Abstract

The theorem on the relationship between the pressure distribution and the frictional force is derived “The frictional force is maximized when the pressure distribution is uniform, if μ (P)P is convex with respect to P”. In order to verify this theorem, the surface shape of the rubber block with the uniform pressure distribution is obtained by the optimization technique. The shape of the optimized surface was round at the edges and concave at the center where the pressure was large in the block with the flat surface. The pressure of the block with the optimized surface became uniform and the frictional force increased by two percent in the small shear deformation and by ten percent in the large shear deformation on a dry steel plate compared with the block with a flat surface. The mechanism of this increase is different in the small and the large deformation. In the small deformation the frictional force is increased by not only the pressure uniformity but also the increase of contact area in the block with optimized surface. On the other hand, in the large deformation the effective contact area decreases due to the“peel-off” deformation at the edges of the block with a flat surface, while the“peel-off”deformation does not occur in the block with the optimized surface.

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