Study On The Theory Of Self-synchronization For Two Unbalanced Rotors In A New Type Of Vibrating Machinery

The self-synchronous phenomena of unbalance rotors has opened up fresh opportunities in the vibration technology, and resulted in the establishment of the vibration utilization engineering. At present, a variety of vibrating machinery has been widely used in industry, such as self-synchronous vibrating feeders, self-synchronous vibrating conveyors, self-synchronous probability screens, etc. These vibrating machines are working at far-resonant state or near-resonant state. For far-resonant vibrating machinery, its opcrating frequency is2-10times the natural frequency of the vibrating system. The far-resonant vibrating machinery has good vibration isolation usually, but at the same time the exciting force is required to be big. In addition, with the increase of materials handled, the amplitude slightly decreases. For near-resonant vibrating machinery, the operating frequency ranges from0.95to1.05times its natural frequency and the exciting force required is small, but at the same time the dynamic load passed to the foundation is very large. In addition, when the amount of materials handled departs from the designed value, the amplitude decreases greatly.This paper proposes a new type of vibrating mechanism, which consists of a material box rigid body and a supporting rigid body, and is driven by two unbalanced rotors. The two unbalanced rotors can be installed on the vibrating mechanism in two formations. In one of them, the two unbalanced rotors are installed symmetrically about a symmetric plane of the material box parallel to the vibration direction and their rotating centers are located on a symmetric axis of the material box. In the other formation, the rotational centers of the two unbalanced rotors are installed symmetrically on the symmetric line of the material box in the vibration direction and their rotational planes is symmetric about the symmetric plane of the material box perpendicular to the vibration direction. In this vibrating mechanism, the material box exhibits four degrees of freedom, i.e., three translation motions and a swing about the vibration direction, while the supporting rigid frame exhibits one degree of freedom, i.e., translation in the vibration direction. In order to reduce the influence of the vibration on the foundation, the vibrating mechanism can be isolated by a vibration isolation frame. When the operating frequency is less than the natural frequency of the system in the vibration direction, the amplitude of vibration of the vibrating mechanism increases with the amount of materials handled, which meets the production line to the requirements of the variable feed. Combined with numerical analysis and computer simulation, the theory of self-synchronization for such vibration systems are studied in this paper. The works in this paper are described as follows:(1) Using the Lagrange’s equations, the paper develops the equations of motion for the vibrating systems in the two formations and their vibration isolation system. For the equations of motion for the vibration isolation system, the analytical solutions are derived by means of the transfer function method.(2) The theory of self-synchronization of such vibrating systems is studied. The dimensionless coupled equations of the two unbalanced rotors are derived by introducing the fluctuation coefficients of the two unbalanced rotors’ angular velocity and the phase difference between them. Then the conditions of implementing synchronization vibrating systems are obtained by the zero solutions of the dimensionless coupled equations. At last, the conditions of stability are derived by using the Routh-Hurwitz criterion.(3) The synchronous ability coefficient of such vibration system has been defined. The relationship between the synchronous ability coefficient and the system structure parameters is analyzed by the numeric methods, and the stability of such vibrating systems under operating synchronous is verified.(4) The computer simulations about such vibrating systems are carried out to verify the theories afore-mentioned.