Effect of excitation frequency on nonlinear vibration of crack fault in multi-stage gear transmission system

In a multi-stage gear transmission system, the motion state of the system will change with the excitation frequency, and the frequency characteristics will also change accordingly. If this change is not taken into account, there is often a great deviation in identifying and judging system faults according to unified standards, especially when the system has such early undetectable fault as crack. In this paper, the dimensionless differential equations of motion of multistage gear transmission system are established. The stiffness model of gear tooth crack is established by potential energy method. The changes of the motion state of the system with the increase of excitation frequency are obtained by calculating the displacement bifurcation diagram of cracked gear tooth. The influences of crack fault on each motion state are studied by using time domain, frequency domain, phase diagram and Poincare cross section, and the fault frequency characteristics are summarized By comparing the theoretical and experimental data of the vibration response characteristics of the system, the motion state of the system can be effectively determined and the crack fault can be identified.