Abstract

The system considered consists of a rigid rotor and N centrifugal pendulum vibration absorbers (CPVAs) riding on epicycloidal paths tuned to order n, the same as the dominant order of the applied torque. An investigation is carried out to determine the effects that a dynamic instability of the synchronous motion of CPVAs has on the system performance. Using various co-ordinate transformations, including a group-theory-based transformation and an angular transformation, the system dynamics are modeled by a set of 2N first-order, averaged, autonomous differential equations. A bifurcation analysis of these equations shows that in the post-bifurcation dynamic, one of the N absorbers moves out of step and at a much larger amplitude than its partners. This localized response is dynamically stable and leads to the worst-case (that is, the smallest) operating torque range of all the possible post-critical steady-state solutions. Analytical estimates of the torque range and the rotor acceleration are derived based on a truncated version of the equations, and more accurate estimates are obtained from a numerical solution of the non-truncated equations. The results are found to be very accurate when compared to numerical simulations.

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