# The Influence of Heat Input on the Surface Quality of Wire and Arc Additive Manufacturing
## 3 Results and Discussion
### Surface Quality Evaluation  
The actual molded specimen was used as the reference model, and the ideal profile model was used as the test model. Figure 6 shows the difference between the actual molded specimen surface and the ideal model surface under different heat input conditions. On the whole, the surface of each specimen has good consistency with the ideal model. However, due to the fact that there are many variables in WAAM, such as heat input, there was a certain difference between the specimen and the ideal model. For example, when the heat input is 11,250 J-mm\({}^{-1}\) and 6160 J-mm\({}^{-1}\), the surface of the specimen is quite different from the ideal model. When the heat input is moderate, the surface quality of the specimen has been improved to a large extent. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Specimen** & \multicolumn{2}{c}{**Parabola**} & \multicolumn{2}{c}{**Half-Period Cosine Curve**} & \multicolumn{2}{c}{**Full Cycle Cosine Curve**} & \multicolumn{2}{c}{**Elliptic Curve**} & \multicolumn{2}{c}{**Extract Model**} \\ \cline{2-9}
**Number** & **S** & **\(\delta\)** & **S** & **\(\delta\)** & **S** & **\(\delta\)** & **S** & **\(\delta\)** & **S\({}_{\text{T}}\)** \\ \hline
1 & 17.137 & 1.089 & 11.902 & 0.756 & 9.348 & 0.594 & 15.628 & 0.993 & 15.737 \\
2 & 14.869 & 1.052 & 10.327 & 0.731 & 8.111 & 0.574 & 13.999 & 0.991 & 14.133 \\
3 & 14.225 & 1.033 & 9.879 & 0.717 & 7.759 & 0.564 & 13.473 & 0.979 & 13.769 \\
4 & 13.171 & 1.076 & 9.147 & 0.747 & 7.184 & 0.587 & 12.897 & 1.053 & 12.246 \\
5 & 14.133 & 1.028 & 9.815 & 0.714 & 7.709 & 0.561 & 13.528 & 0.984 & 13.742 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Integral value and error value of each model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Contour Model** & **Model Equation Prototype** & **Model Formula** \\ \hline Parabola & \(f(x)=ax^{2}+b\) & \(f(x)=-\frac{H}{Hx}x^{2}+H\) \\ Half-period cosine curve & \(f(x)=a\cos(bx)\) & \(f(x)=H\cos\frac{xx}{W}\) \\ Full cycle cosine curve & \(f(x)=a\cos(bx)+c\) & \(f(x)=\frac{H}{\cos\frac{2 mx}{W}}+\frac{H}{\cos\frac{2 mx}{W}}\) \\ Elliptic curve & \(f^{2}(x)=x^{3}+ax+b\) & \(f^{2}(x)=x^{3}+Wx+\frac{2W}{3}+\frac{H}{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mathematical model of the cross-sectional profile of the specimen. The average value of the error between the ideal model of the specimen and the actual formed surface under different heat input conditions is calculated, as shown in Figure 7. The average error of the overall profile tends to be negative, indicating that the actually formed profile is slightly larger than that of the ideal model. However, when the heat input is moderate, the average value of the error is positive, which reflects that the profile of the actual formed sample is smaller than that of the ideal model. The difference in heat input affects the contour shape of the actual formed specimen, which proves that there is a significant correlation between the surface quality of the specimen and the heat input. The error average reflects the overall error of the specimen surface, while the standard deviation and root mean square error can reflect the local conditions of the specimen in more detail. As shown in Figure 7, there are significant differences in the standard deviation and root mean square deviation of the specimens under different heat input conditions. In the specimens, when the heat input is high and low, the surface quality of the specimens is lower than that of the specimens when the heat input is moderate, so the standard deviation and the root mean square value have the same changing trend, and both decrease first and then increase. It can be seen from Figure 7 that specimen 3 has the smallest root mean square value and standard deviation value, while the standard deviation and root mean square value of specimen 4 have changed to a greater extent. Figure 8 is comparison diagrams of the transverse and longitudinal cross-sections of each specimen and the ideal cross-section.