# Dynamic Simulation and Experimental Study of the HDPE Double-Walled Corrugated Pipe Grouting Robot

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## Abstract

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## 1. Introduction

## 2. Overall Design and Repair Process of the Pipeline Grouting Robot

#### 2.1. The Overall Design of the Pipeline Grouting Robot

#### 2.2. Technology Used to Repair Internal Pipeline Collapse

## 3. Mechanical Analysis of the Pipeline Grouting Robot

#### 3.1. Mechanical Analysis of the Grouting Process

_{p}from the multi-stage hydraulic cylinder and resistance P between the soil and the grouting gun body. When the thrust F

_{p}exceeds the soil resistance P, the grouting gun body penetrates the soil. To determine the required thrust F

_{p}, it is necessary to calculate the soil resistance p value.

_{x}, and the upward lifting angle of grouting gun body is $\theta $. According to the trigonometric function relationship, the association between the soil resistance P and its horizontal component is as follows:

_{m}is the side friction resistance of the grouting gun body, P

_{n}is the tip resistance of the grouting gun body, R

_{si}is the dynamic friction resistance of the gun body, R

_{sk}is the standard value of the limit static friction resistance on the side of the gun body, l

_{i}is the length of the grouting gun body in section I, h is the soil penetration depth of the grouting gun body, h

_{j}is the conical tip length of the grouting gun head, W is the perimeter of the grouting gun body, A

_{g}is the cross-sectional area of the tip of the grouting gun head, R

_{g}is the resistance borne by the grouting gun head, R

_{pk}is the standard value of the ultimate resistance borne by the tip of the grouting gun head, and n is the number of sections of the grouting gun body, n = 3.

_{pk}= 3500 kPa, and the standard value of the ultimate static friction resistance at the side of the gun body is R

_{sk}= 50 kPa. The maximum lifting angle of the grouting gun body of the pipeline robot in different pipe diameters is shown in Table 1, according to the theoretical analysis results.

#### 3.2. Mechanical Analysis of the Deflection and Lifting Process

_{G}, in a clockwise direction. The lifting torque of the hydraulic cylinder on the rotation center of the upper plate is set as M

_{p}, in a counterclockwise direction. When M

_{p}> M

_{G}, the upward lifting of the upper plate is initiated.

_{p}is the gravity of the upper plate, its weight L

_{1}is the distance from the center of gravity of the upper plate to the rotation center of the upper plate, and β is the lifting angle of the upper plate.

_{G max}= 90 N.m. Therefore, only when M

_{p}> M

_{G max}= 90 N.m does the hydraulic cylinder lift the upper plate at a certain angle.

_{p}of the hydraulic lifting cylinder to the upper plate can be divided into a vertical component F

_{y}and a horizontal component F

_{x}:

_{2}is the horizontal distance from the rotation center of the upper plate to the action point of the hydraulic lifting cylinder, and L

_{2}= 0.1 m.

_{p}> M

_{G max}= 90 N.m, substituting the relevant parameters yields F

_{p}> 4.856 kN. Therefore, the minimum thrust of the hydraulic lifting cylinder is 4.856 kN.

#### 3.3. Mechanical Analysis of the Support Process

_{x}and vertical component P

_{y}, as shown in Figure 8. The vertical component P

_{y}can be offset by the support force N

_{ls}provided by the inner wall of the pipe, while the horizontal component Px must be offset by the friction between the support mechanism and the inner pipe wall.

_{ts}is the support force of the inner pipe wall on the support top, N

_{ls}is the support force of the inner pipe wall on the lower support and wheel, G is the gravity of the grouting robot in the pipe, and f

_{1}and f

_{3}represent the friction between the support top, lower support, and the inner pipe wall, respectively. f

_{2}is the friction between the wheel and the inner pipe wall, and angle α is the included angle between the soil resistance P and its horizontal component P

_{x}, which is the same as the lifting angle of the grouting gun body. The calculation is performed by simplifying these forces and moving their action points to the same coordinate system for analysis, where N

_{s}is the total support force generated by the vertical component of the gravity and soil resistance of the inner pipe wall on the grouting robot in the pipe, as shown in Figure 9.

_{1}, f

_{2}, and f

_{3}meet the following requirements:

_{s}required to support the hydraulic cylinder can be calculated according to the following formulas:

#### 3.4. Mechanical Analysis of the Traveling Process

_{t}required by the wheel is:

_{f1}is the friction between the wheel of the pipeline grouting robot and the inner pipe wall, F

_{f2}is the friction between the dragging pipe and the inner pipe wall, and F

_{a}represents the acceleration resistance experienced by the pipeline grouting robot while in motion.

_{a}is:

_{a}output by the motor. The output torque ultimately reaches the wheel via the two-stage planetary reducer, becoming the torque T

_{t}of the wheel. The calculation formula is:

_{a}of the motor and the output torque T

_{t}of the wheel is:

## 4. The Dynamic Simulation and Experimental Research of the Pipeline Grouting Robot

#### 4.1. Dynamic Simulation of the Pipeline Grouting Robot

#### 4.2. Horizontal Insertion Test When the Grouting Gun Enters the Soil

#### 4.3. Hot-Melt Test of the Pipeline Grouting Robot

## 5. Conclusions

- (1)
- A new internal grouting and shaping process for pipelines is proposed, which is suitable for repairing the internal collapse in HDPE double-walled corrugated pipelines. The design requirements and indexes of the pipeline grouting robot are presented. Grouting can be performed in HDPE double-walled corrugated pipelines with inner diameters of 300 mm to 600 mm and can be positioned in different areas of the collapse. This robot can penetrate the wall of the HDPE double-walled bellows since it can move on its own power.
- (2)
- The overall scheme of the pipeline grouting robot is determined. It consists primarily of hot-melt, deflection, lifting, support, monitoring, and driving mechanisms. A mechanical analysis of the grouting, deflection, lifting, support, and travel processes is performed. Furthermore, the calculation formula of the thrust required for the grouting gun to penetrate the soil is determined while experimental verification is conducted.
- (3)
- The kinematics simulation of the grouting robot is performed using the ADAMS software, confirming that the thrust of the hydraulic lifting cylinder and the supporting hydraulic rod meets the requirements and that the supporting mechanism of the grouting robot can ensure the stability of the equipment during grouting. The grouting robot designed in this paper has been well applied in practice to avoid the impact of excavation from the ground on traffic.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Internal collapse of a double-walled corrugated pipe. (

**a**) Complete double-walled corrugated pipe, (

**b**) Double wall bellows with internal collapse (The red line is the collapsed part).

**Figure 3.**Pipe-grouting shaping technology. 1. Grouting pump; 2. control cabinet; 3. winding machine; 4. traction hoist; 5. hydraulic oil pipe; 6. hydraulic pump station; 7. cables; 8. tram; 9. ground; 10. operation wellhead I; 11. pipe collapse; 12. in-pipe grouting robot; 13. water supply and drainage pipeline; 14. traction wire rope; 15. grouting hose; 16. corner protector; 17. hydraulic oil pipe; 18. operation wellhead II; 19. soil layer.

**Figure 4.**Grouting solidification treatment. (

**a**) Initial, (

**b**) positioning the grouting robot in the pipe, (

**c**) hot-melt treatment, (

**d**) inserting the grouting gun body into the soil, (

**e**) grouting, and (

**f**) milling and subsequent treatment.

**Figure 11.**The main section of pipeline grouting robot during the ADAMS simulation process. (

**a**) 1 s to 10 s; (

**b**) 10 s to 15 s; (

**c**) 15 s to 20 s; (

**d**) 20 s to 30 s.

**Figure 22.**Hot-melt hole. (

**a**) The heating head enters the pipe, (

**b**) The pipe was melted by the heating head with a hole (The red line is the hole part).

Pipe Inner Diameter (mm) | Maximum Upward Lifting Angle of Grouting Gun Body |
---|---|

300 | 5° |

400 | 11° |

500 | 16° |

600 | 22° |

Project | Parameter |
---|---|

Quality control of in-pipe grouting robot (M1) | 300 kg |

Mass of 50 m drag pipe (M2) | 100 kg |

Travel speed (v) | 0.5 m/s |

Acceleration (a) | 0.2 m/s^{2} |

Gravitational acceleration (g) | 9.8 m/s^{2} |

Wheel radius (r) | 0.05 m |

Name | Poisson’s Ratio | Modulus of Elasticity (MPa) | Density (kg/m^{3}) |
---|---|---|---|

Rubber | 0.45 | 1 × 10^{−2} | 9.6 × 10^{2} |

35 Steel | 0.29 | 2.05 × 10^{5} | 7.85 × 10^{3} |

304 Stainless steel | 0.29 | 1.9 × 10^{5} | 8 × 10^{3} |

Parameter Name | Value |
---|---|

Static friction coefficient | 0.5 |

Dynamic friction coefficient | 0.43 |

Static translation speed (mm/s) | 0.1 |

Friction translation speed (mm/s) | 10.0 |

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**MDPI and ACS Style**

Li, Y.; Xu, J.; Nan, F.; Su, H.; Zhao, T.
Dynamic Simulation and Experimental Study of the HDPE Double-Walled Corrugated Pipe Grouting Robot. *Sustainability* **2022**, *14*, 6776.
https://doi.org/10.3390/su14116776

**AMA Style**

Li Y, Xu J, Nan F, Su H, Zhao T.
Dynamic Simulation and Experimental Study of the HDPE Double-Walled Corrugated Pipe Grouting Robot. *Sustainability*. 2022; 14(11):6776.
https://doi.org/10.3390/su14116776

**Chicago/Turabian Style**

Li, Yufang, Jiyang Xu, Feng Nan, Hongli Su, and Tongxu Zhao.
2022. "Dynamic Simulation and Experimental Study of the HDPE Double-Walled Corrugated Pipe Grouting Robot" *Sustainability* 14, no. 11: 6776.
https://doi.org/10.3390/su14116776