Verification of self-synchronism of a nonlinear oscillatory system with double homodromy rotors

The single-mass nonlinear oscillatory system is presented. The hard characteristics of vibration springs are taken into account. Based on Lagrange Equations, the motion differential equations of the oscillatory system are set up. Based on Hamilton principle, the synchronous operation condition of the system was deduced. According to the first order approximate stability discriminance, the steady-state condition of the oscillatory system in the balance point is obtained. With MATLAB/ Simulink, the dynamic equations of the system are solved by the 4-rank Runge-Kutta algorithm and the parameter data of the oscillatory system at steady state conditions are got. Substitute the obtained steady speed value into the expressions of vibration amplitude, the synchronous operation condition and the stability condition. Then the theoretic calculated results are obtained. By comparison with the calculated results and simulation data, the accuracy of theoretic derivation is proved. Finally, the self-synchronism experiment is conducted on a nonlinear vibration test platform. Through the comparison of experimental result and simulation data, it is observed that the measured parameter data are roughly identical to the simulation results.