The rigid rotor model is widely used in the modeling of rotating machinery. In this paper, a speed-varying transient rigid rotor model that includes the gyroscopic effect and imbalance forces is developed in the state space form. The states of this model are augmented to include imbalance forces and moments. This is done by viewing the imbalance forces and moments as outputs of a dynamic system. If the displacement and the swinging angle of the rigid rotor can be measured, the augmented system will be completely observable and have a fixed lexicographic basis. Therefore, a time-varying observer can be designed for the augmented system by using canonical transformation. A special structure of the estimation error dynamic matrix is selected to obtain good transient performance. After obtaining an estimation of the imbalance forces and moments as the states of the augmented system, the estimated imbalance can be directly calculated. This estimation method can be used in the active vibration control or active balancing schemes for rigid rotor.
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