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 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.

Keywords

• belt friction
• self-locking
• locking condition
• wrapped three times