微分和表观静摩擦系数的表式

当前，工程师和科学家都对微牛和纳牛量级载荷静摩擦系数（以下简称微牛纳牛静摩擦系数）很感兴趣。但文献中至今没有详细讨论过微牛纳牛静摩擦系数与载荷的关系，而且发表的实验结果都不相互讨论。从微分静摩擦系数的定义出发，导出几种典型模型下微分静摩擦系数和表观静摩擦系数的表式，并据此广泛讨论这些文献中的实验结果。

Expressions for Differential and Apparent Coefficients of Static Friction

Recently, scientists and engineers are interested in coefficients of static friction on micro and nano scale. On macro scale, the friction force is proportional to load, the apparent coefficients of static friction are always constant and not related with the load and the contact area between the load and the substrate, which have been described as Amontons' laws. However, a lot of experiments carried out with scanning microscope, atomic force microscope and friction force microscope on micro or nano scale showed that Amontons' laws can not used successfully. On micro or nano scale, there is no general expression published in literatures to describe the relationship between the coefficients of static friction and the load. Also the published data do not compare with and discuss each other. In this paper, from the definition of differential coefficients of static friction, the expressions for differential and apparent coefficients of static friction, and for several models are deduced. Only can be measured in experiments, which can be the coefficients on micro or macro scale depending on the load on the substract, but can not be measured because the differential variables are too small to measure. In Amontons' model, equals to and both are constant. In single asperity model with load on micro or nano scale, and are not constant but propotional to P -1 . In the model based on absoption layers as third bodies between two contact bodies, is a constant, is not a constant but proportional to P -1 . is a constant only in high normal pressure. In the model based on constant P , and are related with F and A . Finally, the experimental data published in literatures have been discussed based on the novelly deduced expressions. [