Tautochronic bifilar pendulum torsion absorbers for reciprocating engines

The model of a forced linear oscillator with instantaneous impacts at one or two stops is discussed. The nonlinearities introduced by the instantaneous impact rule are sufficient to cause typical nonlinear behaviour. The impact rule is discontinuous, introducing discontinuities into discrete time Poincare maps defined from the continuous time dynamical system. Discontinuities also exist in the derivatives of these maps. The implications of these discontinuities are discussed and their relevance to engineering applications is assessed with suggestions for further research.

Dynamical Complexities of Forced Impacting Systems

Due to spatial and balancing considerations, the implementation of centrifugal pendulum absorbers (CPVA's) invariably requires that the total absorber inertia be divided into several absorber masses and stationed about the center of rotation. To achieve the designed-for performance, the CPVA's are expected to move in exact unison, since the selection 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 ofa system of several identical CPVA's is dynamically stable. This is done for the special case of tautochronic absorbers subjected to a purely harmonic torque. The stability criterion is obtained 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 rotating system-an assumption that is almost always satisfied in practice. It is expressed in terms of a critical torque level that is proportional to the square root of the equivalent viscous damping of the individual absorbers. The result is verified by numerical simulations of the system near the critical parameter conditions. A future paper will consider the post-critical response of the system.

Stability of the unison response for a rotating system with multiple tautochronic pendulum vibration absorbers

It is well known that some solutions for a sinusoidally driven oscillator with linear stiffness and impacts at rigid stops modelled with a coefficient of restitution impact law can be located analytically. Recently, new co-dimension one bifurcations called grazing bifurcations have been found in such systems. Here we present analytical results which show how the type of grazing bifurcation changes with parameter, and that when the type of grazing bifurcation changes a codimension two bifurcation occurs. The simplest grazing bifurcations involve orbits of period-1, but we show that the same analytical methods can be used to locate some subharmonics and their bifurcations.

Analytical determination of bifurcations in an impact oscillator

The performance of particle dampers whose behavior under broadband excitations involves internal friction and momentum transfer is a highly complex nonlinear process that is not amenable to exact analytical solutions. While numerous analytical and experimental studies have been conducted over many years to develop strategies for modeling and controlling the behavior of this class of vibration dampers, no guidelines currently exist for determining optimum strategies for maximizing the performance of particle dampers, whether in a single unit or in arrays of dampers, under random excitation. This paper focuses on the development and evaluation of practical design strategies for maximizing the damping efficiency of multi-unit particle dampers under random excitation, both the stationary and nonstationary type. High-fidelity simulation studies are conducted with a variable number of multi-unit dampers ranging from 1 to 100, with the magnitude of the "dead-space" nonlinearity being a random variable with a prescribed probability distribution spanning a feasible range of parameters. Results of the computational studies are calibrated with carefully conducted experiments with single-unit/single-particle, single-unit/multi-particle, and multiple-unit/multi-particle dampers. It is shown that a wide latitude exists in the trade-off between high vibration attenuation over a narrow range of damper gap size versus slightly reduced attenuation over a much broader range. The optimum configuration can be achieved through the use of multiple particle dampers designed in accordance with the procedure presented in the paper. A semi-active algorithm is introduced to improve the rms level reduction, as well as the peak response reduction. The utility of the approach is demonstrated through numerical simulation studies involving broadband stationary random excitations, as well as highly nonstationary excitations resembling typical earthquake ground motions.

M. Sharif-Bakhtiar

Papers

The dynamic response of a centrifugal pendulum vibration absorber with motion-limiting stops

Effects of Nonlinearities and Damping on the Dynamic Response of a Centrifugal Pendulum Vibration Absorber