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 μb, where θ is wrapping angle of a belt around a cylinder, μ is the coefficient of friction between the belt and the cylinder and μb 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 μb<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=μb/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.

Keywords

• euler&apos;s belt formula
• belt friction
• self-locking
• locking condition
• over-wrapping