| Friction-induced vibration exists in the machines and engineering systems. The phenomena such as steady-state error, and limit circle have already become a serious obstacle that impedes the efficiency of the system. Therefore, the research on dynamics of mechanical system with friction is becoming a difficult point in the current times. Based on the above research question, the article has made the following content.In this thesis, first, based on the physics characteristic of friction on the static and dynamic properties is explained. By analyzing the established simple model, the reason and influence factors for Creeping are obtained.In considering the friction factors, the sliding stability of the mechanical systems at steady sliding is investigated. Through the simplified three-degree-freedom belt transmission model, based on the lagrange equation, the nonlinear differential equation of motion is established. Using the linear of the non-linear dynamics equations and the linear stability theorem, the sliding stability of the three-degree-freedom belt transmission system is analyzed. First based on the Coulomb friction law, the stability of steady sliding of a three-degree-freedom belt transmission model is studied; on the basis of above all, the three-degree-freedom belt transmission system is analyzed based on the velocity-dependent friction law, and the influence of the stability of steady sliding system with the variation of the friction force characteristics is considered, the influence factors for affecting the instability of the system are studied. Second in considering the LuGre type friction law, the sliding stability of the three-degree-freedom belt transmission system at steady sliding is investigated, the influence of the rate-dependent effects of LuGre type friction on the system is studied mainly. By the simulation of a simplified three-degree-freedom belt transmission model, the useful conclusion for the reference ofengineering is obtained.
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