Hysteretic friction force

The other most popular model is the frequency independent damping model. The concept of frequency independent damping arose when in 1927 Kimball and Lovell claimed that hysteretic damping is universal in nature. Since then there has been several studies which further strengthened their claim. One of the most popular models in this category is the linear Coulomb friction force model given as (Reid 1956, Muravski 2004)... 

This formula was given by Hunter (1961) for the special case of plane strain conditions and a cylindrical punch. For an elastic medium, this force is zero. However, for a viscoelastic medium, we shall see that this is not the case. The deformation caused by the moving load results in mechanical energy loss, which is manifested by the presence of a resisting force. This is the well-known force of hysteretic friction, first demonstrated experimentally by Tabor (1952). 

If Coulomb s law applies, then s(r), p(r) are related by (2.11.4). Equation (2.11.14) gives the hysteretic contribution. There is also the ordinary frictional force... 

If braking action is now externally applied to the tyre, additional energy losses are caused near the tread/road boundary, and these can be conveniently expressed as the adhesional and the hysteretic components of an interfacial friction force. We must emphasize that energy loss is the fundamental factor in both the internal and external friction mechanisms, and the concept of a frictional force is a convenient means of expressing such energy loss only in the vicinity of a sliding interface. 

Hysteretic whirl. This type of whirl occurs in flexible rotors and results from shrink fits. When a radial deflection is imposed on a shaft, a neutralstrain axis is induced normal to the direction of flexure. From first-order considerations, the neutral-stress axis is coincident with the neutral-strain axis, and a restoring force is developed perpendicular to the neutral-stress axis. The restoring force is then parallel to and opposing the induced force. In actuality, internal friction exists in the shaft, which causes a phase shift in the stress. The result is that the neutral-strain axis and neutral-stress axis are displaced so that the resultant force is not parallel to the deflection. The... 

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