Multi-shaft screw machine comprising pair of screw elements with improved mixing and degassing effects with reduced energy input

Abstract

The invention relates to a pair of screw elements suitable for a multi-shaft screw machine, comprising: m screw shafts SW1 to SWm rotating in the same direction and at the same speed, the respective adjacent axes of rotation X1 to Xm of the screw shafts having a center distance A in a cross-section at right angles to the axes of rotation; and m circular housing bores penetrating each other wherein each circular housing bore has the same housing bore inner diameter D, the distance between the bore centers M1 to Mm of the circular housing bores is the same as the center distance A, the bore centers M1 to Mm of the circular housing bores coincide with the corresponding rotational axes X1 to Xm of the screw shafts SW1 to SWm and coincide with the rotational centers P1 to Pm of the screw elements; wherein two screw elements of a pair of screw elements are opposed to each other on directly adjacent screw shafts; the two screw rod elements in the pair of screw rod elements scrape each other, and the gap between the screw rod elements is s; the two screw rod elements are provided with asymmetric screw rod contours; each of the two screw elements has two tooth crests; for each of the two screw elements, the distances of the two tooth tops thereof from the corresponding center of rotation P of the screw profile are different.

Description

[0001] The present invention relates to a pair of screw elements suitable for a multi-shaft screw machine having:

[0002] m screw shafts SW1 to SW rotating in the same direction and at the same speed m , the m screw shafts SW1 to SW m The corresponding adjacent rotation axes X1 to X m In a cross section at right angles to the axis of rotation, there is a center distance A,

[0003] as well as

[0004] m circular shell holes that penetrate each other, wherein each of the circular shell holes has the same shell hole inner diameter D, and the hole centers M1 to M m The distance between the centers M1 and M2 of the circular shell hole is the same as the center distance A. m With the screw shaft SW1 to SW m The corresponding rotation axis X1 to X m coincides with the rotation center P1 of the screw element to P m coincide,

[0005] wherein the two screw elements of the pair of screw elements are opposite each other on directly adjacent screw axes,

[0006] wherein the two screw elements of the pair of screw elements scrape against each other, and the gap between the screw elements is s,

[0007] wherein the two screw elements have an asymmetrical screw profile,

[0008] wherein each of the two screw elements has two tooth tops,

[0009] wherein for each of the two screw elements, the distances of the two tooth tops from the corresponding rotation center P of the screw profile are different,

[0010] wherein in each case one tooth tip is at a distance D / 2 minus the clearance δ between the screw elements and the housing wall, minus an additional clearance SP, from the corresponding rotation center P, and the other tooth tip is at a distance D / 2 minus the clearance δ between the screw elements and the housing wall, but no longer minus an additional clearance SP,

[0011] wherein the gap δ between the screw element and the housing wall of the two screw elements is identical and the additional gap SP of the two screw elements is identical,

[0012] The sum of the tooth top angles BKW of the two screw elements satisfies the following formula in radians:

[0013] BKW=f*BKGW (1)

[0014] For the coefficient f, the coefficient f is greater than 0 and less than or equal to 0.95.

[0015] Among them, BKGW is determined as:

[0016]

[0017] The parameters required to represent the screw profile are listed in Table 1 below.

[0018] WO2011 / 006516A1 discloses an extruder having a housing with at least two axially parallel shafts that can be driven in the same direction and is equipped with at least two-blade conveying elements that wipe each other at center distances with a small gap around the entire circumference, wherein there is a distance (a) between the tooth top of at least one gear and the inner wall of the housing.

[0019] A multi-shaft screw machine is known from EP 0 875 356 A2. The multi-shaft screw machine is provided with a housing with two housing bores which are parallel to each other and partially penetrate each other, two rotatable drive shafts are arranged in the housing bores, screw elements are mounted on the shafts for co-rotation, kneading disks are mounted on the shafts for co-rotation and meshing with each other, wherein each kneading disk has a width in its top region which is narrower than the disk width (B), thereby forming mixing and scraping projections at the edge.

[0020] Furthermore, DE 10 2008 016 862 A1 describes an extruder having at least two axially parallel shafts which can be driven in the same direction and having at least a twin-screw conveying element (2, 11, 12) which is in substantially close contact at point (C).

[0021] EP0788868A1 describes a method and apparatus for mixing and continuously rolling thermoplastic materials. The apparatus comprises a mixing chamber and at least one pair of screw shafts arranged in the mixing chamber (5), wherein the screw shafts have at least one screw tip portion and at least one screw core portion, which are asymmetrically sunken relative to the longitudinal axis of the shafts to form a surface of the shaft and a gap between the sunken screw portion and the inner surface of the chamber, so that during the process of providing the material to the outlet of the mixing chamber, the material is rolled on at least a part of the surface of the chamber itself.

[0022] In addition, WO2016 / 107527A1 discloses a self-cleaning extruder with two screws rotating in the same direction, wherein the device comprises a screw mechanism, a barrel, a feed port, a vent and a discharge port.

[0023] In the present invention, a multi-axis screw machine is understood to mean a screw machine having more than one screw shaft, for example a screw machine having two, three or four screw shafts, or a screw machine having eight to sixteen, in particular twelve screw shafts arranged in an annular manner. In the case of more than two screw shafts, the rotation axes of the screw shafts can be arranged adjacent to each other, or, for example in a so-called annular extruder, in an annular form. In a multi-axis extruder, the rotation axes of the screw shafts are usually arranged parallel to each other. According to the present invention, this parallel arrangement of the rotation axis is also advantageous. In view of this, the number of screw elements of a pair of screw elements according to the present invention preferably corresponds to the number of screw shafts of the corresponding extruder, wherein the screw shafts are arranged relatively on the extruder. Such a screw machine having more than one screw shaft is also referred to as a multi-spindle screw machine, a multi-axis screw machine or a multi-axis extruder hereinafter. A twin-axis screw machine is also referred to as a twin-screw extruder hereinafter. In the present invention, the term "screw machine" is synonymous with the term "extruder". The extruded mixture or the mixture to be extruded is also referred to below as "extrudate".

[0024] The multi-shaft screw machine is preferably a twin-screw extruder having two screw shafts SW1 and SW2 rotating in the same direction and at the same speed, adjacent rotation axes X1 and X2, bore centers M1 and M2 and rotation centers P1 and P2.

[0025] In the present invention, the extrudate is a plastic or viscoelastic mixture, in particular selected from the group consisting of:

[0026] Suspensions, pastes, molten glass, unfired ceramics, molten metals or plastics.

[0027] In the present invention, plastic refers in particular to:

[0028] Polymer refers in particular to polymer melts or polymer solutions, particularly in particular to melts or solutions of thermoplastic polymers or to melts or solutions of elastomers, in particular rubbers.

[0029] The thermoplastic polymer used is at least one of the following materials: polycarbonate, polyester carbonate, polyamide, polyester (especially polybutylene terephthalate and polyethylene terephthalate), polylactic acid, polyether, thermoplastic polyurethane, polyacetal, fluoropolymer (especially polyvinylidene fluoride), polyether sulfone, polyolefin (especially polyethylene and polypropylene), polyimide, polyacrylate (especially polymethyl methacrylate), polyphenylene ether, polyphenylene sulfide, polyether ketone, polyaryletherketone, styrene polymer (especially polystyrene), styrene copolymer (especially styrene-acrylonitrile copolymer, acrylonitrile-butadiene-styrene block copolymer) and polyvinyl chloride. It is also preferred to use so-called blends of the listed polymers, which are understood by those skilled in the art to mean a combination of two or more polymers. Particularly preferred are polycarbonates and mixtures containing polycarbonates (more particularly preferably polycarbonates), which are obtained, for example, by an interfacial process or a melt transesterification process.

[0030] The rubber used is preferably at least one of the following materials: styrene-butadiene rubber, natural rubber, butadiene rubber, isoprene rubber, ethylene-propylene-diene rubber, ethylene-propylene rubber, butadiene-acrylonitrile rubber, hydrogenated nitrile rubber, butyl rubber, halogenated butyl rubber, chloroprene rubber, ethylene-vinyl acetate rubber, polyurethane rubber, thermoplastic polyurethane, gutta-percha, aryl rubber, fluorinated rubber, silicone rubber, vulcanized rubber and chlorosulfonated polyethylene rubber. Of course, it can also be a combination of two or more of the listed rubbers, or a combination of one or more rubbers and one or more other plastics.

[0031] These thermoplastics or rubbers can be used in pure form or in mixtures with fillers and reinforcing agents, such as in particular glass fibers, either with one another or with other polymers or with customary polymer additives.

[0032] In a preferred embodiment, additives are added to the plastic material, in particular to the polymer melt and the mixture of polymer melts. The additives in solid, liquid or solution form can be added to the extruder together with the polymer, or at least part or all of the additives can be fed to the extruder by side stream.

[0033] Additive can provide multiple characteristics for polymer.For example, described additive can be coloring agent, pigment, processing aid, filler, antioxidant, reinforcing agent, UV absorber and light stabilizer, metal passivator, peroxide scavenger, alkaline stabilizer, nucleator, benzofuran and indoline compound with stable or antioxidative effect, release agent, flame retardant additive, antistatic agent, dyestuff and melt stabilizer.The embodiment of these additives is carbon black, glass fiber, clay, mica, graphite fiber, titanium dioxide, carbon fiber, carbon nanotube, ionic liquid and natural fiber.

[0034] In the present invention, an asymmetric cross-sectional screw profile is distinguished in that no mirror axis or rotation axis passes through any point in the plane of the cross-sectional screw profile, wherein the mirror axis or rotation axis can be used to generate a cross-sectional screw profile consistent with the original cross-sectional screw profile; preferably, no mirror axis passes through any point in the cross-sectional screw profile, and particularly preferably, no mirror axis passes through the structural center KP of the cross-sectional screw profile that can be used to generate a profile consistent with the original profile. In this case, the structural center KP is a point in the cross-sectional screw profile that is the center of all circular arcs that form the tooth tops and grooves. In the present invention, the structural center KP of the screw profile coincides with the rotation center P of the screw profile. For example, EP0002131A1 Figure 5 (A) or Figure 5 (B) shows the screw profile of a pair of screw elements, which screw profile is asymmetrical in the sense of the present invention. Figure 5 (A) or Figure 5 The screw profiles of a pair of screw elements shown in (B) also have non-uniform characteristics, but can be merged with each other by mirroring along an axis and then rotating them.

[0035] The screw cross-sectional profile, also referred to in the present invention as screw profile, refers to the outer contour of the screw element in a plane section at right angles to the axis of rotation of the screw element. For example, in [1] ([1] = Klemens Kohlgrüber: "Der The rules for generating a precisely scraped screw profile are described in [Doppelschneckenextruder] [Co-rotating twin-screw extruder], 2nd edition, Hanser Verlag München 2016, pages 107 to 120]. It is also described here that a given screw profile on the first shaft of a twin-screw extruder determines the screw profile on the second shaft of the twin-screw extruder adjacent to the first shaft ([1], page 108). The screw profile on the first shaft is therefore called the mother screw profile (erzeugendeSchneckenprofil). The screw profile on the second shaft is determined based on the screw profile of the first shaft of the twin-screw extruder and is therefore called the generated screw profile (erzeugteSchneckenprofil).

[0036] Co-rotating twin-screw machines in which the screw shafts scrape exactly against each other have long been known, for example from DE 862668 C. In the production and processing of polymers, screw machines with screw shafts in which the screw elements are based on the principle of a precisely scraped screw cross-sectional profile have been widely used. This is mainly due to the fact that at normal processing temperatures, the polymer melt adheres to the surface and degrades over time, which is avoided by the self-cleaning effect of the screw elements in multi-shaft machines, which scrape exactly against each other in pairs. In multi-shaft extruders, screw elements with a mother screw profile and screw elements with a generating screw profile are always used alternately on adjacent shafts.

[0037] Two points need to be distinguished here: a precisely scraped screw profile (a mathematical construction in which two screw elements are arranged opposite each other on two adjacent screw shafts, scrape against each other and the gap s between the screw elements approaches zero; and a screw profile of a screw element that is designed in material reality for the intended use (i.e., a technically implemented screw element). If the term "precisely scraped" is used in the present invention, unless otherwise stated, this refers to the mathematical construction of a precisely scraped screw profile or a corresponding screw element with this screw profile. If the term "actually scraped" or "implemented" is used in the present invention, unless otherwise stated, this refers to a technically implemented screw element or its screw profile, wherein this actually scraped screw profile is derived from a just-scratched screw profile, preferably by applying one of the following gap strategies: increased center distance, longitudinal cross-sectional equidistance, spatial equidistance or circular equidistance, which will be explained in more detail below.

[0038] Those skilled in the art of screw elements will appreciate that a single screw element or screw profile by itself is not likely to have precise or actual scraping, but pairs of such elements are always required.

[0039] Modern extruders have a modular system in which various screw elements can be mounted on a mandrel to form a screw shaft; the screw shaft is therefore segmented. This enables a person skilled in the art to adjust the extruder to the corresponding processing task. However, the screw shaft can also be manufactured in one piece, i.e. there can be only one screw element extending substantially over the entire length of the screw shaft, or it can be segmented only in parts. The present invention relates both to screw elements that can be mounted on a mandrel and to a screw shaft manufactured in one piece as described above.

[0040] Known multi-shaft extruders, in particular twin-screw extruders, transfer mechanical energy to the extrudate by dissipation. This has both desirable and undesirable consequences, since on the one hand, energy input is required to achieve process tasks such as mixing and degassing, and on the other hand, the consumption of the input mechanical energy leads to an increase in the temperature of the extrudate, which can lead to undesirable chemical reactions that damage the extrudate.

[0041] Mixing is also a known basic operation in multi-shaft extruders, especially twin-screw extruders. Incomplete mixing resulting in inhomogeneities in the extrudate can lead to problems in the further processing of the extrudate and to problems with the final properties.

[0042] Degassing (i.e., removing volatile components) is also a known basic operation in multi-shaft extruders, in particular twin-screw extruders, as described, for example, in [1], pages 494 to 525. For the degassing process, in order to achieve economically high throughput and good extrudate quality, it is desirable to achieve the highest possible degassing efficiency at low energy input. In addition to the general description of [1], such a process is also described in WO2010139413A1 ([2]), which describes an apparatus and a process for degassing a polycarbonate solution containing a solvent.

[0043] For degassing, the polymer is transported as an extrudate through the degassing opening in a partially filled section. Volatile components of the polymer formed in the polycondensation reaction (such as by-products, monomers, oligomers, solvents or degradation products) can be removed through the opening under the influence of temperature, water, oxygen or other components. In order to better remove the volatile components, the pressure in the degassing opening can be lower than the ambient pressure, depending on the specific degassing task. It is also pointed out on pages 494 to 525 of [1] that bubble formation and the resulting foaming in the polymer melt are useful for residual degassing, because this forms an inner surface that improves the material transfer. Foaming requires a sufficiently high overpressure (about 1 bar) of the volatile components in the polymer. The influence of shear forces on the polymer can promote the formation of bubbles and improve the degassing effect.

[0044] In twin-screw extruders, the shear forces to which the extrudate is subjected between the screw tooth tops and the inner wall of the extruder housing bore are particularly strong. This means that a particularly large amount of energy is dissipated into the extrudate, leading to local severe overheating of the extrudate. This is shown, for example, in Figures 4.80 to 4.84 on pages 416 to 423 of [1]. Such local overheating can lead to 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 colloids or spots). In particular, large tooth top angles are disadvantageous, especially the sum of the large tooth top angles of a pair of screw elements that are opposite to each other and scrape against each other on directly adjacent screw shafts.

[0045] There is currently a conflict between the need to degas or disperse (both of which require shearing forces) and the need to avoid extrudate damage. It is advantageous to combine the need to degas or disperse with the need to protect the extrudate so that degassing or dispersion is optimized while extrudate damage is minimized. In addition, if the same portion of the total amount of extrudate is repeatedly sheared, it is not conducive to degassing or dispersion because little extrudate is exchanged at the inner wall of the extruder housing hole.

[0046] The problems of extrudate damage and energy input are addressed, for example, in WO2009152973A1 ([3]), in which pairs of screw elements for a multi-shaft screw machine having screw shafts scrape precisely in the same direction, have two or more screw blades Z, a center distance A, and an outer diameter DE, wherein the sum of the tooth top angles of a pair of screw elements is greater than 0 and less than

[0047]

[0048] Their use is described. The extruder disclosed in [2] also preferably uses such screw elements. However, the use of such screw elements does not improve the degassing effect.

[0049] US 4131371A ([4]) describes eccentric, practically mutually scraping conveying screw elements which rotate in the same direction and have an eccentric profile whose tooth tips are at different distances from the housing. This makes it possible to achieve a uniform loading of the extrudate by spreading it over the wall, providing more surface area for heat and mass transfer. In this way, the degassing effect can be improved. As for the wide tooth tips and the disadvantages associated with them, these are not addressed.

[0050] EP 0002 131 A1 ([5]) describes eccentric, asymmetric screw elements that actually scrape against each other, wherein the distance between one tooth top of the corresponding screw element and the inner wall of the extruder housing bore is smaller than the distance between one or more other tooth tops of the corresponding screw element and the inner wall of the extruder housing bore. The main effects described here are material exchange between the extruder housing bores and uniform high shear forces. These screw elements have Z ≥ 2 blades, Z tooth tops and Z grooves. The gap s between the screw elements (i.e. the distance between the screw profiles of a pair of screw elements facing each other on two directly adjacent screw shafts) is not taken into account.

[0051] It can be deduced from [5] that the sum of the tooth tip angles SKW0 of each screw element in a pair of screw elements (in which the two screw elements just scrape each other) is,

[0052]

[0053] There can be multiple mathematically equivalent formulas.

[0054] It is known to those skilled in the art and stated, for example, on pages 39 to 41 and 113 to 121 of [1] that technically designed screw elements must have clearances, including clearances s between the screw elements and clearances δ between the screw elements and the housing wall, in order to ensure the functioning of the extruder. The clearances are necessary because they avoid metal "seizure", manufacturing tolerances, roughness, angular deviations, uneven thermal expansion and excessive stresses on the extrudate due to insufficient spacing between two directly adjacent screw elements on two directly adjacent screw shafts. The above-mentioned articles also explain methods for determining the exact geometry of the elements to be produced based on the clearances and the precisely scraped profile. These methods are called clearance strategies.

[0055] The longitudinal section equidistance, circular equidistance and spatial equidistance strategies are also referred to as longitudinal section equidistance calculation rules, circular equidistance calculation rules and spatial equidistance calculation rules in the following. Another gap strategy is the strategy of increasing the center distance as described on pages 40 and 41 of [1].

[0056] For example, spatial isometry is mentioned on pages 40 and 41 of [1]. The spatial isometry can be expressed, for example, by the parameter of the outer surface of the precisely scraped screw element: As a starting point, where a and b are based on the equations describing the relevant exact scraping of the outer surface of the screw element The following is an example of the selected parameter.

[0057] For the sake of convenience below, a rectangular coordinate system is assumed in which the coordinate along the extruder rotation axis is designated as z, and x and y are coordinates on a plane perpendicular to the rotation axis, which intersects this plane at x=0, y=0 and z=0.

[0058] For example, in the case of a pair of screw elements, the two screw elements face each other on two adjacent screw shafts and scrape each other exactly, the screw profile of each of the two screw elements is in the xy plane, wherein the corresponding rotation axis X coincides with the z axis and the distance r from the rotation axis e (γ) is defined as a 2π periodic function of the screw profile at the angle γ to the x-axis and can be represented by the following expression (5) for the exactly scraped screw element profile:

[0059]

[0060] In this case, a=γ and b=z can be chosen.

[0061] Such a pair of screw elements can, for example, be configured as a pair of conveying elements, or as a pair of kneading disks.

[0062] To construct the conveying element, the screw profile is continued helically in a plane in order to obtain a precisely scraped limited surface of the screw element. For a screw element with pitch T, the following results are obtained with the z coordinate as an additional parameter,

[0063]

[0064] A positive sign indicates a clockwise rotating screw profile, a negative sign indicates a counterclockwise rotating screw profile.

[0065] For the kneading disk, the screw profile is displaced in space along the z-axis, so that the result is:

[0066]

[0067] If a screw profile (for example a precisely scraped screw profile) is constructed over an area in a plane by an arc i having a center coordinate and radius r i , and β is an angle, for which the arc represents the exact truncated screw profile, the arc can be described as

[0068]

[0069] The following formula applies to the expression of the confined surface of the transmission element that is precisely scratched in space:

[0070]

[0071] And, in contrast, the expression for the confined surface of a precisely scraped kneading disk is as follows

[0072]

[0073] In conveying elements, the pitch T of a screw element is the axial length required for a complete rotation of the screw profile of the screw element.

[0074] When calculating the screw profile, the calculation starts from a pair of screw elements with a screw profile that is just scraped. The screw profile of a pair of screw elements that is actually scraped is determined by taking into account the gap s between the screw elements and the screw elements, which can be defined, for example, in the parameter expression Then, apply the spatial isometric calculation rule as follows: The corresponding normal vector is

[0075]

[0076] The symbol should be selected to make Pointing away from the axis of rotation. The outer surface of the technically designed screw element Then the following parameter expression can be used to process

[0077]

[0078] Other spatial isometric calculation rules according to the present invention may also be used.

[0079] The circular isometry method also assumes an exactly scraped screw profile in the plane. Starting from the exactly scraped screw profile in the xy plane, a vertical line is cut at each point, wherein the direction of the vertical line is chosen to point to the inside of the screw profile. The point is shifted along this vertical line towards the inside of the screw profile by s / 2 so that it belongs to the technically executed screw profile. If a part of the exactly scraped screw profile is a radius r i The corresponding part of the screw profile implemented in the relevant technology has the same center and radius r i -s / 2 arc.

[0080] This is the circle equidistant calculation rule in the present invention.

[0081] Other circle equidistant calculation rules according to the present invention may also be used.

[0082] Through the longitudinal section equidistance, spatial equidistance and circular equidistance methods, different surface curves of the technically executed screw profile may overlap, so starting from the rotation center P of the screw profile, several points on the screw profile curve can be selected at a certain angle. Then, the points closer to the rotation center P among the above points are used to manufacture a technically feasible screw profile.

[0083] Various shapes (e.g., coordinate tables) may be used to represent the technically effective screw profile to be produced. A preferred method specifies the distance r(γ) from the axis of rotation as a periodic function of the angle γ with the x-axis of 2π or 360°, using the following expression:

[0084]

[0085] All of the above methods will slightly increase the wing angle and slightly reduce the tooth top angle compared to the wing angle and tooth top angle of the precisely scraped screw profile. The tooth top angle obtained by the spatial equidistance method is always smaller than the tooth top angle obtained by the longitudinal section equidistance method, and the tooth top angle obtained by the circular equidistance method is always smaller than the tooth top angle obtained by the circular equidistance method. The larger the slope, the larger the tooth top angle of spatial equidistance and longitudinal section equidistance. When the slope tends to infinity, the spatial equidistance and longitudinal section equidistance tend to circular equidistance, that is, when the slope tends to infinity, the tooth top angle provided by the spatial equidistance and longitudinal section equidistance calculation rules is the same as the tooth top angle provided by the circular equidistance calculation rule.

[0086] All methods for determining a technically feasible screw profile geometry based on a precisely scraped screw profile, i.e. a gap strategy, result in a screw element that is smaller in size than a screw element with the precisely scraped screw profile, so that a technically feasible screw profile geometry is obtained: a distance is established between the precisely scraped screw profile and the technically feasible scraped screw profile. The gap strategy serves to determine the gap s between the screw elements, 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. Here, this gap s between the screw elements does not have to be constant between the two screw elements, but is preferably constant.

[0087] In order to produce a constant gap s between the screw elements when the screw elements scrape against each other, the spatial equidistant explained above is preferred.

[0088] Large gaps s between the screw elements reduce the shear forces and thus the energy input to the extrudate. However, too large gaps s between the screw elements and the gaps δ between the screw elements and the housing can also be a disadvantage of the extruder implemented in the technology. These gaps lead to a reduced scraping effect of the screw elements (where the screw elements are positioned opposite each other in pairs on directly adjacent screw shafts) and to a deterioration of the exchange of the extrudate on the screw elements or on the housing bores, thereby increasing the risk of producing extrudates damaged by long residence times and the risk of the damaged extrudates entering the extrudate flow, where the damaged extrudates entering the extrudate flow can lead to spots, gels or discoloration, which in turn affect the quality of the desired final product. Too large gaps s between the screw elements and the gaps δ between the screw elements and the housing can also lead to a reduced degassing effect, and the mixing effect can also be reduced due to the reduced exchange of the extrudate on the screw surface or on the inner wall of the housing bore.

[0089] Furthermore, the influence of the gap s between the screw elements on the sum of the tooth tip angles is limited.

[0090] It is known to the person skilled in the art that, in addition to the screw profile, other variables also have an influence on the geometry of the screw elements. These variables are listed, for example, on page 115 of [1].

[0091] As shown above, the prior art does not address how to achieve good degassing of the extrudate in the extruder (requiring high shear force) while avoiding damage to the extrudate due to excessive energy input (caused by high shear force), and also how to increase the exchange of the extrudate at the inner wall of the extruder housing hole (otherwise the degassing rate of the extrudate is very low) and achieve good mixing and dispersion effects.

[0092] Good mixing is a prerequisite for good degassing, because degassing mainly occurs at the surface of the extrudate, and fresh, undegassed extrudate must be transported to the surface to be further degassed. In addition, the degassed extrudate should be as uniform as possible, which requires uniform energy input and avoidance of local overheating.

[0093] As is known to those skilled in the art and as explained, for example, on pages 475 to 478 of [1], particularly high shear stresses are present in the tooth tip region near the inner wall of the housing bore, which are beneficial to dispersion. This is particularly important when dispersing solid agglomerates used as fillers or reinforcing materials, which is another basic operation of the extruder. Therefore, it is known to those skilled in the art that frequent replacement of the sheared material is also beneficial to the dispersion effect. However, on page 478 of [1], only a reduction in production is mentioned as a method for improving the dispersion effect, which is undesirable for economic reasons.

[0094] It was therefore an object of the present invention to ensure good degassing of the extrudate in the extruder while avoiding damage to the extrudate by low energy input. Another object of the present invention was to additionally ensure good dispersion.

[0095] In particular, the object of the present invention is to provide a pair of screw elements which ensure good degassing of the extrudate in the extruder while preventing damage to the extrudate. The pair of screw elements should also achieve a good dispersion effect and a good mixing effect. Since the pair of screw elements can reduce the energy input to the extrudate while ensuring that the degassing of the extrudate is not affected, damage to the extrudate is preferably avoided.

[0096] Surprisingly, this object can be achieved by a multi-shaft screw machine having the features of the independent claim.

[0097] This object can also be achieved by a method according to claim 12 .

[0098] In the present invention, the following applies:

[0099] The screw profile is a closed convex curve. The screw profile comprises several different curves, which are called "tips", "wings" or "grooves" according to their geometrical properties.

[0100] The radius of curvature at every point of the screw profile is less than or equal to the center distance and greater than or equal to zero. A radius of curvature of zero is equivalent to a kink in the screw profile.

[0101] A kink is a point on the screw profile from which the following parameter expressions are given

[0102]

[0103] Where the parameter value l is the arc length l. k In the case of , the left-hand limit value and the right-hand limit value of the functions x(l) and y(l) coincide (which is consistent with the property that the curve is closed at this point), that is,

[0104]

[0105] And the direction vectors of the curve derivative based on arc length l do not point in the same direction, that is, their vector product does not vanish:

[0106]

[0107] In the case where two arcs as part of the screw profile do not meet each other tangentially, the kink is located at the intersection of the two arcs. A kink can also be considered as an arc with a midpoint equal to the intersection of the two arcs and a radius of zero; this is the case with the kink shown in the embodiment.

[0108] A curve is an unbroken line with a length greater than 0 but no width, where the first endpoint and the second endpoint of the curve are not the same point; that is, the first endpoint and the second endpoint do not coincide.

[0109] The curve may include a finite number of curve segments, wherein a first curve segment has a common contact point with a second curve segment, the second curve segment being directly adjacent to the first curve segment.

[0110] However, the curve may also include only one curve segment.

[0111] A curve may have only a limited number of kinks, and by definition, the kinks of said curve can only be located at common contact points of two directly adjacent curve segments on the curve. A kink can also be located at a common contact point between two directly adjacent curves.

[0112] A curve segment is a segment of a curve, wherein a first endpoint and a second endpoint of the curve segment are not the same point, that is, the first endpoint and the second endpoint do not coincide.

[0113] The curve segment is preferably selected from the group comprising the following members: a circular arc, an elliptical arc, a parabolic arc, or a spline or a portion of a spline, the result obtained by applying the longitudinal section isometry calculation rule described on pages 117 to 121 of [1] to a circular arc, an elliptical arc, a parabolic arc, or a spline or a portion of a spline, the result obtained by applying the spatial isometry calculation rule to a circular arc, an elliptical arc, a parabolic arc, or a spline or a portion of a spline, or the result obtained by applying the circular isometry calculation rule to a circular arc, an elliptical arc, a parabolic arc, or a spline or a portion of a spline.

[0114] For curve segments For example, it is a line that can be represented by a parametric expression for its arc length l:

[0115]

[0116] Among them, x k,l (l) and y k,l (l) is an analytic function, x and y are the coordinates of a line in the plane, so it can be represented by an infinite power series, is continuous, can be differentiated arbitrarily many times, and therefore has no kinks.

[0117] A segment can be a curved segment or a kink.

[0118] A closed convex curve is an uninterrupted line with a length greater than 0 but no width, including one or more curves, each of which includes one or more curve segments. The closed convex curve does not have a distinct start and end point. Starting from any point on the curve, the length of each curve segment around the curve is added to obtain the length of the curve. Each tangent of the closed convex curve is outside the area enclosed by the curve.

[0119] Since all the curve segments of the screw profile are located in one plane, the closed curve (ie the screw profile) divides the area of ​​the plane into the area inside the closed curve and the area outside the closed curve.

[0120] An arc is a curve segment where all points on the arc have the same distance (called radius) from the common center point. The starting point and end point of the arc are not the same point.

[0121] An arc is considered a true arc only if all its points have the same center and radius and the points of the arc form an uninterrupted curve segment; in other words, two directly adjacent arcs with a common contact point are considered two arcs only if they have different centers or different radii. According to the invention, only arcs with a center angle less than π are used.

[0122] The characteristic of arc i is that its center coordinate xm i and ym, radius r i , starting angle β a,i and the central angle α i , where the effective value of the angle β in formula (10) is a,i Between the following formula

[0123] β e,i =β a,i +α i (18).

[0124] The center of rotation P of the screw profile is the intersection of the axis of rotation X of the screw element and a cross section at right angles to this axis of rotation. The center of rotation P of the screw profile (hereinafter also referred to as pivot point P or pivot point) also coincides with the bore center M of the housing bore in which the corresponding screw element is located or for which the corresponding screw element is designed.

[0125] With respect to the screw profile, the pivot point P is the point about which the screw profile, as a cross-sectional image of the screw elements, rotates.

[0126] The tooth tip is a curve of the screw profile in which all points of this curve (except the contact points with the two curve segments immediately adjacent to the tooth tip) are at a greater distance from the pivot point P than the distances of the two curve segments immediately adjacent to the tooth tip from the pivot point P. According to the invention, the curve forming the tooth tip is precisely a curve segment of a circular arc curve centered at the pivot point P of the screw profile.

[0127] According to the invention, all tooth crests of the screw profile are preferably each formed by a single circular arc, wherein each of said circular arcs is centered on a pivot point P of the screw profile.

[0128] The tooth tip radius is the distance of the corresponding tooth tip from the pivot point P of the screw profile.

[0129] A groove is a curve of the screw profile in which all points of this curve (except the contact points with two curve segments adjacent to the groove) are at a smaller distance from the pivot point P than the distances of the two curve segments adjacent to the groove.

[0130] According to the invention, the curve forming the groove is exactly a curve section of a circular arc curve centered at the pivot point P of the screw profile.

[0131] According to the invention, all grooves of the screw profile are preferably each formed by a single circular arc, wherein each of said circular arcs is centered on a pivot point P of the screw profile.

[0132] The wing is a curve of the screw profile between the tooth tip and the groove that is convex toward the rotation center P, wherein this wing has a common contact point with the tooth tip and a common contact point with the groove.

[0133] The wing may be a single curved section, or may include a plurality of curved sections. The radius of curvature of each point of the wing is less than or equal to (preferably less than) the center distance A.

[0134] According to the present invention, the mathematical expression based on the curved section of the ramp is preferably selected from the group of mathematical expressions including the following members: an arc, the result obtained by applying the longitudinal section isometric calculation rule according to pages 117 to 121 of [1] to an arc with a curvature radius less than or equal to the center distance A, the result obtained by applying the spatial isometric calculation rule to an arc with a curvature radius less than or equal to the center distance A, and the result obtained by applying the circular isometric calculation rule to an arc with a curvature radius less than or equal to the center distance A, wherein the center distance A mentioned above is the center distance of the screw profile of the precise scraping including only the arc.

[0135] The components of a pair of screw elements or the associated screw profile according to the invention may be numbered using index symbols such as n, m, or i, or with natural numbers, in order to distinguish these components if they occur multiple times.

[0136] Furthermore, the following also applies in the context of the present invention:

[0137]

[0138]

[0139]

[0140] Table 1: Parameters representing the screw profile

[0141] This specification has so far explained how to "select" a value for a variable, such as selecting: pitch T, gap δ between screw element and housing wall, gap s between screw element and screw element, or additional gap SP, but these variables cannot be assigned arbitrarily if the screw profile obtained from a pair of screw elements is to be used as expected. Those who know the technology of extruder screw element design can estimate or use CFD simulation to determine the reasonable values ​​that should be assigned to these variables for a given extruder based on, for example, the viscosity of the extrudate at the processing temperature, the expected filling level of the extruder, the expected energy input to the extrudate, or the rotation speed of the shaft. In particular, if this value is obtained by estimation, it is usually necessary to confirm this value through simulation or to determine this value more accurately; the above operation is usually performed repeatedly.

[0142] By selecting the additional gap SP, the mixing effect and the mass transfer at the inner wall of the housing can be adjusted. The maximum shear force can be set by appropriately selecting δ and the tooth tip angle, and thus the length between the tooth tip and the housing where the maximum shear force acts can be set by using f.

[0143] (1) In the first embodiment of the present invention, the above object is achieved in the following manner:

[0144] A pair of screw elements for a multi-shaft screw machine having:

[0145] m screw shafts SW1 to SW rotating in the same direction and at the same speed m , the m screw shafts SW1 to SW m The corresponding adjacent rotation axes X1 to X m In a cross section at right angles to the axis of rotation, there is a center distance A,

[0146] as well as

[0147] m circular shell holes that penetrate each other, wherein each of the circular shell holes has the same shell hole inner diameter D, and the hole centers M1 to M m The distance between the centers M1 and M2 of the circular shell hole is the same as the center distance A.m With the screw shaft SW1 to SW m The corresponding rotation axis X1 to X m coincides with the rotation center P1 of the screw element to P m coincide,

[0148] wherein the two screw elements of the pair of screw elements are opposite each other on directly adjacent screw axes,

[0149] wherein the two screw elements of the pair of screw elements scrape against each other, and the gap between the screw elements is s,

[0150] wherein the two screw elements have an asymmetrical screw profile,

[0151] wherein each of the two screw elements has two tooth tops,

[0152] wherein for each of the two screw elements, the distances of the two tooth tops from the corresponding rotation center P of the screw profile are different,

[0153] wherein, in each case, one of the tooth tops is at a distance D / 2 minus the clearance δ between the screw elements and the housing wall, minus an additional clearance SP, from the corresponding rotation center P, and the other tooth top is at a distance D / 2 minus the clearance δ between the screw elements and the housing wall, but no longer minus an additional clearance SP,

[0154] wherein the gap δ between the screw element and the housing wall of the two screw elements is identical and the additional gap SP of the two screw elements is identical,

[0155] The sum of the tooth top angles BKW of the two screw elements is greater than 0 in radians.

[0156] as well as

[0157] For the coefficient f,

[0158] f=BKW / BKGW (19)

[0159] For coefficient f, the coefficient f is greater than 0 and less than or equal to 0.95,

[0160] Where BKW is the sum of the tooth top angles of the two screw elements in radians, and BKGW is determined as:

[0161]

[0162] Equal gaps δ between the screw elements and the housing wall or equal additional gaps SP result in the advantage of a uniform energy input.

[0163] (2) f is preferably greater than or equal to 0.1 and less than or equal to 0.8, and f is particularly preferably greater than or equal to 0.2 and less than or equal to 0.6.

[0164] This preferred embodiment of the invention is a second embodiment according to the first embodiment described above.

[0165] (3) Preferably, the ratio of the gap s between the two screw elements in the pair of screw elements and between the screw elements to the inner diameter D of the housing hole is 0.002 to 0.05, preferably 0.003 to 0.03, and particularly preferably 0.005 to 0.02.

[0166] This preferred embodiment of the present invention is a third embodiment according to the first embodiment or the second embodiment described above.

[0167] (4) More preferably, the ratio of the gap δ between the screw element and the housing wall to the inner diameter D of the housing hole is 0.002 to 0.05, preferably 0.003 to 0.03, particularly preferably 0.005 to 0.02. This particularly preferred embodiment of the method of the present invention is a fourth embodiment according to one of the embodiments described above.

[0168] (5) More preferably, the ratio of the additional gap SP to the groove depth GT of the corresponding screw element is 0.015 to 0.4, preferably 0.02 to 0.3, and particularly preferably 0.025 to 0.25.

[0169] A particularly preferred embodiment of the present invention is the fifth embodiment according to one of the embodiments described above.

[0170] (6) More preferably, the tooth addendum angles of the pair of screw elements having the gap δ between the screw element and the housing wall but not having the additional gap SP with respect to the inner wall of the housing hole are the same.

[0171] This more preferred embodiment of the invention represents a sixth embodiment according to one of the embodiments described above.

[0172] (7) Still more preferably, the tooth addendum angles of the tooth addendums of the pair of screw elements having the gap δ between the screw element and the housing wall and the additional gap SP with respect to the inner wall of the housing hole are the same.

[0173] This more preferred embodiment of the invention represents a seventh embodiment according to one of the embodiments described above.

[0174] (8) It is also preferred that, for two screw elements in the pair of screw elements, the tooth top angle of the screw element tooth top of the pair of screw elements having the gap δ between the screw element and the shell wall and the additional gap SP is greater than the tooth top angle of the screw element tooth top of the pair of screw elements having the gap δ between the screw element and the shell wall but not having the additional gap SP.

[0175] This additional preferred embodiment of the invention represents an eighth embodiment according to one of the embodiments described above.

[0176] (9) Very particularly preferably, the screw profiles of the pair of screw elements do not coincide, wherein the screw profiles of the two screw elements can be brought into contact with one another by mirroring them along an axis and then rotating them.

[0177] This very particularly preferred embodiment of the invention is the ninth embodiment according to one of the first to eighth embodiments described above.

[0178] The fact that the screw profiles of the two screw elements can merge with each other by mirroring along an axis and then rotating them means that the energy input to each of the two screw elements in the pair of screw elements is the same. This has proven to be advantageous because it prevents local overheating of the extrudate when the pair of screw elements of the invention is used as intended.

[0179] (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) wings.

[0180] This very particularly preferred embodiment of the invention is the tenth embodiment according to one of the first embodiments described above.

[0181] (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) wings.

[0182] This particularly preferred embodiment of the invention represents an eleventh embodiment according to one of the tenth embodiments described above.

[0183] The pair of screw elements according to the present invention can be implemented as a pair of conveying elements, or can be a pair of kneading disks; preferably, according to the present invention, they are embodied as a pair of conveying elements.

[0184] The invention also relates to a multi-shaft screw machine comprising a pair of screw elements according to the invention.

[0185] The invention also relates to a method for producing or processing an extrudate in a multi-axis screw machine using a pair of screw elements according to the invention. The extrudate is preferably a plastic or viscoelastic substance, particularly preferably a polymer melt, in particular a melt of a thermoplastic or elastomer, in particular a melt of a polycarbonate or polyester carbonate or a thermoplastic polyurethane or a rubber. The method preferably comprises the following steps:

[0186] (1) providing a multi-shaft screw machine, the multi-shaft screw machine comprising a pair of screw elements according to the present invention;

[0187] (2) Production or processing of extrudates.

[0188] The invention also relates to a method for producing a screw profile of a pair of screw elements according to the invention starting from a precision scraping screw profile according to the prior art.

[0189] The screw profile of a pair of screw elements according to the invention can, for example, be produced as described below, starting from an existing extruder with a center distance A and an inner diameter of the housing bore D, wherein each of the two screw elements has exactly two tooth tops and the two screw elements of the pair of screw elements are designated as left screw element and right screw element, respectively indicated by the subscripts l and r in the formula notation.

[0190] In order to calculate the values ​​of the screw elements for generating the screw profile of a pair of screw elements according to the present invention, the variable values ​​of the pair of screw elements that scrape each other precisely and the variable values ​​of the pair of screw elements that actually scrape each other are used simultaneously, wherein the variable values ​​of the pair of screw elements that actually scrape each other depend on the variable values ​​of the pair of screw elements that scrape each other precisely and can be calculated according to Table 1.

[0191] (I) Step 1: Selecting values ​​of the clearance s between the screw elements and the clearance δ between the screw elements and the housing wall suitable for the screw elements to be implemented.

[0192] (II) Step 2: Determine the value of the outer radius RE of the precisely scraped screw profile according to the following formula:

[0193] RE=DE / 2 (21)

[0194] in

[0195] DE = D - 2δ + s (22).

[0196] (III) Step 3, determining the value of the inner radius RI of the precisely scraped screw profile according to the following formula:

[0197]

[0198] (IV) Step Four, determine the outer radius RA of the technically executable / correctly usable screw element according to the following formula:

[0199] RA = D / 2 - δ (24).

[0200] (V) Step Five, determine the inner radius RK of the technically executable / correctly usable screw element according to the following formula:

[0201] RK = A – D / 2 + δ - s (25).

[0202] (VI) Step Six, calculate the groove depth of the technically executable / correctly usable screw element using the following formula:

[0203] GT = RA - RK (26).

[0204] (VII) Step Seven, select a value for the additional clearance SP of the technically executable / correctly usable screw element, where SP < GT / 2 is always true.

[0205] Steps (II) to (V) can be performed in any order.

[0206] (VIII) Step Eight, according to formula (4) or (27), determine the initial sum SKW0 of the tooth tip angles of each corresponding screw element in a pair of precisely scraped screw elements:

[0207]

[0208] (IX) Step Nine, calculate the sum BSKW0 of the tooth tip angles of a pair of precisely scraped screw elements according to the following formula

[0209] BSKW0 = 2g SKW0 (28)

[0210] where the coefficient g is selected, 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.

[0211] (X) Step Ten, for a pair of screw elements that precisely scrape each other, the tooth tip angle KW0 of the precisely scraped profile of the left screw element l,δ and the tooth tip angle KW0 of the right screw element r,δ are determined for the tooth tips of the corresponding screw elements, in each case, the tooth tips having a clearance δ (marked with subscript δ in the formula notation) between the screw element and the housing wall with respect to the inner wall of the housing hole, but not having the additional clearance SP. Specifically, the sum of the tooth tip angles of these tooth tips applies to the following formula:

[0212] KW0 l,δ + KW0r,δ <BSKW0 (29)

[0213] Preferably

[0214]

[0215] And particularly preferably

[0216]

[0217] All tooth top angles are greater than 0.

[0218] (XI) Step 11: For a pair of screw elements that scrape each other precisely, the tooth top angle KW0 of the screw profile of the left screw element is l,δ+SPO and the tooth top angle KW0 of the right screw element r,δ+SP is determined for the tooth tops of the corresponding screw elements, which in each case have a clearance δ between the screw element and the housing wall and a clearance SP, i.e. δ+SP (indicated by the subscript δ+SP in the formula notation), specifically, the sum of the tooth top angles of these tooth tops applies to the following formula:

[0219] KW0 l,δ+SP +KW0 r,δ+SP =BSKW0-(KW0 l,δ +KW0 r,δ ) (32)

[0220] and preferably

[0221] KW0 l,δ+SP +KW0 r,δ+SP =2KW0 δ+SP =BSKW0-(KW0 l,δ +KW0 r,δ ) (33).

[0222] (XII) Step 12, the screw profile of the first screw element (herein selected as the left screw element, or can also be selected as the right screw element) is used to construct a pair of screw elements for precision scraping and to form the curves described below. These curves are directly connected along the rotation direction specified below, where the rotation direction can be mathematically positive or negative, and the curves merge with each other at their respective endpoints. This screw profile of the first screw element represents the mother screw profile.

[0223] -Arc with radius RE and angle KW0 l,δ , the center is the rotation center P of the screw profile, wherein the arc is the first tooth top;

[0224] - a first wing [wing 1];

[0225] -Arc with radius RI and angle KW0 r,δ , the center is the rotation center P of the screw profile, wherein the arc is the first groove;

[0226] - a second wing [wing 2];

[0227] -Arc with radius RE-SP and angle KW0 l,δ+SP , the center is the rotation center P of the screw profile, wherein the arc is the second tooth top;

[0228] - third wing [wing 3];

[0229] -Arc with radius RI+SP and angle KW0 r,δ+SP , the center is the rotation center P of the screw profile, wherein the arc is the second groove;

[0230] - a fourth wing [wing 4], for closing the profile between the second groove and the first tooth crest.

[0231] (XIII) Step thirteen, the screw profile of the second screw element (here selected as the right screw element) is used to construct a pair of screw elements for precision scraping. 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 curve segments and (if any) kinks i=1..n. Then, the precision scraping screw profile of the right screw element is composed of the curve segments and (if any) kinks corresponding to the screw profile of the left screw element, the kinks are called i'=1..n.

[0232] For curve segment i, in the parameter expression there is

[0233]

[0234] For p a,i ≤p≤p e,i , analytical function x i (p) and y i The derivative of (p) is not zero at the same value. Without general restrictions, as p increases Mathematically speaking, the normalized normal vector is formed by rotating around the pivot point in the sense of being positively pointed.

[0235]

[0236] Here, the sign is chosen so that the normal vector points out of the contour, away from the pivot point.

[0237] Each curve segment has a starting angle β a,iand the end angle β e,i When p=p a When , the starting angle satisfies the following conditions

[0238]

[0239] When p = p a When , the end angles of the components of the normal vector are

[0240]

[0241] where β e,i >β a,i And β e,i <β a,i +π.

[0242] The curve segment i on the left screw corresponds to the curve segment i′ on the right screw, and the coordinate expression is as follows

[0243]

[0244] In a preferred embodiment, the curve segment i represents an arc with the following parameter expression

[0245]

[0246] When β a,i ≤β≤β e,i When , the normalized normal vector is as follows

[0247]

[0248] And the expression for the corresponding arc is

[0249]

[0250] where r i′ =Ar i 、xm i′ =xm i +A and ym i′ =ym i and (as described above) β a,i ≤β≤β e,i .

[0251] If the curve segment represents r i =A circle, then r i′ =0, and the corresponding segment is a kink.

[0252] If segment i represents a kink with coordinates, it corresponds to an arc with radius , the expression of which can be derived from the equation above, where r i′ =A.

[0253] In a preferred embodiment, the screw profile of the screw element according to the invention is derived from a precisely scraped screw profile by using increased center distances, circular equidistance, longitudinal equidistance or spatial equidistance,

[0254] The sum of the tooth top angles of the two screw elements BKW is greater than 0 in radians and for the coefficient f

[0255] f=BKW / BKGW (42)

[0256] For coefficient f, the coefficient f is greater than 0 and less than or equal to 0.95,

[0257] Where BKW is the sum of the tooth top angles of the two screw elements in radians, and BKGW is determined as:

[0258]

[0259] In another preferred embodiment, the curve segment included in the screw profile of the screw element according to the present invention is selected from a group of mathematical formulas, wherein the group of mathematical formulas includes the following members: a circular arc, an elliptical arc, a parabolic arc, a spline or a part of a spline, the result obtained by applying the longitudinal section isometric calculation rule according to pages 117 to 121 of [1] to a circular arc, an elliptical arc, a parabolic arc, a spline or a part of a spline, the result obtained by applying the spatial isometric calculation rule to a circular arc, an elliptical arc, a parabolic arc, a spline or a part of a spline, or the result obtained by applying the circular isometric calculation rule to a circular arc, an elliptical arc, a parabolic arc, a spline or a part of a spline.

[0260] In another preferred embodiment, at least two pairs of screw elements according to the invention are arranged axially directly one behind the other in a multi-shaft screw machine. For example, PCT / EP2021 / 078863 shows such an arrangement in principle, wherein PCT / EP2021 / 078863 specifically describes pairs of screw elements that clean each other precisely, while the present invention relates to screw elements that actually scrape.

[0261] Figure 1 The actual scraped screw profile of the left screw element in Example 2 is shown to illustrate the geometry.

[0262] The present invention will be explained below with reference to Examples, but it is not intended that the present invention be limited to these Examples.

[0263] Example 1 (Comparative Example - No Innovation)

[0264] The non-inventive embodiment 1 is based on EP0002131A1 Figure 5 (A) and Figure 5(B) a pair of screw elements that actually scrape against each other, wherein T / D=1.2, and The spatial equidistant calculation rule is additionally applied according to EP 0002131 A1 Figure 5 (A) or Figure 5 (B) The screw profile of the screw elements is asymmetrical, non-uniform, but can be merged with each other by mirroring along an axis and then rotating them.

[0265] The precisely scraped screw profile of the left screw element comprises segments i=1 to 12, which are arcs or kinks. Table 2 gives the arcs, the starting angle, the ending angle, the radius of the arc relative to the inner diameter D of the housing hole, the x-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P1 of the left screw profile, and the y-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P1 of the left screw profile. The tooth tops of the actual scraped screw profile are arcs 1 and 7. The value to identify kinks.

[0266]

[0267]

[0268] Table 2: Arc of the precise scraping profile of the left screw profile in Example 1

[0269] The precisely scraped screw profile of the right screw element includes segments i=1' to 12', which are arcs or kinks. Table 3 shows the starting angle, the ending angle, the radius of the arc relative to the inner diameter D of the housing hole, the x-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P2 of the right screw profile, and the y-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P2 of the right screw profile. The tooth tops of the actual scraped screw profile are arcs 4' and 10'. The value can be used to identify kinks.

[0270]

[0271] Table 3: Arc of the precisely scraped screw profile of the right screw element in Example 1

[0272] The sum of the tooth tip angles of the two precisely scraped screw profiles of this pair of screw elements is BKW0=1.72356 radians (98.75°).

[0273] The screw profile of the technically executable, practically scraped screw element of a pair of screw elements according to Example 1 is derived from the precisely scraped screw profile, asymmetrical, inconsistent, but capable of merging with each other by mirroring along the axis and then rotating them. The tooth top angle of the practically scraped screw profile of a single screw element is then 0.73115 radians (41.89 degrees). The sum of the tooth top angles of the screw profiles of the pair of screw elements in the radian system BKW=1.462 (83.78°).

[0274] The limit value of the sum of the tooth top angles of the pair of screw elements calculated according to formula (2) is BKGW=1.444 (82.71°). Therefore, BKW>BKGW, and its ratio This pair of screw elements therefore does not comply with the invention.

[0275] Figure 2 The actual scraped screw profiles of two screw elements are shown, as well as the corresponding exact scraped screw profiles from which the actual scraped screw profiles are derived. Table 4 shows the screw profiles of the left screw element on the plane according to formula (13), i.e., starting from the rotation center P1 of the left screw element, the radius about the angle γ l The angular spacing between the radii is two degrees, but additional points are given in the transition to the tooth tip area or the groove area. Table 5 shows the corresponding coordinates of the screw profile of the right-hand screw element starting from the rotation center P2 of the right-hand screw element; Figure 3 A plan view of a pair of screw elements not according to the invention is shown.

[0276]

[0277]

[0278] Table 4: Screw profile of the left screw element of Example 1 without the inventive screw element pair

[0279]

[0280]

[0281] Table 5: Screw profile of the right screw element of the screw element pair without the inventive method in Example 1 Example 2 (innovative)

[0282] Embodiment 2 according to the present invention is a pair of screw elements which actually scrape against each other, wherein T / D=1.2, and That is, the values ​​of the variables are the same as the corresponding variables in Example 1, wherein the spatial equidistant calculation rule is additionally applied. The flight profiles of the screw elements are asymmetrical, non-coincident, but can merge with each other by mirroring along an axis and then rotating them.

[0283] The precisely scraped screw profile of the left screw element comprises segments i=1 to 20, which are arcs or kinks. Table 6 gives the arcs, the starting angle, the ending angle, the radius of the arc relative to the inner diameter D of the housing hole, the x-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P1 of the left screw profile, and the y-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P1 of the left screw profile. The tooth tops of the precisely scraped screw profile are arcs 1 and 11. The values ​​can be used to identify kinks.

[0284] The precisely scraped screw profile of the right screw element includes arcs i=1' to 20', which are arcs or kinks. Table 7 gives the arcs, the starting angles, the ending angles, the arc radius relative to the inner diameter D of the housing hole, the x-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P2 of the right screw profile, and the y-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P2 of the right screw profile. The tooth tops of the actual scraped screw profile are arcs 6' and 16'. The sum of the tooth top angles of the two precisely scraped screw profiles of the pair of screw elements is BKW0=0.8784 radians (50.32°).

[0285]

[0286]

[0287] Table 6: Arc of the precisely scraped screw profile of the left screw element in Example 2

[0288]

[0289] Table 7: Arc of the precisely scraped screw profile of the right screw element in Example 2

[0290] The screw profile of the technically executable, actual scraped screw element of a pair of screw elements according to Example 2 is derived from the exact scraped screw profile, is asymmetrical, inconsistent, but can merge with each other by mirroring along the axis and then rotating them. The tooth top angle of the actual scraped screw profile of a single screw element is then 0.3384 radians (19.30°). The sum of the tooth top angles of the screw profiles of the pair of screw elements is BKW=0.6769 radians (38.78°). The limit value of the sum of the tooth top angles of a pair of screw elements calculated according to formula (2) (as shown in Example 1) is BKGW=1.444 radians (82.71°). Therefore, BKW<BKGW, and its ratio This pair of screw elements is innovative.

[0291] Figure 4 The actual scraped screw profile of a pair of screw elements according to the invention and the corresponding precise scraped screw profile from which the actual scraped screw profile is derived are shown. Table 8 shows the screw profile of the left screw element on a plane according to formula (5), i.e., starting from the rotation center P1 of the left screw element, the radius is about the angle γ l The angular spacing between the radii is two degrees, but additional points are given during the transition to the tooth tip area or the groove area. Table 9 shows the corresponding coordinates of the screw profile for the right-hand screw element; Figure 5 Shown is a plan view of a pair of screw elements according to the present invention.

[0292]

[0293]

[0294] Table 8: Screw profile of the left screw element of the innovative screw element pair in Example 2

[0295]

[0296]

[0297] Table 9: Screw profile of the right screw element of the inventive screw element pair in Example 2 Example 3 (innovative)

[0298] Embodiment 3 is a pair of screw elements according to the present invention that actually scrape against each other, wherein and In addition, the spatial equidistant calculation rules apply. The screw profiles of the screw elements are asymmetrical, not identical, but can be brought into contact with one another by mirroring them along an axis and then rotating them.

[0299] The precisely scraped screw profile of the left screw element comprises segments i=1 to 20, which are arcs or kinks. Table 10 gives the arcs, the starting angle, the ending angle, the radius of the arc relative to the inner diameter D of the housing hole, the x-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P1 of the left screw profile, and the y-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P1 of the left screw profile. The tooth tops of the precisely scraped screw profile are arcs 1 and 11. The values ​​can be used The tops of the screw profile that are actually scraped are arcs 1 and 11.

[0300]

[0301]

[0302] Table 10: Arc of the precise scraping profile of the left screw profile in Example 3

[0303] The precisely scraped screw profile of the right-hand screw element includes arcs 1' to 20', which are arcs or kinks. Table 11 gives the arcs, the starting angle, the end angle, the radius of the arc relative to the inner diameter D of the housing hole, the x-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P2 of the right-hand screw profile, and the y-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P2 of the right-hand screw profile. The tooth tops of the precisely scraped screw profile are arcs 6' and 16'. The sum of the tooth top angles of the two precisely scraped profiles is BKW0 = 0.7716 radians (44.21°).

[0304]

[0305]

[0306] Table 11: Arc of the precise scraping profile of the right screw profile in Example 3

[0307] The screw profile of the technically executable, practically scraped screw element of the innovative pair of screw elements according to Example 3 is derived from the precisely scraped screw profile, and is also asymmetrical and inconsistent, but can be merged with each other by mirroring along the axis and then rotating them. The sum of the tooth top angles of the left screw profile and the right screw profile is 0.3464 radians (20.89°); therefore, the sum of the tooth top angles of the pair of screw elements is BKW=0.6928 (41.78°).

[0308] The limit value of the sum of the tooth top angles of a pair of screw elements calculated according to formula (2) is BKGW = 1.848 radians (105.86°). Therefore, BKW < BKGW, and its ratio This pair of screw elements is innovative.

[0309] Figure 6 The actual scraped screw profile of a pair of screw elements according to the invention and the corresponding precise scraped screw profile from which the actual scraped screw profile is derived are shown. Table 12 shows the screw profile of the left screw element according to formula (5), i.e., starting from the rotation center P1 of the left screw profile, the radius is about the angle γ l The angular spacing between the radii is two degrees, except at the transition to the tooth top or groove area, where additional points are given. Table 13 shows the corresponding coordinates of the screw profile for the right screw profile; Figure 7 Shown is a plan view of a pair of screw elements according to the present invention.

[0310]

[0311]

[0312] Table 12: Screw profile of the left screw element of the innovative screw element pair in Example 3

[0313]

[0314]

[0315] Table 13: Screw profile of the right screw element of the inventive screw element pair in Example 3 Example 4 (innovative)

[0316] Example 4 is a pair of screw elements according to the invention that are actually scraped against each other, wherein A / D=0.84, T / D=0.75, δ / d=0.005 and s / D=0.01, wherein the spatial equidistance calculation rule is additionally implemented. The screw profiles of the screw elements are asymmetrical, non-uniform, but can be merged with each other by mirroring along an axis and then rotating them.

[0317] The precisely scraped screw profile of the left screw element comprises segments i=1 to 20, which are arcs or kinks. Table 14 gives the arcs, the start angle, the end angle, the radius of the arc relative to the inner diameter D of the housing hole, the x-coordinate of the pivot point P1 of the left screw profile relative to the center of the inner diameter D of the housing hole, and the y-coordinate of the pivot point P1 of the left screw profile relative to the center of the arc i relative to the inner diameter D of the housing hole. The tooth tops of the precisely scraped screw profile are arcs 1 and 11. The values ​​can be used to identify kinks.

[0318]

[0319]

[0320] Table 14: Arc of the actual scraped screw profile of the left screw element in Example 4

[0321] The precisely scraped screw profile of the right-hand screw element includes arcs i=1' to 20', which are arcs or kinks. Table 15 gives the arcs, the starting angle, the ending angle, the radius of the arc relative to the inner diameter D of the housing hole, the x-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P2 of the right-hand screw profile, and the y-coordinate of the center of the arc i relative to the inner diameter D of the housing hole relative to the pivot point P2 of the right-hand screw profile. The tooth tops of the precisely scraped screw profile are arcs 6' and 16'.

[0322] The sum of the tooth tip angles of the two precisely scraped screw profiles of a pair of screw elements is BKW0 = 0.69814 radians (40°).

[0323]

[0324]

[0325] Table 15: Arc of the precisely scraped screw profile of the right screw element in Example 4

[0326] The screw profile of the technically executable, practically scraped screw element of the innovative pair of screw elements according to Example 4 is derived from the precisely scraped screw profile, and is likewise asymmetrical, inconsistent, but can be merged with each other by mirroring along the axis and then rotating them. The sum of the tooth top angles of the left screw profile and the right screw profile is 0.25885 radians (14.83°); therefore, the sum of the tooth top angles of the pair of screw elements is BKW=0.51766 (29.66°).

[0327] The limit value of the sum of the tooth top angles of a pair of screw elements calculated according to formula (2) is BKGW = 1.5703 radians (89.97°). Therefore, BKW < BKGW, and its ratio This pair of screw elements is innovative.

[0328] Figure 8 Shown is an actual scraped screw profile of a pair of screw elements according to the invention, and a corresponding precise scraped screw profile from which the actual scraped screw profile is derived. Fig. 9 Shown is a plan view of a pair of screw elements according to the present invention.

[0329] Table 16 shows the screw profile of the left screw element according to formula (5), that is, starting from the rotation center P1 of the left screw profile, the radius about the angle γ lThe angular spacing between radii is two degrees, except at the transitions to the tooth top or groove areas where additional points are given.

[0330] Table 17 shows the corresponding coordinates of the screw profile for the right screw profile.

[0331]

[0332]

[0333] Table 16: Screw profile of the left screw element of the innovative screw element pair in Example 4

[0334]

[0335]

[0336] Table 17: Screw profile of the right screw element of the inventive screw element pair in Example 4

[0337] BRIEF DESCRIPTION OF THE DRAWINGS AND LIST OF REFERENCE NUMBERS:

[0338] Figure 1

[0339] Actual scraped screw profile of the left screw element in Example 2

[0340] 1.1 The inner wall profile of the left part of the shell hole;

[0341] 1.2 Screw groove depth GT;

[0342] 1.3 Inner diameter of shell hole D;

[0343] 1.4 Tip angle of the left screw element with clearance δ between the screw element and the housing wall, but without additional clearance SP: KW l,δ ;

[0344] 1.5 Gap δ between the screw element and the housing wall;

[0345] 1.6 screw groove depth minus additional clearance: GT-SP;

[0346] 1.7 The clearance between the screw element and the housing wall plus the additional clearance: δ+SP;

[0347] 1.8 Tip angle of the left screw element with clearance δ between the screw element and the housing wall and additional clearance SP: KW l,δ+SP ;

[0348] 1.9 Center of rotation P.

[0349] Figure 2

[0350] Screw profile of a pair of screw elements not according to the invention in Example 1

[0351] 2.1 Shell hole inner wall profile;

[0352] 2.2 Left side screw element profile, precise scraping;

[0353] 2.3 Left screw element profile, actual scraping;

[0354] 2.4 Right side screw element profile, precise scraping;

[0355] 2.5 Right side screw element profile, actual scratch.

[0356] Figure 3

[0357] Plan view of a pair of screw elements not according to the invention in Example 1

[0358] 3.1 Shell hole inner wall profile;

[0359] 3.3 Left screw element profile, actual scraping;

[0360] 3.5 Right side screw element profile, actual scraping.

[0361] Figure 4

[0362] Screw profile of a pair of screw elements according to the invention in Example 2

[0363] 4.1 Shell hole inner wall profile;

[0364] 4.2 Left side screw element profile, precise scraping;

[0365] 4.3 Left side screw element profile, actual scraping;

[0366] 4.4 Right side screw element profile, precise scraping;

[0367] 4.5 Right side screw element profile, actual scratch.

[0368] Figure 5

[0369] Plan view of a pair of screw elements according to the present invention in Example 2

[0370] 5.1 The inner wall profile of the shell hole;

[0371] 5.3 Left side screw element profile, actual scraping;

[0372] 5.5 Right side screw element profile, actual scratch.

[0373] Figure 6

[0374] Screw profile of a pair of screw elements according to the invention in Example 3

[0375] 6.1 Shell hole inner wall profile;

[0376] 6.2 Left side screw element profile, precise scraping;

[0377] 6.3 Left screw element profile, actual scraping;

[0378] 6.4 Right side screw element profile, precise scraping;

[0379] 6.5 Right side screw element profile, actual scraping.

[0380] Figure 7

[0381] Plan view of a pair of screw elements according to the present invention in Example 3

[0382] 7.1 Shell hole inner wall profile;

[0383] 7.3 Left screw element profile, actual scraping;

[0384] 7.5 Right side screw element profile, actual scratch.

[0385] Figure 8

[0386] Screw profile of a pair of screw elements according to the invention in Example 4

[0387] 8.1 Shell hole inner wall profile;

[0388] 8.2 Left side screw element profile, precise scraping;

[0389] 8.3 Left screw element profile, actual scraping;

[0390] 8.4 Right side screw element profile, precise scraping;

[0391] 8.5 Right side screw element profile, actual scrape.

[0392] Fig. 9

[0393] Plan view of a pair of screw elements according to the present invention in Example 4

[0394] 9.1 Shell hole inner wall profile;

[0395] 9.3 Left screw element profile, actual scraping;

[0396] 9.5 Right side screw element profile, actual scratch.

Claims

1. A multi-shaft screw machine having a pair of screw elements, comprising: m screw shafts SW1 to SW rotating in the same direction and at the same speed m , the corresponding adjacent rotation axes X1 to X m In a cross section at right angles to the axis of rotation, there is a center distance A, as well as m circular shell holes that penetrate each other, wherein each circular shell hole has the same shell hole inner diameter D, and the hole centers M1 to M m The distance between the centers M1 and M2 of the circular shell hole is the same as the center distance A. m With the screw shaft SW1 to SW m The corresponding rotation axis X1 to X m coincides with the rotation center P1 of the screw element to P m coincide, wherein the two screw elements of the pair of screw elements are opposite each other on directly adjacent screw axes, The two screw elements of the pair of screw elements scrape against each other, and the gap between the screw elements is s, wherein the two screw elements have an asymmetrical screw profile, wherein each of the two screw elements has two tooth tops, wherein for each of the two screw elements, the distances between the two tooth tops of the screw element and the corresponding rotation center P of the screw profile are different, wherein in each case one tooth tip is at a distance D / 2 minus the clearance δ between the screw elements and the housing wall, minus an additional clearance SP, from the corresponding rotation center P, and the other tooth tip is at a distance D / 2 minus the clearance δ between the screw elements and the housing wall, but no longer minus an additional clearance SP, wherein the gap δ between the screw element and the housing wall of the two screw elements is identical and the additional gap SP of the two screw elements is identical, It is characterized in that The sum of the tooth top angles BKW of the two screw elements is greater than 0 in radians. as well as For the coefficient f, f=BKW / BKGW (44) For the coefficient f, the coefficient f is greater than 0 and less than or equal to 0.95, Where BKW is the sum of the tooth top angles of the two screw elements in radians, and BKGW is determined as: The definitions of the above parameters are consistent with the specification. 2 . The multi-shaft screw machine according to claim 1 , wherein f is greater than or equal to 0.1 and less than or equal to 0.8, and f is particularly preferably greater than or equal to 0.2 and less than or equal to 0.

6.

3. The multi-axis screw machine according to claim 1 or 2, wherein the ratio of the gap s between the screw elements and the gap s between the two screw elements in the pair of screw elements to the inner diameter D of the shell hole is 0.002 to 0.05, preferably 0.003 to 0.03, and particularly preferably 0.005 to 0.

02.

4. The multi-shaft screw machine according to any one of the preceding claims, wherein the ratio of the gap δ between the screw element and the housing wall to the inner diameter D of the housing hole is 0.002 to 0.05, preferably 0.003 to 0.03, particularly preferably 0.005 to 0.

02.

5. The multi-shaft screw machine according to any one of the preceding claims, wherein the ratio of the additional gap SP to the groove depth GT of the corresponding screw element is 0.015 to 0.4, preferably 0.02 to 0.3, particularly preferably 0.025 to 0.

25.

6. The multi-shaft screw machine according to any one of the preceding claims, wherein the tooth top angles of the pair of screw elements having the gap δ between the screw element and the housing wall but not having the additional gap SP relative to the housing hole inner wall are the same.

7. The multi-shaft screw machine according to any one of the preceding claims, wherein the tooth top angles of the pair of screw elements having the gap δ between the screw element and the housing wall and the additional gap SP relative to the housing bore inner wall are the same.

8. According to the multi-axis screw machine according to any one of the preceding claims, for two screw elements in the pair of screw elements, the tooth top angle of the screw element tooth top of the pair of screw elements having the gap δ between the screw elements and the inner wall of the shell and the additional gap SP is greater than the tooth top angle of the screw element tooth top of the pair of screw elements having the gap δ between the screw elements and the inner wall of the shell but not having the additional gap SP.

9. The multi-shaft screw machine according to any one of the preceding claims, the screw profiles of the pair of screw elements being non-uniform, the screw profiles of the two screw elements being able to merge with each other by mirroring along an axis and then rotating them.

10. The multi-shaft screw machine according to any one of the preceding claims, each of the two screw profiles of the pair of screw elements having exactly two (2) grooves and exactly four (4) wings.

11. A multi-shaft screw machine according to any one of the preceding claims, the two screw profiles of the pair of screw elements having exactly four (4) grooves and exactly eight (8) wings.

12. A method for producing or processing an extrudate using a multi-shaft screw machine as claimed in any one of claims 1 to 11, the method comprising the following steps: (1) providing the multi-axis screw machine; (2) Producing or processing the extrudate.

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