# Experimental Verification of the CFD Model of the Squeeze Film Lifting Effect
## 2 Materials and Methods  
### Experimental Research  
The idea of the experimental setup and the photograph are presented in Figure 2. The vibrating circular membrane is peripherally fixed. The piezoelectric actuator fixed with a special adhesive beneath the membrane is made from lead zirconium titanate \(Pb(Ti_{x}Zr_{x})O_{3}\)[24], commonly referred to as PZT. The alternating current supplied to the PZT generates vibrations of said membrane. If the current frequency is correlated with the natural frequency of the plate, with sufficient energy supplied, the vibration of the membrane can be observed. Above the working surface, the sample is placed to observe the possible levitation phenomenon resulting from the formation of the gas film due to vibrations of the vibrating plate, as shown in Figure 2c. The measurements of the movement of either the vibrating plate or the lifted sample are accomplished with the use of the confocal optical sensor IFS2403-0.4 distributed by Micro-Epsilon. The sensor has a 0.4 mm measuring range with a dynamic resolution of 47 nm. The power supply for the PZT element allows for control of the offset voltage and the amplitude of the AC. The power supply was defined as 50 V, with an amplitude of 5, 10, 20, and 40 V. The frequencies generated by the setup are in the range between 1 Hz and 54 kHz. Data were collected using a confocal DT 2471 HS distributed by Micro-Epsilon. The optical sensor readings and power supply voltage were collected with a sampling frequency of 50 kHz. The prototype of the plate was designed as a solid block in which a cavity was machined to form a circular membrane with a diameter of 40 mm and a thickness of 1 mm (Figure 3). The thickness of the membrane was limited due to the geometrical presumption of the plate flatness and observing manufacturing technique limitations. After the primary test, the plate has not presented satisfactory results, i.e., the levitation of the samples was not achieved, and the plate did not show the expected deflection during its operation. Due to the aforementioned, the decision was made to subject the plate to electro-drilling to thin the membrane. The process allowed decreasing thickness to 0.5 mm, with the undesired deterioration of the working surface flatness. The surface of the membrane had an eccentrically centrally positioned convexity of 50 \(\upmu\)m (Figure 3d). The thinning of the plate decreased its stiffness eightfold from 2480\(\frac{\text{N}}{\text{mm}}\) for plate thickness of 1 mm to 308 \(\frac{\text{N}}{\text{mm}}\) for 0.5 mm membranes thickness and allowed us to observe its vibration. The first mode of vibration, according to the performed FEM calculations, should occur at 4583 Hz; the obtained experimental results showed a value of 4260 Hz. The inconsistencies can be attributed to the limited knowledge about the mass distribution of the PZT element and the cohesive agent. Moreover, in the calculations, some elements, such as the power supply connectors, are not taken into consideration. The levitation height measured for a \(\mathcal{O}\)40 sample of a mass of 1.2 g was 9 \(\upmu\)m. The height of the levitation was lower than the existing inaccuracies on the surface; therefore, the researchers decided that  
Figure 2: Test setup. (**a**) schematic view. (**b**) picture of the setup. (**c**) idea of the squeeze film lifting effect, where A is an oscillator vibration amplitude \([m]\), and \(x_{0}\) is a mean deflection of the oscillator \([m]\). an alternative design had to be applied to create a working surface of improved flatness (planarity). The alternative design setup (Figure 4) is composed of the base plate (1) and comprises a membrane (2) and a thrust ring (3). The base plate acts as a rigid fixing, while the thrust ring secures the membrane. Such a design allows for a simple exchange of the membrane. The membrane used primarily was the membrane of calibrated steel foil (0.5 mm thick) (Figure 4a) and the brass PZT element (0.3 mm thick) (Figure 4c).