A finite element modeling method for simulating the drop of a corrugated box

Abstract

The application provides a corrugated box finite element modeling method for simulating package falling, comprising the following steps: S1: determining equivalent elastic mechanics parameters of corrugated paperboard; S2: verifying whether the equivalent plate anisotropic elastic mechanics parameters are accurate, and if yes, entering S3, otherwise, returning to S1 until the equivalent plate anisotropic elastic mechanics parameters pass the verification; S3: establishing a paper box geometric model, decomposing the paper box into six surfaces of upper, lower, left, right, front and back, modeling each surface by adopting a shell element, and setting topology sharing; S4: respectively giving each surface of the paper box corresponding material properties; S5: dividing the paper box grid model by adopting a quadrilateral, and completing contact setting of the paper box and other PART, setting boundary conditions and load, and solving setting. The method solves the problem that the simulation calculation result of the package falling is not accurate and reliable due to the modeling error of the paper box by combining mechanical test and theoretical formula.

Description

Technical Field

[0001] This invention relates to the field of drop simulation analysis technology, specifically to a finite element modeling method for simulating the drop of packaging components onto corrugated cardboard boxes. Background Technology

[0002] Currently, drop simulation technology for product packaging structures is widely used and highly accepted. Compared to drop tests on packaging, it saves testing costs and shortens the testing cycle, effectively improving the efficiency of product and packaging structure design. However, as a computational method, the accuracy and realism of simulation results are highly dependent on the input data. The more accurate the input data, the closer the simulation results are to the real-world situation, and the more accurately the analysis results reflect the actual circumstances.

[0003] As an important cushioning packaging structure, corrugated cardboard boxes significantly impact the accuracy and realism of drop simulation results in packaging simulation analysis. Since the actual structure of a corrugated cardboard box includes both the linerboard and the corrugated core, modeling it according to its actual geometry would be too laborious. Therefore, corrugated cardboard is generally simplified to an equivalent homogeneous board, making the selection of material parameters for this equivalent board crucial.

[0004] The two common constitutive models and mechanical parameter selection methods for equivalent plates are as follows:

[0005] 1) Treat the equivalent plate as an isotropic material and select an ideal elastoplastic or bilinear elastoplastic constitutive model to describe its mechanical deformation behavior;

[0006] 2) Treat the equivalent plate as an anisotropic material, and the constitutive model is an anisotropic elastic constitutive model. Consult the literature and calculate each elastic parameter according to the equivalent formula.

[0007] The two commonly used methods mentioned above actually have some shortcomings. First, due to the special nature of its structure, corrugated cardboard actually exhibits anisotropic mechanical properties. Moreover, the drop test conditions usually include six sides, three edges, and one corner. The mechanical properties of cardboard vary depending on the drop location. It is definitely incorrect to use isotropic material constitutive model to describe the mechanical deformation behavior of corrugated cardboard.

[0008] Secondly, the equivalent board elastic parameters calculated using Method 2 are usually greater than the experimental values. This is mainly because there are some defects in the corrugated cardboard production process, which affect the reliability of the cardboard. The parameter values ​​calculated by the equivalent formula do not take these factors into account, hence the equivalent parameters are greater than the experimental values. If these equivalent mechanical parameters are used in simulation analysis, it may lead to an overestimation of the carton stiffness and an underestimation of the deformation during the drop, resulting in a lower energy absorption capacity and affecting the simulation calculation results. Summary of the Invention

[0009] The purpose of this invention is to provide a finite element modeling method for simulating the drop of packaged goods onto corrugated cardboard boxes, thereby addressing the technical problems existing in the background art.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] A finite element modeling method for simulating the drop of packaging materials into corrugated cardboard boxes includes the following steps:

[0012] S1: Determine the equivalent elastic mechanical parameters of corrugated cardboard;

[0013] S2: Verify whether the anisotropic elastic mechanical parameters of the equivalent plate are accurate. If the verification is successful, proceed to S3; otherwise, return to S1 until the anisotropic elastic mechanical parameters of the equivalent plate are verified.

[0014] S3: Establish the geometric model of the cardboard box, decompose the cardboard box into six faces: top, bottom, left, right, front, and back. Each face is modeled using shell elements and topology sharing is set.

[0015] S4: Assign the corresponding material properties to each side of the cardboard box;

[0016] S5: Use quadrilaterals to divide the cardboard box mesh model, complete the contact settings between the cardboard box and other parts, set boundary conditions and loads, and set the solution.

[0017] In some embodiments, S1: determining the equivalent elastic mechanical parameters of corrugated cardboard includes: preparing corrugated cardboard samples, measuring the thickness and mass of the corrugated cardboard samples, performing flat crush tests, edge crush tests and side crush tests on the corrugated cardboard samples respectively, calculating the elastic modulus of the equivalent board according to the load-displacement curve, and consulting literature to calculate the Poisson's ratio and shear modulus of the equivalent board.

[0018] In some embodiments, the corrugated cardboard samples in S1 include three groups: flat crush test samples, edge crush test samples, and side crush test samples, with at least 10 samples in each group, and the thickness and quality of the corrugated cardboard are measured before the test.

[0019] In some embodiments, the method for determining the thickness of corrugated cardboard in S1 is to randomly select 5 points on each cardboard to measure the thickness of the cardboard, then take the average of the 5 thickness values, and finally take the average of the thickness values ​​of 10 cardboards. This average is taken as the thickness of the cardboard, and it is assumed that the equivalent board thickness is the same as the cardboard thickness. The method for determining the density of cardboard is to weigh 10 samples respectively and take the average value, and divide the mass by the volume of the cardboard to obtain the density value of the cardboard.

[0020] In some embodiments, the flat crush test, edge crush test, and lateral crush test of the corrugated cardboard in S1 are all performed on a universal testing machine. After the test, the load-displacement curve is obtained. Substituting the cross-sectional dimensions of the sample, the three elastic moduli of the corrugated cardboard are calculated. Based on the numerical relationship between the elastic modulus, Poisson's ratio, and shear modulus, and combined with relevant literature, the Poisson's ratio and shear modulus of the corrugated cardboard are calculated. The above values ​​are the nine elastic mechanical parameters of the equivalent board of the corrugated cardboard.

[0021] In some embodiments, step S2: verifying the accuracy of the anisotropic elastic mechanical parameters of the equivalent plate includes: firstly, conducting a compressive strength test on the corrugated cardboard box; after the test, observing the deformation of the cardboard box and obtaining the load-displacement curve of the upper pressure plate; then, simulating the compressive strength test process of the cardboard box using the finite element method; the constitutive model of the cardboard box adopts anisotropic elastic constitutive model; the deformation cloud diagram of the cardboard box and the load-displacement curve of the pressure plate are obtained through simulation calculation; the simulation calculation results are compared with the test results; if the two are in good agreement, it indicates that the constitutive model and elastic mechanical parameters are reasonably selected; this set of material constitutive models and parameters can be used in the subsequent drop simulation analysis of the packaging. If the verification fails, it is necessary to return to step S1 to readjust the material parameters until the verification passes.

[0022] In some embodiments, S3: Establish a geometric model of the carton; firstly, decompose the packaging carton into six sides: top, bottom, left, right, front, and back, and model them using shell units respectively; then assemble the six sides of the carton into a whole and set up topology sharing.

[0023] In some embodiments, S4: assigning corresponding material properties to each face of the carton; including creating a local coordinate system on the carton, then setting the anisotropic elastic mechanical parameters of the six faces in the local coordinate system, and then assigning material cards to each face.

[0024] In some embodiments, quadrilateral units are used to divide the carton grid in step S5, and common nodes are achieved at the connection positions between faces.

[0025] In some embodiments, the carton-related settings in the packaging drop finite element model in S5 also include settings such as contact, initial conditions, boundary conditions, load, and solution control parameters.

[0026] Beneficial effects

[0027] The significant advantages of this invention compared to existing technologies are:

[0028] This invention provides a finite element modeling method for corrugated cardboard boxes used to simulate drop tests on packaging. The mechanical parameters of the cardboard material in this method are primarily derived from mechanical experiments, and the accuracy of the constitutive model and parameters is verified through simulation of cardboard box compression tests. The invention also describes the modeling method for the cardboard box's geometric model and the method for assigning material properties. The accurate establishment of the finite element model of the cardboard box can effectively improve the computational accuracy of drop simulation analysis of packaging, which is beneficial for drop strength analysis and structural optimization design of product and packaging structures. Attached Figure Description

[0029] Figure 1 Flowchart of finite element modeling for corrugated cardboard.

[0030] Figure 2 Comparison of the compression test results of corrugated cardboard boxes with the simulation test results.

[0031] Figure 3 A schematic diagram of the local coordinate system of a corrugated cardboard box when the packaging edge falls. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0033] Conversely, this application covers any substitutions, modifications, equivalent methods, and schemes made within the spirit and scope of this application as defined in the claims. Furthermore, to provide the public with a better understanding of this application, certain specific details are described in detail below. However, this application can be fully understood by those skilled in the art even without these detailed descriptions.

[0034] The following will combine Figure 1-3 This application provides a detailed description of a finite element modeling method for simulating package drop scenarios involving corrugated cardboard boxes, as described in the embodiments of this application. It is worth noting that the following embodiments are merely illustrative of this application and do not constitute a limitation thereof.

[0035] A finite element modeling method for simulating package drop testing of corrugated cardboard boxes includes the following steps:

[0036] S1: Prepare corrugated cardboard samples, determine the thickness and mass of the cardboard, and conduct flat crush test, edge crush test and side crush test on the corrugated cardboard samples respectively. Calculate the elastic modulus of the corrugated cardboard according to the load-displacement curve, and consult the literature to calculate the Poisson's ratio and shear modulus of the cardboard.

[0037] First, prepare 3 sets of BC-type double-wall corrugated cardboard samples. The sample dimensions and quantity are as follows:

[0038] 1) Cut the specimens to a size of (100±0.5)mm×(100±0.5)mm, and make at least 10 specimens as specimens for flat pressure test;

[0039] 2) Cut rectangular specimens with the corrugated direction as the short side, with dimensions of (100±0.5)mm×(25±0.5)mm, and at least 10 specimens should be used as edge crush test specimens;

[0040] 3) Cut rectangular specimens with the corrugated direction as the long side, with dimensions of (100±0.5)mm×(25±0.5)mm, and at least 10 specimens should be used as specimens for the lateral pressure test.

[0041] The above-mentioned samples can be used directly when measuring the thickness and quality of corrugated cardboard.

[0042] The thickness of corrugated cardboard was determined by selecting the second group of samples mentioned above. First, the thickness values ​​at any 5 points on the cardboard were measured using an electronic vernier caliper. The average of the 5 thickness values ​​was taken as the thickness of the corresponding cardboard. Then, the average of the thicknesses of the 10 cardboard samples was calculated and taken as the cardboard thickness. It was assumed that the equivalent board thickness was the same as the cardboard thickness.

[0043] The density of corrugated cardboard was determined by selecting the first group of samples mentioned above. Ten samples were weighed using an electronic analytical balance (accuracy of 0.1 mg) and the average value was taken. The density of the cardboard was obtained by dividing the mass by the volume of the cardboard.

[0044] Furthermore, flat compression, edge compression, and lateral compression tests were conducted on the corrugated cardboard using a universal testing machine at a compression speed of (12.5±2.5) mm / min. Load-displacement curves were obtained after the tests. These curves were then converted into engineering stress-strain curves, where the engineering stress value is the load divided by the area of ​​the corrugated cardboard's compression surface. Based on the definition of the modulus of elasticity, the slope of the linear elastic segment of the engineering stress-strain curve was taken as the modulus of elasticity. Using the relationship between the modulus of elasticity, Poisson's ratio, and shear modulus, and in conjunction with relevant literature, the Poisson's ratio and shear modulus of the corrugated cardboard were calculated using empirical formulas, as shown below: μ yz =μ xz =0.01; At this point, all nine anisotropic elastic mechanical parameters of the corrugated cardboard equivalent board have been obtained.

[0045] S2: To verify the accuracy of the anisotropic elastic mechanical parameters of the cardboard, first prepare a corrugated cardboard box sample and conduct a compression test on a cardboard box compression testing machine. The loading speed is set to 10 mm / min. After the test, record the load-displacement curve of the pressure plate and the deformation state of the cardboard box. Next, use the finite element method to simulate the compression strength test process of the corrugated cardboard box. The simulation software is the ANSYSLS_DYNA module. The cardboard box is modeled using a homogeneous equivalent plate, and the constitutive model of the cardboard box is selected as an anisotropic elastic constitutive model. The material mechanical parameters refer to the mechanical parameter values ​​in step S1. After the simulation calculation, extract the load-displacement curve of the pressure plate and the deformation cloud map of the corrugated cardboard box. Compare the simulation calculation results with the experimental results. If the simulation results match the experimental results well, it indicates that the constitutive model of the equivalent plate material and the selection of material parameters are reasonable. Otherwise, return to step S1 to adjust the material parameters until the simulation calculation results match the experimental results well.

[0046] Figure 2 The diagram shows a comparison between simulation and experimental results. The load-displacement curves indicate that the simulated maximum load the carton can withstand is close to the experimental value. The significant difference in displacement value corresponding to the maximum crushing force is mainly due to the fact that the pressure plate and the carton were not in complete contact at the beginning of the compression test, resulting in an experimental displacement value greater than the simulated displacement value. Based on the above comparative analysis, it can be concluded that the simulation results are relatively close to the experimental results.

[0047] S3: The geometric model of the corrugated cardboard box was created using the pre-processing software SpaceClaim for drop simulation analysis of the packaging. Since corrugated cardboard exhibits anisotropic material mechanical properties, and the corrugation orientations differ on each face of the box, material properties need to be assigned to each face separately. The box was decomposed into six faces: top, bottom, left, right, front, and back. Each face was modeled using shell elements, and its thickness was set. After modeling, the six parts were assembled together, and the properties were modified to share topology. The main purpose of this operation was to ensure that faces share nodes during mesh generation.

[0048] S4: This step assigns material properties to the cardboard box. Since the corrugated directions of the top and bottom cardboard are the same, the left and right cardboard are the same, and the front and back cardboard are also the same, three local coordinate systems are first established on the corrugated cardboard box, such as... Figure 3 As shown, the X and Y axes of local coordinate system 1 are perpendicular and parallel to the corrugated directions of the front and rear cardboard of the carton, respectively. Similarly, the X and Y axes of local coordinate system 2 are perpendicular and parallel to the corrugated directions of the left and right cardboard, respectively. The X and Y axes of local coordinate system 3 are perpendicular and parallel to the corrugated directions of the top and bottom cardboard of the carton, respectively. Material cards are created for each of the six faces of the carton, and an anisotropic elastic constitutive model is selected. Since each of the six faces of the carton has a corresponding local coordinate system, the material mechanical parameters are input into the local coordinate system, and then the material cards are assigned to the corresponding PARTs.

[0049] S5: A finite element model of the packaging component's drop test is established in the ANSYS LS_DYNA module. Since this invention focuses on the finite element modeling method for the cardboard box, other components of the packaging are not described in detail. First, quadrilateral elements are used to mesh the cardboard box. Then, frictional contact is established between the cardboard box and the packaging padding, the product, and the rigid surface, with a friction coefficient of 0.2. Next, initial velocities and gravitational accelerations are applied to the cardboard box and other packaging components. Fixed constraints are applied to the rigid surface. In this implementation, the drop height of the packaging is H = 600 mm, so the initial velocity is v = 3430.44 mm / s. Finally, the solution control parameters are set, the solution time is 0.04 s, the mass scaling factor is turned on, and the output settings are modified.

[0050] Therefore, the equivalent board elastic mechanical parameters were determined using the corrugated cardboard compression mechanics test method, and the correctness of the constitutive model and material parameters was verified by comparing the results with the carton compression resistance test results. Furthermore, the differences in mechanical properties of each surface were considered when establishing the carton's geometric model. By establishing a finite element model of the carton using the method of this invention, the drop mechanics of the carton is made closer to reality, thereby effectively improving the calculation accuracy of drop simulation analysis of packaging components. This is beneficial for drop strength analysis and structural design optimization of product and packaging structures.

[0051] This patent primarily addresses the finite element modeling method for corrugated cardboard boxes in drop simulation analysis of packaging. Current drop simulation analyses often neglect the impact of cardboard box modeling errors on the simulation results. The essence of this patented method is to combine mechanical testing methods to make the material parameters of the equivalent board more accurate. Compared to existing finite element modeling methods for equivalent boards, this patent obtains the elastic mechanical parameters of the equivalent board through cardboard compression mechanics tests, which have been verified through simulated cardboard box compression tests. When establishing the cardboard box's geometric model, the anisotropic mechanical properties of the cardboard are fully considered, thus decomposing the cardboard box into six faces for modeling and assigning material properties to each face, resulting in more accurate and realistic performance of the cardboard box in drop simulation calculations.

[0052] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A finite element modeling method for simulating package drop in corrugated cardboard boxes, characterized in that, Includes the following steps: S1: Determine the equivalent elastic mechanical parameters of corrugated cardboard; S2: Verify whether the anisotropic elastic mechanical parameters of the equivalent plate are accurate. If the verification is successful, proceed to S3; otherwise, return to S1 until the anisotropic elastic mechanical parameters of the equivalent plate are verified. S3: Establish the geometric model of the cardboard box, decompose the cardboard box into six faces: top, bottom, left, right, front, and back. Each face is modeled using shell elements and topology sharing is set. S4: Assign the corresponding material properties to each side of the cardboard box; S5: Use quadrilaterals to divide the cardboard box mesh model, complete the contact settings between the cardboard box and other parts, set boundary conditions and loads, and set the solution settings; S1: Determine the equivalent elastic mechanical parameters of corrugated cardboard; including: preparing corrugated cardboard samples, measuring the thickness and mass of the corrugated cardboard samples, conducting flat crush tests, edge crush tests and side crush tests on the corrugated cardboard samples respectively, calculating the elastic modulus of the equivalent board according to the load-displacement curve, and calculating the Poisson's ratio and shear modulus of the equivalent board. The method for determining the thickness of corrugated cardboard in S1 is to randomly select 5 points on each cardboard to measure the thickness, then take the average of the 5 thickness values, and finally take the average of the thickness values ​​of 10 cardboards. This average is taken as the cardboard thickness, and it is assumed that the equivalent board thickness is the same as the cardboard thickness. The method for determining the density of cardboard is to weigh 10 samples respectively and take the average value. The density value of the cardboard is obtained by dividing the mass by the volume of the cardboard. The flat crush test, edge crush test and side crush test of the corrugated cardboard in S1 are all carried out on a universal testing machine. After the test, the load-displacement curve is obtained. Substitute the cross-sectional dimensions of the sample to calculate the three elastic moduli of the corrugated cardboard. Based on the numerical relationship between the elastic modulus, Poisson's ratio and shear modulus, the Poisson's ratio and shear modulus of the corrugated cardboard are calculated. The above values ​​are the nine elastic mechanical parameters of the equivalent board of the corrugated cardboard. S2: Verifying the accuracy of the anisotropic elastic mechanical parameters of the equivalent plate includes: firstly, conducting a compressive strength test on the corrugated cardboard box; after the test, observing the deformation of the cardboard box and obtaining the load-displacement curve of the upper pressure plate; then, simulating the compressive strength test process of the cardboard box using the finite element method; the constitutive model of the cardboard box adopts anisotropic elastic constitutive model; the simulation calculation obtains the deformation cloud map of the cardboard box and the load-displacement curve of the pressure plate; comparing the simulation calculation results with the test results; if the two match well, it indicates that the constitutive model and elastic mechanical parameters are reasonably selected, and the constitutive model and elastic mechanical parameters can be used in the subsequent drop simulation analysis of the packaging. If the verification fails, it is necessary to return to step S1 to readjust the material parameters until the verification passes.

2. The finite element modeling method for simulating package drop of corrugated cardboard boxes according to claim 1, characterized in that, The corrugated cardboard samples in S1 include three groups: flat crush test samples, edge crush test samples, and side crush test samples. Each group contains at least 10 samples, and the thickness and quality of the corrugated cardboard are measured before the test.

3. The finite element modeling method for simulating package drop of corrugated cardboard boxes according to claim 1, characterized in that, S3: Establish the geometric model of the carton; first, decompose the packaging carton into six sides: top, bottom, left, right, front, and back, and build each side using shell units. Then, assemble the six sides of the carton into a whole and set up topology sharing.

4. The finite element modeling method for simulating package drop of corrugated cardboard boxes according to claim 1, characterized in that, S4: Assign corresponding material properties to each face of the carton; including creating a local coordinate system on the carton, then setting the anisotropic elastic mechanical parameters of the six faces in the local coordinate system, and then assigning material cards to each face.

5. The finite element modeling method for simulating package drop of corrugated cardboard boxes according to claim 1, characterized in that, In S5, quadrilateral units are used to divide the carton grid, and common nodes are achieved at the connection positions between faces.

6. The finite element modeling method for simulating package drop of corrugated cardboard boxes according to claim 1, characterized in that, The S5 packaging drop finite element model also includes settings for contact, initial conditions, boundary conditions, loads, and solution control parameters.

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