## 3 Results and Discussion
### Discussion of the Results  
After carrying out different analyses, with different pressure values, the maximum admissible values were determined: 0.3 MPa in the high-pressure piston plunger and 0.15 MPa in the low-pressure piston plunger. Since the steam does not fully expand in the high-pressure cylinder, this would mean a pressure corresponding to the value of the vapor pressure on the opposite side after expansion. For this reason, the value obtained (0.3 MPa) is the maximum admissible pressure difference in the high-pressure cylinder. This is the value resulting from the difference between the intake pressure of the cylinder and the exhaust pressure, the steam pressure after the first expansion. As an example, if the pressure after expansion acquires a value of 0.15 MPa, then the maximum allowable pressure at the  
Figure 19: Mesh convergence analysis graph. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**High-Pressure Piston Rod** & **High-Pressure Piston Rod** & **Iteration** & **Von Mises Stress** & **Relative Error (\%)** \\
**Cap Element Size (mm)** & **Cap Element Size (mm)** & & **(MPa)** & **(**\%**)** \\ \hline
0.88 & 3.90 & 0 & 37.51 & - \\
0.60 & 2 & 1 & 50.12 & 25.16 \\
0.40 & 1.25 & 2 & 80.35 & 37.62 \\
0.38 & 1.15 & 3 & 86.90 & 7.53 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mesh convergence analysis data. intake of the high-pressure cylinder is 0.45 MPa (0.3 + 0.15), since the maximum difference allowable is 0.3 MPa, which is the calculated value. Similarly, the value of the maximum admissible pressure in the low-pressure cylinder is 0.15 MPa, this being a manometric pressure value given that the steam is expelled at atmospheric pressure. Figure 21: Displacement distribution: isometric view (**left**) and front view (**right**). Figure 20: [PERSON] stress distribution (**left**) and location of the highest value (**right**). Therefore, these are the values that offer the operation of the machine under safe conditions, with the failure criterion applied being the reach of the yield strength under the static load of the first cycle for the situation of blocking the flywheel in the start-up of the machine as the most unfavorable situation. Finally, to summarize the results obtained, Tables 6 and 7 show the maximum values of stress and displacement, as well as the minimum value of the safety factor, for each critical position. pressure difference in the high-pressure cylinder corresponds to the difference between the intake pressure value and the exhaust pressure value, i.e., the pressure of the fluid after expansion. In this way, by simulating two critical operating conditions that resemble the start-up of the machine (flywheel locked as the most unfavorable situation), the operating conditions were determined which ensure both its safety and its optimal functioning, since the appearance of plastic deformations of some components of the machine could give rise to an increase in vibrations or pressure losses in the chambers of the cylinders or valves, among other consequences. On the other hand, for critical position 1 (corresponding to the movement of the piston plunger from top dead center to bottom dead center after the intake is closed), different simulations were carried out to determine the optimal operating conditions. These conditions were a maximum allowable pressure difference in the high-pressure cylinder of 0.3 MPa and a maximum allowable pressure in the low-pressure cylinder intake of 0.15 MPa. For these conditions, and for a relative error in the mesh convergence analysis of 0.64% in the fourth iteration, a maximum von Mises stress of 96.57 MPa is obtained in the high-pressure piston rod cap, a maximum displacement of 4.106 \(\times\) 10\({}^{-3}\) mm on the high-pressure piston plunger and a minimum safety factor of 1.785 on the high-pressure piston rod cap.