## 3 Experimental Prototype  
The experimental measurements for the validation of the simulation model were obtained with the help of the prototype in Figure 1 and is shown schematically in Figure 2.  
the electric machine was controlled using an inverter, a linear sensor and a microcontroller from Texas Instruments F28M35H52C. This microcontroller is able to calculate different trajectories, evaluate sensors and calculate manipulated variables (such as ignition sparks, injection times and transistor switch-on times). The data were then sent to a PC, saved and evaluated. The camshaft is connected to a highly dynamic PMSM. With the help of a valve drive, it is possible to operate the valves independently of the piston position. The camshaft and piston are synchronized digitally. To lubricate the cylinder surfaces, a nozzle was inserted which sprays a thin layer of oil under the piston. The most important parameters of the free-piston engine are shown in Table 1.  
The problem with the electrical machine was that high copper losses occur when the four-stroke internal combustion engine is operated. It will be replaced with a self-developed electric machine [29]. The primary part of the electrical machine is not moved. It has a flat geometry, a short stator and is double-sided. The essential characteristic data is illustrated in Figure 3 and shown in Table 2.  
The electrical machine was designed based on a measured force curve through the first prototype. A special feature of the electrical machine is that the primary part has the same length as the secondary part. This creates reluctance forces when the secondary part moves out of the stator. This force acts like a mechanical spring and can minimize copper losses. The reluctance force for this electrical machine is shown in Figure 4a. However, iron losses occur due to the magnetic structure. The iron power loss \(P_{Fe}\) was measured as a \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Linear PMSM**} & \multicolumn{2}{c}{**Combustion Engine**} \\ \hline Rated Power & 3.24 kW & Engine Type & Four-Stroke \\ Rated Speed & 6.6 m/s & Engine Displacement & 99.25 cm\({}^{3}\) \\ Rated Current & 5.6 A\({}_{\text{rms}}\) & Rated Power & 1.9 kW \\ Peak Current & 28 A\({}_{\text{rms}}\) & Bore Diameter & 0.0554 m \\ Rated Force & 491 N & Number of Cylinders & 1 \\ Peak Force & 2455 N & Conventional Stroke & 0.0402 m \\ Mover Mass & 3.271 kg & Maximal Stroke & 0.0566 m \\ Mover Length & 0.505 m & Rated Speed & 4.27 m/s \\ Magnet Yoke length & 0.627 m & Rated Force & 444.96 N \\ Maximum stroke & 0.122 m & Moving Mass & 0.286 kg \\ Resistance per phase & 1.29 \(\Omega\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristic data of the test stand. Figure 3: (a) CAD illustration of the developed electrical machine. (b) Photo of the developed electric machine. function of the electrical frequency \(f_{el}\) at various operating points and a function for this was approximated [35]. The function here corresponds to a Steinmetz model:  
\[P_{Fe}=C_{hy}\cdot\hat{B}^{1,6}\cdot f_{el}+C_{ub}\cdot\hat{B}^{2}\cdot f_{el}^{ 2}, \tag{18}\]  
where \(\hat{B}\) is the magnetic flux density and \(C_{hy}\) and \(C_{ub}\) are two coefficients. The iron power loss is shown in Figure 4b. These special properties were inserted into a simulation model in order to determine the losses in the respective trajectories. For the simulations that were carried out, the parameters of the newly developed machine were used. Since the secondary part moves out of the stator and the proportion of covered magnets to the windings is reduced, the magnetic flux is also reduced. This leads to a reduction in the induced voltage as well as to a reduction in the force per ampere ratio. Therefore, the force of the electrical machine depends on the position and current and is shown in Figure 5. It can be seen in Figure 5 that the force decreases at the stroke limits.