Nonlinear Dynamics and Primary Resonance Characteristics of Spiral Bevel Gear Systems

This paper investigates the nonlinear vibration characteristics of spiral bevel gear transmission systems. A dynamic model was established by incorporating key nonlinear factors, including bearing support forces, time-varying mesh stiffness, gear backlash, mesh damping, and static transmission error. The system’s vibration differential equations were solved using the Runge–Kutta method. The nonlinear dynamic behavior under varying parameters was analyzed through time-domain waveforms, frequency spectra, phase portraits, Poincaré sections, bifurcation diagrams, wavelet time-frequency plots, and Lyapunov exponent spectra. Employing the multiscale method, the primary resonance equation was derived to examine the influence of mesh damping, mesh stiffness, and external load fluctuations on the system’s primary resonance characteristics. The results indicate that spiral bevel gear systems exhibit significant nonlinearity. As the excitation frequency or static transmission error increases, the system transitions from periodic to chaotic motion. Conversely, increasing the driving torque can shift the system from chaotic to periodic motion. To ensure transmission stability and reliability, relevant parameters must be carefully optimized.