# Design and Experiment of a Moving Magnet Actuator Based Jetting Dispenser
## 3 MMA Dispenser Design
### The MMA Simulation  
Since the cross-section of the MMA is constant, a 2D axisymmetric model can be used. The thrust force on the moving core, including the shaft, two ferromagnetic discs, and the permanent magnet, is predicted via a 2D magnetostatic solution type in an ANSYS Maxwell simulation. The MMA geometric dimensions are also determined through the process of modifying the MMA model to get the most suitable result. Figure 5a-d show a 2D axisymmetric model of the MMA in Maxwell simulation. In this simulation model, the permanent magnet material is NdFeB-N-48, which has the relative permeability of \(\mu=1.05\), the magnetic retentivity of Br = 1.4 T, and magnetic coercivity of Hc = \(-1061032.95\) A/m. The two iron-ring poles and ferromagnetic shell are made of carbon steel 1020C with a nonlinear B-H curve indicated in Figure 5e [32]. The bobbin, core/shaft, and adjusting nut are made of AL6061. The wire diameter is 0.32 mm, and the number of turns N is 439 turns for each winding coil. The max voltage ranges from 22 to 24 V, and the current applied to the coil ranges from 1.6 to 2.4 A. The simulation results show that the computed thrust force is 9.72, 10.89, 12.12, 13.3, and 14.47 N corresponding to an applied current of 1.6, 1.8, 2.0, 2.2, and 2.4 A, respectively.  
Figure 5: \(Cont.\)  
The results for the simulated MMA dimensions are listed in Table 1. To confirm that the simulation model is the most approximate description of the actual model, the real MMA model based on the simulated MMA dimensions is fabricated. Figure 6a shows a measuring system designed to measure the thrust force of experimental MMA. The experimental results show that the thrust force is 9.66, 10.47, 11.35, 12.13, and 12.93 N corresponding to an applied current of 1.6, 1.8, 2.0, 2.2, and 2.4 A, respectively. The simulation results are compared with the experimental values with an average error of 5.96%, and shown as Figure 6b. To successfully actuate the dispenser needle, the thrust force Fth generated from the MMA must be greater than the F\({}_{\text{RMS}}\) force. If the safety factor n is 1.3, Fth must take a value greater than 10.5 N. Compared to the experimental results; the current value applied for the MMA must be greater than or equal to 2 A.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dimensions** & **Value (mm)** & **Dimensions** & **Value (mm)** \\ \hline Core radius & \(r_{\text{co}}=2\) & Permanent magnet height & \(h_{\text{pm}}=21\) \\ Ferromagnetic-disc thickness & \(l_{\text{fd}}=4\) & Permanent magnet radius & \(r_{\text{pm}}=6.5\) \\ Needle-piston radius & \(r_{\text{np}}=2.5\) & Bobbin inner radius & \(r_{\text{ib}}=7.5\) \\ Height of coil & \(h_{\text{c}}=15\) & Bobbin outer radius & \(r_{\text{ob}}=12\) \\ Coil thickness & \(r_{\text{ct}}=4\) & Shell inner radius & \(r_{\text{is}}=12.5\) \\ Spacing between two coils & \(l_{\text{sp}}=2\) & Shell outer radius & \(r_{\text{os}}=15\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The main dimensions of the MMA.  
Figure 5: The finite element analysis model of the MMA. (**a**) MMA model; (**b**) mesh model; (**c**) flux distribution at excited current of 2.4 A; (**d**) magnetic flux density at excited current of 2.4 A; (**e**) B–H curve of 1020 C.  
Figure 6: Measuring driving force. (**a**) Measuring system; (**b**) comparison of experiment and simulation results.