Thin-walled spiral bevel gears are critical components in the accessory transmission system of aviation engines. Due to their high rotational speeds and wide operational range, these gears frequently experience nodal diameter vibrations within the operating speed range, which pose a threat to the health and functionality of the entire transmission system. Therefore, identifying dangerous vibration modes within the operating speed range and implementing appropriate vibration reduction measures are of paramount importance. Based on the results of modal analysis and transient response analysis, the forced response model is established in order to evaluate the dangerous mode. Considering the principle of friction energy dissipation, the equivalent parameters are derived to modify the forced response model, and the response amplitude after the addition of the damping ring is obtained. A high-speed spiral bevel gear dynamic stress experiment platform is constructed to validate the accuracy and effectiveness of proposed model. This study provides a theoretical foundation for identifying dangerous vibration modes and utilizing ring damper for vibration reduction of thin-walled spiral bevel gears in the field of aviation engines.