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Dynamic Friction-Slip Model Based on Contact Theory

In ultra-precision positioning equipment, the positioning accuracy is affected by the friction characteristics, especially the pre-slip stage. At present, the research on friction mainly includes contact theory and the dynamic friction process. There is no time variable in contact theory models, so they only apply to the stage of static contact, while the establishment of a friction dynamics model depends on parameter identification and cannot reflect the influence of a rough morphology and load. Therefore, neither theory can elucidate the ultra-precise slip mechanism. In this paper, maximum static friction force, tangential stiffness, and tangential damping models of contact surfaces were deduced through fractal contact theory. By substituting the contact parameters into the modified LuGre model, a dynamic slip model of the mask was established. Finally, the above model was verified by a reticle dynamic slip measurement system. The experimental results showed that in the pre-slip stage of the reticle, with an increase in the normal external load, the slippage of the reticle decreased. The theoretical value calculated by the model was basically consistent with the experimental value, and the slippage of the reticle mainly originated from the tangential deformation and relative sliding of the contact surface. With the increase in the normal external load, the proportion of the tangential deformation in the sliding of the entire contact surface was larger. For the change in slippage during different motion stages, the theoretical value was close to the experimental value after eliminating system errors such as vibration and fiber bending, which proved the correctness of the model in this paper.