## 2 Material and Methods  
We researched the foil bearing's structure on a specially prepared test rig, located in the Vibrodiagnostics Laboratory of the Institute of Fluid-Flow Machinery of the Polish Academy of Sciences (IMP PAN). The tested bearing was mounted on a shaft with a diameter of 34 mm. The shaft was put in rotational motion using an electrospindle whose maximal speed is 24,000 rpm. Figure 1 shows the laboratory test rig with an ultra-high-speed camera. The camera was controlled by the measuring computer that is also shown in this figure. We used two 60 W light-emitting diode (LED) lamps (PRO 2X Oslon 60 model, manufactured by Easy LED) for better illumination of the tested bearing. Each lamp can deliver light output up to 6000 lumens. A diagram of this test stand is presented in Figure 2. The camera was situated almost in front of the rotating shaft and the two light sources were positioned to provide light to the bearing on both sides. Figure 1: Test rig with a foil bearing and a computer-controlled camera. Figure 2: Scheme of the measurement setup. A diagram that shows how the bearing is mounted on the shaft is presented in Figure 3. The shaft is a part of the electrospindle that is attached to the aluminium frame. The shaft's journal was inserted into the bearing sleeve before research. When the rotational speed of the shaft was high enough, a gaseous lubricating film formed itself between the top foil and the bearing journal. During the research, the bearing sleeve rotation was blocked. The sleeve was able to move in the radial direction. The bearing is lifted after the lubrication film appears. The foil bearing consists of two foils. The bump foil is situated between the rigid sleeve and the top foil. The foils were manufactured from Inconel 618 and the top foil was coated with Teflon. The length of the bearing is 40 mm. Vision Research's v2511 ultra-high-speed camera (shown on the left-hand side of Figure 4) was used to record the tests of the bearing carried out under different operating conditions. The camera is equipped with a CMOS sensor that allows capturing high-resolution images at very high speeds (offering a full megapixel resolution of 1280 \(\times\) 800). Moreover, the CMOS sensor has pixels with a diameter of 28 \(\upmu\)m. Acquiring around 25 gigapixels-per-second of data enables frame rates up to 1,000,000 fps at 128 \(\times\) 32 resolution. When recording with the maximum resolution, the maximum frame rate is 25,600 frames per second. We connected the camera with the measuring computer using the Ethernet communication interface. We tested run-ups, stable operation, and impulse excitation--an analysis of the recording in slow-motion followed. We also used the TEMA Motion software, developed by Image Systems, which is dedicated to performing advanced motion analysis. For recording purposes, we used a Zeiss 100 mm f/2 macro lens whose main features are the following: the maximum reproduction ratio is 1:2 and the minimum focusing distance is 0.4 m. Two sets of extension tubes (shown on the right-hand side of Figure 4) were placed between the lens and the camera. The extension tubes do not include any magnifying lenses but can be combined if there is a need to increase the reproduction ratio. Those adapter rings enable increasing the distance between the focal plane of the lens and the CMOS sensor, thus increasing the reproduction ratio. In practice, the farther we move the lens away from the camera (using the extension tubes), the better magnification of the test object we obtain. One set of extension tubes includes rings with three widths (7 mm, 14 mm, and 28 mm) and two bayoret fixings between the camera and the lens. After assembling two such sets, the distance between the lens and the camera was 128 mm. Conducting measurements using the aforementioned high-speed camera has some limitations. The measured vibration frequency is limited by the frame rate of the high-speed camera. During the measurement, we needed to avoid aliasing.