悬挂系统易损件跌落破损评价

以考虑易损件的悬挂系统为研究对象,建立跌落冲击下系统无量纲动力学方程。利用四阶龙格库塔数值分析方法求解动力学方程,以系统参数、无量纲跌落冲击速度、频率比、阻尼比或悬挂角为基本评价量,构建易损件跌落破损边界曲面,讨论系统悬挂角、频率比及阻尼比等对易损件的跌落破损边界的影响。数值分析表明:高频率比有利于系统对产品的保护;小阻尼条件下,阻尼匹配满足一定的范围对产品具有较好的保护作用;较小的系统悬挂角时,系统的安全区域较大;系统设计中应综合考虑各参数的影响,提高系统抗冲击性能,达到保护产品的目的。     

斜支承系统关键件的跌落破损评价

建立考虑关键件的斜支承系统模型,基于系统跌落冲击动力学方程,利用四阶Runge-Kutta法,以系统参数、跌落冲击初始速度、支承角或频率比或系统阻尼比作为三个基本参量,获得关键件跌落破损边界,探讨支承角、频率比、系统阻尼比等对关键件跌落破损边界的影响规律。评价结果显示：较小的支承角或较大的频率比有利于扩大系统关键件的未损坏区;系统阻尼比存在最优值,恰当地选择阻尼比可改善斜支承系统的抗跌落冲击性;为使斜支承系统获得理想的减振和抗跌落冲击性能,需综合考虑内装物主体等效刚度系数、弹簧原长等参数。     

斜支承系统关键件的跌落破损评价

建立考虑关键件的斜支承系统模型,基于系统跌落冲击动力学方程,利用4阶Runge-Kutta法,以系统参数、跌落冲击初始速度、支承角或频率比或系统阻尼比作为三个基本参量,获得关键件跌落破损边界,探讨支承角、频率比、系统阻尼比等对关键件跌落破损边界的影响规律。评价结果显示:较小的支承角或较大的频率比有利于扩大系统关键件的未损坏区;系统阻尼比存在最优值,恰当地选择阻尼比可改善斜支承系统的抗跌落冲击性;为使斜支承系统获得理想的减振和抗跌落冲击性能,需综合考虑内装物主体等效刚度系数、弹簧原长等参数。     

斜支承弹簧系统跌落冲击响应及影响因素分析

以斜支承弹簧系统为研究对象,建立了跌落冲击条件下系统无量纲非线性动力学方程。利用龙格-库塔数值分析方法求解动力学方程,讨论了无量纲跌落冲击速度、系统支承角及阻尼等对系统响应的影响。研究表明,随着无量纲跌落冲击速度的增加,系统位移响应峰值和加速度响应峰值增加;随着支承角的减小,位移响应峰值增大,加速度响应峰值减小;阻尼对系统响应影响显著,对系统加速度峰值影响存在最佳阻尼比,最佳阻尼比随系统支承角减小而减小。通过适当地选取阻尼比及支承角可有效地改善系统的抗冲击能力。     

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。     

基于变分迭代法的悬挂式弹簧系统的跌落破损评价

以悬挂式弹簧系统为研究对象,应用变分迭代法求解系统跌落冲击无量纲动力学方程,得到了系统无量纲位移、加速度响应一阶近似解析解,无量刚位移响应峰值,无量纲加速度响应峰值和无量刚跌落冲击持续时间表达式,与龙格-库塔数值分析结果进行了比较。 结果表明,无量纲加速度响应曲线吻合程度较好,无量纲加速度响应峰值和无量刚跌落冲击持续时间相对误差小于 4% 和 2% 。 建立了包含系统参数、产品脆值、无量纲跌落冲击速度、系统悬挂角等多变量的跌落冲击破损评价方程。 以无量纲跌落冲击速度和系统参数为基本评价量,获得了系统跌落破损边界曲线;以无量纲跌落冲击速度、系统参数和初始悬挂角为基本评价量,获得了系统跌落破损边界曲面。 结果表明,随着系统初始悬挂角减小,系统安全性能提高,悬挂系统几何非线性特性对产品保护性能优于线性系统。 为悬挂式系统缓冲设计提供了理论依据。     

跌落工况下斜支承系统易损件的冲击特性

目的基于斜支承系统双自由度模型,研究系统易损件的跌落冲击特性。方法针对系统无量纲跌落冲击动力学方程,用龙格-库塔数值分析法获得易损件跌落冲击动力学响应,探讨系统支承角、频率比、跌落冲击初始速度、阻尼比等对易损件位移及加速度响应的影响规律。结果通过对易损件位移、加速度响应最值影响因素的分析表明,减小支承角可增加易损件位移响应最值,降低其加速度响应最值,延长响应周期;随着频率比的增加,易损件位移和加速度响应的最值减小;随着初始速度的增加,易损件位移、加速度响应最值上升明显;对于加速度响应最值,系统阻尼比存在最佳值。结论为使斜支承系统获得理想的减振和抗跌落冲击性能,需综合考虑各相关参数。     

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。     

跌落工况下斜支承系统响应分析的变分迭代法

以斜支承缓冲包装系统为研究对象,建立了跌落工况下系统的无量纲非线性动力学方程。应用变分迭代方法求解了系统动力学方程,得到了系统响应的近似解析表达式,并与龙格库塔数值解进行了比较。研究表明:跌落工况下斜支承系统响应频率相对误差小于0.3%,无量纲位移及加速度的响应最大值相对误差小于0.5%,且无量纲位移、加速度响应随支承角及跌落高度的变化趋势,与龙格库塔数值结果相同。变分迭代方法求解斜支承系统的跌落冲击问题,可以得到满意的结果。     

悬挂式缓冲系统易损件冲击响应特性

目的以考虑易损件的悬挂系统为对象,研究跌落冲击条件下易损件响应规律。方法建立系统无量纲动力学模型,利用四阶龙格库塔法分析易损件的位移和加速度响应。讨论系统悬挂角、频率比、阻尼比和无量纲冲击速度等参数对易损件位移、加速度响应的影响。结果系统的悬挂角、频率比以及主体与基础连接处的阻尼对易损件响应影响显著,随着系统悬挂角的增加,易损件加速度响应幅值增加,位移响应幅值减少,响应周期缩短。增加频率比可有效抑制易损件响应幅值。结论在跌落冲击条件下,悬挂系统的设计应选择适当的悬挂角、频率比等相关参数,以满足产品防护的需要。     

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.     

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.     

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.