# Stick-Slip Phenomena and Acoustic Emission in the Hertzian Linear Contact
## 4 Results and Discussion
Therefore, the energies seem to be related to each other and also to the amplitude of the stick-slip movement. The Pearson correlation coefficients were calculated between the energy generated by the acoustic emission, \(W_{AEsl}\) (slip), \(W_{AEsl}\) (stick) and the energy consumed by friction, \(W_{COFl}\) (slip) \(W_{COFl}\) (stick), between the SS amplitude (\(\mu_{e}\)) and these energies as well as between the \(AE_{sl}\) and SS amplitudes and the sliding speed (\(v_{slip}\)) (Table 4). Therefore, the energies appear to be related between themselves and also associated with the amplitude of the stick-slip motion. There was always a good correlation between both energies, with slightly reduced results in the stick phase when the 20 N force was applied. There was not always a burst of AE for the slide phase at this low normal force, so the correlation was not as good as for a greater normal load. In addition, at low normal forces, the deformations at the contact level were small; therefore, reduced tangential force effects caused a reduced AE signal. Figure 10: Variation in energies with different driving speeds (mm/s): (**a**) energy consumed by friction in slip phase, \(W_{COFl}\) (**b**) energy consumed by friction in stick phase, \(W_{COFl}\) (**f**), (**c**) energy generated by AE in slip phase, \(W_{AEsl}\) (V\({}^{2}\)s), (**d**) energy generated by AE in stick phase, \(W_{AEsl}\) (V\({}^{2}\)s). Considering the high value of the correlation coefficients, it seems that the magnitude of the stick-slip phenomenon can be estimated by calculating the energies generated by the acoustic emission, both in the stick phase and the slip phase. The Pearson correlations between the stick-slip amplitude and the COF and AE energies in the stick and slip phases show a close correlation between them (Table 4). The amplitude of stick-slip movement correlates well with the AE energy for the slip phase and not so well (as expected) with the AE energy for the stick phase, but the energy seems not to be as good an indicator of the stick-slip movement amplitude as it is the amplitude of AE. In the stick phase, it is possible that the local elastic deformations were the majority compared to the plastic ones, and as such, the AE energy was reduced. The system (drawbar and cylindrical specimen) was deformed exclusively elastically. The real contact area also contained roughnesses that deformed plastically. There was also a strong positive correlation between the AE and SS amplitudes with the sliding speed for all applied forces (Table 4). In order to ascertain the origin of the AE, the \(W_{AE}\) and \(W_{COF}\) in the slip phase were plotted against the sliding speed in Figure 11. The sliding speed is a direct indicator of the amplitude of the stick-slip movement, and, as expected, the friction energy tended to increase with the sliding speed, and it was dependent on the normal force. In addition, the AE energy tended to grow with the sliding speed as well, but it shows some dependence on the normal force, suggesting that other complex phenomena took place at the contact point zone, such as a reduction in tangential stresses and an increase in the contact area.