On the nonlinear dynamics of centrifugal pendulum vibration absorbers.

Abstract

Centrifugal pendulum vibration absorbers (CPVA's) are used to reduce torsional oscillations in rotating machinery. They consist of masses which are free to move along prescribed paths relative to a rotating system. They have been successfully employed in internal combustion engines and helicopter rotors to counteract the oscillating component of applied torques of a given harmonic order over a continuous range of operating speeds. However, nonlinearities can cause failure of these absorbers at moderate amplitudes of vibration. This dissertation focuses on the design of CPVA's with the consideration of nonlinear effects. The first approach is to seek the possibility of exact cancellation of a given external torque over a finite range of absorber amplitudes, and to determine the dynamic stability of such solutions when they exist. Equations are obtained that verify when a torque can be exactly cancelled by one single absorber or by a pair of identical absorbers moving out-of-phase with respect to each other. The latter are referred to as "subharmonic" absorbers when the absorber mass paths are symmetric about their corresponding vertices, since the torque generated by these absorbers has a frequency twice that of the absorber motions. This method also generates the required absorber paths directly from the applied torque. The second approach is to obtain an approximate nonlinear solution of the system to the first nonlinear order, and to compare this solution with numerical results of the fully nonlinear equations. Among the different absorber paths tested, cycloidal paths offer the best performance in minimizing the peak value of the angular acceleration of the system when a single absorber is employed, while circular path absorbers fail at moderate amplitudes. A mathematical engine model is built to compare the performance of three different configurations of absorbers on an engine at a certain operating condition. Preliminary results show that the best performance is achieved by a configuration consisting of one second order and a fourth order absorber.