Frictional Property of Flexible Element

Abstract

In the calculation of frictional force of a flexible element such as a belt, rope or cable wrapped around the cylinder, the famous Euler's belt formula (Hashimoto, 2006) or simply known as the belt friction equation (Joseph F. Shelley, 1990) is used. The formula is useful for designing a belt drive or band brake (J. A. Williams, 1994). On the other hand, a belt or rope is conveniently used to tighten a luggage to a carrier or lift up the luggage from the carrier. In that case, for the sake of adjusting the belt length and keeping an appropriate tension during transportation, various kinds of belt buckles are used. These belt buckles have been devised empirically and there was no theory about why it can fix the belt. The first purpose of this chapter is to present the theory of belt buckle clearly by considering the self-locking mechanism generated by wrapping the belt on the belt. Making use of the belt tension for a locking mechanism, a belt buckle with no locking mechanism can be made. The principle and some basic property of this new belt buckle are also shown. The self-locking of belt may occur even in the case where a belt is wrapped on an axis two or more times. The second purpose of this chapter is to present the frictional property of belt wrapped on an axis two and three times through deriving the formulas corresponding to an each condition. Making use of this self-locking property of belt, a belt-type one-way clutch can be made (Imado, 2010). The principle and fundamental property of this new clutch are described. As the last part of this chapter, the frictional property of flexible element wrapped on a hard body with any contour is discussed. The frictional force can be calculated by the curvilinear integral of the curvature with respect to line element along the contact curve.