Abstract: Spiral bevel gears are characterized by their high transmission ratio and stable, reliable operational performance, making them extensively applicable in high-speed, heavy-duty fields such as aerospace and aviation, the automotive industry, and precision engineering machinery. Investigating the nonlinear dynamic characteristics of the spiral bevel gears pair transmission system provides valuable reference for the design, manufacturing, and application of these gears. This study first comprehensively considers key nonlinear factors including bearing support forces, time-varying mesh stiffness, tooth side clearance, meshing damping, and static transmission error, establishing a dynamic model of the spiral bevel gears transmission system. The system's vibration differential equations were subsequently solved utilizing the Runge-Kutta method. The nonlinear dynamic behaviors of the system under the influence of varying external excitation amplitudes were then analyzed through multiple methodologies. These analyses employed time domain diagrams, frequency domain diagrams, phase diagrams, Poincaré section diagrams, bifurcation diagrams, wavelet time-frequency diagrams, and Lyapunov exponent diagrams. Finally, a dynamic characteristic verification platform specifically for the spiral bevel gears transmission system was constructed. Experimental test signals were systematically compared with numerical computation results, thereby validating the accuracy and effectiveness of the proposed modeling approach. The research findings conclusively demonstrate that as the external excitation amplitude increases, the system's motion state undergoes a distinct evolution. It transitions progressively from a chaotic motion state to a period-doubling motion state, and ultimately stabilizes into a single-period motion state. This progression indicates that an excessively low external excitation amplitude readily induces the system into an undesirable chaotic motion state. Conversely, appropriately increasing the external excitation amplitude proves highly effective in enhancing the operational stability and reliability of the transmission system.