摘要：To avoid anti-phase synchronization for two co-rotating rotors system that occurs so that exciting force generated by the vibrating system is very small, a mechanical model of two co-rotating rotors installed with nonlinear springs is proposed to implement synchronization in a non-resonance system. The dynamic equations of the system are first built up by using Lagrange's equation. Second, an analytical approach, the average method of modified small parameters, is employed to study the synchronization characteristics of the vibrating system, the non-dimensional coupling equations of two motors are deduced, synchronization problem is converted to that of existence and stability of zero solution for the non-dimensional coupling equations of angular velocity. It is indicated that the synchronous torque of two motors coupled with nonlinear springs in synchronous state must be greater than or equal to the difference of their residual torque. Then, in light of the Routh–Hurwitz criterion, the synchronous criterion of the vibrating system is obtained. Obviously, it is demonstrated that the synchronous state and the stability criterion of the system are influenced by the structural parameters of the coupling unit, coupling coefficients and the positional parameters of two rotors, and so on. Especially, there are clearances in between two nonlinear serial springs, which result in synchronization of the vibrating system that lies in an uncertain state. At last, computer simulations in agreement with the numerical results verify the correctness of the theoretical results for solving the steady phase difference between two rotors. It is demonstrated that adjusting the value of the coupling spring stiffness can make phase difference close to zero to meet the requirements of the strongly exciting force in engineering.
