# Stick-Slip Phenomena and Acoustic Emission in the Hertzian Linear Contact
## 4 Results and Discussion  
The friction coefficient evolution accompanied by AE is presented as an example of the results obtained for the driving speed of 0.01 mm/s at normal forces of 20-60 N. (Figure 3a-c) and the friction coefficient evolution for the force of 60 N at the four driving speeds (Figure 3d). In all cases, the presence of the stick-slip phenomenon was confirmed by COF variation. In general terms, the stick-slip jumps coincided with the sudden increases in AE, although for a 20 N load, this coincidence was not always present. As a general trend, a high normal load and slow driving speed tended to create a stick-slip phenomenon of low frequency and high amplitude, as shown in Table 1, where each value represents an average of all stick-slip events at a specific normal force and driving speed (the same holds for all figures). The driving speed, sliding speed, and normal load are the major factors that play a significant role in the variation of friction coefficients [46; 47; 48]. The driving speed and normal load are directly measured from tests, and the sliding speed is easily calculated from the time and displacement of each phase. The sliding speed is related to the stick-slip frequency and amplitude; therefore, a higher normal load and slower driving speed tended to increase the sliding speed due to the stick-slip phenomena of low frequency and high amplitude (Figure 4). Figure 3: _Cont._  
Figure 5 shows the static and kinetic friction coefficients and the stick-slip amplitude for different driving speeds. As expected, the static and kinetic friction coefficients decreased as the driving speed increased to a specific stiffness. Both friction coefficients increased with the soldering time due to the phenomenon of \"saturation\" of the real contact \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Sliding Speed (mm/s)** & \multicolumn{4}{c}{\(\mathbf{F_{n}=20\) N}} & \multicolumn{4}{c}{\(\mathbf{F_{n}=40\) N}} & \multicolumn{4}{c}{\(\mathbf{F_{n}=60\) N}} \\ \hline  & \(\mu_{s1}\)* & \(\mu_{k1}\)** & \(\mu_{p1}\)** & \(\mu_{s2}\)* & \(\mu_{p2}\)** & \(\mu_{s3}\)* & \(\mu_{k3}\)** & \(\mu_{s3}\)** \\
0.2 & 0.304 & 0.224 & 0.040 & 0.386 & 0.180 & 0.103 & 0.417 & 0.162 & 0.128 \\
0.1 & 0.383 & 0.239 & 0.072 & 0.418 & 0.186 & 0.116 & 0.429 & 0.168 & 0.140 \\
0.05 & 0.461 & 0.246 & 0.108 & 0.47 & 0.189 & 0.141 & 0.485 & 0.175 & 0.155 \\
0.01 & 0.525 & 0.282 & 0.122 & 0.557 & 0.262 & 0.148 & 0.582 & 0.250 & 0.166 \\ \hline \hline \end{tabular}
* Static friction coefficients. ** Kinetic friction coefficients. *** Amplitude of the stick–slip phenomenon.  
\end{table} 
Table 1: Values of the friction coefficients. Figure 4: Variation in sliding speed with driving speeds (mm/s), including error bar. Figure 3: COF and AE amplitude with a driving speed of 0.01 mm/s for the normal force of 20 N (**a**), 40 N (**b**), and 60 N (**c**). Comparison of COF results over time at 60 N force and all driving speeds (**d**). area, so the higher the driving speed, the shorter the soldering time and the lower the static and kinetic coefficients [49; 50]. The increase in driving speed also reduced the contact surface and, accordingly, the friction coefficient tended to decrease, giving, as a result, a stick-slip movement of lower amplitude (measured by the difference between the static and kinetic COFs), as can be seen in Figure 5c, and higher frequency, as shown in Figure 5d. Further increases in the driving speed would lead to the possible cancellation of the stick-slip phenomenon. The effect of the normal load is the increase in the static coefficient of the friction force because the contact pressure and real contact area also increase. In addition, according to the known molecular-mechanical [51; 52] friction theory for conventional dry contact, the kinetic friction coefficient decreases with a decreasing normal force. This divergence in the static and kinetic friction behaviour regarding the normal load leads to a stick-slip movement of a lower frequency and higher amplitude.