Research on Dynamic Characteristics of Split TBM Cutterhead Based on Similarity Theory

Cutterhead with disc cutters is a key component of tunnel boring machine (TBM), and its dynamic characteristics greatly influences the cutting performance of the equipment rock disc cutters. This study investigated the dynamic characteristics of split TBM cutterhead under bolted connection based on the similarity theory. A simplified and scale similarity of split cutterhead was proposed. Based on a virtual material method, a simulation model was established and its dynamic characteristic was analyzed for each block of scaled cutterhead. Dynamic testing experiments of the center block, side block and scaled cutterhead were carried out to achieve the vibration mode and frequency. The results show that the errors of the center block and side block between theoretical natural frequencies and experimental ones are less than 7%, and the theoretical mode shapes are in agreement with the experiments. Besides, the errors between experiment and simulation of the scaled cutterhead are less than 15%, and the virtual material method is verified. The similarity theory and the virtual material method would be used to investigate the dynamic characteristics of split TBM cutterhead. Introduction Tunnel boring machine (TBM) is widespread applied in urban underground, mountain railway and subway tunnels. Mechanized excavation by means of tunnel TBM becomes the most common solution for hard rock tunneling [1]. Cutterhead is a key component of TBM, which can crush and cut rock with disc cutters mounted on its panel [2]. The manufacture of the large cutterhead is divided into parts fixed by bolt welding connection. Rock breaking force of TBM hob is a dynamic process with strong mutation and randomness. The problems of cutterhead such as cutter falling off and cutterhead splitting joint cracking often occur, which are closely related to the dynamic characteristics of cutterhead. Therefore, it is necessary to study the dynamic characteristics of the cutterhead. In recent years, much work has been done on dynamic characteristics analysis of TBM cutterhead and its driving system. Ling et al. [3] proposed the sensitivity analysis method and calculation process of dynamic response of TBM cutterhead, deduced the formula of sensitivity of cutterhead vibration response to design variables by direct derivative method, and obtained the formula of priority matching each body mass of cutterhead reasonably to improve the vibration characteristics of cutterhead. Zhang et al. [2] found the TBM excavation torque may run up to a critical value and fluctuate greatly in adverse excavation environments, and a higher cutterhead revolution and a lower advance velocity can reduce the excavation torque and effectively avoid unexpected TBM stoppage. Sun et al. [4, 5] proposed direct torque control system for three-phase asynchronous motor and purely torsional dynamic model of multistage gear transmission system and established an entirely dynamic model of TBM cutterhead driving system based on hierarchical modeling method and obtained dynamic response. Liu et al. [6] reported the maximum stress of TBM cutterhead is concentrated on the central tool rest and the connection between cutter panel and support beam, and the displacement appears on the TBM edges by finite element analysis under different geological conditions and working condition. For large TBM cutterhead, due to the limitation of manufacturing, processing, transportation and other conditions, it has to be manufactured separately. The interface 428 characteristics of the cutterhead have a great influence on its structural stiffness and dynamic performance. In the study of bolted joint characteristics, Shi et al. [7] proposed a simplified shear behavior model and hysteretic criterion of high strength bolted connection, and reported that the shear behavior presents the isotropic hardening characteristics under cyclic loading. Kim et al. [8] reported solid bolt finite element model is most accurately predict the physical behavior of bolted joint structure compared to coupled bolt model, spider bolt model and no-bolt model. Liao et al. [9-10] proposed a virtual gradient material model to improve dynamic modeling of the bolted joint based on Hertz contact theory and fractal geometry theory, and reported that the theoretical mode shapes were in good agreement with the experimental mode shapes. Tian et al. [11] proposed an analytic method of virtual material hypothesis-based dynamic modeling on fixed joint interface in machine tools to improve the modeling accuracy. The results show that the errors between theoretical natural frequencies and experimental ones are less than 9%, and the theoretical mode shapes are in agreement with the experiments. However, few researches considered the effects of the split connection and bolted joint interface on dynamic behavior and vibration characteristics of the cutterhead. This paper investigated the dynamic characteristics of split TBM cutterhead based on scale similarity theory. The scaled TBM cutterhead was modeled and manufactured. Based on a virtual material method, a free modal simulation analysis of the scaled cutterhead was carried out. The dynamic testing experiments of the scaled cutterhead were carried out. The established simulation model of the scaled cutterhead was also verified. Simplified and Scale Similarity of Split Cutterhead Simplified Equivalent of Split Cutterhead Due to large diameter of split TBM cutterhead, it is too difficult and expensive to conduct the relevant experiment research. The similarity theory was introduced to investigate the dynamic characteristics split TBM cutterhead [12]. The structure of split TBM cutterhead is complex, and it has many internal ribs. It is inconvenient to manufacture when the cutterhead is scaled to smaller size, so it needs to be simplified. The simplification principles are shown in Figure 1. To facilitate the equivalent the loading, the simplified cutterhead only retains hob cutter groove regardless of the cutter. The small bosses, small holes and small ribs are removed in the scale cutterhead. Considering the equivalent of the box-type structural ribs, the 12 main ribs are retained. By changing the thickness of panel, the rib and the block connection plate, the equivalent cutterhead has the same stiffness as the original cutterhead in axial and torsional directions. Firstly, in the Workbench, the axial force of 10 5 N and axial torque of 10 5 N·m are applied to the original model to obtain force and torsional deformation along axial direction. The three parameters are optimized by the response surface optimization in Workbench. The thickness ranges of panel, rib, and plate are limited to the (288 mm, 352 mm), (45 mm, 55 mm), (126 mm, 154 mm), respectively. By the calculation, the panel thickness 320 mm, rib thickness 50 mm and plate thickness 140 mm are obtained. After the stiffness equivalent of disc panel and rib, the structure of simplified cutterhead is scaled by the similarity theory. Figure 1. Simplified equivalent of split TBM cutterhead.