Purpose <p>The traditional vibrating screen has the defect of large reference vibration mass, which leads to the increase of the excitation force required by the vibrating screen and the increase of the power consumption of the motor, and due to the increase of inertial force, it has a large impact on the structure of the vibrating screen, which reduces the vibrating screen life. Therefore, a double eccentric wheel-driven elliptical vibrating screen is proposed and a series of theoretical derivations are carried out.</p> Methods <p>In the paper, the differential equations of motion of the vibrating screen system are derived using Lagrange's equation, and its steady state solution is obtained by the Laplace transform, which in turn obtains the steady state response of the vibrating system in the direction of each generalized degree of freedom. Then the synchronization conditions and stability conditions of the vibration system are derived based on Hamilton's principle, and the effects of each parameter on the self-synchronization and stability of the system are discussed by selecting suitable parameters and applying the control variable method to a single parameter. Finally, Matlab/Simulink is used to verify the results of the above numerical analyses, and the system motion characteristics such as the swing angle of the screen box, the phase difference, and the motion trajectory of the center of mass are observed.</p> Results <p>It is concluded that motor torque difference, rotational speed, eccentricity, screen box mass and support spring stiffness affect the self-synchronization and stability of the system.</p> Conclusion <p>The results indicate that the device is theoretically effective and conforms to the vibration law of the vibrating screen, thus meeting the conditions for experimental operation.</p>