| Abstract | In this article, we focus on analyzing the tip displacement relation for a piezoelectric tube scanner used in scanning probe microscopes. In particular, the finite element model consists of a piezoelectric tube, a tip holder, and a tip in an effort to include the boundary effect on tube deflection. A large number of simulations are conducted for model validation and comparisons with results in the literature. Design formulas commonly suggested by piezotube manufacturers are also used to compare with our simulations. We show that the design formulas provide a good approximation of the tip displacement when tube's aspect ratio is well above 2. In addition, the axial displacement of the tip in tube bending, also known as the coupling term, is analyzed through simulations. A ratio of 4 exists between the axial displacement in tube elongation and that in tube bending caused by energizing single quadrant electrode. The result is shown to be convenient to use to decouple motion in the orthogonal directions. |
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