Starting to consider the topic of the diagnostics of the rotating machines it is worth to spend a few words about the necessary mathematical tools. The system, rotor + bearing + foundation, has to be analysed in its sub-component. In particular the rotor is considered by means a f.e. model and its physical characteristics are represented by the mass [M], the damping [D] and the stiffness [K] matrices. Now we deal with the problem of generating these matrices which are the model of the system analysed. Before considering how to assemble these matrices, some observations are needed in order to generate the f.e. model of the rotor. In particular in the figure is shown that it is necessary to increase the number of the elements when the rotor presents a sharp variation of the diameter. Several criteria exists to perform the increasing the number of the element, but almost all are based on the consideration of the slope between the parts with different diameter.

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