三相驱动下非光滑振动驱动系统的动力学分析

Movable robots have become an important branch in the field of robot research. In order to realize their movement in narrow and special environments, scholars have proposed and studied vibration-driven mobile systems. Based on the two-dimensional LuGre friction model and Lagrange's equations, this paper presents a dynamic modeling method and a numerical algorithm for a class of vibration-driven systems in an isotropic friction environment. This type of vibration-driven system has a simple structure and good sealing performance and realizes its own directional movement relying on the frictional force between the box and the ground. The system consists of an external box and two internal mass blocks. The two mass blocks are driven by three-phase vibration on two parallel tracks inside the box, and the box remains in contact with the ground through three rigid support feet. The use of the two-dimensional LuGre friction model can effectively avoid the difficulties caused by the discontinuity of the Coulomb friction model in the numerical solution of the dynamic equations and can effectively reveal the stick-slip switching phenomenon of the system during movement. The numerical simulation results show that by adjusting the driving parameters of its internal mass blocks, the linear translation, fixed-axis rotation and general planar motion of the box can be realized, and four phenomena such as rubbing-sliding, penetrating-sliding, back-sliding and non-sticking will occur during the movement and rotation of the box; in addition, by adjusting the driving parameters, not only can the speed of the box's movement and rotation be changed, but also the radius of curvature of the trajectory of the box's centroid can be changed.

可移动式机器人已成为机器人研究领域的重要分支,为实现其在狭小特殊环境中的运动,学者们提出并研究了振动驱动移动系统.本文基于二维LuGre摩擦模型和拉格朗日方程,给出了一类振动驱动系统在各向同性摩擦环境中的动力学建模方法和数值算法.这类振动驱动系统结构简单且密封性好,依靠箱体与地面间的摩擦力实现自身的定向运动.该系统由一个外部箱体和两个内部质量块构成,两个质量块在箱体内的两个平行轨道上作三相振动驱动,箱体通过三个刚性支撑足与地面保持接触.二维LuGre摩擦模型的利用,可有效避免库伦摩擦模型的不连续性给动力学方程的数值求解带来的困难,且可有效揭示该系统在运动过程中的黏滞–滑移切换现象.数值仿真结果表明,通过调整其内部质量块的驱动参数,可实现箱体的直线平移、定轴转动和平面一般运动,且箱体在移动和转动过程中会出现擦滑、穿滑、回滑和不黏等4种现象;另外,通过调节驱动参数,不仅可以改变箱体移动和转动的快慢,还可以改变箱体形心运动轨迹的曲率半径.