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
μb <
μ and sufficient wrapping angle of the belt, where
μ is the coefficient of friction between the belt and shaft and
μb 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 =
μb/
μ, some critical over-wrapping angles for self-locking were calculated numerically. Furthermore some normal force distributions in self-locking conditions were calculated theoretically.
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