# Slip and Stick in 1-D Web-Roller Contact

Posted in Mechanics and tagged on .

In the previous note we reviewed the derivation of capstan equation that solves the tension developed in a rope (web, belt) undergoing kinetic friction on a capstan (roller, pulley). We set up a problem in which a 1-D belt is tensioned, constrained statically, and in contact for a wrap angle of 90° on a cylinder that is rotating at a constant angular velocity. So the belt is in equilibrium and the belt-cylinder contact interface is in complete slip condition. This setup avoids the complication that would be introduced by slip-stick condition. However, the slip-stick condition universally exists in similar contact problems. In this note we will review the slip-stick condition, its mechanism, and its location at the contact interface in 1-D belt-roller contact problems with various boundary conditions. We will use $$\{$$rope, belt, web, string $$\}$$ and $$\{$$capstan, cylinder, roller, pulley $$\}$$ interchangeable, respectively, since in 1-D cases elements in each set are equivalent to others in the physical sense. All vector quantities are treated as scalars in computation with their direction visually shown.