## 5 Arcing Characteristics
### Arcing Vibration  
When an arc fault occurs, sound is emitted from the contact point of the plug. The vibration at the contact point was measured using a laser Doppler vibrometer (LV-1300, Onosokki Co., Ltd., Yokohama, Japan). Although it is hard to create identical arc-fault states, the vibration at the contact point is always observed. Typical results for this measurement are shown in Figure 6. According to these results, the vibration strength is directly proportional to the amount of current that is being passed through the contact spot. However, the variations in the vibration velocity every period are due to the contact surface area. The vibration strengthens when the arcing condition is present at the connection. Figure 7 shows an FFT analysis of the vibration velocity waveform in Figure 6. It also shows that the contact area will vibrate at twice the frequency of the AC. The strongest vibration would occur every time the current reached the zero-crossing point. Vibrations that are caused by poor contact may not be present in the direct current setup due to its continuous discharge. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Experiment No. (Cu-Cu Discharge)** & **Temperature Range in Degrees Celsius** & **Resistance Values in Ohms** \\ \hline Sample 1 & 21 \({}^{\circ}\)C-122 \({}^{\circ}\)C-238 \({}^{\circ}\)C-520 \({}^{\circ}\)C & \(\infty\)–124 k\(\Omega\)–16 k\(\Omega\)–530 \(\Omega\) \\ \hline Sample 2 & 21 \({}^{\circ}\)C-  
This phenomenon is poorly understood due to the difficulties presented by the microscopic scale of the contact area in it. We were unable to make measurements of the thickness, width, and girth of the contact point. The amount of current that flows through that small contact area will need to be simulated by computer analysis in future research. Given what we know, there are two possible explanations for the vibration phenomenon. The first explanation attributes it to thermal expansion, and the second explanation attributes it to the electromagnetic field change within the small contact area. We will explain the thermal expansion explanation first. The strength of the vibration in the arc fault depends on multiple factors. The first factor is the amount of heat that is generated and dissipated in the contact area. It is directly proportional to the amount of current that passes through the contact spot and the resistance of the contact area. The second factor is the thickness of the oxide at the location where the current is flowing. As mentioned earlier, the arc fault extinguishes itself or is dimmed at every zero-crossing point and near the points where the current shoulder and voltage drop are observed. It is assumed that the temperature at the affected area initially decreases but then increases again when the arc fault is reinitiated. If the heat affects a large enough area, it may cause thermal expansion when the arc state flashes up. Consequently, the arc state will increase the size of the affected area and push away both contacts. When the arc extinguishes itself at the zero-crossing point, the affected area shrinks in size due to the reduction in temperature. This back-and-forth expansion may also initiate a secondary making or breaking of the contact spark, and it can also reinitiate the arc-fault state if the temperature falls too low near the new contact area. This means that in every arc-fault state, even if the setup is running with the same amount of current, the vibration strength would not be equal in every experiment due to the changes in the contact area. To replicate the vibration strength, the size of the copper oxide bridge at the contact area must always be the same. The other explanation is the electromagnetic field change. A sudden field change is experienced when the arc extinguishes and reignites and is similar to rapidly switching the circuit on and off. This produces an electromagnetic force that can attract the two contacts together. Figure 6: The voltage waveform and the vibration velocity waveform.