CN113190992A - Method, device, equipment and medium for predicting fiber length distribution in blending extrusion process - Google Patents
Method, device, equipment and medium for predicting fiber length distribution in blending extrusion process Download PDFInfo
- Publication number
- CN113190992A CN113190992A CN202110456898.3A CN202110456898A CN113190992A CN 113190992 A CN113190992 A CN 113190992A CN 202110456898 A CN202110456898 A CN 202110456898A CN 113190992 A CN113190992 A CN 113190992A
- Authority
- CN
- China
- Prior art keywords
- fiber length
- extrusion process
- blending extrusion
- fiber
- length distribution
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 239000000835 fiber Substances 0.000 title claims abstract description 268
- 238000000034 method Methods 0.000 title claims abstract description 147
- 238000001125 extrusion Methods 0.000 title claims abstract description 135
- 238000002156 mixing Methods 0.000 title claims abstract description 117
- 238000009826 distribution Methods 0.000 title claims abstract description 106
- 230000008569 process Effects 0.000 title claims abstract description 102
- 238000012545 processing Methods 0.000 claims abstract description 17
- 239000012530 fluid Substances 0.000 claims description 30
- 239000000463 material Substances 0.000 claims description 30
- 239000000945 filler Substances 0.000 claims description 9
- 239000000203 mixture Substances 0.000 claims description 8
- 239000000155 melt Substances 0.000 claims description 6
- 230000000704 physical effect Effects 0.000 claims description 5
- 239000007787 solid Substances 0.000 claims description 5
- 238000004590 computer program Methods 0.000 claims description 2
- 238000003860 storage Methods 0.000 claims description 2
- 238000004898 kneading Methods 0.000 description 6
- 230000007547 defect Effects 0.000 description 3
- 238000004519 manufacturing process Methods 0.000 description 3
- 238000004088 simulation Methods 0.000 description 3
- 230000008859 change Effects 0.000 description 2
- 230000006872 improvement Effects 0.000 description 2
- 239000002245 particle Substances 0.000 description 2
- 239000000243 solution Substances 0.000 description 2
- 230000015556 catabolic process Effects 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 238000010924 continuous production Methods 0.000 description 1
- 238000006731 degradation reaction Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 239000006185 dispersion Substances 0.000 description 1
- 238000001746 injection moulding Methods 0.000 description 1
- 238000002844 melting Methods 0.000 description 1
- 230000008018 melting Effects 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 239000011208 reinforced composite material Substances 0.000 description 1
- 230000002787 reinforcement Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000000717 retained effect Effects 0.000 description 1
- 238000012546 transfer Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/26—Composites
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Extrusion Moulding Of Plastics Or The Like (AREA)
Abstract
The invention discloses a method, a device, equipment and a medium for predicting fiber length distribution in a blending extrusion process. The method comprises the following steps: (1) acquiring flow field data corresponding to a preset blending extrusion process, wherein the flow field data comprises a shear rate field and residence time, the shear rate field comprises N shear rate values which are sequentially arranged along the blending extrusion direction, and N is more than or equal to 2; (2) establishing a fiber length distribution prediction model based on a mass conservation principle, taking the initial fiber length distribution to be subjected to a blending extrusion process as the initial input of the prediction model, then sequentially performing fiber length distribution prediction processing on each shear rate value by using the prediction model along the blending extrusion direction, and taking the prediction result of the previous fiber length distribution as the prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is finished is predicted. The method can predict the information of the whole fiber length distribution in the blending extrusion process.
Description
Technical Field
The invention belongs to the field of fiber reinforced blending extrusion, and particularly relates to a method, a device, equipment and a medium for predicting fiber length distribution in a blending extrusion process.
Background
In industry, the fiber reinforced material is a common reinforced composite material, and has the characteristics of high specific strength and specific modulus, simple forming process, secondary processing and the like. Long fiber reinforced materials have better mechanical properties than short fiber reinforced materials. Therefore, as much long fibers as possible are retained in the production of the fiber-reinforced material. And severe fiber breakage often occurs in the blending and extrusion process, so that the prediction of the fiber length distribution is of great significance to actual production.
The field of injection molding has matured the study of fiber length distribution, and non-patent literature "piping III CL, Phelps JH, Abd El-Rahman AI, Kunc V, Frame BJ. modeling fiber attachment in molded Long-fiber composites. in: Proceedings of PPS-26 annular Meeting, Banff, July 2010" discloses models for predicting the change in fiber length distribution during mold filling. The field of co-extrusion has been less and less well studied with respect to fiber length distribution, and a common process for preparing fiber reinforcement is twin screw extrusion. Non-patent documents "Shon K, Liu D, White JL. Experimental students and modeling of degradation of dispersion and fiber dam in continuous compositions. int Polym Proc 2005; 20: 322-31 "discloses empirical models describing the evolution of the average fiber length in different continuous processes. However, these studies have largely centered on the variation in average fiber length during the blending extrusion process and have not provided information on the overall fiber length distribution.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention provides a method, a device, equipment and a medium for predicting the fiber length distribution in the blending extrusion process, aiming at establishing a fiber length distribution prediction model which can predict the whole fiber length distribution information in the blending extrusion process, thereby solving the technical problem that the prior art can only predict the average fiber length change in the blending extrusion process and can not provide the whole fiber length distribution information.
To achieve the above object, according to one aspect of the present invention, there is provided a method for predicting fiber length distribution in a co-extrusion process, comprising the steps of:
(1) acquiring flow field data corresponding to a preset blending extrusion process, wherein the flow field data comprises a shear rate field and residence time, the shear rate field comprises N shear rate values which are sequentially arranged along the blending extrusion direction, and N is more than or equal to 2;
(2) establishing a fiber length distribution prediction model based on a mass conservation principle, taking the initial fiber length distribution to be subjected to a blending extrusion process as the initial input of the prediction model, then sequentially performing fiber length distribution prediction processing on each shear rate value by using the prediction model along the blending extrusion direction, and taking the prediction result of the previous fiber length distribution as the prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is finished is predicted.
Preferably, the prediction model is represented by the following formula:
wherein m isiIs a fiber length of LiM of the fibers ijIs a fiber length of LjThe mass fraction of the fibers j, piIs a fiber length of LiThe probability of breakage of the fiber i in the pre-set blending extrusion process, pjIs a fiber length of LjThe probability of breakage of the fiber j in the preset blending extrusion process, PijIs the length L in the preset blending extrusion processjIs broken into a length LiThe probability of breakage of the fiber i, t the residence time, and n the total number of fiber length classifications.
It is noted that mass transfer from long fibers to short fibers follows the law of mass conservation. Meanwhile, in the invention, the radius of the fiber is not changed in the whole breaking process, so that the fiber mass fraction distribution and the fiber length distribution can be equivalently expressed.
Here, both the initial fiber length distribution and the fiber length distribution at the time of completion of the co-extrusion process satisfy the following conditions: l isi=(n+1-i)×Ln(ii) a Wherein L isnThe length of the fibre which is the smallest and which cannot be broken, L1Is the length of the largest length of the fibre, LiIs of length LiThe length of the fiber (1 < i < n).
That is, in the present invention, in order to describe the entire fiber distribution, the fibers are classified into n types according to the length of the fibers, wherein the minimum fiber length is set to LnAt this length, it is assumed that the fibers cannot break.
Preferably, the fiber length is LxThe probability P (Bu) of breakage of the fiber x in the pre-set blending extrusion processx) Represented by the formula:
P(Bux)=1;Bux>1
wherein the buckling parameter BuxExpressed as:
wherein eta is the fluid viscosity,is the fluid shear rate, θ andtwo orientation angles of the fibres x, the planes of which are perpendicular to each other, betaxIs a fiber length of LxThe half aspect ratio of the fiber x of (2) and E is Young's modulus.
Wherein, the subscript x satisfies x is more than or equal to 1 and less than or equal to n, and x can be i, j and the like.
For example, when x is j, i.e. when the fiber length is LjThe probability p of the fiber j to break in the preset blending extrusion processjI.e. probability P (Bu)j) Represented by the formula:
P(Buj)=1Buj>1
wherein the buckling parameter BujExpressed as:
wherein eta is the fluid viscosity,is the fluid shear rate, θ andtwo orientation angles of the fibres x, the planes of which are perpendicular to each other, betaxIs a fiber length of LxThe half aspect ratio of the fiber x of (2) and E is Young's modulus.
Similarly, when x is i, i.e. when the fiber length is LiThe probability p of breakage of the fiber i in the preset blending extrusion processiI.e. probability P (Bu)i)。
Note that the buckling parameter BuxObtained by the following method; first, in determining the average orientation of the fibers during the spin cycle, the stress state of the fibers in the flow field is calculated and can be expressed as:
wherein eta is the fluid viscosity,is the fluid shear rate, θ andis the fiber orientation angle, β is the fiber half aspect ratio, and E is the Young's modulus.
Then, the stress σ to which the fiber is subjected before bucklingBAnd maximum stressAnd (3) comparing to obtain a buckling parameter Bu:
wherein, assuming that the fiber rotation conforms to the Jeffrey equation, the equation is suitable for ellipsoidal particles, and the fiber is cylindrical particles, so that the fiber orientation in the flow field can be better described by replacing the equivalent half length-to-diameter ratio beta' with 0.75 beta.
From this, the buckling parameter Bu can be obtainedxExpression (c):
wherein eta is the fluid viscosity,is the fluid shear rate, θ andtwo orientation angles of the fibres x, the planes of which are perpendicular to each other, betaxIs a fiber length of LxThe half aspect ratio of the fiber x of (2) and E is Young's modulus.
In addition, it should be noted that the minimum radius of curvature of a curved fiber is located at the middle, so that the fiber in an ideal state will always break at the midpoint. But the fibers always have defects and break below the critical stress value. It is assumed in the present invention that the fiber breaks below the buckling stress value due to defects, but must break once the buckling stress value is reached.
Preferably, the length L is assumed during the pre-blending extrusion processjIs broken into a length LiThe fiber i conforms to the Weber distribution, and the length of the fiber i in the preset blending extrusion process is LjIs broken into a length LiThe probability of breakage P of the fiber iijRepresented by the formula:
wherein m is the shape parameter and n is the total fiber length classification.
In the present invention, m is preferably 3, and the Weber distribution with a shape parameter of 3 is similar to the Gaussian distribution, so that the fracture probability P is also determined in this caseijGaussian distribution assumptions can be used.
Preferably, the acquiring flow field data corresponding to the preset blending extrusion process includes the following substeps:
(101) acquiring process parameters, material physical parameters and a viscosity constitutive equation corresponding to a preset blending extrusion process, wherein the process parameters comprise internal diameter of threads, external diameter of threads, thread pitch, helical angle, radial distance of a screw, length of the screw, axial pressure drop of fluid, radial pressure drop of fluid, rotating speed of the screw, volume of melt passing through a screw unit in unit time and filler mass of a material to be melted and blended; the material physical property parameters comprise the density of the material to be melt blended; the viscosity constitutive equation is a Carreau-Yasuda model;
(102) establishing a blending extrusion global model, and taking the process parameters and the viscosity constitutive equation as the input of the global model to obtain a shear rate field of a preset blending extrusion process;
the global model of blend extrusion is represented by the following formula:
wherein R is1、R2Respectively the inner diameter and the outer diameter of the thread, D is the diameter of a machine barrel, omega is the rotating speed of a screw, psi is a helical angle, eta is the fluid viscosity, Px、PθFluid axial and radial pressure drops, respectively; r is the radial distance of the screw,is the shear rate;
(103) the residence times of the solid conveying zone, the molten partially filled zone and the completely filled zone in the preset blending extrusion process were calculated respectively according to the following equation:
wherein L is the screw length, B is the screw pitch, ρ is the density of the material to be melt-blended, V is the volume of the melt passing through the screw unit per unit time, Q is the filler mass of the material to be melt-blended, ω is the screw rotation speed, and ψ is the helix angle.
According to another aspect of the present invention, there is provided an apparatus for predicting fiber length distribution in a co-extrusion process, the apparatus comprising:
the data acquisition module is used for acquiring flow field data corresponding to a preset blending extrusion process, wherein the flow field data comprises a shear rate field and residence time, the shear rate field comprises N shear rate values which are sequentially arranged along the blending extrusion direction, and N is more than or equal to 2;
the prediction module is used for establishing a fiber length distribution prediction model based on a mass conservation principle, taking the initial fiber length distribution to be subjected to the blending extrusion process as the initial input of the prediction model, then sequentially performing fiber length distribution prediction processing on each shear rate value by using the prediction model along the blending extrusion direction, and taking the prediction result of the previous fiber length distribution as the prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is finished is predicted.
According to still another aspect of the present invention, there is provided an electronic apparatus, including:
a processor;
a memory storing a computer executable program comprising the blending extrusion process fiber length distribution prediction method as described above.
According to yet another aspect of the present invention, there is provided a computer readable storage medium having stored thereon a computer program comprising a method of predicting fiber length distribution in a co-extrusion process as described above.
In general, at least the following advantages can be obtained by the above technical solution contemplated by the present invention compared to the prior art.
(1) The invention is based on the principle of conservation of massThe vertical fiber length distribution prediction model realizes the prediction of the fiber length distribution in the blending extrusion process, is different from the conventional fiber length simulation method in the blending extrusion process which only can provide the evolution of the average fiber length, and fully considers the fiber length L in the inventioniThe fiber i has a breakage probability in the preset blending extrusion process, and the fiber length is LjThe probability of breakage of the fiber j in the preset blending extrusion process, and the length of L in the preset blending extrusion processjIs broken into a length LiThe breaking probability of the fiber i can be simulated, and the complete fiber length distribution can be predicted, so that the method has important significance for the research on the performance of the fiber reinforced material.
(2) The invention utilizes the blending extrusion global model to quickly acquire the flow field data corresponding to the preset blending extrusion process, avoids the dependence on the existing commercial software, can independently predict without depending on the commercial software, reduces the cost and is suitable for industrial popularization.
(3) In the invention, the radius of the fiber is not changed in the whole breaking process, so that the fiber mass fraction distribution and the fiber length distribution can be equivalently expressed. Therefore, the establishment of a fiber length distribution prediction model by using the mass conservation principle can be realized.
Drawings
FIG. 1 is a flow chart of a method for predicting fiber length distribution in a blending extrusion process according to an embodiment of the present disclosure;
FIG. 2 is a schematic representation of the initial fiber length distribution in example 1 of the present invention;
FIG. 3 is a schematic diagram of a shear rate field in example 1 or 2 of the present invention;
FIG. 4 is a schematic view of the residence time in example 1 or 2 of the present invention;
FIG. 5 is a schematic representation of the fiber length distribution at the completion of the coextrusion process in example 1 of this invention;
FIG. 6 is a schematic representation of the fiber length distribution at the completion of the coextrusion process in example 2 of this invention;
FIG. 7 is a schematic view of shear rate field and residence time in example 3 of the present invention;
FIG. 8 is a schematic representation of the fiber length distribution at the completion of the coextrusion process in example 3 of this invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Example 1
The embodiment of the invention takes a co-rotating meshed double-screw extruder as an example to illustrate the blending extrusion process of the invention in detail.
Specifically, referring to fig. 1, the method for predicting fiber length distribution in a blending extrusion process provided by the embodiment of the present invention includes the following steps:
step 1: an initial fiber length distribution was obtained, wherein the fiber length distribution was converted to a fiber mass fraction distribution, and the initial fiber length used in this example is shown in fig. 2.
Step 2: and acquiring process parameters, material physical property parameters and a viscosity constitutive equation corresponding to the preset blending extrusion process, wherein the viscosity constitutive equation is a Carreau-Yasuda model, and screw data in the process parameters corresponding to the preset blending extrusion process are shown in the following table 1.
TABLE 1 screw size of co-rotating intermeshing twin screw extruder
Wherein data A/B in Table 1 indicates the pitch of the screw/the length of the screw, the suffix L indicates the reverse flight, data C/D/E in Table 1 indicates the dislocation angle of the kneading disks/the number of disks of the kneading disks/the length of the kneading disks, and the unit of data in Table 1 is mm.
The diameter of the machine barrel is 30 mm; the screw rotation speed is 90 rpm;the filler mass of the material to be melt blended is 5 kg/h; the density of the material to be melt blended was 1113.8kg/m3。
And step 3: the shear rate field calculated using the global model of blend extrusion is shown in FIG. 3.
The global model of blend extrusion is represented by the following formula:
wherein R is1、R2Respectively the inner diameter and the outer diameter of the thread, D is the diameter of a machine barrel, omega is the rotating speed of a screw, psi is a helical angle, eta is the fluid viscosity, Px、PθFluid axial and radial pressure drops, respectively; r is the radial distance of the screw,is the shear rate;
the residence times of the solid conveying zone, the molten partially filled zone and the completely filled zone in the preset blending extrusion process were calculated respectively according to the following formula, and the obtained residence times are shown in fig. 4.
Wherein L is the screw length, B is the screw pitch, ρ is the density of the material to be melt-blended, V is the volume of the melt passing through the screw unit per unit time, Q is the filler mass of the material to be melt-blended, ω is the screw rotation speed, and ψ is the helix angle.
And 4, step 4: calculating the rotation of the average length fiber using the Jeffrey equation, assuming that the average fiber should be rotated in the shear plane; for each length class of fibers, the stress exerted on the fibers and the ultimate stress before buckling were calculated separately.
And 5: calculating the fiber breakage probability of each length class in each direction, and deducing the breakage probability of the whole rotation period, namely calculating the fiber length as LxThe probability p of the fiber x breaking in the pre-set blending extrusion processx(ii) a For each length class of fibers, the length L during the pre-blending extrusion is calculatedjIs broken into a length LiThe probability of breakage P of the fiber iij。
The length of the fiber is LxThe probability p of the fiber x breaking in the pre-set blending extrusion processxRepresented by the formula:
P(Bux)=1;Bux>1
wherein the buckling parameter BuxExpressed as:
wherein eta is the fluid viscosity,is the fluid shear rate, θ andof fibres xTwo orientation angles, the planes of which are perpendicular to each other, betaxIs a fiber length of LxThe half aspect ratio of the fiber x of (2) and E is Young's modulus.
The length is L in the preset blending extrusion processjIs broken into a length LiThe probability of breakage P of the fiber iijRepresented by the formula:
wherein m is the shape parameter and n is the total fiber length classification.
Step 6: taking the initial fiber length distribution to be subjected to the blending extrusion process as the initial input of the prediction model, then sequentially performing fiber length distribution prediction processing on each shear rate value by using the prediction model along the blending extrusion direction, taking the prediction result of the previous fiber length distribution as the prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is finished is predicted, wherein the fiber length distribution when the blending extrusion process is finished is shown in fig. 5.
The prediction model is represented by the following formula:
wherein m isiIs a fiber length of LiM of the fibers ijIs a fiber length of LjThe mass fraction of the fibers j, piIs a fiber length of LiThe probability of breakage of the fiber i in the pre-set blending extrusion process, pjIs a fiber length of LjThe probability of breakage of the fiber j in the preset blending extrusion process, PijIs the length L in the preset blending extrusion processjIs broken into a length LiThe probability of breakage of the fiber i, t the residence time, and n the total number of fiber length classifications.
Example 2
The embodiment of the invention takes a fiber length distribution simulation scheme in the co-extrusion process of a co-rotating meshed double-screw extruder as an example to explain the invention in detail.
Specifically, the method for simulating fiber length distribution in the blending extrusion process provided by the embodiment of the invention comprises the following steps:
step 1: obtaining initial fiber length distribution, wherein the fiber length distribution needs to be converted into fiber mass fraction distribution, and the initial fiber length used in this embodiment is 5mm with uniform length and 5 μm of radius;
step 2: and acquiring process parameters, material physical property parameters and a viscosity constitutive equation corresponding to the preset blending extrusion process, wherein the viscosity constitutive equation is a Carreau-Yasuda model, screw data in the process parameters corresponding to the preset blending extrusion process are the same as those in the table 1, and other process parameters are also the same as those in the embodiment 1.
And step 3: the shear rate field calculated using the global model of blend extrusion is shown in FIG. 3.
The global model of blend extrusion is represented by the following formula:
wherein R is1、R2Respectively the inner diameter and the outer diameter of the thread, D is the diameter of a machine barrel, omega is the rotating speed of a screw, psi is a helical angle, eta is the fluid viscosity, Px、PθFluid axial and radial pressure drops, respectively; r is the radial distance of the screw,is the shear rate;
the residence times of the solid conveying zone, the molten partially filled zone and the completely filled zone in the preset blending extrusion process were calculated respectively according to the following formula, and the obtained residence times are shown in fig. 4.
Wherein L is the screw length, B is the screw pitch, ρ is the density of the material to be melt-blended, V is the volume of the melt passing through the screw unit per unit time, Q is the filler mass of the material to be melt-blended, ω is the screw rotation speed, and ψ is the helix angle.
And 4, step 4: calculating the rotation of the average length fiber using the Jeffrey equation, assuming that the average fiber should be rotated in the shear plane; for each length class of fibers, the stress exerted on the fibers and the ultimate stress before buckling were calculated separately.
And 5: calculating the fiber breakage probability of each length class in each direction, and deducing the breakage probability of the whole rotation period, namely calculating the fiber length as LxThe probability p of the fiber x breaking in the pre-set blending extrusion processx(ii) a For each length class of fibers, the length L during the pre-blending extrusion is calculatedjIs broken into a length LiThe probability of breakage P of the fiber iij。
The length of the fiber is LxThe fiber x is broken in the preset blending extrusion processProbability p ofxRepresented by the formula:
P(Bux)=1;Bux>1
wherein the buckling parameter BuxExpressed as:
wherein eta is the fluid viscosity,is the fluid shear rate, θ andtwo orientation angles of the fibres x, the planes of which are perpendicular to each other, betaxIs a fiber length of LxThe half aspect ratio of the fiber x of (2) and E is Young's modulus.
The length is L in the preset blending extrusion processjIs broken into a length LiThe probability of breakage P of the fiber iijRepresented by the formula:
wherein m is the shape parameter and n is the total fiber length classification.
Step 6: taking the initial fiber length distribution to be subjected to the blending extrusion process as the initial input of the prediction model, then sequentially performing fiber length distribution prediction processing on each shear rate value by using the prediction model along the blending extrusion direction, taking the prediction result of the previous fiber length distribution as the prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is finished is predicted, wherein the fiber length distribution when the blending extrusion process is finished is shown in fig. 6.
The prediction model is represented by the following formula:
wherein m isiIs a fiber length of LiM of the fibers ijIs a fiber length of LjThe mass fraction of the fibers j, piIs a fiber length of LiThe probability of breakage of the fiber i in the pre-set blending extrusion process, pjIs a fiber length of LjThe probability of breakage of the fiber j in the preset blending extrusion process, PijIs the length L in the preset blending extrusion processjIs broken into a length LiThe probability of breakage of the fiber i, t the residence time, and n the total number of fiber length classifications.
Example 3
The embodiment of the invention takes a fiber length distribution simulation scheme in the blending extrusion process of a small parallel meshing homodromous three-screw extruder as an example to explain the invention in detail.
Specifically, the method for predicting the fiber length distribution in the blending extrusion process provided by the embodiment of the invention comprises the following steps:
step 1: obtaining initial fiber length distribution, wherein the fiber length distribution needs to be converted into fiber mass fraction distribution, and the initial fiber length used in this embodiment is 5mm with uniform length and 5 μm of radius;
step 2: acquiring process parameters, material physical property parameters and a viscosity constitutive equation corresponding to a preset blending extrusion process, wherein the viscosity constitutive equation is a Carreau-Yasuda model, and screw data in the process parameters corresponding to the preset blending extrusion process are shown in a table 2:
TABLE 2 screw size of parallel-meshing equidirectional three-screw extruder
Wherein data A/B in Table 1 represents the screw pitch of the screw/the length of the screw, data C/D/E in Table 1 represents the dislocation angle of the kneading disks/the number of disks of the kneading disks/the length of the kneading disks, and the unit of data in Table 1 is mm.
The diameter of the machine barrel is 30 mm; the screw rotation speed is 90 rpm; the filler mass of the material to be melt blended is 5 kg/h; the density of the material to be melt blended was 1113.8kg/m3。
And step 3: and calculating by using a blending extrusion global model to obtain a shear rate field.
The global model of blend extrusion is represented by the following formula:
wherein R is1、R2Respectively the inner diameter and the outer diameter of the thread, D is the diameter of a machine barrel, omega is the rotating speed of a screw, psi is a helical angle, eta is the fluid viscosity, Px、PθFluid axial and radial pressure drops, respectively; r is the radial distance of the screw,is the shear rate;
the residence times of the solid conveying zone, the melting part filling zone and the complete filling zone in the preset blending extrusion process are respectively calculated according to the following formula,
wherein L is the screw length, B is the screw pitch, ρ is the density of the material to be melt-blended, V is the volume of the melt passing through the screw unit per unit time, Q is the filler mass of the material to be melt-blended, ω is the screw rotation speed, and ψ is the helix angle.
The resulting shear rate field and residence time are shown in FIG. 7.
And 4, step 4: calculating the rotation of the average length fiber using the Jeffrey equation, assuming that the average fiber should be rotated in the shear plane; for each length class of fibers, the stress exerted on the fibers and the ultimate stress before buckling were calculated separately.
And 5: calculating the fiber breakage probability of each length class in each direction, and deducing the breakage probability of the whole rotation period, namely calculating the fiber length as LxThe probability p of the fiber x breaking in the pre-set blending extrusion processx(ii) a For each length class of fibers, the length L during the pre-blending extrusion is calculatedjIs broken into a length LiThe probability of breakage P of the fiber iij。
The length of the fiber is LxThe probability p of the fiber x breaking in the pre-set blending extrusion processxRepresented by the formula:
P(Bux)=1;Bux>1
wherein the buckling parameter BuxExpressed as:
wherein eta is the fluid viscosity,is the fluid shear rate, θ andtwo orientation angles of the fibres x, the planes of which are perpendicular to each other, betaxIs a fiber length of LxThe half aspect ratio of the fiber x of (2) and E is Young's modulus.
The length is L in the preset blending extrusion processjIs broken into a length LiThe probability of breakage P of the fiber iijRepresented by the formula:
wherein m is the shape parameter and n is the total fiber length classification.
Step 6: taking the initial fiber length distribution to be subjected to the blending extrusion process as the initial input of the prediction model, then sequentially performing fiber length distribution prediction processing on each shear rate value by using the prediction model along the blending extrusion direction, taking the prediction result of the previous fiber length distribution as the prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is finished is predicted, wherein the fiber length distribution when the blending extrusion process is finished is shown in fig. 8.
The prediction model is represented by the following formula:
wherein m isiIs a fiber length of LiM of the fibers ijIs a fiber length of LjThe mass fraction of the fibers j, piIs a fiber length of LiThe probability that the fiber i is broken in the preset blending extrusion processRate, pjIs a fiber length of LjThe probability of breakage of the fiber j in the preset blending extrusion process, PijIs the length L in the preset blending extrusion processjIs broken into a length LiThe probability of breakage of the fiber i, t the residence time, and n the total number of fiber length classifications.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (9)
1. A method for predicting fiber length distribution in a blending extrusion process is characterized by comprising the following steps:
(1) acquiring flow field data corresponding to a preset blending extrusion process, wherein the flow field data comprises a shear rate field and residence time, the shear rate field comprises N shear rate values which are sequentially arranged along the blending extrusion direction, and N is more than or equal to 2;
(2) establishing a fiber length distribution prediction model based on a mass conservation principle, taking the initial fiber length distribution to be subjected to a blending extrusion process as the initial input of the prediction model, then sequentially performing fiber length distribution prediction processing on each shear rate value by using the prediction model along the blending extrusion direction, and taking the prediction result of the previous fiber length distribution as the prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is finished is predicted.
2. The prediction method of claim 1, wherein the prediction model is represented by the following equation:
wherein m isiIs a fiber length of LiM of the fibers ijIs a fiber length of LjThe mass fraction of the fibers j, piIs a fiber length of LiThe probability of breakage of the fiber i in the pre-set blending extrusion process, pjIs a fiber length of LjThe probability of breakage of the fiber j in the preset blending extrusion process, PijIs the length L in the preset blending extrusion processjIs broken into a length LiThe probability of breakage of the fiber i, t the residence time, and n the total number of fiber length classifications.
3. The prediction method of claim 2, wherein the fiber length is LxThe probability P (Bu) of breakage of the fiber x in the pre-set blending extrusion processx) Represented by the formula:
P(Bux)=1;Bux>1
wherein the buckling parameter BuxExpressed as:
5. The prediction method according to any one of claims 1 to 4, wherein the obtaining of the flow field data corresponding to the pre-blending extrusion process comprises the following sub-steps:
(101) acquiring process parameters, material physical parameters and a viscosity constitutive equation corresponding to a preset blending extrusion process, wherein the process parameters comprise the diameter of a machine barrel, the inner diameter of a thread, the outer diameter of the thread, the thread pitch, the helix angle, the radial distance of a screw, the length of the screw, the axial pressure drop of fluid, the radial pressure drop of fluid, the rotating speed of the screw, the volume of a melt passing through a screw unit in unit time and the filler mass of a material to be melted and blended; the material physical property parameters comprise the density of the material to be melt blended; the viscosity constitutive equation is a Carreau-Yasuda model;
(102) establishing a blending extrusion global model, and taking the process parameters and the viscosity constitutive equation as the input of the global model to obtain a shear rate field of a preset blending extrusion process;
the global model of blend extrusion is represented by the following formula:
wherein R is1、R2Respectively the inner diameter and the outer diameter of the thread, D is the diameter of a machine barrel, omega is the rotating speed of a screw, psi is a helical angle, eta is the fluid viscosity, Px、PθFluid axial and radial pressure drops, respectively; r is the radial distance of the screw,is the shear rate;
(103) the residence times of the solid conveying zone, the molten partially filled zone and the completely filled zone in the preset blending extrusion process were calculated respectively according to the following equation:
wherein L is the screw length, B is the screw pitch, ρ is the density of the material to be melt-blended, V is the volume of the melt passing through the screw unit per unit time, Q is the filler mass of the material to be melt-blended, ω is the screw rotation speed, and ψ is the helix angle.
6. The prediction method of claim 1, wherein the initial fiber length distribution and the fiber length distribution at the completion of the co-extrusion process both satisfy the following condition:
Li=(n+1-i)×Ln;
wherein L isnThe length of the fibre which is the smallest and which cannot be broken, L1Is the length of the largest length of the fibre, LiIs of length LiOfThe length of dimension, 1 < i < n.
7. An apparatus for predicting fiber length distribution in a co-extrusion process, the apparatus comprising:
the data acquisition module is used for acquiring flow field data corresponding to a preset blending extrusion process, wherein the flow field data comprises a shear rate field and residence time, the shear rate field comprises N shear rate values which are sequentially arranged along the blending extrusion direction, and N is more than or equal to 2;
the prediction module is used for establishing a fiber length distribution prediction model based on a mass conservation principle, taking the initial fiber length distribution to be subjected to the blending extrusion process as the initial input of the prediction model, then sequentially performing fiber length distribution prediction processing on each shear rate value by using the prediction model along the blending extrusion direction, and taking the prediction result of the previous fiber length distribution as the prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is finished is predicted.
8. An electronic device, characterized in that the device comprises:
a processor;
a memory storing a computer executable program comprising the method for predicting fiber length distribution in a co-extrusion process as claimed in claims 1-6.
9. A computer-readable storage medium having stored thereon a computer program, characterized in that the program comprises the method for predicting fiber length distribution in a co-extrusion process according to claims 1-6.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202110456898.3A CN113190992B (en) | 2021-04-27 | 2021-04-27 | Fiber length distribution prediction method, device, equipment and medium in blending extrusion process |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202110456898.3A CN113190992B (en) | 2021-04-27 | 2021-04-27 | Fiber length distribution prediction method, device, equipment and medium in blending extrusion process |
Publications (2)
Publication Number | Publication Date |
---|---|
CN113190992A true CN113190992A (en) | 2021-07-30 |
CN113190992B CN113190992B (en) | 2024-05-14 |
Family
ID=76979185
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202110456898.3A Active CN113190992B (en) | 2021-04-27 | 2021-04-27 | Fiber length distribution prediction method, device, equipment and medium in blending extrusion process |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN113190992B (en) |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20190236225A1 (en) * | 2016-08-03 | 2019-08-01 | R-Flow Co., Ltd. | Method of deriving buckling condition of fiber moving in fluid, method of calculating breakage condition, and method of forecasting fiber length distribution |
CN110598293A (en) * | 2019-09-03 | 2019-12-20 | 上海交通大学 | Method for predicting fracture damage behavior of micro-nano fiber reinforced composite material |
CN111474043A (en) * | 2020-04-24 | 2020-07-31 | 南京航空航天大学 | Prediction method of residual strength of woven ceramic matrix composite material considering multistage fatigue damage |
-
2021
- 2021-04-27 CN CN202110456898.3A patent/CN113190992B/en active Active
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20190236225A1 (en) * | 2016-08-03 | 2019-08-01 | R-Flow Co., Ltd. | Method of deriving buckling condition of fiber moving in fluid, method of calculating breakage condition, and method of forecasting fiber length distribution |
CN110598293A (en) * | 2019-09-03 | 2019-12-20 | 上海交通大学 | Method for predicting fracture damage behavior of micro-nano fiber reinforced composite material |
CN111474043A (en) * | 2020-04-24 | 2020-07-31 | 南京航空航天大学 | Prediction method of residual strength of woven ceramic matrix composite material considering multistage fatigue damage |
Non-Patent Citations (1)
Title |
---|
文劲松;范德军;谢海玲;尹晨欢;冯彦洪;: "体积拉伸流场中的纤维取向", 华南理工大学学报(自然科学版), no. 11, 15 November 2017 (2017-11-15) * |
Also Published As
Publication number | Publication date |
---|---|
CN113190992B (en) | 2024-05-14 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN206703482U (en) | A kind of glass fiber reinforced polycarbonate mobile phone material bolt special combination | |
US20140133936A1 (en) | Screw | |
León et al. | Rotomolding and polyethylene composites with rotomolded lignocellulosic materials: A review | |
Wilczyński et al. | Experimental study of melting of polymer blends in a starve fed single screw extruder | |
Mohamed et al. | Integration of taguchi-grey relational analysis technique in parameter process optimization for rice husk composite | |
CN113190992A (en) | Method, device, equipment and medium for predicting fiber length distribution in blending extrusion process | |
JP5632236B2 (en) | Simulation device, program, and recording medium | |
Fan et al. | Numerical simulation of mixing characteristics in the eccentric rotor extruder with different process conditions and structural parameters | |
Alsinani et al. | Effect of high pulling speeds on the morphologies of pultrudates in a thermoplastic pultrusion process | |
WO2013190877A1 (en) | Glass fiber length distribution derivation apparatus, program for deriving glass fiber distribution and recording medium for deriving glass fiber distribution | |
Maertens et al. | Development of an injection molding process for long glass fiber-reinforced phenolic resins | |
Bechara et al. | Novel modeling approach for fiber breakage during molding of long fiber-reinforced thermoplastics | |
JP5632235B2 (en) | Method for producing glass fiber reinforced thermoplastic resin composition pellets | |
Alsinani et al. | Effect of Flax/PP pellets’ morphology on the mechanical properties of injection-molded parts | |
Moritzer et al. | Fiber length reduction during injection molding | |
Lopez-Garcia et al. | Compounding process optimization for recycled materials using machine learning algorithms | |
CN112917808B (en) | Continuous fiber composite material injection molding process | |
Qu et al. | Experimental investigation of polymer pellets melting mechanisms in vane extruders | |
CN212072902U (en) | Screw structure for extruding and granulating high-strength glass fiber reinforced material | |
Berzin et al. | Use of flow modeling to optimize the twin-screw extrusion process for the preparation of lignocellulosic fiber-based composites | |
CN208576169U (en) | Double-wall corrugated effective corotating twin-screw plastic extrusion unit | |
JP2012213996A5 (en) | ||
CN101332667A (en) | Long glass fiber-reinforced plastics pipe extruder head | |
CN218557913U (en) | Extrusion screw for BFS | |
CN202668958U (en) | Co-rotating twin screw extruder for long fiber reinfored thermoplitics-polypropylene (LFT-PP) material processing |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
GR01 | Patent grant | ||
GR01 | Patent grant |