Model Properties, Stability, And Application Of Centrifugal Pendulum Vibration Absorber System

Centrifugal pendulum vibration absorber (CPVA) systems are widely used in rotating ma-chinery to reduce translational and rotational vibrations of the rotor. This work develops an analytical model of CPVA systems and uses it to investigate the structure of the modal vibra-tion properties. An in-plane model is first examined. Both systems with single and multiple cyclically symmetric absorber groups are investigated. The planar model admits two trans-lational and one rotational degree of freedom for the rotor and a single arclength degree of freedom for each absorber. The gyroscopic effects from rotor rotation are taken into account. Examination of the associated eigenvalue problem reveals well-defined structure of the vibra-tion modes resulting from the cyclic symmetry of the absorbers in each absorber group. The symmetry breaking due to the use of multiple absorber groups does not destroy this well-defined vibration mode structure. The vibration modes are classified into rotational, translational, and absorber modes. Characteristics of each mode type are analytically proved. The effects of the absorber tuning order on the modes are derived. A three-dimensional model is then employed to study the tilting effect in the systems where the absorbers are attach on one end of the rotating shaft. The tilting motion does not affect rotational and absorber modes. Only the translational modes involve tilting motion, and are called translational-tilting modes in this case. The veering/crossing behavior between the eigenvalue loci is derived analytically. The critical speeds and flutter instability of these systems are studied numerically and analytically.This derived vibration mode structure is then used to obtain the optimal tuning of CPVAs to reduce in-plane translational and rotational vibration for a rotor with N cyclically symmetric substructures attached to it. The reaction forces that the substructures (helicopter or wind turbine blades, for example) exert on the rotor are first analyzed. The linearized equations of motion for the vibration are then solved by a gyroscopic system modal analysis procedure. The solutions show that the rotor translational vibrations are reduced when one group of CPVAs is tuned to order N-1and another group is tuned to order N+1. Derivation of this result is not available in the literature. The current derivation also yields the better known result that tuning CPVAs to order N reduces rotational rotor vibration. This derivation generates a design guideline for CPVAs used to reduce rotor translational and rotational vibrations. Two groups of absorbers tuned to orders jN±1are needed to eliminate the translational vibration at the troublesome excitation order j. The elimination of rotational vibration at order j requires only one absorber group tuned to order jN. The application of CPVAs to reduce vibration at a desired order may increase the vibration at other orders. This can be avoid by adding absorber groups tuned to orders other than the primary concern. The absorber group tuned to an order between jN±1is effective in reducing both translational and rotational vibrations when the number of the substructures N or the order j is large.