Thursday, April 4, 2013

1304.1061 (A. L. O. Bilobran et al.)

Model for the resistance force acting on circular bodies in the
imminence of rolling

A. L. O. Bilobran, R. M. Angelo
The laws of friction are reasonably well understood for the case of blocks in contact with rough plane surfaces. However, as far as bodies with circular sections are concerned, the physics of friction becomes more involving and it is not possible to adopt a simple conceptual framework to explain all phenomena. In particular, to the best of our knowledge, there is no approach so far to the problem of the resistance force that opposes to circular bodies that remain at rest while acted upon by small external forces. Here we fill this gap by introducing a purely mechanical model based on both the elasticity theory and Hertz contact mechanics. Our approach furnishes a quantitative expression for the critical force beyond which rest can no longer be maintained. Besides confirming the expected proportionality of the resistance force with the load, our result contains no free parameters and is expressed solely in terms of physical properties of the problem, such as the pressure of the body per unit of superficial area, a relation between the Young modulus of the surface and its Poisson ratio, and the symmetry of the contact.
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