This paper focuses on studying the correlations of the performance of hard rock tunnel boring machines (TBMs) with operational and rock conditions. Firstly, a rigid-flexible coupled multibody dynamic model of an opening hard rock TBM is established for the analysis of its vibration. Then four performance indexes including mean vibration energy dissipation rate, dynamic specific energy (DSE), disc cutter wear rate, and load sharing coefficient are introduced and formulated, respectively, for evaluating the vibration level, excavation energy efficiency, cutter’s vulnerability to wear, and load transmission performance of cutterhead driving system of the TBM. Finally, numerical simulation results of the TBM tunneling performance evaluation are obtained and validated by on-site vibration measurement and tunneling data collection. It is found that operational and rock conditions exert important impact on TBM vibration level, excavation energy efficiency, and structure damage. When the type of rock to be cut changes from soft to hard with operational parameters held constant, TBM performance evaluated by these three indexes deteriorates significantly, and both the decrease of excavation energy efficiency and the increase of cutter wear rate caused by TBM vibration are obvious. This study provides the foundation for a more comprehensive evaluation of TBM performance in actual tunneling process.
A spectral collocation approach based on integrated polynomials is presented to investigate the statics and free vibrations of Euler–Bernoulli beams with axially variable cross section, modulus of elasticity, and mass density. The basic concept of the approach is the expansion of the highest derivatives appearing in the governing equations instead of the solution function itself by the truncated basis function. Then lower order derivatives and the function itself are obtained by integration. The constants appearing from the integrating process are determined by given classical or elastic restrained boundary conditions. Also, by incorporating the decomposition technique into the present approach, higher order vibration modes can be achieved even for stepped beams. Numerical examples including the statics and free vibrations of the beams with variance in geometry or material have been successfully solved, and the results are compared with those analytical or numerical solutions in the existing literature. The convergence and comparison studies show that convergent speed is rather rapid and the present approach can yield high accurate results with low computational efforts. Furthermore, the accuracy is not particularly affected by the adopted polynomials.
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