# Experimental Verification of a Compressor Drive Simulation Model to Minimize Dangerous Vibrations
## 3 Results and Discussion  
### Determination of the Operating State of the System in Terms of Resonance  
The dynamic model (Figure 4) was created based on the known mechanical parameters of the compressor drive system. By means of the model, the values of natural frequencies and mode shapes were calculated as well as the Campbell diagram devised. The individual elements for the dynamic model are listed in Table 2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Meaning** \\ \hline \(I_{AM}\) & Mass moment of inertia of the electric motor \\ \(I_{P1}\) & Mass moment of inertia of the flange behind the motor \\ \(I_{O1},I_{O2},I_{O3}\) & Mass moment of inertia of the gear \\ \(I_{P2}\) & Mass moment of inertia of the flange behind the gearbox \\ \(I_{SKM}\) & Mass moment of inertia of the torque sensor \\ \(I_{P3}\) & Mass moment of inertia of the flange behind the torque sensor \\ \(I_{LT}\) & Mass moment of inertia of the bearing housing \\ \(I_{P4}\) & Mass moment of inertia of the flange in front of the pneumatic coupling \\ \(I_{SA}\) & Mass moment of inertia of the flange of the pneumatic coupling \\ \(I_{SB}\) & Mass moment of inertia of the pneumatic coupling flange \\ \(I_{P5}\) & Mass moment of inertia of the flange behind the flexible coupling \\ \(I_{PK}\) & Mass moment of inertia of the piston compressor \\ \(k_{H1},k_{H2}\), & Torsional stiffness of shafts between electric motor and gearbox \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of parameters of the system shown on Figure 4.  
Figure 3: Time record from an experiment measurement in the CatmanEasy program. The gear ratios between the shafts of the system are calculated as follows:  
\[i_{\text{1-2}}=\frac{n_{1}}{n_{2}},\ i_{\text{2-3}}=\frac{n_{2}}{n_{3}},\ i_{ \text{1-3}}=\frac{n_{1}}{n_{3}}. \tag{1}\]  
Assuming that the shaft stiffnesses \(k_{\text{H3}}\), \(k_{\text{H4}}\), and \(k_{\text{H5}}\) (Figure 4) show a higher value than the other stiffnesses and the input shaft revolutions of the gearbox are equal to the output shaft revolutions \(n_{1}=n_{3}\), a reduction as shown in Table 3 could be done. This reduction is applied to the high-revolution shaft with stiffness \(k_{\text{H1}}\). Using the method of partial frequencies [42], this twelve-mass system was reduced to a two-mass system. The resulting values after reduction by this method usually show an accuracy of 3-5% [42; 44]. The dynamical model of this reduced two-mass mechanical system is shown in Figure 6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Meaning** \\ \hline \(k_{\text{H3}}\), \(k_{\text{H4}}\), \(k_{\text{H5}}\) & Torsional stiffness of shafts in the gearbox \\ \(k_{\text{H6}}\) & Torsional stiffness of the shaft between \(I_{\text{O3}}\) and \(I_{\text{P2}}\) \\ \(k_{\text{H7}}\) & Torsional stiffness of the shaft between \(I_{\text{P2}}\) and \(I_{\text{SKM}}\) \\ \(k_{\text{H8}}\) & Torsional stiffness of the shaft between \(I_{\text{SKM}}\)and \(I_{\text{P3}}\) \\ \(k_{\text{H9}}\) & Torsional stiffness of the shaft between \(I_{\text{P3}}\) and \(I_{\text{I7}}\) \\ \(k_{\text{H10}}\) & Torsional stiffness of the shaft between \(I_{\text{P4}}\) and \(I_{\text{P4}}\) \\ \(k_{\text{H11}}\) & Torsional stiffness of the shaft between \(I_{\text{P4}}\) and \(I_{\text{S}A}\) \\ \(k_{\text{S}}\) & Torsional stiffness of the pneumatic coupling \\ \(k_{\text{H12}}\) & Torsional stiffness of the shaft between \(I_{\text{SB}}\) and \(I_{\text{P5}}\) \\ \(k_{\text{H13}}\) & Torsional stiffness of the shaft between \(I_{\text{P5}}\) and \(I_{\text{P6}}\) \\ \(b_{\text{S}}\) & Pneumatic coupling damping coefficient \\ \(M_{\text{AM}}\) & Electric motor torque \\ \(M_{\text{P}K}\) & Load torque of the piston compressor \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 5: A twelve-mass chain mechanical system.