# Stick-Slip Phenomena and Acoustic Emission in the Hertzian Linear Contact
## 3 Methodology  
One goal of this study was to demonstrate that the basic parameters of the AE are suitable and sufficient to detect the SS phenomenon and, thus, the adapted configuration of the Tribometer UMT-2 prepared for this type of experiment led to a simplified but sufficient analysis of the AE signals, avoiding the requirements of standard AE equipment. Moreover, the fundamental objective of the experimental tests carried out was to analyse the correlations of the AE and COF parameters, depending on the low and very low driving speeds, because the initiation of the relative motion between two bodies under friction is a fundamental and essential problem in understanding the friction principle in tribology. The tribometer was equipped with tensometric transducers for normal and tangential stresses and AE and driving speed transducers. Due to the calibration of the bending stiffness on the vertical drawbar that was mounted on the cylindrical specimen (the bending deformation occurred depending on the force applied perpendicularly to the drawbar), the tangential force was determined as a frictional force. The driving speed was determined by adjusting the time and distance. The synchronization of the friction force measurement with the AE measurement was automatic. Based on the friction force, the normal force and AE were measured directly by the transducers and could be determined indirectly by calculating the average of each COF (static, kinetic, amplitude), sliding speed, energy consumed by friction, and several AE parameters (counts, amplitude, energy). Before starting the tests, at the lowest normal load and driving speed, five assays were performed in order to \"adapt\" the surfaces to each other, and then the tests were run from the highest to the lowest driving speed with progressively increasing normal force. In order to analyse the phenomenon of stick-slip, 12 tests were performed. For these, four driving speeds (0.2, 0.1, 0.05, and 0.01 mm/s), four time periods (50, 100, 200, and 1000 s), and three normal load forces (20, 40, and 60 N) were set [42], resulting in three Hertzian contact pressures (48.20, 68.16, and 83.48 MPa), determined by calculation. Each test result was obtained from an average of three identical attempts performed under the same conditions (the normal loads and driving speeds applied), and the coefficient of statistical variation was determined as the ratio between the mean square deviation and the arithmetic mean. The highest value of the statistical coefficient of variation for all tests (three forces and four speeds) was 0.08. The stick-slip periods used in the investigation were chosen from the stabilised zone of the movement, taken into account after two or three jumps from the initiation of the movement. The stick and slip periods were analysed, and for each jump sequence between static and kinetic friction, the static friction coefficients \(\mu_{s}\), the kinetic friction coefficients \(\mu_{k}\), and the amplitude of the stick-slip phenomenon \(\mu_{v}\) were determined, where \(\mu_{v}=(\mu_{s}-\mu_{k})/2\). The maximum static friction coefficient is the peak of the phenomenon, and the kinetic one is the minimum. These coefficients are approximately constant at the same load and speed (the COF is considered a deterministic phenomenon). For each normal force and speed, the peaks of the static friction coefficients were counted (the static friction coefficient number is equal to the kinetic friction coefficient number), resulting in a frequency of stick-slip jumps relative to the period time. In this work, the count of AE refers to all AE peaks above the threshold value (set to 0.02 V). Only the signals that exceeded the voltage threshold are identified as AE signals. For each stick and slip phase sequence in a test, each AE count was obtained over time, and finally, the average peak results were obtained for each test. The AE amplitude, directly connected to the AE energy, denotes the highest measured voltage in a waveform.