Coexisting chaotic and periodic dynamics in clock escapements

作者：Francis C. Moon, Preston D. Stiefel · 发表于：Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · 年份：2006 · DOI：10.1098/rsta.2006.1839 · 被引用次数：24 · 研究领域：Chaos control and synchronization、Mechanics and Biomechanics Studies、Music Technology and Sound Studies

This paper addresses the nature of noise in machines. As a concrete example, we examine the dynamics of clock escapements from experimental, historical and analytical points of view. Experiments on two escapement mechanisms from the Reuleaux kinematic collection at Cornell University are used to illustrate chaotic-like noise in clocks. These vibrations coexist with the periodic dynamics of the balance wheel or pendulum. A mathematical model is presented that shows how self-generated chaos in clocks can break the dry friction in the gear train. This model is shown to exhibit a strange attractor in the structural vibration of the clock. The internal feedback between the oscillator and the escapement structure is similar to anti-control of chaos models.