Main influencing parameter screening for the overall dynamics response of a planetary transmission based on a grey relational analysis

• A nonlinear lateral-torsional coupling dynamics model is developed. • A grey relational analysis is proposed to screen the main influencing parameter for overall dynamics response. • The innovative method is verified by tooth profile manufacturing error calculation. As high-speed, heavy-load planetary transmissions are realised, dynamics responses are becoming increasingly demanding. To reduce vibration, multiple components must have overall dynamics optimization under different working conditions, for which main influencing parameter screening is key. Here, a nonlinear lateral–torsional coupling dynamics model is established and verified with experimental data for a single-stage planetary transmission that considers nonlinear factors. Regarding the vibration displacement of a ring gear, the absolute relative errors between the experimental and simulated conditions are below 10% under three working conditions. For the vibration acceleration of a bearing, the corresponding absolute relative errors are below 18%. Based on this dynamics model, the defect of sensitivity analysis on main influencing parameter screening for overall dynamics response is discussed, and a new method based on a grey relational analysis (GRA) is proposed to screen the main influencing parameter for the overall dynamics response under different working conditions. Transmission errors are considered for law exploration and method verification. The tooth profile manufacturing error between the sun and planet gears is the best parameter for reducing the overall x -direction vibration displacement of the studied planetary transmission. This method can also be used to avoid separate overall dynamics optimizations for different design parameters.