Dynamic Modeling of AFM Cantilever Probe Under Base Excitation system

Abstract

Atomic force microscopy (AFM) can be used for atomic and nanoscale surface characterization in both air and liquid environments. AFM is basically used to measure the mechanical, chemical and biological properties of the sample under investigation. AFM contains basically a base-excited microcantilever with nano tip along with a sensing circuit for scanning of images. Design and analysis of this microcantilevers is a challenging task in real time practice. In the present work, design and dynamic analysis of rectangular microcantilevers in tapping mode with tip-mass effect is considered. Computer simulations are performed with both lumped-parameter and distributed parameter models. The interatomic forces between the nano tip mass and substrate surfaces are treated using Lennard Jones (LJ) model and DMT model. The equations of motion are derived for both one-degree of freedom lumped parameter model with squeeze-film damping and distributed parameter model under the harmonic base excitation. Also the nonlinearity of the cantilever is investigated by considering cubic stiffness. The distributed parameter model is simplified with one mode approximation using Galerkin’s scheme. The resulting nonlinear dynamic equations are solved using in numerical Runge-Kutta method using a MATLAB program. The natural frequencies of the microcantilever and dynamic response are obtained. Dynamic stability issues are studied using phase diagrams and frequency responses. An experimental work is carried out to understand the variations in dynamic characteristics of a chromium plated steel microcantilever specimen fabricated using wire-cut EDM process. An electrodynamic exciter is attached at the cantilever base and laser Doppler Vibrometer (LDV) is used to provide sensing signal at the oscilloscope. The sine sweep excitation is provided by a signal generator and power amplifier set-up. The frequency response obtained manually is used to arrive-at the natural frequencies and damping factors.