CN113190992B - Fiber length distribution prediction method, device, equipment and medium in blending extrusion process - Google Patents
Fiber length distribution prediction method, device, equipment and medium in blending extrusion process Download PDFInfo
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Abstract
The invention discloses a fiber length distribution prediction method, device, equipment and medium 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, and the shear rate field comprises N shear rate values which are sequentially arranged along the blending extrusion direction, wherein N is more than or equal to 2; (2) And establishing a fiber length distribution prediction model based on a mass conservation principle, taking initial fiber length distribution to be subjected to a blending extrusion process as initial input of the prediction model, then sequentially carrying out fiber length distribution prediction processing on each shear rate value along the blending extrusion direction by using the prediction model, and taking a prediction result of the previous fiber length distribution as prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is completed is obtained. The invention 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. Thus, as many long fibers as possible are retained in the preparation of the fiber reinforcement. However, severe fiber breakage tends to occur during the process of blending extrusion, and thus prediction of fiber length distribution is of great importance to practical production.
The research on fiber length distribution in the field of injection molding is mature, and non-patent literature "Tucker III CL,Phelps JH,Abd El-Rahman AI,Kunc V,Frame BJ.Modeling fiberlength attrition in molded long-fiber composites.In:Proceedings of PPS-26Annual Meeting,Banff,July 2010" discloses a model for predicting fiber length distribution change in the mold filling process. The field of blend extrusion has little research on fiber length distribution and is not mature enough, and a common process for preparing fiber reinforced materials is twin screw extrusion. Non-patent literature "Shon K,Liu D,White JL.Experimental studies and modelling of development ofdispersion and fiber damage in continuous compounding.Int Polym Proc2005;20:322–31" discloses empirical models describing the evolution of average fiber length over different continuous processes. However, these studies have largely surrounded the variation in average fiber length during the coextrusion process and do not provide information on the overall fiber length distribution.
Disclosure of Invention
In order to meet the above defects or improvement demands of the prior art, the invention provides a fiber length distribution prediction method, a device, equipment and a medium in a blending extrusion process, which aim to establish a fiber length distribution prediction model and predict information of the whole fiber length distribution in the blending extrusion process, thereby solving the technical problems that only the change of the average fiber length in the blending extrusion process can be predicted and the information of the whole fiber length distribution can not be provided in the prior art.
To achieve the above object, according to one aspect of the present invention, there is provided a fiber length distribution prediction method for a blending 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, and the shear rate field comprises N shear rate values which are sequentially arranged along the blending extrusion direction, wherein N is more than or equal to 2;
(2) And establishing a fiber length distribution prediction model based on a mass conservation principle, taking initial fiber length distribution to be subjected to a blending extrusion process as initial input of the prediction model, then sequentially carrying out fiber length distribution prediction processing on each shear rate value along the blending extrusion direction by using the prediction model, and taking a prediction result of the previous fiber length distribution as prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is completed is obtained.
Preferably, the predictive model is represented by the following formula:
wherein m i is the mass fraction of fiber i having a fiber length of L i, m j is the mass fraction of fiber j having a fiber length of L j, P i is the probability of fiber i having a fiber length of L i breaking during a preset blending extrusion, P j is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion, P ij is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion into fiber i having a fiber length of L i, t is the residence time, and n is the total number of fiber length classifications.
The mass transfer from long fibers to short fibers follows the law of conservation of mass. Meanwhile, the radius of the fiber is not changed in the whole breaking process, so that the distribution of the mass fraction of the fiber and the distribution of the length of the fiber can be equivalently represented in the invention.
Here, the initial fiber length distribution and the fiber length distribution at the completion of the blending extrusion process each satisfy the following conditions: l i＝(n+1-i)×Ln; wherein L n is the length of the fiber which has the smallest length and cannot be broken, L 1 is the length of the fiber which has the largest length, and L i is the length of the fiber which has the length of L i, and 1 < i < n.
That is, in order to describe the overall fiber distribution in the present invention, the fibers are classified into n types according to the lengths of the fibers, where the minimum fiber length is set to L n, and at such a length, it is assumed that the fibers cannot be broken.
Preferably, the probability of breakage P (Bu x) of fiber x having a fiber length of L x during the preset blending extrusion is represented by the following formula:
P(Bux)＝1;Bux＞1
Wherein, buckling parameter Bu x is expressed as:
Wherein eta is the viscosity of the fluid, For fluid shear rate, θ and/>Is the two orientation angles of the fiber x, the planes of the two orientation angles are perpendicular to each other, beta x is the half length-diameter ratio of the fiber x with the fiber length of L x, and E is the Young's modulus.
Wherein, the subscript x satisfies that 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 j of fiber length L j breaks during the preset blending extrusion process, probability P j, i.e., probability P (Bu j), is represented by the following formula:
P(Buj)＝1Buj＞1
Wherein, buckling parameter Bu j is expressed as:
Wherein eta is the viscosity of the fluid, For fluid shear rate, θ and/>Is the two orientation angles of the fiber x, the planes of the two orientation angles are perpendicular to each other, beta x is the half length-diameter ratio of the fiber x with the fiber length of L x, and E is the Young's modulus.
Similarly, when x is i, i.e., when fiber i of fiber length L i breaks during the preset blending extrusion process, probability P i, i.e., probability P (Bu i).
It should be noted that, the buckling parameter Bu x is obtained by the following method; first, in determining the average orientation of the fiber over a rotation period, the stress state of the fiber in the flow field is calculated, which can be expressed as:
Wherein eta is the viscosity of the fluid, For fluid shear rate, θ and/>Is the fiber orientation angle, β is the fiber half aspect ratio, and E is the young's modulus.
Then, the stress sigma B and the maximum stress of the fiber before buckling are carried outComparison is performed to obtain buckling parameters Bu:
the fiber rotation is assumed to be in accordance with the Jeffrey equation, the equation is applicable to ellipsoidal particles, and the fiber is cylindrical, so that the fiber orientation in the flow field can be better described by replacing the fiber with the equivalent half-length-diameter ratio beta' =0.75β.
Thus, the expression for the buckling parameter Bu x can be derived:
Wherein eta is the viscosity of the fluid, For fluid shear rate, θ and/>Is the two orientation angles of the fiber x, the planes of the two orientation angles are perpendicular to each other, beta x is the half length-diameter ratio of the fiber x with the fiber length of L x, and E is the Young's modulus.
In addition, the minimum radius of curvature of the bent fiber is located in the middle, so that the fiber in an ideal state will always break at the midpoint. However, the fibers are always defective and fracture occurs below the critical stress value. The present invention assumes that the fiber breaks below the buckling stress value due to defects, and must break once the buckling stress value is reached.
Preferably, assuming that fiber j of length L j breaks into fiber i of length L i following weber distribution during the preset blending extrusion, the probability of breaking P ij of fiber j of length L j into fiber i of length L i during the preset blending extrusion is represented by the following formula:
where m is a shape parameter and n is the total number of fiber length classifications.
In the present invention, m is preferably 3, and the weber distribution with the shape parameter of 3 is similar to the gaussian distribution, so that the probability of fracture P ij can be assumed by the gaussian distribution at this time.
Preferably, the acquiring the flow field data corresponding to the preset blending extrusion process includes the following substeps:
(101) Acquiring technological parameters, material physical property parameters and viscosity constitutive equations corresponding to a preset blending extrusion process, wherein the technological parameters comprise a thread inner diameter, a thread outer diameter, a thread pitch, a helix angle, a screw radial distance, a screw length, a fluid axial pressure drop, a fluid radial pressure drop, a screw rotating speed, a volume of a melt passing through a screw unit in unit time and a filler mass of a material to be melt blended; the physical property parameters of the material 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 technological parameters and the viscosity constitutive equation as inputs of the global model to obtain a shear rate field of a preset blending extrusion process;
the blend extrusion global model is represented by the following formula:
Wherein R 1、R2 is the inner diameter and the outer diameter of a thread respectively, D is the diameter of a machine barrel, omega is the rotating speed of a screw, ψ is the helix angle, eta is the viscosity of fluid, and P x、Pθ is the axial pressure drop and the radial pressure drop of the fluid respectively; r is the radial distance of the screw rod, Is the shear rate;
(103) The residence times of the solid conveying zone, the molten partially filled zone and the fully filled zone in the preset blending extrusion process were calculated separately according to the following equation:
Where L is the screw length, B is the pitch, ρ is the density of the material to be melt blended, V is the volume of melt per unit time through the screw unit, Q is the filler mass of the material to be melt blended, ω is the screw speed, ψ is the helix angle.
According to another aspect of the present invention, there is provided a fiber length distribution prediction apparatus for a blending 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 initial fiber length distribution to be subjected to a blending extrusion process as initial input of the prediction model, then sequentially carrying out fiber length distribution prediction processing on each shear rate value along the blending extrusion direction by using the prediction model, and taking a prediction result of the previous fiber length distribution as prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is completed is obtained.
According to still another aspect of the present invention, there is provided an electronic device including:
A processor;
A memory storing a computer executable program comprising a blend 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 blend extrusion process as described above.
In general, the above technical solutions conceived by the present invention can achieve at least the following advantageous effects compared to the prior art.
(1) The fiber length distribution prediction model is established based on the mass conservation principle, so that the fiber length distribution prediction in the blending extrusion process is realized, and the fiber length distribution prediction method is different from the existing fiber length simulation method which can only provide the evolution of the average fiber length, fully considers the fracture probability of the fiber i with the fiber length of L i in the preset blending extrusion process, the fracture probability of the fiber j with the fiber length of L j in the preset blending extrusion process and the fracture probability of the fiber j with the fiber length of L j in the preset blending extrusion process into the fiber i with the length of L i, thereby being capable of simulating the fracture condition of the fiber, predicting the complete fiber length distribution and having important significance for the research of the performance of fiber reinforced materials.
(2) According to the invention, the blending extrusion global model is utilized, so that flow field data corresponding to a preset blending extrusion process is rapidly acquired, dependence on the existing commercial software is avoided, the prediction can be independently carried out without depending on the commercial software, the cost is reduced, and the method is suitable for industrial popularization.
(3) It is assumed in the present invention that the radius of the fiber does not change throughout the breaking process, and thus the fiber mass fraction distribution and the fiber length distribution in the present invention can be expressed equivalently. Therefore, the establishment of a fiber length distribution prediction model by utilizing a mass conservation principle can be realized.
Drawings
FIG. 1 is a method flow diagram of a method for predicting fiber length distribution in a blending extrusion process according to an embodiment of the present invention;
FIG. 2 is a schematic diagram showing the initial fiber length distribution in example 1 of the present invention;
FIG. 3 is a schematic view of the shear rate field in examples 1 or 2 of the present invention;
FIG. 4 is a schematic illustration of residence time in examples 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 the present invention;
FIG. 6 is a schematic representation of the fiber length distribution at the completion of the coextrusion process in example 2 of the present invention;
FIG. 7 is a schematic 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 the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
Example 1
The embodiment of the invention takes a co-extrusion process of a co-meshed double-screw extruder as an example, and the invention is described 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 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: obtaining technological parameters, material physical parameters and 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 technological parameters corresponding to the preset blending extrusion process are shown in the following table 1.
TABLE 1 screw size for co-rotating intermeshing twin screw extruder
Wherein data A/B in Table 1 represents the pitch of the screw/the length of the screw, suffix L represents the reverse flight, 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 data in Table 1 are in mm.
The diameter of the machine barrel is 30mm; the screw speed was 90rpm; the filler mass of the material to be melt blended is 5kg/h; the density of the material to be melt blended was 1113.8kg/m 3.
Step 3: the shear rate field calculated using the blend extrusion global model is shown in figure 3.
The blend extrusion global model is represented by the following formula:
Wherein R 1、R2 is the inner diameter and the outer diameter of a thread respectively, D is the diameter of a machine barrel, omega is the rotating speed of a screw, ψ is the helix angle, eta is the viscosity of fluid, and P x、Pθ is the axial pressure drop and the radial pressure drop of the fluid respectively; r is the radial distance of the screw rod, Is the shear rate;
The residence times of the solid conveying zone, the molten partially filled zone and the fully filled zone in the preset blending extrusion process were calculated separately according to the following equations, and the resulting residence times are shown in fig. 4.
Where L is the screw length, B is the pitch, ρ is the density of the material to be melt blended, V is the volume of melt per unit time through the screw unit, Q is the filler mass of the material to be melt blended, ω is the screw speed, ψ is the helix angle.
Step 4: calculating the rotation of the average length fiber using Jeffrey's equation, assuming that the average fiber should rotate in the shear plane; for each length class of fiber, the stress applied to the fiber and the ultimate stress before buckling were calculated separately.
Step 5: calculating the fiber fracture probability of each length class in each direction, and deducing the fracture probability of the whole rotation period, namely calculating the fracture probability p x of the fiber x with the fiber length of L x in the preset blending extrusion process; for each length class of fiber, the fracture probability P ij of fiber j of length L j to fiber i of length L i during the preset blending extrusion process was calculated.
The probability of fiber x breaking during the preset blending extrusion p x for fiber length L x is represented by the following formula:
P(Bux)＝1;Bux＞1
Wherein, buckling parameter Bu x is expressed as:
Wherein eta is the viscosity of the fluid, For fluid shear rate, θ and/>Is the two orientation angles of the fiber x, the planes of the two orientation angles are perpendicular to each other, beta x is the half length-diameter ratio of the fiber x with the fiber length of L x, and E is the Young's modulus.
The fracture probability P ij of the fiber j with the length L j to the fiber i with the length L i in the preset blending extrusion process is represented by the following formula:
where m is a shape parameter and n is the total number of fiber length classifications.
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 carrying out fiber length distribution prediction processing on each shear rate value along the blending extrusion direction by using the prediction model, taking the prediction result of the previous fiber length distribution as the prediction processing input of the prediction of the next fiber length distribution until the fiber length distribution when the blending extrusion process is completed is obtained by prediction, wherein the fiber length distribution when the blending extrusion process is completed is shown in figure 5.
The predictive model is represented by the following formula:
wherein m i is the mass fraction of fiber i having a fiber length of L i, m j is the mass fraction of fiber j having a fiber length of L j, P i is the probability of fiber i having a fiber length of L i breaking during a preset blending extrusion, P j is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion, P ij is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion into fiber i having a fiber length of L i, t is the residence time, and n is the total number of fiber length classifications.
Example 2
The embodiment of the invention takes a fiber length distribution simulation scheme in the process of blending extrusion of a co-rotating meshed double-screw extruder as an example, and the invention is described in detail.
Specifically, the fiber length distribution simulation method 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 the embodiment is 5mm with uniform length and 5 mu m radius;
Step 2: obtaining a technological parameter, a material physical property parameter and a viscosity constitutive equation corresponding to a preset blending extrusion process, wherein the viscosity constitutive equation is a Carreau-Yasuda model, screw data in the technological parameter corresponding to the preset blending extrusion process are the same as data in table 1, and other technological parameters are the same as those in the embodiment 1.
Step 3: the shear rate field calculated using the blend extrusion global model is shown in figure 3.
The blend extrusion global model is represented by the following formula:
Wherein R 1、R2 is the inner diameter and the outer diameter of a thread respectively, D is the diameter of a machine barrel, omega is the rotating speed of a screw, ψ is the helix angle, eta is the viscosity of fluid, and P x、Pθ is the axial pressure drop and the radial pressure drop of the fluid respectively; r is the radial distance of the screw rod, Is the shear rate;
The residence times of the solid conveying zone, the molten partially filled zone and the fully filled zone in the preset blending extrusion process were calculated separately according to the following equations, and the resulting residence times are shown in fig. 4.
Where L is the screw length, B is the pitch, ρ is the density of the material to be melt blended, V is the volume of melt per unit time through the screw unit, Q is the filler mass of the material to be melt blended, ω is the screw speed, ψ is the helix angle.
Step 4: calculating the rotation of the average length fiber using Jeffrey's equation, assuming that the average fiber should rotate in the shear plane; for each length class of fiber, the stress applied to the fiber and the ultimate stress before buckling were calculated separately.
Step 5: calculating the fiber fracture probability of each length class in each direction, and deducing the fracture probability of the whole rotation period, namely calculating the fracture probability p x of the fiber x with the fiber length of L x in the preset blending extrusion process; for each length class of fiber, the fracture probability P ij of fiber j of length L j to fiber i of length L i during the preset blending extrusion process was calculated.
The probability of fiber x breaking during the preset blending extrusion p x for fiber length L x is represented by the following formula:
P(Bux)＝1;Bux＞1
Wherein, buckling parameter Bu x is expressed as:
Wherein eta is the viscosity of the fluid, For fluid shear rate, θ and/>Is the two orientation angles of the fiber x, the planes of the two orientation angles are perpendicular to each other, beta x is the half length-diameter ratio of the fiber x with the fiber length of L x, and E is the Young's modulus.
The fracture probability P ij of the fiber j with the length L j to the fiber i with the length L i in the preset blending extrusion process is represented by the following formula:
where m is a shape parameter and n is the total number of fiber length classifications.
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 carrying out fiber length distribution prediction processing on each shear rate value along the blending extrusion direction by using the prediction model, taking the prediction result of the previous fiber length distribution as the prediction processing input of the prediction of the next fiber length distribution until the fiber length distribution when the blending extrusion process is completed is obtained by prediction, wherein the fiber length distribution when the blending extrusion process is completed is shown in figure 6.
The predictive model is represented by the following formula:
wherein m i is the mass fraction of fiber i having a fiber length of L i, m j is the mass fraction of fiber j having a fiber length of L j, P i is the probability of fiber i having a fiber length of L i breaking during a preset blending extrusion, P j is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion, P ij is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion into fiber i having a fiber length of L i, t is the residence time, and n is the total number of fiber length classifications.
Example 3
The embodiment of the invention takes a small parallel meshing unidirectional three-screw extruder blending extrusion process fiber length distribution simulation scheme as an example, and the invention is described in detail.
Specifically, the fiber length distribution prediction method 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 the embodiment is 5mm with uniform length and 5 mu m radius;
Step 2: obtaining technological parameters, material physical parameters and 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 technological parameters corresponding to the preset blending extrusion process are shown in table 2:
TABLE 2 parallel intermeshing co-rotating three screw extruder screw size
Wherein data A/B in Table 1 represents the 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 kneading disks/the length of the kneading disks, and data in Table 1 are in mm.
The diameter of the machine barrel is 30mm; the screw speed was 90rpm; the filler mass of the material to be melt blended is 5kg/h; the density of the material to be melt blended was 1113.8kg/m 3.
Step 3: and calculating by using a blending extrusion global model to obtain a shear rate field.
The blend extrusion global model is represented by the following formula:
Wherein R 1、R2 is the inner diameter and the outer diameter of a thread respectively, D is the diameter of a machine barrel, omega is the rotating speed of a screw, ψ is the helix angle, eta is the viscosity of fluid, and P x、Pθ is the axial pressure drop and the radial pressure drop of the fluid respectively; r is the radial distance of the screw rod, Is the shear rate;
the residence times of the solid conveying zone, the molten partial fill zone and the fully filled zone in the preset blending extrusion process were calculated separately according to the following equation,
Where L is the screw length, B is the pitch, ρ is the density of the material to be melt blended, V is the volume of melt per unit time through the screw unit, Q is the filler mass of the material to be melt blended, ω is the screw speed, ψ is the helix angle.
The resulting shear rate fields and residence times are shown in figure 7.
Step 4: calculating the rotation of the average length fiber using Jeffrey's equation, assuming that the average fiber should rotate in the shear plane; for each length class of fiber, the stress applied to the fiber and the ultimate stress before buckling were calculated separately.
Step 5: calculating the fiber fracture probability of each length class in each direction, and deducing the fracture probability of the whole rotation period, namely calculating the fracture probability p x of the fiber x with the fiber length of L x in the preset blending extrusion process; for each length class of fiber, the fracture probability P ij of fiber j of length L j to fiber i of length L i during the preset blending extrusion process was calculated.
The probability of fiber x breaking during the preset blending extrusion p x for fiber length L x is represented by the following formula:
P(Bux)＝1;Bux＞1
Wherein, buckling parameter Bu x is expressed as:
Wherein eta is the viscosity of the fluid, For fluid shear rate, θ and/>Is the two orientation angles of the fiber x, the planes of the two orientation angles are perpendicular to each other, beta x is the half length-diameter ratio of the fiber x with the fiber length of L x, and E is the Young's modulus.
The fracture probability P ij of the fiber j with the length L j to the fiber i with the length L i in the preset blending extrusion process is represented by the following formula:
where m is a shape parameter and n is the total number of fiber length classifications.
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 carrying out fiber length distribution prediction processing on each shear rate value along the blending extrusion direction by using the prediction model, taking the prediction result of the previous fiber length distribution as the prediction processing input of the prediction of the next fiber length distribution until the fiber length distribution when the blending extrusion process is completed is obtained by prediction, wherein the fiber length distribution when the blending extrusion process is completed is shown in figure 8.
The predictive model is represented by the following formula:
wherein m i is the mass fraction of fiber i having a fiber length of L i, m j is the mass fraction of fiber j having a fiber length of L j, P i is the probability of fiber i having a fiber length of L i breaking during a preset blending extrusion, P j is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion, P ij is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion into fiber i having a fiber length of L i, t is the residence time, and n is the total number of fiber length classifications.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (7)
1. A method for predicting fiber length distribution in a blending 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, and the shear rate field comprises N shear rate values which are sequentially arranged along the blending extrusion direction, wherein N is more than or equal to 2;
(2) Establishing a fiber length distribution prediction model based on a mass conservation principle, taking initial fiber length distribution to be subjected to a blending extrusion process as initial input of the prediction model, then sequentially carrying out fiber length distribution prediction processing on each shear rate value along the blending extrusion direction by using the prediction model, and taking a prediction result of the previous fiber length distribution as prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is completed is obtained by prediction;
The predictive model is represented by the following formula:
Wherein m i is the mass fraction of fiber i having a fiber length of L i, m j is the mass fraction of fiber j having a fiber length of L j, P i is the probability of fiber i having a fiber length of L i breaking during a preset blending extrusion, P j is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion, P ij is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion into fiber i having a fiber length of L i, t is the residence time, and n is the total number of fiber length classifications;
the method for acquiring the flow field data corresponding to the preset blending extrusion process comprises the following substeps:
(101) Acquiring technological parameters, material physical property parameters and viscosity constitutive equations corresponding to a preset blending extrusion process, wherein the technological parameters comprise a machine barrel diameter, a thread inner diameter, a thread outer diameter, a thread pitch, a thread angle, a screw radial distance, a screw length, fluid axial pressure drop, fluid radial pressure drop, a screw rotating speed, the volume of melt passing through a screw unit in unit time and the filler mass of a material to be melt blended; the physical property parameters of the material 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 technological parameters and the viscosity constitutive equation as inputs of the global model to obtain a shear rate field of a preset blending extrusion process;
the blend extrusion global model is represented by the following formula:
Wherein R 1、R2 is the inner diameter and the outer diameter of a thread respectively, D is the diameter of a machine barrel, omega is the rotating speed of a screw, ψ is the helix angle, eta is the viscosity of fluid, and P x、Pθ is the axial pressure drop and the radial pressure drop of the fluid respectively; r is the radial distance of the screw rod, Is the shear rate;
(103) The residence times of the solid conveying zone, the molten partially filled zone and the fully filled zone in the preset blending extrusion process were calculated separately according to the following equation:
Where L is the screw length, B is the pitch, ρ is the density of the material to be melt blended, V is the volume of melt per unit time through the screw unit, Q is the filler mass of the material to be melt blended, ω is the screw speed, ψ is the helix angle.
2. The prediction method according to claim 1, wherein the probability of breakage P (Bu x) of the fiber x having the fiber length L x during the preset blending extrusion is represented by the following formula:
P(Bux)＝1;Bux>1
Wherein, buckling parameter Bu x is expressed as:
Wherein eta is the viscosity of the fluid, For fluid shear rate, θ and/>Is the two orientation angles of the fiber x, the planes of the two orientation angles are perpendicular to each other, beta x is the half length-diameter ratio of the fiber x with the fiber length of L x, and E is the Young's modulus.
3. The prediction method according to claim 2, wherein the fracture probability P ij of the fiber j having the length L j to the fiber i having the length L i during the preset blending extrusion is represented by the following formula:
where m is a shape parameter and n is the total number of fiber length classifications.
4. The prediction method according to claim 1, wherein the initial fiber length distribution and the fiber length distribution at the completion of the blending extrusion process each satisfy the following conditions:
Li＝(n+1-i)×Ln；
Wherein L n is the length of the fiber which has the smallest length and cannot be broken, L 1 is the length of the fiber which has the largest length, and L i is the length of the fiber which has the length of L i, 1< i < n.
5. A fiber length distribution prediction apparatus for a blending 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 initial fiber length distribution to be subjected to a blending extrusion process as initial input of the prediction model, then sequentially carrying out fiber length distribution prediction processing on each shear rate value along the blending extrusion direction by using the prediction model, and taking a prediction result of the previous fiber length distribution as prediction processing input of the next fiber length distribution prediction until the fiber length distribution when the blending extrusion process is completed is obtained;
The predictive model is represented by the following formula:
Wherein m i is the mass fraction of fiber i having a fiber length of L i, m j is the mass fraction of fiber j having a fiber length of L j, P i is the probability of fiber i having a fiber length of L i breaking during a preset blending extrusion, P j is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion, P ij is the probability of fiber j having a fiber length of L j breaking during a preset blending extrusion into fiber i having a fiber length of L i, t is the residence time, and n is the total number of fiber length classifications;
the method for acquiring the flow field data corresponding to the preset blending extrusion process comprises the following substeps:
(101) Acquiring technological parameters, material physical property parameters and viscosity constitutive equations corresponding to a preset blending extrusion process, wherein the technological parameters comprise a machine barrel diameter, a thread inner diameter, a thread outer diameter, a thread pitch, a thread angle, a screw radial distance, a screw length, fluid axial pressure drop, fluid radial pressure drop, a screw rotating speed, the volume of melt passing through a screw unit in unit time and the filler mass of a material to be melt blended; the physical property parameters of the material 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 technological parameters and the viscosity constitutive equation as inputs of the global model to obtain a shear rate field of a preset blending extrusion process;
the blend extrusion global model is represented by the following formula:
Wherein R 1、R2 is the inner diameter and the outer diameter of a thread respectively, D is the diameter of a machine barrel, omega is the rotating speed of a screw, ψ is the helix angle, eta is the viscosity of fluid, and P x、Pθ is the axial pressure drop and the radial pressure drop of the fluid respectively; r is the radial distance of the screw rod, Is the shear rate;
(103) The residence times of the solid conveying zone, the molten partially filled zone and the fully filled zone in the preset blending extrusion process were calculated separately according to the following equation:
Where L is the screw length, B is the pitch, ρ is the density of the material to be melt blended, V is the volume of melt per unit time through the screw unit, Q is the filler mass of the material to be melt blended, ω is the screw speed, ψ is the helix angle.
6. An electronic device, the device comprising:
A processor;
A memory storing a computer-executable program comprising the method for predicting fiber length distribution in a blending extrusion process as in any one of claims 1-4.
7. A computer-readable storage medium having stored thereon a computer program, characterized in that the program comprises a method of predicting the fiber length distribution of a blend extrusion process as in any one of claims 1-4.
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| 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 |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| 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 |
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| Title |
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