Multi-shaft screw machine comprising a pair of screw elements having an improved mixing and degassing effect with reduced energy input

Abstract

The present invention relates to a pair of screw elements suitable for a multi-shaft screw machine, comprising: m screw shafts SW1 to SWm, which rotate in the same direction and at the same speed and the adjacent rotational axes X1 to Xm of which have an axial spacing A in a cross section at a right angle to the rotational axes; and m circular housing bores, which pass into one another and each have an identical housing bore internal diameter D, and the bore midpoints M1 to Mm of which have a spacing identical to the axial spacing A, and the bore midpoints M1 to Mm of which coincide with the respective associated rotational axes X1 to Xm of the screw shafts SW1 to SWm and with the rotational midpoints P1 to Pm of the screw elements; wherein: the two screw elements of the pair of screw elements are opposite each other on directly adjacent screw shafts; the two screw elements of the pair of screw elements scrape against each other with a screw element clearance s; both screw elements have an asymmetrical screw profile; both screw elements have precisely two flight lands; for each of the two screw elements, the two flight lands thereof have different spacings from the respective rotational midpoint P of the screw profile.

Description

[0001] Multi-shaft screw extruder with a pair of screw elements with improved mixing and degassing effect and reduced energy input

[0002] The subject of the present invention is a pair of screw elements, suitable for a multi-shaft screw machine with m screw shafts SWi to SW rotating in the same direction and at the same speed m , whose adjacent axes of rotation X1 to X m in a cross-section perpendicular to the axes of rotation have an axial distance A and with m interpenetrating, circular housing bores, each having an identical housing bore inner diameter D and whose bore centers M1 to M m have a distance equal to the center distance A, and whose bore centers M1 to M m with the respective rotary axes X1 to X m the worm shafts SWi to SW m and with the centers of rotation P1 to P mof the screw elements coincide, wherein the two screw elements of the pair of screw elements are located opposite each other on immediately adjacent screw shafts, wherein the two screw elements of the pair of screw elements scrape each other with a clearance between screw element and screw element s, wherein both screw elements have an asymmetrical screw profile, wherein both screw elements each have exactly two crests, wherein for each of the two screw elements, its two crests have different distances from the respective center of rotation P of the screw profile, wherein one crest in each case has a distance D / 2 reduced by a clearance between screw element and housing wall 5 and further reduced by an additional gap SP from the respective center of rotation P and the other crest has a distance D / 2 reduced by a clearance between screw element and housing wall 5, but not reduced by an additional gap SP, from the respective center of rotation P,where the clearance between the screw element and the casing wall 5 is the same for both screw elements and the additional gap SP is the same for both screw elements, where the sum of the crest angles of both screw elements BKW in radians is the equation,

[0003] BKW = ƒ * BKGW (1) where the factor ƒ is greater than 0 and less than or equal to 0.95, where BKGW is determined by:

[0004]

[0005] The parameters required to represent a screw profile are listed below in Table 1.

[0006] WO 2011 / 006516A1 discloses an extruder having a housing with at least two axially parallel shafts which can be driven in the same direction and are provided with at least two-flight conveying elements which mutually wipe off each other at an axial distance with little play over the entire circumference, wherein a distance (a) exists between the crest of the at least one further flight and the inner wall of the housing.

[0007] A multi-shaft screw extruder is known from EP0875356A2. The multi-shaft screw extruder is provided with a housing, two parallel, partially interpenetrating housing bores, two rotatably driven shafts arranged in the housing bores, screw elements mounted on the shafts in a rotationally fixed manner, and intermeshing kneading discs mounted on the shafts in a rotationally fixed manner. The kneading discs are each narrowed in their crest areas relative to the disc width (B) to form peripherally located mixing and scraping pins.

[0008] Furthermore, DE 10 2008 016862 A1 discloses an extruder with at least two axially parallel shafts which can be driven in the same direction and which has at least two-threaded conveying elements (2, 11, 12) which are in essentially tight contact at one point (C).

[0009] EP 0 788 868 A1 describes a method and apparatus for mixing thermoplastic material with continuous rollers. The apparatus comprises a mixing chamber and at least one pair of threaded shafts arranged within the mixing chamber (5), the threaded shafts having at least one tip portion of the thread and at least one core portion of the thread that are asymmetrically countersunk with respect to the longitudinal axis of the shaft to create surfaces of the shafts and an empty space between the countersunk threaded portion and the inner surface of the chamber to perform rolling of the material on at least a portion of the surface of the chamber itself during the feeding of the material to the outlet of the mixing chamber.

[0010] Furthermore, WO 2016 / 107527 A1 discloses a self-cleaning extrusion device with two co-rotating screws. The device consists of a screw mechanism, a barrel, a feed opening, a vent opening, and an outlet opening.

[0011] For the purposes of the present invention, a multi-screw extruder is understood to mean a screw extruder with more than one screw shaft, for example, a screw extruder with two, three, or four screw shafts or an extruder with eight to sixteen, in particular twelve, screw shafts arranged in a ring. With more than two screw shafts, the axes of rotation of the screw shafts can be arranged side by side or, for example, as in a so-called ring extruder, in a ring to one another. In multi-screw extruders, the axes of rotation of the screw shafts are generally arranged parallel to one another. This parallel arrangement of the axes of rotation is also preferred according to the invention. The screw elements of the pair of screw elements according to the invention are preferably arranged directly opposite one another on the screw shafts in a number corresponding to the number of screw shafts of the respective extruder.Such a screw extruder with more than one screw shaft is also referred to below as a multi-screw extruder, multi-screw extruder, or multi-screw extruder. A twin-screw extruder is also referred to below as a twin-screw extruder. For the purposes of the present invention, the term "screw extruder" is used synonymously with the term "extruder." An extruded or to-be-extruded mass is also referred to below as the "extrudate."

[0012] Preferably, the multi-screw extruder is a twin-screw extruder with two screw shafts SWi to SW2 rotating in the same direction and at the same speed, with adjacent axes of rotation X1 and X2, bore centers M1 and M2 and centers of rotation P1 and P2.

[0013] In the context of the present invention, an extrudate is a plastic or viscoelastic mass, in particular selected from the group comprising the members: suspensions, pastes, glass melts, unfired ceramics, metal melts, or plastics.

[0014] For the purposes of the present invention, plastics are understood to mean in particular: polymers, in particular polymer melts or polymer solutions, in turn in particular melts or solutions of thermoplastic polymers or melts or solutions of elastomers, in particular rubbers.

[0015] As a thermoplastic polymer, at least one from the group consisting of polycarbonate, polyester carbonate, polyamide, polyester, in particular polybutylene terephthalate and polyethylene terephthalate, polylactide, polyether, thermoplastic polyurethane, polyacetal, fluoropolymer, in particular polyvinylidene fluoride, polyether sulfones, polyolefin, in particular polyethylene and polypropylene, polyimide, polyacrylate, in particular poly(methyl) methacrylate, polyphenylene oxide, polyphenylene sulfide, polyether ketone, polyarylether ketone, styrene polymers, in particular polystyrene, styrene copolymers, in particular styrene-acrylonitrile copolymer, acrylonitrile-butadiene-styrene block copolymers, and polyvinyl chloride is preferably used. Also preferred are so-called blends of the listed polymers, which the person skilled in the art understands to be a combination of two or more polymers.Particular preference is given to polycarbonate and mixtures containing polycarbonate, very particular preference being given to polycarbonate, for example obtained by the interfacial process or the melt transesterification process.

[0016] The rubber used is preferably at least one from the group consisting of styrene-butadiene rubber, natural rubber, butadiene rubber, isoprene rubber, ethylene-propylene-diene rubber, ethylene-propylene rubber, butadiene-acrylonitrile rubber, hydrogenated nitrile rubber, butyl rubber, halobutyl rubber, chloroprene rubber, ethylene-vinyl acetate rubber, polyurethane rubber, thermoplastic polyurethane, gutta-percha, arylate rubber, fluororubber, silicone rubber, sulfide rubber, and chlorosulfonyl polyethylene rubber. A combination of two or more of the listed rubbers, or a combination of one or more rubbers with one or more other plastics, is of course also possible.

[0017] These thermoplastics or rubbers can be used in pure form or as mixtures with fillers and reinforcing materials, such as glass fibers in particular, as mixtures with each other or with other polymers or as mixtures with conventional polymer additives.

[0018] In a preferred embodiment, additives are added to the plastic masses, especially polymer melts and mixtures of polymer melts. These additives can be added to the extruder as solids, liquids, or solutions together with the polymer, or at least some or all of the additives are fed to the extruder via a side stream.

[0019] Additives can impart a wide variety of properties to a polymer. These can include, for example, colorants, pigments, processing aids, fillers, antioxidants, reinforcing agents, UV absorbers and light stabilizers, metal deactivators, peroxide scavengers, basic stabilizers, nucleating agents, benzofurans and indolinones acting as stabilizers or antioxidants, mold release agents, flame-retardant additives, antistatic agents, colorants, and melt stabilizers. Examples of these include carbon black, glass fiber, clay, mica, graphite fiber, titanium dioxide, carbon fiber, carbon nanotubes, ionic liquids, and natural fibers.

[0020] For the purposes of the present invention, an asymmetrical screw cross-sectional profile is characterized in that there is no mirror axis or rotation axis through any point in the plane of the screw cross-sectional profile with which a screw cross-sectional profile congruent with an initial screw cross-sectional profile can be generated; preferably, there is no mirror axis through any point within a screw cross-sectional profile, particularly preferably no mirror axis through the design center KP of a screw cross-sectional profile with which a profile congruent with the initial profile can be generated. The design center KP is the point within the screw cross-sectional profile that is the center of all circular arcs that form crests and grooves. For the purposes of the present invention, the design center KP of a screw profile coincides with the rotation center P of this screw profile.For example, EP 0002131 A1, Fig. 5 (A) or Fig. 5 (B), shows the screw profiles of a pair of screw elements that are asymmetrical within the meaning of the present invention. The screw profiles of a pair of screw elements shown in EP 0002131 A1, Fig. 5 (A) or Fig. 5 (B), furthermore have the property that they are not congruent, but can be converted into one another by axial reflection and rotation.

[0021] A screw cross-sectional profile, also referred to as a screw profile in the context of this invention, is understood to be the outer contour of a screw element in a flat section perpendicular to the screw element's axis of rotation. Rules for generating precisely scraping screw profiles are presented, for example, in [1] ([1] = Klemens Kohlgrüber: "Der gleichläufige Doppelschneckenextruder", 2nd edition, Hanser Verlag Munich 2016) on pages 107 to 120. It is also described there that a predetermined screw profile on a first shaft of a twin-screw extruder determines the screw profile on a second shaft of the twin-screw extruder, which is immediately adjacent to the first shaft ([1], page 108). The screw profile on the first shaft is therefore referred to as the generating screw profile.The screw profile on the second screw shaft follows from the screw profile of the first screw shaft of the twin-screw extruder and is therefore referred to as the generated screw profile. Co-rotating twin-screw extruders, whose screw shafts precisely scrape off each other, have been known for a long time, e.g., from DE 862 668 C. In polymer production and processing, screw extruders with screw shafts, whose screw elements are based on the principle of precisely scraping screw cross-sectional profiles, have been widely used. This is primarily due to the fact that polymer melts adhere to surfaces and degrade over time under normal processing temperatures. This is prevented by the self-cleaning effect of pairs of screw elements precisely scraping off each other in multi-screw extruders.In a multi-screw extruder, the screw element with the generating screw profile and the screw element with the generated screw profile are always used alternately on adjacent shafts.

[0022] A distinction must be made between two things here: the precisely scraping screw profile, a mathematical construct in which two screw elements, which are located opposite one another on two immediately adjacent screw edges, scrape each other with a screw element-to-screw element clearance which tends towards zero, and screw profiles for screw elements which are actually used as intended, i.e. technically designed screw elements. If the term “precisely scraping” is used in the context of the present invention, this means – unless otherwise stated – the mathematical construct of a precisely scraping screw profile or the corresponding screw element having this screw profile. If the term “practically scraping” or “designed” is used in the context of the present invention, this means – unless otherwise stated – the technically designed screw element orits snail profile, whereby this practically scraping snail profile was derived from an exactly scraping snail profile, preferably by applying one of the game strategies center distance enlargement, longitudinal section equidistant, spatial equidistant or circular equidistant, as explained in more detail below.

[0023] A specialist in the field of screw elements naturally understands that a single screw element or screw profile cannot be exactly scraping or practically scraping on its own, but that a pair of such elements is always required.

[0024] Modern extruders have a modular system in which various screw elements can be mounted on a core shaft to form a screw shaft. Such a screw shaft is therefore segmented. This allows the expert to adapt the extruder to the respective process task. However, a screw shaft can also be made from a single piece, i.e., have only one screw element that extends essentially over the entire length of the screw shaft, or be only partially segmented. The present invention relates both to screw elements that can be mounted on a core shaft and to the screw shafts made from a single piece as described above.

[0025] Multi-screw extruders, especially twin-screw extruders, are known to introduce mechanical energy into the extrudate through dissipation. This has both desirable and undesirable consequences. This energy input is necessary to perform process-related tasks such as mixing and venting, while the introduced mechanical energy is consumed and also leads to temperature increases in the extrudate, which can lead to undesirable chemical reactions that damage the extrudate.

[0026] Mixing is also a basic operation in multi-screw extruders, especially twin-screw extruders. Inhomogeneities in the extrudate due to incomplete mixing are known to lead to problems in further processing of the extrudate and in the final properties.

[0027] Likewise, degassing, i.e., the removal of volatile components, is known to be a basic operation on multi-screw extruders, especially twin-screw extruders, as described, for example, in [1], pages 494 to 525. For degassing processes, the highest possible degassing efficiency with low energy input is desirable in order to achieve high, economical throughputs and good extrudate quality. Such processes are described, in addition to [1], for example, in WO2010139413A1 [2], which describes an apparatus and method for degassing solvent-containing polycarbonate solutions.

[0028] For devolatilization, a polymer is transported as an extrudate in a partially filled section past a devolatilization opening. Volatile components such as by-products resulting from polycondensation reactions, monomers, oligomers, solvents, or polymer degradation products can be removed through the opening under the influence of temperature, water, oxygen, or other components. To improve the removal of volatile components, the pressure in the devolatilization opening is reduced compared to the ambient pressure, depending on the devolatilization task. [1], pages 494 to 525, also describes that bubble formation and thus foaming of polymer melts is useful for residual devolatilization because it creates an internal surface that improves mass transfer. Foaming requires a sufficiently high overpressure of volatile components in the polymer, approximately 1 bar.By applying shear to the polymer, bubble formation can be promoted, thereby improving the devolatilization effect. The extrudate in a twin-screw extruder is known to be sheared particularly strongly between a screw crest and the inner wall of the extruder barrel bore. This is where a particularly large amount of energy is dissipated into the extrudate, leading to strong local overheating in the extrudate. This is shown, for example, in [1] on pages 416 to 423, Figures 4.80 to 4.84. This local overheating can cause damage to the extrudate, such as changes in odor, color, chemical composition or molecular weight, or to the formation of inhomogeneities in the extrudate, such as gel bodies or specks. A large crest angle, and in particular a large sum of the crest angles of a pair of screw elements that are located opposite each other on directly adjacent screw shafts and thereby scrape each other, is harmful in this regard.

[0029] A contradiction now arises between the requirements of degassing or dispersion, both of which require shearing, and the avoidance of extrudate damage. It would be advantageous to combine the requirements of degassing or dispersion with those of extrudate protection in such a way that optimum degassing or dispersion is achieved with minimal damage to the extrudate. Furthermore, it is neither beneficial for degassing nor for dispersion if the same proportion of the total extrudate is sheared over and over again, because the extrudate exchange on the inner wall of the barrel bore of an extruder is minimal.

[0030] The problem of extrudate damage and energy input can be solved, for example, as in WO2009152973A1 [3], in which screw elements for multi-shaft screw machines with pairs of co-rotating and pairs of precisely scraping screw shafts, with two or more screw flights Z, with center distance A and outer diameter DE, where the sum of the crest angles of a screw element pair is greater than 0 and smaller than and their use are described. Such screw elements are also preferably used in the extruders disclosed in [2]. However, the use of such screw elements does not improve the degassing effect.

[0031] US 4131371 A [4] describes eccentric, mutually scraping conveying screw elements that rotate in the same direction, with eccentric profiles whose crests are at different distances from the barrel. This achieves a uniform loading of the extrudate by spreading it along the wall, providing more surface area for heat and mass transfer. This may potentially improve the degassing effect. The aspect of wide crests and the associated disadvantages is not addressed.

[0032] EP 0002131 A1 [5] describes eccentric, asymmetrical, mutually scraping screw elements, in which each crest of a respective screw element has a smaller distance to the inner wall of the barrel bore of an extruder than the other crest(s) of the respective screw element. The main effect described there is the exchange of material between the barrel bores of the extruder and a uniform, intensive shear. These screw elements have Z crests and Z grooves for Z ≥ 2 flights. The clearance between screw element and screw element s - i.e. the distance between the screw profiles of the screw elements of a pair of screw elements that are opposite each other on two directly adjacent screw shafts - is not taken into account.

[0033] From [5] it can be deduced that the sum of the crest angles S WO of each screw element of a pair of screw elements, in which the two screw elements scrape each other exactly , whereby numerous mathematically equivalent formulations are possible.

[0034] It is known to those skilled in the art, and is stated, for example, in [1], on pages 39 to 41 and on pages 113 to 121, that technically designed screw elements must have clearances - both the screw element-screw element clearances and the screw element-barrel wall clearances 5 - in order to ensure the functionality of the extruder. This is necessary to avoid metallic "seizure", manufacturing tolerances, roughness, angular deviations, uneven thermal expansion and excessive extrudate stress caused by insufficient spacing between two screw elements that are directly adjacent to each other on two directly adjacent screw shafts. The aforementioned pages also explain methods for determining the exact geometry of the element to be manufactured from the clearances and the precisely scraping contour. These methods are called clearance strategies.

[0035] The longitudinal equidistant, circular equidistant, and spatial equidistant game strategies are also referred to below as the longitudinal equidistant calculation rule, circular equidistant calculation rule, and spatial equidistant calculation rule. Another game strategy is the increase in the center distance according to [1], pages 40 and 41.

[0036] The spatial equidistant is mentioned, for example, in [1], pages 40 and 41. A spatial equidistant can, for example, be calculated starting from a parametric representation of the outer surface of an exactly scraping screw element, where a and b are parameters to be selected according to the equation with which the outer surface of the respective screw element is exactly scraping screw element. The following describes some examples of what such a parameter representation might look like.

[0037] For the following considerations, a Cartesian coordinate system is assumed, in which the coordinate along the axis of rotation of the extruder is denoted as z and x and y are the coordinates in the plane perpendicular to the axis of rotation, which intersects this plane at x = 0, y = 0 and z = 0:

[0038] For example, in a pair of screw elements, where the two screw elements are located opposite each other on two immediately adjacent screw shafts and scrape each other exactly, the screw profile of each of the two screw elements in the x - y plane, with the respective axis of rotation X coinciding with the z-axis, and the distance to the axis of rotation r e (γ) is given as a 2 π periodic function of the screw profile of the angle y to the x-axis, by a representation of the exactly scraping screw element profile according to the following equation (5) In such a case, a = y and b = z can be chosen.

[0039] Such a pair of screw elements can, for example, be formed as a pair of conveying elements or as a pair of kneading discs.

[0040] To construct conveyor elements, the screw profile is continued helically in space to obtain the limiting surface of a precisely scraping screw element. For a screw element with pitch T, with the z-coordinate as an additional parameter,

[0041] The positive sign represents a right-turning screw profile, the negative sign represents a left-turning screw profile.

[0042] In kneading discs, the screw profile is shifted into space along the z-axis so that results.

[0043] If a screw profile, for example a precisely scraping screw profile, is constructed in the plane sectionally over circular arcs i with the center coordinates and the radius and β is an angle for whose valid values ​​the circular arc represents an exactly scraping screw profile, then the circular arc can be defined by For the representation of a limiting surface of a precisely scraping conveyor element in space, the following applies: and for the representation of a limiting surface of a precisely scraping kneading disc according to

[0044] For a conveyor element, the pitch T of a screw element is the axial length required for one complete rotation of the screw profile of the screw element. When calculating a screw profile, in which the spatial equistant calculation rule is applied, starting from a pair of screw elements with exactly scraping screw profiles, to determine the screw profiles of a pair of practically scraping screw elements, taking into account the clearance between screw element and screw element s, the following procedure can be followed, for example, after defining a parameter representation r: the corresponding normal vector formed, where the sign is chosen so that away from the axis of rotation. The outer surface of the technically designed screw element to be manufactured is then determined by the Parameter representation

[0045] Further spatial equidistant calculation rules may also be possible according to the invention.

[0046] The method of circular equidistants also assumes a precisely scraping screw profile in the plane. Starting from the precisely scraping screw profile in the x-y plane, a perpendicular is drawn at each point, with the direction of the perpendicular being chosen so that it points into the interior of the screw profile. The point that is shifted by s / 2 along this perpendicular into the interior of the screw profile then belongs to the technically executed screw profile. If a section of a precisely scraping screw profile is a circular arc with radius r i the corresponding section of the corresponding technically designed screw profile is a circular arc with the same center point and the radius

[0047] This is a circular equidistant calculation rule within the meaning of the present invention. Further circular equidistant calculation rules are also possible according to the invention.

[0048] When using the methods of longitudinal equidistant, spatial equidistant, and circular equidistant, overlaps of different surface curves of the technically implemented screw profile to be manufactured may occur, so that for a specific angle starting from the center of rotation P of the screw profile, several points on the screw profile curve are available for selection. To manufacture the screw profile for the technically feasible screw profile, the point that is closer to the center of rotation P is then used. Various forms can be used to represent the technically implemented screw profile to be manufactured, for example, tables of coordinates. A preferred method is to specify the distance to the axis of rotation r(y) as a 2 π or 360° periodic function of the angle γ to the x-axis by representing

[0049] All of the methods mentioned also result in a slight increase in the flank angle and a reduction in the crest angle(s) compared to the flank angles and crest angle(s) of the precisely scraping screw profile. Applying the spatial equidistant method always results in smaller crest angles than applying the longitudinal equidistant method, and this method always results in smaller crest angles than applying the circular equidistant method. For larger pitches, the crest angle becomes larger for spatial and longitudinal equidistant; for a pitch approaching infinity, the spatial and longitudinal equidistant approaches the circular equidistant. This means that for a pitch approaching infinity, the spatial and longitudinal equidistant calculation rules produce the same crest angle as the circular equidistant calculation rules.

[0050] All methods for determining the technically implemented geometry of screw profiles based on a precisely scraping screw profile – i.e., the game strategies – reduce the size of the screw element compared to a screw element with this precisely scraping screw profile in order to obtain the actually technically feasible geometry of a screw element: a gap arises between the precisely scraping screw profile and the technically implemented, practically scraping, screw profile. A game strategy is used to determine the screw element-to-screw element clearance s, i.e., the distance between the screw profiles of a pair of screw elements that are opposite each other on two directly adjacent screw shafts. This screw element-to-screw element clearance s between these two screw elements does not have to be constant, but it is preferably constant.

[0051] To produce a constant clearance between screw element and screw element s during mutual scraping of the screw elements, the spatial equidistant is preferred as explained above.

[0052] Large screw element-to-screw element clearances reduce the energy input into the extrudate by lowering shear. However, excessive screw element-to-screw element and screw element-to-barrel clearances also have disadvantages in technically designed extruders. They lead to reduced scraping of screw elements that are positioned opposite each other in pairs on directly adjacent screw shafts and impaired extrudate exchange on the screw elements or the barrel bore. This increases the risk of extrudate damaged by long residence times entering the extrudate stream. This can lead to specks, gels, or discoloration, which in turn impairs the quality of the desired end product.Excessively large clearances between screw element and screw element s and screw element and barrel δ also lead to reduced degassing and a reduced mixing effect due to reduced extrudate exchange on the screw surfaces or on the barrel bore inner wall.

[0053] In addition, the influence that can be exerted on the sum of the crest angles via screw element-screw element clearances is limited.

[0054] In addition to the screw profile, as is known to those skilled in the art, other parameters play a role in the geometry of a screw element. These are listed, for example, in [1] on page 115.

[0055] As shown above, the state of the art does not provide a solution to the problem of how to achieve good degassing of the extrudate in an extruder, which requires high shear, and at the same time avoid damage to the extrudate due to excessive energy input, which is a consequence of the high shear, whereby in addition, on the one hand, the extrudate exchange on the inner wall of the barrel bore of an extruder is increased, because otherwise the degassing of the extrudate is only low, and on the other hand, a good mixing effect and dispersion can be achieved.

[0056] A good mixing effect is necessary for effective degassing, as degassing primarily occurs from the surface of the extrudate, and fresh, not yet degassed extrudate must be transported there to enable further degassing. Furthermore, the degassed extrudate should also be as homogeneous as possible, which requires a uniform energy input and the avoidance of local overheating.

[0057] As is known to those skilled in the art and explained, for example, in [1] on pages 475 to 478, there is a particularly high shear stress in the area of ​​the combs near the inner wall of the barrel bore, which is beneficial for dispersion. This plays a particularly important role in the dispersing of solid agglomerates used as fillers or reinforcing materials, which is another basic operation on extruders. Frequent replacement of the sheared material is therefore also beneficial for the dispersing effect, as is known to those skilled in the art. However, in [1] on page 478, reference is only made to a reduced throughput as a method for better dispersion, which is not preferred for reasons of cost-effectiveness. The object of the present invention is therefore to ensure good devolatilization of an extrudate in an extruder and at the same time - by low energy input - to avoid damage to the extrudate.A further object of the present invention is to additionally ensure good dispersion.

[0058] In particular, the object of the present invention is to provide a pair of screw elements that ensures good degassing of an extrudate in an extruder while simultaneously avoiding damage to the extrudate. The pair of screw elements should also achieve good dispersion and mixing. Damage to the extrudate should preferably be avoided by the pair of screw elements ensuring reduced energy input into the extrudate without impairing the degassing of the extrudate.

[0059] Surprisingly, the problem is solved by a multi-shaft screw machine with the features of the main claim.

[0060] In particular, the object is further achieved by a method according to claim 12.

[0061] In the context of this invention, the following applies:

[0062] A screw profile is a closed, convex curve. It consists of several distinct curves, which – depending on their geometric properties – are referred to as a "crest," a "flank," or a "groove."

[0063] The radius of curvature of the screw profile is less than or equal to the center distance at every point and greater than or equal to zero. A radius of curvature of zero is equivalent to a kink in the screw profile.

[0064] A kink is a point on a screw profile where, starting from a parameter representation, with the arc length l as a parameter for a parameter value l kholds that the left-valued and right-valued limit for the values ​​of the functions x(l) and y(l) are the same (this is identical to the property that the curve is closed at this point), so and the direction vectors of the derivatives of the curve with respect to the arc length l do not point in the same direction, so their cross product does not vanish:

[0065] In the case where two circular arcs within a screw profile do not merge tangentially, the kink is located at the intersection of the two circular arcs. It is possible to treat a kink as a circular arc with the center point equal to the intersection of the two circular arcs and with a radius of zero; this is how it is done in the examples.

[0066] A curve is a continuous line of length greater than zero but with no width, where a curve has a first endpoint and a second endpoint that are not the same point; that is, the first endpoint does not coincide with the second endpoint.

[0067] A curve can be composed of several, finitely many curve segments, wherein a first curve segment has a common point of contact with a second curve segment that is immediately adjacent to the first curve segment.

[0068] However, a curve can also consist of exactly one curve section.

[0069] A curve may only have a finite number of kinks, which, by definition, can only occur at the common point of contact between two immediately adjacent curve segments. A kink may also be located at the common point of contact between two immediately adjacent curve segments.

[0070] A curve segment is a portion of a curve, the curve segment having a first endpoint and a second endpoint that are not the same point; that is, the first endpoint does not coincide with the second endpoint.

[0071] A curve segment is preferably selected from the group comprising the following members: circular arc, elliptical arc, parabolic arc, or a spline or a section of a spline, result of the application of the longitudinal equidistant calculation rule according to [1], pages 117 to 121 to a circular arc, elliptical arc or parabolic arc, or to a spline or to a section of a spline, result of the application of the spatial equidistant calculation rule to a circular arc, elliptical arc or parabolic arc, or to a spline or to a section of a spline, or result of the application of the circular equidistant calculation rule to a circular arc, elliptical arc, parabolic arc, or to a spline or to a section of a spline. In this case, a curve segment is also defined as a line which, in a parametric representation of its arc length l, can be represented and at the x k,l (l) and y k,l(l) are analytic functions and x and y are the coordinates of the line in the plane, and thus representable by infinite power series, continuous, arbitrarily differentiable and thus kink-free.

[0072] A section is either a curved section or a bend.

[0073] A closed, convex curve is a continuous line with a non-zero length but no width, composed of one or more curve segments, each of which is in turn composed of one or more curve segments. It has no distinct starting or end point. Starting from any point on the curve, the length of the curve can be determined by adding the lengths of the curve segments once around the curve. Every tangent to a closed, convex curve lies outside the region enclosed by the curve.

[0074] Since all curve sections of a screw profile are located in one plane, a closed curve, which is a screw profile, divides the area of ​​this plane into an area inside the closed curve and an area outside the closed curve.

[0075] A circular arc is a segment of a curve in which all points on the arc are the same distance, called the radius, from a common center. A circular arc has a starting point and an end point, which are not the same point.

[0076] A circular arc is considered a circular arc only if and only if all points of this circular arc have the same center and the same radius, and the points of this circular arc form a continuous curved segment. That is, two immediately adjacent circular arcs that share a common point of contact are considered two circular arcs only if they have a different center or a different radius. According to the invention, only circular arcs with a center angle smaller than π in radians are used.

[0077] A circular arc Z is characterized by the coordinates of its center xm i and ym i by its radius r i , by its initial angle β a,i and its central angle α i , where the valid values ​​for the angle β in formula (10) are between β a,i - and β e,i = β a,i + α i (18) lie.

[0078] The center of rotation P of a screw profile is the intersection point of the rotational axis X of a screw element with the cross-sectional plane perpendicular to this rotational axis. The center of rotation P of the screw profile, hereinafter also referred to as the pivot point P or pivot point, also coincides with the bore center M of the housing bore in which the respective screw element is located or for which the respective screw element is designed.

[0079] In relation to a screw profile, a pivot point P is the point around which a screw profile rotates as a cross-sectional image of a screw element.

[0080] A crest is a curve of a screw profile in which all points of this curve, except for the points of contact with the two curve segments immediately adjacent to the crest, are at a greater distance from the pivot point P than the two curve segments immediately adjacent to the crest. According to the invention, the curve forming a crest is precisely one curve segment that is precisely a circular arc with the pivot point P of the screw profile as its center.

[0081] According to the invention, all crests of a screw profile are preferably formed by exactly one circular arc, each of which has the pivot point P of the screw profile as its center.

[0082] The crest radius is the distance of the respective crest from the pivot point P of a screw profile.

[0083] A groove is a curve of a worm profile in which all points of this curve, except for the common contact points with the two curve sections immediately adjacent to the groove, have a smaller distance from the pivot point P than the two curve sections immediately adjacent to the groove.

[0084] According to the invention, the curve forming a groove is exactly a curve section that is exactly a circular arc with the pivot point P of the screw profile as the center.

[0085] According to the invention, all grooves of a screw profile are preferably formed by exactly one circular arc, each of which has the pivot point P of the screw profile as its center.

[0086] A flank is a curve of a worm profile between a crest and a groove that is convex to the center of rotation P, whereby this flank has a common point of contact with the crest and with the groove.

[0087] A flank can be a single curve segment or composed of several curve segments. The radius of curvature of a flank is less than or equal to the center distance A at every point, preferably less than the center distance A.According to the invention, the mathematical expressions underlying a curved section of a flank are preferably selected from the group of mathematical expressions comprising the following members: circular arc, result of the application of the longitudinal section equidistant calculation rule according to [1], pages 117 to 121 to a circular arc with a radius of curvature less than the center distance A or equal to the center distance A of an exactly shaving screw profile composed only of circular arcs, result of the application of the spatial equidistant calculation rule to a circular arc with a radius of curvature less than the center distance A or equal to the center distance A of an exactly shaving screw profile composed only of circular arcs and result of the application of the circular equidistant calculation rule to a circular arc with a radius of curvature less than the center distance A or equal to the center distance A of an exactly shaving screw profile composed only of circular arcs.

[0088] Components of the pair of screw elements according to the invention or the associated screw profiles can be provided with index symbols such as n, m, or i, or also with natural numbers in order to be able to distinguish these components from one another if these components can occur multiple times.

[0089] Furthermore, within the scope of the present invention, the following shall apply:

[0090] Table 1: Parameters for representing a screw profile

[0091] If, within the scope of this description, it is stated that a value is "selected" for a variable, as is the case, for example, with the pitch T, the clearance between the screw element and the barrel wall 8, the clearance between the screw element and the screw element s, or the additional gap SP, this does not mean that any arbitrary value can be assigned to this variable if screw profiles are to be obtained for a pair of screw elements that are to be used as intended. A person skilled in the art of designing screw elements for extruders can estimate or determine through CFD simulations which values ​​should reasonably be assigned to these variables for a given extruder, depending, for example, on the viscosity of the extrudate at the processing temperature, the desired degree of filling of the extruder, the desired energy input into the extrudate, or the speed of the shafts.Especially if such a value was obtained by estimation, it is usually necessary to confirm it or determine it more precisely through simulations; this is usually done iteratively. By selecting the additional gap SP, the mass transfer at the inner wall of the casing and the mixing effect can be adjusted. By appropriately selecting S, the maximum shear can be adjusted, and ƒ can be used to adjust the crest angle and thus the length over which the maximum shear should act between the crest and the casing.

[0092] (1) In particular, the objects are achieved according to a first embodiment of the invention by: a pair of screw elements, suitable for a multi-shaft screw machine with m screw shafts SWi to SW rotating in the same direction and at the same speed m , whose adjacent axes of rotation X1 to X min a cross-section perpendicular to the axes of rotation have an axial distance A and with m interpenetrating, circular housing bores, each having an identical housing bore inner diameter D and whose bore centers M1 to M m have a distance equal to the center distance A, and whose bore centers M1 to M m with the respective rotary axes X1 to X m the worm shafts SW1 to SW m and with the centers of rotation P1 to P mof the screw elements coincide, wherein the two screw elements of the pair of screw elements are located opposite each other on immediately adjacent screw shafts, wherein the two screw elements of the pair of screw elements scrape each other with a clearance between screw element and screw element s, wherein both screw elements have an asymmetrical screw profile, wherein both screw elements each have exactly two crests, wherein for each of the two screw elements, its two crests have different distances from the respective center of rotation P of the screw profile, wherein one crest in each case has a distance D / 2 reduced by a clearance between screw element and housing wall 5 and further reduced by an additional gap SP from the respective center of rotation P and the other crest has a distance D / 2 reduced by a clearance between screw element and housing wall 5, but not reduced by an additional gap SP, from the respective center of rotation P,where the clearance between the screw element and the casing wall 5 is the same for both screw elements and the additional gap SP is the same for both screw elements, where the sum of the crest angles BKW of the crests of both screw elements is greater than 0 in radians and for the factor ƒ with ƒ = BKW / BKGW (19) the factor / is greater than 0 and less than or equal to 0.95, where BKW is the sum of the crest angles in radians of both screw elements and BKGW is determined by:,

[0093] Equal clearances between screw element and housing wall 8 or equal additional gap SP have the advantage of a uniform energy input.

[0094] (2) Preferably, / is greater than or equal to 0.1 and less than or equal to 0.8, and more preferably, f is greater than or equal to 0.2 and less than or equal to 0.6.

[0095] This preferred embodiment of the invention represents a second embodiment after the first embodiment presented above.

[0096] (3) It is preferred that the ratio of the screw element-screw element clearance s between the two screw elements of a pair of screw elements to the housing bore inner diameter D is from 0.002 to 0.05, preferably from 0.003 to 0.03 and particularly preferably from 0.005 to 0.02.

[0097] This preferred embodiment of the invention represents a third embodiment after the first or second embodiment shown above.

[0098] (4) It is further preferred that the clearance between the screw element and the housing wall 5, based on the housing bore inner diameter D, is 0.002 to 0.05, preferably 0.003 to 0.03, and particularly preferably 0.005 to 0.02. This particularly preferred embodiment of the invention represents a fourth embodiment according to one of the embodiments presented above.

[0099] (5) It is further preferred that the additional gap SP, based on the flight depth GT of the respective screw element, is from 0.015 to 0.4, preferably from 0.02 to 0.3 and particularly preferably from 0.025 to 0.25.

[0100] This particularly preferred embodiment of the invention represents a fifth embodiment according to one of the embodiments presented above.

[0101] (6) Further preferably, the crest angles of the crests of the pair of screw elements which have the clearance between the screw element and the housing wall δ but not the additional gap SP between the housing bore inner wall are the same.

[0102] This further preferred embodiment of the invention represents a sixth embodiment according to one of the embodiments presented above.

[0103] (7) Furthermore, further preferably, the crest angles of the crests of the pair of screw elements having the clearance between the screw element and the housing wall δ and the additional gap SP between the housing bore inner wall are equal.

[0104] This further preferred embodiment of the invention represents a seventh embodiment according to one of the embodiments presented above.

[0105] (8) It is additionally preferred that for both screw elements of the pair of screw elements, the crest angles of the crests of the screw elements of the pair of screw elements which have the clearance between the screw element and the housing wall 5 and the additional gap SP are greater than the crest angles of the crests of the screw elements of the pair of screw elements which have the clearance between the screw element and the housing wall 5 but not the additional gap SP.

[0106] This additionally preferred embodiment of the invention represents an eighth embodiment according to one of the embodiments presented above.

[0107] (9) Most preferably, the screw profiles of the pair of screw elements are not congruent, whereby the screw profiles of the two screw elements can be converted into one another by an axial reflection and a rotation.

[0108] This highly preferred embodiment of the invention represents a ninth embodiment according to one of the first to eighth embodiments presented above. Because the screw profiles of the two screw elements can be converted into one another by axial mirroring and rotation, the energy input into each of the two screw elements of a pair of screw elements is equal. This has proven advantageous because it prevents local overheating of the extrudate during the intended use of the pair of screw elements according to the invention.

[0109] (10) It is also preferred that each of the two screw profiles of the pair of screw elements has exactly two (2) grooves and exactly four (4) flanks.

[0110] This very preferred embodiment of the invention represents a tenth embodiment according to one of the first embodiments presented above.

[0111] (11) It is also preferred that the two screw profiles of the pair of screw elements have exactly four (4) grooves and exactly eight (8) flanks.

[0112] This very preferred embodiment of the invention represents an eleventh embodiment according to one of the tenth embodiments presented above.

[0113] The pair of screw elements according to the invention can be designed as a pair of conveying elements or as a pair of kneading disks; according to the invention it is preferably designed as a pair of conveying elements.

[0114] The present invention also relates to a multi-shaft screw machine which has the pair of screw elements according to the invention.

[0115] The present invention also relates to a process for producing or processing an extrudate using the pair of screw elements according to the invention in a multi-screw extruder. The extrudate is preferably a plastic or viscoelastic mass, particularly preferably a polymer melt, in particular a melt of a thermoplastic or an elastomer, most particularly a melt of a polycarbonate or a polyester carbonate or a thermoplastic polyurethane or a rubber. The process preferably comprises the following steps:

[0116] (1) Providing a multi-shaft screw machine comprising a pair of screw elements according to the invention;

[0117] (2) Producing or processing an extrudate. The present invention further relates to a method for producing the screw profiles of the screw elements of the pair of screw elements according to the invention, starting from a precisely scraping screw profile according to the prior art.

[0118] The screw profiles of a pair of screw elements according to the invention can be produced, for example, as explained below, starting from an existing extruder with values ​​predetermined by this for the axis distance A and the barrel bore inner diameter D, wherein each of the two screw elements has exactly two combs and the two screw elements of a pair of screw elements are referred to as the left and right screw element, with formula symbols with subscript l and r respectively.

[0119] In order to calculate the values ​​of the screw profiles of a pair of screw elements according to the invention, both the values ​​of sizes of a pair of screw elements that scrape off each other exactly and the values ​​of sizes of a pair of screw elements that practically scrape off each other are used, wherein the values ​​of the sizes of a pair of screw elements that practically scrape off each other depend on the values ​​of the sizes of a pair of screw elements that scrape off each other exactly and can be calculated from them according to Table 1.

[0120] (I) In a first step, the value for the clearance between screw element and screw element s and the value for the clearance between screw element and casing wall δ are selected, which are to apply to the screw element designed.

[0121] (II) In a second step, the value for the outer radius RE of a precisely scraping screw profile is determined according to the equation:

[0122] RE = DE / 2 (21) with

[0123] DE = D — 2δ + s (22)

[0124] (III) In a third step, the value for the inner radius RI of a precisely scraping screw profile is determined according to the equation: (IV) In a fourth step, the outer radius RA of a technically feasible / intended usable screw element is determined according to the equation:

[0125] RA = D / 2 - δ (24)

[0126] (V) In a fifth step, the inner radius RK of a technically feasible / intended usable screw element is determined according to the equation:

[0127] RK = A - D / 2 + δ — s (25)

[0128] (VI) In a sixth step, the flight depth of a technically feasible / intended usable screw element is determined according to the equation

[0129] GT = RA - RK (26) calculated.

[0130] (VII) In a seventh step, a value for the additional gap SP of a technically feasible / intended-use screw element is selected, whereby SP < GT / 2 is always selected.

[0131] Steps (II) to (V) can be performed in any order.

[0132] (VIII) In an eighth step, for each of the two screw elements of a pair of screw elements that scrape off each other exactly, the initial sum of the crest angles SKWO of the respective screw element is determined according to equation (4) or (27):

[0133] (IX) In a ninth step, the sum of the crest angles of a pair of screw elements BSKW0 which scrape off each other exactly is calculated according to BSKW0 = 2 g SKW0 (28) where the factor g is chosen, where g is greater than 0.1 and less than 0.95, preferably greater than 0.15 and less than 0.8 and particularly preferably greater than 0.2 and less than 0.6.

[0134] (X) In a tenth step, the comb angle KW0 l,δ of the exact scraping profile of the left screw element and the comb angle KW0 r,δ of the right screw element is determined for that crest of the respective screw element, which has the clearance screw element-housing wall 5 to the housing bore inner wall, marked with a subscript 5 in the formula symbol, but not the additional gap SP, in such a way that the sum of the crest angles of these crests applies:

[0135] KW0 l,δ + KW0 r,δ < BSKW0 (29) preferred and especially preferred where all comb angles are greater than 0.

[0136] (XI) In an eleventh step, the comb angle KW0 l,δ+SP of the screw profile of the left screw element and the crest angle KW0 r,δ+SPof the right screw element for the crest of the respective screw element, which has the clearance screw element-housing wall 5 and the gap SP, i.e. S + SP, marked with subscript S + SP in the formula symbols, in such a way that the sum of the crest angles of these crests applies:

[0137] KW0 l,δ+SP + KW0 r,δ+SP = BSKW0 - KW0 l,δ + KW0 r,δ ) (32) and preferably

[0138] KW0 l,δ+SP + KW0 r,δ+SP = 2 KW0 δ+SP = BSKW0 - KW0 l,δ + KW0 r,δ) (33) (XII) In a twelfth step, for a pair of screw elements that scrape off each other exactly, the screw profile of the first screw element, here selected as the left screw element - the right screw element could also be selected similarly - is constructed from the following curves. These curves follow one another directly in a direction of rotation as specified below, whereby the direction of rotation can be mathematically positive or negative, and the curves merge into one another at their respective end points. This screw profile for the first screw element represents the generating screw profile. - A circular arc with radius RE, with the angle KW0 l,δ and with the center of rotation P of the screw profile as the center, this circular arc being the first ridge - A first flank [Flank 1]; - A circular arc with radius RI, with the angle KW0 r,δand with the rotational center P of the screw profile as the center, this circular arc being the first groove; - A second flank [Flank 2]; - ​​A circular arc with radius RE — SP, angle KW0 l,δ+SP and center of the rotational center P of the screw profile, which is the second crest; - A third flank [Flank 3]; - A circular arc with radius RI + SP, angle KW0 l,δ+SP and center of the rotational center P of the screw profile, this circular arc being the second groove; - A fourth flank [flank 4] closing the profile between the second groove and the first crest.

[0139] (XIII) In a thirteenth step, the screw profile of the second screw element, here selected as the right screw element, is constructed for a pair of exactly scraping screw elements. For this purpose, the pivot point of the left screw element is set at the coordinates x = 0 and y = 0, and the pivot point of the right screw element is set at the coordinates x = A and y = 0. The screw profile of the left screw element is geometrically decomposed into its curved segments and, if present, kinks i = 1... n. The exactly scraping screw profile of the right screw element is then constructed from curved segments and, if present, kinks, denoted i' = 1... n, corresponding to the screw profile of the left screw element.

[0140] For a curve segment i, a parameter representation with p a,i ≤ p ≤ p e,i , where the derivative of the analytical functions x i (p) and y i(p) does not become zero for the same value and where it is assumed without loss of generality that with increasing p in the mathematically positive sense winds around the pivot point, a normalized normal vector formed, where the sign is chosen so that the normal vector points out of the profile, away from the pivot point.

[0141] Each curve segment has an initial angle β a,i and an end angle β e,i The initial angle is sufficient for p = p a the condition and the final angle from the components of the normal vector at p = p e to where β e,i > β a,i and β e,i < β a,i + π.

[0142] With the curve section i on the left screw, a curve section i' on the right screw corresponds with the coordinate representation In a preferred embodiment, the curve section i represents a circular arc with the parameter representation (39) with β a,i ≤ β ≤ β e,i , then the normalized normal vector and the representation of the corresponding circular arc is with r i' = A — r i' xm i' = xm i' + A and ym i' = ym i and (as above) β a,i ≤ β ≤ β e,i .

[0143] If the curve segment represents a circle with X = A, then r i' = 0. and the corresponding piece is a kink.

[0144] If the piece i represents a kink with the coordinates , then this corresponds to a circular arc with radius , whose representation from the above formula with r i' = A can be obtained.

[0145] In a preferred embodiment, the screw profile of the screw elements according to the invention is derived from an exactly scraping screw profile by using the axial distance enlargement, the circular equidistant, the longitudinal equidistant or the spatial equidistant, wherein the sum of the crest angles BKW of the crests of both screw elements is greater than 0 in radians and for the factor ƒ with ƒ = BKW / BKGW (42) it applies that the factor ƒ is greater than 0 and less than or equal to 0.95, where BKW is the sum of the crest angles in radians of both screw elements and BKGW is determined by:

[0146]

[0147] In a further preferred embodiment, the screw profile of the screw elements according to the invention is composed of curve sections which are selected from the group of mathematical expressions comprising the following members: circular arc, elliptical arc, parabolic arc, spline or section of a spline, result of the application of the longitudinal equidistant calculation rule according to [1], pages 117 to 121 to a circular arc, elliptical arc, parabolic arc or to a spline or to a section of a spline, result of the application of the spatial equidistant calculation rule to a circular arc, elliptical arc, parabolic arc or to a spline or to a section of a spline, or result of the application of the circular equidistant calculation rule to a circular arc, elliptical arc, parabolic arc or to a spline or to a section of a spline.

[0148] In a further preferred embodiment, at least two pairs of screw elements according to the invention are arranged axially directly one behind the other in a multi-screw screw machine. Such an arrangement is shown in principle, for example, in PCT / EP2021 / 078863, where PCT / EP2021 / 078863 specifically describes pairs of screw elements that precisely clean each other, whereas the present invention relates to screw elements that practically scrape off each other.

[0149] In Fig. 1, the practically scraping screw profile of the left screw element from Example 2 is shown to illustrate the geometric dimensions.

[0150] The invention is explained below using examples, without the invention being restricted to these examples.

[0151] Example 1 (Comparative Example - not according to the invention) The non-inventive Example 1 is a pair of two mutually practically scraping

[0152] Screw elements with and after

[0153] EP 0002131 A1, Fig. 5(A) and Fig. 5(B), whereby the spatial equidistant calculation rule is additionally applied to the screw profile according to EP 0002131 A1, Fig. 5(A) or Fig. 5(B). The screw profiles of the screw elements are asymmetrical and not congruent, but they can be converted into one another by axial reflection and rotation.

[0154] The precisely scraping screw profile of the left screw element consists of the sections i = 1 to 12, which are either circular arcs or kinks. The arc angles, initial angle, end angle, arc radius relative to the barrel bore inner diameter D, x-coordinate of the center of the circular arc i relative to the pivot point P1 of the left screw profile relative to the barrel bore inner diameter D, and y-coordinate of the center of the circular arc i relative to the pivot point of the left screw profile P1 relative to the barrel bore inner diameter D are given in Table 2. The crests of the practically scraping screw profile are circular arcs 1 and 7. Kinks can be identified by the value .

[0155] Table 2: Circular arcs of the exact scraping profile of the left screw profile of Example 1.

[0156] The precisely scraping screw profile of the right-hand screw element consists of the sections i = T to 12', which are either circular arcs or kinks. Table 3 shows the starting angle, end angle, arc radius relative to the barrel bore inner diameter D, x-coordinate of the center of the circular arc i relative to the pivot point P2 of the right-hand screw profile relative to the barrel bore inner diameter D, and y-coordinate of the center of the circular arc i relative to the pivot point P2 of the right-hand screw profile relative to the barrel bore inner diameter D. The crests of the practically scraping screw profile are the circular arcs 4' and 10'. Kinks can be identified by the value '.

[0157] Table 3: Circular arcs of the precisely scraping screw profile of the right screw element from Example 1.

[0158] The sum of the crest angles of both exactly scraping screw profiles of the pair of screw elements together is BKW0 = 1.72356 in radians (98.75 °).

[0159] The technically designed, practically scraping, screw elements of the pair of screw elements according to Example 1, with screw profiles derived from precisely scraping screw profiles, are asymmetrical and not congruent, but can be converted into one another by axial reflection and rotation. The sum of the crest angles of the practically scraping screw profile of a single screw element is 0.73115 radians (41.89 degrees). The sum of the crest angles of the screw profiles of the pair of screw elements in radians is BKW = 1.462 (83.78°).

[0160] The limit value for the sum of the crest angles of the pair of screw elements calculated according to formula (2) is BKGW = 1.444 (82.71°). Thus, BKW > BKGW, their ratio and thus this pair of screw elements is not in accordance with the invention. The practically scraping screw profiles of the two screw elements are shown in Fig. 2, together with the corresponding exactly scraping screw profiles, from which the practically scraping screw profiles were derived. Table 4 gives the screw profile of the left screw element in the plane according to formula (13), i.e., the radius as a function of the angle γ. l starting from the center of rotation P1 of the left screw element. The radii are each given for an angular separation of two degrees, except for the transition into a crest or groove area, where additional points are given. Table 5 shows the corresponding coordinates of the screw profile of the right screw element starting from the center of rotation P2 of the right screw element. Fig. 3 shows the pair of screw elements not according to the invention in a plan view.

[0161]

[0162] Table 4: Screw profile of the left screw element of the pair of non-inventive

[0163] Screw elements from example 1.

[0164]

[0165] Table 5: Screw profile of the right screw element of the pair of non-inventive screw elements from Example 1.

[0166] Example 2 (according to the invention)

[0167] Example 2 according to the invention is a pair of two mutually practically scraping screw elements with and thus the The same values ​​for the corresponding dimensions as in Example 1, with the spatial equidistant calculation rule also applied. The screw profiles of the screw elements are asymmetrical and not congruent, but they can be converted into one another by axial reflection and rotation.

[0168] The precisely scraping screw profile of the left screw element consists of the sections i = 1 to 20, which are either circular arcs or kinks. The arc angles, starting angle, end angle, arc radius relative to the housing bore inner diameter D, x-coordinate of the center of the circular arc i relative to the pivot point of the left screw profile P1 relative to the housing bore inner diameter D, and y-coordinate of the center of the circular arc i relative to the pivot point P1 of the left screw profile relative to the housing bore inner diameter D are given in Table 6. The crests of the precisely scraping screw profile are circular arcs 1 and 11. Kinks can be identified by the value .

[0169] The precisely scraping screw profile of the right-hand screw element consists of the circular arcs i = 1' to 20', which are either circular arcs or kinks. The arc angles, initial angle, end angle, arc radius relative to the barrel bore inner diameter D, x-coordinate of the center of the circular arc i relative to the pivot point P2 of the right-hand screw profile relative to the barrel bore inner diameter D, and y-coordinate of the center of the circular arc i relative to the pivot point P1 of the right-hand screw profile relative to the barrel bore inner diameter D are given in Table 7. The crests of the practically scraping screw profile are the circular arcs 6' and 16'. The sum of the crest angles of both precisely scraping screw profiles of the pair of screw elements is BKW0 = 0.8784 radians (50.32°).

[0170] Table 6: Circular arcs of the precisely scraping screw profile of the left screw element from Example 2.

[0171]

[0172] Table 7: Circular arcs of the precisely scraping screw profile of the right screw element from Example 2.

[0173] The technically designed, practically scraping, screw elements of the pair of screw elements according to Example 2 with screw profiles derived from exactly scraping screw profiles are asymmetrical, not congruent, but can be converted into one another by axial reflection and rotation. The sum of the crest angles of the practically scraping screw profile of a single screw element is 0.3384 radians (19.30°). The sum of the crest angles of the screw profiles of the pair of screw elements is BKW = 0.6769 radians (38.78°). The limit value for the sum of the crest angles of the pair of screw elements, calculated according to formula (2), is (as in Example 1) BKGW = 1.444 radians (82.71°). Thus, BKW < BK GW, the ratio , and this pair of screw elements is according to the invention.

[0174] The practically scraping screw profiles of the pair of screw elements according to the invention are shown in Fig. 4, together with the corresponding exactly scraping screw profiles, from which the practically scraping screw profiles were derived. Table 8 shows the screw profile of the left screw element according to formula (5), i.e., the radius as a function of the angle γ. l starting from the center of rotation P1 of the left screw element. The radii are each given for an angular separation of two degrees, except for the transition into a crest or groove area, where additional points are given. Table 9 shows the corresponding coordinates of the screw profile of the right screw element. Fig. 5 shows the pair of screw elements according to the invention in a top view.

[0175]

[0176] Table 8: Screw profile of the left screw element of the pair of screw elements according to the invention from Example 2.

[0177]

[0178] Screw elements from Example 2. Example 3 (according to the invention)

[0179] Example 3 according to the invention is a pair of two mutually practically scraping screw elements with and , wherein in addition the Spatial equidistant calculation rules were applied. The screw profiles of the screw elements are asymmetrical and not congruent, but they can be converted into one another by axial reflection and rotation.

[0180] The precisely scraping screw profile of the left screw element consists of the sections i = 1 to 20, which are either circular arcs or kinks. The arc angles, initial angle, end angle, arc radius relative to the housing bore inner diameter D, x-coordinate of the center of the circular arc i relative to the pivot point P1 of the left screw profile relative to the housing bore inner diameter D, and y-coordinate of the center of the circular arc i relative to the pivot point P1 of the left screw profile relative to the housing bore inner diameter D are given in Table 10. The crests of the precisely scraping screw profile are circular arcs 1 and 11. Kinks are recognizable by the value = 0. The crests of the practically scraping screw profile are the circular arcs 1 and 11.

[0181] Table 10: Circular arcs of the exact scraping profile of the left screw profile from Example 3.

[0182] The precisely scraping screw profile of the right-hand screw element consists of the circular arcs i = 1' to 20', which are either circular arcs or kinks. The arc angles, initial angle, end angle, arc radius relative to the barrel bore inner diameter D, x-coordinate of the center of the circular arc i relative to the pivot point P1 of the right-hand screw profile relative to the barrel bore inner diameter D, and y-coordinate of the center of the circular arc i relative to the pivot point P1 of the right-hand screw profile relative to the barrel bore inner diameter D are given in Table 11. The crests of the precisely scraping profile are the circular arcs 6' and 16'. The sum of the crest angles of both precisely scraping profiles is BKW0 = 0.7716 in radians (44.21°).

[0183] Table 11: Circular arcs of the exact scraping profile of the right screw profile from Example 3.

[0184] The technically designed, practically scraping screw elements of the inventive pair of screw elements according to Example 3, with screw profiles derived from precisely scraping screw profiles, are also asymmetrical and not congruent, but they can be interconverted by axial reflection and rotation. The sum of the crest angles for both the left and right screw profiles is 0.3464 radians (20.89°), resulting in a sum of the crest angles of the pair of screw elements of BKW = 0.6928 (41.78°).

[0185] The limit value for the sum of the crest angles of the pair of screw elements, calculated according to formula (2), is BKGW=1.848 radians (105.86°). Thus, BKW < BKGW, the ratio , and the screw element pair is in accordance with the invention.

[0186] The practically scraping screw profiles of the pair of screw elements according to the invention are shown in Fig. 6, together with the corresponding exactly scraping screw profiles from which the practically scraping screw profiles were derived. Table 12 shows the screw profile of the left screw element according to formula (5), i.e., the radius as a function of the angle starting from the center of rotation P1 of the left screw profile. The radii are each given for an angular separation of two degrees, except for the transition into a crest or groove region, where additional points are given. Table 13 gives the corresponding coordinates of the screw profile of the right screw profile. Fig. 7 shows the screw element pair according to the invention in a plan view.

[0187]

[0188]

[0189] Table 12: Screw profile of the left screw element of the pair of screw elements according to the invention from Example 3.

[0190] Table 13: Screw profile of the right screw element of the pair of screw elements according to the invention from Example 3.

[0191] Example 4 (according to the invention)

[0192] Example 4 according to the invention is a pair of two screw elements that practically scrape off each other, with A / D = 0.84, T / D = 0.75, δ / d = 0.005, and s / D = 0.01, with the spatial equidistant calculation rule also being applied. The screw profiles of the screw elements are asymmetrical and not congruent, but they can be converted into one another by axial reflection and rotation.

[0193] The precisely scraping screw profile of the left screw element consists of sections i = 1 to 20, which are either circular arcs or kinks. The arc angles, initial angle, end angle, arc radius relative to the inner diameter of the barrel bore D, x-coordinate of the center of the circular arc i relative to the pivot point P1 of the left screw profile relative to the inner diameter of the barrel bore D, and y-coordinate of the center of the circular arc i relative to the pivot point P1 of the left screw profile relative to the inner diameter of the barrel bore D are given in Table 14. The crests of the precisely scraping screw profile are circular arcs 1 and 11. Kinks are recognizable by the value = 0.

[0194] Table 14: Circular arcs of the practically scraping screw profile of the left screw element from Example 4.

[0195] The precisely scraping screw profile of the right-hand screw element consists of the circular arcs i = 1' to 20', which are either circular arcs or kinks. The arc angles, initial angle, end angle, arc radius relative to the barrel bore inner diameter D, x-coordinate of the center of the circular arc i relative to the pivot point P1 of the right-hand screw profile relative to the barrel bore inner diameter D, and y-coordinate of the center of the circular arc i relative to the pivot point P1 of the right-hand screw profile relative to the barrel bore inner diameter D are given in Table 15. The crests of the precisely scraping screw profile are the circular arcs 6' and 16'. The sum of the crest angles of both precisely scraping screw profiles of the pair of screw elements together is BKW0 = 0.69814 in radians (40°).

[0196] Table 15: Circular arcs of the precisely scraping screw profile of the right screw element from Example 4.

[0197] The technically designed, practically scraping screw elements of the inventive pair of screw elements according to Example 4 with screw profiles derived from precisely scraping screw profiles are also asymmetrical and not congruent, but they can be converted into one another by axial reflection and rotation. The sum of the crest angles for both the left and right screw profiles is 0.25885 radians (14.83°), and the sum of the crest angles of the pair of screw elements is BKW = 0.51766 (29.66°). The limit value for the sum of the crest angles of the pair of screw elements, calculated according to formula (2), is BKGW = 1.5703 radians (89.97°). Thus, BKW < BKGW their ratio , and the screw egg element pair is according to the invention.

[0198] The practically scraping screw profiles of the pair of screw elements according to the invention are shown in Fig. 8, along with the corresponding exactly scraping screw profiles from which the practically scraping screw profiles were derived. Fig. 9 shows the pair of screw elements according to the invention in a top view.

[0199] Table 16 gives the screw profile of the left screw element according to formula (5), i.e. the radius as a function of the angle γ l starting from the center of rotation P1 of the left screw profile. The radii are each given for an angular separation of two degrees, except for the transition to a crest or groove area, where additional points are specified. Table 17 shows the corresponding coordinates of the screw profile of the right screw profile.

[0200]

[0201] Table 16: Screw profile of the left screw element of the pair of inventive

[0202] Screw elements from example 4.

[0203]

[0204]

[0205] Table 17: Screw profile of the right screw element of the pair of screw elements according to the invention from Example 4.

[0206] Short description of figures and list of reference symbols

[0207] Figure 1

[0208] Practically scraping screw profile of the left screw element from example 2

[0209] 1. 1 Housing bore inner wall profile of the left part of the housing bore

[0210] 1.2 Gear depth GT

[0211] 1.3 Housing bore inner diameter D

[0212] 1.4 Comb angle of the left screw element, which has a clearance between the screw element and the housing wall 8, but not an additional gap SP: KW l,δ

[0213] 1.5 Clearance screw element-housing wall δ

[0214] 1.6 Gangway depth reduced by the additional gap: GT — SP

[0215] 1.7 Clearance screw element-housing wall increased by the additional gap: δ + SP

[0216] 1.8 Comb angle of the left screw element, which has both a clearance between the screw element and the housing wall δ and an additional gap SP: KW l,δ+SP

[0217] 1.9 Center of rotation P

[0218] Figure 2

[0219] Screw profiles of the non-inventive screw element pair from Example 1

[0220] 2. 1 Housing bore inner wall profile

[0221] 2.2 Profile left screw element, precise scraping

[0222] 2.3 Profile left screw element, practically scraping

[0223] 2.4 Profile right screw element, precise scraping

[0224] 2.5 Profile of the right screw element, practically scraping Figure 3

[0225] Top view of the screw element pair not according to the invention from Example 1

[0226] 3.1 Housing bore inner wall profile

[0227] 3.3 Profile left screw element, practically scraping

[0228] 3.5 Profile right screw element, practically scraping

[0229] Figure 4

[0230] Screw profiles of the screw element pair according to the invention from Example 2

[0231] 4. 1 Housing bore inner wall profile

[0232] 4.2 Profile left screw element, precise scraping

[0233] 4.3 Profile left screw element, practically scraping

[0234] 4.4 Profile right screw element, precise scraping

[0235] 4.5 Profile right screw element, practically scraping

[0236] Figure 5

[0237] Top view of the screw element pair according to the invention from Example 2

[0238] 5.1 Housing bore inner wall profile

[0239] 5.3 Profile left screw element, practically scraping

[0240] 5.5 Profile right screw element, practically scraping

[0241] Figure 6

[0242] Screw profiles of the screw element pair according to the invention from Example 3

[0243] 6. 1 Housing bore inner wall profile

[0244] 6.2 Profile left screw element, precise scraping

[0245] 6.3 Profile of the left screw element, practically scraping 6.4 Profile of the right screw element, precisely scraping

[0246] 6.5 Profile right screw element, practically scraping

[0247] Figure 7

[0248] Top view of the screw element pair according to the invention from Example 3

[0249] 7. 1 Housing bore inner wall profile

[0250] 7.3 Profile left screw element, practically scraping

[0251] 7.5 Profile right screw element, practically scraping

[0252] Figure 8

[0253] Screw profiles of the screw element pair according to the invention from Example 4

[0254] 8.1 Housing bore inner wall profile

[0255] 8.2 Profile left screw element, precise scraping

[0256] 8.3 Profile left screw element, practically scraping

[0257] 8.4 Profile right screw element, precise scraping

[0258] 8.5 Profile right screw element, practically scraping

[0259] Figure 9

[0260] Top view of the screw element pair according to the invention from Example 4

[0261] 9. 1 Housing bore inner wall profile

[0262] 9.3 Profile left screw element, practically scraping

[0263] 9.5 Profile right screw element, practically scraping

Claims

Patent claims 1. Multi-shaft screw machine comprising a pair of screw elements, with m screw shafts SWi to SWm rotating in the same direction and at the same speed, whose adjacent axes of rotation X1 to X m in a cross-section perpendicular to the axes of rotation, they have an axis distance A and m intersecting circular housing bores, each having an identical inner housing bore diameter D and whose bore centers M1 to M m have a distance equal to the center-to-center distance A, and whose bore centers M1 to M m with the respective associated axes of rotation X1 to X m the worm shafts SWi to SWm and with the centers of rotation P1 to P mthe worm elements coincide, wherein the two worm elements of the pair worm element are opposite each other on immediately adjacent worm shafts, wherein the two worm elements of the pair worm elements scrape each other with a worm element-worm element clearance s, wherein both worm elements have an asymmetrical worm profile, wherein both worm elements each have exactly two combs, wherein for each of the two worm elements, its two combs have different distances to the respective center of rotation P of the worm profile, wherein one comb has a distance D / 2 reduced by a worm element-housing wall clearance 5 and further reduced by an additional gap SP to the respective center of rotation P, and the other comb has a distance D / 2 reduced by a worm element-housing wall clearance 5, but not reduced by an additional gap SP, to the respective center of rotation P.wherein the clearance δ between the worm element and the housing wall is the same for both worm elements and the additional gap SP is the same for both worm elements, characterized in that the sum of the comb angles BKW of the combs of both worm elements in radians is greater than 0 and for the factor ƒ with ƒ = BKW / BKGW (44), The factor ƒ is greater than 0 and less than or equal to 0.95, where BKW is the sum of the comb angles in radians of both worm elements and BKGW is determined by: wherein the aforementioned parameters are defined as set out in the description.

2. Multi-shaft screw machine according to claim 1, wherein / is greater than or equal to 0.1 and less than or equal to 0.8, preferably f is greater than or equal to 0.2 and less than or equal to 0.

6.

3. Multi-shaft screw machine according to claim 1 or claim 2, wherein the ratio of the screw element clearance s between the two screw elements of a pair of screw elements to the housing bore inner diameter D is from 0.002 to 0.05, preferably from 0.003 to 0.03, and particularly preferably from 0.005 to 0.

02.

4. Multi-shaft screw machine according to one of the preceding claims, wherein the clearance between the screw element and the housing wall 8, based on the housing bore inner diameter D, is 0.002 to 0.05, preferably 0.003 to 0.03, and particularly preferably 0.005 to 0.

02. 5.Multi-shaft screw machine according to any one of the preceding claims, wherein the additional gap SP, relative to the flute depth GT of the respective screw element, is from 0.015 to 0.4, preferably from 0.02 to 0.3, and particularly preferably from 0.025 to 0.

25.

6. Multi-shaft screw machine according to any one of the preceding claims, wherein the comb angles of the combs of the pair of screw elements, which define the screw element clearance...

7. Multi-shaft screw machine according to one of the preceding claims, wherein the comb angles of the combs of the pair of screw elements having the clearance screw element-housing wall 5 and the additional gap SP to the inner wall of the housing bore are equal.

8. Multi-shaft screw machine according to one of the preceding claims, wherein for both screw elements of the pair of screw elements, the comb angles of the combs of the screw elements of the pair of screw elements having the clearance screw element-housing wall 5 and the additional gap SP are greater than the comb angles of the combs of the screw elements of the pair of screw elements having the clearance screw element-housing wall 5, but not the additional gap SP. 9.Multi-shaft screw machine according to any one of the preceding claims, wherein the screw profiles of the pair of screw elements are not congruent, and wherein the screw profiles of the two screw elements can be transformed into one another by axial symmetry and rotation.

10. Multi-shaft screw machine according to any one of the preceding claims, wherein each of the two screw profiles of the pair of screw elements has exactly two (2) grooves and exactly four (4) flanks.

11. Multi-shaft screw machine according to any one of the preceding claims, wherein the two screw profiles of the pair of screw elements have exactly four (4) grooves and exactly eight (8) flanks.

12. Method for producing or processing an extrudate using a multi-shaft screw machine according to any one of claims 1 to 11, wherein the method comprises the steps of: (1) Provision of the multi-shaft screw machine; (2) Manufacturing or processing the extrudate.

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