Research on TBM Disc Cutter Wear Prediction Based on CSM Model

Abstract

The wear of disc cutters significantly impacts the efficiency and cost of TBM operations. In this study, we established a calculation model for radial wear based on the CSM formula and abrasive wear mechanisms. Experimental validation of the wear mechanism confirmed that abrasive wear is the primary mechanism responsible for disc cutter wear. The predictive model was subjected to engineering validation, where the calculated values from the model were compared and analyzed against actual on-site measurements. This validation process confirmed the accuracy and applicability of the model.

1 Introduction

The disc-shaped cutter is a primary component of Tunnel Boring Machines (TBM), and its cutting ring is a consumable part during construction. The cutting ring is prone to wear due to its interaction with the rock surface to be excavated and the crushed rock particles, leading to a decrease in the excavation performance of the disc-shaped cutter. Studying the forces acting on the cutter during rock rolling and assessing the degree of cutter wear are of significant importance for improving the rock-breaking efficiency of the excavation machine and reducing construction costs. Maidl et al. [1] derived an empirical formula relating the average lifespan of 17-in. cutters to the uniaxial compressive strength and the CAI index of the rock by studying various rock properties. Yu et al. [2] established a mapping model between the new cutter health index and specific field parameters based on one-dimensional convolutional neural networks through the analysis and selection of specific parameters from actual construction sites. Estimating the cutter health index provides information about the cutter's wear state. Koppl and Thuro, as well as Koppl et al. [3], developed empirical predictive models for initial and secondary wear of cutting tools caused by abrasive soil erosion. Li et al. [4] validated the stress of cutters in weathered mudstone formations based on the CSM prediction model and concluded that increasing the ratio of penetration rate to effective torque and thrust could reduce cutter wear. Ko et al. [5] studied various TBM cutter prediction models, including the Gehring model, CSM model, and NTNU model, and analyzed their characteristics. The above-mentioned predictive method in the study has a significant margin of error and cannot accurately forecast disc cutter wear. This paper primarily focuses on the positive cutter, and based on abrasive wear mechanisms, calculates the sliding distance through the CSM cutter stress model and cutter motion analysis to establish a calculation model for radial cutter wear. This model facilitates the assessment of wear severity and is validated through wear volume calculations. Therefore, this research is meaningful for guiding the timely replacement of disc-shaped cutters in TBM excavation processes.

2 Force Analysis During Rock Cutting by the Cutter

The stress state of the cutter during rock breaking is depicted in Fig. 1. In Fig. 1, Fn represents the thrust force generated by the TBM propulsion system, while Ft denotes the rolling force induced by the cutterhead torque system. Additionally, when the cutter rotates around the cutterhead center, it also generates a lateral force. However, due to the typically low rotational speed of the cutterhead, the lateral force is usually negligible [6]. When rolling against the rock, in order to balance the effects of Fn and Ft, the rock exerts a reaction force Fr on the cutter, and Fr is one of the primary causes of cutter wear.

Fig. 1

Schematic diagram of cutter forces

The calculation model for Fr is typically based on the (Colorado School of Mines, CSM) CSM model [7], and its expression is as follows:

$$ \left\{ \begin{gathered} F_{r} = \frac{{P_{0} \phi RT}}{1 + \psi } \hfill \\ \phi = \arccos \left(\frac{R - h}{R}\right) \hfill \\ P_{0} = C\sqrt[3]{{\frac{S}{{\phi \sqrt {RT} }}\sigma_{c}^{2} \sigma_{t} }} \hfill \\ \end{gathered} \right. $$

(1)

In the equation, Fr represents the normal reaction force acting on the cutter, $\psi$ is the distribution coefficient of the cutter's outer edge, $\phi$ is the contact angle of the cutter, R is the cutter's radius, h represents penetration depth, T is the cutter's blade width, S represents the spacing between cutters, σ_c is the uniaxial compressive strength of the rock, σ_t is the uniaxial tensile strength of the rock, C is a dimensionless constant, typically around 2.12, and P₀ is the crushing zone pressure, which is related to rock strength and the size and shape of the cutter.

3 Radial Wear Analysis

Among the various failure modes of cutters, wear consumption is the primary reason, and its predominant form is abrasive wear. The degree of cutter wear primarily refers to the change in the cutter ring's radius, and the wear depth of the cutter ring radius is referred to as “radial wear,” which is a crucial criterion for determining whether a cutter needs replacement. For abrasive wear, a simplified model often used is the one proposed by Rabinowicz [8], as shown in Fig. 2.

Fig. 2

Rabinowicz simplified model

The calculation formula for Rabinowicz wear is as follows:

$$ V = kL_{g} \frac{{P\cot \beta_{g} }}{\pi H} = k_{s} \frac{{PL_{g} }}{H} = k_{d} PL_{g} $$

(2)

In the equation, P represents the applied load, H is the hardness of the metal material, β_g is the half-angle of the abrasive grain, L_g is the sliding distance, and k_s is the abrasive wear coefficient, which is the product of the abrasive grain's geometric cotβ_g and the probability constant k. Typically, its value ranges from 10⁻¹ to 10^–6 [9].

From Eq. (2), it can be observed that the wear amount is primarily related to the magnitude of the load and the distance traveled. Therefore, based on the stress analysis, calculating the sliding distance of the cutter can yield a more accurate estimation of cutter wear.

3.1 Calculation of Sliding Distance

To achieve the rock-breaking operation of the Tunnel Boring Machine (TBM), the cutterhead is subjected to torque. In addition to revolving around the axis of the cutterhead, the disc cutters mounted on the cutterhead also undergo rotational motion. This, in conjunction with the advancement of the system, allows for penetration into the rock to complete the rock-breaking process. Let $\omega$ represent the angular velocity of the cutterhead, $\omega_{0}$ denote the angular velocity of the disc cutter, and r_i be the installation radius of the disc cutter. When the disc cutter rotates by an angle $\phi - \theta$, the relative rotation angle of the cutterhead is $\varphi$ When the cutter edge is located at position N, the linear velocity generated by the rotation of the disc cutter is:

$$ v_{a} = \omega_{0} R $$

(3)

The linear velocity generated under the effect of the cutterhead's revolution is:

$$ v_{b} = \omega R $$

(4)

The penetration velocity under the influence of the propulsion system is:

$$ v_{c} = h\omega_{0} /2\pi = h\omega r_{i} /2\pi R $$

(5)

In accordance with the concept of “one-time penetration displacement” as described in Ref. [10], and considering the dynamic variation of the disc cutter position during rock breaking, we establish the coordinate system shown in Fig. 3.

Fig. 3

Sliding speed diagram of disc cutter

Assuming the sliding distance of the disc cutter within the rock-breaking time t is denoted as L, its components along the x, y, and z axes are as follows:

$$ \left\{ \begin{gathered} L_{x} = \int\limits_{{\theta_{1} }}^{{\theta_{2} }} {( - \omega_{0} R\cos \theta \cos \varphi + \omega r_{i} \cos \varphi )dt} \hfill \\ L_{y} = \int\limits_{{\theta_{1} }}^{{\theta_{2} }} {(\omega_{0} R\cos \theta \sin \varphi - \omega r_{i} \sin \varphi )} dt \hfill \\ L_{z} = \int\limits_{{\theta_{1} }}^{{\theta_{2} }} {(\omega_{0} R\sin \theta + h\omega_{0} /2\pi )dt} \hfill \\ \end{gathered} \right. $$

(6)

From the relationship between the rotation of the cutter and the rotation of the cutter, we can get $\omega_{0} = \omega r_{i} /R$, the relative rotation angle $R(\phi - \theta ) = r_{i} \varphi$. The relationship between θ and t is $\theta = \phi - \omega r_{i} t/R$, so the $d\theta = - (\omega r_{i} /R)dt$ $d\theta = - (\omega r_{i} /R)dt$ transformed to

$$ dt = - \frac{Rd\theta }{{\omega r_{i} }} $$

(7)

Hence, by combining the sliding distances in three directions, the total sliding distance of the disc cutter for one rock-breaking cycle is obtained as follows:

$$ L = \sqrt {L_{x}^{2} + L_{y}^{2} + L_{z}^{2} } $$

(8)

3.2 Calculation of Radial Wear Amount

As shown in Fig. 3, when the disc cutter makes one full rotation from initial contact with the rock to the deepest point of rock breaking at M, the relative rotation angle is φ. Therefore, the integration limits θ2 and θ1 are 0 and φ, respectively. Substituting Eqs. (1) and (8) into Eq. (2), we obtain the volume of wear at the point M from initial contact with the rock to the deepest point of rock breaking as V:

$$ V = k_{d} F \times L = k_{d} \times F_{r} \times \sqrt {L_{x}^{2} + L_{y}^{2} + L_{z}^{2} } $$

(9)

Considering the basic uniformity of the equivalent stress peak values at different points on the cutter ring contact surface, and the relatively stable rotational angular velocity of the disc cutter, it is assumed that the radial wear is consistent at all points on the blade. The expression for the contact area A between the cutter ring and the rock, when the disc cutter completes one rock-breaking cycle, is given by:

$$ A = 2\pi R $$

(10)

Hence, the magnitude of the radial wear amount δ is:

$$ \delta = \frac{V}{{A_{01} }} = \frac{{k_{d} F_{r} }}{2\pi RT} \times \sqrt {L_{x}^{2} + L_{y}^{2} + L_{z}^{2} } $$

(11)

Assuming that the disc cutter completes a certain distance of excavation with Z rotations, the post-wear disc cutter radius is denoted as $R_{i + 1} = R_{i} - \delta_{i}$, and the blade width as $T_{i + 1} = T_{i} + 2\delta_{i} \tan \tfrac{\alpha }{2}$, where i represents the number of rotations of the disc cutter (i = 1, 2, 3, … Z), and α is the blade angle. Therefore, the cumulative radial wear amount H after Z rotations is given by:

$$ H = \sum\limits_{i = 1}^{Z} {\delta_{i} (i = 1,2,3...Z)} $$

(12)

4 Analysis of Experimental Results

4.1 Wear Mechanism Experiment

In this study, we utilized a disc cutter wear experimental setup to conduct tool wear experiments under different environmental conditions. Through observations using a scanning electron microscope (SEM), we obtained the wear morphology of the tool materials. The wear results indicate that in dry/wet conditions, the primary cause of wear failure in excavation machine tools is abrasive wear. Based on the wear experimental results, this paper derives a formula for calculating tool wear, enabling the prediction and calculation of tool wear. Additionally, Fig. 4 presents the design of the disc cutter rock-breaking simulation experimental setup.

Fig. 4

Disc cutter rock-breaking simulation experimental apparatus

During the rock-breaking process of the tunnel boring machine, in order to reduce the heat generated during rock fragmentation, water spray devices are installed on the disc cutters to achieve cooling and suppress the generation of dust. Utilizing the established disc cutter wear experimental platform, wear tests of the disc cutter materials were conducted with the water spray apparatus. The maximum penetration depth of the disc cutter was set to 2 mm, the rotational speed of the disc cutter specimen was 30 rpm, and granite was chosen as the rock material. The post-wear morphology of the disc cutter is shown in Fig. 5.

Fig. 5

Tool wear profile under dry/wet conditions

From Fig. 5, the wear morphology of the disc cutter material reveals that under dry/wet conditions, abrasive wear predominates on the surface of the disc cutter material. Under dry friction conditions, the wear of the disc cutter material is more severe, and there is a noticeable increase in the width of abrasive particle cutting depth.

Based on the three-dimensional morphology analysis in Fig. 6, it can be observed that the addition of water and similar mediums reduces the wear depth of the disc cutter material, indicating a lubricating effect of water. During the cutting of rock, the disc cutter generates numerous cutting furrows on the contact surface, along with a few occurrences of pits and surface oxidation fatigue wear. Under dry friction conditions, the number of furrows on the disc cutter surface is most pronounced, leading to more severe wear. With the introduction of water, the wear level of the disc cutter material is somewhat alleviated. However, abrasive wear remains the primary wear mechanism, albeit with a reduction in the extent of micro-cutting by rock abrasives.

Fig. 6

Three-dimensional wear morphology

In summary, abrasive wear is the primary cause of disc cutter wear, and it primarily occurs on the disc cutter surface in the form of micro-cutting.

4.2 Engineering Case Validation

In a construction section of a tunnel within a mountain range in Zhejiang [11], the predominant geological composition of the strata consists mainly of granite and quartzite. The average uniaxial compressive strength of the rock is approximately 110.9 MPa, and the value of kd is taken as 2 × 10^–6 mm³/(N mm). There are a total of 9 positive disc cutters installed on the cutterhead. The average penetration depth achieved by one rotation of the disc cutter for rock breaking is 4.12 mm. The arrangement of the disc cutters on the cutterhead is shown in Fig. 7, and the basic parameters of the disc cutters are listed in Table 1.

Fig. 7

Installation position diagram of disc disc cutter on cutterhead

Table 1 Basic parameters of disc cutter

Figure 8 depicts the relationship between the cutter position number and the wear amount of the positive disc cutters, which was measured after the tunnel boring machine had operated for 471.16 m. As shown in Fig. 8, the predicted values of radial wear amount exhibit a trend that is generally consistent with the actual wear amount. Due to the complex underground construction conditions and factors such as rock anisotropy and joint characteristics, the predicted values may exhibit some errors when compared to actual wear amounts. However, the average error in the calculation results does not exceed 6%, indicating that the established model can reasonably predict the radial wear amount of the disc cutters during their operation.

Fig. 8

Comparison of predicted and actual values

5 Conclusion

Wear mechanism experiments were conducted using a disc cutter wear test rig, confirming that abrasive wear is the primary mechanism responsible for disc cutter wear. By synthesizing the three movements of disc cutters, namely penetration motion, revolution of the disc cutter, and self-rotation, the sliding distance of the disc cutter after one rotation was determined. This formed the basis for establishing a calculation model for radial disc cutter wear. By inputting actual TBM construction parameters into the predictive model and comparing the results with actual tool wear values, the average error between theoretical values and actual values was within 6%.