# Electromagnetic Characteristics Analysis of a Tubular Moving Magnet Linear Generator System
## 4 Prototype Research
### Prototype Testing Results  
To validate the performance and the characteristics of the linear generator analyzed in the last section, the manufactured prototype was tested. During the testing, the linear generator works in power generation mode and is driven by a prime motor. The linear generator converts the mechanical energy into the electrical energy. Due to the limitations of the prime motor, the prototype is tested at the frequency of 35 Hz with the generating current amplitude of 25 A.  
The prototype testing results are shown from Figures 10-13. Figure 10 shows the tested mover motion during a stroke driven by the prime motor. The tested mover motion is compared with the mover motion simulated by the validated finite element model (FEM). The mover motion curve is designed according to the actual motion of the FPE [17]. As shown in the figure, the time of the stroke is about 14 ms, and the max speed of the mover motion is up to 3.5 m/s. The reciprocating frequency is about 35 Hz, which is equal to 2100 turns every minute of conventional rotary engines. The reciprocating motion is not a standard sinusoidal motion. The average speed of the first half was significantly higher than that of the second half.  
Figure 10: Comparison of the tested and simulated motions of the mover.  
Figure 9: Prototype system: (**a**) prototype, (**b**) mover, (**c**) stator, (**d**) shell.  
Figure 11 shows the tested and simulated currents during the stroke, and the corresponding terminal voltages are shown in Figure 12. The generating current is a standard sine wave controlled by the controller. The amplitude of the generating current is 25 A, and the root mean square (RMS) current is 17.1 A. A short reverse voltage needs to be provided to create the generating current at the beginning of the stroke. The test curve and the simulated current curves agree well. The tested average coil current is about 0.2% higher than the simulated, and the tested average generating voltage is about 5% higher than the simulated. At the end of the stroke, the aimed generating current is set to zero, as the terminal voltages are lower than the battery voltage at this stage.  
Figure 13 shows the tested and simulated generating power during the stroke. It is calculated by multiplying the instantaneous terminal voltage by the instantaneous coil current. As shown in the figure, the tested peak generating power is 2.8 kW at the midpoint of the stroke. The tested average generating power is 1.4 kW. The short negative power at the beginning of the stroke is used to create the generating current, as well as the short reverse voltage shown in the voltage curve. The tested average power is about 6% higher than the simulated. This difference is mainly caused by the manufacturing differences of the prototype. The actual performance of the permanent magnet used in the prototype is likely to be higher than that used in the simulation model.  
Figure 11: Comparison of the tested and simulated currents of the coil.  
Figure 12: Comparison of the tested and simulated terminal voltages of the coil.  
Figure 13: Comparison of the tested and simulated generating power.