# Experimental Verification of a Compressor Drive Simulation Model to Minimize Dangerous Vibrations
## 3 Results and Discussion
### Verification of the Simulation Model Using Experimental Measurement  
After the description of the mechanical system of the compressor drive and the dynamic calculations performed, a description of the experimental measurement follows to determine the torsional vibration values in the mechanical system consisting of a three-cylinder air compressor, driven by an electric motor using a pneumatic flexible coupling. Measuring the Course of the Resonance Curve  
The measurement was carried out with stead (even) cylinder operation and then using a rejector so that one cylinder could be disabled by opening the compressor suction valve. The calculation of the effective value of the dynamic component of the load torque \(RMS\)\(M_{D}\), which is transmitted by the coupling, was the starting point for determining the magnitude of torsional vibration. The formula for its calculation was  
\[RMSM_{D}=\sqrt{\frac{1}{N}.\sum_{i=1}^{N}(M_{Di})^{2}}, \tag{7}\]  
where  
\[M_{Di}=M_{i}-\left(\frac{1}{N}.\sum_{i=1}^{N}M_{i}\right), \tag{8}\]  
where \(M_{i}\) is the \(i\)-th signal sample. The above result from this formula indicates that it was necessary to measure the time course over time of the total load torque, from which the dynamic component \(M_{D}\) was filtered out. In the next calculation of \(RMS\)\(M_{D}\), a moving average was used. The values were read after a steady state was reached. The measurement was carried out at varying revolutions in the range from \(n=105\) min\({}^{-1}\) to \(n=1500\) min\({}^{-1}\), at a pressure in the compression chamber of the pneumatic flexible coupling \(p_{5}=700\) kPa, \(p_{5}=500\) kPa and \(p_{5}=300\) kPa. The compressor output pressure is set to a constant value, \(p_{N}=500\) kPa. The time signal (Figure 3) load torque was recorded with a sampling rate of \(f_{V}=1200\) Hz (number of samples \(N=2400\)) with steady (even) cylinder operation and then with one compressor cylinder out of operation. The Campbell diagram (Figure 22) for pressure coupling 700 kPa compiled from the measured values also contains marked, predetermined operating revolutions and critical revolutions from the principal harmonic. Based on the point of intersection of the critical revolutions and the beam (harmonic component) on the diagram, it is possible to determine the value of the rotational natural frequency \(N_{0}\) and calculate the natural frequency \(f_{0}\) and the angular natural frequency \(\Omega_{0}\). From what is shown, it follows that resonances at higher values of \(RMS\)\(M_{D}\) occur at compressor revolutions of approximately \(n_{K3}=638\) min\({}^{-1}\). These are resonances from the main harmonic component of the torque of the three-cylinder compressor \(i=3\). When the cylinder is out of operation, resonances occur from both the main and the secondary components at critical s \(n_{K4}=450\) min\({}^{-1}\), \(n_{K3}=660\) min\({}^{-1}\) a \(n_{K2}=956\) min\({}^{-1}\). From the measured values, the development of the static (central) load torque is plotted (Figure 23). Figure 24 shows the resonance curve, i.e., the \(RMS\)\(M_{D}\) waveform depending on the revolutions \(n\) of the mechanical system. When the cylinder was out of operation (Figure 25), the value of the effective value of the dynamic component of the load torque \(RMS\)\(M_{D}\) decreased as compared to Figure 24, but secondary harmonic components were manifested. Shown below is the development of frequency analysis at revolutions \(n=500\) min\({}^{-1}\) (Figures 26 and 27). The first representation describes the use of the Hamming window when running evenly, and the second after one cylinder was out of operation. Figure 23: Development of the static component of load torque \(M_{S}\) depending on the engine revolutions \(n\) at pressure 700 kPa. Figure 24: Effective value of the dynamic component of the load torque \(RMS\)\(M_{D}\) of the pneumatic flexible coupling at pressure 700 kPa vs. the engine revolutions \(n\) – steady state. Figure 22: Campbell diagram of the mechanical system from the measured values.