Abstract
An analytical solution to the flexural vibration problem during a nanomachining process using an atomic force microscope (AFM) cantilever is proposed in this paper. The modal superposition method was employed to analyze the response of an AFM subjected to a cutting force with an exciting force of an arbitrarily chosen frequency. The cutting forces were transformed into normal forces, distributed transversal-forces, and bending loading and acting on the end region of the AFM by means of the tip holder. Then, the effects of the axial force were used to solve the dynamic model. The analytical solution can be employed to evaluate vibration shape, model frequencies, and response histories of the cantilever with respect to different axial force effects and excitation frequencies. The results of this study reveal that the cutting force with a low axial effect and a moderately high excitation frequency are the best machining parameters for nanoscale processing using atomic force microscopy.
