Strength of modes in rotating machinery

A new method for the analysis of modal strength of the rotor systems with periodically time-varying parameters due to the presence of either rotating or stationary asymmetry is proposed. The method is based on the complete development of the modal analysis by introducing the modulated coordinates to derive the equivalent infinite-order time-invariant Hillʹs matrix equation from the finite-order time-varying matrix equation. Depending upon the level of possible contribution of each mode to forced response, the modal strength of a mode is rigorously derived from the norm order analysis of the associated eigenvector; thereby, the modes are classified as strong or weak modes. It is shown that the directional frequency response functions are useful in identifying the strength of modes in detail, or equivalently, the modes of symmetry, anisotropy, asymmetry and coupled asymmetry. Two illustrative examples with a simple, yet general, analysis rotor model and a practical flexible asymmetric rotor finite element (FE) model with an open transverse crack are treated to demonstrate the theoretical findings and effectiveness of the proposed method.