CN116277868A - Manufacturing method of double screw, double screw and extruder - Google Patents
Manufacturing method of double screw, double screw and extruder Download PDFInfo
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- CN116277868A CN116277868A CN202211726868.0A CN202211726868A CN116277868A CN 116277868 A CN116277868 A CN 116277868A CN 202211726868 A CN202211726868 A CN 202211726868A CN 116277868 A CN116277868 A CN 116277868A
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- 239000004973 liquid crystal related substance Substances 0.000 description 4
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
- B29C48/25—Component parts, details or accessories; Auxiliary operations
- B29C48/36—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die
- B29C48/50—Details of extruders
- B29C48/505—Screws
- B29C48/507—Screws characterised by the material or their manufacturing process
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C48/00—Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
- B29C48/25—Component parts, details or accessories; Auxiliary operations
- B29C48/36—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die
- B29C48/395—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die using screws surrounded by a cooperating barrel, e.g. single screw extruders
- B29C48/40—Means for plasticising or homogenising the moulding material or forcing it through the nozzle or die using screws surrounded by a cooperating barrel, e.g. single screw extruders using two or more parallel screws or at least two parallel non-intermeshing screws, e.g. twin screw extruders
- B29C48/405—Intermeshing co-rotating screws
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract
The embodiment of the application provides a manufacturing method of a double screw, the double screw and an extruder, which relate to the technical field of extruder equipment, but are not limited to the technical field of extruder equipment, wherein the manufacturing method comprises the steps of determining first line diameters and the number of the first line diameters which are inserted in a first insertion area formed by a group of adjacent root diameters and top diameters on a first cross section of a first screw according to a center distance; determining a first curve segment set arranged on the first screw according to the central angle calculation formula and the first curve segment calculation formula; determining a second central angle of each first arc section in the first arc section set according to the first central angle of each third curve section in the first curve section set; a second set of curvilinear segments corresponding to the first set of curvilinear segments and a second set of arcuate segments corresponding to the first set of arcuate segments are determined on the second screw. And manufacturing a first screw and a second screw respectively according to the first curve segment set, the first arc segment set, the second curve segment set and the second arc segment set. The embodiment of the application can promote the mixing promotion effect on axial flow.
Description
Technical Field
The application relates to the technical field of extruder equipment, in particular to a manufacturing method of double screws, the double screws and an extruder.
Background
In the process of processing high polymer materials, a differential speed co-rotating double screw extruder is one of the most commonly used devices for mixing high polymers and composite materials thereof. Because the flowing main body of the high polymer in the extrusion process of the double-screw extruder advances along the + -shaped spiral, the movement mode of the fluid generates periodic flow along with the rotation of the screws, the two screws exchange flow in the meshing junction area, and because the screws adopt spiral configuration, the conveying unit generates axial dragging action in the rotation process, the axial circulation movement of the melt caused by the pressure gradient action enhances the mixing effect of the fluid, and especially the axial strengthening action at the position far away from the meshing area is more important, but the structures of the two screws of most of the existing homodromous double-screw extruders are completely consistent, and the rotating speeds of the two screws in the processing process of materials are the same. Because the structures of the two screws are the same, consistency of the geometric space experienced by the fluid in the advancing process of the two screws can be caused, the change of the geometric shape in the advancing process of the fluid is lacked, the effect of the shearing process is weakened, and the melt mixing effect is limited, so that the existing double-screw technology has poor promotion effect on mixing in the axial flow. Accordingly, it is desirable to provide a twin screw structure that promotes mixing in axial flow.
Disclosure of Invention
The embodiment of the application mainly aims at providing a manufacturing method of a double screw, the double screw and an extruder, and aims at improving the mixing promotion effect on axial flow.
Determining a root diameter, a top diameter, a rotation speed ratio of the first screw and the second screw, and a center distance between the first screw and the second screw;
determining first wire diameters and the number of the first wire diameters which are inserted in a first insertion area formed by a group of adjacent root diameters and top diameters on a first cross section of a first screw rod according to the center distance;
determining a first curve segment set arranged on a first screw rod according to a preset central angle calculation formula and a first curve segment calculation formula, wherein the first curve segment set consists of a plurality of first curve segments obtained by inserting a first line in the first inserting area and a second curve segment formed by another group of adjacent root diameters and top diameters;
determining a second central angle of each first circular arc section of the first circular arc section set on the first cross section according to a first central angle corresponding to each third curve section of the first curve section set;
manufacturing a first screw according to the first curve segment set and the first arc segment set;
determining a second curve segment set corresponding to the first curve segment set and a second arc segment set corresponding to the first arc segment set on a second screw, wherein the central angle ratio of each fourth curve segment in the second curve segment set to the corresponding third curve segment is the rotation speed ratio, and the central angle ratio of each second arc segment in the second arc segment set to the corresponding first arc segment is the rotation speed ratio;
and manufacturing a second screw rod according to the second curve segment set and the second arc segment set.
An extruder according to some embodiments of the second aspect of the present application, comprising:
the inner cavity of the machine barrel is provided with two intersected cylindrical grooves;
a twin screw made by the method of any of the first aspects, a first screw of the twin screw being located in one of the cylindrical grooves and a second screw of the twin screw being located in the other of the cylindrical grooves.
According to the manufacturing method of the double screw, the double screw and the extruder, the plurality of first curve segments are arranged between one group of adjacent root diameters and top diameters of the first screw, the second curve segments are arranged between the other group of adjacent root diameters and top diameters, so that the first screw is asymmetric, the cross section area of the first screw can be increased, a wedge-shaped space is formed between the first screw and the inner side wall of the accommodating cavity accommodating the first screw, the wedge-shaped space is in a descending or ascending trend along with the rotation of the first screw, meanwhile, a first curve segment set is determined through a central angle calculation formula and a first curve segment calculation formula, and a second curve segment set corresponding to the first curve segment set, the first curve segment set and the second curve segment set are arranged on the second screw, so that the meshing point of the first screw and the second screw rotating in the same direction and differential speed is more complex, and materials are subjected to stronger disturbance and mixing effects; therefore, compared with the related art, the double screws can provide more complex meshing tracks during movement, and the cross section areas of the first screw and the second screw are increased, so that wedge-shaped pressurizing, extruding and stretching effects are generated near the thrust surfaces or the dragging surfaces of the first screw and the second screw, the materials which are not split in the lower meshing area are further extruded and stretched, enter the next screw groove, and meanwhile, the wedge-shaped pressurizing effects can further improve the dispersive mixing capability; thus, the embodiments of the present application can promote the mixing promotion effect in axial flow.
Drawings
FIG. 1 is a schematic flow chart of a method for manufacturing a twin-screw according to an embodiment of the present disclosure;
FIG. 2 is a schematic view of the structure of the twin screw according to the embodiments of the present application during engagement;
FIG. 3 is a schematic illustration of a twin screw cross section of one embodiment of the speed ratio of 2:1 provided by embodiments of the present application;
FIG. 4 is a cross-sectional view of the twin screw shown in FIG. 3 in an embodiment of the present application;
FIG. 5 is a schematic illustration of a twin screw cross section of another embodiment of the present application with a speed ratio of 2:1;
FIG. 6 is a schematic diagram comparing two examples of twin screws made in the examples of the present application with the internal cavity volume of a conventional screw;
FIG. 7 is a graph of the sum of the top and bottom angles of a twin screw made in accordance with an embodiment of the present application versus the number of first curve segments;
FIG. 8 is a schematic view of the movement trace of the meshing point of the twin screws produced in the examples of the present application;
FIG. 9 is a schematic diagram of a conventional twin screw technique and a motion profile of a meshing point;
FIG. 10 is a schematic longitudinal cross-sectional view of the first screw of the twin-screw of FIG. 3, made in accordance with an embodiment of the present application;
FIG. 11 is a schematic longitudinal cross-sectional view of the first screw of the twin screw of FIG. 5, as produced in an embodiment of the present application;
fig. 12 is a schematic cross-sectional view of an extruder provided herein.
Reference numerals:
A first screw 210, a second screw 220,
The flow channel 300.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the present application.
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the present application.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of the present application only and is not intended to be limiting of the present application. The terms "first," "second," "third," "fourth," and the like in the description of the present application and in the above-described figures, if any, are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order.
Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the disclosure. One skilled in the relevant art will recognize, however, that the disclosed aspects may be practiced without one or more of the specific details, or with other methods, components, devices, steps, etc. In other instances, well-known methods, devices, implementations, or operations are not shown or described in detail to avoid obscuring aspects of the disclosure.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of the present application only and is not intended to be limiting of the present application.
Referring to fig. 1 and 2, the manufacturing method includes:
step S100, determining the root diameter, the tip diameter, the rotation speed ratio of the first screw 210 and the second screw 220, and the center distance between the first screw 210 and the second screw 220.
The speed ratio being an irreducible number, e.g. speed ratio
1:3, either 2:3 or 2:1.
The root diameter and the tip diameter of the first screw 210 and the second screw 220 are the same.
Step S200, determining a first wire diameter and the number of first wire diameters inserted in a first insertion area formed by a group of adjacent root diameters and top diameters on a first cross section of the first screw 210 according to the center distance.
The first wire diameter in the first screw 210 is a transition wire diameter, and one end of the first wire diameter is a center of the first screw 210. Since the first screw 210 and the second screw 220 are always engaged, there is a second wire diameter corresponding to the first wire diameter one by one in the second screw 220, and at this time, the first wire diameter is more simply confirmed by determining the length of the first wire diameter based on the center distance. Assuming that there are k intervening wire diameters in the first intervening region, it satisfies the following expression for each wire diameter: r is (r)<R l1 <...<R lk <R, wherein R is root diameter and R is top diameter.
Step S300, determining a first curve segment set on the first screw 210 according to a preset central angle calculation formula and a first curve segment calculation formula, where the first curve segment set is composed of a plurality of first curve segments obtained by inserting a first line in a first inserting area and a second curve segment formed by another group of adjacent root diameters and top diameters.
It should be noted that, when the first curve is determined, only the number of first curve segments interleaved in the first interleaved region can be determined, the central angle calculation formula is used for calculating the first central angle of each first curve segment and each second curve segment, and the first curve segment calculation formula is used for determining the polar diameter of each first curve segment and the polar diameter of each second curve segment. Therefore, the central angles and the polar diameters of the first curve segment and the second curve segment can be further defined through the central angle calculation formula and the first curve segment calculation formula.
It should be noted that the number of second curve segments is one, and the number of first curve segments may be obtained through multiple experiments or may be determined based on the relationship between the first curve segments and the sum of angles of the remaining top angles and bottom angles (i.e., root diameters and central angles corresponding to the top diameters) shown in fig. 7. Illustratively, referring to fig. 7, when the first curve segment is provided with 2, the remaining 131.24 ° may be assigned to the top and bottom angles, when the first curve segment is provided with, the remaining 47.16 ° may be assigned to the top and bottom angles, and so on.
Exemplary, referring to FIG. 4, in the first intervening region O of FIG. 4 1 A 0 A 7 3 first line diameters with different lengths are inserted to obtain first curve sections A respectively 0 A 1 、A 2 A 3 、A 4 A 5 、A 6 A 7 Corresponding first central angles are respectively theta l1 、θ l2 、θ l3 、θ l4 . Second curve segment A 01 A 02 Then by adjacent group of root paths O 1 A 02 And top diameter O 1 A 01 And (5) forming.
Step S400, determining a second central angle of each first arc section in the first arc section set on the first cross section according to the first central angle corresponding to each third curve section in the first curve section set.
The third curve segment is used to represent each member in the first curve segment set, that is, the first curve segment and the second curve segment are both third curve segments.
It should be noted that, because the circumferential angle is 360 degrees, in the case of determining the first central angle, the sum of the central angles corresponding to each first arc segment of the first arc segment set is clear, and at this time, an angle may be allocated to each arc segment according to the requirement, so as to determine the second central angle. It should be noted that the distribution may be performed in an equal manner or in a proportional manner, and in this regard, the embodiments of the present application do not impose excessive constraints here.
It should be noted that, in some embodiments, the first arc segment set is composed of first arc segments corresponding to the root diameter and the top diameter, and in other embodiments, a transition arc is interposed between each first curve segment, so that the first arc segment set is composed of the transition arc and the first arc segments corresponding to the root diameter and the top diameter.
Step S500, manufacturing a first screw 210 according to the first curve segment set and the first arc segment set.
In the case where the central angle and each polar diameter of the third curved section are determined, the manufacturing parameters of the third curved section of the first cross section on the first screw 210 may be determined, and in the case where the central angle and the radius of the first circular arc section are determined, the manufacturing parameters of the first circular arc section may be determined, so that the first screw 210 may be determined.
Step S600, determining a second curve segment set corresponding to the first curve segment set and a second arc segment set corresponding to the first arc segment set on the second screw 220, where a central angle ratio of each fourth curve segment in the second curve segment set to the corresponding third curve segment is a rotation speed ratio, and a central angle ratio of each second arc segment in the second arc segment set to the corresponding first arc segment is a rotation speed ratio.
It should be noted that, the corresponding arrangement of the first curve segment set and the second curve segment set indicates that meshing points exist between the corresponding third curve segment and the fourth curve segment of each group. In the process of manufacturing the second screw 220, the first screw 220 is used for determiningThe second wire diameters corresponding to the first wire diameters are inserted into the second insertion regions corresponding to the insertion regions, and the sum of the first wire diameters and the corresponding second wire diameters is the center distance between the first screw 210 and the second screw 220, that is, the sum of the i-th large second wire diameter and the i-th small first wire diameter is the center distance, and the first wire diameter R is exemplified lk Satisfy r<R l1 <...<R lk <R is a second line diameter R corresponding to R rk Respectively as follows, and satisfy R<R rk <...<R r1 <R, wherein R is r1 And R is R lk The sum is the center distance. The sum of the maximum polar diameter of the fourth curve segment and the minimum polar diameter of the corresponding third curve segment is the center distance. At this time, since the first screw 210 and the second screw 220 move in the same direction and differentially, the corresponding polar diameter of one screw increases along with the increase of the polar diameter of the curved section of the other screw in the rotational speed direction, so that the two screws have engagement points at different positions, and therefore, the engagement track of the first screw 210 and the second screw 220 is more complex due to the corresponding arrangement of the first screw 210 and the second screw 220.
And step S700, manufacturing the second screw 220 according to the second curve segment set and the second arc segment set.
Therefore, by arranging a plurality of first curved sections between a group of adjacent root diameters and top diameters of the first screw rod 210, and arranging a second curved section between another group of adjacent root diameters and top diameters, the first screw rod 210 is asymmetric, and the cross-sectional area of the first screw rod 210 can be increased, so that a wedge-shaped space is formed between the first screw rod 210 and the inner side wall of the accommodating cavity accommodating the first screw rod 210, and the wedge-shaped space is in a descending or ascending trend along with the rotation of the first screw rod 210, meanwhile, a first curved section set is determined by a central angle calculation formula and a first curved section calculation formula, and a second curved section set corresponding to the first curved section set, the first curved section set and the second curved section set are arranged on the second screw rod 220, so that the meshing point of the first screw rod 210 and the second screw rod 220 rotating in the same direction and differential speed is more complex, and the materials are subjected to stronger disturbance and mixing effects; therefore, compared with the related art, the twin-screw can provide more complex meshing tracks during movement, and the cross section areas of the first screw 210 and the second screw 220 are increased, so that wedge-shaped pressurizing, extruding and stretching actions are generated near the thrust surfaces or the dragging surfaces of the first screw 210 and the second screw 220, and the materials which are not split in the lower meshing area are extruded and stretched further and enter the next screw groove, and meanwhile, the wedge-shaped pressurizing actions can further improve the dispersive mixing capability; thus, the embodiments of the present application can promote the mixing promotion effect in axial flow.
The two screws are in a form of unchanged cross section structure, so that the manufacturing process of the screws is relatively simple, and symmetry between the two screws is avoided. Moreover, the cross-sectional profile of the first screw 210 is completely asymmetric, and the extrusion and stretching mixing effect of the co-directional differential twin-screw molding apparatus can be enhanced by using the asymmetric effect of the screws.
The twin screws obtained in steps S100 to S700 always mesh when they rotate in the same direction as shown in fig. 2.
It can be appreciated that determining the first curve segment set on the first screw 210 according to the preset central angle calculation formula and the first curve segment calculation formula includes:
respectively determining first central angles corresponding to the first curve segment and the second curve segment according to a central angle calculation formula;
determining the polar diameters of the first curve segment and the second curve segment respectively according to a first curve segment calculation formula;
the central angle calculation formula comprises a formula I and a formula II, wherein the formula I and the formula II are as follows:
formula one:
formula II:
wherein θ li A first central angle corresponding to the first curve segment; θ l0 A first central angle corresponding to the second curve segment;
is a rotation speed ratio and M and N are irreducible; c is the center distance; r is R li 、R l(i+1) Respectively is theta li The minimum polar diameter and the maximum polar diameter of the corresponding first curve segment, D is 2R, R is top diameter; the value range of i is 1-K+1, and K is the number of the first wire diameters.
It should be noted that, in some embodiments, the first central angle and the second central angle may be determined based on a polar radius formula and a polar angle formula, where the polar radius formula is as follows:
the polar angle formula is as follows: />
R min Is the minimum polar diameter of the curve segment. At this time, since the minimum and maximum polar diameters of one curve segment are determined, cos ε corresponding to the maximum polar diameter can be determined based on the polar diameter formula max The method comprises the steps of carrying out a first treatment on the surface of the Thus can be based on cos epsilon max Solving to obtain epsilon max Corresponding ψ (ε) max ) (i.e. the first central angle θ to be solved for li Or a second central angle theta l0 ) Thereby obtaining the above formulas one and two.
It is understood that the first curve segment calculation formula includes the following formula three and four:
formula III:
formula IV:
wherein ρ is li (epsilon) is theta li The polar diameter of the corresponding first curve segment; ρ l0 And (epsilon) is the polar diameter of the second curve segment.
It should be noted that epsilon is an auxiliary positioning angle and is a variable value.
In some embodiments, ε 1 The minimum polar diameter and the maximum polar diameter passing through the corresponding first curve segment pass through a polar angle formula
And (5) determining.
It is understood that the first set of arc segments is composed of arcs corresponding to the root diameter and the top diameter, or the first set of arc segments is composed of transition arcs and arcs corresponding to the root diameter and the top diameter; determining a second central angle of each first arc segment of the first arc segment set on the first cross section according to the first central angle corresponding to each third curve segment of the first curve segment set, including:
subtracting each first central angle from 2 pi to obtain an angle sum value, wherein the angle sum value is the sum of the second central angles of each first arc section;
and (3) evenly distributing the angles and the values according to the number of the first circular arc sections, and determining each second central angle.
It should be noted that, when the angle sum is larger, a transition arc may be inserted between two adjacent first curve segments, thereby further increasing the complexity of the movement track of the engagement point. A transition arc may be disposed between each adjacent two of the first curve segments.
It is appreciated that determining a second set of curvilinear segments on the second screw 220 corresponding to the first set of curvilinear segments includes:
determining fourth curve segments corresponding to each third curve segment one by one according to a preset second curve segment calculation formula, a rotation speed ratio and each first central angle to obtain a second curve segment set;
wherein the relationship between the third central angle of the fourth curve segment and the first central angle of the third curve segment is as follows:
formula five:
wherein θ ri Represents a third central angle, θ li Represents θ ri A corresponding first central angle;
the second curve segment calculation formula includes a formula six and a formula seven, where the formula six and the formula seven are as follows:
formula six:
formula seven:
wherein, psi (epsilon) is theta ri Polar angle of the corresponding fourth curve segment; ρ ri (epsilon) is theta ri The polar diameter of the corresponding fourth curve segment; r is R l(i+1) Respectively is theta ri The maximum diameter of the corresponding fourth curve segment.
Illustratively, referring to FIG. 4, the first screw 210 and the second screw 220 have a speed ratio of 2:1, a second curvilinear segment A 01 A 02 And a fourth curve segment B 01 B 02 Correspondingly set up, B 01 B 02 Is the central angle of
First curve segment A 0 A 1 And a fourth curve segment B 0 B 1 Is correspondingly arranged, and is shown as the formula 5, B 0 B 1 The central angle of (2) is>
It is understood that the fourth curve segment corresponding to the first curve segment is provided as a straight line.
It should be noted that, in some embodiments, when the number of the first curved sections is greater than the preset threshold, the connection lines of the endpoints corresponding to the first curved sections in the second screw 220 approach a straight line, so that the connection lines of the endpoints corresponding to the first curved sections in the first screw 210 in the second screw 220 (i.e., the fourth curved sections corresponding to the first curved sections) may be all set as fold lines, thereby simplifying the production process of the screw, avoiding the constraint of engineering formulas, and improving the manufacturing efficiency.
It is understood that the number of first curve segments ranges from 2 to 8.
It is understood that the ratio of the number of screw heads of the first screw 210 and the second screw 220 is inversely proportional to the rotation speed ratio.
It should be noted that by setting the screw head ratio to be inversely proportional to the rotation speed ratio, the stability of the twin screw during operation can be increased.
For example, referring to fig. 1 to 3, it is assumed that the rotation ratio of the first screw 210 to the second screw 220 is M: N. The general cross-sectional structure is drawn below with M: N as the rotation speed ratio.
For the first screw 210, K transition polar diameters R are arranged between the root diameter R of the first screw 210 and the screw top diameter R li So that r<R l1 <...<R lk <R, i=1,. -%, K; then a first curve segment of K+1 segments is generated, and transition arcs corresponding to K polar diameters are added, wherein the central angle corresponding to the transition arcs is delta i Indicating that the added K transition arcs are connected with the K+1 first curve segments alternately, as shown in FIG. 3 (O 1 A 01 、O 1 A 00 Is the top diameter, O 1 A 02 、O 1 A 0 As root diameter).
Referring to FIG. 3, for the second curvilinear segment A of the first screw 210 01 A 02 The non-circular curve arc between the root diameter R and the top diameter R of the connecting screw is expressed as O 1 As the center of a circle, O 1 A 02 For the polar axis, the counterclockwise direction is positive, and given the auxiliary angle ε, there are:
the corresponding pole diameters are as follows:
the corresponding polar angle is:
at this time, the second curve segment A 01 A 02 The corresponding central angle is:
further, for any one of the first curvilinear segments A of the first screw 210 i A i+1 By O 1 As the center of a circle, O 1 A i Is a polar axis; clockwise positive, given auxiliary angle
Then there are:
first curve segment A i A i+1 Corresponding polar diameter
Corresponding polar angle
First curve segment A i A i+1 Corresponding central angle
Wherein, the liquid crystal display device comprises a liquid crystal display device,
here, R is li 、R l(i+1) Respectively representing a first curved section A of the first screw 210 i A i+1 Corresponding minimum and maximum polar diameters.
According to the selected polar diameter R li The sum of the central angles corresponding to K+1 first curve segments formed by K polar diameters can be obtained, and finally the vertex angle alpha and the base angle lambda of the first screw 210 and the central angle delta corresponding to each transition arc are determined i The sum satisfies the following formula:
at this time, it can be determined from the formula that the angle sum value is +.>
And performing angle distribution on the angle sum value according to a preset distribution rule.
At this time, referring to fig. 3, in the second screw 220, K transition polar diameters R are provided between the root diameter R of the second screw 220 and the screw tip diameter R ri So that R (R r0 )<R r1 <R r2 …<R ri <…R rK <R(R r(K+1) ) Will likewise produce (K+1) one-to-one correspondence with the first curve segmentFourth curve segment B i B i+1 I=1,..k, when the first curve segment and the corresponding fourth curve segment are operated in mesh with each other.
Any section of curve B for the second screw 220 i B i+1 By O 2 As the center of a circle, O 2 B i+1 For the polar axis, the counterclockwise direction is positive, and given the auxiliary angle ε, there are:
B i B i+1 the corresponding pole diameters are as follows:
wherein R is l(i+1) Representation B i B i+1 Is the maximum diameter of the lens.
B of the second screw 220 i B i+1 Corresponding polar angle theta ri The method comprises the following steps:
wherein θ li Is equal to B i B i+1 A corresponding first central angle of the first screw 210.
Wherein the auxiliary angle is epsilon, the corresponding polar angle is phi (epsilon), and the auxiliary angle is relative to the rotation speed ratio
The function of the change of the center distance C and the transition pole diameter is as follows: />
Similarly, R is substituted as the maximum diameter and R is substituted as the minimum diameter into the polar diameter and polar angle formula for the fourth curve segment corresponding to the second curve segment, and the polar diameter and central angle corresponding to the fourth curve segment can be obtained.
Illustratively, referring to FIG. 4, the first screw 210 and the second screw 220 have a speed ratio of 2:1, the corresponding number of heads is 1:2, 3 transition polar diameters are set, namely k=3, and 3 transition arcs and 4 non-arc curves are added.
For the second curved section A of the first screw 210 01 A 02 I.e. the non-circular curve arc between the root diameter R and the tip diameter R of the connecting screw is expressed as O 1 As the center of a circle, O 1 A 02 For the polar axis, the counterclockwise direction is positive, and given the auxiliary angle ε, there are:
the corresponding pole diameters are as follows:
the corresponding polar angle is:
at this time, non-circular curve arc A 01 A 02 Corresponding central angle theta l0 The method comprises the following steps:
further, for any section of the first screw 210, the non-circular curve arc A i A i+1 By O 1 As the center of a circle, O 1 A i Is the polar axis, clockwise is positive, and an auxiliary angle is given
Then there are:
A i A i+1 the corresponding pole diameters are as follows:
the corresponding polar angle is:
non-circular curve arc A i A i+1 Corresponding central angle theta li The method comprises the following steps:
wherein, the liquid crystal display device comprises a liquid crystal display device,
here, R is li 、R l(i+1) Respectively represent the curve arc A of the first screw 210 i A i+1 Corresponding minimum and maximum polar diameters.
According to the selected polar diameterR li The sum of central angles corresponding to K+1 curve arcs consisting of K polar diameters can be obtained, and finally the vertex angle alpha and the base angle gamma of the first screw 210 and the central angle delta corresponding to each transition polar diameter are determined i The sum satisfies the following formula:
further, for the second screw 220, 3 transition pole diameters R are also provided between the screw root diameter R and the screw tip diameter R ri So that R (R r0 )<R r1 <R r2 …<R ri <R ri+1 <…R rK <R(R r(K+1) ) Then (K+1) curve arcs B will likewise be generated i+1 B i I=1, …, K, at which time the first screw 210 corresponds to curve arc a i A i+1 Corresponding to the second screw 220 is a curve B i+1 B i And (5) mutually meshed operation.
For the fourth curved section B of the second screw 220 01 B 02 By O 2 As the center of a circle, O 2 B 01 The clockwise direction is positive, and given the auxiliary angle epsilon, there are:
any one of the fourth curved sections B for the second screw 220 i+1 B i By O 2 As the center of a circle, O 2 B i+1 Is the polar axis, the anticlockwise direction is positive, and the auxiliary angle epsilon is given by
B i+1 B i The corresponding pole diameters are as follows:
wherein R is l(i+1) Representation B i B i+1 Is the maximum diameter of the lens.
B of the second screw 220 i+1 B i Corresponding polar angle theta ri The method comprises the following steps:
wherein θ li Is equal to B i B i+1 A corresponding first central angle of the first screw 210.
Wherein the auxiliary angle is epsilon, the corresponding polar angle is phi (epsilon), and the auxiliary angle is relative to the rotation speed ratio
Center distance C and transition pole diameter R li Is a function of the change of: />
It should be noted that, on the premise of ensuring the normal use of the first screw 210 and the second screw 220, the more non-circular curves on the surfaces of the grooves of the conical twin-screw device, the more wedge-shaped pressurizing is performed, and the stronger the axial extrusion capability is caused by the cone angle.
Illustratively, referring to FIG. 5, the first screw 210 and the second screw 220 have a speed ratio of 2:1, the corresponding number of heads is 1:2, 6 transition polar diameters are set, namely K=6, 7 sections of non-circular arc curves are added for the non-circular arc A of the first screw 210 01 A 02 I.e. the non-circular curve arc between the root diameter R and the tip diameter R of the connecting screw is expressed as O 1 As the center of a circle, O 1 A 02 For the polar axis, the counterclockwise direction is positive, and given the auxiliary angle ε, there are:
the corresponding pole diameters are as follows:
the corresponding polar angle is:
at this time, non-circular curve arc A 01 A 02 The corresponding central angle is:
further, for any section of the first screw 210, the non-circular curve arc A i A i+1 By O 1 As the center of a circle, O 1 A i Is the polar axis, clockwise is positive, and an auxiliary angle is given
Then there are:
first curve segment A i A i+1 Corresponding polar diameter
Corresponding polar angle
Non-circular curve arc A i A i+1 Corresponding central angle theta li The method comprises the following steps:
Here, R is li 、R l(i+1) Respectively representing a first curved section A of the first screw 210 i A i+1 Corresponding minimum and maximum polar diameters.
According to the selected polar diameter R li The sum of central angles corresponding to K+1 curve arcs composed of K polar diameters can be obtained, and finally the vertex angle alpha and the base angle lambda of the first screw 210 and the central angle delta corresponding to each transition arc are determined i The sum satisfies the following formula:
at this time, it can be determined from the formula that the angle sum value is +.>
And performing angle distribution on the angle sum value according to a preset distribution rule.
Further, as shown in fig. 5, 6 transition polar diameters R are also provided between the screw root diameter R and the screw tip diameter R for the second screw 220 r() So that R (R r0 )<R r1 <R r2 …<R ri <…R rK <R(R r(K+1) ) Then 14 third curve segments B will likewise be produced i B i+1 I=1,..4, K, but the curved arc of the double-threaded second screw 220 approximates a straight line, the second screw 220 removes the bottom and top angles and the bag in order to simplify the screw production process, and to avoid the constraint of engineering formulasExcept the arc line of the angle, all the rest third curve sections are replaced by straight lines, and at the moment, the first screw 210 corresponds to Qu Xianhu and the second screw 220 corresponds to the straight line B i B i+1 I=1,..k, operating in mesh with each other.
Non-circular curve arc B for second screw 220 01 B 02 By O 2 As the center of a circle, O 2 B 01 The clockwise direction is positive, and given the auxiliary angle epsilon, there are:
any section of curve B for the second screw 220 i+1 B i By O 2 As the center of a circle, O 2 B i+1 Is the polar axis, the anticlockwise direction is positive, and the auxiliary angle epsilon is given by
Curve arc B i+1 B i The corresponding pole diameters are as follows:
curve arc B of second screw 220 i+1 B i Corresponding polar angle theta ri The method comprises the following steps:
wherein θ li Is equal to B i B i+1 A corresponding first central angle of the first screw 210.
Wherein the auxiliary angle is epsilon, the corresponding polar angle is phi (epsilon), and the auxiliary angle is relative to the rotation speed ratio
Center distance C and transition pole diameter R li Is a function of the change of: />
It can be understood that referring to fig. 2, fig. 2 is a twin-screw manufactured according to the method for manufacturing a twin-screw according to the embodiment of the present application.
It should be noted that, under the conditions that the center distances are both 30 and the diameters D are both 35, the cavity volumes of the conventional constant-speed twin-screw, the differential twin-screw, the example 1 (the first endpoint connecting line set including the third arc segment and the first curve segment) of the twin-screw manufactured by the application, and the example 2 (the first endpoint connecting line set including only the first curve segment) of the twin-screw are compared, as shown in fig. 6. The double-screw manufactured by the method has smaller inner cavity volume, and the mixing effect is improved by reducing the inner cavity volume.
It should be noted that, a plurality of first diameters are added between the root diameter and the top diameter of the first screw 210, and after a plurality of second diameters are added to the plurality of second screws 220, the motion trace of the meshing point increased by the twin screws along with time is more complex, so as to break symmetry, taking the twin screws in fig. 4 as an example, the motion trace of the twin screws is shown in fig. 8, and the motion trace of the twin screws in fig. 4 is shown as a first arc segment a corresponding to the top diameter of the first screw 210 00 A 01 A first arc section B with a section corresponding to the root diameter of the second screw 220 00 B 01 The meshing point corresponding to the segment is a in fig. 8 701 First arc section A corresponding to root diameter of first screw 210 0 A 02 A first arc section B with a section corresponding to the root diameter of the second screw 220 02 B 0 The corresponding meshing point is at A 020 The engagement points of other first circular arc sections of the first screw 210 and the corresponding second screw 220 on the center distance are respectively A 12 、A 34 、A 56 . At the center distance O between the first screw 210 and the second screw 220 1 O 2 As a boundary line, it can be seen that O 1 O 2 Is an upper engagement zone, O 1 O 2 The lower portion of the meshing point is a lower meshing zone, the melting section 120 mainly occurs in the lower meshing zone, and the meshing point movement track of the lower meshing zone is in a state of half-wave disturbance, compared with the meshing point movement track of the conventional constant-speed twin-screw extruder shown in fig. 9 (the center distance of the two screws is taken as a boundary line in fig. 9, the movement track of the meshing point is vertically and laterally symmetrical, and only one wave disturbance effect is provided, so that the material cannot be sufficiently extruded, stretched and disturbed), the twin screw can increase more meshing points, so that the meshing zone is increased, and the material is subjected to stronger disturbance effect and mixing effect in the meshing zone due to the complex movement track of the meshing point.
By way of example, referring to fig. 4 and 5, according to the method for manufacturing a twin screw described above in the present application, a first one may be manufacturedThe first screw 210 shown in fig. 4, in which the transition arc is inserted in the middle of the curved section, may be manufactured without the first screw 210 shown in fig. 5, in which the transition arc is not included in the first curved section. The first screw 210 and the second screw 220 according to the embodiment of the present application are tapered, and the first screw 210 in fig. 4 is taken as an example, and referring to fig. 10, the included angle between the inner wall surface of the barrel 100 and the surface of the screw, which is approximately straight, is the taper angle β 1 Wherein A 'is' 00 、A′ 01 、A′ 02 、A′ 03 、A′ 1 、A′ 2 、A′ 3 、A′ 4 、A′ 5 And A' 6 A respectively corresponding to the cross-section structure diagram of FIG. 4 7 、A 01 、A 02 、A 0 、A 1 、A 2 、A 3 、A 4 、A 5 And A 6 The method comprises the steps of carrying out a first treatment on the surface of the Taking the first screw 210 of FIG. 5 as an example, referring to FIG. 11, the angle between the inner wall surface of the barrel 100 and the nearly straight surface of the screw is the taper angle β 2 Wherein A 'is' 00 、A′ 01 、A′ 02 、A′ 03 、A′ 1 、A′ 2 、A′ 3 、A′ 4 、A′ 5 And A' 6 A corresponding to the cross-sectional structure diagram of FIG. 5 7 、A 01 、A 02 、A 0 、A 1 、A 2 、A 3 、A 4 、A 5 And A 6 。
As can be appreciated, an extruder according to an embodiment of the present application comprises:
the machine barrel 100, wherein the inner cavity of the machine barrel 100 is provided with two intersected cylindrical grooves;
twin screws are made by the method of making twin screws as described above, with a first screw 210 of a twin screw being located in one of the cylindrical grooves and a second screw 220 of a twin screw being located in the other cylindrical groove.
For the extruder, referring to fig. 12, the procedure was as follows:
after the materials enter the machine barrel 100 from the feed inlet 111, the first screw 210 and the second screw 220 rotate in the same direction and at different speeds; after the material enters the solid conveying section 110, the material is forced to move towards the discharge port 141 under the conveying action of differential rotation positive displacement and friction drag of the first screw 210 and the second screw 220.
As the material is conveyed to the melting section 120, the first screw 210 and the second screw 220 rotate at a differential speed along their respective axes to produce periodic compression and expansion of the conveying space to convey the material; wherein, the two screws are always meshed with each other in the rotation process of the first screw 210 and the second screw 220, the material is pre-melted due to extrusion stretching action caused by wedge-shaped gaps of the materials in the upper and lower meshing areas and extrusion stretching action caused by wedge-shaped gaps of the materials far away from the meshing areas, friction heat is generated by high-speed rotation of the first screw 210 and the second screw 220, meanwhile, the materials are further melted and mixed under the combined action of external heating of the machine barrel 100, and the melting and mixing processes of the materials are accelerated due to the interaction of the first screw 210 and the second screw 220, so that the materials become melt;
after the melt enters the exhaust section 130, the rotation of the first screw 210 and the second screw 220 continuously turns over and forcedly peels off the materials adhered to the screws, the rotation speed of the first screw 210 and the second screw 220 enables the force field in the runner 300 to be unbalanced, a stretching force field, an extrusion effect and an axial mixing effect are generated on the materials, the gas is accelerated to be discharged from the exhaust port 131, and the melt moves further towards the direction of the discharge port 141;
after the melt enters the mixing extrusion section 140, the melt moves forward under the action of periodical compression and expansion spaces generated by the rotation action of the first screw 210 and the second screw 220, the meshing action of the upper meshing area and the lower meshing area and the extrusion stretching action of materials far away from the meshing area caused by wedge-shaped gaps further strengthen the mixing plasticization of the materials, and meanwhile, the mutual wiping action between the first screw 210 and the second screw 220 realizes the self-cleaning action and the extrusion stretching action, so that the melt is stably extruded from the discharge port 141.
Preferred embodiments of the present application are described above with reference to the accompanying drawings, and thus do not limit the scope of the claims of the embodiments of the present application. Any modifications, equivalent substitutions and improvements made by those skilled in the art without departing from the scope and spirit of the embodiments of the present application shall fall within the scope of the claims of the embodiments of the present application.
Claims (10)
1. A method of making a twin screw, the method comprising:
determining a root diameter, a top diameter, a rotation speed ratio of the first screw and the second screw, and a center distance between the first screw and the second screw;
determining first wire diameters and the number of the first wire diameters which are inserted in a first insertion area formed by a group of adjacent root diameters and top diameters on a first cross section of a first screw rod according to the center distance;
determining a first curve segment set arranged on a first screw rod according to a preset central angle calculation formula and a first curve segment calculation formula, wherein the first curve segment set consists of a plurality of first curve segments obtained by inserting a first line in the first inserting area and a second curve segment formed by another group of adjacent root diameters and top diameters;
determining a second central angle of each first circular arc section of the first circular arc section set on the first cross section according to a first central angle corresponding to each third curve section of the first curve section set;
manufacturing a first screw according to the first curve segment set and the first arc segment set;
determining a second curve segment set corresponding to the first curve segment set and a second arc segment set corresponding to the first arc segment set on a second screw, wherein the central angle ratio of each fourth curve segment in the second curve segment set to the corresponding third curve segment is the rotation speed ratio, and the central angle ratio of each second arc segment in the second arc segment set to the corresponding first arc segment is the rotation speed ratio;
and manufacturing a second screw rod according to the second curve segment set and the second arc segment set.
2. The method for manufacturing a twin-screw according to claim 1, wherein determining the first curve segment set provided on the first screw according to the preset central angle calculation formula and the first curve segment calculation formula comprises:
respectively determining first central angles corresponding to each first curve segment and each second curve segment according to the central angle calculation formula;
determining the polar diameters of the first curve segment and the second curve segment according to the first curve segment calculation formula;
wherein the central angle calculation formula comprises a formula I and a formula II as follows:
formula one:
formula II:
wherein θ li A first central angle corresponding to the first curve segment; θ l0 A first central angle corresponding to the second curve segment;
is said speed ratio and M and N are irreducible; c is the center distance; r is R li 、R l(i+1) Respectively is theta li The minimum polar diameter and the maximum polar diameter of the corresponding first curve segment, D is 2R, and R is the top diameter; the value range of i is 1-K+1, and K is the number of the first wire diameters.
3. The method of claim 2, wherein the first curve segment calculation formula includes the following formula three and formula four:
formula III:
formula IV:
wherein ρ is li (epsilon) is theta li The polar diameter of the corresponding first curve segment; ρ l0 And (epsilon) is the polar diameter of the second curve segment.
4. The method for manufacturing a double screw according to claim 2, wherein the first set of arc segments consists of arcs corresponding to the root diameter and the top diameter, or the first set of arc segments consists of transition arcs and arcs corresponding to the root diameter and the top diameter; the determining, according to the first central angle corresponding to each third curve segment of the first curve segment set, the second central angle of each first arc segment of the first arc segment set on the first cross section includes:
subtracting the first central angles from 2 pi to obtain angles and values, wherein the angles and the values are the sum of the second central angles of the first arc sections;
and carrying out average distribution on the angles and the values according to the number of the first circular arc sections, and determining each second central angle.
5. A method of making a twin screw according to claim 2, wherein said determining a second set of curvilinear segments on a second screw corresponding to said first set of curvilinear segments comprises:
determining fourth curve segments corresponding to each third curve segment one by one according to a preset second curve segment calculation formula, the rotation speed ratio and each first central angle, and obtaining a second curve segment set;
wherein the relationship between the third central angle of the fourth curve segment and the first central angle of the third curve segment is as follows:
formula five:
wherein θ ri Represents a third central angle, θ li Represents θ ri A corresponding first central angle;
wherein the second curve segment set calculation formula includes formula six and formula seven as follows:
formula six:
formula seven:
wherein, psi (epsilon) is theta ri Polar angle of the corresponding fourth curve segment; ρ ri (epsilon) is theta ri The polar diameter of the corresponding fourth curve segment; r is R l(i+1) Respectively is theta ri The maximum diameter of the corresponding fourth curve segment.
6. A method of producing a twin screw according to claim 1, wherein a fourth curved section corresponding to the first curved section is provided as a straight line.
7. The method of claim 1, wherein the number of first curvilinear segments ranges from 2 to 8.
8. The method of claim 1, wherein the ratio of the number of screw heads of the first screw to the number of screw heads of the second screw is inversely proportional to the ratio of rotation.
9. A twin screw produced by the method of any one of claims 1 to 8.
10. An extruder, comprising:
the inner cavity of the machine barrel is provided with two intersected cylindrical grooves;
twin-screw, produced by the method according to any one of claims 1 to 8, a first screw of which is located in one of said cylindrical grooves and a second screw of which is located in the other of said cylindrical grooves.
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| Application Number | Priority Date | Filing Date | Title |
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| CN202211726868.0A CN116277868A (en) | 2022-12-30 | 2022-12-30 | Manufacturing method of double screw, double screw and extruder |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211726868.0A CN116277868A (en) | 2022-12-30 | 2022-12-30 | Manufacturing method of double screw, double screw and extruder |
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| CN202211726868.0A Pending CN116277868A (en) | 2022-12-30 | 2022-12-30 | Manufacturing method of double screw, double screw and extruder |
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