Cushioning energy absorption of polyethylene foam single-filledpaper corrugation tubes under axial drop impact
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摘要: 利用聚乙烯闭孔泡沫单填充纸瓦楞管开展轴向跌落冲击试验，对比分析了结构参数和冲击参数对其缓冲吸能特性参数（比吸能、行程利用率、压缩力效率、比总体效率）的影响。结果表明，X向单填充管的动态缓冲吸能特性优于Y向单填充管，而静态缓冲吸能特性差于Y向单填充管。正四边形单填充管的动态缓冲吸能特性优于正五、六边形单填充管，X向正四边形单填充管的比吸能相较于正五、六边形管分别提高了114.4%和182.3%。对于跌落冲击压缩，单填充管的比吸能、行程利用率、比总体效率随着管长比的增大而减小，管长比为1.4的X向单填充管的比吸能相较于管长比为2.2和3.0的单填充管分别增加了45.8%和117.9%，而压缩力效率随着管长比的增大而增大。随着跌落冲击质量或冲击能量的增加，比吸能、行程利用率、压缩力效率和比总体效率皆呈增大趋势，冲击质量对X向单填充管的影响较大，而冲击速度则对Y向单填充管的影响较大。Abstract: This paper investigated comparatively the effect of structural parameters (tube direction, tube cross-section shape, tube length ratio) and impact parameters (impact mass, impact energy) on the cushioning energy absorption characteristics (specific energy absorption, stroke efficiency, crush force efficiency, specific total efficiency) of the polyethylene closed-foam single-filling paper corrugation tubes by axial drop impact tests. The results show that the single-filled X-direction tubes hold better dynamic cushioning energy absorption than the single-filled Y-direction tubes, but weaker static cushioning energy absorption than the single-filled Y-direction tubes. The regular quadrilateral single-filled tubes have superior dynamic cushioning energy absorption to the regular pentagonal and hexagonal single-filled tubes, e.g. the regular quadrilateral single-filled X-direction tubes can respectively increase the specific energy absorption by 114.4% and 182.3% for those with tube cross-section shape of regular pentagon and hexagon. During the drop impact process the specific energy absorption, stroke efficiency and specific total efficiency of the single-filled tubes decrease with the increase of tube length ratio, e.g. the single-filled X-direction tube with the tube length ratio of 1.4 can respectively increase the specific energy absorption by 45.8% and 117.9% for those with tube length ratio of 2.2 and 3.0, moreover the crush force efficiency increases as the tube length ratio increases. The characteristics of dynamic cushioning energy absorption increase with the increase of drop impact mass or impact energy, and the single-filled X-direction tube is greatly controlled by the mass of impact block, while the single-filled Y-direction tube is obviously affected by the velocity of drop impact.
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图 9 不同管横截面形状的应力应变曲线
Figure 9. Stress-strain curves of different tube cross-section shapes
图 15 不同跌落冲击质量的缓冲吸能特性比较
Figure 15. Comparison of cushioning energy absorption for different drop impact masses
图 16 不同跌落冲击能量的应力应变曲线
Figure 16. Stress-strain curves of different drop impact energies
图 18 不同跌落冲击能量的缓冲吸能特性比较
Figure 18. Comparison of cushioning energy absorption for different drop impact energies
表 1 试样结构参数与跌落冲击参数
Table 1. Parameters of sample structures and drop impacts
管结构参数 跌落冲击参数 d n l2/l1 l1/mm l2/mm H/cm M/kg X, Y 4, 5, 6 1.4 35 49 H1=30, H2=50, H3=70 M1=7.000, M2=9.125, M3=11.275, M4=14.550 50 70 X, Y 4, 5, 6 2.2 35 77 H1=30, H2=50, H3=70 M1=7.000, M2=9.125, M3=11.275, M4=14.550 50 110 X, Y 4, 5, 6 3.0 35 105 H1=30, H2=50, H3=70 M1=7.000, M2=9.125, M3=11.275, M4=14.550 50 150 
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表 2 不同管方向的静态缓冲吸能特性比较
Table 2. Comparison of static cushioning energy absorption for different tube directions
试样 σy/MPa σb/MPa E/J ea/(J·g−1) Δs/% ηcf/% ηt/kg−1 CT4X-50/70-SF-12 0.286 0.191 37.90 1.526 61.58 66.82 16.77 CT4Y-50/70-SF-12 0.625 0.467 96.47 3.631 65.13 74.74 18.07 CT5X-50/70-SF-12 0.231 0.173 64.40 2.013 63.62 75.05 19.04 CT5Y-50/70-SF-12 0.631 0.592 167.22 5.097 66.41 93.83 17.63 CT6X-50/70-SF-12 0.195 0.157 68.54 2.023 65.13 80.41 14.71 CT6Y-50/70-SF-12 0.492 0.476 187.29 5.102 66.64 96.82 16.02
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表 3 不同管横截面形状的静态缓冲吸能特性比较
Table 3. Comparison of static cushioning energy absorption for different tube cross-section shapes
试样 σy/MPa σb/MPa E/J ea/(J·g−1) Δs/% ηcf/% ηt/kg−1 CT4X-35/77-SF-12 0.273 0.227 24.41 1.219 56.46 83.15 21.41 CT5X-35/77-SF-12 0.301 0.286 47.91 1.888 59.79 94.95 23.35 CT6X-35/77-SF-12 0.251 0.197 58.74 2.127 65.27 78.64 20.02 CT4Y-35/77-SF-12 0.693 0.642 77.84 3.754 61.73 92.64 25.38 CT5Y-35/77-SF-12 0.950 0.850 141.44 5.602 66.25 89.46 21.98 CT6Y-35/77-SF-12 0.721 0.646 180.73 6.610 71.16 89.54 21.62
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表 4 不同管长比的静态缓冲吸能特性比较
Table 4. Comparison of static cushioning energy absorption for different tube length ratios
l2/l1 试样 σy/MPa σb/MPa E/J ea/(J·g−1) Δs/% ηcf/% ηt/kg−1 1.4 CT4X-35/49-SF-12 0.386 0.273 18.32 1.480 62.61 70.73 28.88 2.2 CT4X-35/77-SF-12 0.273 0.227 24.41 1.219 56.46 83.15 21.41 3.0 CT4X-35/105-SF-12 0.380 0.298 48.92 1.825 62.32 78.42 16.88 1.4 CT4Y-35/49-SF-12 0.729 0.674 51.07 3.814 62.75 92.46 38.52 2.2 CT4Y-35/77-SF-12 0.693 0.642 77.84 3.754 61.73 92.64 25.38 3.0 CT4Y-35/105-SF-12 0.642 0.620 108.90 3.857 64.63 96.57 20.64
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表 5 跌落冲击响应结果
Table 5. Results of drop impact responses
冲击条件 CT5X-50/70-SF CT5Y-50/70-SF CT5X-50/110-SF CT5Y-50/110-SF CT5X-50/150-SF CT5Y-50/150-SF amax/g t/ms amax/g t/ms amax/g t/ms amax/g t/ms amax/g t/ms amax/g t/ms H1/M1 18.85 31.20 52.94 13.40 16.57 20.80 50.37 10.20 17.30 26.40 49.14 8.30 H1/M2 17.45 34.80 43.90 14.75 16.71 38.00 41.07 14.51 14.51 26.00 43.03 9.00 H1/M3 14.87 38.00 41.45 13.60 15.32 41.50 39.52 11.40 13.56 27.40 42.99 10.00 H1/M4 12.97 45.00 39.28 13.60 16.24 36.00 37.73 12.50 10.58 44.00 39.46 13.48 H2/M1 17.89 36.20 51.09 11.80 20.29 38.10 49.53 11.70 19.41 28.04 50.76 8.30 H2/M2 17.23 47.50 49.05 13.75 14.60 48.50 44.58 12.25 17.31 35.18 40.80 8.00 H2/M3 16.36 53.00 33.45 18.20 13.72 49.50 40.80 15.00 13.15 39.60 42.99 12.30 H2/M4 15.28 55.00 40.45 20.20 12.58 61.00 36.05 16.80 11.58 58.07 31.24 15.80 H3/M1 20.88 45.02 48.08 11.48 18.35 37.99 49.98 9.39 19.76 32.75 48.06 11.54 H3/M2 23.06 42.98 45.01 12.95 15.91 42.96 48.05 12.89 16.86 34.95 39.67 10.52 H3/M3 29.05 44.85 41.16 16.21 15.44 52.02 41.26 14.25 16.32 48.46 44.96 13.27 H3/M4 13.45 40.85 33.91 19.31 13.52 62.87 33.97 21.79 13.31 58.21 33.05 17.32
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表 6 不同管方向的跌落冲击缓冲吸能特性比较
Table 6. Comparison of cushioning energy absorption for different tube directions under drop impact
试样 σy/MPa σb/MPa E/J ea/(J·g−1) Δs/% ηcf/% ηt/kg−1 CT4X-50/110-SF-50/11.275 0.316 0.253 51.47 1.333 44.28 80.06 8.44 CT4Y-50/110-SF-50/11.275 0.892 0.592 45.28 1.121 18.25 66.36 2.49 CT5X-50/110-SF-50/11.275 0.232 0.188 23.84 0.482 41.72 81.03 2.89 CT5Y-50/110-SF-50/11.275 0.689 0.556 17.56 0.340 12.05 80.69 0.69 CT6X-50/110-SF-50/11.275 0.140 0.150 26.74 0.438 36.11 107.14 3.14 CT6Y-50/110-SF-50/11.275 0.556 0.429 24.46 0.414 11.91 77.16 0.75
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表 7 不同管横截面形状的跌落冲击缓冲吸能特性比较
Table 7. Comparison of cushioning energy absorption of different tube cross-section shapes under drop impact
试样 σy/MPa σb/MPa E/J ea/(J·g−1) Δs/% ηcf/% ηt/kg−1 CT4X-50/150-SF-50/11.275 0.286 0.206 51.23 0.926 40.42 72.03 4.75 CT5X-50/150-SF-50/11.275 0.190 0.171 26.25 0.432 31.74 90.01 2.32 CT6X-50/150-SF-50/11.275 0.196 0.131 26.23 0.328 26.53 66.84 1.23 CT4Y-50/150-SF-50/11.275 0.615 0.414 37.54 0.668 13.96 67.32 1.58 CT5Y-50/150-SF-50/11.275 0.726 0.504 22.45 0.339 9.54 69.42 0.48 CT6Y-50/150-SF-50/11.275 0.490 0.399 24.91 0.296 9.19 81.43 0.44
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表 8 不同管长比的跌落冲击缓冲吸能特性比较
Table 8. Comparison of cushioning energy absorption for different tube length ratios under drop impact
l2/l1 试样 σy/MPa σb/MPa E/J ea/(J·g−1) Δs/% ηcf/% ηt/kg−1 1.4 CT6X-35/49-SF-50/7.000 0.264 0.182 30.15 1.556 64.72 75.01 21.85 2.2 CT6X-35/77-SF-50/7.000 0.176 0.168 29.46 1.067 48.05 92.05 14.29 3.0 CT6X-35/105-SF-50/7.000 0.215 0.156 29.18 0.714 35.78 72.56 5.74 1.4 CT6Y-35/49-SF-50/7.000 0.595 0.449 28.44 1.487 27.14 78.66 9.27 2.2 CT6Y-35/77-SF-50/7.000 0.538 0.453 26.64 0.974 16.45 90.71 4.27 3.0 CT6Y-35/105-SF-50/7.000 0.602 0.463 24.37 0.606 12.55 76.91 1.74
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表 9 不同跌落冲击条件下冲击能量的计算结果
Table 9. Calculated impact energies under different drop impact conditions
冲击条件 冲击能量/J 冲击条件 冲击能量/J 冲击条件 冲击能量/J 冲击条件 冲击能量/J H1/M1 20.6 H1/M4 42.8 H2/M3 55.2 H3/M2 62.6 H1/M2 26.8 H2/M1 34.3 H2/M4 71.3 H3/M3 77.3 H1/M3 33.1 H2/M2 44.7 H3/M1 48.0 H3/M4 99.8
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