Dynamics of Rotor–Bearing Systems Under Time-Varying Stiffness Excitation of Helical Gears

The time-varying mesh stiffness excitation of helical gears impacts the vibration state of the rotor–bearing systems, while the existence of mechanical dynamic eccentricity makes the rotor–bearing dynamics equation a system of parametric excitation. To address this situation, the time-varying mesh stiffness of the helical gear is substituted into the coupled bending–torsion–axial dynamic equation of the rotor–bearing system. By considering dynamic eccentricity, the rotor’s vibration displacement response is calculated. The unified strength theory is introduced to compute the complex stress state. The study’s results indicate that time-varying stiffness significantly influences the system’s vibration characteristics, with the equivalent stress values exceeding those under twin-shear stress. This finding demonstrates the advantage of using the unified strength theory under high-load conditions, providing an essential reference for optimizing the dynamic performance of high-speed helical gear transmission systems.