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The capstan equation [1] or belt friction equation, also known as Euler–Eytelwein formula [2] (after Leonhard Euler and Johann Albert Eytelwein), [3] relates the hold-force to the load-force if a flexible line is wound around a cylinder (a bollard, a winch or a capstan).
The downward force is carried by the bearing at the top beam in most balance scales, the lower beam just being supported horizontally at midpoint by the body of the scales by a simple peg-in-slot arrangement, so it effectively hangs beneath the top beam and stops the platforms from rotating.
A starting point for solving contact problems is to understand the effect of a "point-load" applied to an isotropic, homogeneous, and linear elastic half-plane, shown in the figure to the right. The problem may be either plane stress or plane strain. This is a boundary value problem of linear elasticity subject to the traction boundary conditions:
This theory is exact for the situation of an infinite friction coefficient in which case the slip area vanishes, and is approximative for non-vanishing creepages. It does assume Coulomb's friction law, which more or less requires (scrupulously) clean surfaces. This theory is for massive bodies such as the railway wheel-rail contact.
Belt friction is a term describing the friction forces between a belt and a surface, such as a belt wrapped around a bollard.When a force applies a tension to one end of a belt or rope wrapped around a curved surface, the frictional force between the two surfaces increases with the amount of wrap about the curved surface, and only part of that force (or resultant belt tension) is transmitted ...
The discovery and underlying research is usually attributed to Richard Stribeck [1] [2] [3] and Mayo D. Hersey, [4] [5] who studied friction in journal bearings for railway wagon applications during the first half of the 20th century; however, other researchers have arrived at similar conclusions before. The mechanisms along the Stribeck curve ...
The system rotates without requiring the application of any external force or couple, other than that required to support its weight. If a system is initially unbalanced, to avoid the stress upon the bearings caused by the centrifugal couple, counterbalancing weights must be added. This is seen when a bicycle wheel gets a buckled rim.
Bearing pressure is a particular case of contact mechanics often occurring in cases where a convex surface (male cylinder or sphere) contacts a concave surface (female cylinder or sphere: bore or hemispherical cup). Excessive contact pressure can lead to a typical bearing failure such as a plastic deformation similar to peening.