Analysis of force and wear mechanism of shield hob under conventional working conditions

In order to study the force and wear of the hob during the excavation of the composite formation, Abaqus simulation is used to simulate the stress state of the hob when breaking the rock and soil. Based on the abrasive wear mechanism, a prediction model of radial wear amount and linear wear rate suitable for a single hob is derived, and verified with actual engineering data. The results show that the normal force plays an important role in the rock breaking of the hob, and the penetration degree and the cutting edge radius are important factors affecting the normal force of the hob. When the penetration degree increases, the normal force and radial wear of the hob will increase, but the increase of radial wear will slow down due to the width of the cutting edge. Working with the “small-large-small” penetration law not only improves the boring efficiency but reduces the loss of the hob. Therefore, the study provided references for the hob wear and optimization research.


Introduction
The wear consumption of a hob is large when TBM is driving in mixed ground, and the frequency of tool changing is related to the efficiency and cost of tunnel construction.Scholars at home and abroad have achieved many results in the research of hob rock breaking.Su [1] optimized the traditional CSM model and realized the segmented solution of the force of the hob in the composite formation.Based on the Drucker-Prager constitutive model, Lian et al. [2] studied the effects of cutter spacings and rock angle on the rock-breaking efficiency of double hobs in composite formations.Gong et al. [3] used the coordinate transformation matrix method to establish a kinematic model of the rock-breaking of the working edge of the disc cutter and used Matlab software to solve the crushing trajectory diagram of the hob theory.Also, the distribution law of the arc length of the rock-breaking arc at each point of the rock-breaking edge was solved.Based on the hysteresis spring contact model, Ucgul et al. [4] analyzed the effects of the root length, tool front angle, and cutting angle of rotary tillage knife on the tensile force in sandy loam soil by using the discretization software DEM.
The research on the wear model and optimization scheme of a single hob is lacking.In this paper, by changing the active control parameters (penetration degree h), the changes of force and wear on the hob are analyzed and studied, and the relevant mathematical prediction model is established to facilitate the optimization of shield design and construction, and the accuracy is verified by engineering data.

Hob rock breaking wear mechanism
In the process of breaking rock and soil, the hob is subjected to normal, lateral, and tangential forces [5~6], as shown in Fig 1 .Among them the normal force Fn is the main force for cutting the rock soil, which is an important cause of the frontal wear of the tool ring; the tangential force Ft action is to make the blade of the hob rotate while pressing into the rock soil; the lateral force Fs is generated by the extrusion of the side of the hob by the geotechnical layer and causes the wear on the sides of the blade.The model of the Northeast Institute of Technology is used to study the force of a single-edged hob, where the normal force expression is: where h is the degree of penetration; φ is the rock breaking angle; σc is the uniaxial compressive strength; k is the rolling conversion coefficient.The wear of disc hob is mainly manifested in the form of abrasive wear.The paper cites the abrasive wear model proposed by Professor Rabinowicz of MIT [7], it is concluded: where V is the wear volume; k s is the abrasive wear coefficient; l 0 is the distance that the hard particles have crossed on the surface; σ s is the yield strength of the grinding material.
The contact distance between the hob blade and the rock and soil every time the hob rotates is: ) When the hob performs for one rotation, different degrees of wear occur on the surface, and the radial wear value [8~9] in the unit working cycle is: When the TBM needs to rotate L/h after boring a certain distance, the number of rotation turns corresponding to the ith hob is: Based on the analysis of Equations ( 1), ( 2), ( 3), (4), and ( 5), the radial wear prediction model of a single-edged disc hob can be established: The reel wire wear rate is the amount of radial wear at the unit distance of a point of rock breaking on the hob cutting edge, which is used to measure the wear resistance of the hob, and its value is: The model combines the boring distance, hob radius, tool width, and other factors to study the radial wear amount and linear wear rate of the hob so that the prediction results are more accurate.

Geotechnical material parameters
Drucker-Prager yield criterion, which can better simulate rock and soil mechanical properties, is selected in Abaqus, and rock and soil are assumed that isotropic and continuous.To reduce model calculation time, geotechnical can be considered of a cuboid of 400×600×300 mm.Mesh thinning is carried out at the contact point between the hob and the soil, material parameters of the geotechnical are shown in Table 1.

Disc Hob Model Parameters
Based on the geological conditions of the Shenzhen Fu-Che area, the diameter of the shield cutter head is 6.28 m, including 6 17-inch center double hobs, and 38 17-inch single blade hobs, for a total of 50 blades.The research object of this paper is a 17 in (1 in=2.54 cm) constant section single-edged hob, according to the tool parameters provided by the project, the outer diameter of the hob is 432 mm, the cutting-edge width is 18 mm, and the cutting-edge angle is 30°.
Because the strength of the hob ring is much higher than that of rock and soil, in the simulation process, the cutter ring is defined as a rigid body, which only interacts with the rock and soil, as shown in Figure 2.

Boundary conditions
Dynamic/Explicit is selected as the simulation method in Abaqus.The tangential contact relation is set as penalty contact (0.3), and the normal contact relation is hard contact.In addition, constraining the bottom surface and sides of the cuboid can better simulate the rock-breaking process of the hob under actual working conditions [10].
The simulation includes two analysis steps.The first step is to simulate the process of hob invading from the top of rock soil to the specified depth.The second step is to simulate rolling crushed rock to form trenches.The hob keeps rotating throughout the simulation.

Analysis of simulation results
According to the experimental study of Yang et al. [11], factors (penetration, cutting edge radius, and blade width) affect the normal force of the hob and also influence the radial wear of the hob.Firstly, taking an 8 mm penetration degree as an example, the stress of hob-breaking rock is analyzed, as shown in Fig. 3. From Fig. 3, when the hob begins to contact the rock soil, the normal force and tangential force slightly increase.With the increase of penetration, the magnitude of change has increased, and normal force reaches the peak value of 99.2 KN.When the hob is cut to 8 mm, the normal force gradually decreases to 80 KN and floats in a small range above and below.In the process, the tangential force and normal force have similar change trends over time, which are a certain proportion relationship.The lateral force is small which varies periodically between -1~1 KN.The normal force affected by the hob has an important effect on the radial wear of the hob, while the other forces have little effect on the process and are not considered for the time being.

Radial wear analysis
During hob excavation, wear occurs between the hob and the geotechnical surface, which leads to a decrease in the diameter of the hob and an increase in the width of the cutting edge [12].According to the empirical formula ( 6), the amount of radial wear is related to parameters such as the driving distance, penetration, and cutting edge width.Now we analyze the No.23 single-edged hob on the front of the cutterhead.As can be seen from Fig. 4(a), the radial wear amount of the cutter ring is positively correlated with the penetration degree.When the penetration degree is constant, with the increase of the driving distance of TBM, the radial wear of the hob gradually increases.When the radial wear amount is certain and the rock breaking depth (penetration degree) of the hob is large, the driving distance of the shield machine is short.From Fig. 4(b), the radial wear of the blade is inversely proportional to the width of the blade, and when a hob with a larger blade width drives the same distance with the same penetration, the radial wear consumption will be smaller.

Line wear rate analysis
According to Formula (7), the radial line wear rate of the hob can be calculated, and the wear parameters of single hob No. 13-33 in the Fu-Che section of the Shenzhen Rail Transit Line 11 project are selected for verification [13].From Fig. 5, the measured mean and calculated values of the line wear rate of a single hob in the Fu-Che section of Shenzhen Rail Transit Line 11 are 0.0552/0.05117mmꞏm-1,respectively, with an error of 7%.The results are close and reliable.Among them, the large fluctuation of the measured results is mainly due to a variety of factors affecting hob wear uneven in the actual construction.
As shown in Fig. 6, when the hob breaks rock from 4 mm to 12 mm, the blade width increases and the line wear rate decreases gradually, with a gentle range of only 8.7%.When the hob changes from 12 mm to 4 mm to rock breaking, the line wear rate is greatly reduced by 60%.When penetration was 8 mm and the blade width was 26 mm, two line wear rate curves intersect, and the line wear rate was 0.0393 mmꞏm-1.(1) In this paper, Abaqus finite element software is used to establish a simulation model of a single hob, analyze the stress of the hob under different penetration and wear conditions, and then explore the optimal rock-breaking efficiency of the hob under wear conditions.It is concluded that the changing trend of the hob force under different penetration degrees is similar, and the normal force of the hob is linearly related to the tangential force and the penetration degree.With the help of the model of Northeast Institute of Technology, the reliability of the simulation results is verified.
(2) Based on the abrasive wear mechanism, the prediction models of hob radial wear and line wear rate were established and verified by the engineering data of Shenzhen Line 11, and the deviation between the measured value of the radial line wear rate and the calculated value was only 7%.For gravel formations, the wear of the hob is difficult to avoid, and the size of the penetration degree can be appropriately adjusted by monitoring the radial wear amount and the width of the cutting edge at all times.In this way, the wear of the hob can be slowed down, the rock-breaking efficiency of the single hob can be improved, and the frequency of tool changes can be reduced.

Figure 1 .
Figure 1.Schematic diagram of rock breaking force of hob.

Figure 2 .
Figure 2. Numerical simulation model of hob rock breaking.

Figure 4 .
Figure 4. Relationship between radial wear and penetration degree, cutting edge width.

Figure 5 .
Figure 5. Wear rate of single hob line in Fu-Che section of Shenzhen Line 11.

Figure 6 .
Figure 6.Relationship between linear wear rate and penetration and edge width 5. Conclusions.(1)In this paper, Abaqus finite element software is used to establish a simulation model of a single hob, analyze the stress of the hob under different penetration and wear conditions, and then explore the optimal rock-breaking efficiency of the hob under wear conditions.It is concluded that the changing trend of the hob force under different penetration degrees is similar, and the normal force of the hob is linearly related to the tangential force and the penetration degree.With the help of the model of Northeast Institute of Technology, the reliability of the simulation results is verified.(2)Based on the abrasive wear mechanism, the prediction models of hob radial wear and line wear rate were established and verified by the engineering data of Shenzhen Line 11, and the deviation between the measured value of the radial line wear rate and the calculated value was only 7%.For gravel formations, the wear of the hob is difficult to avoid, and the size of the penetration degree can be appropriately adjusted by monitoring the radial wear amount and the width of the cutting edge at all