# A Novel Noncontact Ultrasonic Levitating Bearing Excited by Piezoelectric Ceramics
## 5 Fabrication and Measurement  
Three prototypes of piezoelectric transducers are manufactured as shown in Figure 9a. An HP4294A impedance analyzer is used to obtain the resonance frequency and impedance characteristics. The maximum difference of minimum impedance frequency among the three transducers are less than 100 Hz, which is within the error allowed. The mean values of the three transducers' test results are shown in Figure 9b. The error at the resonance frequency point between the test and the above simulation is mainly attributed to the machining tolerance, offset characteristics of PZTs, and the conductivity of the glue. In order to realizing impedance matching for ultrasonic power, an extra LC-type matching network needs to be cascaded in the circuit, which can adjust series resonance frequency to a certain point of the impedance curve with approximate zero phase angle. A KEYENCE laser displacement sensor (LK-H020) is applied to obtain the vibration amplitude in the vertical and lateral directions. By changing the output frequency of the ultrasonic power supply, the resonance frequency can be easily determined. The measurement results shown in Figure 10 show that the maximum vertical and lateral vibration amplitudes are 10.8 \(\upmu\)m and 3.3 \(\upmu\)m, respectively, where the frequency is about 16.11 kHz, which matches well with the simula  
Figure 9: The piezoelectric transducer prototypes and the characteristic parameters: (**a**) transducer prototypes; (**b**) mean impedance and phase angle of the transducers. results. The errors between the actual working frequency and results of simulation or the impedance analyzer measurement can be caused by many factors, but the different boundary conditions may exert the most significant influence. For the purpose of validating the levitation capacity of ultrasonic bearing excited by one piezoelectric transducer, a test system is established shown in Figure 11. The system mainly includes a vibration isolation platform, an ultrasonic bearing, weights, a supported object, a signal generator, a PZT driving amplifier, a laser displacement sensor and a computer, etc. The diameters of the ultrasonic bearing's concave surface and the journal's outer circle are 20.03 mm and 19.97 mm respectively. The mass of the journal is 23 g. Different vertical and lateral loads can be acquired through changing the weights and supported objects with different masses. Sinusoidal voltage is set with an amplitude of 150 V\({}_{\text{P-p}}\) in the test. The comparison between theoretical results and experiment data on radical levitation capacity is shown in Figure 12. It is clear that the levitation force is increased with the diminution of levitation height. When the levitation height is reduced to approximately the vibration amplitude of the radiation concave surface, the bearing force will reach the maximum value. In this case, the journal and radiation are in the critical contact state. The maximum radical levitation force is about 15 N. The main factors limiting radical levitation capacity are the input power and surface machining quality. The input power directly influences the vibrating amplitude of the radiator's surface, and the load capacity will be improved significantly with the increase in vibrating amplitude. According to the radical levitation  
Figure 11: Load-carrying capacity test system. Figure 10: The vertical and lateral vibration amplitudes. curve, surface roughness reveals a significant effect on levitation force, especially when levitation height is in a low value range. Here, the lateral levitation height under different bearing capacities was investigated as shown in Figure 13. The error between the theoretical model and experimental data is mainly ascribed to boundary effect, surface roughness, and the laser displacement sensor's measurement accuracy. Experimental data show that the maximum lateral levitation force is much smaller than the maximum vertical levitation force.