7.3.4 Critical speeds
A stationary shaft supported between bearings has a natural frequency of vibration, depending on its diameter in relation to the distance between bearings. If its speed of rotation corresponds to its natural vibration frequency, the residual out-of-balance forces are amplified, and can build up to a dangerous extent.
This critical speed is either above or below running speed, depending on rotor construction. If below, the shaft is regarded as flexible, and care must be exercised during run-up to ensure that the critical is passed as quickly as possible.
Critical speeds decrease with increased rotor length and with reduction in rotor diameter. On current large units, the trend is to provide a rigid rotor (criticals above running speed). Because of the increased rotor length (necessary to accommodate the required number of moving blade stages) on large units, rigidity has been accomplished by an increase in diameter.
The rotors of large machines are joined by solid couplings, so that the complete shaft, which may comprise seven individual rotors, has to be treated as a whole. Each rotor is supported on two bearings which are not simple supports. The hydrodynamic oil films have flexibilities that significantly affect the critical speed of the shaft. In Fig 1.112, calculated critical speeds of a complete line are shown as functions of bearing flexibility, expressed as the deflection of an equivalent spring under the static load upon the bearing.