## 5 Geometric Deformation Indicators
If the cold state has an elliptical shape in the assumed parameters of the ellipse (see Figure 3), the roundness error is reduced in the fired state significantly from values between 60 \(\upmu\)m and 70 \(\upmu\)m to values between 10 \(\upmu\)m and 15 \(\upmu\)m. This holds true for both the initially straight and the initially conically shaped liners. The roundness error is mainly related to blow-by and oil leakage to the combustion chamber. A larger roundness error implies that the piston rings need an increased pretension to prevent the leakage. This increases the frictional losses to a certain extend. This contribution is, however, rather small. The parallelism error influences the friction losses more directly. On the one hand, the deviation from the straight parallel shape of the liner leads to varying oil film thickness between the piston ring and skirt and the cylinder liner. This can increase the friction. In the extreme case of the bore diameter being locally smaller than the piston diameter, the friction would increase drastically. On the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Cold State**} & \multicolumn{3}{c}{**Fixed State**} \\ \hline \hline
**Shape**Liner Height** & **10 mm** & **50 mm** & **90 mm** & **10 mm** & **50 mm** & **90 mm** \\ \hline Straight circle (ref.) & 0.9 & 0.9 & 0.9 & 59.8 & 57.1 & 58.6 \\ \hline Conical circle & 1.0 & 1.1 & 1.3 & 71.9 & 69.4 & 70.4 \\ \hline Straight ellipse & 60.6 & 60.5 & 60.5 & 15.3 & 9.4 & 8.1 \\ \hline Conical ellipse & 61.4 & 61.4 & 61.4 & 17.3 & 10.8 & 14.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Roundness deviation for the liner in both the cold state and under typical fired operational conditions at different heights within the liner. (Numbers are given in micrometers). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Cold State**} & \multicolumn{3}{c}{**Fixed State**} \\ \hline \hline
**Shape** & **Thrust** & **Anti-Thrust** & **Front** & **Rear** & **Thrust** & **Anti-Thrust** & **Front** & **Rear** \\ \hline Straight circle (ref.) & 0.0 & 0.0 & 0.0 & 0.0 & 5.7 & 5.9 & 6.8 & 7.2 \\ \hline Conical circle & 4.9 & 4.9 & 4.9 & 4.9 & 2.2 & 2.2 & 3.4 & 3.4 \\ \hline Straight ellipse & 0.0 & 0.0 & 0.0 & 0.0 & 6.1 & 6.2 & 6.8 & 6.8 \\ \hline Conical ellipse & 4.9 & 4.9 & 4.9 & 4.9 & 2.2 & 2.2 & 3.5 & 3.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Straightness deviation for the liner in both the cold state and under typical fired operational conditions. (Numbers are given in micrometers). other hand, the clearance between piston ring/skirt and cylinder liner can also increase, which can lead to increased secondary movement of the piston, which affects the friction. This implies that the parallelism error can possibly have more influence on the friction than the roundness error, even if it has smaller values. Although the roundness error is slightly smaller for the initially straight elliptical liner, the influence on the parallelism must be regarded. In sum, both influences are therefore regarded best with the initially conically and elliptically shaped liners. These results agree with and explain the results found in the literature. For example, the study done by [PERSON] et al. [15] showed that using a larger bore diameter in the bottom of the liner decreases the friction. This can be referred to the fact that this type of honing increases the straightness and parallelism of the deformed liner in the hot state.