Stability of a Multiple Rigid Frames Vibrating System Driven by Two Unbalanced Rotors Rotating in Opposite Directions

The synchronization and stability of two unbalanced rotors (URs) separately driven by induction motors rotating in opposite directions, in a new mechanism system with four rigid frames (RFs), are investigated in present work. Applying Lagrange's equation, the differential equations of motion of the system are deduced. The criteria of synchronization and stability of the synchronous states are derived analytically by using the average method and Hamilton's principle, respectively. Based on the theoretical results, the coupling dynamic characteristics of the system are given by numeric, it is shown that the abilities of synchronization and stability, are the best under the condition that the parameters of the system are completely symmetrical. The stable states and the corresponding motion types of the system in different resonant regions, are clarified in detail. A Runge-Kutta simulation routine is employed to verify the validity of the theoretical results, as well as the feasibility of the used theory method. The selecting principle of the stable region with zero phase difference for the two URs, can provide a novel reference for designing a new type of vibrating feeder with the anti-blocking function in engineering.