Accounting for Roller Dynamics in the Design of Bifilar Torsional Vibration Absorbers

Centrifugal pendulum vibration absorbers are used for reducing torsional vibrations in rotating machines. The most common configuration of these devices utilizes a bifilar suspension in which the absorber mass rides on a pair of rollers, whose mass is small compared to that of the absorber. These rollers are typically solid steel cylinders that allow the CPVAs to move along a prescribed path relative to the rotor, determined by the shape of machined cutouts on the rotor and the absorber mass. Previous studies have considered how to account for the roller dynamics in selecting the linear tuning characteristics of the absorber system, but have not quantified the errors induced by the common approximations that either ignores their effects completely, or does not account for the nonlinear aspects of their dynamics. In this paper we systematically investigate these effects. Specifically, we first show that there exists an absorber path for which the absorber/roller system maintains the same frequency of free oscillation over all physically possible amplitudes. This tautochronic path has been well known for the case with zero roller inertia, and herein, for the first time, the corresponding path with rollers is shown to exist and is constructed. In addition, we carry out an analysis of the steady-state response of the rotor/absorber/roller system in order to quantify the effects of various approximations commonly used in regards to the roller dynamics. This analysis is based on the equations of motion, scaled in such a manner so that they are amenable to a perturbation analysis, which includes the effects of rollers in the perturbation terms. It is shown that if one accounts for the linear tuning aspects of the rollers, the system response is essentially insensitive to the selection of the nonlinear tuning parameter, so long as it is close to the tautochronic value. This implies that the approximation commonly used for selecting absorber paths with rollers is adequate.