# Derating of Electrical Contacts with Varying Surface Roughness
## 3 Results  
The formula \(Imax*0.8\) in DIN EN 60512-5-2 is a standard derating factor used to determine the safe operational current for electrical connectors and conductors. This means that the maximum allowable current should be reduced to 80% of the rated maximum current (Imax) to prevent excessive heating, ensure long-term reliability, and account for real-world variations in operating conditions [29]. Tables 2-4 present the measurement data of current values and the corresponding ambient temperatures during testing for R\({}_{\mathrm{z}}\)2 and R\({}_{\mathrm{z}}\)10 values. The first row contains the current values in amperes, ranging from 1 A to 20 A. The second row includes the ambient temperature values in degrees Celsius, measured for each current value. The ambient temperature changes depending on the current intensity, but not in a linear manner. The data shows the variation in ambient temperature depending on the measurement conditions. Figure 4 illustrates the relationship between current (A) and ambient temperature (\({}^{\circ}\)C) in two different cases, labeled as contact with a roughness of R\({}_{\mathrm{z}}\) 10 (blue line) and contact with a roughness of R\({}_{\mathrm{z}}\) 2 (orange line). The horizontal axis represents the ambient temperature ranging from 55 to 100 \({}^{\circ}\)C, while the vertical axis shows the current value in amperes, ranging from 0 to 22 A. The current values decrease as the ambient temperature increases, indicating an inverse relationship between these two variables. Additionally, it highlights the maximum temperature (marked by a red dashed line), which is 100 \({}^{\circ}\)C. The values for R\({}_{\mathrm{z}}\) 10 drop slightly faster than for R\({}_{\mathrm{z}}\) 2, suggesting that at higher R\({}_{\mathrm{z}}\) values, the current is more sensitive to increases in ambient temperature. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Sample 3**} \\ \hline
**Current [A]** & 1 & 3 & 6 & 10 & 12.8 & 16 & 20 \\ \hline
**Ambient T** [\({}^{\circ}\)**C] & 23.67 & 23.69 & 23.85 & 24.00 & 23.12 & 24.27 & 25.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Current and ambient temperature values during samples of both R\({}_{\mathrm{z}}\) (3) values testing. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Sample 1**} \\ \hline
**Current [A]** & 1 & 3 & 6 & 10 & 12.8 & 16 & 20 \\ \hline
**Ambient T** [\({}^{\circ}\)**C] & 23.34 & 23.30 & 23.37 & 24.05 & 24.18 & 24.10 & 23.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Current and ambient temperature values during samples of both R\({}_{\mathrm{z}}\) (1) values testing. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Sample 1**} \\ \hline
**Current [A]** & 1 & 3 & 6 & 10 & 12.8 & 16 & 20 \\ \hline
**Ambient T** [\({}^{\circ}\)**C] & 23.34 & 23.30 & 23.37 & 24.05 & 24.18 & 24.10 & 23.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Current and ambient temperature values during samples of both R\({}_{\mathrm{z}}\) (2) values testing. The image (Figure 5) shows the derating curve for a contact with a surface roughness of R\({}_{\mathrm{z}}\)10. The graph illustrates the relationship between current (A), ambient temperature (\({}^{\circ}\)C), and sample temperature (\({}^{\circ}\)C). The vertical axis represents the current value, while the lower horizontal axis denotes the ambient temperature, and the upper horizontal axis indicates the sample temperature. For further context, Figure 6 complements this plot by charting the allowable current for the same R\({}_{\mathrm{z}}\) 10 surface as a function of ambient temperature, thereby revealing how thermal constraints tighten as the operating temperature rises. Figure 4: Contact resistance reduction behavior of the test specimen under repeated mating cycles, measured in accordance with DIN EN 60512-5-2. Figure 5: Current–voltage characteristics of test samples with different surface roughness values (R\({}_{\mathrm{z}}\)).