Figure 1.
Interaction between temporary support and wall rock.
Figure 1.
Interaction between temporary support and wall rock.
Figure 2.
Theoretical calculation model of equilibrium arch.
Figure 2.
Theoretical calculation model of equilibrium arch.
Figure 3.
Terzaghi’s theoretical model.
Figure 3.
Terzaghi’s theoretical model.
Figure 4.
Roadway wall rock- support system model. (a) Initial model of wall rock, (b) excavation roadway model.
Figure 4.
Roadway wall rock- support system model. (a) Initial model of wall rock, (b) excavation roadway model.
Figure 5.
Vertical displacement distribution of roadway roof. (a) Before support, (b) after support.
Figure 5.
Vertical displacement distribution of roadway roof. (a) Before support, (b) after support.
Figure 6.
Vertical displacement curve of roadway roof. (a) Before support, (b) after support.
Figure 6.
Vertical displacement curve of roadway roof. (a) Before support, (b) after support.
Figure 7.
Roadway roof stress distribution. (a) Before support, (b) after support.
Figure 7.
Roadway roof stress distribution. (a) Before support, (b) after support.
Figure 8.
Stress curve of roadway roof. (a) Before support, (b) after support.
Figure 8.
Stress curve of roadway roof. (a) Before support, (b) after support.
Figure 9.
Distribution of plastic failure of roadway roof. (a) Before support, (b) after support.
Figure 9.
Distribution of plastic failure of roadway roof. (a) Before support, (b) after support.
Figure 10.
Structural diagram of SmTS. 1. Main beam; 2. side guard plate; 3. side guard plate jack; 4. column; 5. base; 6. moving jack; 7. four-bar linkage.
Figure 10.
Structural diagram of SmTS. 1. Main beam; 2. side guard plate; 3. side guard plate jack; 4. column; 5. base; 6. moving jack; 7. four-bar linkage.
Figure 11.
State diagram of front support group.
Figure 11.
State diagram of front support group.
Figure 12.
State diagram of rear support group.
Figure 12.
State diagram of rear support group.
Figure 13.
Roadway heading face system.
Figure 13.
Roadway heading face system.
Figure 14.
Roof beam structure. (a) Front view, (b) side View.
Figure 14.
Roof beam structure. (a) Front view, (b) side View.
Figure 15.
Adaptive support mechanism.
Figure 15.
Adaptive support mechanism.
Figure 16.
Working principle of adaptive support mechanism. (a) Front view, (b) side view.
Figure 16.
Working principle of adaptive support mechanism. (a) Front view, (b) side view.
Figure 17.
Six typical working conditions of the main beam. (a) Uniform loading, (b) loading at both ends, (c) loading on both sides, (d) lateral eccentric loading, (e) longitudinal eccentric loading, and (f) torsional loading.
Figure 17.
Six typical working conditions of the main beam. (a) Uniform loading, (b) loading at both ends, (c) loading on both sides, (d) lateral eccentric loading, (e) longitudinal eccentric loading, and (f) torsional loading.
Figure 18.
Nephogram of equivalent stress and total deformation. (a) Stress and deformation nephogram of main beam under uniform loading; (b) stress and deformation nephogram of main beam under loading at both ends; (c) stress and deformation nephogram of main beam under loading on both sides; (d) stress and deformation nephogram of main beam under lateral eccentric loading; (e) stress and deformation nephogram of main beam under longitudinal eccentric loading; (f) stress and deformation nephogram of main beam under torsional loading.
Figure 18.
Nephogram of equivalent stress and total deformation. (a) Stress and deformation nephogram of main beam under uniform loading; (b) stress and deformation nephogram of main beam under loading at both ends; (c) stress and deformation nephogram of main beam under loading on both sides; (d) stress and deformation nephogram of main beam under lateral eccentric loading; (e) stress and deformation nephogram of main beam under longitudinal eccentric loading; (f) stress and deformation nephogram of main beam under torsional loading.
Figure 19.
First six vibration modes of main beam. (a) First vibration mode, (b) second vibration mode, (c) third vibration mode, (d) fourth vibration mode, (e) fifth vibration mode, and (f) sixth vibration mode.
Figure 19.
First six vibration modes of main beam. (a) First vibration mode, (b) second vibration mode, (c) third vibration mode, (d) fourth vibration mode, (e) fifth vibration mode, and (f) sixth vibration mode.
Figure 20.
Fatigue life nephogram of main beam.
Figure 20.
Fatigue life nephogram of main beam.
Figure 21.
Fatigue damage structural nephogram of main beam.
Figure 21.
Fatigue damage structural nephogram of main beam.
Figure 22.
Security factor nephogram of main beam.
Figure 22.
Security factor nephogram of main beam.
Figure 23.
Fatigue sensitivity characteristic curve of main beam.
Figure 23.
Fatigue sensitivity characteristic curve of main beam.
Figure 24.
Multiobjective optimization of product structure based on RSM.
Figure 24.
Multiobjective optimization of product structure based on RSM.
Figure 25.
Multiobjective optimization module. (A) Set the parameters of “Geomotry”, (B) Set the parameters of “Static Structural”, (C) Set the parameters of “Model”, (D) Set the parameters of “Response Surface Optimization”.
Figure 25.
Multiobjective optimization module. (A) Set the parameters of “Geomotry”, (B) Set the parameters of “Static Structural”, (C) Set the parameters of “Model”, (D) Set the parameters of “Response Surface Optimization”.
Figure 26.
Design variables of main beam.
Figure 26.
Design variables of main beam.
Figure 27.
Fitting degree of test factors to objective function.
Figure 27.
Fitting degree of test factors to objective function.
Figure 28.
Quality response surface.
Figure 28.
Quality response surface.
Figure 29.
Deformation response surface.
Figure 29.
Deformation response surface.
Figure 30.
Equivalent stress response surface.
Figure 30.
Equivalent stress response surface.
Figure 31.
First order natural frequency response surface.
Figure 31.
First order natural frequency response surface.
Figure 32.
Fatigue life response surface.
Figure 32.
Fatigue life response surface.
Figure 33.
Stress nephogram of main beam.
Figure 33.
Stress nephogram of main beam.
Figure 34.
Deformation nephogram of main beam.
Figure 34.
Deformation nephogram of main beam.
Figure 35.
First-order natural frequency nephogram of main beam.
Figure 35.
First-order natural frequency nephogram of main beam.
Figure 36.
Fatigue life nephogram of main beam after optimization.
Figure 36.
Fatigue life nephogram of main beam after optimization.
Table 1.
Parameters of 7900 mining area belt roadway.
Table 1.
Parameters of 7900 mining area belt roadway.
Roadway Parameters | Values |
---|
| 3.5 m |
| 4.5 m |
Cross-sectional area: S | |
| 60 m |
| |
| 3 |
| 1 |
| |
Table 2.
Rock mass parameters of wall rock model.
Table 2.
Rock mass parameters of wall rock model.
Rock Type | Thickness (m) | Cohesion (MPa) | Internal Friction Angle (°) | Density (kg/m3) |
---|
Siltstone | 3.0 | 7.2 | 35.0 | 2730 |
Coal seam | 3.5 | 1.1 | 32.3 | 1330 |
Silty sandstone | 2.5 | 5.6 | 38.4 | 2815 |
Medium fine standstone | 7 | 7.0 | 40.5 | 2615 |
Table 3.
Grid parameters of wall rock model.
Table 3.
Grid parameters of wall rock model.
Rock Type | Length (m) | Width (m) | Height (m) |
---|
Siltstone | 0.5 | 0.2 | 0.6 |
Coal seam | 0.5 | 0.2 | 0.5 |
Silty sandstone | 0.5 | 1.0 | 0.5 |
Medium fine standstone | 0.5 | 1.0 | 0.7 |
Table 4.
Parameters of EBZ135 roadheader.
Table 4.
Parameters of EBZ135 roadheader.
Parameter | Value |
---|
Total length | 8.92 m |
Overall width | 2.83 m |
Total height | 1.48 |
Cutting height | 4.0 m |
Cutting width | 5.1 m |
Cutting area | 20.5 |
Cutting head speed | 44 rpm |
Travel speed | 0~6.6 m/min |
Table 5.
Maximum stress and deformation of main beam.
Table 5.
Maximum stress and deformation of main beam.
Working Condition | Maximum Deformation (mm) | Maximum Stress (MPa) |
---|
Working condition 1: uniform loading | 0.082 | 21.26 |
Working condition 2: loading at both ends | 0.492 | 43.22 |
Working condition 3: loading on both sides | 0.086 | 22.28 |
Working condition 4: lateral eccentric load | 5.810 | 210.29 |
Working condition 5: longitudinal eccentric load | 7.220 | 128.18 |
Working condition 6: torsional loading | 4.219 | 107.93 |
Table 6.
First six natural frequencies of main beam.
Table 6.
First six natural frequencies of main beam.
No. | Vibration Frequency (Hz) |
---|
1 | 26.41 |
2 | 37.16 |
3 | 40.77 |
4 | 77.06 |
5 | 141.92 |
6 | 152.40 |
Table 7.
Parameter values of main beam design variables.
Table 7.
Parameter values of main beam design variables.
Design Variables | Initial Value (mm) | Lower Limit Value (mm) | Upper Limit Value (mm) | Physical Meaning |
---|
P1 | 25.0 | 22.5 | 27.5 | Thickness of left and right walls of longitudinal beam |
P2 | 25.0 | 22.5 | 27.5 | Thickness of upper and lower walls of longitudinal beam |
P3 | 30.0 | 27.0 | 33.0 | Thickness of left and right walls of cross beam |
P4 | 30.0 | 27.0 | 33.0 | Thickness of upper and lower walls of cross beam |
Table 8.
Number of central composite test design sample points.
Table 8.
Number of central composite test design sample points.
| | |
---|
1 | 0 | 5 |
2 | 0 | 9 |
3 | 0 | 15 |
4 | 0 | 25 |
5 | 1 | 27 |
6 | 1 | 45 |
Table 9.
Sample points selected for central composite design.
Table 9.
Sample points selected for central composite design.
No. | P1 (mm) | P2 (mm) | P3 (mm) | P4 (mm) |
---|
1 | 25.0 | 25.0 | 30.0 | 30.0 |
2 | 22.5 | 25.0 | 30.0 | 30.0 |
3 | 27.5 | 25.0 | 30.0 | 30.0 |
4 | 25.0 | 22.5 | 30.0 | 30.0 |
5 | 25.0 | 27.5 | 30.0 | 30.0 |
6 | 25.0 | 25.0 | 27.0 | 30.0 |
7 | 25.0 | 25.0 | 23.0 | 30.0 |
8 | 25.0 | 25.0 | 30.0 | 27.0 |
| | | | |
14 | 23.239 | 23.239 | 32.113 | 27.887 |
15 | 26.760 | 23.239 | 32.112 | 27.887 |
16 | 23.239 | 26.760 | 32.112 | 27.887 |
17 | 26.760 | 26.760 | 32.112 | 27.887 |
18 | 23.239 | 23.239 | 27.887 | 32.112 |
19 | 26.760 | 23.239 | 27.887 | 32.112 |
20 | 23.239 | 26.760 | 27.887 | 32.112 |
21 | 26.760 | 26.760 | 27.887 | 32.112 |
22 | 23.239 | 23.239 | 32.112 | 32.112 |
23 | 26.760 | 23.239 | 32.112 | 32.112 |
24 | 23.239 | 26.760 | 32.112 | 32.112 |
25 | 26.760 | 26.760 | 32.112 | 32.112 |
Table 10.
True response value of sample point objective function.
Table 10.
True response value of sample point objective function.
No. | Max. Deformation (mm) | Max. Equivalent Stress (MPa) | Minimum Fatigue Life (Times) | First Order Natural Frequency (Hz) | Quality (kg) |
---|
1 | 5.810 | 210.288 | 78,810.001 | 26.411 | 8436.186 |
2 | 5.819 | 210.492 | 78,633.709 | 26.644 | 8347.873 |
3 | 5.801 | 209.859 | 79,507.420 | 26.185 | 8524.498 |
4 | 5.815 | 211.099 | 77,807.800 | 26.643 | 8347.873 |
5 | 5.811 | 210.280 | 78,925.294 | 26.184 | 8524.498 |
6 | 6.108 | 221.705 | 65,001.531 | 25.993 | 8204.454 |
7 | 5.587 | 205.360 | 86,086.919 | 26.741 | 8667.918 |
8 | 5.984 | 243.385 | 46,162.493 | 26.237 | 8204.454 |
| | | | | |
14 | 5.766 | 238.070 | 50,057.375 | 26.861 | 8313.802 |
15 | 5.753 | 237.370 | 50,600.337 | 25.938 | 8439.934 |
16 | 5.764 | 237.765 | 50,292.723 | 25.940 | 8439.933 |
17 | 5.747 | 237.277 | 50,672.835 | 25.624 | 8562.561 |
18 | 5.932 | 219.041 | 67,949.483 | 26.861 | 8313.806 |
19 | 5.911 | 217.810 | 69,368.278 | 26.521 | 8439.938 |
20 | 5.920 | 219.261 | 67,699.881 | 26.520 | 8439.937 |
21 | 5.908 | 212.324 | 76,174.330 | 26.209 | 8562.565 |
22 | 5.576 | 206.510 | 84,341.098 | 26.519 | 8634.433 |
23 | 5.555 | 206.278 | 84,689.830 | 26.183 | 8760.565 |
24 | 5.561 | 207.553 | 82,797.412 | 26.188 | 8760.564 |
25 | 5.552 | 206.538 | 84,298.557 | 25.881 | 8883.192 |
Table 11.
Sample point objective function fitting response value.
Table 11.
Sample point objective function fitting response value.
No. | Max. Deformation (mm) | Max. Equivalent Stress (MPa) | Min. Fatigue Life (Times) | First-Order Natural Frequency (Hz) | Mass (kg) |
---|
1 | 5.803 | 205.732 | 82,113.190 | 26.426 | 8436.186 |
2 | 5.822 | 212.233 | 77,230.004 | 26.639 | 8347.852 |
3 | 5.801 | 210.420 | 79,294.534 | 26.181 | 8524.519 |
4 | 5.821 | 212.238 | 77,093.582 | 26.634 | 8347.852 |
5 | 5.811 | 211.445 | 78,022.916 | 26.177 | 8524.519 |
6 | 6.122 | 225.696 | 64,658.508 | 25.970 | 8204.226 |
7 | 5.580 | 203.672 | 84,816.411 | 26.750 | 8668.145 |
8 | 5.989 | 257.428 | 33,054.988 | 26.215 | 8204.220 |
9 | 5.673 | 211.320 | 75,044.701 | 26.516 | 8668.151 |
10 | 6.178 | 257.849 | 37,772.533 | 26.280 | 7981.767 |
| | | | | |
14 | 5.769 | 234.588 | 54,228.663 | 26.859 | 8313.807 |
15 | 5.752 | 235.838 | 52,435.727 | 26.526 | 8439.930 |
16 | 5.760 | 236.030 | 52,316.939 | 26.521 | 8439.930 |
17 | 5.747 | 235.718 | 52,531.648 | 26.210 | 8562.554 |
18 | 5.928 | 220.614 | 65,779.008 | 26.517 | 8313.815 |
19 | 5.911 | 218.374 | 68,471.157 | 26.184 | 8439.938 |
20 | 5.918 | 219.617 | 66,991.589 | 26.189 | 8439.938 |
21 | 5.906 | 215.814 | 71,691.383 | 25.878 | 8562.562 |
22 | 5.580 | 209.575 | 81,676.828 | 27.034 | 8634.355 |
23 | 5.562 | 209.092 | 82,425.723 | 26.703 | 8760.478 |
24 | 5.566 | 210.140 | 80,834.164 | 26.704 | 8760.478 |
25 | 5.553 | 208.095 | 83,590.704 | 26.395 | 8883.102 |
Table 12.
Response surface model significance analysis parameters.
Table 12.
Response surface model significance analysis parameters.
Fit Goodness Index | | | | | |
---|
| 0.999 | 0.946 | 0.945 | 0.999 | 0.999 |
| 0.999 | 0.935 | 0.934 | 0.999 | 0.999 |
| | | | | |
Table 13.
Optimal solution of multiobjective optimization.
Table 13.
Optimal solution of multiobjective optimization.
No. | P1 (mm) | P2 (mm) | P3 (mm) | P4 (mm) | Max. Deform. (mm) | Max. Stress (MPa) | Min. Fatigue Life (Times) | 1st Order Frequency (Hz) | Mass (kg) |
---|
1 | 22.96 | 23.63 | 31.25 | 30.26 | 5.706 | 206.84 | 82566 | 26.89 | 8432.2 |
2 | 23.86 | 22.66 | 31.08 | 30.38 | 5.714 | 207.33 | 82152 | 26.88 | 8426.0 |
3 | 24.86 | 23.04 | 30.09 | 30.52 | 5.778 | 206.35 | 82042 | 26.64 | 8410.9 |
Table 14.
Design variable correction value.
Table 14.
Design variable correction value.
Design Variables | Original Value (mm) | Optimization Value (mm) | Correction Value (mm) |
---|
P1 | 25 | 24.86 | 24.9 |
P2 | 25 | 23.04 | 23.0 |
P3 | 30 | 30.09 | 30.1 |
P4 | 30 | 30.52 | 30.5 |
Table 15.
Performance parameters of main beam before and after optimization.
Table 15.
Performance parameters of main beam before and after optimization.
Index | Max. Deformation (mm) | Max. Stress (MPa) | Min. Fatigue Life (Times) | First-Order Natural Frequency (Hz) | Mass (kg) |
---|
Before optimization | 5.81 | 210.29 | 78810 | 26.41 | 8516.2 |
After optimization | 5.78 | 206.82 | 82769 | 26.72 | 8419.1 |
Variation (%) | −0.51% | −1.65% | +5.02% | +1.17% | −1.14% |