## 2 Materials and Methods
### Welding Process Analysis
#### 2.4.1 Dynamic Resistance  
For the sheet metal joining by RSW in industry, the measured voltage is composed of a resistive and an inductive component: \(u_{\text{RSW}}=ik+Ldi/dt\)[23; 24]. The induced voltage is picked up by the two electrical wires which span the upper and lower electrodes and form an inductance loop [24]. However, for the micro enameled wire joining by MRSW with single electrode, there is not an obvious inductance loop for the \(u_{t}\) measurement (Figure 1c). The \(R_{t}\) is obtained through dividing \(u_{t}\) by \(i_{t}\) in this study. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Normal Welds** & **Incomplete Fusion** & **Abnormal Wire** & **Overheating** & **Other Failures** & **Defectrate** \\ \hline
111,905 & 21 & 22 & 8 & 2 & \textless{}0.25\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Visual testing results. Figure 3: Curves of \(V_{CON}\), \(I_{AVE}\), \(R_{0}\) and \(Q_{E}\) during the electrode life. As shown in Figure 4, the equivalent circuit for the electrode and workpieces can be regarded as resistance in series-parallel connection. \(R_{E}\) represents the resistance from the voltage measuring position to the electrode tip, \(R_{Tip}\) represents the electrode tip resistance, and \(R_{W}\) is used to analyze the workpiece resistance and the contact resistance. The following factors influence \(R_{t}\) and its profile. * Factor 1: the electrode wear. This is caused by several factors, such as frequent tip cleaning and ignition loss, which causes the mass and the size of the tip to decrease (Figure 4b) and \(R_{Tip}\) to increase as the welding number grows [2]. * Factor 2: the temperature increase. The electrode temperature increases because of the net energy input of electrode, and the heat transferred to the workpieces also causes their temperature to increase. Therefore, the resistivity of the electrode and workpieces increases in the welding process. * Factor 3: the shunting effect. Because of the low resistivity of copper, more or less of the current is diverted to the joint of copper wire to the pad. The \(R_{W}\) starts to influence \(R_{t}\) after the insulation coating is removed. When the \(R_{Tip}\) becomes higher in the middle and late stage of the electrode life, the resistance curve may drop obviously due to the shunting effect. According to the change of \(R_{t}\) profile during the electrode life, it is divided into several types based on its main trend described in Table 3. One of the electrodes is taken as an example in Figure 5 to show the change of \(R_{t}\). Figure 6 shows various profiles with arrows used to point out the main trends. Its change can be explained by the above factors. 1. Factor 1: its effect can be observed from the \(R_{0}\), due to the slight effect of Factor 2 and Factor 3 when the welding just starts. After the electrode has been used for a long time, it is prone to wear out, which is reflected in the steep rise of \(R_{0}\). It can be observed in Figure 3 also. 2. Factor 2: it generates the 'Up' profile, which is the majority of the resistance curves shown in Figure 5.
3. Factor 3: it can be seen obviously in the middle and late stage of electrode life. After the removal of the insulation coating, part of current is shunted to the wire and the pad, causing \(R_{t}\) to drop to some extent. Figure 5 shows the 'Up&Down' profile, but the 'Down' profile may occur because of the greater effect of Factor 3 than that of Factor 2. 4. The balance between Factor 2 and Factor 3 may result in the 'Flat' profile. The profile code listed in Table 3 was attributed to each resistance curve by the trend determination rules written in Python. As listed in Table 4, 'Up-Up' and 'Up&Down-Up' have a majority of \(R_{t}\) profiles, accounting for 86.54% of the total weld count. Figure 4: Schematic diagram for dynamic resistance analysis: (**a**) equivalent circuit; (**b**) electrode wear.