V字溝を転がる凸形円板の発散的ローリング振動

抄録

The convex disk rotating along a V-shaped valley causes the excited vibration in a rolling motion. This report represents the mechanism of generating this rolling vibration through an analytical model and the observed results using a simple apparatus. The author makes clear through investigation that these phenomena are derived from the friction induced between the disk and the tilted surface of the valley and that the rolling motion is generated because the rolling moment due to this friction varies synchronously with the rolling angular velocity. Further it is revealed that the greater the frictional coefficient is, the more this vibration is excited, and that the case of the tilted slope with a meeting angle beyond a certain limit of both sides of the valley does not generate these excited behaviors. A sphere instead of a disk behaves simple rotation along a slope without vibration. When this excited vibration in a rolling motion grows severer, the perpendicular resistant force on either surface of the slope of a valley becomes zero alternately. These analytical results tend to coincide with the ones observed on the apparatus. This mechanism inducing the excited vibration is expected to be applicable for polishing the stones of “go” or the convex lenses efficiently and for selecting the medical tablets with poor quality.