恒定外力作用下的碰撞过程恢复系数模型研究

A study on the coefficient of a restitution model considering constant external forces during impact

针对目前恢复系数模型由于忽略恒定外力作用影响,从而导致无法有效预测多体系统碰撞过程中能量耗散的问题,提出一种恒定外力作用下的恢复系数模型。在结合碰撞过程中赫兹在弹性阶段以及Jackson和Green在弹塑性阶段建立的接触力和侵入深度关系模型的基础上,加入恒定外力的作用,同时根据碰撞过程中能量守恒原理,获得碰撞后的分离速度,建立恒定外力作用下的恢复系数模型,同时为提高工程实际应用计算效率,简化该计算过程,获得经验公式。将提出的恒定外力作用下的恢复系数模型与已有的恢复系数模型进行对比分析,结果表明:低速重载时恒定外力对恢复系数影响较大,且随着恒定外力的增加,使得侵入深度增加,进而导致塑性变形增加,分离速度减小,传统恢复系数模型不再适用,因而考虑恒定外力作用下的恢复系数可为不同初始速度和恒定外力作用的多体系统碰撞过程提供更为准确的计算模型。

According to the existing problem that the restitution coefficient models ignoring constant external forces have the inaccurate energy dissipation results in the multibody dynamics,a new restitution coefficient model under a constant external force was presented.Hertz,Jackson and Green established a contact force and penetration depth relationship model,respectively,during the elastic and elastoplastic stages of the collision process.On the basis of the above,a new restitution coefficient model was established considering the constant external force and the principle of energy conservation during the collision process.In order to improve the calculation efficiency of the engineering practice,the calculation process was simplified and the empirical formula was obtained.By comparing with the existing restitution coefficient models,it can be concluded that constant external force has a great influence on the restitution coefficient at low speed and heavy load.Additionally,with the increase of constant external force,the penetration depth and plastic deformation increase,while the separation velocity decreases.According to the results,the new model can provide a more accurate calculation model in the multibody dynamics,with different initial velocities and constant external forces by considering the restitution coefficient under a constant external force.