Cylinder-Flat Contact Mechanics with Surface Roughness
A. Tiwari, B. N. J. Persson
Abstract
Abstract We study the nominal (ensemble averaged) contact pressure p ( x ) acting on a cylinder squeezed in contact with an elastic half space with random surface roughness. The contact pressure is Hertzian-like for $$\alpha < 0.01$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo><</mml:mo> <mml:mn>0.01</mml:mn> </mml:mrow> </mml:math> and Gaussian-like for $$\alpha > 10$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>></mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> , where the dimensionless parameter $$\alpha = h_{\rm rms}/\delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>h</mml:mi> <mml:mi>rms</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:mi>δ</mml:mi> </mml:mrow> </mml:math> is the ratio between the root-mean-square roughness amplitude and the penetration for the smooth surfaces case (Hertz contact).