基于混沌理论的原子力显微镜微悬臂梁结构及材料选择分析  

Structure and Material Selection of Microcantilever for Atomic Force Microscopy Based on Chaos Theory

作　　者：宋佩颉 褚衍东[1] 俞睿 SONG Pei-jie;CHU Yan-dong;YU Rui(School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;Gansu Institute of Metology Institute of Length Measurement,Lanzhou 730050,China)

机构地区：[1]兰州交通大学机电工程学院,兰州730070 [2]甘肃省计量研究院长度计量研究所,兰州730050

出　　处：《兰州交通大学学报》2023年第3期68-78,共11页Journal of Lanzhou Jiaotong University

基　　金：含间隙和闪温的锥齿轮传动系统动力学特性及混沌控制研究(21JR7RA316)。

摘　　要：原子力显微镜微悬臂梁运动方程在特定条件下表现出混沌运动并严重影响其测量精度,如何避免或降低混沌运动的影响,是近年来微悬臂梁系统研究的重点。以原子力显微镜微悬臂梁的运动方程为出发点,确定状态空间方程中各参数的取值范围,然后应用分岔图和李雅普诺夫指数图等方法分析状态空间方程中各参数变化时系统的动态响应,得到系统产生混沌运动时各参数的临界值,进而由参数定义确定各参数变化的影响因素,最终对系统结构及材料选择进行分析。结果表明,在特定条件下,V形结构微悬臂梁,氮化硅和硅混合材质的微悬臂梁能够有效的避免系统出现混沌运动。研究结果对原子力显微镜微悬臂梁结构及材料选择提供了有意义的理论参考,对改善原子力显微镜的测量精度,具有工程实用价值。The motion equation of micro-cantilever beam in atomic force microscope(AFM)shows a chaotic motion under certain conditions,which seriously affects its measurement accuracy.Started from the motion equation of AFM microcantilever beam,the range of parameters in the state space equation was determined.Then,methods such as bifurcation diagram and Lyapunov exponent diagram were used to analyze the dynamic response of the system when each parameter in the state space equation changes,and the critical values of each parameter when the system generates chaotic motion were obtained.Then,the influencing factors of each parameter change were determined by the parameter definition.Finally,the system structure and material selection were analyzed.The results show that under specific conditions,V-type structure microcantilever beams,or microcantilever beam made of a mixture of silicon nitride and silicon can effectively avoid chaotic motion in the system.The research results provide a meaningful theoretical reference for the structure and material selection of the micro-cantilever of AFM and have practical engineering value for improving the measurement accuracy of AFM.

关 键 词：原子力显微镜 微悬臂梁 混沌运动 材料选择 结构选择 

分 类 号：TH16[机械工程—机械制造及自动化]