Hierarchical modeling method and dynamic characteristics of cutter head driving system in tunneling boring machine

• A generalized hierarchical modeling method of the complex systems is proposed.
• A fully coupled dynamic model of the TBM cutter head driving system is established.
• The modal characteristics and their parameter sensitivities are studied.
• Dynamic responses of the driving system under two load conditions are investigated.

Traditional modeling method is difficult to establish the fully coupled model of the cutter head driving system in tunneling boring machine (TBM) owing to the structural complexity. In this paper, a generalized hierarchical modeling method is proposed to establish the entirely dynamic model of the TBM cutter head driving system. The components are equivalent to beam element with the same mass and stiffness characteristics, and the nonlinear coupling factors such as time-varying mesh stiffness, transmission error and gear backlash of both the multiple pinions driving and planetary gearbox are considered. The overall dynamic equation is formed by assembling the unit matrixes of basic finite elements according to the coupling relationships. Based on the proposed model, the vibration modes of driving system are classified into axial modes, rotational modes and lateral modes with distinct characteristics. The effects of coupling parameters on the natural frequency of driving system are investigated as well. The dynamic model is also simulated to analyze the dynamic response of driving system under two load conditions, cyclic external loads and simulated external loads. The main response frequency components and the effect of damping coefficients on vibration amplitudes are investigated. The proposed modeling method can be generalized to other complex driving system, and the obtained results provide data support for the dynamic design of driving system in TBM.