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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).
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:
Half-Sommerfeld boundary condition was shown to be inaccurate and this solution has to be used with care. In case of 1-D Reynolds equation several analytical or semi-analytical solutions are available. In 1916 Martin obtained a closed form solution [5] for a minimum film thickness and pressure for a rigid cylinder and plane geometry. This ...
Classical solutions based on the half-space approach are: Hertz solved the contact problem in the absence of friction, for a simple geometry (curved surfaces with constant radii of curvature). Carter considered the rolling contact between a cylinder and a plane, as described above.
Nikolai Pavlovich Petrov's method of lubrication analysis, which assumes a concentric shaft and bearing, was the first to explain the phenomenon of bearing friction.This method, which ultimately produces the equation known as Petrov's law (or Petroff's law), is useful because it defines groups of relevant dimensionless parameters, and predicts a fairly accurate coefficient of friction, even ...
A ball bearing. A bearing is a machine element that constrains relative motion to only the desired motion and reduces friction between moving parts.The design of the bearing may, for example, provide for free linear movement of the moving part or for free rotation around a fixed axis; or, it may prevent a motion by controlling the vectors of normal forces that bear on the moving parts.
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 ...