Coupled vibrations are difficult to overcome in automatic transmission with mixed gear trains. In this study, a mathematical model for the bending–torsional–axial–oscillation vibrations of mixed gear trains with parallel-axis gear pairs, a clutch, planetary gear sets and a shaft rotor was developed using the concentrated mass method. The dynamic vibration response and transmission error of the meshing gears in different gears were analysed. The response sensitivity of the vibration parameters was obtained using the design coupling function of the peak–peak dynamic transmission error. The degree of coupling of each part with system vibrations was analysed and it was found that the stiffness and damping of gears influenced the coupled vibrations. Finally, the top seven degrees of coupling were obtained, the first two contributions were taken as the target to improve, the thickness of the P1 gear ring was increased by 5?mm and the bushing was added between the P2 planetary and sun gear to increase the stiffn...
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