Q-Factor Analysis of Unbalance Vibration in Rotor-Bearing Systems

概要

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Q-factor is usually a pratical means for predicting maximum amplitude at critical speeds. However, it is not accurate in the case of systems with strong gyroscopic effect, large damping coefficients and asymmetric properties in bearing dynamics. In this study these problems are solved through a new definition of the Q-factor. The unbalance vibration is formulated at each damped critical speed, based upon orthogonality of the undamped critical speed mode, and rearranged by the equation derived from the corresponding damped eigenvalues. The result proves that Q-factor and damped critical speed Ωc are not functions of only modal damping ratio ζ, but also vary with gyroscopic factor γ which is the ratio of modal gyro per modal mass, as follows. [numerical formula1] [numerical formula2] [numerical formula3] The new definition is characterized by value γ reflecting the gyroscopic effect in the system. The value γ=0 is an old and incorrect definition as it does not consider gyroscopic effect. To demonstrate the validity of the method, numerical examples are shown for a 3-disk rotor supported with symmetric and tilting pad type bearings.
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