## 2 Materials and Methods
### Experiments
#### 2.2.1 Experimental Setup  
The calibration setup is mainly composed of an ultrasonic transducer, an ultrasonic pulse generator receiver, a digital oscilloscope, a measurement module, a transducer adjustment module, a force application device, and an industrial computer (as shown in Figure 4). The press-out experiment also can be carried out using this setup to measure the connection force. The reflection coefficient under different loads can be obtained by applying different loads to the force loading tube. It should be noted that the calibrated interface should be consistent with the topography characteristics of the tested interface. The center frequency of the point-focused immersion transducer is 10 MHz, and the wafer radius \(r_{p}\) is 3 mm. The roughness Ra of the upper and lower test plates are 0.09 \(\upmu\)m and 0.3 \(\upmu\)m, respectively. The contact area, \(A_{n}\), of the two calibration plates is 38.48 mm\({}^{2}\). The stress-distribution measurement setup is shown in Figure 5. The setup is mainly composed of a point-focused immersion transducer, an ultrasonic pulse receiver, a digital oscilloscope, a motion control module, a clamping module, an adjustment module, and an industrial computer. The function of the motion control module is to perform motion control on the interference components, thus enabling a full-coverage scan of the entire mating surface (see Figure 6). The clamping module is to ensure the reliable clamping and positioning of components. The adjustment module is to adjust the inclination of the transducer so that the sound beam can irradiate the mating surface vertically. The digital oscilloscope can display the received ultrasonic signal in real time and transmit the data to the computer for signal processing, analysis, and storage. The motion control module consists of XYZ linear stages (GCD-202150M, Daheng Optics, Beijing, China: repeatable positioning accuracy \(<\) 5 \(\upmu\)m, resolution 1 \(\upmu\)m) and a precision turntable (RAK100, Zolix, Beijing, China: repeatability \(<\) 0.005\({}^{\circ}\), radial runout \(<\) 20 \(\upmu\)m, resolution 0.00125\({}^{\circ}\) under eight subdivisions), which can control the translation of interference components in the X, Y, and Z directions and the rotation around the Z axis. The position of the transducer relative to the interference components can be adjusted by the XYZ linear stages. The clamping module consists of two V-blocks, which are installed on the precision turntable. The adjustment module consists of two goniometers on which the transducer is mounted via a clamping rod. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Samples** & \(m_{0}\) (\(\upmu\)m\({}^{2}\)) & \(m_{2}\) & \(m_{4}\) (\(\upmu\)m\({}^{-2}\)) & \(n\) (\(\upmu\)m\({}^{-2}\)) & \(\beta\) (\(\upmu\)m) & \(\sigma\) (\(\upmu\)m) \\ \hline \multirow{2}{*}{Shaft} & 2.96 \(\times\) & 3.36 \(\times\) & 1.89 \(\times\) & 1.96 \(\times\) & \multirow{2}{*}{159.67} & 1.69 \(\times\) \\  & 10\({}^{-2}\) & 10\({}^{-4}\) & 10\({}^{-5}\) & 10\({}^{-3}\) & & 10\({}^{-1}\) \\ \multirow{2}{*}{Hub} & 1.72 \(\times\) & 1.27 \(\times\) & 6.57 \(\times\) & 1.59 \(\times\) & \multirow{2}{*}{82.28} & 4.14 \(\times\) \\  & 10\({}^{-1}\) & 10\({}^{-3}\) & 10\({}^{-5}\) & 10\({}^{-3}\) & & 10\({}^{-1}\) \\ \multirow{2}{*}{Equivalent} & 2.02 \(\times\) & 1.60 \(\times\) & 8.45 \(\times\) & 1.60 \(\times\) & \multirow{2}{*}{72.30} & 4.49 \(\times\) \\  & 10\({}^{-2}\) & 10\({}^{-3}\) & 10\({}^{-5}\) & 10\({}^{-3}\) & & 10\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical parameters of rough surfaces. Figure 4: Schematic diagram of the calibration setup. To ensure the acoustic beam vertically focused on the mating interface, the alignment of the transducer and the component is necessary, as shown in Figure 7. \(\alpha\) are \(\beta\) are the incidence and refraction angles of the ultrasonic wave. \(\gamma\) is the angle between the normal of the incident point and the acoustic beam axis.