Study On Vibration Synchronization Transmission Theory In The Mechanical System With Circular Motion

In mining and chemical industries,the grinding and crushing of raw materials is an important part of the resource processing process,and the required crushers and mills are indispensable.Although the traditional ball mills and crushers have been applied for many years,it still can not solve the defects of low efficiency and poor uniformity of grinding particle size.Starting from the actual needs of engineering,three kinds of new mechanical structures for circular motion are proposed,namely,double rigid frames driven by two exciters,double rigid frames driven by four exciters and outer ring driven by single exciter under dry friction conditions.This paper focuses on the study of a special phenomenon in vibration synchronization theory--vibration synchronization transmission.Its expansive definition can be described as:through the vibration of the vibrating system,one or some components in the system achieve the required synchronous motion.Based on theoretical,numerical and simulation researches,theoretical conditions for achieving vibration synchronization transmission of system are obtained,and some of the research results are applied to engineering,which providing a reference for designing high frequency vibration equipment.The specific research contents are as follows:(1)Taking the dynamic model of two co-directional exciters driving double frames to realize circular motion as the research object,and analyzing the mechanism of vibration synchronization transmission.The system motion differential equations are established by Lagrange equation theoretically.Based on the average method and Hamiltonian principle,the theoretical conditions for synchronization and stability are obtained.According to the theoretical results,the amplitude-frequency response,stable state,phase relationship and corresponding motion types of the system in different resonance regions are qualitatively analyzed numerically.In the part of simulation,the Runge-Kutta algorithm is carried out to verify the availability of previous theoritical and numerical analysis results so that the theoretical reference of system structure parameter optimization design for engineering equipment is provided.(2)On the basis of the dynamic model described in last chapter,two exciters rotating in the same directions are located to the inner mass to form a new type mechanical system driven by four exciters,which can provide a theoretical reference for the realization of the larger-scale and high-power design of the circular motion high-frequency vibration mill.In numerical qualitative analyses,according to the relationships between the natural frequencies of the system and the operating frequency ωm0,the entire working interval is divided into four different resonance regions as follows:(Ⅰ)ωm0<ω2(ωΨ2);(Ⅱ)ω2(ωΨ2)≤ωm0≤ω0;(Ⅲ)ω0<ωm0<ωΨ0;(Ⅳ)ωΨ0<Ψm0,and the effects of key system parameters on system synchronization,stability,phase relationship and motion characteristics in those different resonance regions are discussed.Finally,based on simulations,the validity of the above theoretical and numerical results is verified.(3)This chapter takes the dynamic model of single exciter driving outer ring to realize circular motion mechanical system as the research object under the condition of dry friction,and discusses the effect of different dry friction coefficients on the coupled dynamics of the system in the precondition of the roller rotates against the inner wall of the outer ring.Based on the motion differential equation of the system,the theoretical conditions of the roller close to the inner wall of the outer ring are derived,and then the theoretical basis of the exciter,the roller and the outer ring for vibration synchronization transmission is obtained.In numerical analyses,the amplitude-frequency characteristics of the roller,the coefficient of the inner wall coefficient and the synchronicity of the system are discussed.Finally,the influence of different friction coefficients on the synchronous and stable states of the system is analyzed by simulations,and the validity of above theory and numerical results are verified.Through theoretical and numerical analyses on the synchronization mechanism of the system,it can provide a reference for designing a new type of vibrating grinding and crushing equipment.Finally,summaries of the paper are carried out and the researches that need to be done in the future are pointed out.