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 引用本文: 范纪华, 谷通顺, 王明强, 谌宏, 陈立威. 基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究[J]. 力学学报, 2021, 53(4): 1156-1169.
Fan Jihua, Gu Tongshun, Wang Mingqiang, Shen Hong, Chen Liwei. RESEARCH ON OBLIQUE IMPACT OF ROTATING OF FLEXIBLE BEAM BASED ON CONTACT CONSTRAINT METHOD OF LUGRE FRICTION MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1156-1169.
 Citation: Fan Jihua, Gu Tongshun, Wang Mingqiang, Shen Hong, Chen Liwei. RESEARCH ON OBLIQUE IMPACT OF ROTATING OF FLEXIBLE BEAM BASED ON CONTACT CONSTRAINT METHOD OF LUGRE FRICTION MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1156-1169.

## RESEARCH ON OBLIQUE IMPACT OF ROTATING OF FLEXIBLE BEAM BASED ON CONTACT CONSTRAINT METHOD OF LUGRE FRICTION MODEL

• 摘要: 基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究. 首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模, 在碰撞时采用冲量动量法求出跳跃速度, 其次在法向上引入接触约束求解出碰撞力, 在切向上采用LuGre摩擦模型分两种方式求解摩擦力, 第一种是在滑动时摩擦力由摩擦系数和碰撞力计算得出, 黏滞状态下引入切向约束计算拉格朗日乘子反应实际摩擦力, 根据黏滞/滑动切换判断计算出碰撞过程摩擦力(与Coulomb摩擦模型计算摩擦力一致); 第二种根据LuGre摩擦模型摩擦系数和法向碰撞力计算其摩擦力, 从而在碰撞时无需黏滞/滑动切换, 采用相同的摩擦力计算公式. 通过与Coulomb摩擦模型对比发现, LuGre摩擦模型描述碰撞切向摩擦过程更精确, LuGre摩擦模型黏滞时建立约束方程和碰撞采用统一的摩擦力公式这两种建模方式描述的斜碰撞动力学特性没有区别, 进而说明采用法向接触约束和LuGre摩擦模型具有满足碰撞非嵌入情况、避免黏滞/滑动切换、描述摩擦力相对准确的优势.

Abstract: Based on the contact constraint method and LuGre friction model, the dynamic problem of oblique impact with friction between a flexible beam system and a slope is studied. The rigid-flexible coupling multi-body system dynamics theory is used to discretize and model the flexible beam with large overall motion, at the beginning of the impact, the impulse-momentum method is used to calculate the jumping velocity, and then the contact constraint is introduced in the normal direction to solve the impact force, in tangential direction, LuGre friction model is used to solve the friction force in two ways, the first is that the friction force is calculated by friction coefficient and collision force when sliding, and introducing tangential constraint to calculate Lagrange multiplier response actual friction force, according to the stick / slip switching judgment, the friction force in the impact process is calculated (which is consistent with that calculated by Coulomb friction model); the second method is to calculate the friction force according to friction coefficient of LuGre friction model and normal collision force, so there is no need to switch between stick and slip during impact, and the same friction calculation formula is used. Compared with Coulomb friction model, LuGre friction model is more accurate in describing the tangential friction process. There is no difference between the two LuGre friction model modeling methods to describe the impact dynamics. Therefore, it shows that the establishment of normal contact constraint and LuGre friction model can meet the collision un-embedding situation to avoid stick slip switching and to describe the relatively accurate advantages of friction.

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