Dynamics of Rotating Systems

Chapter 13: Dynamics of Rotating Beams and Blades

The rotors studied in the previous sections were modeled as beamlike structures, spinning about the axis of the beam. In many machines, however, there are elongated elements, which can often be modeled as beams, with their axis lying in radial direction, as for instance turbine or propeller blades. In the simplest models, the dynamics of these elements is neglected, and the blades are assumed to be rigid bodies, which contribute to the inertia of the system but not to its compliance. The dynamics of the blades is then studied separately.

When the aim of the study is to compute the critical speeds, the approximations linked with neglecting blade (and disc) compliance are usually acceptable, because the slope of the branches of the Campbell diagram linked with blades (and discs) vibration is higher than that of the ? = ? line and they do not give way to additional critical speeds.

There are, however, cases where the dynamics of the blades cannot be neglected and influences the dynamics of the whole machine. Moreover, the dynamic behavior of the blades is influenced by the rotational speed and the rotor-blades interaction may give way to dangerous phenomena such as instability.

The present chapter is devoted to give a qualitative understanding of the main phenomena related to the blade dynamics, whereas a more quantitative approach will be seen in the chapter dealing with the tridimensional modeling of rotors.

13.1 Rotating Pendulum

The simplest model for an unidimensional object attached to a rotor...

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