# Simulation Study of a New Magnetorheological Polishing Fluid Collector Based on Air Seal
## 4 Experimental Design Using an Orthogonal Table
### Design of Orthogonal Test Table  
The polishing fluid can enter the collector cavity because the arc magnet of the magnetically sealed collector is semicircular. Similarly, too many nozzles hinders the polishing liquid from entering the collector cavity. Therefore, the number of nozzles selected for simulation is 69, only considering the influence of nozzle spacing.  
Figure 8 is a schematic diagram of the influencing factors of the model. In the previous simulation, it was found that the gas nozzle inclination (\(\varphi\)), nozzle diameter (D), nozzle spacing (\(\theta\)), relative height of the collection tube (L), collection tube inclination (\(\alpha\)), and the nozzle airflow velocity (V) affect the collection of MR polishing fluid.  
After determining six factors, a six-factor, three-level orthogonal table L18(36) is designed for simulation testing. The level of factors selected by the orthogonal table is shown in Table 2. Factor 1 is the nozzle inclination angle, which is the angle between the nozzle and the flow direction of the polishing liquid. Factor 2 is the nozzle diameter. Factor 3 is the nozzle spacing, which is the radian value between adjacent nozzles. Factor 4 is the distance between the collection tube and the polished wheel surface. Factor 5 is the inclination of the collector tube, which is the angle between the collector tube and the upper end face of the collector. Factor 6 is the air velocity.  
In Table 2, the selection principle of factor levels is as follows: The nozzle inclination affects the gas-sealing effect, and three inclination angles of 3\({}^{\circ}\), 6\({}^{\circ}\), and 9\({}^{\circ}\) should be considered. The choice of nozzle diameter should not be too small; the small aperture is not  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Factor 1** & **Factor 2** & **Factor 3** & **Factor 4** & **Factor 5** & **Factor 6** \\  & \(\varphi\) & **D** & \(\theta\) & **L** & \(\alpha\) & **V** \\ \hline Level 1 & 3\({}^{\circ}\) & 1 mm & 2.5\({}^{\circ}\) & 5 mm & 45\({}^{\circ}\) & 25 m/s \\ Level 2 & 6\({}^{\circ}\) & 1.5 mm & 3\({}^{\circ}\) & 8 mm & 90\({}^{\circ}\) & 30 m/s \\ Level 3 & 9\({}^{\circ}\) & 2 mm & 3.5\({}^{\circ}\) & 10 mm & 135\({}^{\circ}\) & 35 m/s \\ \hline \hline \end{tabular}
\end{table}
Table 2: Factor levels.  
Figure 8: Schematic diagram of geometric factors.  
easy to process, and excessive air flow generates heat and noise, so D is set as \(\geq 1\) mm. In terms of the choice of nozzle spacing, a value that is too low causes the nozzles to interfere with one another, whereas excessive spacing does not allow for effective formation of a gas seal; therefore, spacing is set as \(2\leq\theta\leq 5\). There is a gap of 2-3 mm between the collector and the polishing wheel and a gap of 1-2 mm between the collector and the polishing fluid. However, if the collection tube is too high, the polishing liquid cannot be collected, so the height is set as 5 mm \(\leq\) L \(\leq\) 10 mm. The jet velocity of the nozzle is too small to separate the polishing solution from the surface of the polishing wheel, so V \(\geq\) 25 m/s is adopted.