The article highlights the importance of analytical computational models of torsionally oscillating systems and their simulation for estimating the lowest resonance frequencies. It also identifies the pitfalls of the application of these models in terms of the accuracy of their outputs. The aim of the paper is to control the dangerous vibration of a mechanical system actuator using a pneumatic elastic coupling using different approaches such as analytical calculations, experimental measurement results, and simulation models. Based on the known mechanical properties of the laboratory system, its dynamic model in the form of a twelve-mass chain torsionally oscillating mechanical system is developed. Subsequently, the model is reduced to a two-mass system using the method of partial frequencies according to Rivin. The total load torque of the piston compressor under fault-free and fault conditions is simulated to obtain the amplitudes and phases of the harmonic components of the dynamic torque. After calculating the natural frequency and the natural shape of the oscillation, the Campbell diagram is processed to determine the critical revolutions. There is a pneumatic flexible coupling between the rotating masses, which changes the dynamic torsional stiffness. The dynamic torque curves transmitted by the coupling are compared with different dynamic torsional stiffnesses during steady-state operation and one cylinder failure. The monitored values are the position of the critical revolutions, the natural frequency, the natural shape of the oscillation, and the RMS of the dynamic load torque. The experimental model is verified by the simulation model. The accuracy of the developed simulation model with the experimental data are apparently very good (even more than 99% of the critical revolutions value obtained by calculation); however, it depends on the dynamic stiffness of the coupling. In this study, a detailed, comprehensive approach combining analytical procedures with simulation models is presented. Experimental data are verified with simulation results, which show a good agreement in the case of 700 kPa coupling pressure. The inaccuracy of some of the experiments (at 300 and 500 kPa pressures) is due to the interaction of the coupling’s apparent stiffness and the level of the damped vibration energy in the coupling, which is manifested by its different heating. Based on further experiments, a solution to these problems will be proposed by introducing this phenomenon effectively into the simulation model.
