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Detailed analysis showed that the existing theoretical models for near field acoustic levitation are not good enough to interpret the experimental data. The best existing models can only work in a small range of the squeeze numbers even with a fitting parameter. We report here a comprehensive nonlinear model, which takes into account the nonuniform surface vibration profile, gas inertia as well as entrance pressure drop at the film edge. Our model has no empirical parameters and the predicted results agree exceptionally well with our experimental measurements over a wide range of squeeze numbers.

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This paper presents the design of a novel flexure-based vertical (or Z-axis) nanopositioning stage driven by a piezoelectric actuator (PZT), which is capable of executing large travel range. The proposed stage consists mainly of a hybrid displacement amplification mechanism (DAM), a motion guiding mechanism, and a decoupling mechanism. The hybrid DAM with amplification ratio of 12.1 is developed to transfer the transverse motion of the PZT actuator into the vertical motion. The motion guiding mechanism is introduced to avoid cross coupling at the output end. The decoupling mechanism can significantly reduce the cross coupling at the driving end to protect the PZT. The stiffness and dynamics of the proposed stage are improved by these mechanisms. Analytical modeling and finite element analysis (FEA) are then adopted to optimize dimensions of the stage. Finally, a prototype of the stage is fabricated and tested for verification. The results of static and dynamic tests show that the proposed stage is capable of vertical travel range of 214 μm with resolution of 8 nm, and the first two resonance frequencies are 205 Hz and 1206 Hz, respectively. Cross coupling tests under various lateral loads (0 g-1000 g) show that the maximum variances of the lateral and angular cross couplings are less than 0.78 μm and 95 μrad, respectively, indicating good decoupling capability. In addition, the low-profile structure of the stage is well suited to be used in limited vertical space.