# Motion Law and Mechanical Properties of PIGs When Passing through a Pipe Bend

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Equation of Motion

#### 2.2. Experimental System

#### 2.3. Effect of the Number of Leather Cups on PIG Cornering

^{2}, which is the minimum, while the resistance is at its maximum. The PIG of four cups passes through the 4th sensor at 3.96 m/s, passes through the 6th sensor after 0.7 s, decelerates to 0.98 m/s, and the acceleration is −4.26 m/s

^{2}. In addition, the PIG of six cups passes at 2.23 m. After the PIG passes through the 4th sensor, it passes through the 6th sensor after 0.8 s, decelerates to 0.98 m/s, and the acceleration is −1.56 m/s

^{2}which is the maximum. The two-cup PIG has the fastest running speed in the whole process and the smallest bending acceleration, and the contact force between the cup and the pipe wall is the largest during bending; the 6-cup PIG runs the slowest in the whole process and has the largest bending acceleration. Moreover, the indirect contact force is minimal. According to Equation (5), it can be obtained that the two-cup PIG receives the most friction and wears the most severely during cornering. As shown in Figure 5b, acceleration and resistance are negatively correlated with the number of leather bowls. There is a large decrease in acceleration compared to resistance.

## 3. Results

#### 3.1. Effect of Changing the Number of Leather Cups on PIG Cornering

#### 3.2. The Effect of the Cup Spacing Ratio on PIG Cornering

#### 3.3. Analysis of the Cornering Characteristics of Double-Cabin PIGs

#### 3.4. Mechanical Properties of the Cup and the Core Tube

## 4. Conclusions

- (1)
- Through simulation research, the PIG speed of the two leather cups is the fastest in cornering, but the stress on the leather cups is too large, which can easily cause damage to the PIG leather cups. The speed of the leather cup PIG is very low when cornering, which affects its overall ability to pass through the pipe. When choosing the number of leather cups for the PIG to bend, one can give priority to four leather PIGs or six leather PIGs, which can improve the situation in which the PIGs block the pipeline due to wear of the leather cups.
- (2)
- When the leather cup interval ratio is 3%, the running speed is the fastest, but the PIG leather cup is easily damaged when the maximum stress reaches 9 MPa. The ratio of the leather cup interval to 10% of the PIG easily causes jamming when cornering, and the speed sharply decreases. Since the ratio of the leather cup interval to the length of the PIG is 7%, this setup is better than those of the other scenarios.
- (3)
- The increase in the number of cabins will seriously reduce the speed of the PIG movement, and the transmission of the force of the universal joint to the second half of the curve during cornering will also affect the entire PIG cornering speed. The force between the cross-universal joints is basically uniform during the whole movement process, and at some point, the force between the driving fork and the driven fork suddenly increases, which will cause the stress on the cup to increase. Additionally, the cup and pipe disengagement affect the movement of the entire PIG. When using the dual-cabin PIG for cornering, the damage to the leather cup can be decreased to a certain extent, the pressure difference between the front and rear is stable, and the service life of the leather cup is increased. However, the more important task is to solve the PIG power problem.
- (4)
- The contact force between each cup and the core tube remains basically unchanged during the bend, but when the pipeline robot collides with the pipeline, the contact force generated is much greater than the contact force before the collision. At the same time, the second cup closest to the core tube has the largest contact force with the core tube during movement. Therefore, during processing, strengthening the stability of the connection between the leather cup near the core tube and the core tube and thickening the leather cup to prevent damage to the leather cup caused by excessive contact force are considered.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Serving system and observation areas A, B, C, D: (

**a**) 1, 2 and 3 are ball value 1, 2 and 3; (

**b**) A, B, C and D are the four observation areas.

**Figure 4.**Pressure sensor values for each monitoring section: (

**a**) A observation area; (

**b**) B observation area; (

**c**) C observation area; (

**d**) D observation area.

**Figure 5.**Velocity at each node, average acceleration, and resistance during cornering: (

**a**) change of speed; (

**b**) change of acceleration.

**Figure 6.**Comparison of the speed of different cup numbers of pipe cleaners through bends: (

**a**) number of cups is 2, (

**b**) number of cups is 3, (

**c**) number of cups is 4, (

**d**) number of cups is 6, (

**e**) and number of cups is 8.

**Figure 9.**Movement speed of different cup interval ratios: (

**a**) cup spacing ratio of 3%; (

**b**) cup spacing ratio of 10%; (

**c**) cup spacing ratio of 7%; and (

**d**) cup spacing ratio of 8%.

**Figure 13.**Comparison of the maximum stress of each numbered leather cup and the contact force of the previous numbered leather cup.

Parts | Material/Model | Number |
---|---|---|

Straight pipes | Acrylic glass/stainless steel | 4 |

Bends | Acrylic glass/stainless steel | 4 |

Pipe fixing clips | Stainless steel | 8 |

Pressure control pumps | CDMF10-8FSWSC | 1 |

Pressure sensors | MIK-P300 | 13 |

Flow meters | Caliber DN25 | 1 |

Flow control valves | Caliber DN50 | 1 |

Parts | Material | Dimensions (mm) |
---|---|---|

Flanges | Aluminum | 10 |

Mandrel | Aluminum | 60 |

Leather bowls | Polyurethane | 25 |

End caps | Aluminum | 10 |

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**MDPI and ACS Style**

Chen, S.; Xia, L.; Wang, X.; Teng, K.; Zhang, Y.; Zhang, M.; Gong, Y.
Motion Law and Mechanical Properties of PIGs When Passing through a Pipe Bend. *Machines* **2022**, *10*, 963.
https://doi.org/10.3390/machines10100963

**AMA Style**

Chen S, Xia L, Wang X, Teng K, Zhang Y, Zhang M, Gong Y.
Motion Law and Mechanical Properties of PIGs When Passing through a Pipe Bend. *Machines*. 2022; 10(10):963.
https://doi.org/10.3390/machines10100963

**Chicago/Turabian Style**

Chen, Shengtao, Lei Xia, Xiaolu Wang, Kai Teng, Yibo Zhang, Meiyu Zhang, and Yongjun Gong.
2022. "Motion Law and Mechanical Properties of PIGs When Passing through a Pipe Bend" *Machines* 10, no. 10: 963.
https://doi.org/10.3390/machines10100963