Mechanical vibrations and dynamics
In the study of rotor dynamics we can identify two main types: the rigid rotors and flexible rotors.
The rotor dynamics is characterized by the presence of gyroscopic effects. The equation for the dynamics of a rotor must therefore take into account these effects introducing a gyroscopic matrix which multiplies the vector of speed:
M is the mass matrix of the system, G is the gyroscopic matrix, K is the stiffness matrix and F is the vector of applied loads.
A flexible rotor can be analyzed with the theory of the beam according to the formulation of Ritz, with the addition of gyroscopic effects.
A flywheel (as illustrated) can be considered concentrated inertiathat for the purposes of calculating the bending critical speed. It does not present deformation, but it has a gyroscopic effect which tends to increase the stiffness of the shaft.
Do not consider this, leads to an underestimation of the flexural critical speeds and generally underestimate the strength of the system.
Analyses were conducted in the design of rotors working in sub-critical conditions near the critical frequency.
The operating frequency was very close to the natural frequency calculated by FEM without gyroscopic effects. This result showed an apparent criticism of the system.
The correct introduction of gyroscopic effects assessed the real system response that showed a critical frequency higher than initially calculated. This has prevented unnecessary oversizing and wasted materials.
Waterfall diagram showing the measured frequency response of a rotor
Mechanical vibrations and dynamics: