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 引用本文: 高政国, 董朋昆, 张雅俊, 孙卉竹, 迪亚. 一种滞弹簧耗能的新型离散元滚动阻力模型研究. 力学学报, 2021, 53(9): 2384-2394.
Gao Zhengguo, Dong Pengkun, Zhang Yajun, Sun Huizhu, Ndiaye Becaye Cissokho. A novel discrete element rolling resistance model based on hysteresis spring energy dissipation. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2384-2394.
 Citation: Gao Zhengguo, Dong Pengkun, Zhang Yajun, Sun Huizhu, Ndiaye Becaye Cissokho. A novel discrete element rolling resistance model based on hysteresis spring energy dissipation. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2384-2394.

## A NOVEL DISCRETE ELEMENT ROLLING RESISTANCE MODEL BASED ON HYSTERESIS SPRING ENERGY DISSIPATION

• 摘要: 颗粒间滚动阻力对颗粒体系的稳定性起着重要作用. 在传统的离散元法中, 滚动阻力模型通常由转动弹簧、转动黏壶和摩擦元件表达, 颗粒滚动动能由黏滞力(矩)和摩擦力做功耗散. 由于黏滞力(矩)与滚动速度相关, 临近静止状态的颗粒滚动速度变小, 动能耗散减弱, 传统的离散元模拟得到颗粒由滚动到静止耗费的时间比试验观测的结果要长. 为解决这一问题, 基于摩擦学理论分析了滚动阻力产生的材料滞弹性机理, 将其引入离散元滚动阻力模型, 提出了一种速度无关型动能耗散的滞弹簧, 给出了滞弹簧的弹性恢复力计算公式, 建立了一种新型的离散元滞弹性滚动阻力模型(HDEM). 为验证新型滚动阻力模型的正确性, 通过一个光学物理试验对单个圆形颗粒试件的自由滚动过程进行了测量, 将测量数据与新型的滞弹型离散元模型和传统离散元模型计算结果进行了对比. 结果显示, 基于滞弹性滚动阻力模型HDEM计算结果与试验数据吻合程度更高, 而且模拟得到的颗粒摆动频率更符合试验现象.

Abstract: The rolling resistance between particles plays an important role in the stability of the particulate systems. In a conventional discrete element method, the rolling resistance model between particles is usually made of springs, dashpots, and sliders in the rotational direction. The particles rolling kinetic energy is dissipated by the viscous (moment) and friction forces. With this model, the viscous force (moment) is directly related to the rolling velocity. Consequently, the dynamic dissipation capacity of particles close to the static state becomes weaker with the rolling velocity decreasing. It is known that the time required to simulate a particle rolling with a velocity close to zero by using the traditional discrete element method is longer than the experimental results. To solve this problem, the mechanism of rolling resistance caused by material hysteresis is analyzed based on tribological principle, and a new discrete element model of hysteresis rolling resistance (HDEM) is established. A hysteresis spring with velocity-independent kinetic energy dissipation is proposed, and its constitutive law’s formula is derived. To verify the new rolling resistance model, the free-rolling of a single round particle specimen on a flat surface is measured through a physical experiment. The measured data are compared with the results simulated by the new rolling resistance model HDEM and the conventional rolling resistance model. The results show that the results based on HDEM are more consistent with the experimental data, and the particle oscillation frequency is in better agreement with the experimental phenomenon observed.

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