Ball vibration absorbers with radially-increasing rolling friction

Ball vibration absorbers (BAs) are a simple, low-cost and compact way to realize the principle of tuned mass damping. The basic arrangement of a BA consists of a spherical mass rolling without sliding in a rubber-coated spherical cavity, and dissipating through rolling friction. In a conventional BA, the rubber coating is uniform along the cavity, and so is rolling friction. This makes the BA equivalent damping inversely proportional to the excitation amplitude, and its performance amplitude dependent. In this study, two new BA types are proposed. The first type, called the homogeneous BA (HBA), has a rolling friction radially increasing in proportion to the ball angular displacement. Hardly realizable in practice, this ideal friction model is homogeneous in the first order, ensuring an amplitude-independent optimal performance. The second type, called the discrete-homogeneous BA (DBA), is the stepwise approximation of the HBA. Not exactly homogeneous, its variable friction model can be easily realized through the juxtaposition of multiple coating regions, having different thickness or material quality. After establishing a unifying, fully nonlinear, nonholonomic analytical model, valid for various types of friction and viscous BAs, this paper first derives an optimal design procedure applicable to each type, then experimentally and numerically demonstrates (1) the validity of the homogeneous and discrete-homogeneous concepts, (2) their practical feasibility, (3) the accuracy of the proposed model, (4) the effectiveness of the design procedure, and (5) the superior performance of the HBA and the DBA over conventional friction absorbers.