Exploration of System Tautochrones for Centrifugal Pendulum Vibration Absorbers

Abstract Centrifugal pendulum vibration absorbers (CPVAs) have found extensive use across various applications to smooth torsional vibration within rotating machinery. Proper tuning of pendulums, which have natural frequencies that depend on average rotation speed, is critical to generating pendulum dynamics that smooth torsional vibration. For typical CPVA designs, the pendulum natural frequency shifts as a function of swing amplitude. For these designs, the center of mass of the pendulums is kinematically constrained to follow a specific motion path. The design of this path strongly influences the dynamic stability and performance of the overall device. In this article, a new family of system tautochronic paths is identified that produces constant period pendulum/rotor motion that is independent of pendulum swing amplitude. These motion paths greatly reduce nonlinear variability that can complicate the dynamic response and hence the design of a CPVA. We show that the family of curves that produce system tautochronic motion always arises from a transformation that takes a standard-form second-order nonlinear differential equation into a linear oscillator. The family of system tautochrone curves represents pendulum motion paths that show promise in simplifying CPVA design and enhancing CPVA performance.