A general nonlinear time-varying (NLTV) dynamic model and linear time-varying (LTV) dynamic model are presented for shield tunnel boring machine (TBM) cutterhead driving system, respectively. Different gear backlashes and mesh damped and transmission errors are considered in the NLTV dynamic model. The corresponding multiple-input and multiple-output (MIMO) state space models are also presented. Through analyzing the linear dynamic model, the optimal reducer ratio (ORR) and optimal transmission ratio (OTR) are obtained for the shield TBM cutterhead driving system, respectively. The NLTV and LTV dynamic models are numerically simulated, and the effects of physical parameters under various conditions of NLTV dynamic model are analyzed. Physical parameters such as the load torque, gear backlash and transmission error, gear mesh stiffness and damped, pinions inertia and damped, large gear inertia and damped, and motor rotor inertia and damped are investigated in detail to analyze their effects on dynamic response and performances of the shield TBM cutterhead driving system. Some preliminary approaches are proposed to improve dynamic performances of the cutterhead driving system, and dynamic models will provide a foundation for shield TBM cutterhead driving system's cutterhead fault diagnosis, motion control, and torque synchronous control.
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