Many classical applications in machine design and recent ones in the field of electrical contacts or micro-contacts involve surface circular contacts which show important edge effects. To optimize these contacts, a uniform pressure distribution must be generated over an important part of contact area. This requires a specifically profiled front surface. Previously, these authors proposed a solution based on an optimum pressure distribution. This leads numerically to a punch profile which is approximated by a polynomial. The pressure generating this polynomial profile is found and compared to initial proposal. Recent investigations establish a correspondence between a polynomial punch surface and generated pressure. Starting from this correspondence, a new general approach is offered. The same optimum pressure as previously is accepted. Its profile is approximated by a function advanced in the paper. This function yields directly an even polynomial punch profile. Formulae for central pressure and normal approach are derived.

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