Multi-screw machine with pairs of screw elements having improved mixing and degassing effect with reduced energy input

Abstract

The present invention relates to a pair of screw elements suitable for a multi-screw machine, comprising m screw shafts SW1 to SW2 rotating in the same direction at the same speed. m adjacent rotation axes X1 to X m are screw shafts SW1 to SW2 having an axial interval A in a cross section perpendicular to the rotation axis. m m circular housing bores each having the same housing bore inner diameter D, and the bore midpoints M1 to M m are spaced apart from each other by the same axial distance A, and the bore midpoints M1 to M m However, screw shaft SW1~SW m Each of the associated rotation axes X1 to X m and the rotation midpoints P1 to P of the screw elements m and a circular housing bore coinciding with said screw element pair, wherein two screw elements of said screw element pair face each other on immediately adjacent screw shafts, wherein the two screw elements of said screw element pair rub against each other with a screw element spacing s, wherein both screw elements have asymmetric screw profiles, and wherein both screw elements have precisely two flighted lands, and for each of the two screw elements, the two flighted lands have different spacings from a respective midpoint of rotation P of the screw profile.

Description

[Technical field]

[0001] The present invention relates to a pair of screw elements suitable for a multi-screw machine, comprising: m screw shafts SW1 to SW rotate in the same direction at the same speed. m Each of the adjacent rotation axes X1 to X m The screw shafts SW1 to SW2 have a center distance A in a cross section perpendicular to the rotation axis. m and, Each has the same housing bore inner diameter D, and the bore centers M1 to M m m mutually interpenetrating circular housing bores, each having a distance equal to the center distance A, with bore centers M1 to M m However, screw shaft SW1~SW m Each of the associated rotation axes X1 to X m The screw element rotation centers P1 to P m Matching circular housing bore With The two screw elements of a screw element pair are located opposite each other on directly adjacent screw shafts, The two screw elements of a screw element pair rub against each other with a screw element-to-screw element spacing s. Both screw elements have asymmetric screw profiles, Both screw elements each have exactly two apices, For each of the two screw elements, its two apexes have different distances to the respective center of rotation P of the screw profile, In each case, one apex has a distance D / 2, reduced by the spacing δ from the screw element to the housing wall and further reduced by the additional gap SP, relative to the respective center of rotation P, and the other apex has a distance D / 2, reduced by the spacing δ from the screw element to the housing wall, but not reduced by the additional gap SP, relative to the respective center of rotation P, The spacing δ from the screw element to the housing wall is the same for both screw elements, and the additional gap SP is the same for both screw elements; The sum of the vertex angles in radians of both screw elements BKW satisfies the following formula: BKW = f * BKGW (1) For a coefficient f, it is true that coefficient f is greater than 0 and less than or equal to 0.95; BKGW is For pairs of screw elements as determined by TIFF2025511989000002.tif66170. [Background technology]

[0002] Here, the parameters required to describe the screw profile are listed below in Table 1.

[0003] Patent document 1 discloses an extruder having a housing with at least two axially parallel shafts which can be driven in the same direction, are provided with at least double-flight conveying elements and wipe each other at a centre distance with little space therebetween over the entire circumference, and there is a distance a between the top of at least one further gear wheel and the inner wall of the housing.

[0004] A multi-screw machine is known from DE 10 200 03 133 A1, which comprises a housing, two housing bores which are parallel to one another and partially pass through one another, two rotatably drivable shafts arranged in the housing bores, screw elements mounted on the shafts for co-rotation and kneading discs mounted on the shafts which mesh with one another for co-rotation, each disc being narrower in its top area than the disc width B and forming mixing rub lugs located on the periphery.

[0005] Furthermore, US Pat. No. 5,399,633 describes an extruder having at least two axially parallel shafts which can be driven in the same direction and which have at least double-threaded conveying elements 2, 11, 12 which are substantially in contact at one point C.

[0006] US Patent No. 5,399,633 describes a method and an apparatus for mixing by continuous rolling of thermoplastic materials. The apparatus includes a mixing chamber and at least one pair of threaded shafts arranged in the mixing chamber 5, the threaded shafts having at least a tip portion and at least a core portion of the threads asymmetrically countersunk with respect to the longitudinal axis of the shafts, creating an empty space between the surface of the shafts and the countersunk threaded portion and the inner surface of the chamber in order to perform rolling of the material on at least a part of the surface of the chamber during the feeding of the material to the outlet of the mixing chamber.

[0007] Furthermore, US Pat. No. 5,993,336 discloses a self-cleaning extrusion device with two screws rotating in the same direction, which comprises a screw mechanism, a cylinder, a feed opening, a vent opening and an outlet opening.

[0008] In the context of the present invention, a multi-screw machine is understood to mean a screw machine with two or more screw shafts, for example a screw machine with two, three or four screw shafts, or a screw machine with 8 to 16, in particular 12, screw shafts in an annular arrangement. In the case of three or more screw shafts, the rotation axes of the screw shafts may be arranged next to each other or may be in the form of an annulus, for example in the case of what are called ring extruders. In a multi-screw extruder, the rotation axes of the screw shafts are generally arranged parallel to each other. This parallel arrangement of the rotation axes is also preferred according to the present invention. In this respect, the screw elements of a pair of screw elements according to the present invention are preferably of a number corresponding to the number of screw shafts of the respective extruders whose screw shafts are arranged directly opposite each other. Such a screw machine with two or more screw shafts is also referred to below as a multiple screw machine, a multi-screw machine or a multi-screw extruder. A twin-screw machine is also referred to below as a twin-screw extruder. In the context of the present invention, the term "screw machine" is used synonymously with the term "extruder". The extruded compound or the compound to be extruded is hereinafter also called "extrudate".

[0009] Preferably, the multi-screw machine is a twin-screw extruder having two screw shafts SW1 and SW2 rotating in the same direction at the same speed and having adjacent axes of rotation X1 and X2, bore centres M1 and M2, and centres of rotation P1 and P2.

[0010] In the context of the present invention, the extrudate is a plastic or viscoelastic compound, in particular Suspensions, pastes, glass melts, unfired ceramics, metal melts, or plastics The compound is selected from the group consisting of:

[0011] In the context of the present invention, plastics are in particular Polymers, in particular polymer melts or polymer solutions, more particularly melts or solutions of thermoplastic polymers or melts or solutions of elastomers, in particular rubbers, is understood to mean:

[0012] The thermoplastic polymer used is preferably at least one from the group consisting of polycarbonate, polyestercarbonate, polyamide, polyester, in particular polybutylene terephthalate and polyethylene terephthalate, polylactide, polyether, thermoplastic polyurethane, polyacetal, fluoropolymer, in particular polyvinylidene fluoride, polyethersulfone, polyolefin, in particular polyethylene and polypropylene, polyimide, polyacrylate, in particular poly(methyl)methacrylate, polyphenylene oxide, polyphenylene sulfide, polyetherketone, polyaryletherketone, styrene polymer, in particular polystyrene, styrene copolymer, in particular styrene-acrylonitrile copolymer, acrylonitrile-butadiene-styrene block copolymer and polyvinyl chloride. Also preferably used are known blends of the listed polymers, which the skilled person will understand as a combination of two or more polymers. Particularly preferred are polycarbonates and mixtures containing polycarbonate, and very particularly preferred are polycarbonates obtained, for example, by interfacial process or melt transesterification process.

[0013] The rubber used is preferably at least one from the group: 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, fluorinated rubber, silicone rubber, vulcanized rubber, and chlorosulfonyl polyethylene rubber. Combinations of two or more of the listed rubbers, or combinations of one or more rubbers with one or more other plastics, are of course also possible.

[0014] These thermoplastics or rubbers can be used in pure form or as mixtures, especially with fillers and reinforcing agents such as glass fibers, with one another or with other polymers or with customary polymer additives.

[0015] In a preferred embodiment, additives are added to the plastic mass, in particular to the polymer melt and to the mixture of polymer melts. The additives can be added to the extruder in the form of a solid, liquid or solution together with the polymer, or at least part or all of the additives are fed to the extruder via a side stream.

[0016] Additives can impart various properties to polymers. Such additives can be, for example, colorants, pigments, processing aids, fillers, antioxidants, reinforcing agents, UV absorbers and light stabilizers, metal deactivators, peroxide scavengers, base stabilizers, nucleating agents, stabilizing or antioxidant benzofurans and indolinones, mold release agents, flame retardant additives, antistatic agents, dyes and melt stabilizers. Examples of these are carbon black, glass fibers, clay, mica, graphite fibers, titanium dioxide, carbon fibers, carbon nanotubes, ionic liquids and natural fibers.

[0017] In the context of the present invention, an asymmetric cross-sectional screw profile is distinguished by the fact that there is no mirror axis or rotation axis passing through any point in the plane of the cross-sectional screw profile, which can be used to generate a cross-sectional screw profile congruent to the original cross-sectional screw profile, preferably there is no mirror axis passing through any point in the cross-sectional screw profile, particularly preferably there is no mirror axis passing through the structural center KP of the cross-sectional screw profile, which can be used to generate a profile congruent to 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 the arcs forming the lands and grooves of the flights. In the context of the present invention, the structural center KP of the screw profile coincides with the rotation center P of this screw profile. For example, FIG. 5(A) or FIG. 5(B) of Patent Document 6 shows the screw profile of a pair of screw elements that are asymmetric in the sense of the present invention. The screw profiles of the pair of screw elements shown in FIG. 5(A) or FIG. 5(B) of Patent Document 6 are also not congruent, but have the property that they can be merged with each other by mirror-image and rotating the axes.

[0018] The cross-sectional screw profile, also called screw profile for short in the context of the present invention, is understood to mean the outer contour of a screw element in a plane section perpendicular to the axis of rotation of the screw element. Rules for generating precisely interlocking screw profiles are described, for example, in [1] ([1] = Non-Patent Document 1). It is also described that a given screw profile for a first shaft of a twin-screw extruder determines the screw profile for the second shaft of the twin-screw extruder, which is immediately adjacent to the first shaft ([1], p. 108). The screw profile for the first shaft is therefore called the generating screw profile. The screw profile for the second shaft follows the screw profile of the first shaft of the twin-screw extruder and is therefore called the generated screw profile.

[0019] Co-rotating twin-screw machines, whose screw shafts rub precisely against each other, have been known for a long time, for example from US Pat. No. 5,399,363. In the production and processing of polymers, screw machines with screw shafts, which are based on the principle that the screw elements rub precisely against the cross-sectional profile of the screw, have been used in various ways. This is mainly because at normal processing temperatures the polymer melt adheres to the surfaces and deteriorates over time, which is prevented by the self-cleaning effect of the screw elements in multi-screw machines, which rub precisely against each other in pairs. In multi-screw extruders, screw elements with a generating screw profile and screw elements with a generated screw profile are always used alternately on adjacent shafts.

[0020] Two distinctions must be made here: between a precisely interlocking screw profile, i.e. a mathematical configuration in which two screw elements lying opposite each other on two immediately adjacent screw shafts rub against each other with a screw element-to-screw element spacing s tending to zero, and a screw profile for a screw element designed with a material entity for the intended application, i.e. a technically manufactured screw element. When the term "precisely interlocking" is used in the context of the present invention, unless otherwise stated, it means a mathematical configuration of a precisely interlocking screw profile or a corresponding screw element having this screw profile. When the term "practically interlocking" or "manufactured" is used in the context of the present invention, unless otherwise stated, it means a technically manufactured screw element or its screw profile, which is preferably derived from a precisely interlocking screw profile by applying one of the following spacing strategies: increasing center distance, longitudinal cross-sectional equidistance, spatial equidistance or circular equidistance, as will be explained in more detail below.

[0021] Those skilled in the art of screw elements will of course appreciate that no single screw element or screw profile alone can precisely or practically rub against one another, and that pairs of such elements are always necessary.

[0022] Current extruders have a modular system in which various screw elements can be mounted on a core shaft to form a screw shaft, which is therefore segmented. This allows the skilled person to adapt the extruder to the respective processing task. However, the screw shaft can also be made in one piece, i.e. have only one screw element extending substantially over the entire length of the screw shaft, or can be only partially segmented. The present invention relates both to screw elements that can be mounted on a core shaft and to a screw shaft made from a single piece as described above.

[0023] Multi-screw extruders, especially twin-screw extruders, are known to transfer mechanical energy to the extrudate by dissipation, which can have both desirable and undesirable consequences, since on the one hand, energy input is required to perform process engineering tasks such as mixing and degassing, and on the other hand, mechanical energy input is consumed and leads to an increase in temperature in the extrudate, which can lead to undesirable chemical reactions that damage the extrudate.

[0024] Mixing is also known to be a fundamental operation in multi-screw extruders, especially twin-screw extruders: non-uniformities in the extrudate due to incomplete mixing are known to lead to problems in the further processing and final properties of the extrudate.

[0025] Degassing, i.e. the removal of volatile components, is also known to be a fundamental operation in multi-screw extruders, especially twin-screw extruders, as described, for example, in [1], pp. 494-525. For the degassing process, a degassing efficiency as high as possible with low energy input is desirable in order to achieve an economically high throughput and good extrudate quality. Such a process is generally described in [1] and also, for example, in patent document 8 [2], which describes an apparatus and a process for degassing polycarbonate solutions containing solvents.

[0026] For degassing, the polymer is transported through the degassing opening as extrudate in the partially filled section. Through this opening, volatile components such as by-products, monomers, oligomers, solvents or decomposition products of the polymer formed during the polycondensation reaction can be removed by the influence of temperature, water, oxygen or other components. To improve the removal of volatile components, the pressure in the degassing opening is lowered compared to the ambient pressure, depending on the degassing task. It is also mentioned on pages 494-525 of [1] that bubble formation of the polymer melt, and thus foaming, is useful for residual degassing, since it creates an inner surface that improves the mass transfer. Foaming requires a sufficiently high overpressure of the volatile components in the polymer (about 1 bar). The effect of shear on the polymer can promote bubble formation, thus improving the degassing effect.

[0027] In twin-screw extruders, the extrudate is sheared particularly strongly between the top of the screw and the inner wall of the extruder housing bore. This means that a particularly large amount of energy is dissipated into the extrudate, leading to strong localized overheating in the extrudate. This is shown, for example, in images 4.80 to 4.84 of pages 416 to 423 of [1]. This localized overheating can lead to damage in the extrudate, such as changes in odor, color, chemical composition or molecular weight, or the formation of inhomogeneities in the extrudate, such as gel bodies or spots. In particular, large apex angles and especially the sum of the apex angles of pairs of screw elements that are opposite each other on immediately adjacent screw shafts and rub against each other, are harmful.

[0028] Here, there is a trade-off between the requirement of degassing or dispersion, both of which require shearing, and the avoidance of damage to the extrudate. It may be advantageous to balance the requirement of degassing or dispersion with the requirement of extrudate protection, so that optimal degassing or dispersion is achieved with minimal damage to the extrudate. Furthermore, there is only little exchange of extrudate on the inner wall of the extruder housing bore, so that the same percentage of the total amount of extrudate being sheared multiple times does not promote either degassing or dispersion.

[0029] The problems of damage to the extrudate and of the energy input can be solved, for example, as in patent document 9 [3], which describes a screw element for a multi-screw machine having screw shafts that rub against each other in exact pairs in the same direction, with two or more screw flights Z, with a centre distance A and an outside diameter DE, the sum of the apex angles of the pairs of screw elements being greater than 0, and 2π-4Z arccos(A / DE) (3) A screw element smaller than 1.0 mm and its use are described. Such a screw element is also preferably used in the extruder disclosed in [2]. However, the use of such a screw element does not improve the degassing effect.

[0030] Patent document 10 [4] describes eccentric, practically mutually rubbing conveying screw elements that rotate in the same direction and have eccentric profiles with their tops at different distances from the housing. This achieves an even load on the extrudate by spreading it over the walls and provides a larger surface area for heat and mass transfer. In this way, an improved degassing effect can possibly be achieved. The wide top aspect and the associated disadvantages are not addressed.

[0031] Patent document 6 [5] describes eccentric asymmetric screw elements that actually rub against each other, with one crest of each screw element having a smaller distance to the inner wall of the extruder housing bore than the other crest or crests of each screw element. The main effect described in the document is the exchange of material between the extruder housing bores and uniform and concentrated shear. These screw elements have Z≧2 flights, Z crests and Z grooves. The screw element to screw element spacing s, i.e. the distance between the screw profiles of the screw elements of pairs of screw elements facing each other on two directly adjacent screw shafts, is not taken into account.

[0032] From [5], the sum of the apex angles SKW0 of each screw element in a pair of screw elements in which the two screw elements rub against each other exactly is given by: TIFF2025511989000003.tif38170Now, many mathematically equivalent formulations are possible.

[0033] Those skilled in the art are aware that technically designed screw elements must have spacing (both the spacing s from screw element to screw element and the spacing δ from screw element to housing wall) to ensure the functioning of the extruder, as mentioned for example on pages 39-41 and 113-121 of [1]. This is necessary to avoid metallic "seizure", manufacturing tolerances, roughness, angular deviations, non-uniform thermal expansion and excessive extrudate stress due to insufficient spacing between two screw elements directly adjacent to each other on two directly adjacent screw shafts. The above mentioned pages also explain methods for determining the exact geometric shape of the elements to be generated from the spacing and the precise rubbing profile. These methods are called spacing strategies.

[0034] The strategies of longitudinal section equidistance, circular equidistance and spatial equidistance are hereinafter also called longitudinal section equidistance calculation rules, circular equidistance calculation rules and spatial equidistance calculation rules. Another spacing strategy is to increase the centre distance according to pages 40 and 41 of [1].

[0035] Spatial equidistance is described, for example, in [1], pages 40 and 41. Spatial equidistance is, for example, determined by the parameterization of the outer surfaces of precisely mating screw elements: TIFF2025511989000004.tif5170, where a and b are the outer surfaces of the relevant precisely rubbing screw elements. The parameters are selected according to the formula describing TIFF2025511989000005.tif5170. Some examples of what such a parameterization might look like are described below.

[0036] For the purposes of the following discussion, a Cartesian coordinate system is assumed, where the coordinate along the axis of rotation of the extruder is denoted as z, and x and y are coordinates in a plane perpendicular to the axis of rotation that intersects this plane at x=0, y=0 and z=0.

[0037] For example, in the case of a pair of screw elements in which two screw elements face each other on two adjacent screw shafts and rub against each other precisely, the xy plane is such that the axis of rotation X of each screw element coincides with the z axis and the distance r to the axis of rotation e The screw profile of each of the two screw elements in the xy plane, where (γ) is specified as a 2π periodic function of the screw profile of the angle γ with respect to the x-axis, can be reproduced by expressing the profile of the mating screw elements exactly according to equation (5) below. TIFF2025511989000006.tif13170In such a case, one can choose a=γ and b=z.

[0038] Such a pair of screw elements can for example be shaped as a pair of conveying elements or as a pair of kneading discs.

[0039] To construct the conveying elements, the screw profile is a spiral run in a plane in order to obtain a precisely rubbing limit surface of the screw elements. For a screw element with pitch T, the z coordinate results below as an additional parameter: TIFF2025511989000007.tif25170 A positive sign indicates a clockwise rotating screw profile and a negative sign indicates a counterclockwise rotating screw profile.

[0040] In the case of a kneading disc, the screw profile is displaced in space along the z-axis, resulting in: TIFF2025511989000008.tif17170

[0041] The screw profile, e.g. a precisely fitted screw profile, is centered on the coordinates TIFF2025511989000009.tif9170 and radius r i If a circular arc is constructed cross-sectionally in a plane through a circular arc i with TIFF2025511989000010.tif12170Next, for the representation of the limit surface of precisely rubbing conveying elements in space, TIFF2025511989000011.tif26170 holds, and correspondingly, for the expression of the limiting surface of the precisely rubbing kneading disks, TIFF2025511989000012.tif16170 In a conveying element, the pitch T of a screw element is the axial length required for a complete revolution of the screw profile of the screw element.

[0042] When calculating the screw profile, starting from a pair of screw elements having a precisely interlocking screw profile and taking into account the spacing s from one screw element to the other, the screw profile of the pair of screw elements that actually interlocks is determined, e.g., the parameter expression After defining TIFF2025511989000013.tif5170 as follows, the spatial equidistance calculation rules can be applied, and the points In TIFF2025511989000014.tif6170, the corresponding normal vector TIFF2025511989000015.tif19170 is formed, where the code is: TIFF2025511989000016.tif5170 is selected to point outward from the axis of rotation. Next, the outer surface of the technically designed screw element to be manufactured TIFF2025511989000017.tif6170 is a parameter expression TIFF2025511989000018.tif12170 According to the invention, further spatial equidistance calculation rules may also be possible.

[0043] The circular equidistance method also assumes a precisely rubbing screw profile in a plane. Starting with a precisely rubbing screw profile in the xy plane, a perpendicular line is cut at each point, the direction of which is chosen to point to the inside of the screw profile. A point shifted along this perpendicular line by s / 2 to the inside of the screw profile then belongs to the technically constructed screw profile. A part of the precisely rubbing screw profile is located at a radius r i If the screw profile is a circular arc having the same center and radius r, the corresponding section of the screw profile produced in the relevant technology will have the same center and radius r i It is a circular arc with -s / 2.

[0044] This is the circular equidistance calculation rule in the context of the present invention.

[0045] According to the invention, further circular equidistance calculation rules may also be possible.

[0046] Using the methods of longitudinal section equidistance, spatial equidistance and circular equidistance, different surface curves of the generated technically produced screw profile may overlap, so that for a certain angle starting from the rotation center P of the screw profile, several points on the screw profile curve can be selected, where the points closer to the rotation center P are used to manufacture the screw profile for the technically feasible screw profile.

[0047] Various geometries can be used to represent the technically produced screw profile to be produced, such as, for example, a table of coordinates. A preferred method is to specify the distance r(γ) to the axis of rotation as a function of 2π or a 360 degree period of the angle γ with respect to the x-axis, using the following expression: TIFF2025511989000019.tif12170Also, in all of the above methods, there is a slight increase in the flank angle and a decrease in the apex angle or angles compared to the flank angle and apex angle or angles of a precisely rubbing screw profile. The application of the spatial equidistance method always results in a smaller apex angle than the application of the longitudinal section equidistance method, and the circular equidistance method always results in a smaller apex angle than the application of the circular equidistance method. As the gradient increases, the apex angles for the spatial equidistance and longitudinal section equidistance increase, and as the gradient approaches infinity, the spatial equidistance and longitudinal section equidistance tend to the circular equidistance method, i.e., as the gradient approaches infinity, the spatial equidistance calculation rule and the longitudinal section equidistance calculation rule provide the same apex angle as the circular equidistance calculation rule.

[0048] All methods for determining the technically produced geometry of a screw profile based on a precisely interlocking screw profile, i.e., the spacing strategy, reduce the size of the screw element compared to the screw element with this precisely interlocking screw profile, and create a distance between the precisely interlocking screw profile and the technically produced practically interlocking screw profile. The spacing strategy is used to determine the screw element-to-screw element spacing s, i.e., the distance between the screw profiles of pairs of screw elements lying opposite each other on two directly adjacent screw shafts, where this screw element-to-screw element spacing s does not have to be constant between these two screw elements, but is preferably constant.

[0049] Spatial equidistance is preferred, as explained above, to provide a constant spacing s between the screw elements when they rub against one another.

[0050] A large screw element to screw element spacing s reduces the shear and therefore reduces the energy input to the extrudate. However, too large sizes of screw element to screw element spacing s and screw element to housing spacing δ are also disadvantageous in technically made extruders. They lead to reduced rubbing of screw elements positioned opposite each other in pairs on directly adjacent screw shafts and also worsen the exchange of extrudate on the screw elements or housing bores, thereby increasing the risk of damaged extrudate being produced due to long residence times and getting into the extrudate flow, which can lead to spots, gels or discoloration, thus impairing the quality of the desired final product. Excessively large screw element to screw element spacing s and screw element to housing spacing δ also lead to reduced degassing and reduced mixing effect due to reduced exchange of extrudate on the screw surface or on the housing bore inner wall.

[0051] In addition, the effect that can be exerted on the sum of the apex angles via the spacing s from screw element to screw element is limited.

[0052] As known to those skilled in the art, in addition to the screw profile, other variables play a role in the geometry of the screw elements. These are listed, for example, on page 115 of [1].

[0053] As shown above, the prior art does not provide a solution to the problem of how to achieve good degassing of the extrudate in an extruder requiring strong shear and at the same time avoid damage to the extrudate due to excessive energy input resulting from the strong shear, and at the same time further increase the exchange of the extrudate on the inner wall of the housing bore of the extruder, thus achieving a good mixing effect and dispersion, since the extrudate degassing is merely small.

[0054] Since degassing mainly occurs from the surface of the extrudate, a good mixing effect is necessary for good degassing, and fresh extrudate that has not yet been degassed must be transferred thereto to allow further degassing. Furthermore, the degassed extrudate should be as homogeneous as possible, which requires a uniform energy input and the avoidance of localized overheating.

[0055] As known to those skilled in the art and explained, for example, in [1], pages 475-478, there are particularly high shear stresses in the area of ​​the top near the inner wall of the housing bore, which promotes dispersion. This is particularly important when dispersing solid aggregates used as fillers or reinforcing materials, another fundamental operation in extruders. Therefore, as known to those skilled in the art, frequent replacement of the sheared material also promotes the dispersion effect. However, [1], page 478, only mentions reduced throughput as a way for better dispersion, which is not preferred for economic reasons. [Prior art documents] [Patent documents]

[0056] [Patent Document 1] International Publication No. 2011 / 006516 [Patent Document 2] European Patent Application No. 0875356 [Patent Document 3] German Patent Application No. 102008016862 [Patent Document 4] European Patent Application No. 0788868 [Patent Document 5] International Publication No. 2016 / 107527 [Patent Document 6] European Patent Application No. 0002131 [Patent Document 7] German patent no. 862668 [Patent Document 8] International Publication No. 2010139413 [Patent Document 9] International Publication No. 2009152973 [Patent Document 10] U.S. Patent No. 4,131,371 [Non-patent literature]

[0057] [Non-Patent Document 1] Klemens Kohlgrueber: “Der gleichlaeufige Doppelschneckenextruder” [Codirectional Twin-Screw Extruders], 2nd Edition, Hanser Verlag Munich 2016, pages 107 to 120) Summary of the Invention [Problem to be solved by the invention]

[0058] It is therefore an object of the present invention to ensure good degassing of the extrudate in the extruder and at the same time avoid damage to the extrudate by low energy input. A further object of the present invention is to additionally ensure good dispersion.

[0059] In particular, the object of the present invention is to provide a pair of screw elements that ensures good degassing of the extrudate in the extruder while at the same time preventing damage to the extrudate. The pair of screw elements should also achieve a good dispersion and good mixing effect. Damage to the extrudate should preferably be avoided by the fact that the pair of screw elements ensures a reduced energy input to the extrudate without impairing the degassing of the extrudate. [Means for solving the problem]

[0060] Surprisingly, this object is achieved by a multi-screw machine having the features of the main claim.

[0061] This object is further achieved in particular by a method according to claim 12.

[0062] In the context of the present invention the following shall apply.

[0063] A screw profile is a closed convex curve. It is composed of several different curves, which, depending on their geometric characteristics, are called "crowns", "flanks" or "grooves".

[0064] The radius of curvature of the screw profile is at every point 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.

[0065] A kink is a point on the screw profile that originates from the following parameterization: TIFF2025511989000020.tif11170Here, the arc length l is the parameter value l k , the left and right limits of the values ​​of the functions x(l) and y(l) coincide (this is the same as the property that the curve is closed at this point), i.e. TIFF2025511989000021.tif11170, and the directional vectors of the derivative of the curve as a function of the arc length l do not point in the same direction, i.e. their cross product is not zero. TIFF2025511989000022.tif21170 If two arcs as part of the screw profile do not merge with each other tangentially, the kink is located at the intersection of the two arcs. It is also possible to treat the kink as an arc with a center point equal to the intersection of the two arcs and with a radius of zero, which is done in the example.

[0066] A curved line is an unbroken line that has a length greater than zero but no width, and has first and second endpoints that are not exactly the same point, i.e., the first endpoint does not coincide with the second endpoint.

[0067] A curve may be made up of a finite number of curve sections, where a first curve section has a common point of contact with a second curve section that is immediately adjacent to the first curve section.

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

[0069] A curve may only have a finite number of kinks, and a kink may, by definition, only exist at a common tangency point of two directly adjacent curve sections of a curve. A kink may be located at a common tangency point of two directly adjacent curve sections.

[0070] A curve section is a section of a curve, which has first and second endpoints that are not exactly the same point, i.e., the first endpoint does not coincide with the second endpoint.

[0071] The curved section is preferably selected from the group comprising a circular arc, an elliptical arc, a parabolic arc, or a spline or a part of a spline, a result of applying a longitudinal cross-sectional equidistance calculation rule according to pages 117 to 121 of [1] to a circular arc, an elliptical arc, a parabolic arc, or a spline or a part of a spline, a result of applying a spatial equidistance calculation rule to a circular arc, an elliptical arc, a parabolic arc, or a spline or a part of a spline, or a result of applying a circular equidistance calculation rule to a circular arc, an elliptical arc, a parabolic arc, or a spline or a part of a spline.

[0072] Also, the curved section For TIFF2025511989000023.tif5170, a line that can be represented in parameterized form with its arc length l TIFF2025511989000024.tif12170, where x k,l (l) and y k,l(l) is an analytic function, where x and y are the coordinates of a line in the plane, and therefore can be expressed by an infinite power series, is continuous, can be differentiated any number of times, and therefore is free of kinks.

[0073] The section is either a curved section or a kink.

[0074] A closed convex curve is an uninterrupted line made up of one or more curved lines made up of one or more curved sections that have a nonzero length but no width. A closed convex curve does not have a marked beginning or end. Starting at any point on the curve, it is possible to determine the length of the curve by adding up the lengths of the curved sections around the curve. All tangents to a closed convex curve lie outside the area enclosed by the curve.

[0075] Since all the curved sections of the screw profile lie in one plane, the closed curve that is the screw profile divides the area of ​​this plane into an area inside the closed curve and an area outside the closed curve.

[0076] An arc is a curved section in which all points on the arc have the same distance, called the radius, from a common center point. Arcs have a start point and an end point that are not exactly the same point.

[0077] An arc is considered to be a circular arc only if all its points have the same center and the same radius and the points of the arc form an uninterrupted curved section, in other words two directly adjacent arcs having a common point of contact are considered to be two circular arcs only if they have different centers or different radii. According to the invention only arcs having a central angle in radians smaller than π are used.

[0078] Arc i has its center coordinate xm i and ym i , its radius r i , its starting angle β a,i and its central angle α iand valid values ​​for the angle β in equation (10) are a,i and β e,i =β a,i +α i (18) Between.

[0079] The center of rotation P of the screw profile is the intersection of the rotation axis X of the screw element and a cross-sectional plane perpendicular to this axis of rotation. The center of rotation P of the screw profile, also called the pivot point P or pivot point below, also coincides with the bore center M of the housing bore in which the respective screw element is located or in which the respective screw element is designed.

[0080] With respect to the screw profile, the pivot point P is the point around which the screw profile rotates as a cross-sectional image of the screw element.

[0081] An apex is a curve of the screw profile in which all points of this curve, except for the points of contact with the two curve sections immediately adjacent to the apex, have a greater distance from the pivot point P than the two curve sections immediately adjacent to the apex. According to the invention, the curve forming the apex is precisely a curve section which is a circular arc precisely centered on the pivot point P of the screw profile.

[0082] According to the invention, preferably all apexes of the screw profile are each formed by exactly one circular arc, each centered on the pivot point P of the screw profile.

[0083] The apex radius is the distance of each apex from the pivot point P of the screw profile.

[0084] A groove is a curve in the screw profile in which all points of the curve, except for the points of contact 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.

[0085] According to the invention, the curve forming the groove is precisely a curved section which is a circular arc precisely centered on the pivot point P of the screw profile.

[0086] According to the invention, preferably all grooves of the screw profile are each formed by exactly one circular arc, each centered on the pivot point P of the screw profile.

[0087] A flank is a curve of the screw profile that is convex with respect to the center of rotation P between the crest and the groove, and this flank has a common contact point with the crest and the groove.

[0088] The flank may be a single curved section or may be composed of several curved sections. The radius of curvature of the flank is less than or equal to the centre distance A at all points, and preferably less than the centre distance A.

[0089] According to the present invention, the formula on which the curved portion of the slope is based is preferably selected from the group of formulas including a circular arc, a result of applying the longitudinal section equidistance calculation rule according to pages 117 to 121 of [1] to a circular arc having a radius of curvature smaller than or equal to the center distance A of a precisely frictional screw profile composed only of circular arcs, a result of applying the spatial equidistance calculation rule to a circular arc having a radius of curvature smaller than or equal to the center distance A of a precisely frictional screw profile composed only of circular arcs, and a result of applying the circular equidistance calculation rule to a circular arc having a radius of curvature smaller than or equal to the center distance A of a precisely frictional screw profile composed only of circular arcs.

[0090] The components of the screw element pairs or associated screw profiles according to the invention may be given a subscript such as n, m or i or may further be given a natural number to make it possible to distinguish these components from one another when there may be more than one of these components.

[0091] Furthermore, within the context of the present invention the following shall apply:

[0092] [Table 1] TIFF2025511989000026.tif230170TIFF2025511989000027.tif65170

[0093] In the context of this specification, insofar as values ​​are described as being "selected" for variables, such as pitch T, screw element to housing wall spacing δ, screw element to screw element spacing s, or additional gap SP, this does not mean that any value can be assigned to this variable if a screw profile for a pair of screw elements that can be used as intended is to be obtained. A person skilled in the art of designing screw elements for extruders can estimate or use CFD simulations to determine which values ​​should be reasonably assigned to these variables for a given extruder, depending for example on the viscosity of the extrudate at the processing temperature, the desired filling level of the extruder, the desired amount of energy input to the extrudate, or the speed of the shaft. In particular, if such values ​​are obtained by estimation, they usually need to be confirmed or more precisely determined by simulation, which is usually done iteratively.

[0094] By selecting the additional gap SP, the mass transfer and mixing effect at the inner wall of the housing can be adjusted. The maximum shear can be set by appropriately selecting δ and the apex angle, and therefore the length over which the maximum shear between the apex angle and the housing should act can be set using f.

[0095] (1) The above object is particularly to provide, in a first embodiment of the present invention, a pair of screw elements suitable for a multi-screw machine, comprising: m screw shafts SW1 to SW rotate in the same direction at the same speed. m) and each of the adjacent rotation axes X1 to X m The screw shafts SW1 to SW2 have a center distance A in a cross section perpendicular to the rotation axis. m and, Each has the same housing bore inner diameter D, and the bore centers M1 to M m m mutually interpenetrating circular housing bores, each having a distance equal to the center distance A, with bore centers M1 to M m However, screw shaft SW1~SW m Each of the associated rotation axes X1 to X m The screw element rotation centers P1 to P m Matching circular housing bore With The two screw elements of a screw element pair are located opposite each other on directly adjacent screw shafts, The two screw elements of a screw element pair rub against each other with a screw element-to-screw element spacing s. Both screw elements have asymmetric screw profiles, Both screw elements each have exactly two apices, For each of the two screw elements, its two apexes have different distances to the respective center of rotation P of the screw profile, In each case, one apex has a distance D / 2, reduced by the spacing δ from the screw element to the housing wall and further reduced by the additional gap SP, relative to the respective center of rotation P, and the other apex has a distance D / 2, reduced by the spacing δ from the screw element to the housing wall, but not reduced by the additional gap SP, relative to the respective center of rotation P, The spacing δ from the screw element to the housing wall is the same for both screw elements, and the additional gap SP is the same for both screw elements; The sum of the apex angles in radians of the tops of both screw elements BKW is greater than 0, f=BKW / BKGW (19) For a coefficient f such that where BKW is the sum of the apex angles in radians of both screw elements and BKGW is This is achieved by a pair of screw elements, as determined by TIFF2025511989000028.tif65170.

[0096] An equal screw element to housing wall spacing δ, or an equal additional gap SP, has the advantage of uniform energy input.

[0097] (2) Preferably, f is 0.1 or more and 0.8 or less, and particularly preferably, f is 0.2 or more and 0.6 or less.

[0098] This preferred embodiment of the present invention is a second embodiment according to the first embodiment shown above.

[0099] (3) Preferably, the ratio of the screw element-to-screw element spacing s between the two screw elements of a screw element pair to 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.

[0100] This preferred embodiment of the present invention is a third embodiment according to the first or second embodiment shown above.

[0101] (4) It is further preferred that the distance δ from the screw element to the housing wall relative to the housing bore inner diameter D is 0.002-0.05, preferably 0.003-0.03, and particularly preferably 0.005-0.02. This particularly preferred embodiment of the method of the invention is a fourth embodiment according to one of the embodiments shown above.

[0102] (5) Here, the additional gap SP relative to the flight depth GT of each screw element is more preferably 0.015 to 0.4, more preferably 0.02 to 0.3, and particularly preferably 0.025 to 0.25.

[0103] This particularly preferred embodiment of the invention is the fifth embodiment according to one of the embodiments shown above.

[0104] (6) More preferably, the apex angles of the apexes of pairs of screw elements, having a spacing δ from the screw element to the housing wall but no additional gap SP to the inner wall of the housing bore, are the same.

[0105] This further preferred embodiment of the invention represents a sixth embodiment according to one of the embodiments presented above.

[0106] (7) Even more preferably, the apex angles of the apexes of the pairs of screw elements, having the spacing δ from the screw element to the housing wall and the additional gap SP to the inner wall of the housing bore, are the same.

[0107] This further preferred embodiment of the invention represents a seventh embodiment according to one of the embodiments presented above.

[0108] (8) Additionally, it is preferred that it is true that for both screw elements of a screw element pair, the apex angle of the tops of the screw elements of the screw element pair having a spacing δ from the screw element to the housing wall and an additional gap SP is greater than the apex angle of the tops of the screw elements of the screw element pair having a spacing δ from the screw element to the housing wall but without the additional gap SP.

[0109] This further preferred embodiment of the invention represents an eighth embodiment according to one of the embodiments shown above.

[0110] (9) Very particularly preferably, the screw profiles of the pair of screw elements are not congruent, but the screw profiles of the two screw elements can be brought into sync with one another by rotating them on mirror images of their axes.

[0111] This very particularly preferred embodiment of the present invention is a ninth embodiment according to one of the first to eighth embodiments shown above. The fact that the screw profiles of the two screw elements can be merged with each other by rotating them with mirror images of their axes means that the energy input to each of the two screw elements of the screw element pair is the same. This proves to be advantageous, since it prevents localized overheating of the extrudate when the screw element pair according to the present invention is used as intended.

[0112] (10) It is also preferred that each of the two screw profiles of a pair of screw elements has exactly two grooves and exactly four flanks.

[0113] This very particularly preferred embodiment of the present invention is a tenth embodiment according to one of the first embodiments shown above.

[0114] (11) It is also preferred that the two screw profiles of a pair of screw elements have exactly four grooves and exactly eight flanks.

[0115] This particularly preferred embodiment of the present invention represents an eleventh embodiment according to one of the tenth embodiments shown above.

[0116] The pair of screw elements according to the invention can be formed as a pair of conveying elements or as a pair of kneading discs, and is preferably implemented according to the invention as a pair of conveying elements.

[0117] The present invention also relates to a multi-screw machine comprising a pair of screw elements according to the invention.

[0118] The invention further relates to a method for producing or processing an extrudate using pairs of screw elements according to the invention in a multi-screw machine. The extrudate is preferably a plastic or viscoelastic mass, 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 rubber. The method preferably comprises: (1) providing a multi-screw machine including pairs of screw elements according to the present invention; (2) producing or processing an extrudate; Includes.

[0119] The invention also relates to a method for generating the screw profile of the screw elements of a screw element pair according to the invention, starting from a precisely interlocking screw profile according to the prior art.

[0120] The screw profile of a screw element pair according to the invention can be generated, for example, using an existing extruder having as a starting point the values ​​of centre distance A and housing bore inner diameter D, as described below, where each of the two screw elements has exactly two crests, and where the two screw elements of the screw element pair are indicated in the formula symbols as left screw element and right screw element by the subscripts l and r, respectively.

[0121] To calculate the values ​​of the screw elements used to generate the screw profile of a pair of screw elements according to the present invention, both the values ​​of the variables of the pair of screw elements that rub against each other precisely and the values ​​of the variables of the pair of screw elements that rub against each other actually are used, the values ​​of the variables of the pair of screw elements that rub against each other actually depend on the values ​​of the variables of the pair of screw elements that rub against each other precisely and can be calculated therefrom according to Table 1.

[0122] (I) In the first step, the values of the distance s from screw element to screw element and the distance δ from screw element to housing wall, which are applied to the screw element to be produced, are selected.

[0123] (II) In the second step, the value of the outer radius RE of the precisely mating screw profile is determined according to the following formula. RE = DE / 2 (21) Here, DE = D - 2δ + s (22) is.

[0124] (III) In the third step, the value of the inner radius RI of the precisely mating screw profile is determined according to the following formula. RI = DI / 2 = A - (D / 2) + δ - (s / 2) (23)

[0125] (IV) In the fourth step, the outer radius RA of the technically producible / correctly usable screw element is determined according to the following formula. RA = (D / 2) - δ (24)

[0126] (V) In the fifth step, the inner radius RK of the technically producible / correctly usable screw element is determined according to the following formula. RK = A - (D / 2) + δ - s (25)

[0127] (VI) In the sixth step, the flight depth of the technically producible / correctly usable screw element is calculated using the following formula. GT = RA - RK (26)

[0128] (VII) In the seventh step, the value of the additional clearance SP of the technically producible / correctly usable screw element is selected, where SP < GT / 2 is always true.

[0129] Steps (II) to (V) can be executed in any order.

[0130] (VIII) In the eighth step, for each of the two screw elements of the pair of precision rubbing screw elements, the initial sum SKW0 of the apex angles of each screw element is determined according to equation (4) or equation (27). TIFF2025511989000029.tif37170

[0131] (IX) In the ninth step, the sum BSKW0 of the apex angles of the pair of precisely interlocking screw elements is BSKW0=2gSKW0 (28) where a coefficient g is selected which is greater than 0.1 and less than 0.95, preferably greater than 0.15 and less than 0.8, particularly preferably greater than 0.2 and less than 0.6.

[0132] (X) In the tenth step, for a pair of screw elements that precisely rub against each other, the apex angle KW0 of the precisely rubbing profile of the left screw element is l,δ and the apex angle KW0 of the right screw element r,δ is determined for each screw element apex having a spacing δ from the screw element to the housing wall relative to the inner wall of the housing bore, labeled in each case with a subscript δ in the formula symbol, but without additional clearance SP, specifically for the sum of the apex angles of these apexes: KW0 l,δ +KW0 r,δ <BSKW0 (29) Preferably KW0 l,δ +KW0 r,δ <BSKW0 / 2 (30) Particularly preferably KW0 l,δ =KW0 r,δ =KW0 δ <BSKW0 / 4 (31) where all vertex angles are greater than 0.

[0133] (XI) In the eleventh step, for a pair of screw elements that precisely rub against each other, the apex angle KW0 of the screw profile of the left screw element is l,δ+SP and the apex angle KW0 of the right screw element r,δ+SP is determined for each screw element apex having a spacing δ from the screw element to the housing wall and a gap SP, i.e. δ+SP, in each case labelled with the subscript δ+SP in the formula symbol, specifically for the sum of the apex angles of these apexes: KW0 l,δ+SP +KW0 r,δ+SP =BSKW0-(KW0 l,δ +KW0 r,δ ) (32) Preferably KW0 l,δ+SP +KW0 r,δ+SP =2KW0 δ+SP =BSKW0-(KW0 l,δ +KW0 r,δ ) (33) is made to hold true.

[0134] (XII) In the twelfth step, the screw profile of the first screw element, here selected as the left screw element (the right screw element may also be selected), is constructed for a pair of precisely interlocking screw elements and consists of the curves described below. These curves follow each other directly in the rotational direction defined below, which may be mathematically positive or negative, and the curves merge into each other at their respective end points. This screw profile of the first screw element represents the generating screw profile. - has radius RE and angle KW0 l,δ and is a circular arc centered on the center of rotation P of the screw profile, and this circular arc is the first apex. -First Frank [Frank 1]. - has a radius RI and an angle KW0 r,δ and is a circular arc centered on the center of rotation P of the screw profile, and this circular arc is the first groove. -The second Frank [Frank 2]. - has radius RE-SP and angle KW0 l,δ+SP and is a circular arc centered on the center of rotation P of the screw profile, this circular arc being the second apex. -The third flank [Frank 3]. - has radius RI+SP and angle KW0 r,δ+SP and is a circular arc centered on the center of rotation P of the screw profile, and this circular arc is the second groove. a fourth flank [Flank 4], which closes the profile between the second groove and the first crest.

[0135] (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 screw elements that precisely rub against each other. For this purpose, the pivot point of the left screw element is set to coordinates x=0 and y=0, and the pivot point of the right screw element is set to coordinates x=A and y=0. The screw profile of the left screw element is geometrically decomposed into its curved sections and kinks i=1..n, if they exist. The precisely rubbed screw profile of the right screw element is then constructed from the curved sections corresponding to the screw profile of the left screw element and kinks, called i'=1..n, if available.

[0136] For curve section i, the parameterization is TIFF2025511989000030.tif11170, where p a,i ≦p≦p e,i and the analytic function x i (p) and y i The derivative of (p) is non-zero for the same values, and, without limiting generality, It is assumed that TIFF2025511989000031.tif6170 rotates around the pivot point in a mathematically positive direction as p increases, and the normalized vector TIFF2025511989000032.tif26170 is formed, where the sign is chosen such that the normal vector points out of the profile from the pivot point.

[0137] Each curve section has a starting angle β a,i and end angle β e,i The starting angle is p=p a In the condition Fill TIFF2025511989000033.tif11170, p=p e The end angle can be calculated from the components of the normal vector as follows: Given TIFF2025511989000034.tif11170, where β e,i >β a,i And β e,i <β a,i +π.

[0138] Then, curve section i in the left screw corresponds to curve section i' in the right screw, and the coordinate representation is: TIFF2025511989000035.tif12170

[0139] In a preferred embodiment, curve section i is represented by the parameter TIFF2025511989000036.tif12170 represents a circular arc with β a,i ≦β≦β e,i In this case, the normalized normal vector is TIFF2025511989000037.tif11170, and the corresponding arc representation is TIFF2025511989000038.tif11170, where r i’ =Ar i , xm i’ =xm i +A and ym i’ =ym i And (as above) β a,i ≦β≦β e,i It is.

[0140] The curve section is r i If we represent a circle with A = r i’ =0 and the corresponding section is a kink.

[0141] If section i represents a kink with coordinate, which corresponds to a circular arc with radius, then its expression is r i’ This can be obtained from the above formula using =A.

[0142] In a preferred embodiment, the screw profile of the screw element according to the invention is derived from a precisely interleaving screw profile by using increasing center distance, circular equidistance, longitudinal equidistance or spatial equidistance, where the sum of the apex angles of both screw elements in radians BKW is greater than 0 with a factor f f=BKW / BKGW (42) Then, it is true that the coefficient f is greater than 0 and less than or equal to 0.95. where BKW is the sum of the apex angles in radians of both screw elements and BKGW is determined by the following formula: TIFF2025511989000039.tif64170

[0143] In a further preferred embodiment, the screw profile of the screw element according to the present invention is composed of curved sections selected from the group of mathematical expressions including the result of applying the longitudinal section equidistance 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 of applying the spatial equidistance calculation rule to a circular arc, an elliptical arc, a parabolic arc, a spline or a part of a spline, or the result of applying the circular equidistance calculation rule to a circular arc, an elliptical arc, a parabolic arc, a spline or a part of a spline.

[0144] In a further preferred embodiment, at least two pairs of screw elements according to the invention are arranged axially one directly behind the other in a multi-screw machine. Such an arrangement is shown in principle, for example, in International Application No. PCT / EP2021 / 078863, which in particular describes pairs of screw elements which precisely clean each other, but the present invention relates to screw elements which actually rub against each other.

[0145] FIG. 1 shows the actual interfacing screw profile of the left screw element according to Example 2 to illustrate the geometric dimensions. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0146] The present invention will now be described with reference to examples, but it is not intended that the present invention be limited to these examples.

[0147] Example 1 (Comparative Example (Non-Inventive Example)) Example 1, which is a non-inventive example, is a pair of two screw elements that actually rub against each other, with A / D=0.825, T / D=1.2, δ / D=0.015, s / D=0.02, and SP / D=0.01, according to Figures 5(A) and 5(B) of Patent Document 6, and the spatial equidistance calculation rule according to Figures 5(A) or 5(B) of Patent Document 6 is additionally applied to the screw profiles. The screw profiles of the screw elements are asymmetric and not congruent, but can be merged with each other by rotating the axes as mirror images.

[0148] The precise rubbing screw profile of the left screw element consists of sections i=1-12 which are either arcs or kinks. The arcs, start angle, end angle, arc radius relative to the housing bore inner diameter D, x coordinate of the center of 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 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 2. The actual rubbing screw profile apexes are arcs 1 and 7. The kinks are the sections whose values ​​are r i This can be recognized by the fact that / D=0.

[0149] [Table 2]

[0150] The precise rubbing screw profile of the right screw element consists of sections i=1'-12' which are either arcs or kinks. Table 3 shows the start angle, end angle, arc radius relative to the housing bore inner diameter D, the x coordinate of the center of arc i relative to the pivot point P2 of the right screw profile relative to the housing bore inner diameter D, and the y coordinate of the center of arc i relative to the pivot point P2 of the right screw profile relative to the housing bore inner diameter D. The actual rubbing screw profile apexes are arcs 4' and 10'. A kink is one whose value is r i This can be recognized by the fact that / D=0.

[0151] [Table 3]

[0152] The sum of the apex angles of both precision mating screw profiles of a screw element pair together in radians is BKW0 = 1.72356 (98.75 degrees).

[0153] The technically produced, practically interlocking screw elements of the screw element pair according to Example 1, which have screw profiles derived from the precisely interlocking screw profile, are asymmetric and not congruent, but can be merged with each other by rotating the axes in mirror images. The sum of the apex angles of the practically interlocking screw profiles of the individual screw elements is 0.73115 (41.89 degrees) in radians. The sum of the apex angles of the screw profiles of the screw element pair in radians is BKW=1.462 (83.78 degrees).

[0154] The limit calculated according to formula (2) for the sum of the apex angles of the pair of screw elements is BKGW=1.444 (82.71 degrees), therefore BKW>BKGW and their ratio f=BKW / BKGW=1.012, therefore this pair of screw elements is not according to the invention.

[0155] The actual threading screw profiles of the two screw elements are shown in Figure 2 together with the corresponding precision threading screw profiles from which the actual threading screw profiles were derived. Table 4 shows the screw profile of the left screw element in the plane according to equation (13), i.e. the angle γ starting from the center of rotation P1 of the left screw element. l The radii are given for each angular distance of 2 degrees, except for the transitions to the crest or groove areas, where additional points are given. Table 5 gives the corresponding coordinates of the screw profile of the right screw element, starting from the center of rotation P2 of the right screw element, and Figure 3 shows a plan view of a pair of screw elements not according to the invention.

[0156] [Table 4] TIFF2025511989000043.tif253170TIFF2025511989000044.tif75170

[0157] [Table 5] TIFF2025511989000046.tif253170TIFF2025511989000047.tif68170

[0158] Example 2 (invention) Example 2 according to the invention is a pair of two mutually practically rubbing screw elements to which the spatial equidistance calculation rule is additionally applied, with A / D=0.825, T / D=1.2, δ / D=0.015, s / D=0.02 and SP / D=0.01, i.e. the values ​​for the corresponding variables are the same as in Example 1. The screw profiles of the screw elements are asymmetric and not congruent, but can be merged with each other by mirror image rotation of the axes.

[0159] The precision rubbing screw profile of the left screw element consists of sections i=1-20 which are either arcs or kinks. The arc, start angle, end angle, arc radius relative to the housing bore inner diameter D, the x coordinate of the center of arc i relative to the pivot point P1 of the left screw profile relative to the housing bore inner diameter D, and the y coordinate of the center of 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 tops of the precision rubbing screw profile are arcs 1 and 11. The kinks are defined as sections i=1-20 which have a value of r i This can be recognized by the fact that / D=0.

[0160] The precisely mating screw profile of the right screw element consists of arcs i = 1’ to 20’ which are either arcs or kinks. The arc, start angle, end angle, arc radius with respect to the housing bore inner diameter D, x - coordinate of the center of arc i with respect to the pivot point P2 of the right screw profile with respect to the housing bore inner diameter D, and y - coordinate of the center of arc i with respect to the pivot point P2 of the right screw profile with respect to the housing bore inner diameter D are given in Table 7. The tops of the actually mating screw profiles are arcs 6’ and 16’. The sum of the apex angles of the precisely mating screw profiles of both pairs of screw elements is BKW0 = 0.8784 (50.32 degrees) in radians.

[0161]

Table 6

[0162]

Table 7

[0163] The technically produced and actually mating screw elements of the pair of screw elements according to Example 2, having screw profiles derived from precisely mating screw profiles, are asymmetric and not congruent, but can be mated with each other by rotating about the axis as a mirror image. The sum of the apex angles of the actually mating screw profiles of the individual screw elements is 0.3384 (19.30 degrees) in radians. The sum of the apex angles of the screw profiles of the pair of screw elements is BKW = 0.6769 (38.78 degrees) in radians. The limit value calculated according to Equation (2) for the sum of the apex angles of the pair of screw elements is BKGW = 1.444 (82.71 degrees) in radians (similar to that in Example 1). Therefore, BKW < BKGW, and their ratio is f = BKW / BKGW = 0.469, and this pair of screw elements is according to the present invention.

[0164] The practically interlocking screw profile of a pair of screw elements according to the invention is shown in Figure 4 together with the corresponding precise interlocking screw profile from which the practically interlocking screw profile was derived. Table 8 shows the screw profile of the left screw element in the plane according to equation (5), i.e. the angle γ starting from the center of rotation P1 of the left screw element. l Table 9 shows the radii as a function of the angle θ of the screw element θ. These radii are given for each angular distance of 2 degrees, except for the transitions to the crest or groove areas where additional points are given. Table 9 shows the corresponding coordinates of the screw profile of the right hand screw element, and Figure 5 shows a plan view of a pair of screw elements according to the invention.

[0165] [Table 8] TIFF2025511989000051.tif253170TIFF2025511989000052.tif90170

[0166] [Table 9] TIFF2025511989000054.tif253170TIFF2025511989000055.tif83170

[0167] Example 3 (invention) Example 3 according to the invention is a pair of two mutually practically rubbing screw elements to which the spatial equidistance calculation rule is additionally applied, with A / D=0.805, T / D=5, δ / D=0.015 and s / D=0.02. The screw profiles of the screw elements are asymmetric and not congruent, but can be merged with each other by rotating the axes as mirror images.

[0168] The precision rubbing screw profile of the left screw element consists of sections i=1-20 which are either arcs or kinks. The arc, start angle, end angle, arc radius relative to the housing bore inner diameter D, the x coordinate of the center of arc i relative to the pivot point P1 of the left screw profile relative to the housing bore inner diameter D, and the y coordinate of the center of 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 tops of the precision rubbing screw profile are arcs 1 and 11. The kinks are defined as sections i=1-20 which have a value of r i This can be recognized by the fact that / D = 0. The crests of the screw profile that actually rub against each other are arcs 1 and 11.

[0169] [Table 10]

[0170] The precision rubbing screw profile of the right screw element consists of arc i=1'-20' which is either an arc or a kink. The arc, start angle, end angle, arc radius relative to the housing bore inner diameter D, the x coordinate of the center of arc i relative to the pivot point P2 of the right screw profile relative to the housing bore inner diameter D, and the y coordinate of the center of arc i relative to the pivot point P2 of the right screw profile relative to the housing bore inner diameter D are given in Table 11. The apexes of the precision rubbing screw profile are arcs 6' and 16'. The sum of the apex angles of both precision rubbing profiles in radians is BKW0=0.7716 (44.21 degrees).

[0171] [Table 11]

[0172] The technically produced and practically rubbing screw elements of the pair of screw elements according to Example 3, having a screw profile derived from a precisely rubbing screw profile, are likewise asymmetrical and not congruent, but can be joined together by rotating them about the axis as a mirror image. The sum of the apex angles of both the left and right screw profiles is 0.3464 (20.89 degrees) in radians, and thus the sum of the apex angles of the pair of screw elements is BKW = 0.6928 (41.78 degrees).

[0173] The limit value calculated according to Equation (2) for the sum of the apex angles of the pair of screw elements is BKGW = 1.848 (105.86 degrees) in radians. Therefore, BKW < BKGW, and their ratio is f = BKW / BKGW = 0.375, and the pair of screw elements is according to the present invention.

[0174] The practically rubbing screw profiles of the pair of screw elements according to the present invention are shown in FIG. 6 together with the corresponding precisely rubbing screw profiles from which the practically rubbing screw profiles were derived. Table 12 shows the radius as a function of the angle γ starting from the center of rotation P1 of the left screw profile, i.e., the left screw profile, according to Equation (5). These radii are given at 2-degree angular intervals each, except for the transitions to the top or groove areas where additional points are given. Table 13 shows the corresponding coordinates of the right screw profile, and FIG. 7 shows a plan view of the pair of screw elements according to the present invention. l The radii are given at 2-degree angular intervals each, except for the transitions to the top or groove areas where additional points are given. Table 13 shows the corresponding coordinates of the right screw profile, and FIG. 7 shows a plan view of the pair of screw elements according to the present invention.

[0175]

Table 12

[0176]

Table 13

[0177] Example 4 (Invention) Example 4 according to the present invention is a pair of two mutually practically rubbing screw elements, in which the spatial equidistance calculation rule is additionally implemented, with A / D=0.84, T / D=0.75, δ / d=0.005 and s / D=0.01. The screw profiles of the screw elements are asymmetric and not congruent, but can be merged with each other by rotating the axes as mirror images.

[0178] The precision rubbing screw profile of the left screw element consists of sections i=1-20 which are either arcs or kinks. The arcs, start angle, end angle, arc radius relative to the housing bore inner diameter D, the x coordinate of the center of arc i relative to the pivot point P1 of the left screw profile relative to the housing bore inner diameter D, and the y coordinate of the center of 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 14. The tops of the precision rubbing screw profile are arcs 1 and 11. The kinks are defined as sections i=1-20 which have a value of r i This can be recognized by the fact that / D=0.

[0179] [Table 14]

[0180] The precisely mating screw profile of the right screw element consists of arcs i = 1’ to 20’ which are either arcs or kinks. The arc, start angle, end angle, arc radius with respect to the housing bore inner diameter D, x - coordinate of the center of arc i with respect to the pivot point P2 of the right screw profile with respect to the housing bore inner diameter D, and y - coordinate of the center of arc i with respect to the pivot point P2 of the right screw profile with respect to the housing bore inner diameter D are given in Table 15. The tops of the precisely mating screw profiles are arcs 6’ and 16’.

[0181] The sum of the apex angles of the precisely mating screw profiles of both pairs of screw elements is BKW0 = 0.69814 (40 degrees) in radians together.

[0182]

Table 15

[0183] The technically produced and actually mating screw elements of the pair of screw elements according to Example 4, having screw profiles derived from precisely mating screw profiles, are likewise asymmetric and not congruent, but can be made to fit together by rotating them about an axis as a mirror image. The sum of the apex angles of both the left and right screw profiles is 0.25885 (14.83 degrees) in radians, and thus the sum of the apex angles of the pair of screw elements is BKW = 0.51766 (29.66 degrees).

[0184] The limit value calculated according to Equation (2) for the sum of the apex angles of the pair of screw elements is BKGW = 1.5703 (89.97 degrees) in radians. Thus, BKW < BKGW, and their ratio is f = BKW / BKGW = 0.33, and the pair of screw elements is according to the present invention.

[0185] The practically interfacing screw profile of a screw element pair according to the present invention is shown in Figure 8, together with the corresponding precision interfacing screw profile from which it was derived. Figure 9 shows a plan view of a screw element pair according to the present invention.

[0186] Table 16 shows the screw profile of the left screw element according to formula (5), i.e., the angle γ l Table 17 shows the radii as a function of the angle θ of the screw profile. These radii are given for each angular distance of 2 degrees, except at the transitions to the crest or groove areas where additional points are given. Table 17 shows the corresponding coordinates of the screw profile for the screw profile on the right.

[0187] [Table 16] TIFF2025511989000067.tif253170TIFF2025511989000068.tif83170

[0188] [Table 17] TIFF2025511989000070.tif253170TIFF2025511989000071.tif83170

[0189] BRIEF DESCRIPTION OF THE DRAWINGS AND LIST OF REFERENCE SYMBOLS Figure 1 Actual rubbing screw profile of the left screw element according to Example 2 1.1 Housing bore inner wall profile at the left side of the housing bore 1.2 Flight Depth GT 1.3 Housing bore inner diameter D 1.4 Apex angle of the left screw element with clearance δ from the screw element to the housing wall but without additional clearance SP: KW l,δ 1.5 Clearance δ from screw element to housing wall 1.6 Reduced flight depth due to additional clearance: GT-SP 1.7 Distance from screw element to housing wall increased by additional clearance: δ + SP 1.8 Apex angle of the left screw element with both the clearance δ from the screw element to the housing wall and the additional clearance SP: KW l,δ+SP 1.9 Center of rotation P

[0190] Figure 2 Screw profile of a pair of screw elements not according to the invention according to Example 1 2.1 Housing bore inner wall profile 2.2 Profile of the left screw element (precise rubbing) 2.3 Profile of the left screw element (actual rubbing) 2.4 Profile of the right screw element (precise rubbing) 2.5 Profile of the right screw element (actual rubbing)

[0191] Figure 3 FIG. 2 is a plan view of a screw element pair not according to the invention according to Example 1. 3.1 Housing bore inner wall profile 3.3 Profile of the left screw element (actual rubbing) 3.5 Profile of the right screw element (actual rubbing)

[0192] Figure 4 Screw profile of the screw element pair according to the invention according to example 2 4.1 Housing bore inner wall profile 4.2 Profile of the left screw element (precision rubbing) 4.3 Profile of the left screw element (actual rubbing) 4.4 Right-hand screw element profile (precision rubbing) 4.5 Profile of the right screw element (actual rubbing)

[0193] Figure 5 FIG. 3 is a plan view of a screw element pair according to the invention according to Example 2 5.1 Housing bore inner wall profile 5.3 Profile of the left screw element (actual rubbing) 5.5 Profile of the right screw element (actual rubbing)

[0194] Figure 6 Screw profile of the screw element pair according to the invention according to example 3 6.1 Housing bore inner wall profile 6.2 Profile of the left screw element (precision rubbing) 6.3 Profile of the left screw element (actual rubbing) 6.4 Right-hand screw element profile (precision rubbing) 6.5 Profile of the right-hand screw element (actual rubbing)

[0195] Figure 7 FIG. 3 is a plan view of a screw element pair according to the invention according to Example 3 7.1 Housing bore inner wall profile 7.3 Profile of the left screw element (actual rubbing) 7.5 Profile of the right-hand screw element (actual rubbing)

[0196] Figure 8 Screw profile of the screw element pair according to the invention according to Example 4 8.1 Housing bore inner wall profile 8.2 Profile of the left screw element (precision rubbing) 8.3 Profile of the left screw element (actual rubbing) 8.4 Right-hand screw element profile (precision rubbing) 8.5 Profile of the right hand screw element (actual rubbing)

[0197] Figure 9 FIG. 4 is a plan view of a screw element pair according to the invention according to Example 4 9.1 Housing bore inner wall profile 9.3 Profile of the left screw element (actual rubbing) 9.5 Profile of the right hand screw element (actual rubbing)

Claims

1. A multi-screw machine having pairs of screw elements, m screw shafts SW rotating in the same direction at the same speed １ ~SW ｍ And each adjacent axis of rotation X １ ~X ｍ However, the screw shaft SW has a center distance A in a cross-section perpendicular to the rotation axis. １ ~SW ｍ and, Each having the same housing bore inner diameter D and bore center M １ ~M ｍ There are m circular housing bores that penetrate each other and have a distance equal to the center distance A between bore centers M １ ~M ｍ coincides with each respective associated rotation axis X １ ~SW ｍ of the screw shaft SW １ ~X ｍ and the circular housing bore coincides with the rotation center P １ ~P ｍ of the screw element Equipped with, The pair of screw elements of the aforementioned screw element are located directly adjacent to each other on the screw shaft, facing each other. The two screw elements of the aforementioned screw element rub against each other at a distance s from one screw element to the other. Both screw elements have an asymmetrical screw profile. Both screw elements each have exactly two peaks, For each of the two screw elements, its two vertices are at different distances from the respective rotation centers P of the screw profile. In each case, one vertex has a distance D / 2 with respect to each rotation center P that is reduced by the distance δ from the screw element to the housing wall and further reduced by an additional gap SP, and the other vertex has a distance D / 2 with respect to each rotation center P that is reduced by the distance δ from the screw element to the housing wall but not by an additional gap (SP), The distance δ from the screw element to the housing wall is the same for both screw elements, and the additional gap SP is the same for both screw elements. The sum of the vertex angles in radians at the tops of both screw elements, BKW, is greater than 0. f=BKW / BKGW (44) For a coefficient f, it is true that the coefficient f is greater than 0 and less than or equal to 0.

95. Here, BKW is the sum of the vertex angles of both screw elements in radians, and BKGW is, A multi-screw machine characterized in that the parameters are determined by and described above, and are defined as presented in the specification.

2. The multi-screw machine according to claim 1, wherein f is 0.1 or greater and 0.8 or less.

3. The multi-screw machine according to claim 1 or 2, wherein the ratio of the distance s between two screw elements of a pair of screw elements to the inner diameter D of the housing bore is 0.002 to 0.

05.

4. The multi-screw machine according to claim 1 or 2, wherein the distance δ from the screw element to the housing wall with respect to the inner diameter D of the housing bore is 0.002 to 0.

05.

5. The multi-screw machine according to claim 1 or 2, wherein the additional gap SP between each of the screw elements relative to the flight depth GT is 0.015 to 0.

4.

6. A multi-screw machine according to claim 1 or 2, wherein there is a distance δ from the screw element to the housing wall, but there is no additional gap SP with respect to the inner wall of the housing bore, and the apex angles of the tops of the pair of screw elements are the same.

7. A multi-screw machine according to claim 1 or 2, having a distance δ from the screw element to the housing wall and the additional gap SP with respect to the inner wall of the housing bore, wherein the apex angles of the tops of the pair of screw elements are the same.

8. A multi-screw machine according to claim 1 or 2, wherein for both screw elements of a pair of screw elements, the apex angle of the top of the screw elements of the pair of screw elements having a distance δ from the screw element to the housing wall and the additional gap SP is greater than the apex angle of the top of the screw elements of the pair of screw elements having a distance δ from the screw element to the housing wall but not having the additional gap SP.

9. The multi-screw machine according to claim 1 or 2, wherein the pair of screw profiles of the screw elements are not congruent, and the screw profiles of the two screw elements can be combined by rotating them with their axes mirrored.

10. The multi-screw machine according to claim 1 or 2, wherein each of the two screw profiles of the pair of screw elements has exactly two grooves and exactly four flanks.

11. The multi-screw machine according to claim 1 or 2, wherein the pair of screw profiles of the screw element have exactly four grooves and exactly eight flanks.

12. A method for producing or processing an extruded product using a multi-screw machine according to claim 1 or 2, wherein the method is: (1) The step of installing the multi-screw machine, (2) A step of producing or processing the extruded product, Methods that include...

Images