机械臂臂杆刚度主动控制下的末端振动特性研究

机械臂在运动过程中会因臂杆柔性引发结构变形和弹性振动,降低机械臂末端的定位精度和运动稳定性,将结构振动控制方法用于机械臂的振动抑制研究具有重要意义. 基于变刚度主动控制的设计思想,提出了臂杆刚度主动控制方法,通过改变机械臂臂杆的轴向受力状况来主动改变机械臂的刚度. 采用变形耦合法描述了机械臂的非线性变形,进而结合假设模态法和拉格朗日方程建立了臂杆的变刚度动力学模型,并进行了数值仿真. 在此基础上,设计了基于臂杆刚度主动控制方法的单自由度实验台,分析了不同预紧力下机械臂末端的振动特性. 数值仿真和实验结果表明,随着预紧力的增加,机械臂末端的振动幅值得到衰减,验证了臂杆刚度主动控制方法的有效性. 通过采用响应面法建立了机械臂末端的振动响应与预紧力的关系,并基于内部映射牛顿法的子空间置信域法优化算法对预紧力进行了优化分析,得到了最优预紧力. 该研究可为机械臂的精细动力学建模和振动抑制提供一定的理论依据,并为研究经济型低刚度材料的刚化问题提供了方向,以利用廉价低刚度材料取代目前所应用的昂贵高刚度材料. 

RESEARCH ON VIBRATION CHARACTERISTICS OF THE MANIPULATOR END UNDER ACTIVE CONTROL OF ARM STIFFNESS

The structural deformation and elastic vibration of the manipulator will be caused by the flexibility of the manipulator arm during the movement, which will reduce the positioning accuracy and motion stability of the manipulator end. It is of great significance to apply structural vibration control method to the vibration suppression of the manipulator. Based on the design idea of variable stiffness active control, an active control method of arm stiffness is proposed. The stiffness of the manipulator is actively changed by changing the axial force of the manipulator arm. The nonlinear deformation of the manipulator is described by the deformation coupling method, and then the variable stiffness dynamic model of the manipulator arm is established by using the assumption mode method and Lagrange equation. Further, numerical simulation is performed to solve the variable stiffness dynamic model of the manipulator arm. On this basis, a single degree of freedom experimental device based on the active control of arm stiffness method is designed, and the vibration characteristics of the manipulator end under different preloading forces are analyzed. Numerical simulation and experimental results show that the vibration amplitude of the manipulator end is suppressed with the increase of preloading force, which verifies the effectiveness of the active control of arm stiffness. The relationship between the vibration response of the manipulator end and the preloading force is established by using the response surface method. Then the preloading force is optimized by using the Subspace Trust-region algorithm based on Interior-reflective Newton Method, and the optimal preloading force is obtained. This study can provide a theoretical basis for the fine dynamic modeling and the vibration suppression of the manipulator, and provide a direction for the study of the rigidization of economical low-stiffness materials, so as to replace the currently used expensive high-stiffness materials with cheap low-stiffness materials.