# Precision Manufacturing of Patterned Beryllium Bronze Leaf Springs via Chemical Etching
## 3 Process Parameter Optimization  
### Taguchi Experiments  
The precision of a fabricated pattern on a leaf spring can be evaluated based on the roundness of its circle or arc, the straightness of the lines and the offset of the position. The roundness and straightness reflect formation errors of the pattern. An offset reflects a size error, such as the diameter, width, or position. Many factors are related to these three indicators. However, we found that the key processing parameters are the concentration and temperature of the etchant solution and the exposure time based on analysis and experience. The concentration of the etchant solution directly affects the etching speed and pH of the solution, thereby influencing the quality of the leaf spring. The temperature of the etchant solution will also affect the etching speed. A lower temperature will  
Figure 7: Finished leaf springs.  
slow down the reaction speed and a higher temperature will make the photoresist membrane fall off. An inadequate exposure time cannot solidify the photoresist completely. Instead, it will result in poor roundness or straightness and may even force the photo-sensory membrane to drop off. An overly long exposure time will bring about difficulties in the development and mold unloading and make the photoresist crisper. Therefore, proper experimental parameters are vital for us to fabricate high-precision leaf springs.  
The Taguchi method was usually employed to obtain the optimal process parameters in different applications [16; 17; 18; 19; 20], which was also used in the present study. The roundness, straightness and offset of the leaf springs are regarded as three responsive variables. The three control factors are the concentration and temperature of the etchant solution and the exposure time. The levels of the control factors, presented in Table 2, were determined experimentally.  
The orthogonal table of L9 (3\({}^{3}\)) was used to design the test parameters. The parameters of each factor were filled into the orthogonal table according to the rules, as presented in Table 3.  
The signal-to-noise (S/N) ratio is applied in the Taguchi method as the quality characteristic of choice. In the pursuit of smaller characteristics of the roundness, straightness and offset of the leaf springs, a smaller-the-better (STB) type characteristic was used as the objective function (Equation (2)) in this experiment.  
\[\eta=-10\log(\frac{1}{n}{\sum_{i=1}^{n}{y_{i}}^{2}}) \tag{2}\]  
Here, \(\eta\) is the signal to noise ratio (S/N: dB), \(n\) indicates the experimental period and \(y_{i}\) can be the roundness, straightness, or offset of the leaf springs.  
According to the experimental requirements of the orthogonal table, nine group experiments manufacturing the leaf springs shown in Figure 1 were carried out and repeated five times for each group. One of the holes on the leaf springs was selected to evaluate roundness. One of the branches on the leaf springs was selected to evaluate straightness and offset. The selected hole and branch were measured each time using an image profile projector (2011, MUMA200, 3 DFamily, Inc., Nanjing China, with a resolution of 1 \(\upmu\)m). The mean values of the roundness, straightness and offset are shown in Table 4. The values of \(\eta\) were also calculated and listed in Table 4.  
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Level**} & **Factor A** & **Factor B** & **Factor C** \\ \cline{2-4}  & **Concentration (Etchant: Water)** & **Temperature (\({}^{\circ}\)C)** & **Time (min)** \\ \hline
1 & 1:3 & 50 & 2 \\
2 & 1:4 & 60 & 2.5 \\
3 & 1:5 & 70 & 3 \\ \hline \end{tabular}
\end{table}
Table 2: Control factors and their levels.  
\begin{table}
\begin{tabular}{c c c c} \hline
**L9** & **Factor A** & **Factor B** & **Factor C** \\ \hline
2 & 2 & 1 & 2 \\
3 & 3 & 1 & 3 \\
4 & 2 & 2 & 1 \\
5 & 3 & 2 & 2 \\
6 & 1 & 2 & 3 \\
7 & 3 & 3 & 1 \\
8 & 1 & 3 & 2 \\
9 & 2 & 3 & 3 \\ \hline \end{tabular}
\end{table}
Table 3: Orthogonal table of L9 (3\({}^{3}\)).