# Wear Characteristics of Metallic Counterparts under Elliptical-Locus Ultrasonic Vibration
## 2 Experimental Details
### Materials and Methods  
Alternative friction pairs of metallic that are particularly machinable, retrievable and inexpensive are most desired for standing-wave motors. In this study, contact interfaces of VUM consist of 2A12 alloy tips and metallic sliders. Material properties of friction pairs consisting of V-shape vibrators of 2A12 alloy and metal sliders (45 steel, quenched 45 steel, 7075 aluminum alloy, low-alloy structural steel Q345B, and nodular cast iron QT700) are shown in Table 1.  
Wear tests were carried out under dry conditions in air at room temperature with a relative humidity of 45% \(\pm\) 5%. Before each wear test, the surfaces of the driving tips were polished with abrasive paper #800 to ensure the reproducibility of test conditions. The operating conditions of ultrasonic motors are provided in Table 2. The amplitude of the exciting voltage is 150 V and the driving frequency is 39.8 kHz. The output power and thrust force of ultrasonic motors at a driving frequency of 39.8 kHz is higher and more stable than that of other frequencies under the uniform of applied preload and driving voltage. To investigate surface characteristics and wear behavior of the sliders made of different metallic materials, statistical analysis in this study was carried out on the roughness parameters [30], such as the arithmetical mean deviation of the profile \(R_{a}\), the maximum height of profile peak \(R_{p}\), the maximum depth of profile valley \(R_{v}\), and the mean spacing of local peaks of the profile \(R_{s}\). \[\left\{ \begin{array}{l}R_{a}=\frac{1}{\tau}\int_{0}^{l}\left|h\left(x\right) \right|dx\\ R_{p}=\max\left[h\left(x\right)\right],0\leq x\leq L\\ R_{p}=\min\left[h\left(x\right)\right],0\leq x\leq L\\ R_{s}=\frac{1}{h}\sum\limits_{i=1}^{i=n}S_{i}=\frac{S_{1}+S_{2}+S_{3}+...+S_{n }}{n}\end{array} \right. \tag{1}\]  
A roughometer surface roughness measuring instrument (JB-4C, Shanghai, China) was used to measure the surface roughness parameters before and after wear tests. This instrument conformed \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Properties** & **2A12** & **45** & **7075** & **Q345B** & **QT700** \\ \hline Density (g/cm\({}^{3}\)) & 2.85 & 7.89 & 2.81 & 7.87 & 7.09 \\ Elastic modulus (GPa) & 74.2 & 209 & 72 & 212 & 169 \\ Shear modulus (GPa) & 27.3 & 82.3 & 26.9 & 80.7 & 64.7 \\ Yield stress (MPa) & 265 & 355 & 505 & 250 & 420 \\ Poisson ratio & 0.36 & 0.269 & 0.33 & 0.31 & 0.305 \\ Specific heat (J/(kg-K)) & 460 & 450 & 960 & 450 & 510 \\ Thermal diffusivity (\(10^{-6}\)/K) & 23.8 & 11.7 & 24 & 12.8 & 10.8 \\ Heat conductivity (W/(m-K)) & 44 & 48 & 130 & 48 & 47 \\ HBS (MPa) & 187 & 214/292 \({}^{*}\) & 242 & 218 & 262 \\ \hline \hline \end{tabular}  
* HBS292 indicates Brinell hardness of quenched 45 steel. The Brinell hardness values of various metal sliders were obtained through hardness measurement using an HBE-3000A electric Brinell hardness tester.  
\end{table} 
Table 1: Material properties of friction pairs consisting of metal tips and sliders. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **45 \({}^{\text{\#1}}\)** & **45 \({}^{\text{\#2}}\)** & **7075** & **Q345B** & **QT700** \\ \hline Preload (N) & 22 & 22 & 22 & 22 & 22 \\ Voltage (V) & 150 & 150 & 150 & 150 & 150 \\ Frequency (kHz) & 39.8 & 39.8 & 39.8 & 39.8 & 39.8 \\ Mean velocity (mm/s) & 208 & 130 & 105 & 102 & 101 \\ \hline \hline \end{tabular}  
* \({}^{\text{\#1}}\) Common steel; \({}^{\text{\#2}}\) quenched steel. Reciprocated stroke of the sliders is 0.1 m.  
\end{table} 
Table 2: Sliding conditions of ultrasonic motors consisted of metallic tips and sliders. to international standards ISO05436 and ISO11562. In addition, wear topography of contact surfaces for the sliders made of different metallic materials was investigated using a metallurgical microscope (MM, CMM-20, Shanghai, China) accompanied by a confocal laser-scanning microscope (CLSM, OLS3000, Tokyo, Japan). Fractal dimensions of contact surfaces were analyzed by power spectral density method before and after wear tests.