A general analysis and computational method is presented for calculating the unbalance and self-excited response of high-speed rotor-bearing systems. The analysis is applied to the calculation of the transient response of a rotor supported by two floating ring bearings. Included in the analysis are rotor gyroscopic moments as well as the flexibility of the shaft. Emphasis is placed on determining rotor whirl orbits as influenced by rotor unbalance, the phase angle of the unbalance masses, the clearances of the bearings, the viscosity of the lubricant, and the shock loads that the rotor may be subjected to. It is found that the rotor-bearing system normally operates in an unstable mode in the linear stability sense. However, the nonlinear forces developed by the fluid films of the floating ring bearing will bring the rotor-bearing system to whirl at a limit cycle well within the clearance circles. It is also shown that the rotor assembly will undergo a conical motion when the rotor and wheel configuration is asymmetrical.

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