# Parametric Simulations on Leakage and Performance of a Miniature Free-Piston Generator (MFPG)
## 2 MFPG Prototype  
The schematic configuration and test bench of the proposed MFPG system are shown in Figure 1a,b. As is seen from the picture, the proposed MFPG consists of a reciprocating internal combustion engine (ICE), a voice coil motor (VCM), a control unit and a super capacitor-battery energy storage device pack (SC-Batt ES). The conventional rod-crankshaft unit is diminished, and the ICE and the VCM are coupled directly through an integrated piston-valve rod. Thus, the piston-valve rod moves without the constraint of the crankshaft and  
Figure 1: The miniature free-piston generator (MFFG) prototype. (**a**) The MFPG schematic diagram; (**b**) The MFPG test bench. its movement is governed by the external force acting on the rod. It has been proven that the quenching effect increases with the decrease in cylinder diameter [47] and the piston frequency soars with the reduction in piston mass, which is adverse to trajectory control [48]. Therefore, in order to obtain better combustion and easier trajectory control for future work, a 2.5 cc small scale ICE cylinder is selected. It is a smaller version of a conventional two-stroke ICE. [PERSON] et al. [49] built a prototype on the same cylinder structure with a larger diameter and explained the structure in detail. For a conventional engine, thanks to the rod-crankshaft unit and the flywheel, the energy and torque generated during the compression stage are stored and released in the other stages. Thus, the energy is transferred continuously and smoothly during a complete working cycle. In contrast, the energy flow in a free-piston engine is balanced during a single stroke, so continuous motion is a big challenge for free-piston structures. Usually, an extra piston rebounding unit is a necessary part of a free-piston heat engine. However, the proposed MFPG prototype is designed as simply as possible to accommodate size reduction and reduce the risk of failure [22]. The major simplifications include: (1) the common used spark plug is replaced by a platinum glow plug; (2) A miniature atomizer is used for the fuel atomization instead of the electronic fuel injection system; (3) A self-designed linear valve-port scavenging case without extra electrical and moving parts is applied; (4) The VCM serves as both the energy storage and piston rebounding component, compared to other configurations usually contain separate parts for the piston rebounding. The MFPG is essentially an internal combustion engine and needs to follow the basic thermodynamic cycle to output work. Thus, a complete working cycle of the MFPG also consists of four main stages, which are scavenging, compression, expansion and exhaust. Figure 2 shows a complete working cycle of the MFPG system. The scavenging stroke starts when the scavenging port opens (SPO), the piston is driven by the in-cylinder pressure to the BDC and motored back by the VCM to the scavenging port closing (SPC). When the piston moves negatively to the position of exhaust port closing (EPC), the combustion chamber III is sealed and the system enters the compression stroke. When the piston stops at the top dead center, with the assistant of the glow plug, the combustible mixture ignites and the in-cylinder pressure rises rapidly to push the piston back. The MFPG enters the expansion stroke, in which the VCM is working on the generator mode. The exhaust stroke starts when the piston reaches EPO and ends after the piston stops at BDC. These entire four strokes constitute a complete working cycle, then the piston is ready to start the next cycle. The piston continuously moves back and forth to transform the fuel energy into electricity. Figure 2: _Cont._  
The MFPG specifications are listed in Table 1 and the configuration of the piston coordinates is shown in Figure 3. The MFPG has a shorter residence time at the TDC than conventional ICEs, so the fuel adopted in the MFPG prototype has to be faster in flame speed [50,51].