# Design of a Solenoid Actuator for a Cylinder Valve in a Fuel Cell Vehicle
## 5 Performance Test  
Figure 13 shows a picture of an actuator prototype and an instrument for measuring the attractive force. The instrument consists of a solenoid actuator (YOUNGDO Ind. Co., Ltd., Busan, Korea), load cell (FUTEK, Irvine, CA, USA), laser displacement sensor (Keyence, Osaka, Japan), thermocouple (OMEGA Engineering Inc., Seoul, Korea), linear stage (SCIENCEtown, Incheon, Korea), power supply (Tektronix Inc., Beaverton, OR, USA) and data acquisition system (National Instruments, Austin, TX, USA). Before the test, the solenoid was fixed to the linear stage, which can move vertically to adjust the distances between magnetic poles [20].  
Figure 12: Contour of magnetic flux lines at ambient temperature and 100% duty ratio.  
Figure 13: Experimental setup for attraction force and saturation temperature.  
To measure the attractive force of the plunger generated by the magnetization of the core, the load cell was placed on the same central axis as the fixed solenoid, and plunger A was fastened to the load cell to measure the attractive force. Then, the linear stage was moved at intervals of 0.1 mm from the point where plunger B and the core are in complete contact with each other. The actual shift displacement was checked using the laser displacement sensor. When the distance between magnetic poles was completely adjusted, voltage was applied to the actuator using the power supply, and the attractive force was measured from the load cell using the data collection system. To compare the results of the experiment and electromagnetic field analysis, the spring was removed to measure only the attractive force. Sufficient time was given between measurements to maintain the temperatures of the two coils at the same level, and the measured temperatures were checked using the thermocouple to ensure reliability of the data.  
Figure 14 shows the measurements of coil temperatures at intervals of 30 s with 40% duty ratio applied. The coil temperature was saturated at approximately 77.7 \({}^{\circ}\)C, which was different by approximately 2.2 \({}^{\circ}\)C from the results of heat transfer analysis. The power consumption in the analysis was calculated for 97.0 \({}^{\circ}\)C (the theoretical saturation temperature), which is smaller than the power consumption obtained in experiments. The measured saturation temperature of the coil was 82.8 \({}^{\circ}\)C. The reason for the differences is that the assumed convection heat transfer coefficient and emissivity values are different from the actual values.  
Table 5 and Figure 15 show the measured results of attractive forces and the analysis results with respect to temperature. The force cannot be measured when the distance between magnetic poles is 0 mm, because the plunger and the core are in complete contact with each other, so this point was excluded. At 100% duty ratio and ambient temperature, the minimum, maximum, and average errors between the measured and analytical results were 3.21, 3.71, and 3.56 N respectively. At the saturation temperature, they were 2.96, 3.60, and 3.33 N, while at 40% duty ratio at the saturation temperature, they were 2.33, 3.85, and 3.17 N. These errors occurred because the 2D model was only the left part of the solenoid, so the magnetic flux leakage in the connector area could not be reflected. In addition, the self-weight of the plunger was reflected in the measured values but not the analysis.  
Figure 14: Measured results of coil temperature.