NONLINEAR LOCALIZATION IN SYSTEMS OF TAUTOCHRONIC VIBRATION ABSORBERS

摘要

The system considered consists of a rigid rotor and N centrifugalpendulum vibration absorbers (CPVAs) riding on epicycloidalpaths tuned to order n, the same as the dominant order ofthe applied torque. An investigation is carried out to determinethe effects that a dynamic instability of the synchronous motionof CPVAs has on the system performance. Using various coordinatetransformations, including a group-theory-based transformationand an angular transformation, the system dynamicsare modeled by a set of 2N first-order, averaged, autonomousdifferential equations. A bifurcation analysis of these equationsshows that in the post-bifurcation dynamic, one of the N absorbersmoves out of step and at a much larger amplitude thanits partners. This localized response is dynamically stable andleads to the worst-case (that is, the smallest) operating torquerange of all the possible post-critical steady-state solutions. Analyticalestimates of the torque range and the rotor accelerationare derived based on a truncated version of the equations, andmore accurate estimates are obtained from a numerical solutionof the non-truncated equations. The results are found to be veryaccurate when compared to numerical simulations.