CN101470070B - Honeycomb paper sheet energy absorption diagram and its use in honeycomb paper sheet production - Google Patents

Abstract

The invention belongs to the application field of honeycomb paperboard performance detection, and in particular relates to a method for optimizing and selecting a honeycomb paperboard structure and a method for selecting honeycomb base paper according to the energy absorption diagram of the honeycomb paperboard. Detect the solid modulus of the honeycomb base paper with a detector, and draw the relationship curve between the standardized energy absorption per unit volume and the standardized stress; the energy obtained by connecting the shoulder points of the energy absorption curve corresponding to the ratio of the thickness of the honeycomb paperboard to the span The absorption curves are summarized to obtain an energy absorption diagram for testing the performance of the paper honeycomb core. Using the energy absorption diagram, the structure optimization design and material selection of honeycomb paperboard can be quickly and accurately realized, which provides accurate reference data for the production of honeycomb paperboard under different conditions, and realizes energy-saving and efficient packaging.

Description

Optimal selection method using energy absorption diagram of honeycomb paperboard

technical field

The invention belongs to the application field of honeycomb paperboard performance detection, and in particular relates to a method for optimizing and selecting a honeycomb paperboard structure and a method for selecting honeycomb base paper according to the energy absorption diagram of the honeycomb paperboard.

Background technique

With the strengthening of people's understanding of resources, environmental protection and sustainable development, environmentally friendly products are more and more popular. As a non-polluting, novel structure, large load-bearing, low cost, good elasticity and good cushioning performance packaging material, honeycomb paperboard has been highly concerned by the packaging industry and has been successfully applied to the packaging of large mechanical and electrical products, furniture, construction materials etc.

At present, due to the lack of a systematic and effective testing method for the cushioning performance of honeycomb paperboard, the design and material selection of the cushioning pad made of honeycomb paperboard is mainly completed by the experience of the honeycomb paperboard supplier, and the accuracy of the design completed through experience not tall.

The design and selection of cushioning materials for packaging are mainly divided into two parts, one part is to select the best available material for a given use among all candidate materials; the other part is how to select the structure of the selected material, Performance indicators such as density and thickness are optimally selected to maximize packaging efficiency. Traditional cushioning material characterization methods, such as stress-strain curve, maximum acceleration-static stress curve, etc., can only represent a specific material performance. If optimization is performed, it is necessary to test and measure the cushioning characteristics of each possible material, and then obtain Make an optimization. In fact, it is unrealistic to make every possible material and test it, which would require a lot of manpower and resources. Another thing is that the cushioning performance of honeycomb paperboard is greatly affected by the strain rate. For any material, it is necessary to do the cushioning performance test under different strain rates, which makes the traditional stress-strain curve and maximum acceleration-static stress curve. Difficulties encountered in the optimization design and material selection of honeycomb paperboard. Although the above two curves can be used as a reference for the optimal design of honeycomb paperboard, the optimal selection of honeycomb base paper and the structure of honeycomb paperboard cannot be realized.

Contents of the invention

In order to solve the existing technical problems in the structure design and material selection of the honeycomb board core, there is a lack of a systematic and effective method, which cannot meet the cushioning packaging requirements of specific products, and optimize the honeycomb paperboard structure and material selection to improve the unit cost. To solve the technical problem of packaging efficiency of materials, the invention provides the energy absorption diagram of honeycomb paperboard and its application in the production of honeycomb paperboard.

The technical solution adopted by the present invention to solve the problems of the prior art is to provide a method for optimizing the structure of honeycomb paperboard by using the energy absorption diagram of honeycomb paperboard, said method comprising the steps of:

A1: Find the corresponding peak stress value σ _p /E _s in the honeycomb paperboard energy absorption diagram, and draw the corresponding stress line in the honeycomb paperboard energy absorption diagram;

估算出近似应变率

A2: Choose an appropriate honeycomb paperboard thickness T ₁ , use it from the impact velocity v, according to the formula

approximate strain rate

的直线，该线与所述A1步中所画的应力线相交，由交叉点确定log(W/E_s)的对应值，且由蜂窝原纸的固体模量E_s计算出单位体积的吸能量W；A3: Use interpolation to find the strain rate in the family of parallel lines of the strain rate

A straight line, which intersects the stress line drawn in the A1 step, determines the corresponding value of log(W/E _s ) by the intersection point, and calculates the energy absorption per unit volume from the solid modulus E _s of the honeycomb base paper W;

A4: Using the W value obtained in the A3 step, the known absorbed energy U and the contact area A between the packaged object and the honeycomb paperboard, calculate the thickness _T2 of the new honeycomb paperboard;

再按所述A3步中的方法确定新的log(W/E_s)、W，再按所述A4步中的方法得到新的T₃；A5: Use the _T2 value in the A4 step to calculate the new strain rate according to the method in the A2 step

Then determine new log(W/E _s ), W by the method in the A3 step, and then obtain a new _T by the method in the A4 step;

A6: Repeat the above steps until the calculated thickness T of the honeycomb paperboard converges to a certain value, which is the optimal thickness of the honeycomb paperboard, and then according to the position of the intersection of the final strain rate and the stress line, according to the energy The paper honeycomb cell wall thickness-span ratio parallel line family on the absorption diagram finds the optimal paper honeycomb cell wall thickness-span ratio, and the obtained optimal thickness of the honeycomb paperboard and the optimal paper honeycomb cell wall thickness-span ratio are The optimized structure of the honeycomb paperboard.

A method for selecting honeycomb base paper using the energy absorption diagram of honeycomb paperboard, said method comprising the steps of:

B1: According to the drop height H of the packaged object, the impact velocity v of the packaged object and the impact energy U=mv ² /2 absorbed by the packaged object are obtained, from the contact area between the honeycomb paperboard and the packaged object The thickness T of A and honeycomb paperboard, obtain the volume V of described honeycomb paperboard, and thus obtain the energy W=U/V that described honeycomb paperboard absorbs per unit volume; Because the brittle value a of described packaged object is known , then the maximum allowable packaging force F=ma and the maximum allowable peak stress σ _p =F/A of the packaged object;

B2: Select an appropriate value E _s of the solid modulus of the honeycomb base paper, draw a straight line corresponding to the values of W/E _s and σ _p /E _s in the known energy absorption diagram of the honeycomb paperboard, and the two lines intersect at point A;

B3: Draw a straight line with a slope of 1 through the point A, move along the line, keep the values of W and σ _p unchanged, and only change E _s ;

计算应变率，在该应变率下选择所述B3步中的直线与该应变率下的能量吸收线的交叉点，得点B；B4: According to the formula

Calculate the strain rate, select the intersection of the straight line in the B3 step and the energy absorption line under the strain rate under the strain rate, and obtain point B;

B5: Read the W/E _s and σ _p /E _s values corresponding to the point B in the energy absorption diagram of the honeycomb paperboard, and calculate the elastic modulus of the honeycomb base paper according to the values of W and σ _p in the B1 step Quantity E _s , according to the paper honeycomb cell wall thickness-span ratio parallel line family corresponding to point B, determine the optimal thickness-span ratio of point B by interpolation.

An energy absorption diagram for testing the performance of a paper honeycomb panel core. The drawing method of the energy absorption diagram is as follows: the solid modulus of the honeycomb base paper is detected by a detector; the static compression energy absorption of the honeycomb paper core is obtained according to the static compressive stress curve, and the honeycomb paper core is measured by the solid modulus. The energy absorption of the normalized unit volume is standardized to obtain the relationship curve between the standardized energy absorption per unit volume and the standardized stress, that is, the energy absorption curve; at a low strain rate, the energy corresponding to the ratio of the thickness and span of the honeycomb paperboard obtained by static compression The shoulder points of the absorption curve are connected to obtain an approximately linear energy absorption curve; under high strain rate, the dynamic compression maximum acceleration static stress curve is obtained by polynomial fitting according to the dynamic compression curve; under dynamic compression, the thickness of the honeycomb paperboard The shoulder points of the energy absorption curve corresponding to the ratio of the span and the span are connected to form an approximately linear energy absorption curve; the above energy absorption curves under different strain rates are summarized to obtain the energy used to detect the performance of the paper honeycomb panel core Absorption graph.

According to a preferred embodiment of the present invention: the detector is a stiffness meter, and the solid modulus is E _s =0.89GPa.

式中：ε为材料的压缩应变、σ为材料的压缩应力、W为对应于压缩应变为ε时单位体积的变形能。According to a preferred embodiment of the present invention: the static buffer performance is:

In the formula: ε is the compressive strain of the material, σ is the compressive stress of the material, and W is the deformation energy per unit volume corresponding to the compressive strain of ε.

According to a preferred embodiment of the present invention: the relationship curve between the normalized energy absorption per unit volume and the normalized stress is in the form of logarithmic coordinates.

式中，

为压缩应变率；v为压缩位移变化率；T为纸蜂窝夹层板的厚度。According to a preferred embodiment of the present invention: under quasi-static compression, the compressive strain rate can be estimated by the following formula:

In the formula,

is the compression strain rate; v is the change rate of compression displacement; T is the thickness of the paper honeycomb sandwich panel.

式中，W为材料单位体积最大变形能；σ_m为压缩最大静应力；σ_st为压缩静应力；H为冲击高度；T为缓冲材料厚度；G为冲击最大加速度。According to a preferred embodiment of the present invention: the dynamic energy absorption of cushioning material can be represented by following formula:

In the formula, W is the maximum deformation energy per unit volume of the material; _σm is the maximum compressive static stress; _σst is the compressive static stress; H is the impact height; T is the thickness of the buffer material; G is the maximum impact acceleration.

式中，v为冲击最大速度，根据自由落体原理 According to a preferred embodiment of the present invention: under dynamic compression, the compressive strain rate can be estimated by the following formula:

In the formula, v is the maximum impact velocity, according to the principle of free fall

The method for optimizing the honeycomb paperboard structure by applying the energy absorption diagram comprises the steps of:

1. Find the corresponding peak stress value σ _p /E _s in the honeycomb paperboard energy absorption diagram, and draw the corresponding stress line in the honeycomb paperboard energy absorption diagram;

估算出近似应变率

2. Choose an appropriate honeycomb paperboard thickness T ₁ , use it to get the impact velocity v according to the formula

approximate strain rate

的直线，该线与所述一步中所画的应力线相交，由交叉点确定log(W/E_s)的对应值，且由蜂窝原纸的固体模量E_s计算出单位体积的吸能量W；3. Use the interpolation method to find the strain rate in the parallel line family of the strain rate

A straight line, which intersects the stress line drawn in the step, determines the corresponding value of log (W/E _s ) by the intersection point, and calculates the energy absorption per unit volume W from the solid modulus E _s of the honeycomb base paper ;

Four, with the W value that obtains in described three steps, known absorbed energy U and the contact area A of packaged object and honeycomb paperboard, calculate the thickness T of new honeycomb paperboard ₂ ;

再按所述三步中的方法确定新的log(W/E_s)、W，再按所述四步中的方法得到新的T₃；Five, use the _T2 value in the four steps to calculate the new strain rate according to the method in the A2 step

Then determine new log(W/E _s ), W by the method in the three steps, and then obtain new _T by the method in the four steps;

6. Repeat the above steps until the calculated thickness T of the honeycomb paperboard is closed to a certain value, which is the optimal thickness of the honeycomb paperboard, and then according to the position of the intersection point of the final strain rate and the stress line, according to the The paper honeycomb cell wall thickness-span ratio parallel line family on the energy absorption diagram finds the best paper honeycomb cell wall thickness-span ratio, the optimal thickness of the obtained described honeycomb paperboard and the best paper honeycomb cell wall thickness-span ratio are It is the optimized structure of the honeycomb paperboard.

The method for selecting the honeycomb base paper by applying the energy absorption diagram comprises the steps of:

First: According to the drop height H of the packaged object, the impact velocity v of the packaged object and the impact energy U=mv ² /2 absorbed by the packaged object are obtained, and the contact between the honeycomb paperboard and the packaged object Area A and the thickness T of honeycomb paperboard, obtain the volume V of described honeycomb paperboard, and thus obtain the energy W=U/V that described honeycomb paperboard absorbs per unit volume; Because the brittle value a of described packaged object is already Known, then the maximum allowable packaging force F=ma and the maximum allowable peak stress σ _p =F/A of the packaged object;

Second: Select an appropriate value E _s of the solid modulus of the honeycomb base paper, draw a straight line corresponding to the values of W/E _s and σ _p /E _s in the known energy absorption diagram of the honeycomb paperboard, the two straight lines intersect at point A;

Third: draw a straight line with a slope of 1 across the point A, move along the line, keep the values of W and σ _p constant, and only change E _s ;

计算应变率，在该应变率下选择所述第三步中的直线与该应变率下的能量吸收曲线的交叉点，得点B；Fourth: According to the formula

Calculate the strain rate, select the intersection point of the straight line in the third step and the energy absorption curve under the strain rate under the strain rate, and obtain point B;

Fifth: read out the W/E _s and σ _p /E _s values corresponding to the point B in the energy absorption diagram of the honeycomb paperboard, and calculate the value of the honeycomb base paper according to the values of W and σ _p in the first step. Elastic modulus E _s , according to the paper honeycomb cell wall thickness-span ratio parallel line family corresponding to point B, determine the optimal thickness-span ratio of point B by interpolation.

The beneficial effects of the present invention are: the honeycomb paperboard cushioning performance testing method of the present invention can quickly and accurately realize the structural optimization design and optimal material selection of the honeycomb paperboard, providing accurate reference data for the production of honeycomb paperboard under different conditions, In this way, energy-saving and high-efficiency packaging is realized.

Description of drawings

Fig. 1. is used to detect the drawing method flowchart of the energy absorption figure of paper honeycomb board core performance;

Figure 2. Schematic diagram of the honeycomb paper core structure;

Figure 3. Static compressive stress-strain curve;

Figure 4. Normalized energy absorption and normalized stress static compression experimental curves on a logarithmic scale;

Figure 5. Dynamic compression maximum acceleration static stress curve;

Figure 6. The normalized energy absorption and normalized stress dynamic compression experimental curves on a logarithmic scale;

Figure 7. Energy absorption diagram for testing the performance of the paper honeycomb core;

Figure 8. Schematic diagram of the energy absorption diagram used in the optimal design of the honeycomb paperboard structure;

Figure 9. Schematic diagram of the energy absorption map used for the selected design of honeycomb base paper.

Detailed ways

Below in conjunction with accompanying drawing and embodiment the present invention will be further described:

Please refer to Fig. 1 for the drawing method flowchart of the energy absorption figure that is used to detect papery honeycomb plate core performance, as shown in Figure 1, the present invention is used to detect the drawing method of the energy absorption figure of papery honeycomb plate core performance as: by The detector detects the solid modulus of the honeycomb base paper; obtains the static compression energy absorption of the honeycomb paper core according to the static compression stress curve, and uses the solid modulus to standardize the energy absorption of the honeycomb paper core to obtain a standardized unit volume absorption The relationship curve between energy and normalized stress, that is, the energy absorption curve; under low strain rate, the shoulder points of the energy absorption curve corresponding to the ratio of the thickness and span of the honeycomb paperboard obtained by static compression are connected to obtain an approximate Linear energy absorption curve; under high strain rate, the dynamic compression maximum acceleration static stress curve is obtained by polynomial fitting according to the dynamic compression curve; under dynamic compression, the energy absorption curve corresponding to the ratio of the thickness of the honeycomb paperboard to the span The shoulder points are connected to form an approximately linear energy absorption curve; the above energy absorption curves under different strain rates are summarized to obtain an energy absorption diagram for testing the performance of the paper honeycomb core.

Fig. 2 is a schematic diagram of the structure of the honeycomb paper core, in which t is the thickness of the honeycomb paperboard described in claim 1, and 1 is the side length of the single-layer cell wall of the hexagonal paper honeycomb, that is, the span of the honeycomb paperboard described in claim 1.

At present, there are few experimental methods to directly measure the energy absorption of cushioning materials, which can only be calculated through static compression stress-strain curves, dynamic compression maximum acceleration-static stress curves, and energy conservation principles. The experiments introduced in this patent are divided into two parts, static compression and dynamic impact experiments. The experimental materials are all three paper honeycomb materials with different thickness-span ratios: 350/150A/350-20, 350/150B/350-20, 350 /150C/350-20 (The surface paper of the three kinds of paper honeycomb sandwich panels is 350g/m ² kraft cardboard, the material of the paper honeycomb core cell wall is 150g/m ² honeycomb base paper, the paper honeycomb core is a regular hexagon, and its pore size type They are A, C and D types respectively, and their cell wall side lengths are 5.8mm, 12.1mm and 14.4mm respectively). The static compression test adopts CMT universal material testing machine and constant temperature and humidity box, and refers to the national standard GB8168-87 packaging buffer material static compression test method and ISO 2233-1986, GB/T4857.2-2005 packaging temperature and humidity adjustment treatment for pretreatment , the sample size is 100mm*100mm, and the temperature is 23°C, the relative humidity is 50%, and the displacement change rate is 12mm/min. Standard ASTM D5169 ^[12] and GB/T4857.2-2005 packaging temperature and humidity adjustment treatment for environmental pretreatment, using a variety of quality-calibrated weights as weights, impacting the samples from a height of 50cm, and the sample size is 150mm* 150mm, the bottom area of the French weight is greater than 150mm*150mm, the test temperature is 23 ℃, and the relative humidity is 50%. Among them, the solid modulus of the paper honeycomb core is calculated by measuring with a stiffness meter, and its solid modulus is

E _s =0.89GPa (1)

Experimental results and analysis

1. Optimal energy absorption curves of paper honeycomb sandwich panels with different thickness-to-span ratios under static compression

The static cushioning performance of a material can be obtained from its static compressive stress-strain curve. The deformation energy per unit volume can be described as:

$\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}\mathrm{<span\; class="notranslate">\; \&sigma;d\&epsiv;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

In the formula: ε is the compressive strain of the material, σ is the compressive stress of the material, and W corresponds to the deformation energy per unit volume when the compressive strain is ε; the static compressive stress-strain curve is shown in Figure 3, and the paper can be obtained according to formula (2). The energy absorption per unit volume of the honeycomb sandwich panel, in order to calibrate the performance of the paper honeycomb structure, the solid modulus of the paper honeycomb - formula (1) is used to standardize it, and the relationship curve between the standardized energy absorption per unit volume and the normalized stress can be obtained, as shown in Figure 4 shown. In order to make the curves easier to compare, logarithmic coordinates are used in Fig. 4. Under quasi-static compression, the compressive strain rate can be estimated by the following formula:

$\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

为压缩应变率；v为压缩位移变化率；T为纸蜂窝夹层板的厚度。根据式(3)，本实验中纸蜂窝夹层板的压缩应变率

为10^-2/s。在相同的应变率下，将不同t/l所对应的能量吸收曲线的肩点连接起来，形成的最佳能量吸收曲线呈近似线性(如图4中黑色的粗实线所示)，随着纸蜂窝胞元厚跨比t/l的增大，最佳吸能点向右上方移动。In formula (3),

is the compression strain rate; v is the change rate of compression displacement; T is the thickness of the paper honeycomb sandwich panel. According to formula (3), the compressive strain rate of the paper honeycomb sandwich panel in this experiment

is 10 ^-2 /s. Under the same strain rate, the shoulder points of the energy absorption curves corresponding to different t/l are connected, and the optimal energy absorption curve formed is approximately linear (as shown by the black thick solid line in Fig. 4). The optimal energy-absorbing point moves to the upper right with the increase of the thickness-to-span ratio t/l of paper honeycomb cells.

2. Optimal energy absorption curves of paper honeycomb sandwich panels with different thickness-to-span ratios under dynamic compression

The dynamic cushioning performance of materials is usually characterized by the maximum acceleration static stress curve measured by the free drop test machine. According to literature ^[13] , the dynamic energy absorption of the buffer material can be expressed by the following formula:

$\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; GT</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; st</span>}}\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the formula, W-maximum deformation energy per unit volume of material; σ _m -maximum compressive static stress; σ _st -compressive static stress; H-shock height; T-buffer material thickness; G-shock maximum acceleration. The dynamic compression curve is fitted by polynomial as shown in Figure 5. The corresponding equations are as follows:

G＝17.866σ _st ² -78.024σ _st +143.83 350/150D/350-20

G＝3.627σ _st ² -34.926σ _st +151.01 350/150C/350-20

G＝1.9219σ _st W-30.053σ _st +172.58 350/150A/350-20

The maximum acceleration static stress curves are all concave, and there is only one extreme point. When the static stress is less than the static stress at the minimum extreme point, as the static stress increases, the energy absorbed by the material increases, and the acceleration transmitted through the material decreases; when the static stress exceeds the static stress at the minimum extreme point, through The impact acceleration transmitted by the material increases. This is because the material has been completely crushed, and the phenomenon of "bottoming" appears during the impact process. At this time, the material has no cushioning capacity at all. Under dynamic compression, the compressive strain rate can be estimated by the following formula:

$\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In the formula, v is the maximum impact velocity, according to the principle of free fall:

$\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; =</span>\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; g\; H</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

In this experiment, the impact height is H=0.5m, so the dynamic compressive strain rate is 1.7*10 ² /s.

Under dynamic compression, the shoulder points of the energy absorption curves corresponding to different t/l are connected - as shown by the black thick solid line in Figure 6, the optimal energy absorption curve formed is also approximately linear. With the increase of paper honeycomb cell thickness-span ratio t/l, the optimal energy-absorbing point moves to the upper right.

3. Energy absorption diagram of paper honeycomb sandwich panels with different thickness-to-span ratios

为蜂窝纸板的压缩应变率；W为蜂窝纸板压缩过程中单位体积材料的最大吸能量；E_s为蜂窝原纸的固体模量；σ_p/E_s为用蜂窝原纸固体模量标定的蜂窝纸板压缩应力；W/E_s为用蜂窝原纸固体模量标定的蜂窝纸板单位体积变形能。在同一应变率下，随着纸蜂窝胞壁厚跨比t/l的增大，蜂窝纸板的承压性能和单位体积吸能量都所有增加，且线性增加。因此，在某一应变率下优化选材时，可以用插值法找到纸蜂窝胞壁的最佳厚跨比。From the analysis of static and dynamic compression experiments above, it can be seen that under the same strain rate, as the thickness-to-span ratio t/l of paper honeycomb increases, its pressure-bearing performance and energy absorption per unit volume increase, and increase linearly. Therefore, when optimizing material selection at a certain strain rate, the best thickness-to-span ratio of paper honeycomb can be found by interpolation. In order to examine the cushioning energy absorption characteristics of the same structural paper honeycomb under different loading strain rates, the energy absorption diagrams of the above experiments were gathered to obtain an energy absorption diagram for testing the performance of the paper honeycomb core, as shown in Figure 7. Figure 7 shows a family of curves, which shows that with the increase of the strain rate, the pressure-bearing performance and the maximum energy absorption per unit volume of the paper honeycomb sandwich panel increase. The meaning of each letter among Fig. 7 is as follows: t is the thickness of honeycomb base paper; l is the side length of hexagonal paper honeycomb single-layer cell wall;

is the compressive strain rate of the honeycomb paperboard; W is the maximum energy absorbed per unit volume of material during the compression process _of the honeycomb paperboard; _{E s} is the solid modulus of the honeycomb base paper; Stress; W/E _s is the deformation energy per unit volume of the honeycomb paperboard calibrated by the solid modulus of the honeycomb base paper. Under the same strain rate, with the increase of the paper honeycomb cell wall thickness-to-span ratio t/l, the pressure-bearing performance and energy absorption per unit volume of the honeycomb paperboard both increase, and increase linearly. Therefore, when optimizing material selection at a certain strain rate, the best thickness-to-span ratio of paper honeycomb cell walls can be found by interpolation.

The cushioning and energy-absorbing performance of the paper honeycomb sandwich panel described above can be characterized by an energy absorption diagram. The energy absorption diagram in this patent is standardized by the solid modulus of the paper honeycomb material, so that the honeycomb sandwich materials of different materials can be integrated on the same diagram. . Moreover, the strain rate and paper honeycomb structure information are contained in the same energy absorption diagram, and the strain rate parallel family lines and the paper honeycomb thickness-span ratio parallel family lines are formed. With the help of the energy absorption diagram, the interpolation method can be used to optimize the thickness-span ratio of the paper honeycomb, which is beneficial to the optimal design and material selection of the paper honeycomb structure.

The practical application of the energy absorption diagram of the honeycomb paperboard in the present invention is mainly manifested in the optimal selection of the honeycomb base paper and the optimal selection of the honeycomb paperboard structure.

The energy absorption diagram of the honeycomb paperboard shown in FIG. 7 in the present invention can be used for the optimal design and material selection of the honeycomb paperboard used as a buffer bearing.

The optimization of the honeycomb paperboard structure is mainly to design the optimal thickness of the paper honeycomb core and the optimal cell wall thickness-span ratio of the paper honeycomb (because the thickness of the face paper of the honeycomb paperboard is usually much smaller than the thickness of the paper honeycomb core, the thickness of the paper honeycomb core is usually taken as thickness of honeycomb paperboard).

Specific Example 1: It is known that the mass of the packaged object is m=10kg, the contact area between the packaging material and the packaged object is A=0.01m ² , the drop height of the packaged object is H=0.5m, and the fragility value of the packaged object The solid modulus of honeycomb base paper for making honeycomb paperboard is E _s = 0.89GPa. Here, we introduce the use of honeycomb paperboard cushioning performance testing method combined with the energy absorption diagram of honeycomb paperboard to optimize the design of paper honeycomb core cell wall thickness-span ratio and honeycomb Method of cardboard thickness.

From the drop height H=0.5m of the packaged object, its maximum impact velocity v=3.2m/s, and the absorbed impact energy U=mv ² /2=51.2J; because the brittle value a of the packaged object is 30g, its The maximum allowable packaging force, F=ma=3000N, the maximum allowable peak stress σ _p =F/A=300KN/m ² ; the maximum allowable standardized peak stress σ _p /E is known from the solid modulus E _s of the honeycomb base paper as 0.89GPa _s = 3.4*10 ^-4 . The method for optimizing the honeycomb paperboard structure by means of Fig. 7 is as follows:

(1) Draw a vertical line corresponding to the peak stress value σ _p /E _s in the schematic diagram 8 of the known energy absorption diagram;

(2) Select a suitable honeycomb paperboard thickness T ₁ and use it to estimate the approximate strain rate from the impact velocity v

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(3), use the interpolation method to find the strain rate in the parallel line family of the strain rate , the line intersects the stress line drawn in (1), the corresponding value of log(W/E _s ) is determined by the intersection point, and the energy absorption per unit volume W is calculated from the solid modulus E _s of the honeycomb base paper;

(4), with the W value that (3) obtains, known absorbed energy U and the contact area A of packaged object and honeycomb paperboard, calculate the thickness T of new honeycomb paperboard ₂ ;

再按(3)的方法确定新的log(W/E_s)，W，再按(4)的方法得到新的T₃。(5), calculate the new strain rate according to the method of ( ₂ ) with T in (4)

Then determine the new log(W/E _s ), W by the method of (3), and then obtain the new T ₃ by the method of (4).

Repeat the above steps until the calculated thickness of the honeycomb paperboard reaches a certain value, which is the optimal thickness of the honeycomb paperboard. Then according to the position of the intersection of the final strain rate and the stress line, according to the paper honeycomb cell wall thickness-span ratio parallel line family on the energy absorption graph, find the best paper honeycomb cell wall thickness-span ratio. The detailed iterative process of the above process is as follows:

first iteration

Initial selection of T ₁ 50mm

The resulting strain rate, 63.2/s

When σ _p /E _s =3.4*10-4, the corresponding W/E _s is 7.5*10 ^-4

Energy absorption per unit volume, W 6.25*10 ⁵ J/m ³

second iteration

It can be seen from U=WAT that T ₂ 8.24mm

                            383/samended

383/s

Corrected W 5.92*10 ⁵ J/m ³

third iteration

It can be seen from U=WAT that T ₃ 8.65mm

The optimal thickness-to-span ratio t/l is slightly lower than 0.020

In this example, after 3 iterations, the thickness of the selected honeycomb paperboard is reduced to 8.65mm, which can be taken as 10mm in practical application, and the corresponding optimal thickness-to-span ratio t/l of the paper honeycomb cell wall is 0.020.

Specific embodiment 2: the mass of the packaged object is known, m=10kg, the contact area between the packaging material and the packaged object, A=0.01m ² , the drop height of the packaged object H=0.5m, the The brittle value a is 20g, and the thickness of the honeycomb paperboard is 20mm. According to the energy absorption chart 7, find out the best elastic modulus of the honeycomb base paper and the best thickness-to-span ratio of the honeycomb cell wall.

Before optimizing material selection, you can try to give a specific value to the elastic modulus of honeycomb base paper. The process is shown in Figure 4. The specific method is as follows:

(1) The maximum impact velocity v=3.2m/s is known from the drop height H=0.5m of the packaged object, the absorbed impact energy U=mv ² /2=51.2J, and the distance between the honeycomb paperboard and the packaged object The contact area is A=0.01m ² and the thickness of the honeycomb paperboard is 15mm. The volume of the honeycomb paperboard is 2*10 ^-4 m ³ , so the energy absorbed per unit volume of the honeycomb paperboard is W=341KJ/m ³ ; If the brittle value a is 20g, then its maximum allowable packaging force, F=ma=2000N, and the maximum allowable peak stress, σ _p =F/A=200KN/m ² ;

(2) Select an appropriate value of the solid modulus of honeycomb base paper, such as E _s =1GPa, draw W/E _s =3.41*10-4 and σ _p /E _s =2*10 in the known energy absorption schematic diagram 7 The straight line of -4, the two intersect at point A, as shown in Figure 9;

(3) Draw a straight line with a slope of 1 through point A, move along the line, keep the values of W and σ _p unchanged, and only change E _s ;

(4) Calculate the strain rate according to formula (1), select the intersection point of the straight line in (3) and the energy absorption line under the strain rate under the strain rate, and obtain point B;

(5) Read out the W/E _s and σ _p /E _s values corresponding to point B in Figure 9, and then calculate the elastic modulus E _s of the honeycomb base paper according to the values of W and σ _p in (1), and then according to The paper honeycomb cell wall thickness-span ratio parallel line family corresponding to point B, the best thickness-span ratio of point B is determined by interpolation method.

In this example, the elastic modulus E _s of the base paper is 0.85Gpa, and the optimum thickness-span ratio of the paper honeycomb core cell wall is slightly lower than 0.043.

Compared with the traditional stress-strain curve and maximum acceleration static stress curve, the energy absorption diagram has great advantages and universality. With the help of the honeycomb paperboard energy absorption diagram, the optimal design of the honeycomb paperboard structure and the design of the honeycomb base paper can be systematically realized without a large number of experiments. Optimize selection. The optimal design of the honeycomb paperboard structure can calculate its final convergence value with the help of a small computer program with an iterative method.

The method for detecting the cushioning performance of the honeycomb paperboard according to the present invention can quickly and accurately realize the structural optimization design and material selection of the honeycomb paperboard, provide accurate reference data for the production of the honeycomb paperboard under different conditions, and thereby realize energy saving and high efficiency Package.

The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be assumed that the specific implementation of the present invention is limited to these descriptions. For those of ordinary skill in the technical field of the present invention, without departing from the concept of the present invention, some simple deduction or replacement can be made, which should be regarded as belonging to the protection scope of the present invention.

Claims (2)

1. A method for utilizing honeycomb paperboard energy absorption diagram to carry out honeycomb paperboard structure optimization selection, is characterized in that, adopts following method to draw honeycomb paperboard energy absorption diagram: Detect the solid modulus of the honeycomb base paper by a detector; obtain the static compression energy absorption of the honeycomb paper core according to the static compression stress curve, and use the solid modulus to standardize the energy absorption of the honeycomb paper core to obtain a standardized energy absorption per unit volume The relationship curve between the normalized stress and the normalized stress, that is, the energy absorption curve; at a low strain rate, connect the shoulder points of the energy absorption curve corresponding to the ratio of the thickness of the honeycomb paperboard obtained by static compression to the span, and obtain an approximately linear Under high strain rate, the dynamic compression maximum acceleration static stress curve is obtained by polynomial fitting according to the dynamic compression curve; under dynamic compression, the shoulder of the energy absorption curve corresponding to the ratio of the thickness of the honeycomb paperboard to the span The points are connected to form an approximately linear energy absorption curve; the above energy absorption curves under different strain rates are summarized to obtain an energy absorption diagram for testing the performance of the paper honeycomb panel core; The method for optimizing the honeycomb paperboard structure by using the energy absorption diagram of the honeycomb paperboard includes the steps of: A1: Find the corresponding peak stress value σ _p /E _s in the honeycomb paperboard energy absorption diagram, and draw the corresponding stress line in the honeycomb paperboard energy absorption diagram; A2: Choose an appropriate honeycomb paperboard thickness T ₁ , use it from the impact velocity v, according to the formula

approximate strain rate

; A3: Use interpolation to find the strain rate in the family of parallel lines of the strain rate

A straight line, which intersects the stress line drawn in the A1 step, determines the corresponding value of log(W/E _s ) by the intersection point, and calculates the energy absorption per unit volume from the solid modulus E _s of the honeycomb base paper W; A4: Using the W value obtained in the A3 step, the known absorbed energy U and the contact area A between the packaged object and the honeycomb paperboard, calculate the thickness _T2 of the new honeycomb paperboard; A5: Use the _T2 value in the A4 step to calculate the new strain rate according to the method in the A2 step

, then determine new log(W/E _s ), W by the method in the A3 step, and then obtain new _T by the method in the A4 step; A6: Repeat the above steps until the calculated thickness T of the honeycomb paperboard converges to a certain value, which is the optimal thickness of the honeycomb paperboard, and then according to the position of the intersection of the final strain rate and the stress line, according to the energy The paper honeycomb cell wall thickness-span ratio parallel line family on the absorption diagram finds the optimal paper honeycomb cell wall thickness-span ratio, and the obtained optimal thickness of the honeycomb paperboard and the optimal paper honeycomb cell wall thickness-span ratio are The optimized structure of the honeycomb paperboard. 2. A method for selecting honeycomb base paper using the energy absorption diagram of honeycomb paperboard, characterized in that: the following method is used to draw the energy absorption diagram of honeycomb paperboard: Detect the solid modulus of the honeycomb base paper by a detector; obtain the static compression energy absorption of the honeycomb paper core according to the static compression stress curve, and use the solid modulus to standardize the energy absorption of the honeycomb paper core to obtain a standardized energy absorption per unit volume The relationship curve between the normalized stress and the normalized stress, that is, the energy absorption curve; at a low strain rate, connect the shoulder points of the energy absorption curve corresponding to the ratio of the thickness of the honeycomb paperboard obtained by static compression to the span, and obtain an approximately linear Under high strain rate, the dynamic compression maximum acceleration static stress curve is obtained by polynomial fitting according to the dynamic compression curve; under dynamic compression, the shoulder of the energy absorption curve corresponding to the ratio of the thickness of the honeycomb paperboard to the span The points are connected to form an approximately linear energy absorption curve; the above energy absorption curves under different strain rates are summarized to obtain an energy absorption diagram for testing the performance of the paper honeycomb panel core; The method for selecting honeycomb base paper using the honeycomb paperboard energy absorption diagram includes steps: B1: According to the drop height H of the packaged object, the impact velocity v of the packaged object and the impact energy U=mv ² /2 absorbed by the packaged object are obtained, from the contact area between the honeycomb paperboard and the packaged object The thickness T of A and honeycomb paperboard, obtain the volume V of described honeycomb paperboard, and thus obtain the energy W=U/V that described honeycomb paperboard absorbs per unit volume; Because the brittle value a of described packaged object is known , then the maximum allowable packaging force F=ma and the maximum allowable peak stress σ _p =F/A of the packaged object; B2: Select an appropriate value E _s of the solid modulus of the honeycomb base paper, draw a straight line corresponding to the values of W/E _s and σ _p /E _s in the known energy absorption diagram of the honeycomb paperboard, and the two lines intersect at point A; B3: Draw a straight line with a slope of 1 through the point A, move along the line, keep the values of W and σ _p unchanged, and only change E _s ; B4: According to the formula Calculate the strain rate, select the intersection of the straight line in the B3 step and the energy absorption line under the strain rate under the strain rate, and obtain point B; B5: Read the W/E _s and σ _p /E _s values corresponding to the point B in the energy absorption diagram of the honeycomb paperboard, and calculate the elastic modulus of the honeycomb base paper according to the values of W and σ _p in the B1 step Quantity E _s , according to the paper honeycomb cell wall thickness-span ratio parallel line family corresponding to point B, determine the optimal thickness-span ratio of point B by interpolation.

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