Experimental Verification of Torque Calculation Method for Shield Screw Conveyor

The normal function of the shield spiral dumper has an important impact on the safe and efficient tunnelling of EPB shield, and the driving torque is the key decisive parameter that determines whether the spiral dumper can function normally. On the self-designed and commissioned manufacturing model test platform, the indoor reproduction test of EPB shield screw conveyor slag simulation was carried out. The theoretical calculated values were highly consistent with the test results, and the average relative error of the three tests was 8.65% to 9.18% at 6 rpm. The average relative error after entering the steady state was 4.6%, and the maximum relative error was 8.9% at 15 rpm. Through the shield model screw conveyor laboratory test, the correctness and validity of the proposed shield screw driving torque calculation model were verified and the proposed theoretical calculation method has good practical application. It is obvious that this calculation method has sufficient validity in the design of shield screw device.


Introduction
Shield screw conveyor has been widely used in the test of soil conditioning scheme.Due to the low fluidity and high water permeability of sandy muck, Vinai et al. (2008) [1] mixed medium sand with different amounts of silt, then conditioned it with a foaming agent solution and carried out an indoor model screw conveyor experiment.In order to understand the mechanical properties of the conditioned sandy muck in depth, Peila et al. (2007) [2] used a spiral excavator to simulate the discharge process of the muck in the pressurized excavation chamber during shield construction.In order to better understand the ability of the muck to transfer pressure and solve the problem of homogeneous flow of the muck in the screw machine, some scholars used the screw excavator model machine to study the flow characteristics of the muck [3][4][5][6][7].
The driving torque required for the rotation of the shield screw conveyor depends on the torque generated when the muck interacts with the tube and the screw, and the friction torque generated by the driving end bearing and seal ring during rotation.The model machine laboratory test verifies the rationality and effectiveness of the theoretical calculation method, and also points out the limitations of the theoretical calculation method.

Drive Torque of Shield Screw Conveyor
Through the structural analysis and mechanical derivation of the earth pressure balance shield tunnel boring machine with a screw conveyor, the calculation expression for its driving torque can be obtained as shown in equation 1.
( ) where τc is the shear stress between the spiral shell and the muck section, s is the pitch, e is the thickness of the spiral blade, φ is the spiral angle of the outer edge of the spiral blade , θ is the soil flow conveying angle, and 2R is the diameter of the spiral blade, ρ is the average density of conditioned soil, g is the acceleration of gravity constant, the groove depth is d, φm is the average blade helix angle, φ is the angle of inclination when the shield screw conveyor is installed, L is the length of the Spiral, F is the bearing load, rb is the radial roller contact radius, μb is the rolling friction coefficient, rs is the radius of the sealing ring, ws is the width of the sealing ring, Ps is the sealing pressure of the sealing ring, ns is the number of sealing rings, and μs is the friction coefficient between the sealing ring and the shaft.

Testing Soil Sample
In order to verify the scientificity and validity of the proposed formula for calculating the driving torque of the shield screw conveyor, an indoor model machine test was carried out.Taking Changzhou Metro Line 2 from Qingyang Road Station to Dingtanghe Park Station in the shield tunnel crossing the clay layer as the engineering background (Yang et.al., 2019) [8].Shield tunnelling in this area is more complicated to traverse the strata.The section of shield tunnelling strata is shown in figure 1, and the physical and mechanical parameters of the main strata are shown in table 1.The soil layers traversed by the shield in this area are mainly silty clay and clay layers.The highcohesive clay layers 2 and 3 are the stratum prone to "clogging" risk.In the natural state, the 2 clay layer is in a plastic state, and the 3 clay layer is in a hard plastic state.When the shield is tunneling, it is easy to cause the cutter head and the conveyor to be clogged, making it impossible to tunnel.During normal excavation, the conditioning material is foam, and the foam injection rate FIR is 20%~30%.At the same time, part of the water is injected according to the actual water content of the strata to help conditioning; in the section where the full section crosses the clay layer, a small amount of dispersant with a mass ratio of 1.5% is added.Figure 2 shows the conditioned soil, which is also the test soil sample.The mechanical characteristics of the treated soil are presented in table 2. When the screw speed is set at 6rpm (15rpm), the rate of muck transportation is measured at 0.19m3/h (0.27m3/h), with the soil flow conveying angle being 51.5° (57.3°).Under these conditions, the model machine achieves an average transportation efficiency of 76.4% (83.2%).

Shield Model Screw Conveyor
The shield model screw conveyor test device for indoor testing is shown in figure 3. The model machine system consists of an excavation chamber, inclined spiral tube with spiral structure installed inside, a coupling, a torque sensor, a geared motor, a frequency converter, and a horizontal direction pressurizing subsystem in the excavation chamber.The driving torque and speed are collected by a torque sensor.The soil flow conveying angle is calculated according to Equation 11 in (Li et. al., 2020) [9].The muck transfer rate is calculated based on the transportation situation in the excavation chamber.The specific technical parameters of each component are shown in table 3.

Testing Results
When the spiral speed is 6rpm, the driving torque during the three indoor tests is shown in figure 4. At this time, the theoretical value of the driving torque is 30.4Nm.After the longest running time of the model machine is about 24s, the driving torque enters the steady state interval.The average change of the torque of the three tests is shown in figure 5, and its average value is 33.13N.m.The average relative error of the three tests is 8.65% ~ 9.18%.The speed of the screw conveyor matches the advance speed of the shield machine, which is limited by the limited pressure of the excavation face.According to the size of the excavation face pressure, stepless speed regulation can be realized to maintain the excavation face pressure balance.When the limiting pressure changes due to changes in geological conditions, the efficiency of soil discharge of the screw conveyor or the mixing conditions in the chamber, the speed of the screw conveyor must be adjusted.In order to comprehensively measure the calculation method of the proposed spiral driving torque of shield machine, conditioned soil discharge simulation tests of 15rpm screw speed were also carried out.The test result and theoretical calculation value are shown in figure 6.According to the shield screw conditioned soil discharge simulation test, after entering steady-state operation at a speed of 15rpm, the average driving torque is 101.7N.m.The average relative error after entering the steady state is 4.6%, and the maximum relative error is 8.9%.

Conclusion
(1) During steady tunnelling of shield machine, the screw driving torque theoretical model defines the linear relationship between the shear stress acting on the conveyor shell and the screw shaft torque, and is also affected by the mechanical properties of the conditioned soil and the spiral structure parameters.
(2) The shield screw conveyor in the project is equipped with front and rear gates.The influence of gate opening on the screw driving torque is not involved in the proposed theoretical model and the model screw conveyor.This is also one of the contents to be considered in the next research work.
(3) In this indoor model machine test, only cohesive soil was used as the soil sample to carry out relevant research work.For other types of soil samples such as sandy soil, it will also be the object of the next indoor test research.

Figure 1 .
Figure 1.Stratum plan of shield tunneling

Figure 3 .
Figure 3. Shield model screw conveyor for testing.

Figure 4 .
Figure 4. Results of three indoor tests.Figure 5. Average value of three measurement results and its mean value.

Figure 5 .
Figure 4. Results of three indoor tests.Figure 5. Average value of three measurement results and its mean value.

Figure 6 .
Figure 6.Test results and calculated values at 15rpm.

Table 1 .
Physical and mechanical parameters of the strata.

Table 2 .
Mechanical parameters of conditioned soil.

Table 3 .
Parameters of the model screw conveyor.