There are many methods for attenuation of end effects in finite length line Hertz contacts. A new one is proposed herein by using an even polynomial generatrix for the equivalent rigid roller. The elastic contact between high order polynomial surfaces is used to get a nearly flat maximum pressure along the line contact. According to a reversed method, contact half-axes and central pressure are imposed. The longitudinal roller profile found numerically is indeed an even order polynomial. The method is validated numerically by a GC-DCFFT method.

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