Cutter performance evaluation is important for shield TBM during the design and refurbishment stage. To face the challenges of choosing the proper cutters for tunneling in complex condition, according to the concept of parameter profile analysis, a systematic evaluation method was proposed. In this novel method, by comparing with their expected best value and the corresponding unacceptable limit, all of the selected performance parameters can be synthesized to assess the proximity of the overall merit of each cutter with respect to all the performances considered under all possible geological conditions. Performance indexes including cutting efficiency, structural strength, wear life, and dynamic response were individually analyzed based on linear cutting tests, finite element analyses, and theoretical calculations. Finally, a case study was carried out to demonstrate how the method is applied to find the optimal cutter among a small-scale disc cutter and two scrapers used for cutting multiple soft rock. In this case, three types of concrete specimens with distinct mechanical properties were carefully prepared to substitute for soft rock. The evaluation results show that the method has an intrinsic applicability in helping to make a reasonable trade-off between cost and cutting performance during the cutter selection process.
Shield tunnel boring machine (TBM) is an advanced tunneling device, commonly employing scrapers and disc cutters to excavate soft rock and soil encountered [
Currently, most researchers focus on the study of cutting forces and their associated performances such as specific spacing/penetration corresponding to the minimum specific energy based on cutting tests [
In this context, a novel evaluation method is proposed, which considers a comprehensive list of individual performances at varying geological grounds. To illustrate how the evaluation method is applied to find the optimal cutter, a case study was then given. In this case, the cutting performance of a small-scale disc cutter and two scrapers which were originally designed for excavating soft rock was analyzed and evaluated individually based on linear cutting tests, finite element analyses, and theoretical calculations; three types of concrete specimens with distinct mechanical properties were carefully prepared to substitute for soft rock. Finally, all the performance indexes of the cutters were then systematically analyzed and the overall merits of the cutter design were discussed.
Based on linear cutting tests and finite element analyses (FEA), the following performance parameters can be obtained.
It is a widely used index for assessing the cutting efficiency of TBM cutters. Unexpected high SE not only suggests that the cutting process is inefficient, but also implies that potential failures such as excessive wear happen [
Illustration of sensors attached on the saddle.
The ratio of the horizontal force to the vertical force is expressed as a percentage which can be considered as an indicator of the amount of torque needed for a given amount of thrust; the higher the CC, the higher the torque needed by TBMs [
Due to the characteristics of rock and discontinuities, the cutting vibration is a ubiquitous problem, resulting in seal failures, fatigue cracks on cutter tips, and bolt looseness [
Structural strength of TBM cutters is another criterion to check whether the cutters can withstand heavy cutting load and to examine whether the stress concentration occurs on the cutter tips. It is hard to directly obtain the stress distribution of the cutters by theoretical calculation. Considering that FEA is widely used in engineering analysis and calculation, we use the finite element analysis software ANSYS to calculate the maximum equivalent stress
Cutter wear incurs the costs of downtime as well as the costs of refurbishing and replacing the cutters [
Multiple performance parameters and geological conditions would make the evaluation more realistic but also would greatly complicate the evaluation process. To tackle this problem, a systematic evaluation method is proposed based on the concept of parameter profile analysis [
The system should be best considered with respect to the limits of performances that may be acceptable, and the best performances that can be expected from the TBM applications. Therefore, upper boundary matrix (UBM) (
To ensure that the data point in the PPM (
To analyze the performance at a more advanced level, a parameter performance index PPI
From equations ( A comparison of PPIs will indicate whether the system performs better with respect to some performances than others A comparison of CPIs will show whether the system performs significantly better at some geological conditions than others
The mean values, CPIs, PPIs, and SDs provide an efficient way to analyze the system from different perspectives. An overall performance index (OPI) is then used to develop the overall objective function. The OPI, which takes the form of a qualitative score, can be established for the system by considering all the performances and all the geological conditions. The OPI function lies in the range of 0–100. Each performance parameter and each geological condition are given a weighting value according to its importance. The OPI can be expressed as follows:
The cutting tests were performed on the standard linear cutting machine (LCM) with the size of 3.7 m × 1.7 m × 3 m (see Figure
(a) main frame of LCM; (b) disc cutter; (c) two scrapers.
As the LCM was originally designed for cutting granite by roller cutters such as disc cutters and spherical tooth hob cutters [
It is hard to control rock-breaking tests due to the randomness of natural rocks. To overcome this shortcoming, concrete specimens were used to substitute for soft rock in this paper. By strictly controlling concrete curing time and the ratios of fine sand (0–4 mm), cobblestones, commercial cement, and water, three sets of concrete specimens with distinct mechanical properties (referred to as S1, S2, and S3) were separately casted in specimen boxes. During cutting tests, each box can be firmly fixed on the granite base.
Rock samples’ mechanical properties were tested on WHY-200 automatic compression testing machine. CAIs were measured according to Cerchar method ASTM D7625-10 [
Mechanical properties and component ratios of the specimens.
No. | Elastic module, MPa | CAI | Component ratiosa | Cure time (weeks) | Moisture content (%) | ||
---|---|---|---|---|---|---|---|
S1 | 1880 | 31.82 | 1.39 | 2.4 | 15%–0–85% | 3 | 3.5 |
S2 | 898.6 | 19.14 | 2.55 | 4.0 | 35%–0–65% | 2 | 8 |
S3 | 683.58 | 10.59 | 1.29 | 3.5 | 20%–25%–55% | 1 | 17 |
aIn sand-cobblestone-cement order.
During the tests, the hydraulic system moves three cylinder rams: the two vertical rams force the cutters to penetrate the specimen surface to depths of 8 mm while the other one moves the specimen box horizontally to cut the specimen. The moving direction of the support is away from the viewer (Figure
Set P = [SE, CC,
Performance data (
C1–S1 | C1–S2 | C1–S3 | C2–S1 | C2–S2 | C2–S3 | C3–S1 | C3–S2 | C3–S3 | |
---|---|---|---|---|---|---|---|---|---|
SE, (MJ/m3) | 12.52 | 15.84 | 18.28 | 9.02 | 6.32 | 4.85 | 8.28 | 6.93 | 4.40 |
CC (%) | 15.6 | 16.1 | 18.7 | 36.4 | 33.5 | 32.6 | 32.0 | 31.7 | 29.1 |
0.44 | 0.39 | 0.32 | 0.46 | 0.38 | 0.53 | 0.38 | 0.32 | 0.46 | |
33.91 | 9.77 | 6.82 | 270.64 | 158.93 | 64.80 | 278.99 | 165.08 | 67.14 | |
7.21 | 8.60 | 30.63 | 3.68 | 2.13 | 12.85 | 3.43 | 1.99 | 12.0 |
Rock-breaking phenomena captured in the tests. (a) C1–S1. (b) C1–S2. (c) C1–S3. (d) C3–S1. (e) C3–S1. (f) Wear surface of C3.
In Table
The vibration data can help gain a better understanding of the underlying mechanisms with respect to dynamic performance. Frequency-domain analysis shows that TBM cutters are vibrating at low frequency. Vertical vibration amplitude of C1 is appreciably larger in S1 than that in S2 and S3, which suggests that UCS contributes more to vibrational components than the discontinuities. On the contrast, intense vibration can be found when C2 (C3) cut cobblestone-rich specimen S2. This may be explained by the fact that C2 (C3) has higher odds of crashing against these hard cores than C1 due to the larger contact area.
The UBM and MRM are listed in Table
UBM and MRM for the three specimens.
C1 | C2 (C3) | |||
---|---|---|---|---|
UBM | MRM (%) | UBM | MRM (%) | |
SE, (MJ/m3) | 20 | 65 | 10 | 65 |
CC, (%) | 20 | 45 | 40 | 30 |
1 | 80 | 1 | 80 | |
100 | 85 | 300 | 85 | |
1/5.4 | 85 | 1/1.8 | 90 |
PPM (nondimensional).
C1–S1 | C1–S2 | C1–S3 | C2–S1 | C2–S2 | C2–S3 | C3–S1 | C3–S2 | C3–S3 | |
---|---|---|---|---|---|---|---|---|---|
SE | 5.75 | 3.20 | 1.32 | 1.51 | 5.66 | 7.92 | 2.65 | 4.72 | 8.62 |
CC | 4.89 | 4.33 | 1.44 | 3.00 | 5.42 | 6.17 | 6.67 | 6.92 | 9.08 |
7.00 | 7.63 | 8.50 | 6.75 | 7.75 | 5.88 | 7.75 | 8.50 | 6.75 | |
7.78 | 10.00 | 10.00 | 1.15 | 5.53 | 9.22 | 0.82 | 5.29 | 9.13 | |
2.96 | 4.38 | 9.70 | 5.68 | 1.72 | 9.55 | 5.28 | 1.06 | 9.44 |
The nondimensional data in PPM represents the proximity of the calculated performance to the limits of performance. As shown in Table
To reveal the character of the cutters more clearly, the means, SDs, and PPIs are listed in Table
Profile analysis for the performance parameters across all the specimens (nondimensional data).
Mean | SD | PPI | |||||||
---|---|---|---|---|---|---|---|---|---|
C1 | C2 | C3 | C1 | C2 | C3 | C1 | C2 | C3 | |
SE | 3.43 | 5.03 | 5.33 | 2.22 | 3.25 | 3.03 | 2.42 | 3.11 | 4.25 |
CC | 3.56 | 4.86 | 7.56 | 1.85 | 1.65 | 1.33 | 2.66 | 4.41 | 7.41 |
7.71 | 6.79 | 7.67 | 0.75 | 0.94 | 0.88 | 7.66 | 6.71 | 7.60 | |
9.26 | 5.30 | 5.08 | 1.28 | 4.04 | 4.16 | 9.13 | 2.59 | 1.98 | |
5.68 | 5.65 | 5.26 | 3.56 | 3.92 | 4.19 | 4.48 | 3.48 | 2.42 |
Profile analysis of PPM is conducted for each row. Similarly, inspection of Table
Profile analysis of the cutters under three specimens (nondimensional).
Mean | SD | CPI | |||||||
---|---|---|---|---|---|---|---|---|---|
C1 | C2 | C3 | C1 | C2 | C3 | C1 | C2 | C3 | |
S1 | 5.68 | 3.62 | 4.63 | 1.88 | 2.50 | 2.86 | 5.06 | 2.28 | 2.43 |
S2 | 5.91 | 5.22 | 5.30 | 2.82 | 2.18 | 2.79 | 4.99 | 3.99 | 3.11 |
S3 | 6.19 | 7.75 | 8.61 | 4.43 | 1.69 | 1.08 | 2.83 | 7.44 | 8.48 |
As discussed above, an overall analysis across all specimens and across all performance parameters is conducted separately, which enables the designers to quickly find the weakest performance spot and toughest geological condition. It is a powerful tool in product trial and cutter refurbishment to improve the weak spots. For example, according to the above analysis, C1 can be redesigned as a double-edge cutter which is made from the same steel used in the original cutter due to the sufficient structural strength. As the cutting spacing between two edges may induce their lateral cracks to interact, a significant improvement in SE can be expected [
For evaluating the overall performance, the OPI functions are used to quantitatively estimate the performance levels of the cutters incorporating their expected best performances. Prior to the calculation of OPIs, it is necessary to define the importance levels of the criteria. Specifically, weighting factors of performance parameters can be determined by their contributions to the overall TBM performance such as tunneling cost and advance rate; weighting factors of geological conditions are largely dependent on the corresponding proportions along the tunnel alignment (rock types). For illustration purpose, the OPIs of the three cutters under different sets of weighting factors (simply given by expert scoring method, see Table
Different sets of weighting factors (%).
Performance parameters | Specimens | ||||||||
---|---|---|---|---|---|---|---|---|---|
P1 | P2 | P3 | P4 | P5 | S1 | S2 | S3 | ||
Ia | 20 | 20 | 20 | 20 | 20 | 1a | 33 | 33 | 33 |
II | 60 | 10 | 10 | 10 | 10 | 2 | 80 | 10 | 10 |
III | 10 | 10 | 10 | 60 | 10 | 3 | 10 | 80 | 10 |
VI | 10 | 10 | 10 | 10 | 60 | 4 | 10 | 10 | 80 |
Ia and 1a denote the first set of weighting factors of the performance parameters and specimens, respectively.
OPIs of the three cutters under different sets of weighting factors of performance parameters. (a) Set I. (b) Set II. (c) Set III. (d) Set VI.
OPIs of the three cutters under different sets of weighting factors of geological conditions. (a) Set 1. (b) Set 2. (c) Set 3. (d) Set 4.
From these figures, it can be seen that the OPIs are determined by both the performances and the weighting factors. Undoubtedly, when high priority is put in
When the tunneling ground only (or mainly) contains S3-like composition (e.g., Figure
Based on the above analyses, the performance of the cutters is systematically evaluated with respect to the performance parameters which collectively describe the overall performance. In order to combine these parameters, the results obtained from experiments, FEA, and theoretical calculation are converted into nondimensional scores using a linear relationship based on the actual performance to its performance limit. The core of the above conversion is the proximity of the level at which the cutters will perform with respect to the expected best level and acceptable level of the performance described by two matrixes: UBM and MRM. They should be reasonably given by the designers based on their engineering experience; otherwise, the evaluation could be subjected to errors. However, the introduction of these two matrices is inevitable in a design assessment because the evaluation results would not be meaningful unless the performances are judged against the design criteria.
It is a common practice that detailed engineering analyses might be carried out by several engineers with different specialisms especially for large and complex systems like TBMs. The process proposed in this paper brings together the separate analyses and combines them into a manageable design review procedure, which means that the evaluation method has an intrinsic applicability to evaluate the suitability of a TBM cutterhead on a given project. Particularly, this design synthesis concept provides a framework for formulating the quantifiable portion of a system design on which advanced optimization techniques can be brought to bear. It would be the future work that a computer-aid optimization program should be developed for TBM cutterheads.
A novel systematic method has been devised to evaluate the overall performance of TBM cutters with respect to different kinds of performances and geological conditions. This method enables the designers to make a quick selection of proper cutters prior to layout design of the cutterheads.
For a design review exercise, the method aims to identify the “weak spots” in the original design, which could help the designers to make a more targeted redesign for refurbishment.
The merits of the three experimental cutters are discussed by applying the proposed evaluation method. By using the method, a reasonable selection among the cutters could be made quantitatively for a mixed geological condition.
The data to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest.
This project was supported by the National Natural Science Foundation of China (51704256, 11832016, and 51775471), Natural Science Foundation of Hunan Province, China (2020JJ4583 and 2017JJ3292), and Scientific Research Project of Hunan Education Department (19C1756), China. This project was also supported by the Changsha Zhuzhou Xiangtan Landmark Engineering Technology Project (2019XK2303 and 2020GK2014) and Xiangtan Science and Technology Project (ZD-ZD20191007).