# Stick-Slip Phenomena and Acoustic Emission in the Hertzian Linear Contact
## 4 Results and Discussion
However, the fact that some of the bursts are missing due to the low sampling frequency used in this work must be taken into account in consideration of the results related to the counts. The amplitudes of the AE signal were plotted against driving speed for different loads (Figure 9). In general terms, the AE amplitudes for both the stick and slip phenomena seem to be rather related to the kind of stick-slip movement: the increase in the normal force and the decrease in driving speed led to an increase in the stick-slip movement amplitude, with a consequent rise in the amplitude of the AE bursts. In addition, the amplitude in the stick phase was significantly lower than the amplitude in the sliding phase (Figure 9a, b), as was expected, since the AE caused during the stick phase was only prompted by the  
Figure 8: Distribution of the AE burst counts along the slip time (**a**), and AE counts along the stick time (**b**). Figure 7: AE counts in the slip (**a**) and stick (**b**) phases, including the fitted curves of the counts of AE with a force of 20 N.  
contact surface deformation, while for the slip phase, other phenomena, such as a part of the plastic deformation occurred. In the process of transmitting normal forces between the two bodies and in the presence of relative motion, the \"third body\" was formed with properties specific to the material couple. Thus, the structure of the material changed, the existing microcracks joined, and new cracks appeared, especially during the appearance of plastic deformations (Figure 9). It was also observed that the AE amplitude follows a logarithmic curve, similar to the friction coefficients, depending on the movement speed. The Pearson correlation coefficients were calculated between the amplitude of the acoustic emission, \(A_{AEsl}\) and \(A_{AEsl}\) from the slip and stick phases, respectively, as an independent variable and the amplitude of the stick-slip phenomenon(\(\mu_{v}\)) as a dependent variable. The obtained results can be found in Table 3.  
The Pearson coefficients fall within the 95% confidence interval (\(p<0.05\)), and it can be seen that there was a very high correlation between the AE amplitude and the amplitude of the stick-slip phenomena. Considering the high value of the correlation coefficients, we can conclude that the appearance of the stick-slip phenomenon can be identified by determining the amplitude of the acoustic emission. Knowing that the amplitude of AE is correlated to the amplitude of the stick-slip movement, and the number of counts seems to be rather independent of the amplitude of the movement, it seems that the energy consumed by friction (\(W_{COF}\)) and the AE (\(W_{AE}\)) energy could also be related. The energy consumed by friction (\(W_{COF}\)) and the AE (\(W_{AE}\)) energy were calculated for the three forces, 20, 40, and 60 N, and for each phase of soldering and sliding (Figure 10). In general terms, the higher the amplitude of the stick-slip movement, the higher the energy consumed by friction (\(W_{COF}\)) due to increases \begin{table}
\begin{tabular}{c c c} \hline \hline
**Coefficients** & \(\mathbf{A_{AEsl}}\)/\(\mathbf{\mu_{v}}\) & \(\mathbf{A_{AEsl}}\)/\(\mathbf{\mu_{v}}\) \\ \hline \hline \multicolumn{3}{c}{\(F_{n}=20\) N} \\ \hline Pearson correlation & 0.980 ** & 0.997 ** \\ \hline \hline \multicolumn{3}{c}{\(F_{n}=40\) N} \\ \hline Pearson correlation & 0.930 * & 0.96 * \\ \hline \hline \multicolumn{3}{c}{\(F_{n}=60\) N} \\ \hline Pearson correlation & 0.961 ** & 0.970 ** \\ \hline \hline \end{tabular}  
* Correlation is significant at the \(p=0.05\) level (95% level of confidence). ** Correlation is significant at the \(p=0.01\) level (98% level of confidence).  
\end{table} 
Table 3: Correlations between the AE and stick–slip amplitudes. Figure 9: Variation in AE amplitude with driving speed in slip phase (**a**) and stick phase (**b**). in the friction force and sliding distance, and the higher energy generated by AE, due to the intensity of the deformation mechanisms in the contact zone.