| We consider the transient behavior of centrifugal pendulum vibration absorbers (CPVAs), specifically, the overshoot problem encountered when these absorbers are suddenly activated. CPVAs are passive devices used to address torsional vibrations in rotating systems, for example, helicopter rotors and crankshafts of internal combustion engines. They consist of pendulums mounted on a rotor, driven by system rotation, and tuned in such a manner that in steady-state operation they counteract engine-order fluctuating torques acting on the rotor, thereby smoothing vibrations. The primary feature of these devices is that they are order tuned, that is, tuned to a given multiple of the rotation rate, as opposed to the more common frequency tuned absorbers. Recently these absorbers have been proposed to expand the operating envelope for cylinder deactivation in variable displacement engines, in order to improve fuel economy. In these applications, the system encounters conditions in which the absorbers are suddenly activated and undergo a beating-type transient motion, resulting in overshoot of the absorber amplitude before it reaches steady-state. This overshoot depends on a number of parameters, including the difference between the absorber's natural frequency and the frequency of excitation, the ratio of absorber inertia to rotor inertia, the system damping, and system nonlinearities. An approximate analytical model is developed, using perturbation methods, that predicts the overshoot in terms of these parameters, and the model results are verified by simulations of the equations of motion and by experiments using a fully instrumented spin rig. The predictive results are found to provide a useful bound on the overshoot, and will be of use when designing absorber systems so that they do not exceed rattle space constraints during startup. It is found that absorbers with near tautochronic paths behave much like linear absorbers, and when lightly damped and start from small initial conditions, they have an overshoot close to 100%. For absorbers with softening paths, such as the commonly used circular path absorbers, the overshoot can reach up to 173%, depending on system and input parameters. |
