A study of chatter-induced loss of mechanical contact

chatter;contact;friction;impact;paradox

Sanders, John W. ; Dankowicz ; Harry

关键词: chatter;    contact;    friction;    impact;    paradox;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/45337/John_Sanders.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This thesis concerns a recently discovered paradox in rigid body mechanics called reverse chatter, in which friction can cause the problem of two rigid bodies in sustained contact to admit multiple solutions. In particular, when the point of contact between the two bodies comes to rest, under certain conditions the rigid body model-coupled with Amontons-Coulomb friction and Stronge's energetic impact termination condition-allows for sustained stick, as well as an infinite number of other trajectories, each involving an infinite number of impacts in finite time. A similar mechanism can occur between two bodies with a compliant contact model, though in this case there are only finitely many impacts. The purpose of the present work is to call attention to this reverse chatter phenomenon, and to explore it in greater depth. In particular, we investigate what becomes of reverse chatter under alternative impact termination conditions to that of Stronge, namely those of Newton and Poisson. We begin by establishing, for the first time to our knowledge, that Poisson's impact termination condition is energetically consistent (i.e., it cannot generate energy during a frictional impact). We then show that reverse chatter is possible under Poisson's impact termination condition, but not under Newton's, thus establishing that, while the possibility of reverse chatter is sensitive to the impact termination condition used, it is not simply an artifact of Stronge's hypothesis. Additionally, we consider what becomes of chatter in the presence of an external control scheme which attempts to keep two bodies in sustained contact. We find that chatter-like behavior is still possible, and can lead to a loss of contact followed by a sequence of impacts qualitatively similar to that observed when chalk hops on a chalkboard. It is argued that reverse chatter may be responsible for this and similar phenomena. Furthermore, the present results suggest that reverse chatter occurs under easily achievable laboratory conditions, setting the stage for reverse chatter to be studied experimentally in the future.