Micro/nanoscale lubrication must take into account the fractal profile of the shaft and bearing surfaces. A new fractal rheological model is proposed to describe the properties of the non-Newtonian fluid, and a fractal variational principle is established by the semi-inverse method, and finally the Lagrange multipliers can be found in the obtained variational formulation. This work provides a new fractal approach to nano/micro lubrication.

中文翻译：

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分形润滑问题的变分原理

微/纳米级润滑必须考虑轴和轴承表面的分形轮廓。提出了一种新的分形流变模型来描述非牛顿流体的性质，并通过半逆方法建立了分形变分原理，最终在得到的变分公式中求出拉格朗日乘子。这项工作为纳米/微米润滑提供了一种新的分形方法。