基于摩擦与变形耗能的滚石切向恢复系数影响因素

切向恢复系数是滚石碰撞回弹的重要控制参数，目前的理论公式不能完全反映其作用机制，这是滚石动力学研究的一个难点问题.为此，根据滚石不同的回弹状态，提出基于入射角度变化的切向力模型；进一步，以切向接触理论和动能定理为基础，考虑碰撞过程中切向的摩擦耗能与变形耗能，推导了切向恢复系数的理论公式；最后研究入射速度、入射角、被撞击物体的变形模量对切向恢复系数的影响.结果表明:滚动回弹的切向恢复系数主要受切向变形量的影响；滑动回弹时，入射速度对切向恢复系数的影响参数为begin{document}$ {v}^{frac{1}{20}} $end{document}，切向恢复系数随着其增加而缓慢减少；入射角度对切向恢复系数的影响参数为$ frac{mathrm{c}mathrm{o}{mathrm{s}}^{frac{1}{20}}{beta }_{i}}{mathrm{t}mathrm{a}mathrm{n}{beta }_{i}} $，切向恢复系数随其增加而增大；被撞击物体的变形模量对切向恢复系数的影响参数为$ {E}_{2}^{-frac{5}{8}} $，切向恢复系数随其增加而增加.基于摩擦与变形耗能的切向恢复系数计算公式为滚石的碰撞回弹过程提供了新的计算模型. 

Influence Factors of Tangential Restitution Coefficient of Rolling Stone Based on Friction and Deformation Energy Dissipation

The tangential restitution coefficient is an important control parameter for the rebound of the rolling stone, and the current theoretical formula can not fully reflect its mechanism. Firstly, according to the different rebound states of the rolling stone, a tangential force model based on the change of incident angle is proposed. Further considering the tangential friction energy dissipation and deformation energy dissipation in the collision process, the theoretical formula of tangential restitution coefficient is derived based on tangential contact theory and kinetic energy theorem. Finally, the influence of various factors on the tangential restitution coefficient is studied. The results show that the tangential restitution coefficient of rolling rebound is mainly affected by tangential deformation. When the rolling stone slips, the influence parameter of incident velocity on the tangential restitution coefficient isbegin{document}$ {v}^{frac{1}{20}} $end{document}, and the tangential restitution coefficient decreases slowly as it increases, while the influence parameter of incident angle on tangential restitution coefficient is$ frac{mathrm{c}mathrm{o}{mathrm{s}}^{frac{1}{20}}{beta }_{i}}{mathrm{t}mathrm{a}mathrm{n}{beta }_{i}} $, and the tangential restitution coefficient increases with its increase, the influence parameter of the deformation modulus of the impacted object on the tangential restitution coefficient is$ {E}_{2}^{-frac{5}{8}} $, and the tangential restitution coefficient increases with its increase. The tangential recovery coefficient based on friction and deformation energy dissipation provides a new computational model for the collision process of rolling stone.