基于变分迭代法的悬挂式弹簧系统的跌落破损评价

Dropping Damage Evaluation of Suspension Spring System Based on Variational Iteration Method

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。

Suspension spring system was taken as research object. The non-dimensional dynamic equation of dropping impact of the system was solved by variational iteration method. The first-order approximate analytical solutions such as non-dimensional displacement and non-dimensional acceleration were obtained. Analytical solutions of non-dimensional peak displacement, non-dimensional peak acceleration, and dropping shock extended period were obtained and com- pared with Runge-Kutta method. The results showed that the non-dimensional acceleration response-time curves agree well, and relative errors of non-dimensional acceleration peak value and dropping shock extended period are less than 4% and 2% respectively. The damage evaluation equation combined with system parameter, product fragility, non-di- mensional dropping velocity and suspension angle was established. System parameter and dimensionless dropping shock velocity were selected as two basic evaluation quantities, and dropping damage boundary curves were obtained. Curved surface of dropping damage boundary was obtained by using dimensionless dropping shock velocity, system parameter, and initial suspension angle as basic evaluation quantity. The results showed that the system security performance in- crease with decrease of suspension angle; the suspension geometry nonlinear system characteristics is superior to the linear system in product protection. The purpose was to provide reference for suspension spring system design.