缓冲包装系统跌落破损边界曲线研究

建立了线性和非线性缓冲包装系统的无量纲跌落冲击方程,得到了产品最大加速度响应,提出了评价线性和非线性包装系统产品安全与否的跌落破损边界曲线概念。对于线性包装系统,固有频率和跌落冲击速度是产品跌落破损的评价量;对于非线性包装系统,系统参数和无量纲跌落冲击速度是产品跌落破损的评价量。     

矩形脉冲激励下正切型包装系统关键部件破损曲面研究

研究了正切包装系统的关键部件在矩形脉冲激励下的冲击破损评价方法。建立了二自由度非线性产品包装系统模型,得到了该系统的冲击动力学方程,并进行了数值求解。依据数值求解结果得到该系统的关键部件破损边界曲线和破损边界曲面,并讨论了频率比、阻尼、脉冲激励幅值和系统参数对关键部件破损边界的影响规律。结果表明,频率比、阻尼、脉冲激励幅值和系统参数对关键部件破损边界影响显著。     

矩形波冲击下C 楞瓦楞纸板系统的冲击谱研究

基于C 楞瓦楞纸板动态本构模型,建立了C 楞瓦楞纸板包装系统动力学模型。借助三维冲击谱、破损边界曲面的概念,利用Rnuge-Kutta 算法,研究了C 楞瓦楞纸板缓冲包装系统在矩形波冲击下,不同阻尼、线性参量、正弦参量、正切参量对C 楞瓦楞纸板包装系统易损件冲击谱和破损边界的影响。计算结果表明:C 楞瓦楞纸板缓冲性能受阻尼系数、线性参量、正弦参量及正切参量的制约,且对C 楞瓦楞纸板缓冲包装系统的冲击谱和破损边界有显著影响。     

后峰锯齿脉冲激励下正切型非线性包装系统的冲击响应

应用数值方法,求解单自由度产品包装系统的非线性动力学方程,得到了后峰锯齿波冲击下正切型非线性包装系统的冲击响应,讨论了相关参数对冲击谱曲线和边界破损曲线的影响。     

半正弦波冲击下瓦楞纸板缓冲包装衬垫破损边界的研究

以瓦楞纸板平压本构模型为基础,建立动力学方程,研究相关参量对瓦楞纸板缓冲包装系统冲击谱和破损边界的影响,并通过数值计算得到结果,表明瓦楞纸板缓冲性能与阻尼系数、线性参量、正弦参量及正切参量关系显著.     

双曲正切非线性系统跌落冲击响应分析的 一种近似解析法

针对典型双曲正切缓冲包装系统, 跌落冲击条件下讨论系统近似解 析解。将系统简化为三次 - 五次非线性系统,引入无量纲参数推导无量纲动 力学方程, 应用牛顿谐波平衡法获得系统响应一阶、二阶、三阶近似解析解。 算例分析表明,牛顿谐波平衡法获得的三阶近似解与龙格 - 库塔法的数值解 最为接近,位移响应最大值、加速度响应最大值以及跌落冲击时间的相对误 差控制在 1% 以内。为双曲正切型非线性系统跌落冲击响应分析提供了一种 新的近似分析方法。     

前峰锯齿脉冲激励下正切非线性包装系统的冲击响应

研究肯有正切型非线性特性的包装系统在前峰锯齿脉冲激励下的冲击响应，求得了产品包装系统的非线性动力学方程，讨论了相关参数对冲击谱曲线和边界破损曲线的影响。     

矩形脉冲激励下双曲正切包装系统非线性动力学特性研究

建立了二自由度非线性包装系统模型,得到了冲击动力学方程并对其进行了数值求解,在此基础上,研究了带有关键部件双曲正切包装系统的冲击响应特性。矩形脉冲为各种脉冲激励中最严酷的,因此选矩形脉冲为研究对象,得到了关键部件的三维冲击谱图。从谱图中进一步讨论了频率比、脉冲激励幅值、阻尼和系统参数对关键部件冲击谱的影响规律,结果表明频率比、脉冲激励幅值、阻尼和系统参数对关键部件冲击响应峰值均有显著影响。为产品缓冲包装设计提供一定的科学依据。     

正切型缓冲系统跌落冲击响应分析的NHB方法

目的为了获得正切型缓冲系统跌落冲击响应的近似解析解。方法将正切型系统简化为3次、5次非线性系统,经无量纲处理后获得无量纲动力学方程,应用牛顿谐波平衡法求解系统无量纲动力学方程,得到跌落冲击响应一阶、二阶近似解析解,并获得系统位移响应最大值、加速度响应最大值以及跌落冲击持续时间等重要参数的解析表达式。结果通过算例分析表明,牛顿谐波平衡法二阶近似解与龙格-库塔数值解接近,相对误差控制在2%以内。结论牛顿谐波平衡法为非线性缓冲系统跌落冲击响应分析提供了一种新的有效解析方法。     

前峰锯齿脉冲激励下正切型非线性包装系统的冲击响应

研究具有正切型非线性特性的包装系统在前峰锯齿脉冲激励下的冲击响应,求得了产品包装系统的非线性动力学方程,讨论了相关参数对冲击谱曲线和边界破损曲线的影响。     

On evaluation of product dropping damage

As an extension of the classical damage boundary curve in the case of product dropping shock, the concept of a dropping damage boundary curve for linear and non‐linear packaging system to evaluate the dropping damage of product is developed in this paper. The dropping damage boundary curves are given for linear and hyperbolic tangent packaging systems with different damping. For a linear packaging system the dropping damage of a product is determined only by the natural frequency of the corresponding packaging system without damping and the dropping shock velocity of package except the system damping, and they compose the basic evaluation quantities of product dropping damage. For a non‐linear hyperbolic tangent packaging system, the system parameter and the dimensionless dropping shock velocity are two basic quantities in the evaluation of product dropping damage. It should be emphasized that the dimensionless dropping shock velocity is related not only to the dropping height of package box but also to the system parameter integration. This is the important feature differentiating a non‐linear packaging system from a linear one. The influence of system damping on the dropping damage boundary curves is also discussed. This concept and the results have important value in the design of cushioning packaging. Copyright © 2002 John Wiley & Sons, Ltd.     

矩形脉冲激励下斜支承系统易损件的破损评价

以考虑易损件的斜支承系统为研究对象,建立矩形脉冲激励下系统无量纲非线性冲击动力学方程。以脉冲激励幅值与易损件加速度响应峰值之比作为系统无量纲临界加速度,临界加速度与无量纲脉冲时间乘积为系统无量纲临界速度,引入系统支承角或频率比或质量比,构建斜支承系统易损件破损边界曲面。利用龙格-库塔数值分析方法求解方程,分析讨论频率比、质量比、支承角等因素对易损件破损边界的影响。研究表明,增大频率比、减小系统支承角、增大质量比等可增加易损件安全区域;随无量纲脉冲激励幅值增加,易损件破损区域减小。研究结论为斜支承系统的设计提供理论依据。     

考虑易损件的正切型包装系统冲击破损边界曲面研究

以正切包装系统为例,研究考虑易损件的非线性包装系统在半正弦脉冲激励下的冲击特性,提出考虑易损件的产品包装系统冲击破损边界曲面新概念,讨论了频率比、脉冲激励幅值和系统参数对易损件破损边界的影响规律.结果表明,频率比、脉冲激励幅值和系统参数对易损件冲击破损边界影响显著.研究结论为产品包装设计提供科学依据.     

Shock spectra and damage boundary curves for non‐linear package cushioning systems

This paper suggests a general approach for obtaining shock spectra and damage boundary curves for cushioning packaging systems. This approach can treat both linear and non‐linear cushioning systems such as cubic, tangent and hyperbolic tangent systems. Corresponding software has been developed for analysing different cushioning systems, and the shock spectra and the damage boundary curves are given for a tangent non‐linear cushioning system under the action of a rectangular, half‐sine, terminal‐peak saw‐tooth and initial‐peak saw‐tooth pulse, respectively. It is worth noting that the shock spectrum is affected not only by the damping parameter but also by the dimensionless pulse peak, and that both the damping parameter and the dimensionless fragility also influence the damage boundary curve. These are important features of non‐linear cushioning system. Copyright © 1999 John Wiley & Sons, Ltd.     

双曲正切包装系统在半正弦脉冲作用下的冲击特性

研究双曲正切包装系统在半正弦脉冲作用下的冲击响应。结果表明：脉冲幅值ｕｅｍ、系数参数Ｆｍ及阻尼ξ对系统冲击谱和破损边界曲线有显著的影响,且该包装系统与立方型和正切型包装系统在冲击响应上有着本质的区别。     

后峰锯齿脉冲激励下双曲正切包装系统的非线性动力学特性研究

建立了二自由度的双曲正切包装系统模型,并应用四阶龙格-库塔法对得到的冲击动力学方程进行数值求解,研究了其冲击响应特性。采用后峰锯齿脉冲作为激励,得到了关键部件的三维冲击谱,进一步讨论了频率比、脉冲激励幅值、包装材料阻尼和脉冲周期对关键部件冲击谱的影响规律。结果表明,频率比、脉冲激励幅值、包装材料阻尼和脉冲周期均对关键部件冲击响应峰值有显著影响。     

Evaluation of product dropping damage based on key component

This paper analyses the packaging system of a product as a two‐degrees‐of‐freedom system, one degree for the key component and the other for the main part of the product. The dropping damage boundary curve was developed based on the key component for linear and non‐linear packaging systems to predict product damage as a result of drop impacts. The dynamic models of two‐degrees‐of‐freedom dropping shock were obtained. For a linear packaging system, the dropping response of the key component was determined by the dimensionless dropping shock velocity, the frequency parameter ratio, the mass ratio and the damping parameters; for a non‐linear system, the system parameter was also used. The frequency parameter ratio of the packaging system and the dimensionless dropping shock velocity were selected as the basic evaluation quantities for the dropping damage of the key component. As an example, the dropping damage boundary curves based on the key component were given for linear and tangent packaging systems. The influence of related parameters such as the mass ratio, the system parameter and the damping parameters on the dropping damage boundary curve was investigated. To verify the theory, experiments were designed and completed. Experiment results for both linear and tangent packaging systems were consistent with the theory suggested in this paper. These results have important value not only for the design of cushioning packaging but also for the improvement of products. Copyright © 2010 John Wiley & Sons, Ltd.