Study of dynamics of rotational centrifugal pendulum vibration absorbers based on tautochronic design

A method for designing the key parameters of rotational centrifugal pendulum vibration absorbers is proposed herein. The vibration equations of the pendulum and rotor were established by utilizing Lagrange’s equations. It was found that there were two kinds of rotational centrifugal pendulum vibration absorbers (CPVAs): a linear rotational CPVA and a nonlinear rotational CPVA, which both behaved approximately as linear oscillators. The choice of the linear rotational coefficient and the nonlinear rotational coefficient (only for the nonlinear rotational CPVA) was analyzed, and the selection of the tuning order and trajectories of the centroid of the pendulum was investigated based on tautochronic design theory. In this study, the time variables were transformed to angle variables in the vibration equations. The parameters in the equations were then non-dimensionalized, and the equations were decoupled. Finally, the vibration responses of the pendulum and rotor were solved using the harmonic balance method. The results demonstrated that the linear rotational CPVA designed by utilizing tautochronic theory provided a better damping effect than the nonlinear rotational and non-rotational CPVAs. Furthermore, the linear rotational CPVA could decrease the impact effect on the rotor by adjusting the linear rotational angle and ensure its damping performance.