# Experimental Verification of a Compressor Drive Simulation Model to Minimize Dangerous Vibrations
## 5 Conclusions  
The main focus of the research was vibrations, or torsional oscillations, often accompanying the operation of mechanical systems. These disturbances, if not controlled, result in machine unreliability in mechanical systems, compromising the safe operation of the plant. Based on the general knowledge of vibration and the known parameters of a real laboratory mechanical system, a simulation model was developed. The original twelve-mass mechanical system was reduced to a two-mass system by the partial frequency method. The MATLAB simulation program was used in the calculations and analyses. The results obtained by calculation were experimentally verified by measurements on a laboratory mechanical system. After comparing the calculated natural angular frequency with the measured value, we can evaluate that the applied mathematical model is accurate to 99.53% at 700 kPa coupling pressure. In potential future research, it is possible to include the temperature value of the elastic element of the coupling in the calculations and to determine more accurately the mass moments of inertia of the individual members of the mechanical system. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Pressure in Coupling [kPa]** & **Parameter** & **Value [rad\(\cdot\)s\({}^{-1}\)]** & **Parameter** & **Value [min\({}^{-1}\)]** & **Accuracy [\%]** \\ \hline \multirow{3}{*}{700} & \(\Omega_{\text{0 SEM}}\) & 201.431 & \(n_{K3\text{SIM}}\) & 641 & \multirow{3}{*}{\(-0.47\)} \\  & \(\Omega_{\text{0 EXP}}\) & 200.434 & \(n_{K3\text{EXP}}\) & 638 & \\ \cline{1-1}  & \(\Omega_{\text{0 SUM}}\) & 179.167 & \(n_{K3\text{SIM}}\) & 570 & \\ \cline{1-1}  & \(\Omega_{\text{0 EXP}}\) & 188.496 & \(n_{K3\text{EXP}}\) & 600 & \\ \cline{1-1}  & \(\Omega_{\text{0 SUM}}\) & 156.610 & \(n_{K3\text{SUM}}\) & 498 & \\ \cline{1-1}  & \(\Omega_{\text{0 EXP}}\) & 172.788 & \(n_{K3\text{EXP}}\) & 550 & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of simulation and experimental results. At the same time, it is planned to include in the simulation the occurrence of non-equilibrium condensation in the compressor, taking into account the research results presented in publications [49; 50; 51]. The aim of our paper is to show the importance of analytical calculations in estimating the natural frequencies and the corresponding mode shapes of oscillations in engineering work. A mathematical model for a torsionally oscillating mechanical system has been developed where the stiffness of the elastic coupling can be continuously varied. Thus, the critical revolutions at different stiffnesses (pressures in the coupling) can be determined. It was solved in steady state with harmonic excitation, amplitude, and phase over resonance curves for the individual harmonic components, which were then summed. We have simplified the multi-mass system to a two-mass system to analyze the effect of oscillations on the elastic coupling. This is under the condition of accuracy, where the frequencies differed from each other minimally. Benefits of the simulation model:  
* The mass reduction method used allows the use of a two-mass instead of a multi-mass system, which greatly simplifies the calculations. * We can calculate the critical revolutions as a function of coupling pressure quite accurately. So, with a system operating with a range of operating revolutions, we can avoid resonance without having to directly measure the torque; we just need to know the revolutions, and we can determine the appropriate pressure accordingly. * Characteristic depending on the ratio of the critical revolutions to the coupling pressures. Conceptualization, M.M., P.K. and F.L. ; methodology, M.M. and D.M. ; software, M.M. ; validation, P.K. and F.L. ; formal analysis, D.M. and M.M. ; investigation, M.M. and P.K. ; resources, M.M. and P.K. ; data curation, M.M. ; writing--original draft preparation, M.M. ; writing--review and editing, P.B. and M.O. ; visualization, M.M., P.B. and M.O. ; supervision, P.K. ; project administration, D.M. ; funding acquisition, D.M.