Roller Ball Indentation

Now we consider roller ball indentations. Let us consider first a rigid ball that does not roll but indents a viscoelastic half-space this analysis will be extended to a rolling ball. This is a typical situation in which the elastic-viscoelastic analogy is, in general, no longer applicable. 

To solve this problem, we shall refer to the elastic solution given in Ref. 15 (p. 25). According to this approach, the displacement of a point x, j) of the half-plane caused by the load applied at (x, j ) is given by 

Using the same approach as in the plane indentation of elastic materials, the displacement of a viscoelastic system by the action of a concentrated load is given by 

For a given this problem can be solved by using the correspondence principle. Thus, for a monotonically increasing a t), can be replaced by the current contact area Q t). In these conditions, Eq. (16.211) can be written as 

The response to a total applied force given by P t) can be easily found by inversion of Eq. (16.218). The pertinent result is 

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When long idle storage is foreseen, arrangements may be made to rotate the rotor periodically by hand by 90° or so to shift the position of balls or rollers. This will prevent the grease from leaving any marks on the races and avoid any static indentation on the bearings. 

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