A forming test method for sandwich cushioning structure based on fractal theory

Abstract

The present invention discloses a sandwich buffer structure forming test method based on fractal theory. It includes the following steps: S1, constructing a Hilbert fractal sandwich buffer structure model using Hilbert fractal theory; S2, preparing a Hilbert fractal sandwich buffer structure model; S3, conducting a uniaxial quasi-static compression test; S4, conducting a dynamic impact test; S5, obtaining material mechanical data based on static tensile test, and inputting it into finite element analysis software; S6, establishing a method for simulating the use of thermoplastic polyurethane materials in finite elements; S7, establishing a three-dimensional model using modeling software, and inputting it into simulation software for finite element simulation; S8, obtaining the ability to absorb energy during compression. The advantage is that the purpose of superimposed energy absorption can be achieved, thereby completely solving the technical problem of poor force bearing in the current honeycomb sandwich structure, and greatly expanding the scope of application.

Description

Technical Field

[0001] The invention relates to a sandwich structure for transport packaging, in particular to a sandwich buffer structure forming test method based on fractal theory. Background Art

[0002] Transport packaging refers to a storage method that exists to protect products and facilitate storage and transportation during logistics transportation. During transportation, there will inevitably be transportation bumps that cause certain damage or destruction to the products. Therefore, in order to avoid product damage caused by excessive impact and vibration during transportation, designing a reasonable cushioning packaging for the product plays a vital role in the transportation of the product. For this reason, various cushioning packaging designs have appeared on the market. In the prior art, conventional cushioning packaging is usually composed of an outer packaging container, a cushioning medium, and an inner product. The design of the cushioning medium is the core, which is used to support the wrapped product and cushion the product. Cushioning packaging is classified according to quality into fiber, foam, air bag structure, and spring. Fiber mainly includes paper fiber materials, etc. Foam The main types are foam plastics, etc. Cushioning packaging needs to have good physical and chemical properties: good elasticity and recovery, the ability to return to the original state after the force is removed, good cushioning performance, the ability to absorb and consume the energy of external vibration and impact, a certain degree of resistance to breakage, maintaining the shape of the cushioning material, good temperature and humidity stability, maintaining the basic properties of the material under different working conditions, good chemical stability, in order to prevent pollution to the product, good moisture absorption resistance, and the ability to maintain the performance of the material. However, in addition to the buffer medium as a factor in the performance of cushioning packaging, its buffer structure design has a more important impact on its performance. The existing conventional buffer structures are usually similar to honeycomb structures. This conventional structure, due to its single structure, cannot be superimposed on energy absorption, limiting its scope of application. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a sandwich buffer structure forming test method based on fractal theory which can not only fully absorb and consume external vibration impact energy but also has excellent elasticity and recovery.

[0004] In order to solve the above technical problems, the sandwich buffer structure forming test method based on fractal theory of the present invention comprises the following steps:

[0005] S1. Hilbert fractal parametric modeling: Modeling is done using L system language and Python language, thereby achieving parametric design and recursion. Hilbert fractal theory can be used to construct a Hilbert fractal sandwich buffer structure model consisting of a top plate, a bottom plate and a Hilbert fractal structure between the top plate and the bottom plate.

[0006] S2. Model 3D printing: Using the light curing method, a Hilbert fractal sandwich cushioning structure model is prepared using thermoplastic polyurethane material;

[0007] S3. Static compression test of the model: a uniaxial quasi-static compression test is performed on the Hilbert fractional core-sandwich cushioning structure model using a testing machine;

[0008] S4. Dynamic impact test of the model: A dynamic impact test is performed on the Hilbert fractal sandwich cushioning structure model using a dynamic impact tester;

[0009] S5. Uniaxial tensile test of the model: obtain material mechanical data based on static tensile test and input into finite element analysis software;

[0010] S6, constructing a constitutive model of the thermoplastic polyurethane material based on step S5, and using the constitutive model of the thermoplastic polyurethane material to simulate the use of the thermoplastic polyurethane material in the finite element method;

[0011] S7. Finite element model establishment of the model: using modeling software to establish a three-dimensional model, and inputting it into simulation software for finite element simulation;

[0012] S8. Through the energy absorption analysis of the model, the energy absorption capacity of the Hilbert fractal sandwich cushioning structure model during compression is obtained.

[0013] In step S1, the L system consists of a triple<V,ω,P> Composition, whose items are defined as:

[0014] V={L,R,F,+,-}

[0015] ω=L

[0016] P={L→+RF-LF;-FR+, R→-LF+RFR+FL-}

[0017] In step S1, the Hilbert curve is expressed using the L system language. The drawing of the Hilbert curve is a process of continuously applying rules to symbols. Each order of the Hilbert curve can be expressed by L, F, and R in the L system, which is specifically expressed as follows:

[0018] S1=L

[0019] S2=+RF-LFL-FR+

[0020] S3=+-LF+RFR+FL-F-+RF-LFL-FR+F+RF-LFL-FR+-F-LF+RFR+FL-+.

[0021] In step S2, the printing temperature is 20-30°C, the printed layer thickness is 0.1-0.3 mm, the single layer exposure time is 5-15 s, and the exposure intensity is 7-12 mW / cm 2 .

[0022] In step S3, the speed of the uniaxial quasi-static compression test is set to 10-15 mm / min.

[0023] In step S4, a mass block is dropped in a dynamic impact test to test the Hilbert fractal structure. The mass blocks used are 1.1 kg, 2.2 kg, 3 kg, and 4.1 kg, and the drop heights are 10 cm, 20 cm, 30 cm, and 40 cm, respectively.

[0024] In step S6, the constitutive model of the thermoplastic polyurethane material is established by the formula:

[0025]

[0026] The specific constants obtained from the uniaxial tension data are: C 10 =1.223MPa C 20 =-0.0113MPa D1=D2=0.1. The obtained data can be used to verify the finite element model.

[0027] In step S8, the energy absorption analysis includes the following steps:

[0028] S81: The formula for total energy absorption is as follows:

[0029]

[0030] Where F(x) represents the compressive load, x represents the displacement in the equation, and d represents the effective displacement load;

[0031] S82: The formula for energy absorption per unit mass is as follows:

[0032]

[0033] Where m represents the mass of the energy absorbing structure;

[0034] S83: The formula for energy absorption per unit volume is as follows:

[0035]

[0036] Where V represents the volume of the energy absorbing structure;

[0037] S84: The energy absorption efficiency formula is as follows:

[0038]

[0039] Where σ represents stress, ε d represents the densification strain, where the subscript d represents the densification stage;

[0040] S85: Energy absorption under quasi-static compression: During the compression process, the axial deformation starts from the top and gradually expands to the bottom. The Hilbert fractal structures between the sandwich layers formed by the top plate and the bottom plate are squeezed and deformed against each other.

[0041] S86: Energy absorption in dynamic impact: During the impact, the axial deformation starts from the top and gradually expands to the bottom. The Hilbert fractal structures between the sandwich layers formed by the top plate and the bottom plate are mutually squeezed and deformed. The advantages of the present invention are:

[0042] The sandwich buffer structure is designed through Hilbert fractal parametric modeling, thereby forming a Hilbert fractal sandwich buffer structure composed of a top plate, a bottom plate and a Hilbert fractal structure located between the top plate and the bottom plate. During the design process, the fractal structure can fill the plane in a recursive manner, increase the number of effective structures, more efficiently realize the transfer of mechanical loads, effectively suppress global failure, and improve the recoverability of the structure. It can not only fully absorb and consume external vibration impact energy, but also has excellent elasticity and recovery. After experimental verification of the product model, the purpose of superimposed energy absorption can be achieved, thereby completely solving the technical problem of poor force resistance of the current honeycomb sandwich structure and greatly expanding the scope of application. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the first-order curve of the Hilbert fractal in the present invention;

[0044] Figure 2 It is a schematic diagram of the second-order curve of the Hilbert fractal in the present invention;

[0045] Figure 3 It is a schematic diagram of the third-order curve of the Hilbert fractal in the present invention;

[0046] Figure 4 It is a schematic diagram of the three-dimensional structure of the dumbbell specimen in the present invention;

[0047] Figure 5 It is a schematic diagram of the Yeoh fitting curve in the present invention;

[0048] Figure 6 It is a three-dimensional schematic diagram of the (first-order) Hilbert fractal sandwich buffer structure of the present invention;

[0049] Figure 7It is a schematic diagram of the dynamic impact state of the (first-order) Hilbert fractal sandwich buffer structure of the present invention;

[0050] Figure 8 It is a schematic diagram of strain and energy absorption efficiency in the present invention;

[0051] Fig. 9 It is a schematic diagram of dynamic impact test data in the present invention;

[0052] Fig.10 It is a three-dimensional schematic diagram of the test state of the (second-order) Hilbert fractal sandwich buffer structure in the present invention;

[0053] Fig.11 This is a schematic diagram of the dynamic impact test verification in the present invention;

[0054] Fig.12 It is a schematic diagram of the static compression test verification in the present invention;

[0055] Fig.13 It is a schematic diagram for comparative analysis of the Hilbert fractal structure and the cross-shaped structure in the present invention. DETAILED DESCRIPTION

[0056] The sandwich buffer structure forming test method based on fractal theory of the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0057] As shown in the figure, the sandwich buffer structure forming test method based on fractal theory of the present invention includes the following steps:

[0058] S1. Hilbert fractal parametric modeling: Modeling is done using the L system (Lin's) language and the Python language, thereby achieving parametric design and recursion. The Hilbert fractal theory can be used to construct a Hilbert fractal sandwich buffer structure model consisting of a top plate, a bottom plate, and a Hilbert fractal structure between the top plate and the bottom plate.

[0059] The essence of the L system language is the string rewriting technology based on the LOGO language. The L system consists of a triple<V,ω,P> Composition, whose items are defined as:

[0060] V={L,R,F,+,-}

[0061] ω=L

[0062] P={L→+RF-LF;-FR+, R→-LF+RFR+FL-}

[0063] In this step, the Hilbert curve is expressed in L system language and recursively deduced through ternary variables and formulas. The drawing of the Hilbert curve is a process of continuously applying rules to symbols. Each order of Hilbert curve can be expressed by L, F, and R in the L system, as shown below:

[0064] S1=L

[0065] S2=+RF-LFL-FR+

[0066] S3=+-LF+RFR+FL-F-+RF-LFL-FR+F+RF-LFL-FR+-F-LF+RFR+FL-+These three levels represent Hilbert first-order, second-order, and third-order curves respectively;

[0067] S2. Model 3D printing: Using the light curing method, a Hilbert fractal sandwich buffer structure model is prepared using thermoplastic polyurethane material (TPU material). The printing temperature is 20-30°C, preferably 25°C, the printed layer thickness is 0.1-0.3mm, preferably 0.1mm, the single layer exposure time is 5-15s, preferably 10s, and the exposure intensity is 7-12mW / cm 2 , preferably 9mW / cm 2 .

[0068] S3. Static compression test of the model: a uniaxial quasi-static compression test is performed on the Hilbert fractional sandwich cushioning structure model using a testing machine, wherein the speed of the uniaxial quasi-static compression test is set to 10-15 mm / min, preferably 12 mm / min.

[0069] S4. Dynamic impact test of the model: A dynamic impact tester is used to carry out a dynamic impact test on the Hilbert fractal sandwich buffer structure model. In the dynamic impact test, a mass block is used to drop to test the Hilbert fractal structure. The mass blocks used are 1.1kg, 2.2kg, 3kg, and 4.1kg, and the drop heights are 10cm, 20cm, 30cm, and 40cm, respectively.

[0070] S5. Uniaxial tensile test of the model: The material mechanical data is obtained based on the static tensile test and input into the finite element analysis software. The size is designed according to ISO527-2 "Plastic Tensile Properties Test Method" 14 standard, and type 1B is selected. In this process, the test specimen is used for testing. The specimen is designed as a dumbbell specimen, and the dumbbell specimen is printed by a 3D printer;

[0071] S6, constructing a constitutive model of the thermoplastic polyurethane material based on step S5, and using the constitutive model of the thermoplastic polyurethane material to simulate the use of the thermoplastic polyurethane material in the finite element method;

[0072] Among them, the constitutive model of thermoplastic polyurethane material is established as follows:

[0073]

[0074] The specific constants obtained from the uniaxial tension data are: C 10 =1.223MPaC 20 =-0.0113MPaD1=D2=0.1. The obtained data can be used to verify the finite element model.

[0075] S7. Establishment of finite element model of the model: Use modeling software to establish a three-dimensional model and input it into simulation software for finite element simulation. The specific method is as follows:

[0076] S71: Establish a finite element model, which is specifically composed of a Hilbert fractal sandwich buffer structure model, a mass block and a support plate;

[0077] S72: Selection of unit type and setting of real constants. The Hilbert fractal sandwich buffer structure model, mass block and support plate use solid164 solid units.

[0078] S73: Set material properties. The Hilbert fractal sandwich buffer structure model uses rubber material for finite element analysis. The material uses the Yeoh second-order constitutive model. The rigid mass block and the rigid support plate are set according to the material properties of steel. When adjusting the mass of the mass block, it can be simplified to change the density of the mass block to control;

[0079] S74: Divide the model into grids. First, assign material properties to the calculation model, and then use an appropriate method to divide the grid. The solid unit uses hexahedral unit mapping grid. The unit size of the Hilbert fractal sandwich buffer structure model is 1.5mm. The rigid mass block and the rigid support plate are not deformed obviously due to stress, and the unit size is 15mm. The overall grid division and local grid division are basically kept uniform.

[0080] S75: Setting contact and loading. This paper takes the descending time and speed of the rigid mass block as variables to simulate the static compression process of the Hilbert fractal sandwich buffer structure. To simplify the optimization calculation process, the analysis step length is set to 0.12s and the speed of the rigid mass block is set to 100mm / s. In order to obtain the stress-strain curve of the Hilbert fractal sandwich buffer structure, it is necessary to obtain the contact force between its surface and the surface of the mass block. The surface contact is set between the two, and the other areas are set to single-sided contact.

[0081] S76: Solve. Calculate the approximate solution time according to the quasi-static compression speed and height, select the output contact force, and obtain the relevant contact force, displacement data, and stress distribution and animation of the quasi-static compression process.

[0082] S8. Through the energy absorption analysis of the model, the energy absorption capacity of the Hilbert fractal sandwich cushioning structure model during compression is obtained.

[0083] The energy absorption analysis includes the following steps:

[0084] S81: Total energy absorption (EA), mainly used to evaluate the ability of the Hilbert fractal sandwich cushioning structure to absorb energy during compression. The formula is as follows:

[0085]

[0086] Where F(x) represents the compressive load, x represents the displacement in the equation, and d represents the effective displacement load;

[0087] S82: Unit mass energy absorption (SEA m ), which is used to measure the energy strength of different materials and structures. The formula is as follows:

[0088]

[0089] Where m represents the mass of the energy absorbing structure;

[0090] S83: Energy Absorption per Unit Volume (SEA V ), which is used to measure the energy strength of structures of different volumes. The formula is as follows:

[0091]

[0092] Where V represents the volume of the energy absorbing structure;

[0093] S84: Energy absorption efficiency (η), the energy dissipation method is used to determine the densification strain and energy absorption efficiency, the formula is as follows:

[0094]

[0095] Where σ represents stress, ε d represents the densification strain, where the subscript d represents the densification stage;

[0096] S85: Energy absorption under quasi-static compression: In the quasi-static compression test of the Hilbert fractal sandwich cushioning structure, each fractal structural unit undergoes a regular stable collapse, which is an ideal energy absorption mode. During the compression process, its axial deformation starts from the top and gradually expands to the bottom. The Hilbert fractal structures between the sandwich layers formed by the top plate and the bottom plate are squeezed and deformed against each other.

[0097] S86: Energy absorption under dynamic impact conditions: The dynamic impact results of the Hilbert fractal sandwich cushioning structure are divided into linear stage, platform stage and densification stage. In the ANSYS finite element software, each fractal structural unit undergoes a regular stable collapse, which is an ideal energy absorption mode. During the impact process, its axial deformation starts from the top and gradually extends to the bottom. The Hilbert fractal structures between the sandwich layers formed by the top plate and the bottom plate are squeezed and deformed against each other.

[0098] Among them, in step S85, the compression process of the Hilbert fractal structure can be divided into two parts, the platform area and the densification area. Analysis of the quasi-static compression test data of the Hilbert fractal structure shows that when subjected to a maximum compression stress of 4.17 MPa, the structural deformation is 13.5 mm, and the resulting compression strain is 0.71. The energy absorption efficiency reflects the energy absorption in the densification stage. When the compression strain is lower than 0.5, the energy efficiency gradually increases, reaching a maximum of 15%. 0.5 is taken as εd (densification strain). As shown in the figure, as the compression process continues, the densification stage is not immediately entered when compressed. There is a long-term platform stress that can absorb energy, and the buffering performance is good. At the same time, the stress does not fluctuate periodically at regular intervals. This result shows that the Hilbert fractal structure always maintains a stable state during the deformation process, which is an ideal deformation state.

[0099] In step S86, the weight of the selected mass block is 4.1 kg, the drop height is 30 cm, the finite element calculation results are used to derive equivalent stress and displacement, and the stress-strain curve of the Hilbert fractal structure under dynamic impact is made, as shown in the figure. Analysis of the dynamic impact experimental data of the Hilbert fractal structure shows that when subjected to a maximum stress of 3.94 MPa, the structural deformation is 12.77 mm, and the strain generated is 0.64. When the strain is lower than 0.02, it is a linear stage, and the maximum stress in the linear stage is 0.16 MPa. The strain range of 0.02 to 0.62 is a platform stage. As the impact process continues, there is a longer platform stress that can absorb energy, and the buffering performance is better. At the same time, the stress does not fluctuate periodically at regular intervals. This result shows that the Hilbert fractal structure always maintains a stable state during the deformation process, which is an ideal deformation state.

[0100] The method of the embodiment is used for detection and analysis, and compared with the prior art, the following data are obtained:

[0101] Design Steps Design efficiency Example Simple Higher Prior art complex Lower

[0102] According to the data in the above table, it can be concluded that when the embodiment is implemented, through the sandwich buffer structure forming test method based on fractal theory, the designed Hilbert fractal sandwich buffer structure can fill the plane in a recursive manner, increase the number of effective structures, more efficiently realize the transfer of mechanical loads, effectively suppress global failure, and improve the recoverability of the structure.

[0103] The above description is only a preferred embodiment of the present invention and does not limit the present invention in other forms. Any technician familiar with the profession may use the technical content disclosed above to change or modify it into an equivalent embodiment with equivalent changes and apply it to other fields. However, any simple modification, equivalent change and modification made to the above embodiment based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the protection scope of the technical solution of the present invention.

Claims

1. A sandwich buffer structure forming test method based on fractal theory, characterized in that: The following steps are involved: S1. Hilbert fractal parametric modeling: Modeling is done using L system language and Python language, thereby achieving parametric design and recursion. Hilbert fractal theory can be used to construct a Hilbert fractal sandwich buffer structure model consisting of a top plate, a bottom plate and a Hilbert fractal structure between the top plate and the bottom plate. S2. Model 3D printing: Using the light curing method, a Hilbert fractal sandwich cushioning structure model is prepared using thermoplastic polyurethane material; S3. Static compression test of the model: a uniaxial quasi-static compression test is performed on the Hilbert fractional core-sandwich cushioning structure model using a testing machine; S4. Dynamic impact test of the model: A dynamic impact test is performed on the Hilbert fractal sandwich cushioning structure model using a dynamic impact tester; S5. Uniaxial tensile test of the model: obtain material mechanical data based on static tensile test and input into finite element analysis software; S6, constructing a constitutive model of the thermoplastic polyurethane material based on step S5, and using the constitutive model of the thermoplastic polyurethane material to simulate the use of the thermoplastic polyurethane material in the finite element method; S7. Finite element model establishment of the model: using modeling software to establish a three-dimensional model, and inputting it into simulation software for finite element simulation; S8. Through the energy absorption analysis of the model, the energy absorption capacity of the Hilbert fractal sandwich cushioning structure model during compression is obtained.

2. The sandwich buffer structure forming test method based on fractal theory according to claim 1, characterized in that: In step S1, the L system consists of a triple 〈V, ω, P〉, each of which is defined as: V={L,R,F,+,-} ω=L P={L→+RF-LF; -FR+, R→-LF+RFR+FL-}.

3. The sandwich buffer structure forming test method based on fractal theory according to claim 1 is characterized in that: In step S1, the Hilbert curve is expressed using the L system language. The drawing of the Hilbert curve is a process of continuously applying rules to symbols. Each order of the Hilbert curve can be expressed by L, F, and R in the L system, which is specifically expressed as follows: S1=L S2=+RF-LFL-FR+ S3=+-LF+RFR+FL-F-+RF-LFL-FR+F+RF-LFL-FR+-F-LF+RFR+FL-+.

4. The sandwich cushioning structure forming test method based on fractal theory according to claim 1 is characterized in that: In step S2, the printing temperature is 20-30°C, the printed layer thickness is 0.1-0.3 mm, the single layer exposure time is 5-15 s, and the exposure intensity is 7-12 mW / cm 2 .

5. The sandwich cushioning structure forming test method based on fractal theory according to claim 1 is characterized in that: In step S3, the speed of the uniaxial quasi-static compression test is set to 10-15 mm / min.

6. The sandwich cushioning structure forming test method based on fractal theory according to claim 1, characterized in that: In step S4, a mass block is dropped in a dynamic impact test to test the Hilbert fractal structure. The mass blocks used are 1.1 kg, 2.2 kg, 3 kg, and 4.1 kg, and the drop heights are 10 cm, 20 cm, 30 cm, and 40 cm, respectively.

7. The sandwich cushioning structure forming test method based on fractal theory according to claim 1 is characterized in that: In step S6, the constitutive model of the thermoplastic polyurethane material is established by the formula: The specific constants obtained from the uniaxial tension data are: C 10 =1.223MPa C 20 =-0.0113MPa D1=D2=0.

1. The obtained data can be used to verify the finite element model.

8. The sandwich cushioning structure forming test method based on fractal theory according to claim 1 is characterized in that: In step S8, the energy absorption analysis includes the following steps: S81: The formula for total energy absorption is as follows: Where F(x) represents the compressive load, X represents the displacement in the equation, and d represents the effective displacement load; S82: The formula for energy absorption per unit mass is as follows: Where m represents the mass of the energy absorbing structure; S83: The formula for energy absorption per unit volume is as follows: Where V represents the volume of the energy absorbing structure; S84: The energy absorption efficiency formula is as follows: Where σ represents stress, ε d represents the densification strain, where the subscript d represents the densification stage; S85: Energy absorption under quasi-static compression: During the compression process, the axial deformation starts from the top and gradually expands to the bottom. The Hilbert fractal structures between the sandwich layers formed by the top plate and the bottom plate are squeezed and deformed against each other. S86: Energy absorption under dynamic impact conditions: During the impact, the axial deformation starts from the top and gradually extends to the bottom. The Hilbert fractal structures between the sandwich layers formed by the top plate and the bottom plate are squeezed and deformed.

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