In this article we study a lubricated system consisting on a slider moving over a smooth surface and a known external force (the load) applied upon the slider. The slider moves at constant velocity and close proximity to the surface and the gap is filled by an incompressible fluid (the lubricant).At the equilibrium, the position of the slider presents one degree of freedom to be determined by the balance of forces acting on the system: the load and the total force exerted by the pressure of the lubricant. The pressure distribution is described by a variational inequality of elliptic type known as Swift–Stieber model and based on Reynolds equation. The distance h between the surfaces in a two dimensional domain Ω is given by hη(x1,x2,y)=h0(x1,x2)+h1(y)+η,(x1,x2)∈Ω,y∈[0,1] where h0(x1,x2)∼|x1|α for α>0 and h1(y)∼|y−y0|β for y being the homogenization variable. The main result of the article quantify the influence of the roughness in the load capacity of the mechanism in the following way: If α<3γfor 0<γ⩽2α<min{1γ−2,3γ}for γ>2 then, the mechanism presents finite load capacity, i.e. limη→0∫Ωpη<∞. Infinite load capacity is obtained for γ>1 and α>2/(γ−1). A one dimensional particular case is given for γ>3/2 with infinite load capacity.

中文翻译：

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外加载荷对润滑平衡问题中粗糙度的影响

在本文中，我们研究了一种润滑系统，该系统由在光滑表面上移动的滑块和施加在滑块上的已知外力（负载）组成。滑块以恒定速度运动并紧贴表面移动，间隙被不可压缩的流体（润滑剂）填充。在平衡状态下，滑块的位置呈现出一个自由度，该自由度取决于作用在其上的力的平衡系统：由润滑剂的压力施加的载荷和总力。压力分布由椭圆形的变分不等式描述，该模型被称为Swift–Stieber模型并基于雷诺方程。二维域Ω中的曲面之间的距离h由hη（x1，x2，y）= h0（x1，x2）+ h1（y）+η，（x1，x2）∈Ω，y∈[0 ，1]，其中α>> h0（x1，x2）〜| x1 |α 0和h1（y）〜| y-y0 |β，其中y是均化变量。本文的主要结果通过以下方式量化了粗糙度对机构负载能力的影响：如果α<3γ对于0 <γ⩽2α<min {1γ-2,3γ}对于γ> 2，则该机构表示有限的负载能力，即limη→0∫Ωpη<∞。对于γ> 1和α> 2 /（γ-1），可获得无限的负载能力。给出了γ> 3/2且具有无限载荷能力的一维特殊情况。