Abstract: Spiral bevel gears are characterized by their high transmission ratio, strong load-carrying capacity, and operational stability and reliability, 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 gear pair transmission system can provide a valuable reference for the design, manufacturing, and application of spiral bevel gears. This study first undertakes a thorough consideration of key nonlinear factors within a spiral bevel gear transmission system, specifically including bearing support forces, time-varying mesh stiffness, tooth side clearance, meshing damping, and static transmission error. Based on this comprehensive analysis, a dynamic model of the system was subsequently established. Following model development, the system's vibration differential equations were then solved utilizing the Runge-Kutta method. The nonlinear dynamic behaviors of the system under the influence of a range of varying external excitation amplitudes were then systematically analyzed through multiple methodologies. This comprehensive analysis employed time domain diagrams, frequency domain diagrams, phase diagrams, Poincaré section maps, bifurcation diagrams, wavelet time-frequency diagrams, and corresponding Lyapunov exponent diagrams. Finally, a dynamic characteristic verification platform specifically designed for the spiral bevel gear transmission system was constructed. Thereafter, experimental signals were systematically compared with numerical simulation results, thereby rigorously 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.