纳米薄膜润滑物理—数学模型及数值分析

基于润滑剂分子通常具有链状结构的事实，在分析润滑剂分子链长同膜厚关系的基础上，建立了纳米薄膜润滑物理模型，并利用含旋转量的流体力学运动方程得到了相应的Reynolds方程，同时对薄膜润滑Reynolds方程进行了数值计算，以考察特征长度对薄膜润滑状态参数的影响。结果表明，同相应的厚膜解相比，薄膜模型中润滑剂的粘度及承载能力均明显提高，且其提高幅度随着特征长度的增大而增大。根据润滑剂分子链长度确定的薄膜润滑区间以及膜厚－速度关系数值解同相应的试验结果一致。

Physical-Mathematical Model and Numerical Analysis of Nano Thin Film Lubrication

With a view to the fact that lubricant molecules usually have chain structure, a physical model has been established to analyze the lubrication characteristics of nano thin film, by correlating the molecular chain length of the lubricants and the film thickness. Thus the equivalent Reynolds equations for the nano thin film lubrication have been derived from the basic equations of fluid mechanics, by taking into account the rotation terms. Numerical analysis has also been carried out to investigate the influence of the characteristic length of the lubricant molecules on thin film lubrication performance. Results indicate that the load carrying capacity of the thin lubricating film calculated by the present model is significantly larger than that based on the conventional fluid lubrication theory for a thicker film. This is because the length effect of the lubricant molecules is significant in thin film lubrication. Moreover, the range of thin film lubrication and the relationship between the film thickness and velocity determined with the present model agree well with the reported experimental ones.