Numerical Simulation Method for the Filling Process of the Composite Material RTM Process Based on the Nesting Effect

Abstract

The present invention discloses a numerical simulation method for the filling process of resin transfer molding, including: based on the VBA language, a set of permeability number combinations with discrete random distributions are formed by grouping and numbering multiple permeabilities measured in experiments, and the permeabilities in the set of permeability number combinations are randomly distributed to each unit feature area of the composite material component; setting molding process parameters and material parameters, and calculating the resin filling time and pressure distribution by using Darcy's law. This method takes into account the variability of permeability caused by the nesting effect during the filling process, making the filling time and the internal pressure distribution of the product obtained by the simulation of the filling process more accurate.

Description

Technical Field

[0001] The present invention belongs to the technical field of simulation and prediction of composite material liquid molding, and particularly relates to a numerical simulation method for the filling process of a composite material RTM process based on the nesting effect. Background Art

[0002] As one of the advanced preparation technologies for composite materials, the resin transfer molding process has received increasing attention due to its advantages of integration, intelligence, low cost, and high quality in manufacturing. To solve the problems of high cost and low efficiency caused by the need for a large number of experiments in setting die and process parameters, as well as the problems of possible defects such as dry spots and resin-rich areas in products, by means of simulation technology, the state and change law of resin in the mold cavity can be simulated, which can reduce the product development cost and improve the product quality.

[0003] During the mold closing and filling processes, due to the thickness-direction compression, the internal structure of the fiber preform changes, which causes the nesting effect and changes its permeability. However, the nesting effect has a certain spatial dispersion, resulting in variability in the preform permeability. Existing resin injection molding process simulations generally assume a homogeneous medium with a constant permeability, having a constant permeability value, which affects the model accuracy. The literature "Djebara Y, Imad A, Saouab A, Kanit T. A numerical modelling for resin transfer molding (RTM) process and effective thermal conductivity prediction of a particle–filled composite carbon–epoxy. Journal of Composite Materials, 2020, 55(1): 3-15." discloses the simulation of the flow of particle-reinforced carbon fiber epoxy composites during the RTM process based on the Stokes-Darcy coupling equation, and this model assumes a constant permeability. The literatures "Ding Y, Jia Y, Dong S, Xu Y. Non-isothermal simulation of resin transfer molding process with edge effect. Polymers and Polymer Composites, 2014; 22(3): 355-360." and "Yang W, Lu S, Xiang L, Liu W. Simulation of non-isothermal resin transfer molding process cycle and optimization of temperature system. Journal of Reinforced Plastics and Composites, 2019; 38(1): 3-14." disclose that the permeability used in the established non-isothermal resin filling process simulation models considering edge effects and process temperatures is still a constant.The literature "Okabe T, Oya, Y, Yamamoto G, Sato J, Matsumiya T, Matsuzaki R, Obayashi S. Multi-objective optimization for resin transfer molding process. Composites Part A: Applied Science and Manufacturing, 2017; 92: 1–9." discloses that the permeability involved in the multi-objective optimization method of RTM multi-point injection used to evaluate the optimal injection port position is a constant.

[0004] During the liquid composite molding process, the interaction between adjacent fabric preforms causes changes in their local structures, resulting in the nesting effect. The nesting effect has a certain spatial dispersion, so the permeability of the preform is variable. A single fixed permeability value cannot accurately reflect and predict the change in the permeation ability during the mold filling process of the fiber preform. Therefore, in the simulation of the resin filling process of the preform, it is urgent to design a random discrete distribution method of permeability that takes into account the influence of the local structure change of the preform to avoid inaccurate prediction of the mold filling time and pressure distribution. Summary of the Invention

[0005] The present invention provides a numerical simulation method for the resin mold filling process in the resin transfer molding process, which takes into account the permeability variability caused by the nesting effect during the mold filling process, making the mold filling time and the internal pressure distribution of the product obtained by the simulation of the mold filling process more accurate.

[0006] A numerical simulation method for the mold filling process of a composite material RTM process based on the nesting effect includes:

[0007] Step 1: Based on the VBA language, a set of permeability arrays with discrete random distributions are formed by multiple measured permeabilities according to the group numbers, and the permeabilities in the set of permeability arrays are randomly distributed to each unit feature area of the composite material component;

[0008] Step 2: Set the molding process parameters and material parameters, and use Darcy's law to calculate the resin filling time and the pressure distribution.

[0009] The present invention constructs a set of arrays with discrete random distributions based on multiple measured permeability values, and randomly distributes the permeability values to multiple unit feature areas of the composite material component according to the distribution of the occurrence frequencies of the permeability values, thereby taking into account the permeability variability caused by the nesting effect during the mold filling process in the simulation process, making the mold filling time and the internal pressure distribution of the product obtained by the simulation of the mold filling process more accurate.

[0010] The above-mentioned set of arrays of discrete random distributions formed by grouping multiple measured permeabilities according to group numbers based on the VBA language includes:

[0011] S1: The multiple permeability values are represented in the form of a permeability array {K} ({K1, K2... K n}), where n is the total number of group numbers, and the frequency of occurrence of the permeability values is represented by a first frequency array The total number of measurements N is obtained from formula (1):

[0012]

[0013] where i is the index of the group number;

[0014] S2: Generate N random numbers in the range [0, 1], which are represented in the form of a random array {r} ({r1, r2... r N}). The ranking of the random numbers in the random array is represented in the form of a random number ranking array {R} ({R1, R2... R N}). Divide the N random numbers into n groups, and form a random group number array {G} ({G1, G2... G N}) with the group numbers of the groups;

[0015] S3: Use the VBA language "Application.WorksheetFunction.CountIf(GN initial n, {G})" to calculate the number of occurrences of each permeability group number in the array {G} to obtain a second frequency array Calculate the difference GN between the first frequency array and the second frequency array diff , store the frequencies with a difference of "0" in the true frequency array {GN True}, store the frequencies with a difference greater than "0" as the first pseudo-frequencies in the first pseudo-frequency array, and store the multiple group numbers corresponding to the first pseudo-frequencies in the first pseudo-batch number array to obtain the first pseudo-label array {GN sum_diff_pos}, store the frequencies with a difference less than "0" as the second pseudo-frequencies in the second pseudo-frequency array, and store the multiple group numbers corresponding to the second pseudo-frequencies in the second pseudo-batch number array to obtain the second pseudo-label array {GN sum_diff_neg};

[0016] Obtain the total number of measurements N of the first pseudo-frequency diff_pos , and the total number of measurements N of the second pseudo-frequency diff_neg is:

[0017]

[0018] where i is the index of the frequency count;

[0019] S4: Generate N diff_pos random numbers in the range [0, 1], write them as an array and combine them with {GN sum_diff_pos} to form an array {A pos} ({{GN sum_diff_pos}, {r T}}). diff_pos} T )

[0020] Generate N diff_neg random numbers in the range [0, 1], write them as an array and combine them with {GN sum_diff_neg} to form an array {A neg} ({{GN sum_diff_neg}, {r T}}). diff_neg} T )

[0021] Use the VAB language ActiveWorkbook.Worksheets(Sheet).Sort to select {A pos} and {A neg}, and sort them in ascending order using {r diff_pos} T and {r diff_neg} T as the criteria. Then the elements in the arrays {GN sum_diff_pos} T and {GN sum_diff_neg} T will also be reordered to generate the arrays {GN cor_sum_diff_pos} and {GN cor_sum_diff_neg};

[0022] S5: Define N Loop as the number of loops, with an initial value of 1; randomly generate a fetch integer N md in the range [1, N] according to formula (3);

[0023] N rnd = Int(Rnd × N) + 1 (3)

[0024] where Rnd is a random number between [0, 1], and Int(·) is to obtain an integer.

[0025] The group number of the N md th group in the random group number array {G} is G rnd . Determine whether G rnd is equal to the array {GN cor_sum_diff_pos}N Loop The group number in, if not equal, regenerate N according to formula (3) md , if equal, use VBA language For Each G rnd in {GN True} to determine whether the array {GN True} stores the group number G rnd , if already stored, exit the loop and regenerate N according to formula (3) md , if not stored, replace the Nth group number in the random group number array {G} of the array with the group number of {GN md}N cor_sum_diff_neg}N Loop , exit the loop, and reassign N according to formula (4) Loop ;

[0026] N Loop = N Loop +1 (4)

[0027] S6: Regenerate N according to formula (3) md , repeat step S5 until the replacement of the group numbers of the array {GN cor_sum_diff_neg} is completed, generate the final random group number array {G final}, and use the VBA language Application.WorksheetFunction.VLookup to assign the permeability values to {G final} based on the correspondence between the permeability and the group number in the permeability array, and obtain the permeability number combination set {G K} that forms a discrete random distribution according to the group number.

[0028] Mesh the composite component based on its geometric characteristics to obtain a finite element model of the composite component, and establish the multiple unit feature regions according to the shape and size of the component.

[0029] The permeability number combination set includes multiple permeability values, the occurrence frequency of each permeability value and the group number. Different permeability values are assigned to the multiple unit feature regions according to the occurrence frequency of the permeability. To achieve the purpose of simulating the nesting effect, so as to be able to more accurately predict the filling time and the internal pressure of the product.

[0030] In step S2, divide the same number of random numbers as the permeability frequency N into n groups with the same number as the permeability group number, and obtain the random group number array {G} ({G1, G2... G N}) according to formula (5).

[0031] G i = Ri Mod n+1 (5)

[0032] Wherein, R i is the ranking of the i-th random number, and Mod is to find the remainder.

[0033] The described permeability is 0.614 - 4.127×10 -10 m 2 .

[0034] The described process parameters are the position and quantity of the glue injection / outlet, injection pressure, speed and temperature.

[0035] The described resin viscosity is 0.1 - 0.3 Pa·s.

[0036] Calculate the resin flow velocity V in the mold cavity using Darcy's law:

[0037]

[0038] Wherein, K is the permeability of the preform, μ is the resin viscosity, P is the pressure, is the gradient operator.

[0039] The described resin filling time is 11.8 - 58 s. It is relatively close to the actual resin filling time.

[0040] Compared with the prior art, the beneficial effects of the present invention are:

[0041] During the resin filling stage of the fabric preform, the interaction between adjacent layers causes random changes in the fabric thickness direction, resulting in the nesting effect. The internal flow path of the fabric changes, leading to significant differences in the penetration ability within the preform fabric. Compared with the assumption in the conventional resin transfer molding process simulation that the permeability is a constant value, the present invention realizes the random distribution of permeability to different unit sets of the fiber preform fabric, effectively solves the problem of permeability variability during the fabric forming process, improves the accuracy and reliability of the simulation results, and provides a theoretical basis for mold correction and process parameter optimization. Description of the Drawings

[0042] Figure 1 is the numerical simulation flow chart of the filling stage of the resin transfer molding process provided by the embodiment of the present invention;

[0043] Figure 2 is the flow chart of obtaining an array of internal units that conform to the actual distribution of permeability provided by the embodiment of the present invention;

[0044] Figure 3 is the schematic diagram of different unit characteristic regions of the composite member in the embodiment of the present invention;

[0045] Figure 4 Schematic diagram of the design of the glue injection / extrusion position and quantity in the embodiment of the present invention;

[0046] Figure 5 Schematic diagram of the resin filling time distribution in the embodiment of the present invention;

[0047] Figure 6 Schematic diagram of the pressure distribution in the embodiment of the present invention. Specific implementation manners

[0048] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0049] The present invention provides a simulation method for the resin filling process considering the nesting effect of the preform, and the overall technical solution is as Figure 1 shown. The specific steps are as follows:

[0050] Step 1, as Figure 2 shown, the specific steps are: establish a set of permeability number combinations in which the internal units conform to the discrete random distribution of the actual permeability by the method of numbering the permeability groups with the internal units:

[0051] As shown in Table 1, the in-plane permeability measurement values are expressed as a permeability array {K} ({K1, K2... K n}), the corresponding number of measurements, that is, the first frequency number array {GN initial}, and the total number of group numbers n corresponding thereto. First, calculate the final random group number array {G final} of the in-plane 1-direction permeability:

[0052] First, obtain the total number of measurements N in the in-plane 1 direction as: N = 88 according to formula (1)

[0053]

[0054] Table 1 Group numbers, measurement values and number of measurements of in-plane permeability

[0055]

[0056] Group N random numbers between [0, 1]. The random numbers are represented in the form of a random number array {r} ({r1, r2... r N}), the rankings of the random numbers in the random number array are represented in the form of a random number ranking array {R} ({R1, R2... R N}), divide the N random numbers into n groups, and obtain a random group number array {G} ({G1, G2... G N}) with group numbers inside. The i-th random group number Gi is:

[0057] G i = R i Mod n + 1(2)

[0058] where R i is the ranking of the i-th random number, and Mod is to find the remainder.

[0059] Use the VBA language "Application.WorksheetFunction. " to calculate the number of occurrences of each permeability group number in the array {G} to obtain the second frequency array In this embodiment, the second frequency array {GN process} is {7, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7}

[0060] Obtain the difference array according to formula (3) for judging whether the newly generated GN process is consistent with the actual measured value GN initial In this embodiment, the array {GN diff} is {-3, 1, 5, 2, 6, 3, 0, -3, -3, -3, -3, -2}

[0061]

[0062] where is the i-th difference in the difference array is the i-th frequency in the second frequency array is the i-th frequency in the first frequency array

[0063] If the cell value in {GN diff} is equal to 0, it means that the random number of occurrences of the group number conforms to the actual measured value, and the group number that conforms to the actual measurement is stored in the true frequency array {GN True}, in this embodiment the cell

[0064] If the cell value in {GN diff} is not equal to 0, obtain the first pseudo-frequency array {GN diff_pos} and the second pseudo-frequency array {GN diff_neg} according to formula (4), in this embodiment, the array {GN diff_pos} is {1, 5, 2, 6, 3}, {GN diff_neg} is {-3, -3, -3, -3, -3, -2}

[0065]

[0066] And store the group numbers corresponding to the first pseudo-frequency into the first pseudo-batch number array to obtain the first pseudo-label array {GN sum_diff_pos} as Store the group numbers corresponding to the second pseudo-frequency into the second pseudo-batch number array to obtain the second pseudo-label array {GN sum_diff_neg} as

[0067] Obtain the total number of measurements N that do not conform to the actual measured values according to formula (5) diff_pos , N diff_neg , in this embodiment N diff_pos = 17, N diff_neg = 17.

[0068]

[0069] Among them, i is the index of the frequency number, judge whether N diff_pos is equal to N diff_neg , if not equal, report an error, if equal, continue with the following operations, in this embodiment N diff_pos = N diff_neg .

[0070] Generate N diff_pos random numbers in the range of [0, 1], written as an array And combine it with {GN sum_diff_pos} to form an array {A pos} ({{GN sum_diff_pos} T , {r diff_pos} T}).

[0071] Generate N diff_neg random numbers in the range of [0, 1], written as an array And combine it with {GN sum_diff_neg} to form an array {A neg} ({{GN sum_diff_neg} T , {r diff_neg} T}).

[0072] Use the VAB language ActiveWorkbook.Worksheets(Sheet).Sort to select {A pos} and {A neg}, and sort them in ascending order with {r diff_pos} T and {r diff_neg} T as the criteria, then the array {GNsum_diff_pos} T and {GN sum_diff_neg} T Each unit in it will also be reordered to generate the array {GN cor_sum_diff_pos} as {4, 3, 5, 6, 3, 6, 3, 6, 5, 4, 5, 3, 5, 3, 5, 5, 2}, and {GN cor_sum_diff_neg} as {1, 11, 12, 11, 10, 8, 11, 9, 10, 9, 10, 1, 1, 12, 8, 9, 8};

[0073] Define N Loop as the number of cycles, with an initial value of 1; randomly generate a retrieval integer N within [1, N] according to formula (3) md ;

[0074] N rnd = Int(Rnd × N) + 1 (6)

[0075] where Rnd is a random number between [0, 1], and Int(·) is to find the integer;

[0076] The group number of the Nth group in the random group number array {G} is G md , determine whether G rnd is equal to the group number in the array {GN rnd cor _sum_diff_pos}N Loop md , if not equal, regenerate N according to formula (6) rnd , if equal, use the VBA language For Each G rnd in {GN True} to determine whether the array {GN True} stores the group number G rnd , if already stored, exit the loop and regenerate N according to formula (6) md , if not stored, replace the group number of the Nth group in the array random group number array {G} with the group number of {GN md}N cor_sum_diff_neg Loop , exit the loop, and reassign N according to formula (7) Loop Loop ;

[0077] N Loop = N Loop + 1 (7)

[0078] Use formula (6) to repeatedly generate random numbers until all units of the array {GN cor_sum_diff_neg} are changed, generating the final random group number array {G final}, and use the VBA language Application.WorksheetFunction.VLookup. Based on the correspondence between the permeability and the group number in the permeability array, assign the permeability values to {G final} to obtain a set of permeability value arrays {G K} that are discretely and randomly distributed according to the group number.

[0079] Step 2: In the embodiment of the present invention, based on the geometric characteristics of the composite material component, perform mesh division to establish its finite element model. According to the shape and size of the component, establish the multiple unit feature regions, that is, the unit set. In the embodiment of the present invention, the effective size of the composite material component is 100mm×100mm×1mm, and 25 different unit sets are established, as Figure 3 shown.

[0080] The set of permeability value arrays includes multiple permeability values, the frequency of occurrence of the permeability value, and the group number. Different permeabilities are assigned to the multiple unit sets according to the frequency of occurrence of the permeability. In the embodiment of the present invention, the in-plane permeability values of different unit sets are shown in Table 2

[0081] Table 2 In-plane permeability values are randomly assigned to different unit sets

[0082]

[0083] The specific process of Step 3 is as follows:

[0084] Step 3.1: Input material parameters. In this embodiment, it is necessary to input the permeability value and the relevant property values of the fiber and resin.

[0085] Step 3.2: Design the position and number of the injection / gel outlet, injection pressure, speed, and temperature. In this embodiment, injection is performed at the center point of the composite material component under room temperature conditions, as Figure 4 shown for the position and number of the injection ports in this embodiment. Table 3 shows the numerical simulation parameters for the resin filling process.

[0086] Table 3 Numerical simulation parameters for the filling process

[0087] Injection pressure (MPa) 0.6 Resin viscosity (Pa.s) 0.3

[0088] Step 3.3: Submit the solution processor, and use Darcy's law to obtain the filling time and pressure distribution of the resin in the mold cavity in this embodiment, Figure 5 and Figure 6 are the contour map of the resin filling time distribution and the pressure distribution contour map when the resin filling is completed in this embodiment, respectively. Although the injection port is at the center position of the composite material component, Figure 5It shows that since the permeability is not a single constant value but a random distribution, the resin filling time is not a completely symmetric distribution but an approximately symmetric distribution. In this embodiment, the resin filling time is 39 seconds.

Claims

1. A numerical simulation method for the filling process of the RTM process of a composite material based on the nesting effect, characterized in that, Including: Step 1: Based on the VBA language, multiple measured permeabilities are grouped according to the group number to form a combined set of permeabilities with discrete random distribution, and the permeabilities in the combined set of permeabilities are randomly distributed to each unit feature area of the composite material component; Step 2: Set the molding process parameters and material parameters, and use Darcy's law to calculate the resin filling time and pressure distribution; Based on the geometric characteristics of the composite material component, mesh division is performed to obtain its finite element model, and the multiple unit feature areas are established according to the shape and size of the component; The combined set of permeabilities includes multiple permeability values, the occurrence frequency of each permeability value and the group number, and different permeability values are assigned to multiple unit feature areas according to the occurrence frequency of the permeability; 2. The numerical simulation method for the mold filling process of the composite material RTM process based on the nesting effect according to claim 1, wherein The method of forming a combined set of numbers with discrete random distribution by grouping multiple measured permeabilities according to the group number based on the VBA language includes: S1: Multiple permeability values are represented in the form of a permeability array {K} (K1, K2... Kn), where n is the total number of group numbers, and the occurrence frequency of the permeability values is represented by the first frequency array n}, and the total number of measurements N is obtained from formula (1): ​ where i is the index of the group number; S2: Generate N random numbers in the range of [0, 1], which are represented in the form of a random number array {r} ({r1, r2...... r N}), represent the ranking of the random numbers in the random number array in the form of a random number ranking array {R} ({R1, R2...... R N}), divide the N random numbers into n groups, and form the group numbers into a random group number array {G} ({G1, G2...... G N}); S3: Use the VBA language "Application.WorksheetFunction.CountIf(GN initial n,{G})" to calculate the number of occurrences of each permeability group number in the array {G} to obtain the second frequency array Calculate the difference between the first frequency array and the second frequency array GN diff , store the frequencies with a difference of "0" in the true frequency array {GN True}, store the frequencies with a difference greater than "0" as the first pseudo-frequencies in the first pseudo-frequency array, and store the multiple group numbers corresponding to the first pseudo-frequencies in the first pseudo-batch number array to obtain the first pseudo-label array {GN sum_diff_pos}, store the frequencies with a difference less than "0" as the second pseudo-frequencies in the second pseudo-frequency array, and store the multiple group numbers corresponding to the second pseudo-frequencies in the second pseudo-batch number array to obtain the second pseudo-label array {GN sum_diff_neg}; The total number of measurements N for the first spurious frequency count diff_pos , and the total number of measurements N for the second spurious frequency count diff_neg is as follows: where i is the index of the frequency number; S4: Generate N diff_pos random numbers in the range of [0, 1], written as an array and combine them with {GN sum_diff_pos} to form an array {A pos} ({{GN sum_diff_pos} T , {r diff_pos} T}); Generate N diff_neg random numbers in the range [0, 1], written as an array and combine them with {GN sum_diff_neg} to form an array {A neg} ({{GN sum_diff_neg} T , {r diff_neg} T}); Using the VBA language, ActiveWorkbook.Worksheets(Sheet).Sort is used to select {A pos} and {A neg}, and sort them in ascending order with {r diff_pos} T and {r diff_neg} T as the standards respectively. Then, each cell in the arrays {GN sum_diff_pos} T and {GN sum_diff_neg} T will also be reordered to generate the arrays {GN cor_sum_diff_pos} and {GN cor_sum_diff_neg}; S5: Define N Loop as the number of cycles, with an initial value of 1; randomly generate a retrieval integer N within the range of [1, N] according to formula (3) md ; N rnd = Int(Rnd × N) + 1 (3) where Rnd is a random number between [0, 1], and Int(·) is to obtain an integer; The Nth group number in the random group number array {G} md is G rnd . Determine whether G rnd is equal to the group number in the array {GN cor _sum_diff_pos}N Loop . If not equal, regenerate N according to formula (3) md ; if equal, use VBA language For Each G rnd in {GN True} to determine whether the array {GN True} stores the group number G rnd . If it has been stored, exit the loop and regenerate N according to formula (3) md . If not stored, replace the Nth group number in the random group number array {G} with the group number of {GN md}N cor_sum_diff_neg . Exit the loop and reassign N according to formula (4) Loop ; Loop ​ N Loop = N Loop +1 (4) S6: Regenerate N according to formula (3) md , repeat step S5 until the replacement of the group numbers in the array {GN cor_sum_diff_neg} is completed, generate the final random group number array {G final}, and use the VBA language Application.WorksheetFunction.VLookup to assign the permeability values to {G final} based on the correspondence between the permeability and the group numbers in the permeability array, obtaining the permeability number combination set {G K} that forms a discrete random distribution according to the group numbers.

3. The numerical simulation method for the mold filling process of the composite material RTM process based on the nesting effect according to claim 2, characterized in that In step S2, the i-th random group number G N in the random group number array {G} ({G1, G2... G i}) is as follows: G i = R i Mod n+1 (5) Among them, R i is the ranking of the i-th random number, and Mod is to find the remainder.

4. The numerical simulation method for the filling process of the composite material RTM process based on the nesting effect according to claim 1, wherein, The described permeability value is 0.614 - 4.127 10 -10 m 2 .

5. The numerical simulation method for the filling process of the composite material RTM process based on the nesting effect according to claim 1, characterized in that, The process parameters are the position and quantity of the injection / gel outlet, injection pressure, speed and temperature; 6. The numerical simulation method for the mold filling process of the composite material RTM process based on the nesting effect according to claim 1, wherein Use Darcy's law to calculate the resin flow velocity V in the mold cavity: where K is the permeability of the preform, μ is the resin viscosity, and P is the pressure, is the gradient operator.

7. The numerical simulation method for the mold filling process of the composite material RTM process based on the nesting effect according to claim 6, characterized in that, The resin viscosity is 0.1 - 0.3 Pa·s.

Images