## 7 Results  
This chapter shows the results of the efficiency loss analysis for the trajectory variation. The losses of the internal combustion engine and the electrical machine were shown together in a diagram in order to evaluate the influence of the trajectory. For the evaluation of the energy conversion from chemical to mechanical energy the courses for the piston motion, the corresponding pressure and temperature as well as a PV diagram of the compared trajectories will be shown and discussed. For the energy conversion from mechanical to electrical energy, the position and speed of the piston, the electrical machine force and the resulting power are shown and discussed. The loss analysis for the reference is shown in Figure 14. The summation of all energy shares is the chemical energy from the fuel. This energy is divided into the losses for unburned fuel, the wall heat losses, the losses inside the exhaust gas, the friction losses, the iron losses and the copper losses. The last share is the electrical energy, which is issued by the free-piston engine. Figure 14: Energy losses for trajectory REF. Corresponding to the trajectory variation described in Section 6, the courses for the piston motion, the pressure and temperature are shown in Figure 15. The PV diagram for variant A1 and A2 in comparison to the reference is shown in Figure 16. The moved position in time of top dead center firing (TDCF) affects the pressure and temperature courses identically. The moved TDCF of variant A1 and A2 leads to earlier increasing pressure and temperature in comparison to the reference due to the fact that the combustion is initialized early. The decrease of the pressure and temperature is shifted in parallel. At the end of the expansion stroke all courses approach until the exhaust valve opens (EVO). After that, the courses are similar. Figure 16: Comparison of trajectories REF, A1 and A2 related to the energy conversion of the internal combustion engine: cylinder pressure depending on volume. Figure 15: Comparison of trajectories REF, A1 and A2 related to the energy conversion of the internal combustion engine: illustration of the stroke, cylinder pressure and temperature depending on time. For the evaluation of the electrical energy conversion of the trajectory REF, A1, A2, the stroke, speed and force of the electrical machine are shown in Figure 17 and the volume change, copper, friction and electrical power in Figure 18.  
Figure 17: Comparison of trajectories REF, A1 and A2 related to the energy conversion of the electrical machine: illustration of the stroke, velocity and electric machine force depending on time. Figure 18: Comparison of trajectories REF, A1 and A2 related to the energy conversion of the electrical machine: volume change power, copper power losses, friction power losses and electric power depending on time. The shift of the trajectory from REF to A2 is realized by further accelerating the drive train. The required trajectory can be implemented using the force \(F_{EM}\) of the electrical machine. Due to the increased force \(F_{EM}\), the required current and, thus, the copper losses \(P_{Cu}\) increase. Since the speed is increased, the friction losses also increase. In addition to the volume change work, it can be seen that the electrical machine requires energy in the intake and exhaust cycle so that the four-cycle process can be implemented. The longer expansion time with a higher temperature and similar pressure leads to the higher wall heat losses and reduced exhaust losses shown in Figure 19. This phenomenon can be seen when moving the TDCF to an earlier point in time. Due to the fact that the increase of the wall heat losses combined with the copper losses is higher than the decrease of the exhaust losses, both variants show a lower effective efficiency than the reference.