On the Repetitive Impact Dynamics of One and Two Degree of Freedom Systems

Abstract

Repetitive collision occurring between structural and machine components is a topic of practical and scientific importance. Some types of machinery are inherently susceptible to impacts because of the small clearances present between adjacent components, thermal expansion, and relative motion as in gear trains. One can observe repetitive impacts in milling machines, shakers and off-shore structures. Energy transfer between components that are subjected to repetitive impacts is a complex phenomenon that often exhibits deceptive and non-intuitive behavior. Even in seemingly simple structures, period-doubling bifurcations, sub-harmonic resonances, and chaotic responses occur. This paper presents detailed experimental data obtained from an impact vibration test stand that was instrumented for displacement, velocity, and impact force measurements. In addition, the apparatus was fabricated in such a way to allow for precise positioning of the impact point, and varying of the gap distance between impacting components. The paper includes companion simulation results obtained from a model for the repetitive impact dynamics of otherwise linear single or multiple degree of freedom discrete structures. Simulation results are presented for the effect of natural frequency placement, model dimension, and gap clearance on the qualitative and quantitative character of the response. Of particular interest is the transition of behavior as the system’s model is augmented from having one to several degrees of freedom.

Experiments on a beam-rigid body structure repetitively impacting a rod

“…The primary findings of this investigation pertain to measurements of repetitive impact vibration in a built-up beam structure, validation of the modal mapping approach (Figs. [5][6][7][8], and identification of the model parameters such as asymmetry and clearance (Fig. 15) that influence the complexity of response.…”

“…For an analogous single degree of freedom system, the period-one motion bifurcated into period-three and higher-order motions, and subsequently evolved into aperiodic motion. Fang and Wickert [6] and Yagci et al [7] obtained the experimental frequency response of a cantilever beam that supported an end mass and that could impact a vibrating surface. The response exhibited a recurring pattern of resonances, period-doubling bifurcations, and regions of aperiodic motions.…”