Study of Belt Friction with Three Times Wrapping Condition

Abstract

Theoretical study was carried out to investigate the frictional property of belt wrapped three times around a circular shaft. A belt equation of fractional expression was derived. The self-locking mechanism was investigated theoretically by the equation. The discriminant of self-locking condition was clarified. The necessary conditions for self-locking are µ b < µ and sufficient wrapping angle of the belt, where µ is the coefficient of friction between the belt and shaft and µ b is the coefficient of friction between the belt and belt. According to the formula derived, self-locking occurs even under a realistic condition. It occurs when the ratio of belt tensions becomes 0 or negative. 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. Furthermore some normal force distributions in self-locking conditions were calculated theoretically.

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).…”

Study of Euler&rsquo;s Belt Formula

“…The calculation method has to be verified so that it satisfies the static equilibrium of force and moment to an entire body. Equations were derived by which the frictional force of a belt wrapped two and three times around a cylindrical surface can be calculated [3,4]. By using these equations, the self-locking condition of belt was clarified.…”