This paper considers the passive control of lateral critical speeds in high-speed rotating shafts through application of eccentric balancing sleeves. Equations of motion for a rotating flexible shaft with eccentric sleeves at the free ends are derived using the extended Hamilton Principle, considering inertial, non-constant rotating speed, Coriolis and centrifugal effects. A detailed analysis of the passive control characteristics of the eccentric sleeve mechanism and its impact on the shaft dynamics, is presented. Results of the analysis are compared with those from three-dimensional finite element simulations for 3 practical case studies. Through a comparison and evaluation of the relative differences in critical speeds from both approaches it is shown that consideration of eccentric sleeve flexibility becomes progressively more important with increasing sleeve length. The study shows that the critical speed of high-speed rotating shafts can be effectively controlled through implementation of variable mass/stiffness eccentric sleeve systems.

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