The tuning conditions for circular, cycloidal and epicycloidal centrifugal pendula: a unified cartesian approach

The centrifugal pendulum is a device used to reduce torsional vibrations generated by mo- tion irregularities of rotating machinery. It is adopted in many engineering applications. Even though different arrangements have been developed, because of its versatility, bifilar pendulum is the most commonly used architecture. In this paper, a new modeling approach and a novel design chart procedures for the trapezoidal bifilar centrifugal pendulum vibration absorber are proposed. In the first part, the case of parallel bifilar centrifugal pendulum is considered. In the second part, an innovative approach for the trapezoidal bifilar centrifugal pendu- lum design is proposed. For the first time, it has been established a dynamic equivalence between the trapezoidal bifilar and the unifilar centrifugal pendulum. This allowed the de- velopment of designs charts for trapezoidal bifilar pendulum. The dynamic equivalence is not only based on inertia, but involves concepts from the theory of curvature kinematics. The numerical results, obtained by means of multibody dynamics simulations, con- firm the reliability of the procedure in terms of rotor torsional vibrations suppression. The methodology herein presented could be extended to cycloidal and epicycloidal vibration absorbers.