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.

Experimental Study of Clutch Utilizing Self-Locking Property of Belt

“…So far, the properties of belt friction in two and three times wrapping condition have been studied theoretically [1,2]. According to the results of these studies, it was found that a belt has self-locking property.…”

Study of Belt Friction with Three Times Wrapping Condition

“…The belt tensions 1 1 2 , ", ′ T T T and 2 T ′ in Eq. (17) should be expressed by the function of T 4 .…”

“…But so far, self-locking phenomenon of belt friction was not clearly understood. Imado clarified the mechanism of self-locking of belt in two times wrapping condition [2]. But as the theory was limited to the two times wrapping condition, somewhat severe condition was required to generate the self-locking.…”

Novel coupling applicable in off-centered condition

“…Imado found the self-locking property of the belt in the course of his study and showed the theoretical self-locking condition for two and three times wrapping condition of belt (Imado, 2008;Imado, et al, 2013a). He devised a one-way clutch by utilizing the self-locking property of belt (Imado, et al, 2010;Imado, et al, 2013b).…”