Ye Zhu， Xulong Wang and Xiangyu Chen

（School of Mechanical Engineering, Dalian Jiaotong University, Dalian 116028, China）

Abstract: A comprehensive performance evaluation method for the tunnel boring machine(TBM)cutterhead is proposed in this paper. The evaluation system is established on strength and vibration. Based on fracture mechanics theory, fatigue strength evaluation indices are determined under critical crack length. The concept of crack regions division is proposed to evaluate fatigue strength more accurately and specifically. In addition, the velocities in three directions of critical locations are obtained with dynamics equations. Then, the root-mean-square values of velocities are taken as the vibration severity indices. Taking the cutterhead of Jilin diversion engineering as an example,the evaluations of each index are completed; then, the vibration of the TBM cutterhead is measured and compared with the theoretical calculation results. There are similar change laws between the theoretical calculation results and the testing results of the cutterhead acceleration, which proves that the method of calculation of the vibration index is effective, the reliability of the cutter saddle welding should be paid attention to when the TBM is working, and the condition of vibration severity of the TBM cutterhead meets the requirements but needs to be improved.

Key words: cutterhead evaluation；fatigue strength；vibration severity

As a key component of a full face rock tunnel boring machine (TBM), the cutterhead plays the roles of crushing rock and stabilizing the tunnel face, which affects the boring performance and efficiency of the whole machine[1]. A great number of scholars have conducted research on the design of the TBM cutterhead system.Samuel[2]studied the variation law of cutter load with site testing on a Robbins cutterhead whose diameter was 4.1 m, comparing and analyzing Pressure Balance Shield Machines, Opening Tunnel Boring Machines, Single Shield TBMs, and Double Shield TBMs with the TOPSIS. A calculation model of the cutterhead’s specific energy[3-4]was created for evaluating the energy consumption of a tunnel machine by Cai Zongxi and Kang Yilan. Sun et al.[5-8]studied the simulation process of rock fragmentation with multi-cutters and space design. Moreover, based on genetic algorithms and collaborative evolutionary reinforcement learning, the plane layout design methods of disc cutters were proposed, and the optimal design for the master parameter of cutterhead structures and support ribs was processed.

Besides these theoretical and empirical models, soft-computing methods have been used to predict the rate of penetration. Grima et al.[9]utilized a neuro-fuzzy method for TBM performance prediction. Benardos and Kaliampakos[10-11]utilized artificial neural networks (ANNs) for prediction of TBM performance. Zhao et al.[12]introduced a neural network-based model to predict the performance of TBMs. Acaroglu et al.[13]introduced a fuzzy logic model to predict specific energy requirement for prediction of TBM performance. In another attempt by Yagiz[14], two nonlinear prediction tools (ANNs and non-linear multiple regression) were presented for the estimation of TBM performance. Torabi et al.[15]investigated two main elements of TBM performance, including the rate of penetration and utilization factor, using ANN and regression models.Ghasemi et al.[16]developed a fuzzy logic model to predict the penetration rate of hard rock TBMs based on rock properties.

As mentioned above, scholars have studied rock fragmentation mechanisms, force models of disc cutters, stochastic loads of excavation, disc cutters’ plane layouts and so on, using the methods of similar model experiments, numerical simulations and field tests. However, the study of TBM cutterhead performance evaluation is still uncertain, lacking systematic and comprehensive theoretical approach, and especially lacking industry evaluation criteria. Therefore, this paper builds a multi-hierarchy evaluation system of TBM cutterhead and completes the evaluation of the each index individually, which provides an effective foundation for improving driving speed,prolonging cutter life and reducing mining costs of TBMs.

1 Performance Evaluation System of TBM Cutterhead

1.1 Performance evaluation model of cutterhead

In order to establish a good performance evaluation system of cutterheads, scholars have toured construction sites and enterprises to study situations of breakage in the construction, and the requirements and difficulties in the manufacturing of TBM cutterheads. It was found that the cutterheads had intense vibration and the cutter abrasion was terrible. Furthermore, a large number of cracks appeared on the surface of cutterhead, along with cutterhead local distortion.As a result, this paper establishes a multi-hierarchy evaluation system taking fatigue strength and vibration severity as indices as shown in Fig.1.

Fig.1 Performance evaluation system of TBM cutterhead

1.2 Vibration index

Excessive vibration can damage equipment,reducing its application and shortening its life.Vibration severity is recognized as the index of evaluating vibration. However, the vibration at various locations is different, so to evaluate vibration more accurately, this paper derives dynamic equations using mode superposition method and finite-element method to obtain situations of various locations. The specific idea is shown in Fig.2.

1.2.1 External excitations of TBM cutterhead system

Due to complicated geological environments,a 3D simulation model with multi-cutters is established under typical geological conditions based on the procedure of LS-DYNA. Then, the dynamic loads between the disc cutters and the surrounding rock are obtained, which are modified according to the field data[2]. Consequently,the total load of the TBM cutterhead system is calculated by summing the individual force of each cutter, which can be external excitations of the dynamics model.

Theoretically speaking, the disc cutters suffer normal forces Fv, tangential forces Fr, and side forces Fswhen the cutterhead rotates, as shown in Fig.3, where ρ is the radius from the center of the cutterhead, θ is the position angle of cutters, and β is the tilt angle of the gauge cutter. For the convenience of load calculation,the following assumptions are formulated:

① The total load of cutterhead is equal to the resultant force of each disc cutter, ignoring the losses in transfer process.

Fig.2 Calculation process of vibration intensity

Fig.3 Forces of the cutter

② Considering the complexity of actual rock breaking load, the mean normal force is equal to nominal load of the disc cutter, and it is 0.15 times the mean tangential force and 0.1 times the mean side force[2].

Calculating formula of the three-direction load of the center cutter:

Calculating formula of the three-direction load of the face cutter:

Calculating formula of the three-direction load of the gauge cutter:

1.2.2 Multi-degree of freedom dynamics equations of TBM cutterhead

To evaluate the situations of vibration more accurately, the dynamics equations are established by the finite element method and the mode superposition method. The situations of various locations are obtained, which lays a foundation for analyzing subsequent dynamic characteristics, parameter sensitivity, and many influence factors in the future work. The process is shown in Fig.4.

Fig.4 Calculation process of vibration response

1.2.3 Vibration severity model of TBM cutterhead

For evaluating the vibration situation more accurately and specifically, the vibration severity model of a cutterhead is defined as the average of vibration severity of each element that is most likely to fail because of vibration on the cutterhead.

VxDi, VyDi, and VzDiare each element’s vibration velocity in three directions of the locations prone to vibration failure on the cutterhead.

1.2.4 Locations prone to vibration failure on the cutterhead

Vibration causes a series of points of damage to the TBM cutterhead in practice, as shown in Fig.5.

Through analysis of statistics of TBM cutterhead failures in the engineering field, the locations most vulnerable to vibration failures include the bolted flange and the gauge cutter saddle, so they are taken as the checking positions.

1.3 Intensity index

Strength is the ability to resist damage under load. The shapes of parts change under external load; the parts are broken when the load exceeds a certain limit. The parts should have the ability to bear the load in order to ensure machine work.

Through statistics and analysis for failure of TBM, it is found that fatigue is the main failure mode of TBM cutterheads. The failure of TBM cutterheads is due to cracks. A crack region division method is proposed. Then the structural forms of regions in which cracks appear are measured and counted, and the breaking loads of different parts in the cutterhead are obtained by the LS-DYNA simulation, which is incentive load. The dangerous regions are divided according to the differences in stress and structure; a fatigue strength evaluation model is created based on Paris crack propagation criterion, which takes critical crack as evaluation criterion and takes crack fatigue damage accumulation as basic variable. To estimate the degree of reliability of the cutterhead, the TBM cutterhead of the Jilin water diversion project has been taken as an example.

Fig.5 TBM cutterhead’s engineering failures

① Divide the crack damage regions of the cutterhead based on the crack region division method

A number of cracks will arise on the surface of the cutterhead after a period of time because of space multi-point impact load in tunneling. It is found that the frequency of cracks appearing in the cutterhead and the fatigue crack growth rate are different owing to different stresses and structures of TBM cutterheads. The crack region division method is proposed in order to evaluate cutterhead fatigue and strength more accurately; the process is shown in Fig.6.

Fig.6 Division process of crack failure region of TBM cutterhead

The frequency, size, and locations of cracks that appear on the TBM cutterhead are estimated by nondestructive detection. Then the locations which are more likely to crack are analyzed and summarized.

Rock breaking of center cutters, face cutters,and gauge cutters is simulated by LS-DYNA to obtain the load time history, which is used as an external load to analyze dynamic stress distributions of the TBM cutterhead.

The regions that develop cracks are divided according to the different stresses and structures,to be treated differently.

② A model for calculating the fatigue strength of TBM cutterhead

Combined with the Paris criterion to describe the state of crack propagation, a fatigue strength calculation model is created according to the actual situation of TBM cracks, which takes crack fatigue damage accumulation as a basic variable. Because the behavior of fatigue crack growth is characterized by a strong uncertainty,crack length distribution is assumed to obey a normal distribution according to J.N.Yang[17-18],as is shown in Fig.7. Then, the TBM cutterhead fatigue strength calculation equations are created.

Fig.7 Model of crack length interference

The limit state equation for the crack length model of a TBM is

where ψ(ac,a0) is fatigue cumulative damage from the initial crack size value a0to the critical value of ac. ψ(aN,a0) is fatigue cumulative damage from the initial crack size value a0to aNafter N stress cycles.

Based on linear elastic fracture mechanics,the limit state equation of fatigue fracture reliability can be expressed as[19]

where C, m are material parameters; Y is random vector; S is stress amplitude; F is shape function.

When fatigue failure occurs, g(X)≤0. The calculation model of fatigue fracture reliability of components is

2 Engineering Project

The Jilin water diversion tunnel project has been taken as an example to verify the indices of the TBM cutterhead above.

2.1 Index of vibration severity

2.1.1 Calculation of external excitations

Based on the field data and simulation load of rock breaking under the action of multi-cutters, the load time histories of three types of cutters (center cutters, normal cutters, and gauge cutters) can be obtained combined with the above assumptions, partially as shown in Fig.8.

2.1.2 Vibration response of TBM cutterhead

A TBM cutterhead model is established in ANSYS workbench. Eight-order vibration models of the TBM cutterhead are solved as shown in Fig.9.

As shown the results above, the first eightorder natural frequencies are 51.6 Hz, 52.6 Hz,68.2 Hz, 76.3 Hz, 81.5 Hz, 82.8 Hz, 90.5 Hz, 93.8 Hz,and the eight-order model of each node can be obtained by ANSYS workbench.

Both sides of the contact between each cutter and the cutter mousing are taken as input points of external load. The corresponding element number is searched in the ANSYS workbench. Take the first six cutters as an example,as shown in Tab. 1.

Through above analysis, the vibration severity of the welding point of the cutter saddle and the bolted flange can be calculated on the basis of Eqs.(4)(5), as shown in Tab.2.

According to the international vibration intensity standard[20], the condition of vibration severity of the TBM cutterhead meets the requirement but needs to be improved.

2.2 Fatigue strength index of TBM cutterhead

2.2.1 Crack region division of TBM cutterhead in Jinlin tunnel

① Statistics information of TBM cutterhead cracks

Fig.8 Load time histories of three types of cutters

Fig.9 TBM cutter disc eight-order vibration model

Tab. 1 Number of excitation elements

Tab. 2 Vibration severity calculation results of Jilin water diversion TBM cutterhead

The situation of the crack failure and the section where the cracks easily exhibit are collected. The data is shown in Tab. 3.

According to the statistics, the main failure modes include cutterhead dislocation, center segment damage, gauge segment fracture, cutterhead deformation, cutter saddle loss, cutter saddle deformation, cutter fracture, and mucking slot failure.

② The stress conditions on various locations of cutterhead are defined by FEM.

This paper applies transient dynamics to the TBM cutterhead of the Jilin tunnel to perform stress analysis by taking the three-direction stress of cutters as the input conditions. The multipoint distribution stress of the cutterhead is calculated and the mean of the stress time history is solved, as shown in Tab. 4 and Fig.10.

③ Crack regions division of TBM cutterhead

Based on the data above, the crack-prone regions of the TBM cutterhead are divided by combining the different stress situations and structure characteristics of each part, as shown in Tab. 5.

2.2.2 TBM cutter stress amplitude statistics

The stress distribution is obtained with the rain-flow counting method to count the stresstime history of each location. As an example, the stress-time history of the edge plate is shown in Fig.11a. The stress amplitude distribution is obtained from the statistics, which is taken as an input condition to calculate cutterhead fatigue strength, as shown in Fig.11b.

From the results, it is known that the stress distribution of the edge plate obeys a normal

Tab. 3 Failure data of cutterhead

Tab. 4 Stress mean of each region

Fig.10 Force situation of cutterhead by ANSYS simulation

Tab. 5 TBM cutterhead risk regions division

Fig.11 Stress amplitude distribution statistics

distribution. The mean and variance of the stress distribution are calculated with Matlab. The results are μΔσ=82.2 MPa and σΔσ=14.8 MPa. Similarly, the results of other locations are shown in Tab. 6.

2.2.3 Calculation results

The reliability of each region of the five fraction TBM cutterhead in the middle Jilin water diversion project is 2 000 000 stress cycles. 2 000 000 stress cycles of the cutterhead are converted into the accumulation working time of the cutterhead,as follows

From the parameters of the TBM cutterhead system, it is known that the cutterhead speed ω=6 r/min, the penetration rate p=10 mm/r,and the driving speed V=1 mm/s. Changing thecrack growing time into kilometers:

Tab. 6 Each region sensitive site of cutterhead stress

The reliability of each region of the TBM cutterhead in the middle Tianshan tunnel when the TBM has driven 4 km is shown in Fig.12.

Fig.12 Each region reliability of TBM cutterhead when stress cycles are 2 000 000 times

The calculation results basically match with empirical observations when the TBM has driven 4 km.

3 Experimental Verification

3.1 Detection objectives

In order to verify the vibration response results of the TBM cutterhead, the vibration condition of the Jilin TBM cutterhead is measured and compared with the results of the calculation.Then the dynamics model is verified to have reliability and validity.

3.2 Sensors selection

Considering the hard working conditions of the driving site and the limited space for installing detection equipment, it is not effective to lay out the lines of detection devices. In addition to the difficulty and accuracy problem of displacement and speed signal detection on the TBM cutterhead, wireless acceleration sensors are chosen to detect three-direction accelerations of TBM cutterhead. The technical parameters of the sensors are shown in Tab. 7.

Tab. 7 Technical parameters of the wireless acceleration sensors

3.3 Detection scheme construction

Considering the actual operating mode of TBM cutterhead, the sensors must be installed in a closed space to avoid the damage from the rock slag. Therefore, the acceleration sensors are put in the inner space of TBM cutterhead, and the three-direction vibration acceleration signal of the cutterhead is transmitted to a computer by sensor nodes and a receiving gateway. Finally,the data acquisition software records and stores the information. The vibration test schematic of the TBM cutterhead is shown in Fig.13a, and the layout of the sensors is shown in Fig.13b.

Fig.13 Data acquisition of cutter head vibration

3.4 Comparison between testing data and theoretical results

To verify the dynamics model mentioned above, the acceleration of the cutterhead is collected from the excavation site. After eliminating the effect of gravitational acceleration, the stable theoretical calculation results after 2 s are obtained. The comparison between the two results is shown in Fig.14.

Fig.14 Comparison between the actual and theoretical results of cutterhead accelerations

It can be known from the above comparison and statistical results:

① There are similar change laws between the theoretical calculation and the testing results of the cutterhead’s acceleration. A high degree of match between them shows that the calculation method of vibration response is practical and valid to some extent.

② In the theoretical calculation and the statistical results of the rain flow counting of the three-direction accelerations of the cutterhead,there is a certain error in the mean value of the amplitude. The longitudinal acceleration error is the largest, at 39%. Axial error is the smallest,only 7%. The mean square error of longitudinal acceleration amplitude is also the largest, which is 55%, while the transverse and axial are smaller, at 8% and 12%, respectively.

③ Considering the complexity of the TBM cutterhead structure and hardness of the driving environment, a lot of actual factors cannot be considered when establishing the dynamics model. There are some inevitable errors between the theoretical calculation and testing results, but basically they remain on the same order of magnitude and their change laws are similar. The calculation method has theoretical and practical guiding significance on the structure design and site operation of the cutterhead.

4 Conclusions

This paper has presented a multi-level evaluation system of TBM cutter performance, and takes the cutterhead in the Jilin water diversion project as an example. The specific conclusions are as follows:

① Through the failure statistics of the TBM cutterhead driving site and the calculation results of cutterhead stress distribution with ANSYS, according to the different structure of positions that have cracks and different force conditions of cracks, the TBM cutterhead is divided into different dangerous regions where cracks may appear. Based on the actual engineering situation at the Jilin water diversion project, the TBM cutterhead has been divided into 10 regions, such as the fission junction and the support rib.

② With the stress amplitude distribution and crack parameters of each region on the TBM cutterhead, the fatigue strength of each region was calculated with a Monte Carlo simulation of the cutterhead reliability. After converting the time into path length, the responsibility when the TBM was driven 4 km was matched with the calculation results. The fatigue strength reliability of the cutter mousing welding is 38.37%, making it the most likely to be a failure area. Measures should be taken to control the length of the crack during construction.

③ The dynamics equations of the cutterhead were established, and the dynamic response was solved by the modal superposition method.The dynamics equations were verified by the comparison between the calculation results and the vibration collected from Jilin project. The vibration condition of the cutter mousing welding and the connecting point of the flange bolts was used as the vibration intensity of the cutterhead.The results showed that the vibration intensity of the two places was 4.3 mm/s and 3.2 mm/s,respectively. Therefore, the vibration intensity of the cutterhead can meet the requirements.

④ A metal structure fatigue calculation model of the TBM cutterhead is established in this paper. But in the process of modeling, the influence of the welding system on fatigue failure was not considered. Currently, most calculation models of crack propagation life are established on the basis of linear fracture mechanics, so they need to be further researched.

⑤ In this paper, the performance of the cutterhead is evaluated using vibration and fatigue,mainly from the quality of the cutterhead. If the comprehensive performance of the cutterhead is further evaluated, the driving efficiency and slag discharge capacity of the cutterhead need to be supplemented.