STABILITY OF THE UNISON RESPONSE FOR A ROTATING SYSTEM WITH MULTIPLE TAUTOCHRONIC PENDULUM VIBRATION ABSORBERS

Due to spatial and balancing considerations, the implementation of cen trifugal pendulum absorbers (CPVA's) invariably requires that the tota l absorber inertia be divided into several absorber masses and station ed about the center of rotation. To achieve the designed-for performan ce, the CPVA's are expected to move in exact unison, since the selecti on of the total absorber mass is made by assuming an equivalent single absorber mass. In this paper, we determine the conditions under which the unison motion of a system of several identical CPVA's is dynamica lly stable. This is done far the special case of tautochronic absorber s subjected to a purely harmonic torque. The stability criterion is ob tained by an asymptotic method that exploits certain symmetries in the equations of motion and is based on the assumption that total moment of inertia of the absorbers is much smaller than that of the entire ro tating system-an assumption that is almost always satisfied in practic e. It is expressed in terms of a critical torque level that is proport ional to the square root of the equivalent viscous damping of the indi vidual absorbers. The result is verified by numerical simulations of t he system near the critical parameter conditions. A future paper will consider the post-critical response of the system.