Study of Belt Friction in Over-Wrapped Condition

Abstract

The property of belt friction in an over-wrapped condition was studied. A fractional expression with respect to the ratio of belt tensions was derived by this study. The Euler's belt formula was included as a special case in the equation derived. The equation is a function of the contact angle θ and two kinds of the coefficient of friction μ and μ_b, where θ is wrapping angle of a belt around a cylinder, μ is the coefficient of friction between the belt and the cylinder and μ_b is the coefficient of friction between the belt and belt respectively. As the equation signifies the possibility of self-locking, the self-locking mechanism was investigated theoretically by the equation. It occurs when the discriminant of self-locking condition became 0 or negative. The necessary conditions for self-locking are μ_b<μ and a sufficient over-wrapping angle of the belt. Providing the coefficient of friction μ and the ratio of the coefficients of friction κ=μ_b/μ, some critical over-wrapping angles for self-locking were calculated numerically. Experiments were carried out to confirm the occurrence of self-locking predicted by the equation by using a polyethylene film to reduce friction between the belt. Self-locking occurred in the experiment with the polyethylene film wrapped around the belt. But it never occurred without the polyethylene film as predicted by the equation.