System tautochrone motion path for centrifugal pendulum vibration absorbers

Abstract

Centrifugal Pendulum Vibration Absorbers (CPVAs) have been in use for over a century and have become integral in addressing torsional vibrations in rotating machinery across a wide range of applications in both the aerospace and automotive industries. Proper tuning of the pendulum, such that it counteracts the engine-order fluctuating torques acting on the rotor during operation, enables the device to effectively attenuate vibrations across the full range of engine operating speeds. However, as operating amplitudes increase, the dynamic stability and performance of these passive torsional smoothing devices are highly dependent upon the motion path defined for their pendulous masses. In fact, the pendulum natural frequency commonly shifts as a function of their swing amplitude. Tautochronic motion paths can eliminate this resonant frequency shift as excitation levels increase and can thus overcome the common detuning issues associated with existing paths within the epicycloid family. At present, approximate tautochrone motion paths for CPVAs are derived using simplifying assumptions, which uncouples the pendulum and rotor dynamics. In this paper, using variational calculus, a system tautochrone motion path that accounts for the pendulum to rotor inertial coupling is derived. Its use results in tautochronic motion of the entire oscillatory system including both pendulum and rotor. Numerical simulations of the system forced response show that a system tautochrone motion path has distinct vibration control advantages, including enhanced stability and vibration correction performance. Most fundamentally, a new concept of order-tuning in these systems is for the first time identified, where a pendulum following a system tautochrone motion path retains a fixed order tuning for all feasible system energy levels. That is, the paper presents a more exact order tuning concept, expressed in terms of the square root of system energy, thereby accounting for pendulum motion in addition to rotor speed effects on tuning order.