Non-linear vibration analysis of hard rock TBMs with regenerative and stick-slip effects

The significant vibration caused by hard rock tunnel boring machines (TBMs) increases structural damage and reduces excavation efficiency and therefore has become a subject of major study within the tunnelling process. A two degrees-of-freedom model that accounts for axial and torsional vibrations that are coupled through the disc cutter-rock interaction is established in order to qualitatively analyse the complicated dynamic behaviours of the TBM system. Introducing a regenerative cutting effect into the cutter-rock interaction laws results in three interaction modes which are formulated based on the Colorado School of Mines (CSM) model. The regenerative effects and the friction caused by axial stick-slip motion are the sources responsible for the TBM self-excited vibration, of which the dynamics are described by state-dependent delay differential equations (DDEs). The DDEs are linearised and discretised into piecewise ordinary differential equations (ODEs) by using the semi-discretization method. Based on the Floquet theory, the stability limits of a TBM system are obtained, showing that the stable lobes are intermittently distributed in the operational parameter space. The parameter regime corresponding to the practical tunnelling is unstable, indicating that the vibrations of TBMs are easily excited by disturbances and never vanish in practical tunnelling. The axial vibration of TBMs with regenerative and stick-slip effects experiences a subcritical Hopf bifurcation, when the TBM goes from unstable to stable parameter regimes. The stick-slip effect suppresses the vibrations, which would otherwise increase without limit until cutter bounce appears if only the regenerative effect is considered. It is found that both the amplitude and the frequency of the axial stick-slip vibration increase with the increase in the steady advance velocity. The predicted axial stick-slip vibration and its amplitude in this investigation are both in good agreement with the observations obtained from a practical tunnelling project. This study provides reasonable insight into the vibration mechanism of TBMs and serves as a basis for choosing proper operational parameters in a practical project to achieve smooth and efficient tunnelling.