目的 针对缓冲包装设计中最大加速度-静应力曲线触底边界缺乏定量界定方法的问题,提出一种精确测定触底临界点的夹逼法,并建立高精度预测模型,为缓冲包装精细化设计提供理论依据。方法 以密度25 kg/m3的发泡聚乙烯为研究对象,采用ANSYS LS-DYNA有限元仿真软件开展落锤冲击试验。在0.31、0.51、0.66、0.81、0.97 m 5个跌落高度下,对厚度为0.02~0.06 m的9组试样进行测试。提出基于静应力区间逐次收缩的夹逼法,以触底前相邻2次未触底测试的最大加速度相对误差小于0.5%为收敛准则,精确测定触底临界点。选取0.06、0.05、0.04、0.03、0.02 m 5个厚度数据作为训练集,构建以跌落高度和材料厚度为自变量、临界最大加速度为因变量的三次多项式完全交互模型;以0.055、0.045、0.035、0.025 m 4个厚度数据作为测试集验证模型精度。结果 临界最大加速度随厚度增加呈非线性递减,随高度升高而增大。表征模型拟合精度的决定系数为0.994 8,表征测试集的预测精度的决定系数为0.991 4,平均绝对百分比误差为3.99%,表明模型具有优异的拟合能力与预测精度。结论 采用提出的夹逼法实现了触底临界点的精确测定,所建模型可有效描述临界点变化规律,为缓冲包装精细化设计提供了可靠依据。但本研究仅针对单一密度发泡聚乙烯材料且采用ANSYS/LS-DYNA有限元仿真方法,后续可开展不同材料、不同工况的对比研究以验证模型的泛化能力。
Abstract
To address the lack of a quantitative method for determining the bottoming boundary of the maximum acceleration-static stress curve in cushioning packaging design, the work aims to propose a successive approximation method for accurately determining the bottoming critical point, and establish a high-precision prediction model to provide a theoretical basis for refined cushioning packaging design. Expanded polyethylene with a density of 25 kg/m3 was selected as the research object, and drop impact tests were conducted via ANSYS LS-DYNA finite element simulations. Tests were carried out on nine groups of specimens with thicknesses ranging from 0.02 to 0.06 m. A successive approximation method based on iterative contraction of the static stress interval was proposed, with the convergence criterion defined as the relative error of the maximum acceleration between two consecutive non-bottoming tests prior to bottoming being less than 0.5%, to accurately determine the bottoming critical point. Data from five thicknesses (0.06, 0.05, 0.04, 0.03, 0.02 m) were selected as the training set. A fully interactive cubic polynomial model was then constructed, with drop height and material thickness as the independent variables and the critical maximum acceleration as the dependent variable. Data from four thicknesses (0.055, 0.045, 0.035, 0.025 m) were used as the test set to validate the model accuracy. The critical maximum acceleration decreased nonlinearly with the increasing thickness and increased with the increasing drop height. The coefficient of determination for the fitting accuracy of the model is 0.9948, and the coefficient for the prediction accuracy of the test set was 0.991 4 with a mean absolute percentage error of 3.99%, indicating that the model had outstanding fitting performance. The proposed successive approximation method enables accurate determination of the bottoming critical point, and the established model effectively characterizes its variation law of the critical point, providing a reliable basis for refined cushioning packaging design. However, this work is limited to a single density of EPE material and employs the ANSYS LS-DYNA finite element simulation method, and future research should conduct comparative studies on different materials and different working conditions to further verify the generalizability of the model.
关键词
缓冲包装 /
最大加速度-静应力曲线 /
触底临界点 /
夹逼法 /
发泡聚乙烯 /
多元非线性回归
Key words
cushioning packaging /
maximum acceleration-static stress curve /
bottoming critical point /
successive approximation method /
expanded polyethylene /
multivariate nonlinear regression
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基金
河南牧业经济学院博士启动基金（2019HNUAHEDF021）
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