Elements for reverse-rotating twin-screw processing apparatus
Elements with continuous self-wiping flights and defined lobe contours enhance mixing and melting capacity in twin screw processing apparatuses, addressing mixing and residence time challenges while enabling efficient processing of temperature-sensitive materials.
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- STEER ENG PRIVATE
- Filing Date
- 2024-05-29
- Publication Date
- 2026-05-12
AI Technical Summary
Counter-rotating twin screw processing apparatuses face challenges in improving material mixing ability, reducing material residence time, and enhancing wiping capability.
The introduction of elements with continuous self-wiping flights and defined lobe contours, formed by joining functionally continuous curves, enhances the mixing and melting capacity of twin screw processing apparatuses, reducing material stagnation and facilitating homogeneous mixing.
The solution improves mixing and melting efficiency, reduces material residence time, and allows for processing temperature-sensitive materials at lower temperatures, achieving a homogeneous melted mixture.
Smart Images
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Figure 0007857340000029
Abstract
Description
Technical Field
[0001] The present disclosure relates to the field of twin screw processing apparatuses. More particularly, the present disclosure relates to elements for a counter-rotating twin screw processing apparatus.
Background Art
[0002] Counter-rotating twin screw processing apparatuses, such as twin screw extruders, are known in the art to comprise a long barrel having two parallel holes that overlap each other. Processing elements, such as screws, each attached to one of two parallel shafts, are disposed within the holes. Each element is formed with flights consisting of raised portions or lobes that extend along the length of the element and have a radial diameter that is larger than the root diameter of the element. The number of lobes may be an integer or a non-integer that forms integer-lobe or non-integer-lobe flights, respectively.
[0003] In a counter-rotating twin screw processing apparatus, the processing elements are configured to rotate in opposite directions to each other and generally are not of a self-wiping type. Counter-rotating twin screw processing apparatuses are used in the manufacture, formulation, and processing of plastics, foods, paints, and pharmaceuticals, among others. The main task performed by a counter-rotating twin screw processing apparatus is to mix materials to produce a melt. There is a need to improve the material mixing ability of counter-rotating twin screw processing apparatuses and elements for counter-rotating processing apparatuses. There is also a need for elements for a counter-rotating processing apparatus that reduce material residence and improve wiping ability.
Summary of the Invention
[0004] In one aspect of the present disclosure, an element for a counter-rotating twin-screw processing apparatus having an axial hole for mounting on a screw shaft of the processing apparatus is disclosed. The element comprises at least one continuous self-wiping flight helically formed thereon. The element also comprises one or more lobes having lobe contours defined in the radial plane of the element. The lobe contour of each lobe is provided by a functionally continuous curve obtained by joining a first curve to a second curve. The first curve is expressed by a mathematical formula, and the second curve is a mirror image of the first curve with respect to the radial axis passing through the central axis of the element and one of the two poles of the first curve. The first curve is defined by the following mathematical formula:
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[0005] In other aspects of this disclosure, a reverse-rotating screw for a reverse-rotating twin-screw processing apparatus is disclosed. The reverse-rotating twin-screw processing apparatus defines an axial bore for housing the reverse-rotating screw. At least a portion of the reverse-rotating screw is provided with at least one continuous self-wiping flight helically formed thereon. The reverse-rotating screw also comprises one or more lobes having lobe contours defined in the radial plane of the reverse-rotating screw. The lobe contour of each lobe is provided by a functionally continuous curve obtained by joining a first curve to a second curve. The first curve is expressed by the following formula, and the second curve is a mirror image of the first curve with respect to the radial axis passing through the central axis of the element and one of the two poles of the first curve. The first curve is defined by the following formula:
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[0006] In yet another aspect of this disclosure, a counter-rotating twin-screw processing apparatus is disclosed. The counter-rotating twin-screw processing apparatus comprises a barrel defining a first cylindrical bore and a second cylindrical bore. The first and second cylindrical bore overlap to form a chamber. A first shaft rotates within the first cylindrical bore about its axis, and a second shaft rotates within the second cylindrical bore about its axis. At least one element is coupled to the first and second shafts, respectively. This element comprises axial holes for mounting to the first and second shafts, respectively. The element also comprises a continuous self-wiping flight helically formed thereon. Furthermore, the element comprises one or more lobes having lobe contours defined in the radial plane of the counter-rotating screw. The lobe contour of each lobe is provided by a functionally continuous curve obtained by coupling a first curve to a second curve. The first curve is expressed mathematically, and the second curve is a mirror image of the first curve with respect to the radial axis passing through the central axis of the element and one of the two poles of the first curve. The first curve is defined by the following formula.
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[0007] In still other aspects of the present disclosure, a pair of elements for a twin screw processing apparatus are disclosed. The twin screw processing apparatus includes a first shaft and a second shaft. The pair of elements includes a first element adapted to be coupled to the first shaft and a second element adapted to be coupled to the second shaft. The first element and the second element each have a continuous self-wiping flight formed spirally thereon. Further, the first element and the second element each have one or more lobes having a lobe profile defined in the radial plane of the first element and the second element. The lobe profile is provided by a functionally continuous curve obtained by joining a first curve to a second curve. The first curve is represented by a mathematical formula, and the second curve is a mirror image of the first curve with respect to a radial axis passing through the central axis of the first element or the second element and one of the two extreme points of the first curve. The first curve is defined by the following mathematical formula.
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Brief Description of the Drawings
[0008] [Figure 1]Exemplary explanatory drawing of a reverse rotation twin screw processing apparatus according to an embodiment of the present disclosure. [Figure 2] Exemplary drawing of a side view of a processing element in the reverse rotation twin screw processing apparatus of FIG. 1 according to an embodiment of the present disclosure. [Figure 3A] Exemplary side view of the processing element of FIG. 2 according to an embodiment of the present disclosure. [Figure 3B] Exemplary front view of the processing element of FIG. 2 according to an embodiment of the present disclosure. [Figure 4] Exemplary side view showing the relative rotational movement of the processing elements of FIG. 2 with respect to each other in the reverse rotation twin screw processing apparatus of FIG. 1 according to an embodiment of the present disclosure. [Figure 5] Exemplary side view showing the relative rotational movement of the processing elements of FIG. 2 with respect to each other in the reverse rotation twin screw processing apparatus of FIG. 1 according to an embodiment of the present disclosure. [Figure 6A] Exemplary side view showing the relative rotational movement of the processing elements of FIG. 2 with respect to each other in the reverse rotation twin screw processing apparatus of FIG. 1 according to an embodiment of the present disclosure. [Figure 6B] Exemplary side view showing the relative rotational movement of the processing elements of FIG. 2 with respect to each other in the reverse rotation twin screw processing apparatus of FIG. 1 according to an embodiment of the present disclosure. [Figure 6C] Exemplary side view showing the relative rotational movement of the processing elements of FIG. 2 with respect to each other in the reverse rotation twin screw processing apparatus of FIG. 1 according to an embodiment of the present disclosure. [Figure 7] Exemplary side view of a 4-lobe processing element in the reverse rotation twin screw processing apparatus of FIG. 1 according to an embodiment of the present disclosure. [Figure 8] Exemplary side view of a 2-lobe processing element in the reverse rotation twin screw processing apparatus of FIG. 1 according to an embodiment of the present disclosure. [Figure 9] Exemplary side view of a 1-lobe processing element in the reverse rotation twin screw processing apparatus of FIG. 1 according to an embodiment of the present disclosure.
Modes for Carrying Out the Invention
[0009] Referring to Figure 1, an exemplary diagram of a counter-rotating twin-screw processing apparatus 100, referred to herein as “processing apparatus 100,” is disclosed. The processing apparatus 100 may comprise a housing 102 having two cylindrical housing holes 104, 106. The two cylindrical housing holes 104, 106 may each have shafts 108, 110 arranged parallel to each other. A first screw shaft 112 and a second screw shaft 114 are respectively positioned within the two cylindrical housing holes 104, 106. A pair of processing elements 116, 118 or “elements” may be attached to the screw shafts 112, 114, respectively. In one embodiment, a plurality of such pairs of elements attached to each screw shaft can define various regions within the processing apparatus 100, including an intake region, a mixing region, and an output region. The elements 116, 118 may each comprise grooved axial holes 120, 122, into which the splines of the screw shafts 112, 114 engage. It will be apparent that elements 116 and 118 may also be configured to be attached to screw shafts 112 and 114 via different engaging means. In some embodiments, elements 116 and the first screw shaft 112 may not be separate components and may be defined as a single component referred to herein as “reverse-rotating screw”. Similarly, elements 118 and the second screw shaft 114 may not be separate components and may be defined as another reverse-rotating screw. The two reverse-rotating screws may be housed in two cylindrical housing holes 104 and 106, respectively. In such embodiments, the two reverse-rotating screws may each have an external shape similar to that of elements 116 and 118.
[0010] Referring to Figure 2, illustrative side views of elements 116 and 118 in the processing apparatus 100 of Figure 1 are disclosed. In one embodiment, elements 116 and 118 may each be three lobes defined by lobes 205 and 210. Lobes 205 and 210 define the screw contours 215 and 220 of elements 116 and 118, respectively. The screw contour 215 of element 116 determines the screw contour 220 of element 118, and vice versa. Thus, the screw contour 215 is called the generating screw contour, and the screw contour 220 is called the generated screw contour. In one embodiment of this disclosure, elements 116 and 118 are self-wiping such that when elements 116 and 118 are simultaneously reverse-rotated in opposite directions A and B, respectively, element 116 effectively wipes element 118, and vice versa. In one embodiment, elements 116 and 118 may rotate clockwise and counterclockwise, respectively, or vice versa. A clearance 225 is provided between elements 116 and 118, and the curvature of the screw contours 215 and 220 is also configured based on a predefined formula so that elements 116 and 118 can self-wipe. The provided clearance 225 is predefined and may extend between elements 116 and 118 along their longitudinal lengths. In one embodiment, the clearance 225 may be in the range of 150 μm to 250 μm. In one embodiment, the clearance 225 may be defined between the apex 230 of the screw contour 215 defined by the lobe 205 associated with element 116 and the valley 235 of the screw contour 220 formed between the lobe 210 associated with element 118. In one embodiment, elements 116 and 118 can together define a pair of elements with a clearance 225 between them such that each cross-section of element 116 on the first screw shaft 112 has a corresponding conjugate or substantially conjugate cross-section of element 118 on the second screw shaft 114. For clarity and understanding, element 116 will be described in detail below, but it will be understood that the same applies to element 118.
[0011] Referring to Figures 3A and 3B, exemplary side and front views of element 116 of Figures 1 and 2 are disclosed. The lobes 205 of element 116 each define a lobe contour 315. When a reverse-rotating screw is used, it can be understood that instead of element 116 mounted on the first screw shaft 112, the reverse-rotating screw may have lobes 205 defining the lobe contour 315. Element 116 defines an inner diameter 305 and an outer diameter 310. In one embodiment, the inner diameter 305 is defined by valleys 240 formed between the lobes 205, and the outer diameter 310 is defined by the apex 230 of the lobes 205. In one embodiment, the inner diameter 305 may correspond to the inner diameter of the lobe contour 315, and the outer diameter 310 may correspond to the outer diameter of the lobe contour 315. The lobe contour 315 is defined in the radial plane R of element 116. Element 116 comprises at least one continuous self-wiping flight 300 formed spirally on it. The lobe contours 315 of each lobe 205 define the self-wiping flight 300 when they change spirally in the axial direction. The formed flights 300 are continuous without breaks or interruptions. The number of flights formed on element 116 corresponds to the number of lobes provided on element 116. For example, in an element having three lobes, such as element 116, having three lobes can define three continuous self-wiping flights formed spirally on it. The flights 300 may change one or more times along the longitudinal length L of element 116. Flight changes may be accompanied by changes in the lobes 205 along the longitudinal length L. Changes in the lobes 205 may correspond to changes in the number of lobes formed on element 116 and / or changes in the lobe contours associated with the lobes. In some embodiments, the lobe contours 315 of the lobes 205 may each extend along the entire longitudinal length L of the element 116. In some embodiments, the lobe contours 315 of the lobes 205 may each extend along one or more portions along the longitudinal length L of the element 116.In such embodiments, the flight 300 may define a continuous self-wiping flight along one or more portions constituting the lobe contour 315 of the lobe 205 and a continuous non-self-wiping flight along the remaining one or more portions along the longitudinal length L of the element 116. In some embodiments, the number of lobes and / or each lobe contour in the remaining one or more portions along the longitudinal length L of the element 116 may differ from the number of lobes 205 and / or each lobe contour 315 in the one or more portions constituting the lobe contour 315. If a counter-rotating screw is used instead of the element 116 mounted on the first screw shaft 112, it can be understood that the lobe contour 315 of the lobe 205 may each extend along one or more portions along the longitudinal length L of the counter-rotating screw. The flight 300 may have integer lobes, called "integer lobes," extending along the longitudinal length L of the element 116, typically varying between one and four lobes. Such elements are referred to as "integer lobe flights" or elements having integer lobe flights. Flight 300 may also have non-integer lobes, such as fractional lobes or irrational lobes, extending along the longitudinal length L of element 116, which are referred to as "non-integer lobes." Such elements are referred to as "non-integer lobe flights" or elements having non-integer lobe flights. Furthermore, Flight 300 may have different combinations of integer and / or non-integer lobes extending along the longitudinal length L of element 116. In one embodiment, Flight 300 can start as an integer or non-integer lobe. In one embodiment, Flight 300 may change from an integer lobe flight to a non-integer lobe flight, or vice versa, or from an integer lobe flight to another integer lobe flight, or from a non-integer lobe flight to another non-integer lobe flight.
[0012] Non-integer lobe elements may also be fractional lobe elements. Examples of fractional lobe elements formed from 1-lobe, 2-lobe, 3-lobe, and / or 4-lobe elements are described in U.S. Patent No. 6,783,270, U.S. Patent No. 1,020,7423, and U.S. Patent No. 1,023,9233. Non-integer lobe elements may also be irrational lobe elements. Irrational lobe elements are described in U.S. Patent No. 8,753,003. A fractional lobe element is an element with a predefined fraction between a first integer element (n) and a second integer element (N), where N / n is an integer and the fraction determines the degree of transition between the first and second integers. 1-flight lobes and 2-lobes can form fractional lobes such as 1.2.xx, where xx can be any number from 1 to 99. The number from 1 to 99 determines whether the fractional lobe looks more like a 1-flight or 2-lobe element. The numbers 1 and 2 in the notation 1.2.xx represent lobe elements that are intermediate between a 1-flight element (1) and a 2-lobe element (2), respectively. Therefore, a fractional lobe element represented as 1.4.50 represents an element that is intermediate between a 1-flight element and a 4-lobe element.
[0013] The lobe contour 315 of each lobe 205 is provided by a functionally continuous curve obtained by joining a first curve 320 to a second curve 325. The first curve 320 is represented by a predefined formula. The second curve 325 is a mirror image of the first curve 320 with respect to the central axis C of element 116 and the radial axis RA passing through one of the two poles (330, 335) of the first curve 320. The first curve 320 is defined by the following formula:
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[0014] In one embodiment, the second curve 325 is a mirror image of the first curve 320 with respect to the radial axis RA passing through the pole 330 of the first curve 320, which lies on the central axis C of the element 116 and the outer diameter 310(Do) of the element 116 or the lobe contour 315. In one embodiment, the angle α of the radial portion 340 varies between 0 and 2π radians. In one embodiment, the radial portion 340 corresponds to a circular portion derived from the outer diameter 310(Do) of the element 116 or the lobe contour 315. In one embodiment, the radial portion 340 is defined by π radians / N.
[0015] Referring to Figures 4-5 and 6A-6C, illustrative side views of the relative rotational motion of element 118 with respect to element 116 in the counter-rotating twin-screw processing apparatus 100 of Figure 1 are disclosed. When elements 116 and 118 are simultaneously rotated in opposite directions A and B, respectively, element 116 results in complete wiping of element 118. In particular, the clearance 225 provided between elements 116 and 118 facilitates a self-wiping action as the apex 230 of the lobe contour 315 defined by one or more lobes 205 of element 116 moves into and / or away from the valleys 235 of the lobe contour 315 formed between one or more lobes 210 of element 118 while they are simultaneously rotated in opposite directions A and B. Similarly, element 118 also performs complete wiping of element 116 when elements 116 and 118 are simultaneously rotated in opposite directions A and B, respectively. In particular, the clearance 225 provided between elements 116 and 118 facilitates a self-wiping action when, while they are simultaneously rotated in opposite directions A and B, the peaks 245 of the lobe contour 315 defined by one or more lobes 210 of element 118 move into and / or away from the valleys 240 of the lobe contour 315 formed between one or more lobes 205 of element 116. Thus, elements 116 and 118 provide a continuous self-wiping action between them when they are simultaneously rotated in opposite directions A and B.
[0016] Referring to Figures 7 to 9, exemplary side views of the one-lobe, two-lobe, and four-lobe elements 116, 118 of Figure 1 are disclosed. The lobes 705, 805, 905 associated with the one-lobe, two-lobe, and four-lobe elements 116, 118 are defined by lobe contours 710, 810, 910, respectively. The lobe contours 710, 810, 910 of each element, for example, element 116, are provided by functionally continuous curves 715, 815, 915 obtained by joining the first curves 720, 820, 920 to the second curves 725, 825, 925, respectively. The first curves 720, 820, 920 are expressed mathematically. The second curves 725,825,925 are mirror images of each of the first curves 720,820,920 with respect to the radial axis RA that passes through the central axis C of element 116 and one of the two poles of each of the first curves 720,820,920 (730,735), (830,835), and (930,935). The first curves 720,820,920 are defined by the following formulas.
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[0017] Specific embodiments are described below. An element for a counter-rotating twin-screw processing apparatus, the element having an axial hole for mounting on the screw shaft of the processing apparatus, the element comprising at least one continuous self-wiping flight helically formed thereon, the element comprising one or more lobes having a lobe profile provided by a functionally continuous curve obtained by combining a first curve and a second curve, the first curve being expressed by a mathematical formula, the second curve being a mirror image of the first curve with respect to a radial axis passing through the central axis of the element and one of the two poles of the first curve, the first curve being defined by the following mathematical formula.
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[0018] One or more elements such that the angle α of the radial portion varies in the range from 0 to 2π.
[0019] One or more such elements whose radial cross-section is defined by π / N.
[0020] One or more elements such that one of the two poles of the first curve lies on the outer diameter (Do) of the element or lobe contour.
[0021] One or more elements such that one or more lobes are integer lobes and one or more flights are integer lobe flights.
[0022] One or more elements such that one or more lobes are non-integer lobes and one or more flights are non-integer lobe flights.
[0023] One or more elements such that one or more lobes are fractional lobes and one or more flights are fractional lobe flights.
[0024] One or more elements such that the flight changes one or more times along the axial length of the element, and the change in flight is accompanied by one or more changes in lobes along the axial length.
[0025] One or more elements such that a flight changes from an integer lobe flight to a non-integer lobe flight, or vice versa, or from one integer lobe flight to another integer lobe flight, or from one non-integer lobe flight to another non-integer lobe flight.
[0026] One or more elements such that the lobe contours of one or more lobes that change spirally in the axial direction define at least one continuous self-wiping flight.
[0027] A reverse-rotating screw for a reverse-rotating twin-screw processing apparatus having an axial hole for housing a reverse-rotating screw, wherein at least a portion of the reverse-rotating screw comprises one or more lobes having a lobe profile provided by a functionally continuous curve obtained by joining a first curve and a second curve, the first curve being expressed by a mathematical formula, the second curve being a mirror image of the first curve with respect to a radial axis passing through the central axis of the element and one of the two poles of the first curve, and the first curve being a reverse-rotating screw defined by the following mathematical formula.
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[0028] One or more counter-rotating screws, wherein at least a portion of the counter-rotating screw defines at least one continuous self-wiping flight formed helically thereon.
[0029] A pair of elements for a twin-screw processing apparatus having a first shaft and a second shaft, comprising a first element adapted to be coupled to the first shaft and a second element adapted to be coupled to the second shaft, wherein the first and second elements each have a continuous self-wiping flight formed thereon in a helical manner and have one or more lobes having lobe contours defined in the radial plane of the first and second elements, respectively, wherein the lobe contours are provided by a functionally continuous curve obtained by joining a first curve and a second curve, the first curve being expressed by a mathematical formula, and the second curve being a mirror image of the first curve with respect to a radial axis passing through the central axis of the first or second element and one of the two poles of the first curve, and the first curve being an element defined by the following mathematical formula.
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[0030] Elements 116,118 as taught by this disclosure are self-wiping and suitable for use in reverse-rotating twin-screw processing equipment. As a result, elements 116,118 as taught can improve the mixing and / or melting capacity of the processing equipment 100 and may help achieve homogeneous melted mixture. In addition, elements 116,118 as taught can also reduce material stagnation and improve the extensional flow of material during the melting and homogenization process. Furthermore, elements 116,118 as taught can facilitate the melting and / or homogenization of material at process temperatures lower than those generally involved in the melting and / or homogenization process in the processing equipment 100. In particular, elements 116,118 are suitable for processing temperature-sensitive materials such as pharmaceutical components containing APIs. Elements 116,118 are also suitable for processing mixed materials with different melting or softening points, such as waste for recycling.
Claims
1. An element for a counter-rotating twin-screw processing apparatus, the element having an axial hole for mounting on a screw shaft of the processing apparatus, the element comprising at least one continuous self-wiping flight helically formed thereon, the element having one or more lobes having a lobe profile provided by a functionally continuous curve defined in the radial plane of the element and obtained by combining a first curve and a second curve, the first curve being expressed by a mathematical formula, the second curve being a mirror image of the first curve with respect to a radial axis passing through the central axis of the element and one of the two poles of the first curve, and the first curve being defined by the following mathematical formula. [Number 19] [Number 20] Here, x and y are Cartesian coordinates defined in the radial plane. Do is the outer diameter of the element or the lobe contour. Di is the inner diameter of the element or the lobe contour. N is the number of the one or more lobes mentioned above. α is the angle of the radial portion defined by the first curve on the radial plane. That is the case.
2. The element according to claim 1, wherein the angle α of the radial portion varies from 0 to 2π.
3. The element according to claim 1, wherein the radial portion is defined by π / N.
4. The element according to claim 1, wherein one of the two poles of the first curve is located on the outer diameter (Do) of the element or the lobe contour.
5. The element according to claim 1, wherein the one or more lobes are integer lobes and the flight is an integer lobe flight.
6. The element according to claim 1, wherein the one or more lobes are non-integer lobes and the flight is a non-integer lobe flight.
7. The element according to claim 1, wherein the one or more lobes are fractional lobes and the flight is a fractional lobe flight.
8. The element according to claim 1, wherein the flight changes one or more times along the axial length of the element, and the change in the flight is accompanied by a change in one or more lobes along the axial length.
9. The element according to claim 8, wherein the flight changes from an integer lobe flight to a non-integer lobe flight, or vice versa, or from an integer lobe flight to another integer lobe flight, or from a non-integer lobe flight to another non-integer lobe flight.
10. The element according to claim 1, wherein the lobe contours of the one or more lobes that change spirally in the axial direction define the at least one continuous self-wiping flight.
11. A reverse-rotating screw for a reverse-rotating twin-screw processing apparatus having an axial hole for housing a reverse-rotating screw, wherein at least a portion of the reverse-rotating screw comprises one or more lobes having a lobe contour provided by a functionally continuous curve obtained by joining a first curve and a second curve, wherein the first curve is represented by a mathematical formula, the second curve is a mirror image of the first curve with respect to a radial axis passing through the central axis of the element and one of the two poles of the first curve, and the first curve is defined by the following mathematical formula: [Math 21] [Number 22] Here, x and y are Cartesian coordinates defined in the radial plane. Do is the outer diameter of the reverse-rotating screw or the lobe contour. Di is the inner diameter of the reverse-rotating screw or the lobe contour. N is the number of the one or more lobes mentioned above. α is the angle of the radial portion defined by the first curve on the radial plane. That is the case.
12. The reverse-rotating screw according to claim 11, wherein at least a portion of the reverse-rotating screw defines at least one continuous self-wiping flight formed thereon in a helical manner.
13. A reverse-rotating twin-screw processing apparatus, A barrel defining a first cylindrical bore and a second cylindrical bore, wherein the first cylindrical bore and the second cylindrical bore intersect to form a chamber, A first shaft that rotates about an axis within the first cylindrical bore, A second shaft that rotates about an axis within the second cylindrical bore, The present invention comprises at least one element coupled to the first shaft and the second shaft, having an axial hole for attachment to the first shaft and the second shaft, and comprising a continuous self-wiping flight formed helically thereon, and comprising one or more lobes having a lobe contour defined in a radial plane and provided by a functionally continuous curve obtained by combining a first curve and a second curve, A counter-rotating twin-screw processing device wherein the first curve is represented by a mathematical formula, the second curve is a mirror image of the first curve with respect to a radial axis passing through the central axis of at least one element and one of the two poles of the first curve, and the first curve is defined by the following mathematical formula. [Number 23] [Number 24] Here, x and y are Cartesian coordinates defined in the radial plane. Do is the outer diameter of at least one element or the lobe contour. Di is the inner diameter of at least one element or the lobe contour. N is the number of the one or more lobes mentioned above. α is the angle of the radial portion defined by the first curve on the radial plane. That is the case.
14. The reverse-rotating twin-screw processing apparatus according to claim 13, wherein the lobe contour defines the apex and the valley such that a clearance is defined between the apex of the at least one element coupled to the first shaft and the valley of the at least one element coupled to the second shaft.
15. The reverse-rotating twin-screw processing apparatus according to claim 13, wherein the clearance is in the range of 150 μm to 250 μm.
16. A pair of elements for a twin-screw processing apparatus having a first shaft and a second shaft, comprising a first element adapted to be coupled to the first shaft and a second element adapted to be coupled to the second shaft, wherein the first and second elements each have a continuous self-wiping flight helically formed thereon, and each has one or more lobes having lobe contours defined in the radial plane of the first and second elements, wherein the lobe contours are provided by a functionally continuous curve obtained by joining a first curve and a second curve, the first curve being represented by a mathematical formula, and the second curve being a mirror image of the first curve with respect to a radial axis passing through the central axis of the first or second element and one of the two poles of the first curve, and the first curve being defined by the following mathematical formula. [Number 25] [Number 26] Here, x and y are Cartesian coordinates defined in the radial plane. Do is the outer diameter of the first element, the second element, or the lobe contour. Di is the inner diameter of the first element, the second element, or the lobe contour. N is the number of the one or more lobes mentioned above. α is the angle of the radial portion defined by the first curve on the radial plane. That is the case.