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 PDF

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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
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fiber length
extrusion process
blending extrusion
fiber
length distribution
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CN113190992B (en
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张云
王子钦
高煌
余文劼
周晓伟
李茂源
周华民
黄志高
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Huazhong University of Science and Technology
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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

Method, device, equipment and medium for predicting fiber length distribution in blending extrusion process
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:
Figure BDA0003040825470000021
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:
Figure BDA0003040825470000031
P(Bux)＝1；Bux＞1
wherein the buckling parameter BuxExpressed as:
Figure BDA0003040825470000032
wherein eta is the fluid viscosity,
Figure BDA0003040825470000033
is the fluid shear rate, θ and
Figure BDA0003040825470000034
two 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:
Figure BDA0003040825470000035
P(Buj)＝1Buj＞1
wherein the buckling parameter BujExpressed as:
Figure BDA0003040825470000041
wherein eta is the fluid viscosity,
Figure BDA0003040825470000042
is the fluid shear rate, θ and
Figure BDA0003040825470000043
two 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:
Figure BDA0003040825470000044
Figure BDA0003040825470000045
wherein eta is the fluid viscosity,
Figure BDA0003040825470000046
is the fluid shear rate, θ and
Figure BDA0003040825470000047
is 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 stress
Figure BDA0003040825470000048
And (3) comparing to obtain a buckling parameter Bu:
Figure BDA0003040825470000049
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):
Figure BDA00030408254700000410
wherein eta is the fluid viscosity,
Figure BDA00030408254700000411
is the fluid shear rate, θ and
Figure BDA00030408254700000412
two 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:
Figure BDA0003040825470000051
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:
Figure BDA0003040825470000061
Figure BDA0003040825470000062
Figure BDA0003040825470000063
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,
Figure BDA0003040825470000064
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:
Figure BDA0003040825470000065
Figure BDA0003040825470000066
Figure BDA0003040825470000067
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
Figure BDA0003040825470000091
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:
Figure BDA0003040825470000092
Figure BDA0003040825470000101
Figure BDA0003040825470000102
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,
Figure BDA0003040825470000103
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.
Figure BDA0003040825470000104
Figure BDA0003040825470000105
Figure BDA0003040825470000106
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:
Figure BDA0003040825470000111
P(Bux)＝1；Bux＞1
wherein the buckling parameter BuxExpressed as:
Figure BDA0003040825470000112
wherein eta is the fluid viscosity,
Figure BDA0003040825470000113
is the fluid shear rate, θ and
Figure BDA0003040825470000114
of 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:
Figure BDA0003040825470000115
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:
Figure BDA0003040825470000116
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:
Figure BDA0003040825470000121
Figure BDA0003040825470000122
Figure BDA0003040825470000123
Figure BDA0003040825470000131
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,
Figure BDA0003040825470000132
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.
Figure BDA0003040825470000133
Figure BDA0003040825470000134
Figure BDA0003040825470000135
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:
Figure BDA0003040825470000136
P(Bux)＝1；Bux＞1
wherein the buckling parameter BuxExpressed as:
Figure BDA0003040825470000141
wherein eta is the fluid viscosity,
Figure BDA0003040825470000142
is the fluid shear rate, θ and
Figure BDA0003040825470000143
two 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:
Figure BDA0003040825470000144
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:
Figure BDA0003040825470000145
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
Figure BDA0003040825470000151
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:
Figure BDA0003040825470000161
Figure BDA0003040825470000162
Figure BDA0003040825470000163
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,
Figure BDA0003040825470000164
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,
Figure BDA0003040825470000165
Figure BDA0003040825470000166
Figure BDA0003040825470000167
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:
Figure BDA0003040825470000171
P(Bux)＝1；Bux＞1
wherein the buckling parameter BuxExpressed as:
Figure BDA0003040825470000172
wherein eta is the fluid viscosity,
Figure BDA0003040825470000173
is the fluid shear rate, θ and
Figure BDA0003040825470000174
two 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:
Figure BDA0003040825470000175
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:
Figure BDA0003040825470000181
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:
Figure FDA0003040825460000011
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:
Figure FDA0003040825460000012
P(Bux)＝1；Bux＞1
wherein the buckling parameter BuxExpressed as:
Figure FDA0003040825460000021
wherein eta is the fluid viscosity,
Figure FDA0003040825460000022
is the fluid shear rate, θ and
Figure FDA0003040825460000023
two 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.
4. The prediction method of claim 2, wherein the length L during the pre-blending extrusion processjOfThe vij is broken to a length LiThe probability of breakage P of the fiber iijRepresented by the formula:
Figure FDA0003040825460000024
wherein m is the shape parameter and n is the total fiber length classification.
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:
Figure FDA0003040825460000031
Figure FDA0003040825460000032
Figure FDA0003040825460000033
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,
Figure FDA0003040825460000034
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:
Figure FDA0003040825460000035
Figure FDA0003040825460000036
Figure FDA0003040825460000037
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.
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