Dynamic buffer coefficient maximum unit volume energy absorption method for simplified measurement of material buffer curve

Abstract

A dynamic buffer coefficient maximum unit volume energy absorption method for simplified measurement of a material buffer curve comprises the following steps: determining the value range of maximum unit volume energy absorption sigma s and h / t, and further determining the value range of em: properly selecting the values of sigma s and h / t, and dividing the maximum unit volume energy absorption em from (em) Min to (em) Max into a plurality of value points (em) i at certain intervals; measuring to obtain a [G] value ([G]) i corresponding to each maximum unit volume energy absorption (em) i value, and calculating to obtain a corresponding dynamic buffer coefficient C value (C) i; sequentially measuring nc dynamic buffer coefficients and maximum unit volume energy absorption type value points ((em) i, (C) i); constructing a dynamic buffer coefficient and maximum unit volume energy absorption relation curve C-em curve of the buffer material; and constructing a [G]-sigma s buffer curve of the buffer material under the ratio h / t of any drop height to the thickness of the liner by using a relational expression between the dynamic buffer coefficient and the maximum unit volume energy absorption. Therefore, a [G]-sigma s buffer curve under the ratio of any drop height of the buffer material to the thickness of the liner can be constructed.

Description

Technical Field

[0001] The invention belongs to the technical field of product cushioning packaging design, and in particular relates to a method for simplifying the determination of a material cushioning curve to determine the maximum unit volume energy absorption of a dynamic cushioning coefficient. Background Art

[0002] During product logistics and transportation, drops and impacts can lead to product damage, resulting in significant economic losses. Only by inserting cushioning material of appropriate thickness and load-bearing area between the inner product and the outer packaging can we prevent overpacking while minimizing the risk of poor packaging. This is the key to effective product protection and effective cushioning material utilization. To effectively design cushioning packaging for products, a cushioning curve must be constructed. This curve determines the appropriate thickness and load-bearing area based on information such as the fragility and mass of the object being cushioned, as well as the equivalent drop height in the distribution environment.

[0003] Currently, according to the standards "GB / T8167-2008 Dynamic Compression Test Method for Packaging Cushioning Materials" and "ASTMD1596-2014 Standard Test Method for Dynamic Shock Cushioning Characteristics of Packaging Material," a static stress buffering curve, the [G]-σs curve, can be constructed based on the ratio of maximum acceleration to gravitational acceleration (product brittleness). Furthermore, according to the standard "GB / T8166-2011 Cushioning Packaging Design," the [G]-σs buffering curve of the cushioning material can be used to design cushioning packaging for the product. The dynamic impact test of the cushioning pad, on which the [G]-σs buffering curve is based, reproduces the process of a product packaging falling. This buffering curve is the most reasonable, scientific, and practical, making it the preferred buffering curve for product cushioning packaging design. The test principle diagram is shown below. Figure 1 The corresponding drop hammer impact test device includes an impact testing machine, a testing machine controller, and a data acquisition and processing system, the latter of which includes a charge amplifier, a data acquisition card, data acquisition and processing software, and a computer.

[0004] The drop hammer is equivalent to a cushioning protection product, with a mass of m, placed on a cushioning pad with a bearing area of ​​A. The static stress σs generated by its gravity satisfies

[0005] σ s =mg / A (1)

[0006] Where g is the acceleration of gravity. Assuming that the deformation of the cushion pad under impact is x, the transient reaction force of the cushion pad against the drop weight impact is F(x), and the initial thickness of the cushion along the impact direction is t, then the corresponding strain of the cushion ε=x / t, and the strain rate is Assume the acceleration of the drop hammer is a. According to Newton's second law, there is a relational expression

[0007] F(x) = m(a + g) (2)

[0008] The stress generated by the buffer material resisting the impact is related to ε and [[ID=~10]]is defined as

[0009]

[0010] Then during the impact process, the energy absorption per unit volume e of the buffer pad is

[0011]

[0012] Assume the velocity of the drop hammer when it contacts the buffer pad is the initial impact velocity v0. Then the equivalent drop height h of the drop hammer is h = v0 2 / 2g. When the impact deformation amount x of the buffer pad is equal to the maximum deformation amount x m (generally x m << h), the kinetic energy of the drop hammer is all converted into the deformation energy of the buffer material, that is

[0013]

[0014] In the formula, ε m is the maximum strain corresponding to x m of the buffer pad, ε m = x m / t. Then corresponding to ε m , the maximum energy absorption per unit volume e m of the pad is

[0015]

[0016] So, from the above formula, we can get

[0017]

[0018] When x ∈ (0, x m , that is, ε ∈ (0, ε m , the maximum value of m is the impact peak stress σ. According to equations (1) and (2), there should be an equation

[0019]

[0020] In the formula, [G] is the product fragility value, that is, the ratio of the maximum acceleration it can withstand to g. From the above two formulas, we can get

[0021]

[0022] Define the Cushion factor C as

[0023] C=σ m / e m (10)

[0024] C is also called the buffer coefficient. According to the above two formulas, C can also be expressed as

[0025]

[0026] According to the standards "GB / T 8167-2008 Dynamic Compression Test Method for Packaging Cushioning Materials" and "ASTM D1596-2014 Standard Test Method for Dynamic Shock Cushioning Characteristics of Packaging Material", the DY-2 drop hammer impact tester (manufactured by Xi'an Guangbo Testing Equipment Co., Ltd.) for measuring the [G]-σs curve of the cushioning material is as follows: Figure 2 As shown. According to these two experimental standards, the impact tester is used to conduct a drop hammer impact test on a certain buffer material at a certain drop height and pad thickness. The cross section of the test sample along the impact direction is generally rectangular, with a length and width of not less than 100 mm or 4 inches. During the drop hammer impact test, the bottom surface of the sample is fixed to the center of the upper surface of the rigid support base, ensuring that its center is on the same vertical line as the center of the drop hammer, and its bearing surface is parallel to the bottom surface of the drop hammer. The drop hammer falls freely from the drop height and hits the sample. An acceleration sensor is installed on the drop hammer. After sampling by the data acquisition and processing system, the acceleration-time aT curve of each drop hammer impact can be obtained, from which the maximum acceleration of the impact is obtained. The same sample is impacted five times continuously, with the time interval between two adjacent impacts being 1-30 minutes. A number of the five consecutive impacts are selected, and the ratio of the average value of the maximum acceleration of the last four impacts to g is generally taken as the [G] value. According to formula (1), the weight of the drop hammer at this time is divided by the cross-sectional area of ​​the pad along the impact direction to obtain σs. By changing the configuration of the mass block on the drop hammer, the mass and impact energy of the drop hammer can be adjusted to obtain different maximum accelerations. At least 5 different mass block combinations are required to generate the final buffer curve. In this way, a series of (σs, [G]) test values ​​of the pad of this thickness at this drop height are obtained, and the final [G]-σs curve is constructed with the help of curve fitting. Pad samples of different thicknesses are made for the buffer material, and the above drop test process is repeated at different drop heights to obtain a series of [G]-σs curves of the buffer material. s Buffer curve.

[0027] It can be seen from this that in order to obtain the [G]-σs buffering curve of a certain buffering material, it must be carried out under a certain drop height and padding thickness. It is difficult to enumerate all drop heights and padding thicknesses, and it is impossible to achieve the continuity of the buffering curve with respect to the drop height and padding thickness. It is impossible to calculate the buffering curve of the buffering material under any drop height and padding thickness within a certain range.

[0028] To determine the [G]-σs cushioning curve for a specific cushioning material under a specific drop height and cushioning thickness, impact tests using at least five different mass combinations are required. The same sample must be subjected to five consecutive impacts, with a significant time interval between each impact. To obtain a family of [G]-σs curves for a specific cushioning material under different drop heights and cushioning thicknesses, impact tests must be conducted for each drop height and cushioning thickness combination, requiring a significant number of test specimens. Furthermore, considering the time required for sample preparation and interval testing, existing methods for determining [G]-σs cushioning curves are inherently costly, in terms of sample procurement, testing time, and equipment costs.

[0029] The existing [G]-σs buffer curve measurement method has the following problems:

[0030] (1) It can only be used for a certain combination of drop height and pad thickness, and cannot be exhaustive. It is impossible to achieve the continuity of the buffer curve with respect to the drop height and pad thickness. It is impossible to calculate the buffer curve of the buffer material under any combination of drop height and pad thickness within a certain range.

[0031] (2) For a certain combination of drop height and cushion thickness, at least 5 (usually 10) impact tests with different drop weights should be carried out on the cushioning material sample. If the [G]-σs cushioning curves under different combinations of drop height and cushion thickness are to be measured, a large number of test samples are required, and the corresponding sample purchase and production costs are high.

[0032] (3) For each impact, the drop hammer must impact the same sample five times in succession, and a long time interval must be maintained between two adjacent impacts. The test process is complex and requires multiple repetitions.

[0033] (4) The large number of samples required requires a long time in the production, testing and waiting stages, resulting in a large total time consumption.

[0034] (5) The purchase cost of the drop hammer impact test equipment is high, and each test takes a long time, which means that the total cost of using the test equipment and determining the cushioning curve is high.

[0035] In summary, it is necessary to propose an effective simplified method for determining the [G]-σs buffer curve in order to significantly reduce the amount of experiments and improve the efficiency of constructing the buffer curve. Summary of the Invention

[0036] In order to overcome the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a method for simplifying the measurement of the dynamic buffering coefficient and the maximum unit volume energy absorption of the material buffering curve. By constructing a relationship between the dynamic buffering coefficient and the maximum unit volume energy absorption of the buffering material, the measurement process of the [G]-σs buffering curve of the buffering material is simplified, thereby constructing the [G]-σs buffering curve of the buffering material under any ratio of drop height and pad thickness.

[0037] In order to achieve the above object, the technical solution adopted by the present invention is:

[0038] A method for simplifying the determination of a material's cushioning curve to determine the maximum energy absorption per unit volume of a dynamic cushioning coefficient comprises the following steps:

[0039] Step 1. Meet the requirements of the relevant standard GB / T 8167-2008. Consider the production dimensions and specifications of the cushioning material sample, as well as the sample size, drop weight, and drop height range required by the impact testing machine. When the sample cross-sectional area A along the impact direction and the cushion thickness t are maximized, and the drop height h and drop weight m are minimized, the static stress σs takes the minimum value (σs)Min, h / t takes the minimum value (h / t)Min, and em takes the theoretical minimum value (em)Min. Conversely, σs takes the maximum value (σs)Max, h / t takes the maximum value (h / t)Max, and em takes the theoretical maximum value (em)Max. The minimum value (em)Min of em should be slightly larger than the theoretical minimum value. The determination of (em)Max should also be based on the energy absorption curve of the static compression of the cushioning pad. Samples were prepared in accordance with the provisions of the standard GB / T8168-2008, and pre-treated in a constant temperature and humidity chamber in accordance with the standard GB / T4857.2-2005. A quasi-static compression test was then performed on the sample using a universal material testing machine in accordance with the standard GB / T 8168-2008 until the sample was densified. The pressure and displacement data of the buffer material were measured, and both were standardized using the bearing area A of the buffer material and the sample thickness t, respectively. Finally, the static compression σ(ε)-ε curve of the buffer material was obtained, and the corresponding unit volume energy absorption and strain E(ε)-ε curve was obtained by integrating the curve. The densification strain ε of the buffer material D =1-1.4ρ / ρ s =1-1.4ρ * ,ρ * is the relative density of the cushioning material, ρ and ρs are the densities of the cushioning material and its base material respectively. The energy absorption per unit volume of the cushioning material corresponding to εD is called the densified energy absorption per unit volume ED. Taking the dynamic coefficient c0 = 1.5, then (e m ) Max=c0E D , and finally em∈[(em)Min,(em)Max].

[0040] Step 2: Increase both σs and h / t simultaneously, or fix one while increasing the other continuously, or alternate between them, or randomly select one, as long as the product of the two (maximum energy absorption per unit volume) increases from (em)Min to (em)Max. Assume that the em value is divided into nc points (em)i with a certain spacing, and the corresponding σs and h / t values ​​are (σs)i and (h / t)i, respectively. The serial variable i = 1, 2, 3, ... nc, and generally nc = 10 to 20.

[0041] Step 3. Corresponding to any (em)i value in step (2), while ensuring that the corresponding (σs)i and (h / t)i values ​​remain unchanged, refer to the relevant standard GB / T 8167-2008 and the production size specifications of the cushioning material sample and the drop height range of the impact testing machine, and take five groups of different drop height h and pad thickness t value combinations, namely (h)j and (t)j, where j is another serial variable, j = 1, 2, 3, 4, 5; at the same time, select the cross-sectional length Lj and width Wj of the cushioning pad along the impact direction, as well as the mass (m)j of the drop hammer, to ensure that (σs)i = (m)jg / (Lj×Wj). For each group of (m)j, (h)j, (t)j, Lj, and Wj values, the corresponding samples were pre-treated in a constant temperature and humidity chamber according to the provisions of standard GB / T 4857.2-2005, and then the cushioning material liner samples were subjected to a drop impact test according to standard GB / T8167-2008 to obtain the corresponding [G] measurement value ([G])j). For the same type of cushioning material, there is a definite C-em function relationship; under fixed (em)i and (h / t)i values, there is naturally a definite σ m , the ([G])j values ​​of the five groups should be close to equal, and their average value is taken as the [G] value ([G])i corresponding to (em)i, that is, Finally, the corresponding dynamic buffer coefficient (C) of this group is calculated i =((G) i +1) / (h / t) i .

[0042] Step 4: For each maximum unit volume energy absorption (em)i value in step (2), repeat step (3) to obtain all nc type value points ((em)i, (C)i) of the dynamic cushioning coefficient and maximum unit volume energy absorption relationship curve, i = 1, 2, 3...nc.

[0043] Step 5. For most cushioning materials, the cushioning effect is generated by the deformation of enclosed gas, such as foam, corrugated cardboard, honeycomb cardboard, bubble cushion and air pillow. Based on the ideal gas model, when the units of the two are consistent, the maximum stress and the maximum energy absorption per unit volume numerically satisfy the following relationship: a and b are dimensionless relationship coefficients, e = 2.71828. Combining with formula (10), we get Based on this formula, nc ((em)i, (C)i) coordinate points are fitted to obtain the specific values ​​of the relationship coefficients a and b.

[0044] Step 6. Refer to the production size specifications of the buffer material sample mentioned in step (1), as well as the sample size and drop weight range required by the impact tester, and take a reasonable value range of static stress σs [((σs)Min, (σs)Max]. Define another serial variable k, and take a series of σs values ​​(σs)k from (σs)Min to (σs)Max, ensuring that (σs)k increases with the increase of k value, k = 1, 2, 3...ns. From k = 1 to ns, at any ratio of drop height to pad thickness h / t, calculate the maximum unit volume energy absorption (e) corresponding to the static stress (σs)k on the [G]-σs buffer curve to be constructed according to the above formula (13). m ) k =(σ s ) k h / t. Then, according to the relationship between the dynamic coefficient of the buffer material obtained in step (5) and the maximum unit volume energy absorption, the dynamic buffer coefficient corresponding to (em)k is directly calculated. Finally, according to the above formula (11), the corresponding [G] value ([G]) is calculated k =(C) j Based on the calculated coordinate points ((σs)k, ([G])k), these coordinate points are connected by means of appropriate curve interpolation or fitting to obtain the [G]-σs buffer curve to be constructed.

[0045] The beneficial effects of the present invention are:

[0046] (1) It is only necessary to conduct a limited number of impact tests on the cushioning material, and then generate a relationship between the dynamic cushioning coefficient of the cushioning material and the maximum unit volume energy absorption. From this, the [G]-σs cushioning curve of the cushioning material under any drop height and cushion thickness ratio can be constructed, thus realizing the continuity of the cushioning curve with respect to the drop height, cushion thickness and their ratio.

[0047] (2) There is no need to conduct tests on a variety of drop weights at different drop heights and pad thickness combinations as in the existing methods. In order to first test the relationship curve between the dynamic cushioning coefficient and the maximum unit volume energy absorption of the cushioning material, only 50 to 100 test samples are needed, and the corresponding sample purchase and production costs are low.

[0048] (3) This method requires at most a limited number of impact tests. Compared with the existing [G]-σs buffer curve determination method, the number of impact tests in this method is significantly reduced, and the testing process becomes simpler.

[0049] (4) Compared with the existing [G]-σs buffer curve determination method, the number of samples required is greatly reduced, and the total time consumption such as sample preparation and test interval waiting is greatly reduced.

[0050] (5) The number of samples and the number of impact tests required are greatly reduced, and the total cost of using the corresponding test equipment is also greatly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is a schematic diagram of the principle of dynamic impact test of cushioning pad;

[0052] Figure 2 This is a diagram of the DY-2 impact testing machine;

[0053] Figure 3 It is the static stress-strain σ(ε)-ε curve of closed-cell EVA foam material (ρ = 106 kg / m3);

[0054] Figure 4 It is the static unit volume energy absorption-strain E(ε)-ε curve of closed-cell EVA foam material (ρ=106kg / m3);

[0055] Figure 5 This is the dynamic cushioning coefficient-maximum unit volume energy absorption C-em curve of closed-cell EVA foam material (ρ=106kg / m3);

[0056] Figure 6 It is the [G]-σs cushioning curve of closed-cell EVA foam material (ρ=106kg / m3) at h / t=9. DETAILED DESCRIPTION

[0057] The present invention is further described below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0058] like Figure 1As shown in FIG, by constructing a relationship between the dynamic cushioning coefficient and the maximum energy absorption per unit volume of the cushioning material, the measurement process of the [G]-σs cushioning curve of the cushioning material is simplified. Thus, the [G]-σs cushioning curve of the cushioning material under any ratio of drop height h and pad thickness t can be constructed. The construction process specifically includes the following steps:

[0059] A method for simplifying the determination of a material's cushioning curve to determine the maximum energy absorption per unit volume of a dynamic cushioning coefficient comprises the following steps:

[0060] Step 1: Determine the value range of the maximum unit volume energy absorption σs and h / t, and then determine e m The value range of .

[0061] Under the requirements of the relevant standard GB / T 8167-2008, taking into account the production size of the buffer material sample, as well as the sample size, drop weight mass and drop height range required by the impact testing machine, according to formula (1), when the cross-sectional area A of the sample along the impact direction is the largest and the drop weight mass m is the smallest, the static stress σs takes the minimum value (σs) Min , otherwise σs takes the maximum value (σs) Max When the static stress σs and the drop height h take the minimum value, and the pad thickness t takes the maximum value, that is, h / t takes the minimum value (h / t) Min When, e m Take the theoretical minimum value (e m ) Min ; When σs and h take the maximum value, and t takes the minimum value, that is, h / t takes the maximum value (h / t) Max When, e m Take the theoretical maximum value (e m ) Max This is just a theoretical prediction. m The minimum value should be larger than the theoretical minimum value. Similarly, under actual experimental conditions, the maximum drop weight is rarely used to impact a cushion pad with a small cross-sectional area and thin thickness. In this case, the cushion deformation is in a densified state and the drop weight acceleration value will be very high, causing damage to the acceleration sensor. Therefore, (e m ) Max The determination must also be combined with the energy absorption curve of the static compression of the buffer pad.

[0062] Samples were prepared according to the requirements of GB / T 8168-2008 and pre-treated in a constant temperature and humidity chamber according to the requirements of GB / T 4857.2-2005. Furthermore, static compression tests were performed on the samples using a universal materials testing machine, as specified in GB / T 8168-2008, until the samples were densified. Pressure and displacement data of the cushioning material were directly measured, and both were normalized by the material's bearing area A and the sample thickness t, respectively. The resulting static compression σ(ε)-ε curve was then integrated to obtain the corresponding unit volume energy absorption and strain E(ε)-ε curve.

[0063] Here, we define a physical term: the densification strain εD of a cushioning material. This refers to the strain at which the entire cushioning material is compressed and the corresponding stress begins to increase rapidly and continuously. Generally speaking, the densification strain of a cushioning material under dynamic impact is slightly greater than the densification strain εD under static compression. The formula for calculating the static densification strain of a cushioning material is (Gibson LJ, Ashby M F. Cellular Solids: Structure and Properties (2nd ed). Cambridge, UK: Cambridge University Press, 1997).

[0064] ε D =1-1.4ρ / ρ s =1-1.4ρ * (14);

[0065] Where, ρ * is the relative density of the cushioning material, ρ and ρ s The energy absorption per unit volume of the buffer material corresponding to the static densification strain εD is called the densification energy absorption per unit volume E D Taking into account the influence of dynamic effects, or the situation where the impact slightly exceeds the densification strain and causes a sharp increase in dynamic stress, the dynamic coefficient c0 is generally taken as around 1.5. Then (e m ) Max The value of can be determined according to the following formula (e m ) Max =c0E D (15);

[0066] So far, e has been determined m The minimum and maximum values ​​of e m ∈[(e m ) Min ,(e m ) Max ].

[0067] Step 2: Select the values ​​of σs and h / t appropriately to convert the maximum unit volume energy absorption e m From (e m ) Min to (e m ) Max Divide into several value points with a certain spacing (e m ) i .

[0068] Increase the values ​​of σs and h / t simultaneously, or fix one and increase the other continuously, or increase them alternately, or randomly select them as long as the product of the two (maximum energy absorption per unit volume) is from (e m ) Min to (e m ) Max Just increase it and calculate the corresponding e according to formula (13) m Assume that e m Values ​​are divided into n c There are certain intervals between the value points (e m ) i , the corresponding σs and h / t values ​​are (σ s ) i and (h / t) i Value, where serial number variable i=1,2,3...n c , generally n c =10~20.

[0069] Step 3: Measure and obtain the maximum energy absorption per unit volume (e m ) i The corresponding [G] value ([G]) i , calculate the corresponding dynamic cushioning coefficient C value (C) i .

[0070] Corresponding to any one of the steps (e m ) i value, ensuring the corresponding (σs) i and (h / t) i Under the condition that the value remains unchanged, refer to the requirements of the relevant standard GB / T8167-2008 and the production size of the cushioning material sample, as well as the drop height range of the impact tester, and take five different combinations of drop height h and cushion thickness t values, which are (h) j and (t) j , j is another serial number variable, j = 1, 2, 3, 4, 5; at the same time, the cross-sectional length L of the buffer pad along the impact direction is selected j and width W j , and the mass of the falling weight (m) j , ensuring (σs)i =(m) j g / (L j ×W j ).

[0071] For each group (m) j 、(h) j , (t) j , L j and W j The sample was pre-treated in a constant temperature and humidity chamber according to the provisions of GB / T4857.2-2005, and then the sample was pre-treated in a constant temperature and humidity chamber according to the provisions of GB / T8167-2008. Figure 2 The DY-2 impact tester shown in the figure is used to perform a drop impact test on the cushioning material pad sample, and the corresponding [G] measurement value ([G]) is obtained. j According to formulas (12) and (13), for the same buffer material, there is a certain Ce m Function relationship; at a fixed (e m ) i and (h / t) i Under the value of σ, there is naturally a certain σ m , five groups of ([G]) j The values ​​should be close to equal, and their average value is taken as the value corresponding to (e m ) i [G] value ([G]) i ,Right now According to formula (12), the corresponding dynamic buffer coefficient (C) of this group is calculated. i =((G) i +1) / (h / t) i .

[0072] Step 4: Measure n c The dynamic cushioning coefficient and the maximum energy absorption per unit volume ((e m ) i ,(C) i ).

[0073] For each maximum unit volume energy absorption (e m ) i Repeat step (3) to get all n c The type value point of the relationship curve between the dynamic cushioning coefficient and the maximum unit volume energy absorption (e m ) i ,(C) i ), i=1,2,3...n c .

[0074] Step 5: Construct the curve Ce of the relationship between the dynamic buffering coefficient and the maximum unit volume energy absorption of the buffer material m curve.

[0075] With the help of a certain relationship equation, we can fit the n obtained in step (4) c Individual value points (e m ) i ,(C) i ) to obtain the specific relationship between the dynamic cushioning coefficient and the maximum energy absorption per unit volume. Most cushioning materials, such as foam, corrugated cardboard, honeycomb cardboard, bubble cushions, and air pillows, rely on the deformation of enclosed gases to produce their cushioning effect. Based on the ideal gas model, when the units of the two are consistent, the maximum stress and the maximum energy absorption per unit volume numerically satisfy the following relationship (Daum MA simplified process for determining cushion curves the stress-energy method. http: / / talkpkg.com / Papers-Presentations / Presentation / Daum%20Matthew%20Dimensions06%20paper.pdf.1999):

[0076]

[0077] In the formula, a and b are dimensionless relationship coefficients, whose values ​​depend on the material and density of the cushioning material; e is a natural constant, e = 2.71828. Combined with formula (12), we can get

[0078]

[0079] The present invention only supports the buffer materials whose dynamic buffer coefficient and maximum unit volume energy absorption satisfy the relationship (17). For other types of buffer materials, according to their buffering mechanism, the dynamic buffer coefficient and maximum unit volume energy absorption can be fitted with other relationship. c ((e m ) i ,(C) i ) point, and the values ​​of the relationship coefficients a and b in formula (17) are obtained by curve fitting.

[0080] Step 6: Use the relationship between the dynamic cushioning coefficient and the maximum energy absorption per unit volume to construct a [G]-σs cushioning curve for the cushioning material at any drop height to cushion thickness ratio h / t;

[0081] Refer to the production size limit of the buffer material sample mentioned in step (1), as well as the sample size and drop weight range required by the impact testing machine. Of course, you can also take any value range of the static stress σs. Assume that the minimum and maximum values ​​of σs are (σs) Min and (σs) Max . Define another serial variable k, in the interval [((σs) Min ,(σs) Max ] from (σs) Min to (σs) Max Take any series of σs values ​​(σs) k , to ensure (σ s ) k As the value of k increases, it is generally calculated by taking the interval [(σs) Min ,(σs) Max ] is divided equally into n s -1 equal parts and get this n s σs value.

[0082] From k=1 to n s At any drop height and cushion thickness ratio h / t, calculate the static stress (σ) on the [G]-σs buffer curve to be constructed according to the above formula (13) s ) k The corresponding maximum energy absorption per unit volume (e m ) k =(σ s ) k h / t. Then, according to the relationship between the dynamic coefficient of the buffer material and the maximum unit volume energy absorption (17) obtained in step (5), (e m ) k Corresponding dynamic cushioning coefficient Finally, according to the above formula (12), the corresponding [G] value ([G]) is calculated k =(C) j h / t-1.

[0083] Based on the calculated coordinate point ((σs) k ,([G]) k ), by means of appropriate curve interpolation or fitting, these coordinate points are connected to obtain the [G]-σs buffer curve to be constructed. s The larger the value, the more and denser the coordinate points on the constructed buffer curve will be. Finally, these coordinate points will be directly connected in sequence to construct the final [G]-σs buffer curve.

[0084] Theoretical basis for the feasibility of the inventive method:

[0085] For a [G]-σs curve, h / t is a constant, and according to equations (11) and (6), C and e are obtained. m , at this time both are variables that change with the static stress σs, that is,

[0086]

[0087] It can be seen that from any [G]-σs curve, the corresponding Ce can be obtained according to the above two equations. m curve. In fact, Ce m Each coordinate point on the curve can correspond to a series of (G, σs) points on multiple [G]-σs buffer curves when h and t take different values. It no longer depends on specific h and t values ​​and becomes more universal. C is also called the dynamic buffer coefficient, which is essentially related to the maximum stress σ m and the maximum energy absorption per unit volume e m Similarly, C is also ε m For a specific cushioning material, there must be a certain Ce m The functional relationship between them.

[0088] Example:

[0089] Taking a closed-cell EVA (Ethylene Vinyl Acetate) foam material as an example, the test principle diagram is as follows: Figure 1 As shown in the figure, after more than ten drop hammer impact tests, the relationship between its dynamic cushioning coefficient and maximum unit volume energy absorption was constructed. The [G]-σs cushioning curve of this cushioning material under any drop height and cushion thickness ratio h / t was constructed, and compared with the [G]-σs cushioning curve measured in the corresponding experiment to illustrate the feasibility and beneficial effect of this method. The density of the closed-cell EVA foam is ρ = 106 kg / m 3 , assuming that the ratio of any drop height to pad thickness is h / t = 9. The specific implementation steps for this case are as follows:

[0090] (1) According to the relevant standard GB / T 8167-2008, the length and width of the cross section of the pad sample along the impact direction shall not be less than 100mm×100mm, and the pad thickness t shall not be less than 25mm. The used ρ=106kg / m 3 The sizes of closed-cell EVA foam with the highest density are 35, 40, 50 and 60 mm. All impact tests were carried out using Figure 2The DY-2 impact tester shown in the figure has a drop weight range of m = 2 to 50 kg, a maximum drop height of 1200 mm, and a maximum impact size of the test bench sample of 210 mm × 210 mm. For ease of operation, the drop height of the impact tester should not be less than 40 mm. According to formula (1), the static stress σ s The minimum value of (σs) Min =2×9.8 / (0.21×0.21)=0.444kPa, the maximum value of static stress σs is (σs) Max =50×9.8 / (0.1×0.1)=49kPa. Minimum value of h / t (h / t) Min =40 / 60=2 / 3=0.6667, the maximum value of h / t (h / t) Max =1200 / 35=34.2857. Of course, thicker pad samples can be obtained by stacking as needed. m The theoretical minimum value e mMin =(σs) Min ×(h / t) Min =0.296kPa and the theoretical maximum value e mMax =(σs) Max ×(h / t) Max =1680kPa.

[0091] e m The minimum value e mMin Take a value slightly larger than the theoretical minimum, such as e mMin =1kPa. Samples were prepared in accordance with the provisions of standard GB / T8168-2008. The length and width of the sample cross section along the compression direction were 200mm×200mm respectively, and the sample thickness was 50mm. The samples were pre-treated in a constant temperature and humidity chamber in accordance with the provisions of standard GB / T 4857.2-2005. Then, in accordance with the provisions of standard GB / T 8168-2008, a quasi-static compression test was performed on the sample using a universal material testing machine until the sample was densified. The pressure and displacement data of the buffer material were directly measured. Both were standardized using the bearing area A of the buffer material and the sample thickness, and finally the static compression σ(ε)-ε curve of the buffer material was obtained, as shown in the figure. Figure 3 As shown. Then the corresponding unit volume energy absorption and strain E(ε)-ε curve is obtained by integrating the curve, as shown Figure 4 shown.

[0092] The density of the closed-cell EVA foam material is ρ = 106 kg / m 3 and the density of the solid substrate ρ s =950kg / m 3Therefore, according to the above formula (14), the densification strain of the buffer material can be calculated as εD=1-1.4ρ / ρ s =1-1.4×106 / 950=0.8438, the corresponding strain should be Figure 4 The corresponding energy absorption per unit volume of densification can be obtained from the E(ε)-ε curve D =361.5044kPa, and finally, according to the above formula (15), e can be calculated mMax =c0×E D =1.5×361.5044kPa=542.2566kPa. Finally, e was determined. m The minimum and maximum values ​​of e m ∈[1,542.2566].

[0093] (2) From i=1,2,3...n c (In this c =10), according to the range of σs of 0.444~49kPa and the range of h / t of 0.6667~34.2857 determined in step (1), the series values ​​of σs and h / t (σs) are appropriately selected. i and (h / t) i , increase the values ​​of both at the same time to ensure that the product of the two, that is, the maximum energy absorption per unit volume, is increased from (e m ) Min to (e m ) Max Incrementally, list the two values ​​in the first two columns of Table 1. Calculate the corresponding e according to formula (13) m Value (e m ) i , listed in the third column of Table 1.

[0094] Table 1 corresponds to Ce in each step of the dynamic buffer coefficient-kinetic energy method m Determination of coordinate values ​​on the curve

[0095]

[0096] In this way, the maximum energy per unit volume is absorbed from e mMin =1kPa to e mMax =542.2566kPa, divided into n c = 10 value points with a certain distance between them (e m ) i . From i=1,2,3...n c ,(e m ) iThe values ​​are 1kPa, 62kPa, 119.2kPa, 182.6kPa, 241.8kPa, 303kPa, 361.6kPa, 421.2kPa, 484kPa and 541.2kPa respectively.

[0097] (3) For each maximum unit volume energy absorption (e m ) i value, ensuring the corresponding (σs) i and (h / t) i When the value remains unchanged, refer to the requirements of the relevant standard GB / T 8167-2008, as well as the production size of the cushioning material sample mentioned in step (1), the sample size of the impact testing machine and the drop height range, and take five groups of different drop heights (h) j and pad thickness (t) j Combination values ​​(j is another serial variable, j = 1, 2, 3, 4, 5), all satisfy (h) j / (t) j =(h / t) i The σs value of each group is consistent (σs) i , and then refer to the configuration of the impact tester drop weight weight, give the corresponding reasonable drop weight (m) j , and then calculate the cross-sectional area A of the pad along the impact direction according to formula (1) j =(m) j g / (σs) i , and give the corresponding cross-sectional length L j and width W j , make sure that the pad size meets the requirements of GB / T 8167-2008, the production size of the cushioning material sample and the sample size of the impact testing machine. For example, for (e m ) i2 =62kPa, (σs)2=12.4kPa, (h / t) i =5, (h) j , (t) j 、(m) j 、A j , L j and W j There are five possible combinations of values ​​listed in Table 2.

[0098] Table 2 corresponds to (e m )2=12.4kPa(i=2)(σs) i 、(h / t) i 、(h) j , (t) j 、(m) j 、Aj , L j and W j Five combination values

[0099]

[0100] For each group (m) j 、(h) j , (t) j 、A j , L j and W j The sample was pre-treated in a constant temperature and humidity chamber according to the provisions of GB / T4857.2-2005, and then the sample was pre-treated in a constant temperature and humidity chamber according to the provisions of GB / T 8167-2008. Figure 2 The DY-2 impact tester shown in the figure is used to perform a drop impact test on the cushioning material pad sample, and the corresponding [G] measurement value ([G]) of each group is obtained. j Theoretically, for the same cushioning material, five groups of ([G]) j The values ​​should be close to equal, and their average value is taken as the value corresponding to (e m ) i [G] value ([G]) i , listed in the fourth column of Table 1. Then calculate according to formula (12) to obtain the corresponding (e m ) i Dynamic cushioning coefficient C value (C) i .

[0101] (4) For each maximum unit volume energy absorption (e m ) i Repeat step (3) to get all n c = 10 points of maximum energy absorption per unit volume and dynamic cushioning coefficient ((e m ) i ,(C) i ). From i=1,2,3...n c , (C) i The values ​​are 32.3807, 0.9995, 1.0156, 1.3334, 1.9810, 3.1478, 5.1287, 8.6198, 15.2626 and 26.0403 respectively. i The values ​​are listed in the last column of Table 1.

[0102] (5) For the closed-cell EVA foam material, the n obtained in step (4) is fitted based on the aforementioned formula (17). c = 10 type value points ((e m ) i ,(C)i ), construct the dynamic buffering coefficient C and the maximum unit volume energy absorption e of the buffer material m The relationship curve, such as Figure 5 As shown, a=32.00783 and b=0.01125 are obtained.

[0103] The dynamic cushioning coefficient C and the maximum unit volume energy absorption e of the EVA foam material are obtained. m The relationship between Where e is a natural constant, e=2.71828.

[0104] (6) Finally, the [G]-σs cushioning curve of the EVA foam cushioning material is constructed under any drop height and cushion thickness, such as h / t=9. As described in step (1), according to the relevant standard GB / T 8167-2008, the length and width of the cross section of the cushion sample along the impact direction shall not be less than 100mm×100mm, and the maximum impact size of the test bench sample is 210mm×210mm; the mass range of the drop hammer of the DY-2 impact testing machine used is m=2~50kg. Then according to formula (1), the minimum value of the static stress σs is 2×9.8 / (0.21×0.21)=0.444kPa, and the maximum value of the static stress σs is 50×9.8 / (0.1×0.1)=49kPa. With reference to this σs value range, σ is given s A range of values, the minimum and maximum values ​​of which are (σs) Min =1kPa and (σs) Max =26kPa. Take the integer variable n s =150, the interval [(σ s ) Min ,(σ s ) Max ] is divided equally into n s -1 equal parts, ensure that the sequence variable k = 1 to n s When increasing (σ s ) k Increase in sequence.

[0105] The [G]-σs cushioning curve of the cushioning material to be constructed in this case corresponds to a drop height and a cushion thickness ratio of h / t=9. Of course, [G]-σs cushioning curves with other drop height and cushion thickness ratios can also be constructed. According to the above formula (13), the static stress (σs) on the [G]-σs cushioning curve to be constructed is calculated as k The corresponding maximum energy absorption per unit volume (e m ) k =(σ s ) k h / t=9(σ s ) kThen, according to the relationship between the dynamic buffer coefficient and the maximum unit volume energy absorption obtained in step (5), we can directly calculate (e m ) k Corresponding dynamic cushioning coefficient Finally, according to the above formula (12), the corresponding [G] value ([G]) is calculated k =(C) k h / t-1=9(C) k -1.

[0106] Based on the calculated coordinate point ((σs) k ,([G]) k ), by means of appropriate curve interpolation or fitting, these coordinate points are connected to obtain the [G]-σs cushioning curve of the EVA foam cushioning material to be constructed. s The larger the value, the more and denser the coordinate points on the constructed cushioning curve will be. By directly connecting these coordinate points in sequence, the final [G]-σs cushioning curve can be constructed. The [G]-σs cushioning curve of the EVA foam cushioning material constructed in this case under the ratio of drop height to cushion thickness h / t=9 is as follows: Figure 6 shown.

[0107] At the same time, the static stresses were taken as 2kPa, 4.67kPa, 7.33kPa, 10kPa, 12.67kPa, 15.33kPa, 18kPa, 20.67kPa, 23.33kPa and 26kPa respectively. According to GB / T8167-2008 "Test method for dynamic compression of cushioning materials for packaging", the test specimens with a thickness of 40mm of the closed-cell EVA foam material were prepared, and the length and width of the cross section in the impact direction were both in the range of 100mm to 210mm; according to GB / T4857.2-2005 "Basic tests for packaging and transport packages - Part 2 - Temperature and humidity adjustment treatment", the specimens were pretreated in a constant temperature and humidity chamber; and then according to GB / T8167-2008 "Test method for dynamic compression of cushioning materials for packaging", the specimens were pretreated in a constant temperature and humidity chamber. Figure 5 The DY-2 impact testing machine produced by Xi'an Guangbo Testing Equipment Co., Ltd. is shown in the figure. The impact test is carried out on the sample. The tested [G] values ​​are 17.8786, 10.1002, 7.9473, 7.7602, 8.1647, 8.93569, 9.91187, 11.8993, 13.9028 and 16.0321 respectively. These test values ​​are plotted on Figure 6 , it can be seen that the two are very consistent, proving the feasibility of this buffer curve determination method.

[0108] From this embodiment, the present invention constructs the relationship between the dynamic cushioning coefficient and the maximum unit volume energy absorption of the cushioning material, thereby constructing the [G]-σ of the cushioning material at any ratio of drop height and cushion thickness. s Buffer curve.

Claims

1. A method for simplifying the determination of the maximum energy absorption per unit volume of the dynamic cushioning coefficient of a material cushioning curve, characterized in that: The following steps are involved: Step 1: Determine the value range of the maximum unit volume energy absorption σs and h / t, and then determine the value range of em: Step 2: Appropriately select the values ​​of σs and h / t to divide the maximum unit volume energy absorption em from (em)Min to (em)Max into several value points (em)i with a certain spacing; Step 3, measure and obtain the [G] value ([G])i corresponding to each maximum unit volume energy absorption (em)i value, and calculate and obtain the corresponding dynamic cushioning coefficient C value (C)i; Step 4: sequentially measure nc dynamic cushioning coefficients and model value points ((em)i, (C)i) of maximum unit volume energy absorption; Step 5: constructing a C-em curve, a relationship curve between the dynamic cushioning coefficient and the maximum unit volume energy absorption of the cushioning material; Step 6: Use the relationship between the dynamic cushioning coefficient and the maximum energy absorption per unit volume to construct the [G]-σs cushioning curve of the cushioning material under any ratio of drop height to cushion thickness h / t.

2. The method for determining the maximum energy absorption per unit volume of a dynamic buffer coefficient by simplifying the measurement of a material buffer curve according to claim 1, characterized in that: Step 1: Determine the value range of the maximum unit volume energy absorption σs and h / t, and then determine the value range of em: Under the requirements of relevant standards GB / T 8167-2008, taking into account the production size of the cushioning material sample, as well as the sample size, drop weight and drop height range required by the impact testing machine, according to the formula σ s =mg / A (1) , when the cross-sectional area A of the sample along the impact direction is the largest and the drop weight mass m is the smallest, the static stress σs takes the minimum value (σs)Min, otherwise σs takes the maximum value (σs)Max; according to the formula When the static stress σs and the drop height h take the minimum value, and the cushion thickness t takes the maximum value, that is, h / t takes the minimum value (h / t)Min, em takes the theoretical minimum value (σs)Min; when σs and h take the maximum value, and t takes the minimum value, that is, h / t takes the maximum value (h / t)Max, em takes the theoretical maximum value (em)Max. The determination of (em)Max must also be determined in conjunction with the energy absorption curve of the static compression of the cushioning cushion; Samples were prepared in accordance with the provisions of standard GB / T8168-2008, and pretreated in a constant temperature and humidity chamber in accordance with the provisions of standard GB / T4857.2-2005. Then, in accordance with the provisions of standard GB / T8168-2008, a quasi-static compression test was performed on the samples using a universal material testing machine until the samples were densified. The pressure and displacement data of the buffer material were directly measured, and both were standardized using the bearing area A of the buffer material and the sample thickness t, respectively. Finally, a static compression σ(ε)-ε curve of the buffer material was obtained, and the corresponding unit volume energy absorption and strain E(ε)-ε curve was obtained by integrating the curve. The densification strain of the buffer material under dynamic impact is slightly greater than the densification strain εD of its static compression. The calculation formula for the static densification strain of the buffer material is ε D =1-1.4ρ / ρ s =1-1.4ρ * (14), where ρ * is the relative density of the cushioning material, ρ and ρs are the densities of the cushioning material and its base material, respectively. The energy absorption per unit volume of the cushioning material corresponding to the static densification strain εD is called the densification energy absorption per unit volume ED. Considering the influence of dynamic effects, or the situation where the impact slightly exceeds the densification strain and causes a sharp increase in dynamic stress, the dynamic coefficient c0 is taken as about 1.

5. The value of (em)Max can be determined according to the following formula (e m ) Max =c0E D (15), so far the minimum and maximum values ​​of em are determined, em∈[(em)Min,(em)Max].

3. The method for determining the maximum energy absorption per unit volume of a dynamic buffer coefficient by simplifying the measurement of a material buffer curve according to claim 1, wherein: Step 2: Select appropriate values ​​of σs and h / t to divide the maximum unit volume energy absorption em from (em)Min to (em)Max into several value points (em)i with a certain spacing; Increase σs and h / t values ​​simultaneously, or fix one and increase the other continuously, or increase them alternately, or randomly select them. Just make sure that the product of the two (maximum unit volume energy absorption) increases from (em)Min to (em)Max. According to the formula Calculate the corresponding em value. Assume that the em value is divided into nc value points (em)i with a certain spacing. The corresponding σs and h / t values ​​are (σs)i and (h / t)i values ​​respectively. Here, the serial variable i = 1, 2, 3...nc, generally nc = 10~20.

4. The method for simplifying the determination of the dynamic buffer coefficient maximum unit volume energy absorption by a material buffer curve according to claim 1, characterized in that: Step 3: Measure and obtain the [G] value ([G])i corresponding to each maximum unit volume energy absorption (em)i value, and calculate the corresponding dynamic cushioning coefficient C value (C)i; Corresponding to any (em)i value in step 2, while ensuring that the corresponding (σs)i and (h / t)i values ​​remain unchanged, refer to the requirements of the relevant standard GB / T 8167-2008 and the production dimensions of the cushioning material sample, as well as the drop height range of the impact testing machine, and take five different combinations of drop height h and cushion thickness t values, namely (h)j and (t)j, where j is another serial variable, j = 1, 2, 3, 4, 5; at the same time, select the cross-sectional length Lj and width Wj of the cushioning cushion along the impact direction, as well as the mass (m)j of the drop weight, to ensure that (σs)i = (m)jg / (Lj × Wj); For the combined values ​​of (m)j, (h)j, (t)j, Lj and Wj in each group, the samples were pre-treated in a constant temperature and humidity chamber according to the provisions of standard GB / T 4857.2-2005, and then the cushioning material liner samples were subjected to a drop impact test using a DY-2 impact testing machine according to the provisions of standard GB / T 8167-2008 to obtain the corresponding [G] measurement value ([G])j. According to the formula and For the same type of cushioning material, there is a definite C-em function relationship; under fixed (em)i and (h / t)i values, there is naturally a definite σm, and the ([G])j values ​​of the five groups should be close to equal. Their average value is taken as the [G] value ([G])i corresponding to (em)i, that is, According to the formula Calculate the corresponding dynamic buffer coefficient (C) of this group i =((G) i +1) / (h / t) i。 5. The method for simplifying the determination of the dynamic buffer coefficient maximum unit volume energy absorption by a material buffer curve according to claim 1, characterized in that: Step 4: sequentially measure nc dynamic cushioning coefficients and model value points ((em)i, (C)i) of maximum unit volume energy absorption; For each maximum unit volume energy absorption (em)i value in step 2, repeat step 3 to obtain all nc type value points ((em)i, (C)i) of the dynamic cushioning coefficient and maximum unit volume energy absorption relationship curve, i = 1, 2, 3...nc.

6. The method for simplifying the determination of the dynamic buffer coefficient maximum unit volume energy absorption by a material buffer curve according to claim 1, characterized in that: Step 5: Construct a C-em curve, which is a relationship curve between the dynamic cushioning coefficient and the maximum unit volume energy absorption of the cushioning material; Fitting steps 1 to 4 to obtain n c Individual value points (e m ) i ,(C) i ), the specific relationship between the dynamic cushioning coefficient and the maximum unit volume energy absorption is obtained. When the units of the two are consistent, the maximum stress and the maximum unit volume energy absorption numerically satisfy the following relationship In the formula, a and b are dimensionless coefficients, whose values ​​depend on the material and density of the cushioning material; e is a natural constant, e = 2.71828. Combined with the formula The formula can be obtained According to the coordinate values ​​of nc points ((em)i, (C)i), the values ​​of the relationship coefficients a and b in formula (17) are obtained by curve fitting.

7. The method for simplifying the determination of the dynamic buffer coefficient and the maximum energy absorption per unit volume of a material buffer curve according to claim 1, characterized in that: Step 6 uses the relationship between the dynamic cushioning coefficient and the maximum energy absorption per unit volume to construct the [G]-σs cushioning curve of the cushioning material under any drop height to cushion thickness ratio h / t. Refer to the cushioning material sample production size limit mentioned in step 1, as well as the sample size and drop weight range required by the impact testing machine. Of course, you can also take any range of static stress σs values. Assume that the minimum and maximum values ​​of σs are (σs)Min and σs)Max respectively, define another serial variable k, and take any series of σs values ​​(σs)k from (σs)Min to (σs)Max in the interval [((σs)Min,(σs)Max], ensuring that (σs)k increases with the increase of k value. Generally, these ns σs values ​​are obtained by dividing the interval [(σs)Min,(σs)Max] into ns-1 equal parts; from k=1 to ns, under any drop height to cushion thickness ratio h / t, according to the formula Calculate the maximum energy absorption per unit volume (e) corresponding to the static stress (σs)k on the [G]-σs buffer curve to be constructed m ) k =(σ s ) k h / t; then according to the dynamic coefficient of the buffer material obtained in step 5 and the maximum unit volume energy absorption Directly calculate the dynamic buffer coefficient corresponding to (em)k Finally, according to the formula Calculate the corresponding [G] value ([G]) k =(C) j h / t-1; Based on the calculated coordinate points ((σs)k, ([G])k), these coordinate points are connected by means of appropriate curve interpolation or fitting methods to obtain the [G]-σs buffer curve to be constructed. If the ns value is larger, the number of coordinate points on the constructed buffer curve will be more and denser. Finally, these coordinate points are directly connected in sequence to construct the final [G]-σs buffer curve.

Images