# Design and Simulation of Electromagnetic Linear Actuators for Jet Dispensers
## 3 Experimental Measuring of Necessary Thrust Force
\begin{table}
\begin{tabular}{c c c c} \hline
**Geometric Dimension** & **Symbol, Value (mm)** & **Geometric Dimension** & **Symbol, Value (mm)** \\ \hline Needle radius & \(r_{n1}=1\); \(r_{n2}=2\) & O-ring groove radius & \(r_{ag}=3.9\) \\ Nozzle radius & \(r_{nw}=0.25\) & O-ring groove length & \(l_{d}=5.2\) \\ Chamber radius & \(r_{c1}=1.5\); \(r_{c2}=2\) & Chamber length & \(l_{c1}=9.5\); \(l_{c2}=5.4\) \\ Fluid line radius & \(r_{f}=1\) & Nozzle length & \(l_{nw}=3\) \\ \hline \end{tabular}
\end{table} 
Table 1: Main geometric dimensions of experiment jet valve. Figure 5: Experimental setup used to measure resistance force acting on jet valve needle during operation. The acceleration force, \(F_{M}\), was calculated directly as  
\[F_{M}=a\cdot m_{T} \tag{7}\]  
\[m_{T}=m_{n}+m_{m}+m_{s} \tag{8}\]  
where \(m_{T}\), \(m_{n}\), \(m_{m}\), and \(m_{s}\) are the total mass, the needle mass, coil winding/magnet/plunger mass, and the sub-components' mass, respectively; and \(a\) is the acceleration. The \(m_{T}\) value was estimated to be approximately 0.031 kg. Assume that the jet dispenser operates at a frequency of 250 Hz, and the time required for the needle to complete the full stroke length of 0.5 mm in the rising or dispensing stage is 1.5 \(\upmu\)s, the needle velocity increases from 0 m/s to the maximum velocity at the end of the stroke length, and the average velocity and acceleration are calculated based on equations, \(v=\Delta x/\Delta t\) and \(a=\Delta v/\Delta t\), then calculated average acceleration is equal to approximately 220 m/s\({}^{2}\). The inertia force, \(F_{M}\), is then determined from Equation (7) to be 6.8 N at the maximum backpressure of 0.5 bar. In practice, the magnitude of the necessary thrust force (\(F_{NTF}\)) to be produced by the actuators depends on whether or not a return spring is used to assist the needle motion in the dispensing stage. For the SA, the thrust force acts only in one direction, and hence a return spring must be used. However, for both the MCA and the MMA models, the thrust force may act in either direction (up or down) and hence a return spring can be employed if desired. Thus, the following formulations for \(F_{NTF}\) are derived  
\[F_{NTF}=a_{s}\cdot F_{TRF} \tag{9}\]  
\[F_{NTF}=a_{s}\cdot(F_{TRF}+F_{S}) \tag{10}\]  
where \(F_{NTF}\) and \(F_{NTF}\) denote the necessary thrust force without and with a spring, respectively. In addition, as is a safety factor (described in the following paragraph) and \(F_{S}\) is the spring force. From Equation (6), the total resistance force, \(F_{TRF}\), is equal to 11.1 N for backpressure of 0.5 bar. However, to ensure that the thrust force produced by the actuator under realistic working conditions characterized by a temperature change in the coil windings or variations in the adhesive viscosity, for example, the total resistance force should be multiplied by a safety factor, \(a_{s}\), as shown in Figure 3. Assuming that \(a_{s}\) is assigned a value of 1.2, the value of \(F_{NTF}\) is determined to be 13.3 N (Equation (9)) if no return spring is used. For the case, where a spring is used to drive the needle in the dispensing stage, the spring force value, \(F_{S}\), can be set equal to the same \(F_{NTF}\) value. In other words, the necessary thrust force, \(F_{NTF}\), is determined from Equation (10) to be 29.3 N (i.e., \(1.2\times(11.1+13.3)\approx 29.3\)).