应用于扫描探针显微镜的石英音叉机械模型研究

石英音叉作为力传感器广泛地应用于各种扫描探针显微镜,主要涉及石英音叉的同相振动和反相振动两种振动模式.通过实验方法和有限元仿真方法对石英音叉的两种振动模式进行研究,发现石英音叉的双臂之间以及双臂与音叉的基部之间都存在耦合作用,双臂之间的耦合使音叉的反相共振频率升高,双臂与基部之间的耦合使音叉的同相共振频率降低.针对两种振动模式的动态特性建立了石英音叉的机械模型并进行合理简化.简化模型是一个四弹簧三质点系统,计算了简化模型的参数.通过一个音叉臂等效质量变化与音叉反相共振频率变化之间的定量关系证明了简化机械模 关键词： 扫描探针显微镜 石英音叉 振动模式 机械模型

Mechanical model of tuning forks used in scanning probe microscopes

Quartz tuning forks have been widely used as force sensors in scanning probe microscopes. The anti-phase and in-phase eigenmodes of a tuning fork are involved during microscope operations. Dynamic characteristics of both eigenmodes are studied by experiments and finite element analysis simulations. It is demonstrated that elastic couplings exist between not only both the prongs but also two prongs and the base of the tuning fork. Experimental results show that the coupling between both the prongs increases the anti-phase mode eigenfrequency while the coupling between two prongs and the base of the tuning fork decreases the in-phase mode eigenfrequency. A mechanical model of the tuning fork is introduced and simplified. Parameters of the simplified model are calculated, which is described as a four-springs-three-point-masses system. The quantitative relation between the effective mass of one prong and the eigenfrequency of the anti-phase mode of the mechanical model is in good agreement with that of finite element simulations.