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TECHNICAL BRIEFS

Dynamic Responses of an Atomic Force Microscope Interacting with Samples

[+] Author and Article Information
Jih-Lian Ha

Department of Mechanical Engineering,  Far East College, 49 Chung-Hua Road, Shin-Shi, Tainan, Taiwan 744, ROC

Rong-Fong Fung1

Department of Mechanical and Automation Engineering,  National Kaohsiung First University of Science and Technology, 1 University Road, Yenchau, Kaohsiung, Taiwan 824, ROCrffung@ccms.nkfust.edu.tw

Yi-Chan Chen

Department of Mechanical and Automation Engineering,  National Kaohsiung First University of Science and Technology, 1 University Road, Yenchau, Kaohsiung, Taiwan 824, ROC

1

Corresponding author.

J. Dyn. Sys., Meas., Control 127(4), 705-709 (Oct 17, 2004) (5 pages) doi:10.1115/1.2101851 History: Received June 13, 2003; Revised October 17, 2004

The objective of this paper is to formulate the equations of motion and to analyze the vibrations of an atomic force microscope (AFM), which contains a piezoelectric rod coupling with a cantilever beam, and the tip mass interacting with samples. The governing equations of the AFM system are formulated completely by Hamilton’s principle. The piezoelectric rod is treated as an actuator to excite the cantilever beam via an external voltage. The repulsive forces between the tip and samples are modeled by the Hertzian, the Derjaguin-Müller-Toporov, and Johnson-Kendall-Roberts models in the contact region. Finally, numerical results are provided to illustrate the coupling effects between the piezoelectric actuator and the cantilever beam and the interaction effects between the tip and samples on the dynamic responses.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagrams of (a) the cantilever beam with a PEA and (b) the deformed configuration of the AFM system

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Figure 2

Deformation of a sphere on a flat surface following the HZ and JKR models, where f is the loading force, R is the radius of the sphere, δ is the deformation of the spherical tip, and aHZ and aJKR are the contact radii. of the HZ and JKR models, respectively. The profile of the spherical tip in the DMT model is the same as that in the HZ model.

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Figure 3

The relationships between the interaction forces and the deformations of the spherical tip. (⋯ HZ; -∙- DMT; — JKR)

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Figure 4

The diagram of the cantilever beam system with three atomic force models. (a) The displacement of the PEA at the end. (b) The displacement of the cantilever beam at the end. (c) The distance between the tip and the sample. (d) The relations of the atomic force and time. (⋯ HZ; -∙- DMT; — JKR)

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