# Predicting Ceramic Wool Diameter by Motor Frequency Using Improved BP Neural Network
## 3 Experimental Procedure  
In this experimental part, the main raw materials with additives (mainly Al\({}_{2}\)O\({}_{3}\) and SiO\({}_{2}\)) were used to prepare the ceramic wool. To predict the relationship between the main  
Figure 2: Planar diagram of the simplified fiberization process: (**a**) The moment of the fixed viscous fluid falling downward onto the spinning wheel; (**b**) Droplet stretch stage; (**c**) Droplet final filament stage.  
motor frequency and the ceramic wool diameter, different samples were prepared with the main motor frequencies ranging from 220.9 to 378.5 Hz which was in the certain frequency range of the real produce process. The corresponding relationship between the frequency and rotation speed of the main motor is 1 Hz for 30 rad/min, the wheel rotation speed range is between 6627 rad/min and 11625 rad/min. The mixture could not be rolled into wool when the main motor rotation speed was too low. However, at high frequency, the mechanical vibrations were inevitable which affected the fiber quality.  
The diameters were tested according to the standard procedure of GBT7690.5-2001 while the histogram and normal distribution curves were drawn according to the data observed by VOM.100 points. Figures 3 and 4 show the SEM images of the ceramic fibers with different diameters with the specified main motor frequency. The values of the diameters varied from 1.058 um to 4.538 um, which verified that the ceramic fibers were discrete. Hence, to obtain the mean ceramic wool diameter, Figure 5 illustrated the diameter distribution of 100 ceramic fibers with the main motor frequency of 280.0 Hz. As shown in the picture, 100 squares with different colors matched 100 values and the white square represents the highest value. It indicated that the fiber diameters ranged from 1.950 to 5.210 um in the same sample. The mean ceramic wool diameter was 3.524 um. However, the diameters of the ceramic fiber fluctuated greatly in the actual production. To improve the results accuracy, five samples were collected at a constant frequency, and the final data with ten different motor frequencies are shown in Table 1.  
Figure 3: SEM images of ceramic fibers with different diameters.  
Figure 4: Diameter distribution of 100 ceramic fibers.  
Figure 5: Nonlinear compensation model based on LSM.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**The Main Motor Frequency/Hz**} & \multicolumn{4}{c}{**The Mean Diameter of Each Sample/\(\upmu\)m**} & \multicolumn{2}{c}{**The Mean Ceramic**} \\ \cline{2-6}  & **1** & **2** & **3** & **4** & **5** & **Wool Diameter/\(\upmu\)m** \\ \hline
220.9 & 4.154 & 4.158 & 4.135 & 4.152 & 4.156 & 4.151 \\
235.2 & 4.023 & 4.025 & 3.994 & 4.031 & 4.024 & 4.019 \\
256.8 & 3.851 & 3.859 & 3.812 & 3.867 & 3.869 & 3.852 \\
267.1 & 3.731 & 3.719 & 3.687 & 3.721 & 3.716 & 3.715 \\
280.0 & 3.524 & 3.519 & 3.489 & 3.513 & 3.511 & 3.511 \\
309.4 & 3.347 & 3.345 & 3.337 & 3.342 & 3.343 & 3.343 \\
321.6 & 3.309 & 3.313 & 3.267 & 3.305 & 3.310 & 3.301 \\
334.4 & 3.252 & 3.245 & 3.226 & 3.243 & 3.245 & 3.242 \\
360.8 & 3.158 & 3.156 & 3.148 & 3.152 & 3.15 & 3.153 \\
378.5 & 3.176 & 3.181 & 3.160 & 3.172 & 3.174 & 3.173 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The Mean Fiber Diameter Date with Ten Different Main Motor Frequencies.