Screw elements with improved dispersing action and low energy input

Abstract

The present invention relates to new screw elements for multi-screw extruders with pairs of co-rotating and fully wiping screws.

Claims

1. Screw elements for multiscrew extruders with screws co-rotating in pairs and being fully self-wiping in pairs, wherein the screws comprise screw profiles and sections, and having two or more flights, wherein the screw profiles have continuously differentiable profile contours over the entire cross-sections and comprise at least a generating screw profile and a generated screw profile, wherein each screw profile of the screw profiles is composed of four or more arcs over the entire cross-section that merge tangentially into each other at starting and end points of each arc, and wherein at least one screw profile, selected from the generating screw profile and the generated screw profile, comprises a first arc and a second arc, and wherein a center point of the first arc is located on a line segment that extends from a center point of the second arc to a rightmost end point of the second arc, both the first arc and the second arc share a common line segment that extends from the center point of the first arc to the rightmost end point of the second arc and a leftmost end point of the first arc, a leftmost end point of the second arc is located at a point that corresponds to an inner radius of the screw profile, and a rightmost end point of the first arc is located at a point that corresponds to an outer radius of the screw profile, and wherein both the center point of the first arc and the center point of the second arc are located within a circle having a radius equal to the outer radius of the screw profile and having a center point corresponding to the point of rotation D, and wherein the center point of the first arc is located on a line segment, which starts at the point of rotation D and ends at the point that corresponds to the outer radius of the screw profile, and wherein the center point of the second arc is located on a line segment, which starts at the point of rotation D and ends at the point that corresponds to the inner radius of the screw profile.

2. The screw elements according to claim 1, wherein both the center point of the first arc and the center point of the second arc are located within the screw profile.

3. Screw elements for multiscrew extruders with screws co-rotating in pairs and being fully self-wiping in pairs, wherein the screws comprise screw profiles and sections, and having two or more flights, wherein the screw profiles have continuously differentiable profile contours over the entire cross-sections and comprise at least a generating screw profile and a generated screw profile, wherein each screw profile of the screw profiles is composed of four or more arcs over the entire cross-section that merge tangentially into each other at starting and end points of each arc, and wherein at least one screw profile, selected from the generating screw profile and the generated screw profile, comprises a first arc, a second arc and a third arc, and wherein a center point of the first arc is located on a line segment that extends from a center point of the second arc to a rightmost end point of the second arc, both the first arc and the second arc share a common line segment that extends from the center point of the first arc to the rightmost end point of the second arc and a leftmost end point of the first arc, a center point of the second arc is located on a line segment that extends from a center point of the third arc to a rightmost end point of the third arc, both the second arc and the third arc share a common line segment that extends from the center point of the second arc to the rightmost end point of the third arc and a leftmost end point of the second arc, a leftmost end point of the third arc is located at a point that corresponds to an inner radius of the screw profile, and a rightmost end point of the first arc is located at a point that corresponds to an outer radius of the screw profile.

4. The screw element according to claim 3, wherein the center points of the first arc, the center point of the second arc, and the center point of the third arc are located within a circle having a radius equal to the outer radius of the screw profile and having a center point corresponding to the point of rotation D.

5. The screw element according to claim 3, wherein the center points of the first arc and the center point of the second arc are located within the screw profile.

6. The screw element according to claim 3, wherein the center point of the first arc is located on a line segment, which starts at the point of rotation D and ends at the point that corresponds to the outer radius of the screw profile, and wherein the center point of the third arc is located on a line segment, which starts at the point of rotation D and ends at the point that corresponds to the inner radius of the screw profile.

7. Screw elements for multiscrew extruders with screws co-rotating in pairs and being fully self-wiping in pairs, wherein the screws comprise screw profiles and sections, and having two or more flights, wherein the screw profiles have continuously differentiable profile contours over the entire cross-sections and comprise at least a generating screw profile and a generated screw profile, wherein each screw profile of the screw profiles is composed of four or more arcs over the entire cross-section that merge tangentially into each other at starting and end points of each arc, and wherein at least one screw profile, selected from the generating screw profile and the generated screw profile, comprises a first arc, a second arc, a third arc, and a fourth arc, and wherein a center point of the first arc is located on a line segment that extends from a center point of the second arc to a rightmost end point of the second arc, both the first arc and the second arc share a common line segment that extends from the center point of the first arc to the rightmost end point of the second arc and a leftmost end point of the first arc, a center point of the second arc is located on a line segment that extends from a center point of the third arc to a rightmost end point of the third arc, both the second arc and the third arc share a common line segment that extends from the center point of the second arc to the rightmost end point of the third arc and a leftmost end point of the second arc, a center point of the third arc is located on a line segment that extends from a center point of the fourth arc to a rightmost end point of the fourth arc, both the third arc and the fourth arc share a common line segment that extends from the center point of the third arc to the rightmost end point of the fourth arc and a leftmost end point of the third arc, a leftmost end point of the fourth arc is located at a point that corresponds to an inner radius of the screw profile, and a rightmost end point of the first arc is located at a point that corresponds to an outer radius of the screw profile.

8. The screw elements according to claim 1, wherein the screw elements are dot-symmetrical and the profile contour in a segment of 360/(2.Math.Z) is composed of at least two arcs, wherein Z is the number of flights of the screw elements.

9. The screw elements according to claim 1, wherein the screw elements are axially symmetrical and the profile contour in a segment of 360/(2.Math.Z) is composed of at least two arcs, wherein Z is the number of flights of the screw elements.

10. The screw elements according to claim 9, wherein the profile contour in a section is composed of two arcs which merge into each other in a continuously differentiable manner at point P.sub.FP, wherein point P.sub.FP is located on a straight line FP and the perpendicular to FP at point P.sub.FP passes through the centre points of the two arcs.

11. The screw elements according to claim 10, wherein the screw elements have a point of rotation D, a point P.sub.A which is located on a circle around the point of rotation having an outer radius ra of the screw element, a point P.sub.I which is located on a circle around the point of rotation having an inner radius r.sub.I of the screw element, a straight line DP.sub.A which passes through points P.sub.A and D and a straight line DP.sub.I which passes through points P.sub.I and D, and which, using a Cartesian coordinate system with point D at its origin and point P.sub.A on its x-axis, are characterized in that a vertical line intersects straight line DP.sub.A at the centre point of one of the arcs and the straight line passing through points D and P.sub.I intersects the centre point of the other arc, and in that the straight line FP is located at a distance from the point of rotation which corresponds to half the centre distance a and has a gradient, in terms of radian measurement, of 1/tan(/(2.Math.Z)).

12. The screw elements according to claim 1, wherein the screw elements are designed in the form of mixing elements or conveying elements.

13. The screw elements according to claim 1, wherein the screw elements are designed in the form of kneading elements.

14. A method of using screw elements in a multi-screw extruder, the method comprising providing screw elements including pairs of co-rotating, fully wiping extruder screws according to claim 1, and using the screw elements for conveying, kneading or mixing.

15. The method according to claim 14, wherein the pairs of screw elements wipe each other with a constant intermediate gap over entire peripheries of the pairs of screw elements.

16. The method according to claim 14, wherein the pairs of screw elements wipe each other with an intermediate gap that is not constant over entire peripheries of the pairs of screw elements.

17. The method according to claim 14, wherein the profiles of the pairs of screw elements are shifted in relation to the point of rotation located at a center of a barrel bore.

18. The screw elements according to claim 1, wherein only a single point on the outer radius ra of the generating screw profile wipes a barrel.

19. The screw elements according to claim 1, wherein only one of two tips of each screw fully wipes a barrel.

20. The screw elements according to claim 1, wherein the screws completely wipe each other and only two tips of three tips of each screw wipe a barrel.

21. The screw elements according to claim 1, wherein the screw profiles are shifted within clearances.

22. The screw elements according to claim 20, wherein the screw profiles are shifted within the clearances at an angle greater than 0 and no more than 90.

23. The screw elements according to claim 1, wherein clearances in a range of 0.1 to 0.001, relative to the outer radius ra of a generating screw profile, are present between at least one of (i) screw elements and a barrel and (ii) adjacent screw elements.

24. A method of generating screw profiles of screw elements for multi-screw extruders having pairs of co-rotating and fully wiping screws, whereas the screw profiles have continuously differentiable contours with a centre distance a and two or more flights, wherein entire cross-sections of the screw profiles consist of n/n arcs, wherein n/n is an integer which is greater than or equal to 2, n is the number of arcs of a generating screw profile, and n is the number of arcs of a generated screw profile, and further wherein, in a first step, an outer radius ra of the generating screw profile is selected in such a way that the outer radius ra is greater than 0 (ra>0) and smaller than the centre distance (ra<a), an inner radius ri of the generating screw profile is selected in such a way that the inner radius ri is greater than 0 (ri>0) and smaller than or equal to ra (rira), and, in a second step, the arcs are arranged in succession by determining their position and size in such a manner that all of the arcs of the generating screw profile merge tangentially into each other, the arcs form a closed, convex screw profile, all of the arcs of the generating screw profile are located between and/or on the boundary rings (circles) of an annulus which has the outer radius ra and the inner radius ri, whose centre points are positioned at the point of rotation of the generating screw profile, at least one of the arcs of the generating screw profile touches the outer radius ra of the generating screw profile at point PA and at least one of the arcs of the generating screw profile touches the inner radius ri of the generating screw profile at point PI, wherein the n arcs of the generated screw profile are based on the n arcs of the generating screw profile such that the number of arcs n of the generated screw profile is identical to the number of arcs n of the generating screw profile, the outer radius ra of the generated screw profile equals the difference between the centre distance a and the inner radius ri of the generating screw profile (ra=ari), the inner radius ri of the generated screw profile equals the difference between the centre distance a and the outer radius ra of the generating screw profile (ri=ara), angle aj of the jth arc of the generated screw profile is the same as angle aj of the jth arc of the generating screw profile, wherein j is an index which represents all integers in the range from 1 to the number of arcs n and j is an index which represents all integers in the range from 1 to the number of arcs n, the sum of radius rj of the jth arc of the generated screw profile and radius rj of the jth arc of the generating screw profile equals the centre distance a, wherein j is an index which represents all integers in the range from 1 to the number of arcs n and j is an index which represents all integers in the range from 1 to the number of arcs n, wherein rj is the radius of the jth arc of the generating screw profile, the distance between the centre point of the jth arc of the generated screw profile and the centre point of the jth arc of the generating screw profile equals the centre distance a and the distance between the centre point of the jth arc of the generated screw profile and the point of rotation of the generated screw profile is the same as the distance between the centre point of the jth arc of the generating screw profile and the point of rotation of the generating screw profile, and the connecting line between the centre point of the jth arc of the generated screw profile and the centre point of the jth arc of the generating screw profile is a line parallel to the connecting line between the point of rotation of the generated screw profile and the point of rotation of the generating screw profile, wherein j is an index which represents all integers in the range from 1 to the number of arcs n and j is an index which represents all integers in the range from 1 to the number of arcs n, and the starting point of the jth arc of the generated screw profile lies in an opposite direction in relation to the centre point of the jth arc of the generated screw profile, to that of the starting point of the jth arc of the generating screw profile in relation to the centre point of the jth arc of the generating screw profile, wherein j is an index which represents all integers in the range from 1 to the number of arcs n and j is an index which represents all integers in the range from 1 to the number of arcs n, and wherein at least one screw profile, selected from the generating screw profile and the generated screw profile, comprises a first arc and a second arc, and wherein a center point of the first arc is located on a line segment that extends from a center point of the second arc to a rightmost end point of the second arc, both the first arc and the second arc share a common line segment that extends from the center point of the first arc to the rightmost end point of the second arc and a leftmost end point of the first arc, a leftmost end point of the second arc is located at a point that corresponds to the inner radius of the screw profile, and a rightmost end point of the first arc is located at a point that corresponds to the outer radius of the screw profile, and wherein both the center point of the first arc and the center point of the second arc are located within a circle having a radius equal to the outer radius of the screw profile and having a center point corresponding to the point of rotation D, and wherein the center point of the first arc is located on a line segment, which starts at the point of rotation D and ends at the point that corresponds to the outer radius of the screw profile, and wherein the center point of the second arc is located on a line segment, which starts at the point of rotation D and ends at the point that corresponds to the inner radius of the screw profile.

25. A method of generating screw profiles of screw elements for multi-screw extruders having pairs of co-rotating and fully wiping screws, whereas the screw profiles have continuously differentiable contours with a centre distance a and two or more flights, wherein entire cross-sections of the screw profiles consist of n/n arcs, wherein n/n is an integer which is greater than or equal to 2, n is the number of arcs of a generating screw profile, and n is the number of arcs of a generated screw profile, and further wherein, in a first step, an outer radius ra of the generating screw profile is selected in such a way that the outer radius ra is greater than 0 (ra>0) and smaller than the centre distance (ra<a), an inner radius ri of the generating screw profile is selected in such a way that the inner radius ri is greater than 0 (ri>0) and smaller than or equal to ra (rira), and, in a second step, the arcs are arranged in succession by determining their position and size in such a manner that all of the arcs of the generating screw profile merge tangentially into each other, the arcs form a closed, convex screw profile, all of the arcs of the generating screw profile are located between and/or on the boundary rings (circles) of an annulus which has the outer radius ra and the inner radius ri, whose centre points are positioned at the point of rotation of the generating screw profile, at least one of the arcs of the generating screw profile touches the outer radius ra of the generating screw profile at point PA and at least one of the arcs of the generating screw profile touches the inner radius ri of the generating screw profile at point PI, wherein the n arcs of the generated screw profile are based on the n arcs of the generating screw profile such that the number of arcs n of the generated screw profile is identical to the number of arcs n of the generating screw profile, the outer radius ra of the generated screw profile equals the difference between the centre distance a and the inner radius ri of the generating screw profile (ra=ari), the inner radius ri of the generated screw profile equals the difference between the centre distance a and the outer radius ra of the generating screw profile (ri=ara), angle aj of the jth arc of the generated screw profile is the same as angle aj of the jth arc of the generating screw profile, wherein j is an index which represents all integers in the range from 1 to the number of arcs n and j is an index which represents all integers in the range from 1 to the number of arcs n, the sum of radius rj of the jth arc of the generated screw profile and radius rj of the jth arc of the generating screw profile equals the centre distance a, wherein j is an index which represents all integers in the range from 1 to the number of arcs n and j is an index which represents all integers in the range from 1 to the number of arcs n, wherein rj is the radius of the jth arc of the generating screw profile, the distance between the centre point of the jth arc of the generated screw profile and the centre point of the jth arc of the generating screw profile equals the centre distance a and the distance between the centre point of the jth arc of the generated screw profile and the point of rotation of the generated screw profile is the same as the distance between the centre point of the jth arc of the generating screw profile and the point of rotation of the generating screw profile, and the connecting line between the centre point of the jth arc of the generated screw profile and the centre point of the jth arc of the generating screw profile is a line parallel to the connecting line between the point of rotation of the generated screw profile and the point of rotation of the generating screw profile, wherein j is an index which represents all integers in the range from 1 to the number of arcs n and j is an index which represents all integers in the range from 1 to the number of arcs n, and the starting point of the jth arc of the generated screw profile lies in an opposite direction in relation to the centre point of the jth arc of the generated screw profile, to that of the starting point of the jth arc of the generating screw profile in relation to the centre point of the jth arc of the generating screw profile, wherein j is an index which represents all integers in the range from 1 to the number of arcs n and j is an index which represents all integers in the range from 1 to the number of arcs n, and wherein at least one screw profile, selected from the generating screw profile and the generated screw profile, comprises a first arc, a second arc, a third arc, and a fourth arc, and wherein a center point of the first arc is located on a line segment that extends from a center point of the second arc to a rightmost end point of the second arc, both the first arc and the second arc share a common line segment that extends from the center point of the first arc to the rightmost end point of the second arc and a leftmost end point of the first arc, a center point of the second arc is located on a line segment that extends from a center point of the third arc to a rightmost end point of the third arc, both the second arc and the third arc share a common line segment that extends from the center point of the second arc to the rightmost end point of the third arc and a leftmost end point of the second arc, a center point of the third arc is located on a line segment that extends from a center point of the fourth arc to a rightmost end point of the fourth arc, both the third arc and the fourth arc share a common line segment that extends from the center point of the third arc to the rightmost end point of the fourth arc and a leftmost end point of the third arc, a leftmost end point of the fourth arc is located at a point that corresponds to the inner radius of the screw profile, and a rightmost end point of the first arc is located at a point that corresponds to the outer radius of the screw profile.

26. The method according to claim 24, wherein the tangential transition between the jth and the (j+1)th arc of the generating screw profile is constructed by forming a circle with a radius rj+1 around the end point of the jth arc, and that point of intersection between this circle and a straight line through the centre point and the end point of the jth arc which is located nearer the point of rotation of the generating screw profile is the centre point of the (j+1)th arc.

27. The method according to claim 26, wherein the method is carried out by a computer system.

28. The method according to claim 27, wherein the entire screw elements are constructed virtually in a computer and the construction results are fed to a milling machine for producing the screw elements.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention is illustrated in more detail hereinbelow by means of the figures, without however being limited thereto.

(2) FIG. 1 shows a cross-section of two fully wiping two-flight prior art screw elements arranged at a distance A from each other.

(3) FIG. 2a shows a cross-section of a quarter of the profile of a two-flight fully wiping screw element (a generating screw element).

(4) FIG. 2b shows an example of a profile section of a two-flight screw element according to the invention which consists of three circles.

(5) FIG. 2c shows an example of screw elements according to the invention in which the profile sections depicted by broken lines are not superimposable by axial mirroring on the profile sections depicted by continuous lines.

(6) FIG. 3 shows a special embodiment of screw elements according to the invention is shown as an example in FIG. 3.

(7) FIG. 4 a-d shows examples of profiles of screw elements according to the invention which have gaps (clearances). In FIG. 4a, gap S between the reciprocally wiping screws is equally as large as gap D in the region where the screws wipe the barrel. In FIG. 4b gap S is smaller than D and in FIGS. 4c and 4d the opposite is the case, i.e. D is smaller than S.

(8) FIG. 5 a-d shows that eccentric profiles are also obtained when a screw profile is constructed with gaps and the profiles are then shifted within the gaps.

(9) FIG. 6a shows a thread obtained.

(10) FIG. 6b shows one example of a kneading element with seven kneading discs staggered around the axis at angles of in each case 30.

(11) FIG. 7 is a cross-sectional view of two three-flight screw elements according to the prior art.

(12) FIG. 8 shows a profile section of a three-flight screw element according to the invention.

(13) FIG. 9a shows a generation of profile in which the profile is shifted horizontally towards the right until the righthand screw tip reaches the contour of the barrel.

(14) FIG. 9b-c shows additional arrangements in which one of the three screw tips wipes the barrel are obtained on shifting the profiles at an angle of 20 or 40 in relation to a straight line passing through the points of rotation.

(15) FIG. 9d shows the profile at an angle of 60 in relation to a straight line passing through the points of rotation.

(16) FIG. 10a shows three-flight profiles employed in the form of a continuous conveying thread.

(17) FIG. 10b shows three-flight profiles employed in the form of kneading discs.

(18) FIG. 11 shows a profile section of a four-flight screw element according to the invention which is composed of two segments of circles.

(19) FIG. 12a shows the four-flight profiles in form of a continuous conveying thread.

(20) FIG. 12b shows the four flight profiles in form of a kneading discs.

(21) FIG. 13a depicts a cross-sectional diagrammatic example of a pair of screw elements.

(22) FIG. 13b shows the coordinate values.

DETAILED DESCRIPTION OF THE INVENTION

(23) It is recommendable to use dimensionless parameters in order to simplify the process of applying the method to different extruder sizes. The centre distance a is a useful reference value for geometrical dimensions such as, for example, lengths or radii, since this value cannot be changed in an extruder.

(24) The following rules apply to the figures hereinbelow: The origin of the coordinates x and y is located at the point of rotation of one of the screws. All of the angles are stated in terms of radian measurement. All of the other dimensions are normalized in relation to the centre distance and are written in capital letters: A=a/a; R.sub.j=r.sub.j/a; RA=ra/a; RI=ri/a T=t/a etc. Mx and My are the x and y coordinates of the centre of the circle of a profile-generating arc, R is the radius normalized in relation to the centre distance a and a is the angle of an arc. In addition, RG=the normalized barrel radius, RV=the normalized virtual barrel radius, RA=the normalized outer radius of the fully wiping profile, RF=the normalized outer radius of the screw to be produced, S=the normalized clearance (gap) between the individual screws, D=the normalized clearance between the screw and the barrel, VPR=the normalized degree of shift of the profiles, VPW=the angle of the shift of the profiles in terms of radian measurement, VLR=the normalized degree of shift of the lefthand screw, VLW=the angle of shift of the lefthand screw, VRR=the normalized degree of shift of the righthand screw, VRW=the angle of shift of the righthand screw.

(25) FIG. 1 shows a cross-section of two fully wiping two-flight prior art screw elements arranged at a distance A from each other. The screw elements have the same axially symmetrical profile. The righthand screw element is rotated through an angle of 90 in relation to the lefthand screw element. The points labelled 1-1 are the points of rotation of the shafts on which the screw elements are arranged. The profile depicted is composed of several symmetrical sections. Bends are formed at the transitions between the sections (one of the bends is labelled 1-2). In the region of the tip angle KW the product is subject to a high degree of shear without elongation when multi-screw extruders are operated using such screw elements.

(26) This disadvantage is avoided by a screw element according to the invention with a profile according to FIG. 2. FIG. 2a shows a cross-section of a quarter of the profile of a two-flight fully wiping screw element (a generating screw element). This profile is axially symmetrical to the x and y axes, so that the entire profile would be formed by mirroring the depicted quarter about the x and y axes. The profile of the corresponding (generated) screw element is then formed by rotating the profile of the generating screw element through an angle of 90. The origin of the coordinates is the point of rotation D of the screw in this and all the other figures. The outer radius RA is depicted in the form of a broken circle around the profile. The barrel bore is depicted in the form of a concentric circle around the latter with a radius RG, which exceeds the outer radius by clearance S (RG=RA+S). The screw profile according to FIG. 2a consists of two arcs which merge into each other without a bend. The coordinates of the arcs are shown in FIG. 2a. The centre point M.sub.1 of arc 1 is located on a horizontal line through the point of rotation, and the centre point M.sub.1 of arc 1 is located on a vertical line through the point of rotation (M.sub.1y=0; M.sub.1x=0). The transition from arc 1 to arc 1 takes place at point P.sub.FP, at which both arcs touch straight line FP.

(27) The depicted profile section can be constructed by: fixing a point P.sub.A at a distance from the point of rotation D of the screw element which corresponds to the outer radius RA of the screw element, fixing a point P.sub.I at a distance from the point of rotation D of the screw element which corresponds to the inner radius RI of the screw element, point P.sub.I being located on a straight line DP.sub.I through point D which, together with a straight line DP.sub.A through points P.sub.A and D, encloses an angle of 360/(2.Math.Z), fixing straight line FP at a distance from the point of rotation D which corresponds to half the centre distance A of the screw element, the slope of FP, in terms of radian measurement, being 1/tan((2.Math.Z)), fixing the point of intersection between the tangent T.sub.A at point P.sub.A on the outer circle having radius RA around point of rotation D and the straight line FP and fixing point P.sub.FP on straight line FP at the same distance from the aforesaid point of intersection as P.sub.A and at a distance from the point of rotation which is smaller than that of radius RA, fixing centre point M.sub.1 at the point of intersection between the vertical line to FP beginning at point P.sub.FP and the straight line DP.sub.A, fixing the centre point M.sub.1 at the point of intersection between the vertical line to FP beginning at point P.sub.FP and the straight line passing through D and P.sub.I, generating an arc 1 about centre point M.sub.1 between points P.sub.A and P.sub.FP, generating an arc 1 about centre point M.sub.1 between points P.sub.I and P.sub.FP.

(28) FIG. 2b shows an example of a profile section of a two-flight screw element according to the invention which consists of three circles. Point D is the point of rotation of the screw element (the generating screw element). The point of rotation of the corresponding screw element (the generated screw element) is at a distance A from the point of rotation D. A circle with an inner radius RI (the inner boundary ring) and a circle with an outer radius RA (the outer boundary ring) are depicted around the point of rotation D. The inner circle and the outer circle form an annulus. All of the points of the profile section and the resulting overall profile of the screw element according to the invention are located between or on the inner and outer circles (boundary rings) of this annulus. Point P.sub.A is the starting point of a first arc 1 with radius R.sub.1 and centre point M.sub.1, which is located on the straight line between D and P.sub.A. Point P.sub.A is located on the outer circle. Point P.sub.I is the starting point of arc 3 with a radius R.sub.3=AR.sub.1. Its centre point M.sub.3 is positioned on the vertical line passing through P.sub.I and D. Arc 2 with a radius R.sub.2=A/2 extends with continuous differentiability (i.e. smoothly) between arc 1 and arc 3. Its centre point M.sub.2 is located at a distance (A/2)R.sub.1 from point P.sub.I and at a distance R.sub.3(A/2) from point M.sub.3. By continuously mirroring the depicted profile section about a straight line passing through points D and P.sub.A and about a straight line passing through points D and P.sub.I, the overall profile of the (generating) screw element according to the invention can be constructed. The profile of the corresponding (generated) screw element is in this case obtained simply by rotating the profile of the generating screw profile through an angle of 90 around the point of rotation D.

(29) FIG. 2c shows an example of screw elements according to the invention in which the profile sections depicted by broken lines are not superimposable by axial mirroring on the profile sections depicted by continuous lines. Instead, the profiles are dot-symmetrical in relation to the point of rotation.

(30) A special embodiment of screw elements according to the invention is shown as an example in FIG. 3. It is characterized in that the barrel bores have a larger radius than the outer radius of the screw profiles and the pairs of screw profiles are shifted in relation to the centre points of the barrel bores, while the points of rotation (depicted by small circles) remain in the centres of the barrel bores. This surprisingly produces an additional considerable reduction in energy input. The resulting eccentrically rotating screw elements, i.e. which do not revolve around the centres of their own profiles but around the centre points of the barrel bores, can be shifted freely within the barrel bores. FIG. 3 shows a particularly poignant case where the two profiles are shifted in parallel to the same degree along a straight line passing through the two points of rotation as that to which they are shifted vertically in relation to this line until they touch the barrel contour. As a result, the screws fully wipe each other, although only one of the two tips of each screw in each case fully wipes the barrel. This arrangement provides complete wiping of all of the surfaces while at the same time reducing the energy input.

(31) So far in the present specification only fully wiping screw profiles have been described. In industrially designed extruders it is however necessary to use geometries which are not fully wiping in order to obtain precisely defined gaps during the wiping process. This is necessary to prevent metallic erosion, to cater for manufacturing tolerances and to avoid excessive dissipation of energy in the gaps. Various strategies are possible for producing uniform gaps. The most commonly used strategy is that of producing gaps which are of equal width throughout the longitudinal cross-section of the extruder. The method of producing such screw profiles is described on pages 103 et seq. of Kohlgrber.

(32) The rules for generating screw profiles with specifically defined gaps can be applied to the screw elements according to the present invention.

(33) FIG. 4 shows examples of profiles of screw elements according to the invention which have gaps (clearances). In FIG. 4a, gap S between the reciprocally wiping screws is equally as large as gap D in the region where the screws wipe the barrel. In FIG. 4b gap S is smaller than D and in FIGS. 4c and 4d the opposite is the case, i.e. D is smaller than S.

(34) FIG. 5 shows that eccentric profiles are also obtained according to the invention when a screw profile is constructed with gaps and the profiles are then shifted within the gaps. The profiles of FIGS. 5 a-d are identical to the profile of FIG. 4d. In relation to a straight line through the points of rotation of the screw element the shift takes place at an angle of 0 in FIG. 5a, at an angle of 30 in FIG. 5b, at an angle of 60 in FIG. 5c and at an angle of 90 in FIG. 5d.

(35) FIG. 5 shows examples in which both screws are shifted by the same shift vector. Fundamentally it is also possible to shift both screws by a different vector within the clearances. Profiles are then obtained which wipe each other with an intermediate gap which varies over one revolution of the screws.

(36) As is known, the conveying effect of a pair of profiles is obtained by continuously rotating the profiles in an axial direction. A conveying thread is thereby obtained as shown, for example, in FIG. 6a.

(37) Kneading elements with increased dispersing power compared with the conveying thread are obtained by arranging prismatic discs consisting of self-cleaning profiles in a rotationally staggered relationship to each other around the axis. FIG. 6b shows one example of a kneading element with seven kneading discs staggered around the axis at angles of in each case 30.

(38) FIGS. 1 to 6 relate solely to two-flight screw elements. The same principles can however also be applied to screw elements with three and more flights. FIG. 7 is a cross-sectional view of two three-flight screw elements according to the prior art (see, for example, page 103 of Kohlgrber). The three-flight profile in FIG. 7 consists of three symmetrical sections. Bends and the screw tips between the bends form transitional regions between these sections. In FIG. 7 one of these transitional regions is labelled 7-1. In this region the profile rotates at a narrow distance from the barrel and imposeswith the abovementioned disadvantagespure shear forces on the polymer melt.

(39) In contrast, FIG. 8 shows a profile section of a three-flight screw element according to the invention. Since this profile is axially symmetrical about three straight lines (S1, S2, S3) which are arranged at angles of 60 to each other and pass through the origin of the coordinates, only one 60 section is shown in this figure. The entire profile is formed by continuously mirroring the depicted profile contour about the mirroring straight lines S1, S2 and S3. The profile contour consists of two arcs. The resulting screw has a convergent/divergent channel which imposes on the material to be mixed a combination of shear and elongational flow over its entire periphery. The tangential transition between the profile-producing arcs 1 and 1 takes place at the point at which the profile touches the straight line FP. For three-flight profiles the straight line FP, which is at a distance from the point of rotation of half the centre distance, has a slope of 1.73. The configuration shown in FIG. 8 can be applied analogously to all ratios between the outer screw radius and the centre distance in the range from 0.5 to 0.577.

(40) Eccentrically rotating profiles can be constructed for the three-flight profiles. Such screw profiles are shown in FIGS. 9a-d. This method of construction is similar to that used for the two-flight profiles. The outer radius of the profile is smaller than that of the barrel radius and the profile of pairs of screws is shifted, the point of rotation at the centre of the barrel being maintained. Of particular interest are screw profiles in which the screws completely wipe each other and in which the barrel is only wiped by one of three tips. FIG. 9a depicts the generation of such a profile in which the profile is shifted horizontally towards the right until the righthand screw tip reaches the contour of the barrel. In this arrangement symmetrical screw channels are formed between the profile and the barrel. Additional arrangements in which one of the three screw tips wipes the barrel are obtained on shifting the profiles at an angle of 20 (FIG. 9b) or 40 in relation to a straight line passing through the points of rotation (FIG. 9c). In these profiles the resulting screw channel is asymmetrical. As the shift increases, one region with more intense shear (at the top of FIGS. 9b and 9c) and one region with less intense shear (at the bottom of FIGS. 9b and 9c) is formed. On shifting the profile at an angle of 60 in relation to a straight line passing through the points of rotation (FIG. 9d), an arrangement can be obtained in which two of the three tips wipe the barrel. In this arrangement the asymmetry is at its greatest. Two regions with very intense shear stress (at the top of FIG. 9d) and one region with low shear stress (at the bottom of FIG. 9d) are obtained. The material to be processed is therefore exposed to highly fluctuating degrees of stress, this being helpful for dispersing processes.

(41) The generation of gaps in the reciprocal wiping of the profiles and in the wiping of the barrel is completely analogous to the method used for two-flight profiles.

(42) Three-flight profiles can be employed according to the invention in the form of a continuous conveying thread according to FIG. 10a or in the form of kneading discs according to FIG. 10b.

(43) Axially symmetrical four-flight screw profiles are completely defined by a 45 section of the screw profile. FIG. 11 shows a profile section of a four-flight screw element according to the invention which is composed of two segments of circles. This construction is applied analogously to all ratios between the outer screw radius and the centre distance from 0.5 to 0.541.

(44) The generation of eccentric profiles and the generation of gaps during wiping is similar to that used for two- and three-flight profiles and is not shown in the present case.

(45) The four-flight profiles can be used in the form of a continuous conveying thread according to FIG. 12a or in the form of kneading discs according to FIG. 12b.

(46) Profiles according to the invention with more than four flights can be produced in an analogous manner. The gaps can be varied and eccentric profiles generated in an analogous manner.

(47) FIG. 13a depicts a cross-sectional diagrammatic example of a pair of screw elements according to the invention. The generating screw profile is depicted by the screw profile on the left. The generated screw profile is depicted by the screw profile on the right. Both screw profiles consist of 16 arcs. The arcs of the generating and the generated screw profiles are depicted by thick, continuous lines labelled with the respective arc numbers. The centre points of the arcs are depicted by means of small circles. The centre points of the arcs are connected by thin, continuous lines (boundary lines) to their respective starting and end points. The outer screw radius is the same both for the generating and the generated screw profile. The outer screw radius is depicted by a thin broken line in the region of the screw barrel and by a thin dotted line in the intermeshing zone. Due to the large number of arcs and the generation of the figures by means of a computer program the numbering of individual arcs in some cases overlaps the boundary lines and is therefore difficult to read. Despite the poor legibility of some of the numbers the construction of the profiles is however still clear from the context in conjunction with the present description and the coordinate values in FIG. 13b.

(48) The pair of screw profiles according to the invention shown in FIG. 13a is dot-symmetrical but not axially symmetrical. The straight line FP (shown as a dash-dotted line) does not form a tangent on the arcs. Such a screw element provides particularly high degrees of freedom for the dispersing effect, since the regions upstream and downstream of the tips, which are crucial for the dispersing effect, can be adapted precisely to suit the task at hand without having to make allowances for the geometrical restriction imposed by straight line FP. FIG. 13b lists the x- and y-coordinates of the centre points (Mx and My), the radii R and the angles of all of the arcs of FIG. 13a. The angles are stated in terms of radian measurement; all of the other dimensions are normalized in relation to the centre distance and are therefore dimensionless.