Stability study of centrifugal pendulum vibration absorbers in gravity field

Abstract

In this study, Lyapunov stability theory was used to systematically investigate the stability of centrifugal pendulum vibration absorber (CPVA) in terms of the shape of the absorber path, mistuning levels, damping coefficient, number of absorbers, and force of gravity. Our approach improved upon previous studies by introducing a gravity term, optimising the calculation method, and using a function diagram to represent the asymptotically stable region to produce more accurate results. Our finding that the influence of gravity on the stability of the CPVA system is reflected in the change of the tuning order prompted us to define new terminology—’gravity mistuning factor ( $\mathrm{\Delta }{\sigma }_{\eta }$ )’ and ‘zone yielding to gravity ( $\mathrm{ZY}$ )’—to intuitively reflect the influence of gravity. Comparison of the results obtained from numerical simulation based on a fully nonlinear equation of motion with analytical results revealed nonlinear dynamic characteristics such as bifurcation to asynchrony response, nonlinear jump, and beat phenomena. The approach and results of this study are more practical in settings in which gravity plays an important role, including vehicle engine idling, low-speed locomotive or marine engines, and drum washing machines.