## 2 Experimental Setup
### Ultrasonic Transducer Design  
The design of the ultrasonic transducers used in the linear tribometer was based on the USDC ultrasonic shock drilling system developed by the Jet Propulsion Laboratory of NASA [19] due to its compact design and high vibration amplitudes, and the good linearity between the applied current and the vibration velocity. However, the original design was constructively optimized in terms of longevity through damping reduction and high amplitude for the oscillating systems. For example, the bolt used to preload the piezoceramics was designed together with the horn (sonotrode) as one part, which avoids the usual screw connection near the vibration node and thus unnecessarily high material stresses. The design of the bolt head (nut) has also been optimized with regard to dynamically occurring stresses at the bolted joint. Furthermore, a notch has been designed at the junction between the piezo package and the bearing near the node to protect the outer ceramic from any high stresses that may occur during operation outside the resonant frequency. The piezoceramics used are z-polarized PIC181 rings with a thickness of 5 mm, an outer diameter of 25 mm and an inner diameter of 16 mm. The transducer is operated resonantly in his respective longitudinal eigenmode at 20 kHz. After a rough calculation for the rod oscillator, further calculations regarding the choices of materials and the mass distributions of the oscillating structures were carried out with the institute's in-house-developed 2D FE tool _BeK_ based on the transfer matrix method [20]. The final geometric design was carried out with the help of CADFEM's FE tool ANSYS Workbench [21]. A linear approach for the material damping was used. The properties of the piezoceramics have been taken into account by specifying appropriate matrices for stiffness, piezoelectricity and permittivity according to [22]. Figure 3 shows the structure and the normalized velocity distribution in the longitudinal direction along the length of the sonotrode. In addition, the design elements' boundaries of the underlaid CAD model are shown as dashed lines. The titanium alloy Ti-6 Al-4V was chosen for the transducer's sonotrode. Due to the material's high specific strength and hardness, it can be assumed that the contact surface remained in the same conditions for the complete investigation. For the investigation of the piston sealing, the groove at the tip of the sonotrode ensured that the seal always remained on the sonotrode tip while relative movements of the housing and sonotrode were performed. Thus, the ultrasonic velocity amplitude can be assumed to have remained constant in the contact area, on average. The designed transducer was characterized both electrically and mechanically by means of fitting of frequency response function measurements. Figure 4 shows the fitting results of the measured electrical admittance of the 20 kHz transducer. The identified parameters of the Butterwoth Van Dyke model are listed in the locus curve plot. Measurements of mechanical admittance by laser Doppler vibrometry revealed a ratio between vibration amplitude \(\hat{x}_{US}\) and driving current \(\hat{l}\) of 0.076 \(\upmu\)m/mA. This means that a ratio of 9.7 m/As prevailed between the ultrasonic velocity \(\hat{v}_{US}\) and current \(\hat{l}\). This ensured a wide bandwidth for the variation of the relative velocity in the friction contact. Figure 2: Control loops implemented in the novel tribometer. 3. Design of the Experiment and Experimental Procedures  
The investigation procedures required the implementation of two different control modes. The control of the velocity of the sealing holder allowed is to determine the sliding friction force under constant parameters. The force control was implemented for the identi cation of the breakaway force as a function of the ultrasonic amplitude and the sealing ring material. Figure 5 shows the parameter tree for the investigation of contact behavior induced by a superposition of 20 kHz.