Micro Friction Mechanism Based On Fractal Contact Theory

In the ultra precision equipment such as Lithography,the contact and friction of nano rough surfaces are widespread,and will have a significant impact on the dynamic characteristics of the equipment.From the microscopic perspective,the contact surface is not smooth and flat,but there are numerous asperities with different heights.The contact and friction are essentially caused by the adhesion,extrusion,shear and other actions of many asperities on the contact surfaces,so they have complex nonlinear characteristics.At present,the mechanism of contact and friction of nano rough surfaces has not been studied thoroughly,which makes it difficult to establish a precise dynamic model in theory.This paper is devoted to theoretically studying the contact and dynamic friction characteristics of nano rough contact surfaces,establishing contact surface adhesion,maximum static friction,contact stiffness,damping and friction dynamics models,analyzing the influencing factors of various parameters,and elaborating the contact friction mechanism of rough surfaces,so as to provide a theoretical basis for the enhancement or suppression of slip of ultra precision equipment.The main research contents of this paper are as follows:(1)Aiming at the problem that the morphology characterization in traditional statistical contact theory depends on the sampling length and frequency of the measurement,the fractal contact model is established based on the f ractal theory and the elastic-plastic contact theory.Firstly,the rough contact surface is characterized based on YK model.Secondly,combined with the elastic-plastic contact theory,the contact mechanical characteristics of four deformation stages of single asperity,namely,fully elastic,1st elastic-plastic,2nd elastic-plastic and fully plastic,are analyzed from a microscopic perspective,and the normal contact load and contact area models are established.Finally,based on the density distribution function of the contact truncated area of asperities,the normal contact load and the real contact area model of the nano rough contact surface are established,and the influence of fractal parameters and contact load on the above model is analyzed.(2)Aiming at the problem that the existing static friction models of rough surfaces do not consider the influence of the scale of asperities and elastic-plastic deformation state on the adhesive force,an adhesion model is established based on the elastic-plastic contact theory;Combined with fractal contact model,the static friction characteristics of contact surface are studied.Through L-J potential function and fractal theory,the point contact adhesive force model of a single asperity is established,the expression of critical cut-off area of adhesion is proposed,and the piecewise adhesion model of a single asperity is established in fully elastic,1st elastic-plastic regime,2nd elastic-plastic regime.Based on Tersca yield condition,the maximum static friction models of asperities in fully elastic region and 1st elastic-plastic region are established.The models of adhesion,maximum static friction and static friction coefficient are established based on the density distribution function of contact truncated area of asperity,and the influence of fractal parameters and contact load on them was analyzed.Based on the contact between the reticle and the fused silica chuck of Lithography,the maximum static friction experimental system is built,and the experimental values are compared with the theoretical values of the model in this paper.The comparison results of the two groups of experiments show that the relative error of the model is reduced from37.7% and 35.0% to 13.2% and 18.2% respectively after cons idering the adhesive force.(3)Aiming at the problem that the existing friction dynamics model depends on parameter identification and cannot explain the dynamic sliding mechanism of the contact surface,based on the fractal contact theory,a theoretical model of dynamic parameters such as damping and stiffness of the contact surface is established.Based on fractal theory,elastic-plastic contact theory and Mindlin local sliding sphere contact theory,the normal and tangential contact static stiffness models of the asperity with complete elasticity,1st elastic-plastic regime and 2nd elastic-plastic regime are established.On this basis,the normal and tangential stiffness models of nano rough contact surfaces are established.Based on Sabot contact theory and Mindlin contact theory,the normal and tangential energy loss and storage expressions of each cycle of the contact surface are derived,and the normal and tangential contact damping models of nano rough surfaces are established.Based on the above model,the influence of fractal parameters,contact load and other parameters on contact stiffness and contact damping of rough surfaces is further studied.(4)Based on the dry friction contact and pre-sliding state between reticle and the chuck of Lithography,combined with the fractal contact theory,the dynamic sliding model of the reticle is established,and on this basis,the reticle sliding suppression method is proposed.First,the Lu Gre model is modified according to the contact state between the reticle and the chuck.By introducing the tangential contact stiffness and tangential contact damping parameters of the nano rough contact surface,a dynamic sliding model of the reticle is established to analysis the influence of the fractal parameters of the contact surface,material parameters and contact load on the slippage of the reticle.Based on this model,a theoretical method for reticle slippage suppression is proposed.By setting up reticle dynamic slip experimental system,the reticle dynamic slip model and slip suppression method are verified.The experimental results show that the slip curve calculated by the model in this paper has the same trend with the experimental slip curve.For different motion stages,the error range of the model is 0.1 n m to 17.2 nm;During uniform exposure of reticle stage,the slip of the reticle can be reduced from 28.3nm to 3.1 nm by reducing the equivalent contact surface roughness and increasing the surface energy.