First-order optimal linear and nonlinear detuning of centrifugal pendulum vibration absorbers

Abstract

Centrifugal pendulum vibration absorbers are used to attenuate steady-state torsional vibrations in rotating and reciprocating machines. In most practical implementations, a set of multiple absorbers is symmetrically arranged on a rotor. Typically, each absorber mass is bifilar suspended, which allows the absorber mass to be moved along a prescribed path. Previous studies have considered how to determine absorber paths in order to obtain absorbers with amplitude-independent frequency known as tautochronic absorbers. It is known that a tautochronic absorber is highly desirable if only one absorber is installed on the rotor. However, in most applications multiple interacting absorbers are installed and as a result symmetry-induced nonlinear instabilities or localization caused by relative imperfections among the absorbers may occur. An effective strategy to avoid such situations is to perturb the tautochronic tuning which has been confirmed in practice and by previous theoretical investigations.This paper presents an approach for detuning a recently developed general tautochronic absorber design. The general design makes it possible to consider a wide class of tautochronic absorbers, e.g. absorbers without bifilar suspensions. The intent of this paper is to extend the existing tautochronic design guideline to non-tautochronic designs. As a result, different absorber designs can be addressed by one uniform theoretical approach, and existing absorber designs are included as special cases. Former studies on detuning of bifilar tautochronic absorbers use a one-parameter family of curves on which the absorber mass rides. Here, however, the detuning is not restricted to a one-parameter family of curves, which makes it possible to either optimize system performance or to avoid asynchronous absorber responses. In the case of synchronously responding equal absorbers, a necessary condition for optimal performance is derived analytically. Further, it is shown that asynchronous responses can be avoided by applying positive detuning.