Mathematical modeling of nanomachining with atomic force microscope cantilevers

This article theoretically analyzes the cutting depth and material removal rate of an atomic force microscope (AFM) cantilever during nanomachining An analytical expression for the vibration frequency and displacement of the cantilever has been obtained by using the modified couple stress theory. The theory includes one additional material length scale parameter revealing the micro-scale effect. According to the analysis, the results show that the effect of size-dependent on the vibration behavior of the AFM cantilever is obvious. The maximum displacement of nanomachining with the AFM cantilever represents the cutting depth. The area under the displacement-time curve is related to the material removal rate. When the excitation frequency is closer to the nature frequency of the cantilever, a larger material removal rate is obtained.