Study On The Theory Of Self-synchronization In A Resonant And Non-resonant Combined Vibrating System

In engineering, the mechanical system driven by two or more motors need generally cooperate to complete uniform task, so that the synchronization characteristic of the machine is realized, and the technics purpose is reached. It is necessary to research the vibration synchronization theory. Therefore, the further study should be done to investigate the dynamics characteristics of the synchronous vibrating system and to provide theoretical basis for the design of this sort of system by using the theory of electromechanical coupling. In the field of vibrating mechanical, the near-resonant mechanical has a significant advantage which is the exciting force required is small, but the non-resonant mechanical has a simple structure and good vibration isolation performance usually. At present, there has little research about to achieve resonance vibration and non-resonant vibration combination in a same vibration machine. In this paper, a new combination of resonance and non-resonant vibration system was advanced, which can achieve spatial motion. Specifically, it is to do similar to a circle non-resonance vibration in the horizontal plane, and do linear vibration near resonance in the vertical direction. The vibration system’s oscillation amplitude in y-and z-direction can be changed by adjusting the angle between the rotating plane of eccentric rotors and the horizontal plane, which can meet the different techniques requirements in engineering. The theories of self-synchronization for vibration system and dynamic characteristics are studied in this paper. The works in this paper are described as follows:(1) Equations of motion of vibrating system with single mass and dual-mass were established, according to Lagrange’s equations. And solutions of coupling motion differential equations were obtained with the transfer function method.(2) The theories of self-synchronization of vibration machine with single mass are studied. Taking the fluctuation coefficient of the average value of two eccentric rotors’ angular velocity and their phase differences’ fluctuation coefficient as variable, the equations of frequency capture is derived by kinetic analysis, and the conditions of the frequency capture are obtained. At last, the condition of stability is recieved by using the Routh-Hurwitz criterion.(3)The theory of self-synchronization of the resonance and non-resonant combined vibration system with dual-mass was studied with an improved average small parameter method. Through introducing the fluctuation coefficients of two eccentric rotors’ angular velocity, and these two fluctuation coefficients is considered to be small parameters, the synchronization problem of the vibration system is transformed into the solutions of the frequency capture equation is exist or not, and the generalized system of these two small parameter is stable or not.(4)The coupling dynamic characteristics of the vibration system are discussed. Including coupling load torque of two motors and coupling moment of inertia of two eccentric rotors, which revealed the internal factors of vibration system realized self-synchronization.(5)The computer simulations are carried out to verify the results of the theoretical analysis afore-mentioned by using VC++and Origin7.0.