Obtaining the best operating parameters of the internal combustion engine has focused the attention of designers and researchers since the first years of its creation. Initial research focused on increasing engine power and overall efficiency. As time passed, these aspirations became more sophisticated and began to concern other operating parameters of the drive unit. The basic problem, however, remained the improvement of filling the cylinder with the working medium. Turbocharger charging consists in using the energy of the exhaust gases to drive a turbine placed on a common shaft with a compressor supplying air under increased pressure to the cylinders. Over time, the turbocharger became one of the key elements and its technical condition began to play a key role in the operation and performance of modern drive units. Like every element, the turbocharger itself is not without its faults. This procedure is known among manufacturers who, when designing power units and their assemblies, pay special attention to the essence of turbocharger construction. Since it is impossible to predict all the phenomena accompanying a working turbocharger at the design stage, the authors of this paper conducted bench tests of a selected batch of turbochargers, focusing mainly on the vibration measurements of the turbocharger rotating assembly. At the same time, we present a dynamic model of the mentioned system based on the analyses resulting from the solutions of the equations of a numerical model. In order to give the research a practical aspect, the results of the theoretical research were compared with the results of bench tests. It has been shown that the basic problem is to guarantee the correct operating parameters of the bearings in the position of static and dynamic equilibrium. Obtaining such operating parameters requires finding a compromise solution, e.g., between the maximum temperature in oil films and the amplitudes of vibration accelerations in bearing nodes. The research results presented in the article can be used as a field for further discussion in the field of research on the reliability of turbochargers and be helpful in the design process in order to avoid design errors and reduce production costs.