Abstract
One of the authors has shown in previous papers (Enrich, 1995; Ehrich, 1996) that, when high speed rotors are operated in the transcritical range with the rotor located eccentrically in its rotor/stator clearance with the rotor in intermittent contact with the stator, a nonlinear response, at speeds both slightly above and slightly below the critical speed, is induced. The response at a particular speed will include significant components at an asynchronous frequency which is approximately equal to the natural frequency of the system. In particular, when the speed (normalized by the natural frequency) S is approximately (J+1)/J, the dominant frequency (normalized by the natural frequency) F is precisely J/(J+1) times S or approximately 1 (where values of the whole number J < 1 give the subcritical set of speeds and values J > 1 give the supercritical set of speeds). The phenomenon has been termed spontaneous sidebanding.
Observations of similar asynchronous responses noted in a Campbell diagram of the rotordynamic response of an actual high speed rotor clustered around a subharmonic response peak at a rotational speed twice the natural frequency suggest that the phenomenon is also possible at any subharmonic pseudo-critical response peak. In this more general case, we would expect that at rotational speeds in the vicinity of the M th subharmonic pseudo-critical normalized speed where S is approximately (MJ+1)/J and the dominant normalized frequency F is precisely J/(MJ+1) times S or approximately 1 [where values of the whole number J < 1 give the sub(pseudo)critical set of speeds and values J > 1 give the super(pseudo)critical set of speeds].
A simple numerical model of the nonlinear system verifies that these asynchronous responses are indeed possible. Operation of the model at a rotational speed approximately double the natural frequency yields data which closely reproduce the asynchronous response seen in the actual machine.
