An analytical solution of the rope-sheave contact in static conditions based on a bristle model

This paper presents an analytical solution for the rope-sheave contact problem in static conditions, also applicable to belt-pulley problems and similar mechanisms. The rope is assumed under constant unequal loads at two ends, as elevator when brake acting on drive sheave weights of cabin counterweights are different. behave a rod without bending stiffness. Assuming bristle model Coulomb friction, balance forces differential slice used obtain closed-form axial force field normal tangential fields. found first case with flexibility but axially rigid. Then, extended flexible bristles, that allows relative penetration. valid until one cross-section achieves saturated friction force. value load this condition met identified. If high-load further increases, separated areas, area next low-load remains fully stuck while shows exactly calculates angle separation between areas fields, being all these functions piece-wisely defined. Finally, numerical results particular example solutions.