Rocking and rolling down an incline : the dynamics of nested cylinders on a ramp

• Main Author: Vener, David Paul
• Other Authors: John W.M. Bush.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2008
• Subjects: Mathematics.
• Online Access: http://dspace.mit.edu/handle/1721.1/34616; http://hdl.handle.net/1721.1/34616

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006. === Includes bibliographical references (p. 109-111). === In this thesis, I report the results of a combined experimental and theoretical investigation of a journal bearing, specifically, a cylinder suspended in a viscous fluid housed within a cylindrical shell, rolling down an incline under the influence of gravity. Particular attention is given to rationalizing the distinct modes of motion observed. We performed a series of experiments in which the inner cylinder density and the fluid viscosity were varied. Three distinct types of behavior were observed. First, in what we shall call the "rocking" mode, after an initial settling period, the shell rocks back and forth without moving down the ramp. Second, we observed "slow, quasi-steady rolling"; this mode is characterized by the system proceeding down the hill at essentially a constant velocity. Finally, the cylinders roll down the incline with constant acceleration; we shall call this mode "unbounded acceleration." An accompanying theoretical model is developed and enables us to rationalize the rocking and accelerating modes. In the rocking solutions, potential and kinetic energy are dissipated in the fluid as the inner cylinder approaches the bottom of the outer cylinder. === (cont.) In the accelerating solutions, the whole system moves as a solid body so that no dissipation occurs and potential energy is continually converted into kinetic energy. In order to understand the quasi-steady motion, we analyze the motion of a similar system: a metal cylinder is placed inside a larger plastic cylinder filled with fluid and attached to a motor which fixes the larger cylinder's rotation rate. Our observations of this system, specifically, the differences between experiments and theory lead us to consider the effect of internal friction due to surface roughness. The resulting model's predictions are well supported by our observations. Finally, to rationalize the slow, quasi-steady rolling motion of the system, we incorporate surface roughness and cavitation into the theoretical model. These effects provide a restoring force on the inner cylinder; however, we find that surface roughness is the dominant effect. === by David Paul Vener. === Ph.D.