Dynamics of Rotating Systems

The dynamic study of rotors is usually performed assuming that the spin speed is maintained constant by a suitable driving device. As seen in Chapter 2, the torque exerted by the driving system must overcome not only the bearing drag, but also a peculiar form of drag caused by rotordynamic reasons or, to use a different phrasing, must supply a power equal to that dissipated by the rotating and nonrotating damping.
When studying the unbalance response, it was clearly stated that the plot of the amplitude as a function of speed had to be interpreted as a representation of the amplitude of the synchronous whirling occurring during steady-state working at different values of the spin sped and not as the amplitude during an acceleration or a spinning down of the rotor. In many cases, this is, however, just a theoretical statement, because the angular accelerations encountered in operation are so low that their effects on the overall dynamic behaviour are very weak.
In the present chapter, on the contrary, the assumption of constant speed is removed and the effects of nonstationary operation on the dynamic behavior of rotors are studied.
As usual, the study is started using the simplest rotor model: the Jeffcott rotor. The scheme of the system is again that sketched in Figure 2.2a. and (b), with the difference that now angle ? is no more equal to ?t but must be considered as a variable,...