*2.2. Operation Velocity of the Rotor-Bearing System*

Two different conditions for the operation velocity of the rotor-bearing system are considered: constant velocity and a linear ramp excitation.

Under the constant velocity scheme, no time variation of the rotating machine excitation is considered. This condition can be expressed as

$$
\dot{\phi}(t) = \Omega = \text{constant} \tag{5}
$$

The term "ramp excitation" means a continuous variation in the excitation frequency with a specific ratio with respect to time and can be ascendant (up) or descendent (down). With most real rotating systems, the excitation frequency does not change in a linear manner with respect to time. However, in some cases, frequency variation is sufficiently slow to be approximated by a linear function. For the solution of Equation (3), it is considered a variation of the excitation frequency of the form

$$
\dot{\phi}(t) = \dot{\phi}\_0 + \ddot{\phi}t \tag{6}
$$

where:

. *<sup>φ</sup>*<sup>0</sup> is the excitation frequency at the ramp beginning; .. *φ* is the change ratio with respect to time of the excitation frequency; *t* is the time.
