Tightening dynamics of wound rolls: The interplay of solid friction and interfacial compressibility.

Abstract

The capstan equation predicts that the tension along a flexible band wrapped around a cylinder decreases exponentially with the number of turns due to solid friction, preventing relative slipping. However, we demonstrate in a controlled experiment that a loosely wound roll can in fact be tightened efficiently. The key lies in the interplay between solid friction and interfacial compressibility due to surface roughness: a circular slipping zone nucleates at the fixed core and propagates outwards through a stick-slip sequence, producing successive tightening waves. Each wave slightly reduces the interlayer spacing while conserving length, so that slack accumulates and the outer part rewinds onto the inner layers. We quantify the front kinematics and the force build up, and demonstrate that the process is governed by the compression of interfacial roughness, which depends logarithmically on the pressure.