Screw elements having improved mixing effect and improved heat transfer capacity, and their use

Abstract

The present invention relates to a pair of three lead screw elements for a multi-screw machine having screw shafts rotating in the same direction and at the same speed. Two screw elements of the pair of screw elements according to the present invention, which are directly adjacent and facing each other on two directly adjacent screw shafts, are practically cleaned from each other. The present invention also relates to the use of the pair of screw elements according to the present invention in a multi-screw machine, a multi-screw machine equipped with the pair of screw elements according to the present invention, and a method for extruding plastics or viscoelastic compounds using the pair of screw elements according to the present invention.

Description

[Technical Field]

[0001] The present invention relates to a pair of three-flight screw elements for a multi-screw machine having screw shafts rotating in the same direction and at the same speed. The two screw elements of the pair of screw elements according to the present invention, which are directly adjacent and facing each other on two directly adjacent screw shafts, practically clean each other. The present invention also relates to the use of the pair of screw elements according to the present invention in a multi-screw machine, a multi-screw machine equipped with the pair of screw elements according to the present invention, and a method for extruding plastic or viscoelastic lumps using the pair of screw elements according to the present invention. [Background technology]

[0002] In the context of the present invention, a multi-screw machine is understood to mean a screw machine having two or more screw shafts, for example, a screw machine having two, three, or four screw shafts, or a screw machine having eight to sixteen, particularly twelve, screw shafts in an annular arrangement. In the case of three or more screw shafts, the axes of rotation of the screw shafts may be arranged adjacent to each other, or they may be in an annular shape, for example, in what is called a ring extruder. In a multi-screw extruder, the axes of rotation of the screw shafts are generally arranged parallel to each other. This parallel arrangement of the axes of rotation is also preferred according to the present invention. The screw elements according to the present invention are preferably arranged opposite each other on the screw shafts in a number corresponding to the number of screw shafts of each extruder. Such a screw machine having two or more screw shafts is hereafter also called a multi-screw machine, a multi-screw machine, or a multi-screw extruder. A twin-screw machine is hereafter also called a twin-screw extruder. In the context of the present invention, the term "screw machine" is used synonymously with the term "extruder."

[0003] Existing extruders have a modular system in which various screw elements can be mounted on a core shaft to form a screw shaft, and therefore such a screw shaft is segmented. This allows those skilled in the art to adapt the extruder to various processing tasks. However, a screw shaft can also be made as a single unit, that is, having only one screw element extending substantially along the entire length of the screw shaft, or it can be segmented only in part. The present invention relates to both screw elements that can be mounted on a core shaft and a screw shaft made from a single part as described above.

[0004] Co-rotating twin-screw machines, in which the screw shafts precisely clean each other, have long been known, for example from Patent Document 1. In polymer production and processing, screw machines having screw shafts based on the principle that the screw elements precisely clean the screw cross-sectional profile have been used in various ways. This is mainly because, at normal processing temperatures, molten polymer adheres to the surface and deteriorates over time, but this is prevented by the self-cleaning effect of the screw elements in a multi-screw machine where they precisely clean each other in pairs. Rules for generating the cross-sectional screw profile of screw elements that precisely clean each other are shown, for example, in [1] ([1] = Non-Patent Document 1). According to the description therein, in the case of screw elements that precisely clean each other, a predetermined cross-sectional screw profile on the first shaft of a twin-screw extruder determines the cross-sectional screw profile on the second shaft of the twin-screw extruder ([1], p. 108). In the context of the present invention, the screw cross-sectional profile, also abbreviated as screw profile, is understood to mean the outer contour of the screw element in a planar cross-section perpendicular to the axis of rotation of the screw element, according to the axis of rotation of the associated screw shaft. The screw profile of the screw element on the first shaft is called the generated screw profile. The screw profile of the screw element on the second shaft follows the screw profile of the first shaft of the twin-screw extruder and is therefore called the generated screw profile. In a multi-screw extruder, screw elements with generated screw profiles and screw elements with generated screw profiles are always used alternately on adjacent shafts.

[0005] Anyone skilled in the art of screw elements will understand that a single screw element or screw profile alone cannot precisely or practically rub against another, and that a pair of such elements is always necessary.

[0006] Here, two distinctions need to be made: a precisely rubbing screw profile, i.e., a mathematical configuration in which two screw elements located opposite each other on two adjacent screw shafts clean each other without any gaps; and a screw profile for a screw element designed with a material entity for its intended use, i.e., a screw element that is technically fabricated.

[0007] Those skilled in the art will recognize that technically designed screw elements must have spacing (both the spacing s between screw elements and the spacing δ from a screw element to the inner wall of the housing bore (referred to as the gap S from the screw element to the inner wall of the housing bore within the scope of this invention)) to ensure the function of the extruder, as referred to, for example, on pages 39-41 and 113-121 of [1]. This is necessary to avoid metallic seizure, manufacturing tolerances, roughness, angular deviations, uneven thermal expansion, and excessive stress on the extruded material due to insufficient spacing between two screw elements directly adjacent to each other on two directly adjacent screw shafts. The aforementioned pages also describe methods for determining the precise geometric shape of the elements to be produced from the spacing and precisely rubbing contours. These methods are referred to as spacing strategies.

[0008] For the purposes of the present invention, the interval (also referred to as s within the scope of the invention) is understood to be the distance between the closest points of the screw profiles of two screw elements that practically clean each other. The rules for generating screw profiles having the interval described in [1] are applicable to screw elements according to the present invention.

[0009] For the purposes of this invention, the gap (also referred to as S within the scope of this invention) is understood to be the distance between the top of the screw profile and the closest point on the inner wall of the extruder housing bore. The inner wall of the extruder housing bore will hereafter be abbreviated as the housing wall.

[0010] In the context of the present invention, when the term "precision cleaning" is used, unless otherwise stated, it means the mathematical configuration of a screw profile for precision cleaning or the corresponding screw element having this screw profile. When the term "actual cleaning" is used in the context of the present invention, unless otherwise stated, it means a technically produced screw element or its screw profile, and this actually cleaning screw profile preferably, as will be explained in more detail below, by applying one of the spacing strategies of increasing center distance, longitudinal cross-sectional equidistance, circular equidistance or spatial equidistance, particularly preferably by applying one of the spacing strategies of longitudinal cross-sectional equidistance, circular equidistance or spatial equidistance, is derived from the screw profile for precision cleaning.

[0011] The strategies of longitudinal cross-sectional equidistance, circular equidistance, and spatial equidistance are hereinafter also referred to as the longitudinal cross-sectional equidistance calculation rule, circular equidistance calculation rule, and spatial equidistance calculation rule.

[0012] Multiaxial extruders, particularly twin-screw extruders, are known to transfer mechanical energy to the extrudate by dissipation. This, on the one hand, requires an energy input to perform processing engineering tasks such as mixing and degassing, and on the other hand, consumes mechanical energy input and leads to a temperature rise in the extrudate, which can lead to undesirable chemical reactions that damage the extrudate, resulting in both desirable and undesirable results.

[0013] Mixing is also known to be a basic operation in multiaxial extruders, particularly twin-screw extruders. Non-uniformity in the extrudate due to incomplete mixing is known to lead to problems in the further processing and final properties of the extrudate.

[0014] In a twin-screw extruder, the extrudate is sheared particularly strongly between the top of the screw and the inner wall of the extruder housing bore. This means that particularly large amounts of energy dissipate into the extrudate, leading to strong localized overheating in the extrudate. This is shown, for example, in FIGS. 4.80 to 4.84 on pages 416 to 423 of [1]. This local overheating can lead to damage in the extrudate, such as odors, color, changes in chemical composition or molecular weight, or the formation of inhomogeneities in the extrudate such as gels or specks. In particular, it is harmful if the sum of the large apex angle and the apex angles of pairs of screw elements that are opposite each other and rub against each other on immediately adjacent screw shafts is large.

[0015] Screw elements aimed at improving the mixing effect have long been the subject of technological development. For example, many known geometric shapes, like all variants of the toothed mixing elements of Patent Document 2, Patent Document 3 or Patent Document 4, ignore the fact that the screw elements should advantageously clean each other. This class of mixing elements is basically characterized in that the screw thread has openings or grooves that interrupt the transport of the material and ensure improved mixing. However, since the surfaces in the openings or grooves are not kinematically cleaned, material can adhere to these points and deteriorate, becoming a source of contamination for the extrudate (in this case the plastic or viscoelastic mass to be extruded).

[0016] However, mixing elements with complete self-cleaning have also long been known. For example, Patent Document 5 already discloses a three-flight kneading disk that provides an improved mixing effect compared to a continuously operating screw flight.

[0017] Patent document 6 teaches how the gap between the screw crown and the housing wall can be designed for 3-flight and 4-flight screw elements for a twin-screw extruder. The extruded material is sheared in a manner targeted by the different gaps at the screw crown. For this purpose, a symmetrical arrangement of 3-flight or 4-flight screw profiles of a twin-screw, having the same a priori gap S (referred to as s in Patent document 6) with respect to the housing wall at all screw crowns, is offset parallel to the center of rotation by an eccentricity e smaller than s.

[0018] Patent Document 7 discloses a method for manufacturing a pair of self-cleaning screw elements, wherein the individual screw vertices of these screw elements have different gaps with respect to the inner wall of the housing. The gap width of the individual screw vertices can be increased here to half the flight depth H. The objective here is also to cause material exchange between the individual screw flights and to shear the material in a targeted manner as it passes through the screw vertices. The resulting two-flight screw elements have no axis of symmetry and have different vertex angles at the two screw vertices. Three-flight and four-flight screw elements are also claimed. In the three-flight screw elements, the gap is increased at the screw spacing (Figure 4). The flight depth H is understood here to be half the distance which is the difference between the outer diameter da of the screw element and the core diameter di of the screw element, i.e., H = (DA - DA) / 2. This application does not teach anything about avoiding damage to the extruder or improved heat transfer.

[0019] Patent document 8 describes a three-flight screw element having different gaps and different apex angles at three apex points, where the screw apex with the smallest gap to the inner wall of the housing has the largest apex angle. This makes it possible to construct a three-flight screw profile in which the ratio of outer diameter da to core diameter di is greater than 1.366. However, a screw element designed according to this construction principle is disadvantageous because the screw apex with the narrowest gap and the largest apex angle has a zone of high shear stress for the polymer to be processed, and is easily damaged by high shear and thermal stress.

[0020] Patent Document 9 describes, in particular, three-flight and four-flight screw elements, and the apex angles at each screw crown of the three-flight or four-flight screw elements can be designed differently. However, Patent Document 9 does not teach which embodiment is advantageous in terms of their mixing and dispersion effects or their behavior during pressure rise. The design specifications for these elements are limited to transition elements (referred to as "fractional elements" in Patent Document 9) between one-flight and three-flight elements or between two-flight and four-flight elements, thus limiting the degrees of freedom.

[0021] Patent document 10 describes a screw profile for a pair of three-flight self-cleaning screw elements for a twin-screw extruder, which has a high distribution and dispersion mixing effect. However, the screw elements described in patent document 10 have the disadvantage of having a wide apex angle at the point where the narrowest gap is with respect to the inner wall of the housing, resulting in a zone with high energy dissipation and high local temperature peaks, which can lead to damage in the case of sensitive polymers. [Prior art documents] [Patent Documents]

[0022] [Patent Document 1] German patent no. 862668 [Patent Document 2] German Patent Application Publication No. 4134026 [Patent Document 3] German Patent Application Publication No. 19706134 [Patent Document 4] International Publication No. 2004 / 009326 [Patent Document 5] German Patent No. 940109 [Patent Document 6] German Patent Application Publication No. 3412258 [Patent Document 7] European Patent Application Publication No. 0002131 [Patent Document 8] German Patent Application Publication No. 4239220 [Patent Document 9] International Publication No. 2002 / 009919 [Patent Document 10] European Patent Application Publication No. 1093905 [Non-patent literature]

[0023] [Non-Patent Document 1] Klemens Kohlgrueber: "Der gleichlaeufige Doppelschneckenextruder" [Codirectional Twin-Screw Extruders], 2nd Edition, Hanser Verlag Muenchen 2016, pages 107 to 120 [Overview of the project] [Problems that the invention aims to solve]

[0024] The present invention is based on the objective of providing a screw element that can achieve improved mixing and dispersion effects compared to the prior art, along with good heat transfer.

[0025] The pair of three-flight screw elements according to the present invention should also provide a larger volume within the housing bore for the extruder compared to conventional three-flight screw elements.

[0026] In addition, the two screw elements of the screw element pair according to the present invention should practically rub against each other when used as intended. [Means for solving the problem]

[0027] Surprisingly, it was found that this problem could be solved by a pair of screw elements having the features of the main claim. [Modes for carrying out the invention]

[0028] In the context of this invention, the following terms apply:

[0029] A screw profile is a closed convex curve. A screw profile is composed of several different curves, which, depending on their geometric properties, are called "vertices," "flanks," or "grooves." A vertex is always adjacent to a flank on both sides. A groove is always adjacent to a flank on both sides. The vertices and grooves are separated from each other by the flanks and always alternate in the same direction within the screw profile. This results in the sequence vertex-flank-groove-flank-vertex-and so on.

[0030] A curve is a continuous line that has length but no width, and has a first endpoint and a second endpoint that are not exactly the same point; that is, the first endpoint does not coincide with the second endpoint.

[0031] The curve may consist of several curve sections, in which case the first curve section has a common point of contact with a second curve section that is directly adjacent to the first curve section.

[0032] However, the curve may consist of exactly one curved section.

[0033] A curved section is a section of a curve that has a first endpoint and a second endpoint that are not exactly the same point; that is, the first endpoint does not coincide with the second endpoint.

[0034] The formulas on which the curved sections are based are preferably selected from a group of formulas including those for circular arcs, elliptical arcs, parabolic arcs, longitudinal equidistant calculation rules, circular equidistant calculation rules, and spatial equidistant calculation rules, as shown on pages 117-121 of [1]. A longitudinal equidistant calculation rule or a circular equidistant calculation rule is preferred to generate a constant spacing when the screw elements are cleaned from one another.

[0035] Also, curved section

number

number

[0036] The rules for calculating longitudinal equidistant distances are disclosed on pages 117-121 of [1].

[0037] The circular equidistant rule is based on the assumption that screw profiles rub precisely against each other in the xy-plane of a Cartesian coordinate system, where perpendiculars are drawn at each point of the screw profile in the direction of the rotation center DP. Points shifted by half a distance relative to the rotation center along these perpendiculars belong to the technically fabricated screw profile. For example, a portion of a precisely rubbing screw profile has a radius r i If it is an arc having the same center and radius, the corresponding section of the related technically fabricated screw profile will have the same center and radius.

number

[0038] Spatial equidistance is described on page 41 of [1], and is available, for example, through a parameterized representation. Spatial equidistance is described in detail in International Application PCT / EP2023 / 058951.

[0039] A closed convex curve is a continuous line composed of one or more curves, each consisting of one or more curve sections that have a non-zero length but no width. The closed convex curve has no marked start or end points. The length of the curve can be determined by adding the lengths of the curve sections around it, starting from any point on the curve. All tangents to a closed convex curve lie outside the area enclosed by the curve.

[0040] Since all the curved sections of a screw profile are located within a single plane, the closed curve that constitutes the screw profile divides the area of ​​this plane into an area inside the closed curve and an area outside the closed curve.

[0041] An arc is a curved section in which all points are at the same distance, called the radius, from a common center point. An arc has a start and end point that are not exactly the same.

[0042] An arc is considered an arc only if all points of the arc share the same center and radius, and the points of the arc form an unbroken curved section. In other words, two directly adjacent arcs sharing a common point of contact are considered two separate arcs only if they have different centers or different radii.

[0043] center coordinate x m , y m And an arc with radius r is, as is generally known, parametrically expressed x = xm +r·cosβ y = y m +r·sinβ has, where for the parameter β, β a ≦β≦β e where the starting angle β of the arc a and the ending angle β of the arc e are defined, and β in radians e <β a +π is applied. For a point with coordinates x, y, the starting angle is defined to be equal to the ending angle with respect to the labeled point having coordinates x m , y m . Thus, according to the above equations, the following applies. β a =β = β e

[0044] The arc has a starting point AP with coordinates having x a and y a . x a = x m +r·cosβ a y a = y m +r·sinβ a

[0045] The central angle of the arc (also briefly called the angle of the arc) is α = β e [[ID=6I]]- β a is.

[0046] The arc is completely defined by specifying the coordinates of the center point, the coordinates of the starting point AP, and the central angle. At this time, the radius r is the distance from the starting point AP to the center point. In the following table, the radius for characterizing the arc is also given for clarification.

[0047] The radius of curvature is the reciprocal of the curvature of the circle of curvature at a given point on a curve segment. The circle of curvature at that point is, for example, the circle that best approximates the curve at that point, as described in Wikipedia (https: / / de.wikipedia.org / wiki / Kr%C3%BCmmungskreis, accessed May 4, 2023).

[0048] The rotation center DP of a screw profile is the intersection of the rotation axis of the screw element and the cross-sectional plane perpendicular to this rotation axis X. The rotation center of the screw profile, also referred to simply as the rotation center below, coincides with the center of the housing bore in which each screw element is located, or in which each screw element is designed to correspond.

[0049] Regarding the screw profile, the center of rotation is the point around which the screw profile rotates as a cross-sectional image of the screw element.

[0050] The outer radius RA of a screw profile is the maximum distance from the center of rotation of the screw profile; therefore, the outer radius RA is the radius of the circle that encloses the entire screw profile, the circle whose center is the center of rotation associated with this screw profile.

[0051] The inner radius RI of the screw profile is the minimum distance from the center of rotation of the screw profile.

[0052] The top is, (i) The exact arc of the screw profile, with the center of rotation of the screw profile as its center point, such that all points of this arc are at a greater distance from the center of rotation than the two curve sections immediately adjacent to the apex, except for the common point of contact with the two curve sections immediately adjacent to the apex, or (ii) A point in the screw profile that is further from the center of rotation than the two immediately adjacent points. Thus, the point that is the vertex in this case (ii) is the local maximum value of the screw profile with respect to the distance from the center of rotation. Preferably, in case (ii), the point that is the vertex is the point of an arc with a radius smaller than the distance between this point and the center of rotation. Here, in case (ii), the point that is the vertex may be the midpoint of an arc with a radius smaller than the distance between this point and the center of rotation. In case (ii), the curves immediately adjacent to the vertex converge tangentially at the point that is the vertex.

[0053] In case (i), the vertex angle is the angle of the arc, that is, the difference between the end angle and the start angle. In case (ii), the vertex angle is zero.

[0054] In case (i), the vertex radius is the distance from the center of rotation of the screw profile to each vertex, which is an arc, and in case (ii), it is the distance from the center of rotation of the screw profile to the point that is a vertex.

[0055] A groove is, (iii) The exact arc of the screw profile, with the center of rotation of the screw profile as its center point, such that all points of this arc are less from the center of rotation than the two curved sections immediately adjacent to the groove, except for the points of contact with the two curved sections immediately adjacent to the groove, or (iv) A point in the screw profile that is less from the center of rotation than the two points immediately adjacent to it. Thus, the point that is the apex in this case (iv) is the local minimum of the screw profile with respect to the distance from the center of rotation. Preferably, in case (iv), the point that is the groove is the point of an arc with a radius greater than the distance between this point and the center of rotation. Here, in case (ii), the point that is the groove may be the midpoint of an arc with a radius greater than the distance between this point and the center of rotation. In case (iv), the curves immediately adjacent to the groove converge tangentially at the point that is the groove.

[0056] In case (iii), the groove angle is the angle of the arc, that is, the difference between the end angle and the start angle. In case (iv), the groove angle is zero.

[0057] In case (ii), the groove radius is the distance of each circular groove from the center of rotation of the screw profile, and in case (iv), it is the distance of the groove point from the center of rotation of the screw profile.

[0058] A flank is a curve in the screw profile such that, except for the common point of contact with the first curved section immediately adjacent to the flank, all points of this curve are at a smaller distance from the center of rotation than the first curved section immediately adjacent to the flank, and simultaneously, except for the common point of contact with the second curved section immediately adjacent to the flank, all points of this curve are at a larger distance from the center of rotation than the second curved section immediately adjacent to the flank in the screw profile.

[0059] A Franck curve can consist of several curved sections to which the above definition applies. In this case, the Franck curve is represented by a convex curve consisting of several curved sections, and the radius of curvature of each curved section is always smaller than the center distance A.

[0060] According to the present invention, the flank is preferably formed from a convex curve whose curved section is exclusively formed from an arc having a radius less than or equal to the center distance A, and according to the present invention, the flank is particularly preferably formed from exactly one arc having a radius smaller than the center distance A. According to the present invention, it is particularly preferable that each flank of the screw cross-sectional profile is formed from exactly one arc having a radius smaller than the center distance A.

[0061] Two screw profiles are said to be congruent in the same direction if they can be transformed into each other by shift and rotation. Two screw profiles are said to be congruent in opposite directions if they can be transformed into each other by shift, rotation and mirroring. Two screw profiles are said to be congruent without rotation if they can be transformed into each other by displacement.

[0062] The screw profile according to the present invention has exactly six flanks. According to the present invention, the following is preferable: For each of the six flanks, independently of each of the other five flanks, the following applies: On the other hand, the flank is formed from exactly one single arc, and this arc has a center point that is not the center of rotation of the screw profile. Or, One flank may be exclusively formed from multiple arcs, and for all the center points of these arcs, it is true that these center points are different from the center of rotation of the screw profile. Or, The flank may be formed from at least one arc and at least one non-arc curved section, and neither arc has a center point which is the center of rotation of the screw profile. Or, Frank may be formed from only a single curved section that is not an arc. Or, Frank may be formed exclusively from multiple curved sections, none of which are circular arcs.

[0063] Alternatively, according to the present invention, the flank is preferably formed from a convex curve whose curved sections are exclusively formed according to a longitudinal section equidistant, circular section equidistant, or spatial section equidistant calculation rule, and according to the present invention, the flank is particularly preferably formed from exactly one curved section which is exclusively formed according to a longitudinal section equidistant, circular section equidistant, or spatial section equidistant calculation rule. Alternatively, according to the present invention, it is particularly preferable that all flanks of the screw cross-sectional profile are exclusively formed according to a longitudinal section equidistant, circular section equidistant, or spatial section equidistant calculation rule, and according to the present invention, it is particularly preferable that each flank of the screw cross-sectional profile is formed from exactly one curved section which is exclusively formed according to a longitudinal section equidistant, circular section equidistant, or spatial section equidistant calculation rule. Alternatively, particularly preferable, all curves of the screw profile are formed according to the same longitudinal section equidistant, circular section equidistant, or spatial section equidistant calculation rule.

[0064] For the purposes of the present invention, a screw element is described as having three flights if it has exactly three peaks.

[0065] In particular, this objective is achieved by a pair of three flight screw elements. A pair of screw elements consists of screw element SE and screw element SE'. The pair of screw element SE and screw element SE' is, m screw shafts SW1~SWm that rotate in the same direction and at the same speed, wherein each adjacent axis of rotation X1~Xm has a center distance A in a cross section perpendicular to the axis of rotation, m circular housing bores that penetrate each other, each having the same internal housing radius R, with bore centers M1 to Mm at a distance equal to the center distance A, and bore centers M1 to Mm coinciding with the respective associated rotation axes X1 to Xm of screw shafts SW1 to SWm, Suitable for multi-screw machines, Screw element SE has screw profile SP, screw element SE' has screw profile SP', (1) Each of the two screw profiles SP and SP' is a closed convex curve, This closed convex curve consists only of curve sections whose radius of curvature is less than or equal to the center distance A. (2) Neither of the two screw profiles SP and SP' exhibits mirror symmetry. In the context of the present invention, a screw profile is considered to be mirror symmetry if it is mapped to itself by a vertical axis reflection on any axis passing through its respective center of rotation, or if the screw profiles SP and SP' are not congruent to each other. (3) Each of the two screw profiles SP and SP' has three precisely spaced grooves. (4) Each of the two screw profiles SP and SP' has exactly three peaks, with screw profile SP being labeled K1, K2, and K3 around its periphery, and screw profile SP' being labeled K1', K2', and K3'. (6) Two screw elements of a pair of screw elements, positioned directly adjacent to each other, facing each other in a pair on the two screw shafts of a multi-screw machine, and rotating in the same direction at the same speed, practically clean each other as a pair. (7) The groove is separated by the flank from the nearest point of the adjacent apex. (8) Frank, having exactly six curves, That is true, especially, (9) r(Ki) is the vertex radius of vertex Ki, and r(Ki') is the vertex radius of vertex Ki', where, r(K1)>r(K2) and r(K1)>r(K3) and r(K1')>r(K2') and r(K1')>r(K3') and r(K2)≧r(K3) and r(K2')≧r(K3'), and at least one of condition a) or b) is true, where, a) r(K2) > r(K3) and r(K2’) > r(K3’) b) r(K2) is not equal to r(K2’), and r(K3) is not equal to r(K3’), where r(K1) is the top radius of the screw top K1, r(K2) is the top radius of the screw top K2, r(K3) is the top radius of the screw top K3, r(K1’) is the top radius of the screw top K1’, r(K2’) is the top radius of the screw top K2’, and r(K3’) is the top radius of the screw top K3’. (10) The screw top K1 has an apex angle KW1, the screw top K2 has an apex angle KW2, the screw top K3 has an apex angle KW3, the screw top K1’ has an apex angle KW1’, the screw top K2 has an apex angle KW2’, and the screw top K3 has an apex angle KW3’. (10.1) (10.1.a) When KW / 1 > 0, KW1 < KW2 and KW1 < KW3, and (10.1.b) When KW1’ > 0, KW1’ < KW2 and KW1 < KW3. Or (10.2) (10.2.a) When KW1 > 0, KW1 < KW2 and KW1 < KW3, and (10.2.c) When KW1’ = 0, KW2 ≥ 0 and KW3 ≥ 0. Or (10.3)<9000357>(10.3.b) When KW1’ > 0, KW1’ < KW2 and KW1 < KW3, and (10.3.d) When KW1 = 0, KW2 ≥ 0 and KW3 ≥ 0. Or (10.4) (10.4.d) When KW1 = 0, KW2 ≥ 0 and KW3 ≥ 0, and (10.4.c) When KW1’ = 0, KW2 ≥ 0 and KW3 ≥ 0. Here, r(K1) is equal to r(K1’), and is equal to the outer radius RA or RA’ of the screw element, which is true, m is an integer greater than 1, preferably 2 to 16, particularly preferably 2, 3, 4, 6, 8, 10, 12, and 16, i can take a value of 1, 2, or 3, The outer radius RA is the radius of a circle surrounding the entire screw profile, the center point of that circle is the center of rotation associated with this screw profile, and the top K1 is a segment of this circle.

[0066] For the screw profile according to the present invention, the following occurs.

[0067] The three respective screw tops K1, K2, K3 and K1’, K2’, and K3’ of the screw element according to the present invention (collectively referred to as Ki and Ki’ respectively) have gaps S1, S2, S3 and also S1’, S2’, and S3’ with respect to the inner wall of the housing. S1 or S1’ is the gap between the screw top K1 or K1’ and the inner wall of the housing, S2 or S2’ is the gap between the screw top K2 or K2’ and the inner wall of the housing, S3 or S3’ is the gap between the screw top K3 or K3’ and the inner wall of the housing, and the following relationships apply.

[0068] For the purpose of the present invention, the gap S is defined as the distance between the screw top and the inner wall of the housing. Thus, the equations S1 = R - r(Ki), and S i = R - r(Ki), that is, S1 = R - r(K1), S2 = R - r(K2), and S3 = R - r(K3), and also Si’ = R - r(Ki’), that is, S1’ = R - r(K1’), S2’ = R - r(K2’), and S3’ = R - r(K3’) are followed.

[0069] Regarding the features in number (10), according to the present invention, the following is preferred. (10.1) (10.1.a) When KW1 > 0, KW1 < KW2 and KW1 < KW3, and (10.1.b) When KW1’ > 0, KW1’ < KW2 and KW1 < KW3 or (10.4) (10.4.c) When KW1 = 0, KW2 ≥ 0 and KW3 ≥ 0 and (10.4.d) When KW1’ = 0, KW2 ≥ 0 and KW3 ≥ 0

[0070] Furthermore, for the screw element according to the present invention, the following applies.

[0071] Each top Ki or Ki’ corresponds to the groove Ni’ or Ni on the corresponding screw element, that is, N1’ corresponds to K1, N2’ corresponds to K2, N3’ corresponds to K3, N1 corresponds to K1’, N2 corresponds to K2’, and N3 corresponds to K3’. For each of the two screw elements SE and SE’ according to the present invention, the following formula applies to the groove radius r(Ni’), r(Ni’) = RI + Si - S1, and correspondingly r(Ni) = RI’ + Si’ - S1’, and for the start angle of the top i and the start angle of the groove i’ it is β a,Ki ≥ β a,Ni’ + π and for the end angle of the top i and the end angle of the groove i’ it is β e,Ki ≤ β e,Ni’ + π and for the start angle of the top i’ and the start angle of the groove i it is β a,Ki’ - π ≥ β a,Ni and β e,Ki’ - π ≤ β e,Ni is true. It is always true that KWi ≤ NWi’ and KWi’ ≤ NWi. In other words, the top Ki of one screw element of the pair of screw elements according to the present invention and the groove Ni’ of the other screw element of this pair of screw elements according to the present invention are on the opposite sides with respect to the respective screw elements.

[0072] The pair of screw elements according to the present invention achieves improved mixing and dispersion effects compared to the prior art, along with good shear and good heat transfer, and ensures that two screw elements according to the present invention, which are located directly adjacent to each other on two directly adjacent screw shafts, practically clean each other.

[0073] Due to the larger gaps between the tops K2 and K3 compared to the gap between the tops K1, the energy input in the screw element according to the present invention is reduced compared to conventional screw elements known in the prior art. Surprisingly, the pair of three-flight screw elements according to the present invention nevertheless exhibits excellent mixing effects.

[0074] In a preferred embodiment of the three-flight screw element pair according to the present invention, the following also applies to the screw profile having the features shown in (1) to (10): (11) Each of the three vertices K1, K2, and K3 of the screw element SE is formed from only one curved section that is an arc, having a center that is a common rotation center DP for the vertices K1, K2, and K3 in each case, and each of the three vertices K1', K2', and K3' of the screw element SE' is formed from only one curved section that is having a center that is a common rotation center DP' for the vertices K1', K2', and K3' in each case, and, Each of the three grooves of screw element SE is formed from only one curved section, which is an arc, with a center that is the rotation center DP of screw element SE common to all three grooves, and there is exactly one groove whose distance from the rotation center DP is smaller than the distance from the rotation center DP of the other grooves, and each of the three grooves of screw element SE' is formed from only one curved section, which is an arc, with a center that is the rotation center DP' of screw element SE' common to all three grooves.

[0075] In this preferred case of the present invention having additional features (11), it also applies that the core radius RI is the radius of the groove having the smallest radius among all the grooves of the screw element SE, starting from the rotation center DP of the screw profile, and similarly the core radius RI' is the radius of the groove having the smallest radius among all the grooves of the screw element SW', starting from the rotation center DP of the screw profile, and RI is preferably equal to RI'.

[0076] In this preferred case of the present invention having additional features (11), it also applies that the outer radius RA is the radius of the top having the largest radius among all the tops of the screw element SE, starting from the rotation center DP of the screw profile, and similarly, the outer radius RA' is the radius of the top having the smallest radius among all the tops of the screw element SW', starting from the rotation center DP' of the screw profile, and RA is preferably equal to RA'.

[0077] In this preferred embodiment of the present invention, the arcs representing exactly three grooves, like the arcs representing exactly three vertices K1, K2, and K3, have the same center point, i.e., the center of rotation of one of the elements. Therefore, the center of rotation DP is the common center point of all three vertices K1, K2, and K3 and all three grooves.

[0078] As a result, in this preferred embodiment of the present invention, the screw profile has kinks in all transitions from the screw apex to the flank. A kink in the screw profile means that a rim is formed on the screw element at the corresponding point. Mathematically, a kink means that the curve is not continuously differentiable at the point of the kink.

[0079] In preferred embodiments of the three-flight screw element pair according to the present invention, the following also applies to a screw profile having the features shown in (1) to (10), or a screw profile having the features shown in (1) to (10) and an additional feature (11). (12) In the case of screw profile SP, the screw apex having the largest apex radius r(Ki), i.e., apex K1, has the smallest apex angle among apex K1, K2, and K3. Similarly, in the case of screw profile SP', the screw apex having the largest apex radius r(Ki)', i.e., apex K1', has the smallest apex angle among apex K1', K2', and K3'.

[0080] In this way, the energy input is reduced, and the thermal load on the polymer is reduced. For the multi-screw machines described above, this means that the screw apex having the narrowest gap with respect to the inner wall of the housing, i.e., the apex K1 with gap S1, has the smallest apex angle. The same is true for the apex K1' and gap S1'.

[0081] According to the present invention, it also applies that two screw elements according to the present invention, positioned in a pair directly adjacent to each other on two screw shafts of the described multi-screw machine, practically clean each other as a pair, and such two screw elements according to the present invention are referred to as a pair of screw elements according to the present invention. The screw profiles of these two screw elements according to the present invention may be the same or different.

[0082] According to the present invention, it is preferable that all screw elements practically clean each other in pairs in a cross section perpendicular to the screw shaft. Of course, this is true except for any technically required spacing. Here, the screw profiles of these screw elements according to the present invention may be the same or different.

[0083] In a more preferred embodiment of the three-flight screw element pair according to the present invention, the following also applies to a screw profile having the features shown in (1) to (10), or a screw profile having the features shown in (1) to (11), or a screw profile having the features shown in (1) to (12). (13) The screw profile SP is continuously differentiable at all of its apex K1, K2, and K3, and the screw profile SP' is also continuously differentiable at all of its apex K1', K2', and K3'.

[0084] In a more preferred embodiment of the three-flight screw element pair according to the present invention, the following also applies to a screw profile having the features shown in (1) to (10), or a screw profile having the features shown in (1) to (11), or a screw profile having the features shown in (1) to (11) and an additional feature (13). (14) Each of the three vertices K1, K2, and K3 of the screw element SE is formed from exactly one point, i.e., KW1=KW2=KW3=0, and similarly, each of the three vertices K1', K2', and K3' of the screw element SE' is formed from exactly one point, i.e., KW1'=KW2'=KW3'=0.

[0085] In a more preferred embodiment of the three-flight screw element pair according to the present invention, the following also applies to a screw profile having the features shown in (1) to (10), or a screw profile having the features shown in (1) to (11), or a screw profile having the features shown in (1) to (12), or a screw profile having the features shown in (1) to (13). (15) The vertices K1 and K1' are formed from exactly one point, the vertices K2 and K3 are each formed from exactly one arc whose respective center coincides with the center of rotation DP, and the vertices K2' and K3' are each formed from exactly one arc whose respective center coincides with the center of rotation DP', and thus the vertices K2 and K3 and the vertices K2' and K3' each have a vertex angle greater than zero.

[0086] In a more preferred embodiment of the three-flight screw element pair according to the present invention, the following also applies to a screw profile having the features shown in (1) to (10), or a screw profile having the features shown in (1) to (11), or a screw profile having the features shown in (1) to (12), or a screw profile having the features shown in (1) to (13). (16) All vertices of screw profile SP and all vertices of screw profile SP' have a vertex angle greater than zero.

[0087] The order of the vertices and grooves can be designed differently according to the present invention. To clarify the features, the order of the vertices and grooves is listed mathematically in the positive direction, starting from the vertex K1 on the screw shaft SW.

[0088] In a more preferred embodiment of the present invention, of a pair of three-flight screw elements according to the present invention, the following also applies to a screw profile having the features shown in (1) to (10), or a screw profile having the features shown in (1) to (10) plus one additional feature from features (11) to (16), or a screw profile having the features shown in (1) to (10) plus two or more additional features from features (11) to (16). (17) Given a given center distance A and a given housing inner radius R with respect to a given housing inner diameter D=2R, the distance r(K1) from the center of rotation to the top K1 is within the following range for r(K1) or r(K1'), i.e., r(K1) is less than or equal to R-0.002D, r(K1) is R-0.05D or higher. r(K1') is less than or equal to R-0.002D, r(K1') is greater than or equal to R-0.05D. Selected to apply.

[0089] In a more preferred embodiment of the present invention, of a pair of three-flight screw elements according to the present invention, the following also applies to a screw profile having the features shown in (1) to (10), or a screw profile having the features shown in (1) to (10) plus one additional feature from features (11) to (17), or a screw profile having the features shown in (1) to (10) plus two or more additional features from features (11) to (17). (18) Given a given center distance A and a given housing inner radius R for a given housing inner diameter D=2R, the distance r(K1) from the center of rotation to the apex K1 is within the following range for apex K2 and K2', i.e., r(K2) is less than or equal to r(K1) - 0.002D, r(K2) is greater than or equal to r(K1) - 0.08D, r(K2') is less than or equal to r(K1')-0.002D, r(K2') is greater than or equal to r(K1') - 0.08D, Here, it is also true that r(K2) is greater than (r(K1)+r(N1)) / 2 and r(K2') is greater than (r(K1')+r(N1')) / 2. Selected to be preferably applied.

[0090] In a more preferred embodiment of the present invention, of a pair of three-flight screw elements according to the present invention, the following also applies to a screw profile having the features shown in (1) to (10), or a screw profile having the features shown in (1) to (10) plus one additional feature from features (11) to (18), or a screw profile having the features shown in (1) to (10) plus two or more additional features from features (11) to (18). (19) Given a given center distance A and a given housing inner radius R for a given housing inner diameter D=2R, the distance r(K1) from the center of rotation to the apex K1 is within the following range for apex K3 and K3', i.e., r(K3) is greater than or equal to r(K1) - 0.09D, r(K3) is less than or equal to r(K2), r(K3) is greater than or equal to r(K2) - 0.05D. r(K3') is greater than or equal to r(K1')-0.09D, r(K3') is less than or equal to r(K2'), r(K3') is greater than or equal to r(K2') - 0.05D, Also, (r(K1)+r(N1)) / 2, and r(K3') is greater than (r(K3')+r(N1')) / 2. Selected to be preferably applied.

[0091] According to the present invention, the following occurs: Regarding multi-screw machines, m screw shafts SW1 to SWm rotate in the same direction and at the same speed, wherein each adjacent axis of rotation X1 to Xm has the same center distance A in a cross section perpendicular to the axis of rotation, m circular housing bores that penetrate each other, each having the same internal housing radius R, with bore centers M1 to Mm at a distance equal to the center distance A, and bore centers M1 to Mm coinciding with the respective associated rotation axes X1 to Xm of screw shafts SW1 to SWm, It has, The clearance S1 is preferably S1 / D = 0.002 to S1 / D = 0.05 with respect to the housing inner diameter D, and the clearance S1' is preferably S1' / D = 0.002 to S1' / D = 0.05 with respect to the housing inner diameter D. The clearance S2 is preferably S2 / D = 0.004 to S2 / D = 0.082 with respect to the housing inner diameter D, and the clearance S2' is preferably S2' / D = 0.004 to S2' / D = 0.082 with respect to the housing inner diameter D. The clearance S3 is preferably S3 / D = 0.004 to S3 / D = 0.1 with respect to the housing inner diameter D, and the clearance S3' is preferably S3' / D = 0.004 to S3' / D = 0.1 with respect to the housing inner diameter D.

[0092] In a further preferred embodiment according to the invention of the pair of three-flight screw elements according to the invention, the following also applies: a screw profile having the features shown in (1) to (10), or a screw profile having one additional feature of features (11) to (19) together with the features shown in (1) to (10), or a screw profile having two or more additional features of features (11) to (19) together with the features shown in (1) to (10). (20) The apex angle KW1 is 0° < KW1 < 10°, preferably 2° < KW1 < 8°, and the apex angle KW1' is 0° < KW1' < 1°0, preferably 2° < KW1' < 8°.

[0093] Alternatively, according to the invention, the apex angle KW1 is preferably 0° when the screw profile at the top is continuously differentiable, i.e., when the screw profile at the top has no kink.

[0094] In a more preferred embodiment of the present invention, of a pair of three-flight screw elements according to the present invention, the following also applies to a screw profile having the features shown in (1) to (10), or a screw profile having the features shown in (1) to (10) plus one additional feature from features (11) to (20), or a screw profile having the features shown in (1) to (10) plus two or more additional features from features (11) to (20). (21) The screw profiles SP and SP' of a pair of screw elements SE and SE' are congruent without rotation and can be transformed into each other by displacement from the center of rotation of one screw profile to the other screw profile. This means that the screw elements are identical. The order of the top and grooves of the screw profile SP is then K1 N2 K3 N1 K2 N3 or K1 N3 K2 N1 K3 N2.

[0095] In a more preferred embodiment of the present invention, of a pair of three-flight screw elements according to the present invention, the following also applies to a screw profile having the features shown in (1) to (10), or a screw profile having the features shown in (1) to (10) plus one additional feature from features (11) to (20), or a screw profile having the features shown in (1) to (10) plus two or more additional features from features (11) to (20). (22) The screw profiles SP and SP' of the pair of screw elements SE and SE' are congruent in opposite directions. - Displacement of the screw profile from the rotation center of one screw profile to the rotation center of the other screw profile, - A reflection along the line connecting the centers of rotation, - Rotation of one screw profile by an angle other than zero, Depending on the order of the operations, they can be converted to one another.

[0096] Screw elements designed as transport elements are preferably designed according to the rule of spatial equidistantness, and all have a vertex angle greater than zero.

[0097] Screw elements designed as mixing discs are preferably designed according to the circular equidistant rule, and the profile consists only of arcs. In a particularly preferred embodiment of such a screw element, the screw profile consists of arcs having two different radii, and all vertex angles are 0.

[0098] A further subject of the present invention is the use of the screw element pair according to the present invention in multi-screw machines. Preferably, the screw element pair according to the present invention is used in a twin-screw machine, i.e., a twin-screw extruder.

[0099] Accordingly, the present invention also relates to a multi-screw machine comprising a pair of screw elements according to the present invention. The multi-screw machine preferably comprises, herein, at least the same number of screw elements as the number of shafts the screw machine has. The screw elements according to the present invention are, herein, arranged on the screw shaft such that each of the screw elements according to the present invention is practically cleaned by at least one other screw element according to the present invention.

[0100] The screw element pairs according to the present invention may exist in a multi-screw machine in the form of kneading, conveying, or mixing elements. It is possible to combine kneading, conveying, and mixing elements in a screw machine. The screw element pairs according to the present invention can also be combined with other screw elements known, for example, in the prior art.

[0101] As is known, a feature of the conveying element (see, for example, pages 136-142 of [1]) is that the screw profile has a continuous helical winding that is continuous in the axial direction. The conveying element may be right-handed or left-handed. The pitch of the conveying element according to the present invention is preferably in the range of 0.5 to 5 times the center distance A, and the axial length of the conveying element according to the present invention is preferably in the range of 0.25 to 2 times the pitch. The length of the conveying element is particularly preferably equal to the pitch, and therefore the conveying element represents the complete rotation of the screw profile.

[0102] As is known, a characteristic feature of the mixing element (see, for example, pages 142-145 of [1]) is that the screw profile continues axially, offset parallel to the axis in the form of mixing discs. The mixing discs may be arranged to be either right-handed or left-handed, producing either a conveying effect or a reverse conveying effect. A 45-degree offset angle between two axially adjacent mixing discs results in a neutral arrangement with no conveying effect for the three-flight screw. The axial length of the mixing discs is preferably in the range of 0.05 to 0.5 times the axial distance A. The axial distance between two adjacent mixing discs is preferably in the range of 0.0005 to 0.02 times the axial distance A.

[0103] As is particularly well known (see, for example, pages 148-151 of [1]), the mixing elements are formed such that the conveying elements have openings in the land portions of the screw flight. The mixing elements may be right-handed or left-handed. Their pitch is preferably in the range of 0.1 to 10 times the axial distance A, and the axial length of the elements is preferably in the range of 0.5 to 5 times the axial distance A. The openings are preferably U-shaped or V-shaped and preferably positioned opposite or parallel to the axis.

[0104] The arrangement of screw elements, consisting of conveying elements and / or kneading elements and / or mixing elements, on a screw shaft is also called a screw configuration.

[0105] The screw element according to the present invention may also be configured as a transition element, meaning that the screw profile at any point in the axial range of the screw element is different from that at another point in the axial range of the screw element, and these different screw profiles cannot be converted to each other by rotation.

[0106] The screw element according to the present invention is suitable for extruding plastics and viscoelastic materials such as suspensions, pastes, glass, ceramic ingots, molten metals, plastics, plastic melts, polymer solutions, elastomers, and rubber ingots.

[0107] Therefore, the present invention also relates to a multi-screw machine comprising at least one pair of screw elements according to the present invention.

[0108] Accordingly, the present invention also relates to a method for extruding a plastic or viscoelastic mass using a pair of screw elements according to the present invention, or using a screw machine equipped with a pair of screw elements according to the present invention.

[0109] A plastic mass is understood to be a deformable mass. Examples of plastic masses include polymer melts, particularly thermoplastics, and mixtures of polymer melts, elastomers, or dispersions of polymer melts with solids, liquids, or gases.

[0110] Thermoplastic polymers (also known as thermoplastics), or mixtures of thermoplastic polymers from the following series, are preferably used: polycarbonates, polyamides, polyesters, especially polybutylene terephthalate and polyethylene terephthalate, as well as polyethers, thermoplastic polyurethanes, polyacetals, fluoropolymers, especially polyvinylidene fluoride, as well as polyethersulfones, polyolefins, especially polyethylene and polypropylene, as well as polyimides, polyacrylates, especially poly(methyl)methacrylate, as well as polyphenylene oxide, polyphenylene sulfide, polyether ketones, polyaryl ether ketones, styrene polymers, especially polystyrene, as well as styrene copolymers, especially styrene-acrylonitrile copolymers, as well as acrylonitrile-butadiene-styrene block copolymers, and also polyvinyl chloride. Equally preferred are mixtures of the listed plastics, which will be understood by those skilled in the art as combinations of two or more plastics.

[0111] Viscoelastic masses are materials and mixtures that exhibit elasticity dependent on time, temperature, and frequency. Viscoelasticity is characterized by partially elastic, partially viscous behavior. After an external force is removed, the material relaxes only partially, and the remaining energy dissipates in the form of a flow process (delay).

[0112] Examples of viscoelastic materials include 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, sulfurized 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 plastics, are also possible, of course.

[0113] The plastic or viscoelastic mass to be extruded can be used in its pure form, or as a mixture with fillers and reinforcing agents such as glass fibers, as a mixture with each other or with other polymers, or as a mixture with conventional polymer additives.

[0114] The additive can be added to the extruder in solid, liquid, or solution form along with the polymer, or at least some or all of the additive can be supplied to the extruder via a sidestream.

[0115] Additives can impart various properties to polymers. Examples of such additives may include plasticizers, colorants, pigments, processing aids, fillers, antioxidants, reinforcing agents, UV absorbers and light stabilizers, spreading oils, metal deactivators, peroxide scavengers, basic stabilizers, nucleating agents, benzofurans and indolinones having stabilizing or antioxidant properties, mold release agents, flame retardant additives, antistatic agents, dyes, and melt stabilizers. Examples of fillers and reinforcing agents include carbon black, glass fibers, clay, mica, graphite fibers, titanium dioxide, carbon fibers, carbon nanotubes, ionic liquids, and natural fibers.

[0116] As described above, the screw element pair according to the present invention is particularly suitable for extruding viscoelastic masses. Method steps that can be carried out with the help of this screw element pair are, for example, mixing or dispersing a solid, liquid, or gas. The solid may be, for example, the solid additive described above. The liquid may be, for example, the additive in liquid form described above, but may also be, for example, water. The gas may be, for example, nitrogen or carbon dioxide.

[0117] In particular, a single-screw or multi-screw machine comprising a pair of screw elements according to the present invention, or at least one pair of screw elements according to the present invention, can also be advantageously used for compounding colorants, pigments, or additives into thermoplastic plastics, especially polycarbonate or thermoplastic polyurethane.

[0118] Accordingly, the present invention relates to both a method of using a pair of screw elements according to the present invention for compounding colorants and additives into thermoplastics, particularly polycarbonate or thermoplastic polyurethane, and the use of a pair of screw elements according to the present invention for compounding colorants and additives into thermoplastics, particularly polycarbonate or thermoplastic polyurethane.

[0119] The present invention will be described below by reference to the accompanying drawings and by example using preferred exemplary embodiments, the features specified below may constitute embodiments of the present invention individually or in combination.

[0120] For the purposes of the present invention, it should be noted that the rotation center DP is the cross-sectional profile of the rotation axis X. Therefore, the screw elements of a twin-screw extruder having rotation axes X1 and X2 and positioned directly opposite each other have rotation centers DP1 and DP2, which are hereafter also referred to as DP and DP'.

[0121] Figure 1 is a cross-sectional view of a pair of three-flight screw elements for a co-rotating twin-screw extruder, and thus shows the screw cross-sectional profiles of these screw elements. The values ​​RI (inner radius of SP), RA (outer radius of SP), RI' (inner radius of SP'), RA' (outer radius of RA'), gaps S1, S2 and S3 and S1', S2' and S3', and the rotation centers DP and DP' are shown to indicate the geometric variables. Furthermore, the vertices K1, K2 and K3 and K1', K2' and K3', and the grooves N1, N2 and N3 and N1', N2' and N3' are shown along with the vertex radii r(K1), r(K2) and r(K3).

[0122] Figure 1 shows the top and groove order K1 N1 K2 N2 K3 N3 of the left screw profile.

[0123] Figure 2A shows a plan view of a pair of three-flight screw elements for a co-rotating twin-screw extruder according to the present invention, which practically rub against each other. The housing walls are indicated by vertical lines in Figure 2A. In this pair of screw elements according to the present invention, the two screw profiles are identical.

[0124] The screw tips are labeled K1-K3 on the left screw element and K1'-K3' on the right screw element, and correspondingly the grooves are labeled N1-N3 and N1'-N3', respectively. Screw tip K1 cleans the inner wall of the housing with a gap S1, screw tip K2 cleans with a gap S2, and so on. The ratio A / D of the center distance A to the housing inner diameter D is 0.91. The ratio of S1 / D is 0.005, the ratio of S2 / D is 0.01, and the ratio of S3 / D is 0.015. Screw elements SE and SE' have the same screw profile. The ratio T / D of the pitch to the housing inner diameter is 1. The apex angles are given in radians, with KW1=KW1'=0.1224, KW2=KW2'=0.1362, and KW3=KW3'=0.2306. The groove angles, similarly expressed in radians, are NW1=NW1'=0.17453, NW2=NW2'=0.18789, and NW3=NW3'=0.28184.

[0125] The order of the screw profile tops and grooves is K1 N2 K3 N1 K2 N3 or K1' N2' K3' N1' K2' N3'.

[0126] Figure 2B shows the screw profiles of the screw elements according to Figure 2A. The two screw profiles can be transformed from one another by shifting the rotation center DP of one screw element to the rotation center DP' of the other screw element. The coordinates of the screw profiles are given in Table 2B.

[0127] TIFF2026514238000005.tif247170TIFF2026514238000006.tif91170

[0128] Figure 2C shows a cross-sectional view of a pair of precisely rubbing three-flight screw elements according to Figures 2A and 2B, i.e., the screw cross-sectional profiles of these screw elements. Figure 2C shows the screw profiles of two screw elements that precisely clean each other, i.e., there is no gap between the screw elements when they clean each other. In practice, a non-zero gap will be set between the screw elements. As already mentioned above, the procedure for this is shown, for example, on pages 40 and 41 of [1], and also on pages 117-121. The arcs that make up the screw profiles are labeled 1-12 for the left screw profile and 1'-12' for the right screw profile. The gap between the screw top and the inner wall of the housing is labeled S1-S3 for the left screw element and S1'-S3' for the right screw element. The construction lines of the arcs that make up the screw profiles are also shown as dashed lines.

[0129] The screw profile of the screw element in Figure 2C consists only of arcs. Table 1B below shows the radius r of the screw profile in Figure 2C for arcs 1-12 and 1'-12', in relation to the center distance A of each arc. i The ratio of the distance to the center A, the central angle, and the coordinates of the circle's center (x m,i and y m,i ), and the coordinates of the starting point AP (x a and y a The following are listed. The arcs are numbered counterclockwise for the generated screw profiles, in this case the left-hand screw profiles, and clockwise for the generated screw profiles, in this case the right-hand screw profiles. All length dimensions are normalized to the distance A between the rotation centers DP and DP'. The origin of the coordinate system is located at the rotation center of each screw profile. Central angle α i The specifications are in radians. Since the two screw profiles are identical, only one profile is specified in each case.

[0130] TIFF2026514238000007.tif70170

[0131] The profiles in Figures 2A and 2B are screw profiles that practically clean each other, derived from the profile in Figure 2C during the manufacturing of the screw elements. These screw profiles were calculated so that the screw elements clean each other at spatially equidistant intervals, i.e., calculated using spatial equidistant calculation rules. Alternatively, such screw profiles that practically clean each other can also be calculated using longitudinal equidistant calculation rules.

[0132] Figure 3 shows the screw profiles of a pair of screw elements according to the present invention. The screw profiles are composed of arcs. The construction lines of the arcs that make up the screw profiles are also shown as dashed lines. The screw profile of the left screw element SE is: - Displacement of the screw profile from the rotation center DP of the left screw profile to the rotation center DP' of the right screw profile. - Reflection along the line connecting the two centers of rotation, - A mathematically positive rotation of only 15 degrees, Depending on the order of the steps, it can be converted to a screw profile SE'. The screw profile of the left screw element SE and the screw profile of the right screw element SE' are therefore congruent in opposite directions.

[0133] The ratio of the center distance to the housing inner diameter is A / D = 0.82, the ratio of gaps S1 and S1' to the housing inner diameter is S1 / D = S1' / D = 0.018, the ratio of gaps S2 and S2' to the housing inner diameter is S2 / D = S2' / D = 0.05, the ratio of gaps S3 and S3' to the housing inner diameter is S3 / D = S3' / D = 0.077136, and the ratio of the spacing between screw profiles SW and SW' is s / D = 0.022. All apex angles of this screw profile are KW1 = KW2 = KW3 = KW1' = KW2' = KW3' = 0.

[0134] The order of the tops and grooves on the screw element is K1 N2 K2 N1 K3 N2.

[0135] Table 3A contains a list of arcs of the screw profile SW for coordinates x and y relative to the rotation center DP. TIFF2026514238000008.tif39170

[0136] Table 3B shows a list of arcs of the screw profile SW' for coordinates x' and y' relative to the rotation center DP'. TIFF2026514238000009.tif39170

[0137] Figures 4A to 4H show various screw profiles according to the present invention, having vertices and grooves in different orders. For all of these screw profiles, the ratio of the center distance to the housing inner diameter is A / D = 0.82, the ratio of the gaps S1 and S1' to the housing inner diameter is S1 / D = S1' / D = 0.018, and the ratio of the distance between screw profiles SW and SW' to the diameter is s / D = 0.022. All vertex angles of the screw elements according to the present invention in Figures 4A to 4H are zero. The screw profile in Figure 4E corresponds to the screw profile of Example 2. Table 4 provides an overview of the various screw profiles, and the vertices and grooves Ki, Ni, Ki' and Ni' are also shown therein. Figure 4B shows a screw profile that is not congruent but has mirror symmetry with respect to the x-axis.

[0138] TIFF2026514238000010.tif72170

[0139] Figure 5 shows a pair of screw profiles of another screw element according to the present invention. The screw profile is composed of arcs. The construction lines of the arcs that make up the screw profile are also shown as dashed lines. The screw profile SW of the left element is - Displacement of the screw profile from the rotation center DP of the left screw profile to the rotation center DP' of the right screw profile. - Reflection along the line connecting the two centers of rotation (labeled Y here), - A mathematically positive rotation of 15.72025 degrees, where line Y is transformed into Y'. Depending on the order of the steps, it can be converted to a screw profile SW'.

[0140] The ratio of the center distance to the apex angle is A / D = 0.8, the ratio of gaps S1 and S1' to the housing inner diameter is S1 / D = S1 / D = 0.025, the ratio of gaps S2 and S2' to D is S2 / D = S2' / D = 0.062, and the ratio of gaps S3 and S3' to D is S3 / D = S3' / D = 0.095.

[0141] The vertex angles are given in radians as KW1=KW1'=0, KW2=KW2'=0.102871, and KW3=KW3'=0.162301. The groove angles are similarly given in radians as NW1=NW1'=0, NW2=NW2'=0.114586, and NW3=NW3'=0.171879.

[0142] The screw profiles on the left and right sides in Figure 5 are composed of arcs, with the radius of the arc r being based on the inner diameter of the housing. i / D and r i ' / D, central angle, housing inner diameter, coordinates SP of the starting point relative to the origin x,y and x',y' of the coordinate system. x,i / D and SP y,i / D, and SP'x,i / D and SP' y,i / D, coordinates MP of the center of the arc relative to the diameter x,i / D and MP y,i / D is shown in Tables 5A and 5B.

[0143] TIFF2026514238000011.tif89170

[0144] TIFF2026514238000012.tif90170

Claims

1. A pair of three flight screw elements, The aforementioned pair of screw elements consists of screw element SE and screw element SE', The pair of screw element SE and screw element SE' is, m screw shafts SW1 to SWm that rotate in the same direction and at the same speed, wherein each adjacent rotation axis X1 to Xm has a center distance A in a cross section perpendicular to the rotation axis, m circular housing bores that penetrate each other, each having the same internal housing radius R, with bore centers M1 to Mm at a distance equal to the center distance A, and the bore centers M1 to Mm coinciding with the respective associated rotation axes X1 to Xm of the screw shafts SW1 to SWm, Suitable for multi-screw machines, The screw element SE has a screw profile SP, and the screw element SE' has a screw profile SP'. (1) Each of the two screw profiles SP and SP' is a closed convex curve, This closed convex curve is composed only of curve sections whose radius of curvature is less than or equal to the center distance A. (2) Neither of the two screw profiles SP and SP' has mirror symmetry, or the screw profiles SP and SP' are not congruent to each other. (3) Each of the two screw profiles SP and SP' has three precisely spaced grooves. (4) Each of the two screw profiles SP and SP' has exactly three peaks, and the screw profile SP is labeled K1, K2, and K3 around its periphery, and the screw profile SP' is labeled K1', K2', and K3'. (6) The two screw elements of the pair of screw elements of the multi-screw machine, which are positioned opposite each other in pairs on the two screw shafts, directly adjacent to each other, and rotating in the same direction at the same speed, practically clean each other as a pair. (7) The groove is separated by the flank from the nearest point of the adjacent apex. (8) Frank, having exactly six curves, That is true, (9) r(Ki) is the vertex radius of vertex Ki, and r(Ki') is the vertex radius of vertex Ki', where, r(K1) > r(K2) and r(K1) > r(K3) and r(K1') > r(K2') and r(K1') > r(K3') and r(K2) ≥ r(K3) and r(K2') ≥ r(K3'), and at least one of condition a) or b) is true, where, a) r(K2) > r(K3) and r(K2') > r(K3') b) r(K2) is not equal to r(K2'), and r(K3) is not equal to r(K3'), Here, r(K1) is the top radius of screw crown K1, r(K2) is the top radius of screw crown K2, r(K3) is the top radius of screw crown K3, r(K1') is the top radius of screw crown K1', r(K2') is the top radius of screw crown K2', and r(K3') is the top radius of screw crown K3'. (10) The screw top K1 has a vertex angle KW1, the screw top K2 has a vertex angle KW2, the screw top K3 has a vertex angle KW3, the screw top K1' has a vertex angle KW1', the screw top K2 has a vertex angle KW2', the screw top K3 has a vertex angle KW3', （１０．１） (10.1.a) If KW1 > 0, then KW1 < KW2 and KW1 < KW3, and, (10.1.b) If KW1' > 0, then KW1' < KW2 and KW1 < KW3. Or, （１０．２） (10.2.a) If KW1 > 0, then KW1 < KW2 and KW1 < KW3, and, (10.2.c) When KW1' = 0, KW2 ≥ 0 and KW3 ≥ 0. Or, （１０．３） (10.3.b) If KW1' > 0, then KW1' < KW2 and KW1 < KW3, and, (10.3.d) When KW1 = 0, KW2 ≥ 0 and KW3 ≥ 0. Or, （１０．４） (10.4.d) When KW1 = 0, KW2 ≥ 0 and KW3 ≥ 0, and, (10.4.c) If KW1' = 0, then KW2 ≥ 0 and KW3 ≥ 0. Here, r(K1) is equal to r(K1'), and is equal to the outer radius RA or RA' of the screw element. m is an integer greater than 1, preferably 2 to 16, and particularly preferably 2, 3, 4, 6, 8, 10, 12, and 16. i can take the value 1, 2, or 3. A pair of three-flight screw elements, characterized in that the outer radius RA is the radius of a circle enclosing the entire screw profile, the center point of the circle is the rotation center associated with this screw profile, and the apex K1 is a segment of this circle.

2. Each of the three vertices K1, K2, and K3 of the screw element SE is formed from only one curved section that is an arc, having a center that is a common rotation center DP for the vertices K1, K2, and K3 in each case, and each of the three vertices K1', K2', and K3' of the screw element SE' is similarly formed from only one curved section that is having a center that is a common rotation center DP' for the vertices K1', K2', and K3' in each case, and, The screw element according to claim 1, characterized in that each of the three grooves of the screw element SE is formed from only one curved section that is an arc, having a center which is the rotation center DP of the screw element SE common to the three grooves, and there is exactly one groove whose distance from the rotation center DP is smaller than the distance from the rotation center DP of the other grooves, and each of the three grooves of the screw element SE' is formed from only one curved section that is an arc, having a center which is the rotation center DP' of the screw element SE' common to the three grooves.

3. In the case of screw profile SP, the screw apex having the largest apex radius r(Ki), i.e., apex K1, has the smallest apex angle among apex K1, K2, and K3, and in the case of screw profile SP', the screw apex having the largest apex radius r(Ki)', i.e., apex K1', has the smallest apex angle among apex K1', K2', and K3', characterized in that a pair of screw elements according to claim 1 or 2.

4. A pair of screw elements according to any one of claims 1 to 3, characterized in that the screw profile SP is continuously differentiable at all of the top portions K1, K2, and K3, and the screw profile SP' is also continuously differentiable at all of the top portions K1', K2', and K3'.

5. A pair of screw elements according to any one of claims 1, 2, or 4, characterized in that each of the three vertices K1, K2, and K3 of the screw element SE is formed from exactly one point, and similarly, each of the three vertices K1', K2', and K3' of the screw element SE' is formed from exactly one point.

6. A pair of screw elements according to any one of claims 1 to 4, characterized in that the tops K1 and K1' are formed from exactly one point, the tops K2 and K3 are each formed from exactly one arc whose respective center coincides with the rotation center DP, and the tops K2' and K3' are each formed from exactly one arc whose respective center coincides with the rotation center DP'.

7. A pair of screw elements according to any one of claims 1 to 4, characterized in that all the vertices of the screw profile SP and all the vertices of the screw profile SP' have a vertex angle greater than zero.

8. Given a given center distance A and a given housing inner radius R with respect to a given housing inner diameter D = 2R, the distance r(K1) from the rotation center to the top K1 is within the following range for r(K1) or r(K1'), i.e., r(K1) is less than or equal to R - 0.002D, r(K1) is R-0.05D or higher. r(K1') is less than or equal to R - 0.002D, r(K1') is R-0.05D or higher. A pair of screw elements according to any one of claims 1 to 7, characterized in that they are selected so that the following can be applied.

9. Given a given center distance A and a given housing inner radius R with respect to a given housing inner diameter D = 2R, the distance r(K1) of the apex K1 from the center of rotation is within the following range for the apex K2 and K2', i.e., r(K2) is less than or equal to r(K1) - 0.002D, r(K2) is greater than or equal to r(K1) - 0.08D. r(K2') is less than or equal to r(K1') - 0.002D, r(K2') is greater than or equal to r(K1') - 0.08D, Here, it is also true that r(K2) is greater than (r(K1) + r(N1)) / 2, and r(K2') is greater than (r(K1') + r(N1')) / 2. A pair of screw elements according to any one of claims 1 to 8, characterized in that they are selected so as to apply.

10. Given a given center distance A and a given housing inner radius R relative to a given housing inner diameter D = 2R, the distance r(K1) of the apex K1 from the center of rotation is within the following range for the apex K3 and K3', i.e., r(K3) is greater than or equal to r(K1) - 0.09D. r(K3) is less than or equal to r(K2), r(K3) is greater than or equal to r(K2) - 0.05D. r(K3') is greater than or equal to r(K1') - 0.09D, r(K3') is less than or equal to r(K2'), r(K3') is greater than or equal to r(K2') - 0.05D, Also, (r(K1) + r(N1)) / 2, and r(K3') is greater than (r(K3') + r(N1')) / 2. A pair of screw elements according to any one of claims 1 to 9, characterized in that they are selected so that the following is preferably applied.

11. Regarding the screw profiles SP and SP', independently of each other, A pair of screw elements according to any one of claims 1 to 10, characterized in that the vertex angle KW1 is true to be 0 degrees < KW1 < 10 degrees, preferably 2 degrees < KW1 < 8 degrees, and the vertex angle KW1' is true to be 0 degrees < KW1' < 10 degrees, preferably 2 degrees < KW1' < 8 degrees.

12. A pair of screw elements according to any one of claims 1 to 11, characterized in that the screw profiles of the two screw elements SE and SE' are congruent without rotation, or the screw profiles SP and SP' of the two screw elements SE and SE' are congruent in opposite directions.

13. Use of a pair of screw elements according to any one of claims 1 to 12 in a multi-screw machine.

14. A multi-screw machine comprising a pair of screw elements according to any one of claims 1 to 12.

15. A method for extruding a plastic or viscoelastic mass using a pair of screw elements as described in claim 1, or using a screw machine as described in claim 14.

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