Rolling contact with friction and non-Hertzian pressure distributions
Abstract
A numerical technique is suggested to solve rolling contact problems with friction, for an arbitrary contact patch under any pressure distribution. Results obtained by this technique are checked against some existing results and are shown to be satisfactory for small rotational slippage about the z axis (normal to the plane of contact). To cover the opposite extreme, we develop an alternative solution for fully developed sliding with rotation.^ Under the condition of gross sliding, the tangential forces ($F\sb{x},F\sb{y}$) and spin moment $M\sb{z}$ transmitted between two bodies in contact depend on the coordinates of the instantaneous center (IC) of the impending planar motion. For circular contact patches under Hertzian pressure or pressure produced by a rigid flat punch on an elastic medium, analytical expressions for the forces and the coordinates of the associated IC are derived. These are the first analytical solutions to these problems. For patches of any other shapes, another numerical algorithm has been developed to find the relationship between the tangential forces, the spin moment, and the location of the IC. Contour curves are shown such that if any two of the quantities $F\sb{x},F\sb{y}$ and $M\sb{z}$ are known, the third may be found from these curves. Carpet plots are shown, which represent the relationship between the coordinates of the IC and forces ($F\sb{x},F\sb{y}$).^ The two new numerical solutions developed allow us to establish reasonable upper bounds on the spin moment for large or small amount of spin. ^
Subject Area
Applied Mechanics|Engineering, Mechanical
Recommended Citation
Chaohwa Liu,
"Rolling contact with friction and non-Hertzian pressure distributions"
(January 1, 1988).
Dissertations available from ProQuest.
Paper AAI8816200.
http://repository.upenn.edu/dissertations/AAI8816200
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