The Generalized Frenkel-kontorova Model—three-layer Model

In recent years, with the rapid development of the superlubrication technology,the understanding about microscopic mechanism of friction has been improving constantly. The science and technology represented by the low friction and the lubrication has been developed rapidly.This paper has mainly studied the generalized Frenkel-Kontorova model. In one-dimensional underdamped system, we has built three-layer model with the commensurate structure(are all rational Numbers). Three-layer model consisting of two harmonic chains of interacting particles moves over the substrate potential. When the top chain is driven by gradually increasing external driving force,the upper chain will start to move first, then the middle layer move, i.e., there exist two critical depinning forces at which the upper or the middle layer transfers from locked to the sliding state. We define two static friction force as the external driving forces at which the average atomic velocities of the upper and the middle layers reach nonzero values, respectively. There are also another two critical pinning forces at which the upper or the middle layer transfers from the sliding state to the locked one as the external driving forces decreases. We define two kinetic friction forces as the values of the external driving forces at which the average atomic velocities of the upper and the middle layers reach zero values from the nonzero ones, respectively.Dependences of two static friction forces and the kinetic friction forces on the system parameters are investigated in the present paper.