## 6 Conclusions  
The uneven distribution of combustion heat within an internal combustion engine leads to a significant increase of the diameter at the upper part of the liner compared to that at the lower part. This leads to increased friction and oil losses. This study assumed that an originally conical liner in its cold state could be used to reach a nearly cylindrical form in its fired operation state. This would improve the PRCL conformation and thus reduce the friction and the oil losses. To study that, a numerical validated gasoline engine model was used. With a numerical FEM simulation model, the deformation behavior of the liner was investigated between the cold state and a typical operation point of the engine at 4000 rpm. The simulation case was based on a four-cylinder NISSAN CA18 gasoline engine, and experimental data of the roundness influence was given as a validation case. The study was done for the terminal cylinder located at the end of the engine with regard to the asymmetric thermal load from the neighbor cylinder on one side. From the first simulations of the deformation of the initially cylindrical liner for experimentally given temperature profiles, the resulting deformation was determined as a function of height. The larger temperatures in the upper section of the liner led to increased deformation. In the given case, the radius was increased by 30 \(\upmu\)m.  
In order to reach a nearly cylindrical liner shape, an initially conical liner was designed where the inclination angle was derived from the inverse of the calculated difference of the deformation between the upper and the lower section of the liner. Based on an earlier study [14], the cross section of the liner was also regarded and was varied to be either circular in the cold state or to be slightly elliptical in such a way that the uneven thermal load led to a circular cross section in the fired state. In this study, both effects were regarded in a combined way. Using the validated FEM model, the detailed liner deformation was simulated for the thermal and stress conditions which were relevant for a full load operation point of the engine at 4000 rpm. The numerical simulation results showed that the use of the conical liner in the cold state enhanced the parallelism in the fired state by a factor of three in such a way that the parallelism error reduced from about 12 \(\upmu\)m to values in the range of 4 \(\upmu\)m. Moreover, the straightness in the fired state enhanced by a factor of two in such a way that the straightness deviation error reduced from about 6 \(\upmu\)m to values in the range of 3 \(\upmu\)m. This indicates that the liner's walls became more parallel and straighter. The remaining straightness error occurred at the upper part of the liner and was the result of the pre-tightening load. The utilization of a conical elliptical liner also reduced the roundness error in the fired state significantly from roundness error values of 60 \(\upmu\)m to 70 \(\upmu\)m to values in the range of 10 \(\upmu\)m to 15 \(\upmu\)m. The combination of both effects in conically and elliptically shaped liners has a great potential for increasing roundness, parallelism, and straightness in the fired engine state. This can possibly lead to reduced friction. Moreover, the oil losses can be reduced. With that, it might be possible to reduce the contact pressure of the piston rings, which, by itself, would additionally reduce the friction loss of the engine. The approach and methodology described in this article provide a good starting point to analyze one of the most complex and critical areas in internal combustion engines. It has to be seen, if such complex shaped liners, i.e., the combination of a conically and elliptically shaped liners, will lead to advantages in real engines. For that, detailed measurements of the crank-angle resolved friction forces are planned in the near future on the single cylinder diesel test engine at the Leibniz University of Hannover [29; 30; 31]. Conceptualization, A.A., F.P.-T. and F.D.