Reduction of Flexible Supports
Consider a harmonic motion with a frequency of ω. The 4 DOF journal-bearing-support system can be reduced to be a 2 DOF journal-bearing system with the reduced equivalent bearing-support dynamic coefficients. Normally, the shaft rotational speed is selected to be the reduction frequency. Thus, the reduced bearing coefficients are called the synchronously reduced coefficients. This reduction procedure is commonly used to demonstrate the effects of the flexible support. However, it is not advisable to perform this reduction in the analysis of complete rotor-bearing systems due to the single harmonic motion assumptions. The reduced coefficients are frequency dependent and can be used in the steady state synchronous response analysis, but not suitable for the whirl speed and stability analysis and the transient analysis.
For the harmonic motions, it is convenient and desirable to introduce the impedance notation in the complex form as:
Several special cases are discussed below:
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