Design of a New TBM Integrated Cutter System Based on Analysis of Mechanical Properties and Dynamic Characteristics
Abstract
:1. Introduction
2. Mechanical Performance Experiment of New TBM Integrated Cutter System
2.1. Structure Design of New TBM Cutter System
2.2. Finite Element Stress Calculation of New TBM Integrated Cutter System
2.3. Similarity Theory and Scaled Cutter System
- (a)
- Structural parameters: the side length l of a single cutter holder.
- (b)
- Physical properties: material density ρ, Poisson’s ratio μ, and elastic modulus E.
2.4. The Scheme Design of Scaled Loading Experiment
2.5. Processing and Analysis of Experimental Data
3. Multi-DoF Coupled Dynamic Model of New TBM Integrated Cutter System
3.1. Equivalent Dynamic Model of New Integrated TBM Cutter System
3.2. Dynamic Differential Equations of Vibration System
- 1.
- Vertical direction
- 2.
- Lateral direction
- 3.
- Rolling direction
- 4.
- Swing direction
3.3. Structural Dynamic Parameters of the Vibration Model
3.3.1. Equivalent Mass of the Cutter System Components
3.3.2. Equivalent Stiffness of the Cutter System Components
- (1)
- Equivalent stiffness of node W1
- (2)
- Equivalent stiffness of node W2
- (3)
- Equivalent stiffness of node W3
3.3.3. Equivalent Damping of the Cutter System Components
- (1)
- Equivalent damping of node W1
- (2)
- Equivalent damping of node W2
- (3)
- Equivalent damping of node W3
4. Dynamic Characteristics Analysis of New TBM Integrated Cutter System
4.1. Vibration Response Solution of Cutter System
4.1.1. Numerical Solution of Differential Equations
4.1.2. Vibration Response of Each Component
- (1)
- The new cutter system’s each component response will oscillate in the initial loading stage. In this stage, each component acceleration changes dramatically under the load action, which leads to the reduction in the system’s stability. Under the common influence of internal and external excitation, each component vibration displacement response is the same as that of external load excitation, and the vibration displacement response changes sinusoidal after the stability.
- (2)
- Order the mean value and amplitude of each component vibration displacement. In the vertical direction: cutter system > disc cutter side panel > shift fork > wedge > cutter holder; in the lateral direction: cutter system > disc cutter side panel > shift fork > wedge > cutter holder; and in the rolling direction: cutter system > cutter side panel > cutter holder. The above shows that each component vibration amplitude decreases gradually along the force transmission direction. Therefore, in the design process, those parts that are prone to failure due to the vibration influence should be placed as far back as possible.
- (3)
- Order the mean value and amplitude of most of the components’ vibration displacement in different directions: vertical direction > lateral direction > rolling direction, which is caused by the order: vertical load > lateral load > rolling load. The rock-breaking process is mainly carried out by a vertical load, which is one order of magnitude higher than the lateral and rolling load. Therefore, the vertical direction should have a high stiffness during the cutter system design, to ensure the system’s reliability in the rock-breaking process.
4.2. Scaled Vibration Experiment of Cutter System
4.2.1. Vibration Loading Experiment Scheme Design
- (1)
- Critical experimental devices
- (2)
- Experimental scheme
4.2.2. Experimental Results and Comparative Analysis
4.3. Dynamic Response of Cutter System Based on Measured Load
5. Conclusions
- (1)
- In this paper, the statics performance experiment is carried out first. The finite element method is used to calculate the new cutter system stress distribution under the nominal load, and different values of the load are applied to calculate the position of the maximum stress point, so as to verify the accuracy of the finite element model. A new scaled cutter system is manufactured based on the similarity theory, and the statics performance experiment is carried out. It is found that the relative error between the calculated stress values and the measured stress values is less than 10%, which further verified the accuracy of the finite element model.
- (2)
- Then, the dynamic characteristics is analyzed. The multi-DoF equivalent mechanical model of the new cutter system and the dynamic differential equations in each direction are established by the concentrated mass method. The vibration response of each cutter system component is solved by the Newmark method. The vibration test of the scale sample is carried out based on the hydraulic loading test bench. It is found that the relative error between the theoretical mean value of the vertical vibration displacement and what is measured is less than 10%, which verifies the correctness of the vertical dynamics model which is established. The real load in the disc cutter linear cutting experiment is used as the external excitation to analyze the dynamic response of each component. The maximum vibration RMS and amplitude of the system are 0.2300 mm and 0.7003 mm, respectively. Additionally, the feasibility of the new cutter system’s design scheme during the real rock breaking process is verified finally.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Cutter System Design Scheme | Number of Disassembly Parts | Number of Disassembly Procedures |
---|---|---|
Double wedge blocks cutter system | 11 | >15 |
Upper and lower wedge blocks cutter system | 17 | >25 |
Rear-installed cutter system | 5 | >7 |
New TBM integrated cutter system | 0 | 2 |
Classification | Physical Quantity | Similar Relationship | Scaled Ratio |
---|---|---|---|
Material characteristics | Stress σ | Cσ = CE | 1:1 |
Elastic modulus E | CE = 1 | 1:1 | |
Poisson’s ratio μ | Cμ = 1 | 1:1 | |
Density ρ | Cρ = 1 | 1:1 | |
Geometric quantity | Side length l | Cl | 1:1 |
Load quantity | Loading force F | CF = CE | 1:4 |
Moment M | CM = CE | 1:16 | |
Surface load P | CP = CE | 1:1 | |
Dynamic quantity | Mass m | Cm = Cρ | 1:16 |
Stiffness k | Ck = CE Cl | 1:1 | |
Damping c | Cc = (CE Cρ)1/2 | 1:4 |
Node | m1 (kg) | m2 (kg) | m3 (kg) | m4 (kg) | m5 (kg) |
Equivalent Mass | 141.17 | 77.19 | 4.57 | 77.19 | 4.57 |
Node | m6 (kg) | m7 (kg) | m8 (kg) | m9 (kg) | m10 (kg) |
Equivalent Mass | 5.51 | 156.74 | 5.51 | 156.74 | 0.96 |
Node | ky1 | ky2 | ky3 | ky4 | ky5 | ky6 |
Stiffness (N/m) | 3.66 × 108 | 3.66 × 108 | 2.09 × 109 | 2.09 × 109 | 5.64 × 108 | 5.64 × 108 |
Node | ky7 | ky8 | ky9 | ky10 | ky11 | ky12 |
Stiffness (N/m) | 1.52 × 109 | 1.52 × 109 | 1.47 × 109 | 1.47 × 109 | 2.62 × 1010 | 2.62 × 1010 |
Node | kx1 | kx2 | kx3 | kx4 | kx5 | kx6 |
Stiffness (N/m) | 1.82 × 108 | 5.71 × 108 | 1.12 × 108 | 4.62 × 109 | 5.71 × 108 | 3.99 × 1010 |
Node | kz1 | kz2 | kz3 | kz4 | kz5 | kz6 |
Stiffness (N/m) | 3.24 × 109 | 3.24 × 109 | 2.38 × 109 | 2.38 × 109 | 1.5 × 109 | 1.5 × 109 |
Node | cy1 | cy2 | cy3 | cy4 | cy5 | cy6 |
Damping (Ns/m) | 1.75 × 103 | 1.75 × 103 | 1.61 × 104 | 1.61 × 104 | 2.03 × 103 | 2.03 × 103 |
Node | cy7 | cy8 | cy9 | cy10 | cy11 | cy12 |
Damping (Ns/m) | 1.37 × 104 | 1.37 × 104 | 3.60 × 103 | 3.60 × 103 | 8.11 × 104 | 8.11 × 104 |
Node | cx1 | cx2 | cx3 | cx4 | cx5 | cx6 |
Damping (Ns/m) | 3.54 × 103 | 8.40 × 103 | 9.05 × 102 | 6.38 × 103 | 8.40 × 103 | 1.00 × 105 |
Node | cz1 | cz2 | cz3 | cz4 | cz5 | cz6 |
Damping (Ns/m) | 2.71 × 104 | 2.71 × 104 | 1.71 × 104 | 1.71 × 104 | 1.94 × 104 | 1.94 × 104 |
Parameter | lC/mm | lD/mm | lE/mm | dC/mm |
Mean value of vibration | 0.450393 | 0.261204 | 0.259630 | 0.414589 |
Amplitude of vibration | 0.042180 | 0.014945 | 0.014575 | 0.038827 |
Parameter | dD/mm | dE/mm | d(C–E)/mm | d(D–E)/mm |
Mean value of vibration | 0.240440 | 0.238991 | 0.175598 | 0.001449 |
Amplitude of vibration | 0.013757 | 0.013417 | 0.025411 | 0.000341 |
Direction | Parameter | Cutter System | Side Panel | Fork | Wedge | Holder |
---|---|---|---|---|---|---|
Vertical | RMS/mm | 0.2300 | 0.0753 | 0.0688 | 0.0442 | 0.0024 |
Amplitude/mm | 0.7003 | 0.2246 | 0.2051 | 0.1320 | 0.0070 | |
Lateral | RMS/mm | 0.0977 | 0.0223 | 0.0188 | 8.0318 × 10−4 | 3.6542 × 10−4 |
Amplitude/mm | 0.3055 | 0.0701 | 0.0592 | 0.0025 | 0.0011 | |
Rolling | RMS/mm | 0.0116 | 0.0090 | / | / | 0.0055 |
Amplitude/mm | 0.0168 | 0.0131 | / | / | 0.0081 |
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Yang, F.; Lan, T.; Huo, J.; Shi, Y.; Chen, H. Design of a New TBM Integrated Cutter System Based on Analysis of Mechanical Properties and Dynamic Characteristics. Appl. Sci. 2022, 12, 12332. https://doi.org/10.3390/app122312332
Yang F, Lan T, Huo J, Shi Y, Chen H. Design of a New TBM Integrated Cutter System Based on Analysis of Mechanical Properties and Dynamic Characteristics. Applied Sciences. 2022; 12(23):12332. https://doi.org/10.3390/app122312332
Chicago/Turabian StyleYang, Fan, Tian Lan, Junzhou Huo, Yiting Shi, and Hao Chen. 2022. "Design of a New TBM Integrated Cutter System Based on Analysis of Mechanical Properties and Dynamic Characteristics" Applied Sciences 12, no. 23: 12332. https://doi.org/10.3390/app122312332
APA StyleYang, F., Lan, T., Huo, J., Shi, Y., & Chen, H. (2022). Design of a New TBM Integrated Cutter System Based on Analysis of Mechanical Properties and Dynamic Characteristics. Applied Sciences, 12(23), 12332. https://doi.org/10.3390/app122312332