**8. Conclusions**

The use of a harmonic sinus function for the piston motion leads to an imperfect conversion from chemical energy into electrical energy by using a free-piston engine. The optimization of the energy conversion is a complex challenge, because of several influences by the thermodynamic and electrical conversion. The results of the trajectory variation described in Section 7 have shown that an increased acceleration of the piston from TDCF to BDC leads to a strong decrease of the peak pressure, which results in a strong decrease of the wall heat losses. The analyzed trajectory B1 could show an increase of the efficiency by 41% for the energy conversion. In addition to the efficiency increase, it is possible to increase the inlet pressure to reach the same peak pressure as the reference. This would lead to an increased power density of the free-piston engine. Despite the optimization, the absolute electrical energy share is still low for the test engine. This is based on the fact that the test engine is very small and has a low thermal efficiency. Therefore, the results of this investigation have to be verified for bigger engines. Due to differing surface-to-volume ratios, it is possible that another trajectory shows better results than B1. The further steps for the free-piston engine investigations are the described verification for engines with higher bore diameter as well as an automated trajectory optimization. When optimizing the geometric parameters of the internal combustion engine, it must be considered that this leads to different requirements for the electrical machine. Combustion engines and electrical machines should, therefore, be optimally designed for each other.

**Author Contributions:** Conceptualization, R.T. and A.G.; methodology, K.K.; software, R.T. and A.G.; validation, R.T. and A.G.; formal analysis, K.K.; investigation, R.T., A.G. and K.K.; resources, A.G. and S.B.; data curation, R.T. and A.G.; writing—original draft preparation, R.T., K.K. and A.G.; writing—review and editing, S.B., R.L. and H.R.; visualization, R.T. and A.G.; supervision, H.R. and R.L.; project administration, R.T. and A.G.; funding acquisition, R.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The authors would like to know who re-uses their research materials and research data, which is why they would only share them on personal request.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **Nomenclature and Abbreviations**

