cross-sections with eight or fewer sides values between more than 900 - 180 ° / m and less than 900 + 18o0 / m, where m again corresponds to the exact number of sides of the die opening. 17. Die according to claim 10, / characterized in that the cohesive pressures increase over an initial area O ## ° max of the transverse surfaces of the segments and in the same area the cross-sectional curves r = f (O) of the transverse surfaces give the inequality f () + f "(B) (O meet and also for the case in the same area the inequality satisfy, where n and K are independent positive quantities. 18. Die according to one of claims 1 to 17, characterized in that that essential parts of the cross-sectional curve of the transverse surfaces of the segments according to any one of claims lo to 17 are shaped. 19. Die after one of claims 1 to 18, characterized in that one or more cross-sectional curves of the segment transversal surfaces are different from one another. 20. Die according to claim 19, characterized in that within a predetermined starting interval 04 0 018Bmax for segment transverse surfaces whose cross-sectional curves are given by r = f (9), the inequality f () + f "(e) + f" (O) applies to O, and that in the same interval or ° max the cross-sectional curves of the segment transversal surfaces the equation in polar coordinates approximate, where K and n are positive, independent quantities that correspond to the inequality suffice. 21. Die according to claim 19, characterized in that the equation of the cross-sectional curve of the transverse surface of each die segment in polar coordinates is given, where the angle N is that angle which the tangent to the curve includes at the starting point with the horizontal and assumes values between more than Oo and less than 900 and determines the width of the effective part of the die by the expression cscoc - 1 is, and where the cohesive pressure between the segments is represented by the symbol P and the formula expressed along the effective parts of the contact surfaces the segment equals fe, which is why 2 of the segments is equal, which is why (f ()) 2 A must be constant for all O in the effective area. 22. Die according to claim 19, characterized in that the equation of the cross-sectional curve of the segment transversal surfaces r = f (O) is given in polar coordinates and is derived from the inequality 2f '() (f "(O) + f (O))> 0 , where the starting angle of the tangent to the curve with the horizontal includes an angle between more than 0 ° and less than 900, the maximum width of the effective part of the matrix for cross-sectional curves in the form of logarithmic spirals is given by exp (S ctgα) - 1 istl while the polar angle in rad that the curve traverses from its starting point to its end point at the die periphery, and the cohesive pressure P between the segments by the relationship is expressed, in which H represents a proportionality factor and the denominator (f (g)) 2 + (f '(9)) 2 is a function of e increasing over the effective range of the cross-sectional curve. 23. Die according to claim 19, characterized in that the equation of the cross-sectional curve of the segment transversal surfaces r = f (9) is given in polar coordinates, the starting angle x, which the tangent to the curve includes with the horizontal, from more than 0 ° to less than 900 can range, the maximum wall thickness tmax by the relationship is determined with the independent quantities K and n, where for K and n the inequality holds, and the cohesive pressure between the die segments by the relationship is expressed in which H represents a proportionality factor and (f '(e)) 2 + (f ()) 2 in an initial area Oc 8 <max in which the cohesive pressure increases along the effective area of the transverse surfaces starting from the initial point of the segment curves on the inner wall of the die is a decreasing function of @. characterized 24. Die according to claim 23, / characterized in that the equation the cross-sectional curve of the segment transversal surface through r = f (g) = ei ctg ctgα is pressed. 25. Die according to claim 23, characterized in that the equation of the cross-sectional curve of the segment transverse surface is through is given, where K and n are independent, positive quantities that correspond to the inequality suffice. 26. Die according to one of claims 19 to 25, characterized in that r = f (O) is the equation of the cross-sectional curve of the segment transversal surfaces, the tangent of which at the starting point with the horizontal includes an angle between more than OO and less than 9o °, and the cohesive pressure P between segments expressed by the relationship where H represents an experimentally determinable proportionality factor, which is maximized on the inner wall of the die within an effective area by mirroring the original, counterclockwise oriented segment cross-section curves along a straight line. 27. Die according to one of claims 1 to 26, characterized in that the cohesive pressure between the segments in the direction of the die inner wall is greater and the cross-sectional curves of the segment transverse surfaces mirror images of the curves in 32) along a straight line passing through the starting point of the cross-sectional curve on the die inner wall goes and with the straight line through the same point r = 1, e = 0 encloses a positive angle v, are mirrored and by the four equations tx = r cos (2g - e) + 2 sin²γ yy = r sin C2 - e) - sin are determined, where r = f (9) is the equation of the unreflected curve. 28. Die according to claim 27, characterized in that the cohesive pressure P between the die segments is expressed by the relationship where H represents an experimentally determinable proportionality factor and r = f (9) is the representation equation of the effective part of the cross-sectional curve of the segment transversal surfaces, is maximized on the inner wall of the die by mirroring those cross-sectional curves oriented in the counterclockwise direction, for which the cohesive pressure between the segments in the direction of the inner wall of the die is greater is as in the direction of the matrix periphery, (f '(9)) 2 + (f (9)) 2 is an increasing or not decreasing function of 9, the angle α, which the tangent encloses at the starting point of the curve with the horizontal, values assumes between more than Oo and less than 90 °, and the maximum die width for logarithmic spirals is expressed by exp (S ctgx) - 1, where S is the angle in radii that the segment curve sweeps between its starting point and its end point at the die periphery . 29. A die according to claim 26, characterized in that the cohesive pressure P between the segments is expressed by the relationship where H represents an experimentally determinable proportionality factor and r = f () is the representation equation of the effective part of the cross-sectional curve of the segment transversal surfaces, is maximized on the inner wall of the die by mirroring those cross-sectional curves oriented in the counterclockwise direction, for which the cohesive pressure between the segments over a certain initial area O e <emax of the segment curves increases, the expression (f '(e)) 2 + (f (9)) in the same range O # O # Omax is a decreasing function of e and the starting angle assumes values between more than Oo and less than 900 . L e r s e e