# Stability Analysis of a Vehicle–Cargo Securing System for Autonomous Trucks Based on 6-SPS-Type Parallel Mechanisms

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^{5}

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## Abstract

**:**

## 1. Introduction

## 2. Cargo Securing Model Based on the 6-SPS Type Parallel Mechanism

#### 2.1. Cargo Securing System Modeling

_{1}~b

_{6}are the six connecting points of the moving platform, B

_{1}~B

_{6}are the six connecting points of the fixed platform.

_{1}and d

_{2}are the unilateral distances between the cargo and the platform in X and Y directions. b

_{1}~b

_{6}are the six securing points (connecting points) of the upper face of the cargo. B

_{1}~B

_{6}are the six securing points (connecting points) of the transportation platform. l

_{1}~l

_{6}are the securing lengths of the cargo. Assume that l

_{1}, l

_{3}, l

_{4}, l

_{6}have the same securing length l′, and the angles between the ropes (links) and the platform are γ

_{1}; l

_{2}, l

_{5}have the same securing length l″, and the angles between the ropes and the platform are γ

_{2}. Due to oblique rope tension in the securing process, the angle between its component in the XOY plane and X-axis is γ

_{3}.

**R**′,

**R**and

**T**are the cargo vector in the coordinate system of the cargo, cargo vector described in the coordinate system of the transportation platform and the corresponding homogeneous transformation matrix, respectively.

_{ij}(i = 1,2,3, j = 1,2,3), X

_{p}, Y

_{p}, and Z

_{p}are the rotational and translational elements of the transformation matrix.

_{1}$\in $ [0, π/2] is the value of the azimuth angles of B

_{1}, B

_{3}, B

_{4}and B

_{6}with respect to the X-axis in O-XYZ. α

_{2}$\in $ [0, π/2] is the value of the azimuth angles of b

_{1}, b

_{3}, b

_{4}and b

_{6}with respect to the X′-axis in O′-X′Y′Z′.

_{i}can be obtained as

_{1}, γ

_{2}and γ

_{3}can be calculated as

#### 2.2. Tension Analysis of Securing Ropes

^{3}).

_{1}in the cargo securing model as an example, the length is 916.254 mm, and the pre-tightening length is about 13.74 mm. According to the tension calculation, the tension force F

_{1}is

_{1}are the sectional area and the elongation of the heavy-duty securing ropes, respectively.

_{p}of the securing ropes is

_{p}and k

_{r}are the nominal load (5000 kg in this paper), the safety coefficient of polyester and the dynamic load coefficient caused by the vertical vibration acceleration, respectively. k

_{p}and k

_{r}are 2 and 1 in this paper.

_{1}< S

_{p}, which means that the tension force of the securing rope is less than its strength, the rope will not break during pre-tightening, so this pre-tightening tension is safe. After determining the pre-tightening tension, it is necessary to compare it with the pre-tightening tension in the standard. The pre-tightening tension must be greater than the pre-tightening tension in the standard to determine whether the cargo securing model is safe. The standard tension F for the securing model given in Standard EN-12195:2010 [18] is

_{x}, μ, f

_{μ}and c

_{z}are the vertical dynamic coefficient, the frictional coefficient, the conversion coefficient and the horizontal dynamic coefficient, respectively. From Equation (12), the calculated pre-tightening tension force meets the requirement of the standard, indicating the feasibility of the cargo securing model.

_{1}and γ

_{2}in Figure 5 are the same as those defined in the cargo securing model in Figure 3. G is the gravity of the whole system; v is the driving speed of the vehicle. During the transportation process, the cargo suffers from the longitudinal inertial force F

_{z}and the transverse inertial force F

_{H}. The pre-tensioning force F

_{i}provided by the securing ropes can prevent the cargo from dangerous working conditions to ensure the safety of cargo transportation.

## 3. Dynamics Analysis of the Vehicle–Cargo Securing System

_{3}is the mass of the cargo; k

_{3}and c

_{3}represent the equivalent stiffness and damping of the simplified securing ropes; m

_{2}is the mass of the transportation platform; k

_{2}and c

_{2}represent the equivalent stiffness and damping of the dashpot system of the vehicle; m

_{1}and k

_{1}represent the mass and stiffness of tires of the vehicle; v indicates that the vehicle drives along the positive direction of the X-axis at that speed; z(t) is the input excitation from the road pavement roughness; and z

_{1}, z

_{2}and z

_{3}are the dynamic responses of the tires, the transportation platform and the cargo with the input excitation, respectively.

_{0}, v and λ are the amplitude of road pavement roughness excitation, the speed of the vehicle and the wavelength of road pavement roughness excitation, respectively.

_{i}in Equation (16) as the Fourier transform of z

_{i}(i = 0, 1, 2, 3), the expression can be solved using Kramer’s rule:

_{1}, D

_{2}and D

_{3}are expressed by Equations (18)–(21), respectively.

_{3}, φ

_{3}and θ

_{3}are expressed as

## 4. Stability Analysis of Vehicle–Cargo Securing System

_{2}/l

_{5}and the kinetic energy curve of the cargo are plotted in Figure 14, Figure 15 and Figure 16.

_{2}and l

_{5}have the largest tension force under the same amplitude of vertical displacement response. From Figure 15, it is seen that the tension values of the securing ropes fluctuate within a range from 17.5 kN to 20.5 kN, and the maximum reaches 21.5 kN, less than the safety threshold of the securing ropes, whose maximum allowable tension is 22.34 kN. It is indicated that the securing ropes have the capability for large cargo transportation and will not break when suffering from the given road pavement roughness excitation during the transportation process.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Loske, D.; Klumpp, M. Intelligent and efficient? An empirical analysis of human-AI collaboration for truck drivers in retail logistics. Int. J. Logist. Manag.
**2021**, 4, 32. [Google Scholar] [CrossRef] - Wang, D.; Gao, L.; Lan, Z.; Li, W.; Ren, J.; Zhang, J.; Zhang, P.; Zhou, P.; Wang, S.; Pan, J.; et al. An intelligent self-driving truck system for highway transportation. Front. Neurorobotics
**2022**, 16, 843026. [Google Scholar] [CrossRef] [PubMed] - Chen, Y.; Zheng, X.; Zhang, Z.; Ahmadian, M. Effect of off-centred loading on roll stability of multi-trailer trucks. Int. J. Veh. Perform.
**2022**, 8, 271–295. [Google Scholar] [CrossRef] - Mindlin, R.D. Dynamics of Package Cushioning. Bell Syst. Tech. J.
**1945**, 24, 353–461. [Google Scholar] [CrossRef] - Jagelčák, J.; Saniga, J. Analysis of elongation of lashing straps on movements of cargo secured by a top-over lashing at sliding in longitudinal direction. Load Restrain. Road Veh. Saf.
**2013**, 2, 53–62. [Google Scholar] - Dai, H.; Yuan, W.; Du, R.; Dong, L. Relaxation characteristics and modeling of cargo package binding in cargo spacecraft. IOP Conf. Ser. Mater. Sci. Eng.
**2018**, 392, 062029. [Google Scholar] [CrossRef] - Zhang, D.; Tang, Y.; Clarke, D.B.; Peng, Q.; Dong, C. An innovative method for calculating diagonal lashing force of cargo on railway wagons in a curve alignment. Veh. Syst. Dyn.
**2019**, 11, 352–374. [Google Scholar] [CrossRef] - Turanov, K.; Ruzmetov, Y.; Shikhnazarov, J. Incorrectness of the method of calculating cargo fastening on railway platforms. In Proceedings of the E3S Web of Conferences, Topical Problems of Green Architecture, Civil and Environmental Engineering, TPACEE 2019, Moscow, Russia, 20–22 November 2019; Volume 164, p. 03040. [Google Scholar]
- Blumhardt, R. FEM-crash simulation and optimization. Int. J. Veh. Des.
**2001**, 26, 331–347. [Google Scholar] [CrossRef] - Zeng, X. Research of frontal energy-absorbing structure of light truck. Mod. Manuf. Eng.
**2012**, 8, 36–40. [Google Scholar] - Zong, C.; Zhang, H.; Huang, C.; Dong, J. Research on the influence of cargo securing force with typical road alignments and vehicle working conditions. In Proceedings of the 2017 4th International Conference on Transportation Information and Safety, Banff, AB, Canada, 8–10 August 2017; pp. 27–32. [Google Scholar]
- Dong, M.; Wang, J.; Pang, B.; Wang, S. Maximum oscillation amplitude of cargo caused by inertia forces for tower cranes. In Proceedings of the International Conference on Education, Management, Computer and Society, Shenyang, China, 1–3 January 2016; pp. 1410–1413. [Google Scholar]
- Fleissner, F.; Lehnart, A.; Eberhard, P. Dynamic simulation of sloshing fluid and granular cargo in transport vehicles. Veh. Syst. Dyn.
**2010**, 48, 3–15. [Google Scholar] [CrossRef] - Oliveira, L.A.; Lima, V.L.; Queiroz, T.; Miyazawa, F.K. The container loading problem with cargo stability: A study on support factors, mechanical equilibrium and grids. Eng. Optim.
**2020**, 12, 1192–1211. [Google Scholar] [CrossRef] - Junqueira, L.; Morabito, R.; Yamashita, D.S. Three-dimensional container loading models with cargo stability and load bearing constraints. Comput. Oper. Res.
**2012**, 39, 74–85. [Google Scholar] [CrossRef] - Xiong, L.; Xia, X.; Lu, Y.; Liu, W.; Gao, L.; Song, S.; Yu, Z. IMU-based automated vehicle body sideslip angle and attitude estimation aided by GNSS using parallel adaptive Kalman filters. IEEE Trans. Veh. Technol.
**2020**, 69, 10668–10680. [Google Scholar] [CrossRef] - Xia, X.; Hashemi, E.; Xiong, L.; Khajepour, A. Autonomous vehicle kinematics anddynamics synthesis for sideslip angle estimation based on consensus Kalman filter. IEEE Trans. Contr. Syst. Technol.
**2023**, 31, 179–192. [Google Scholar] [CrossRef] - EN 12195-1:2010; Lod Restraining on Road Vehicles-Safety-Part 1: Calculation of Securing Forces. European Committee for Standardization: Brussels, Belgium, 2010. Available online: https://standards.iteh.ai/catalog/standards/cen/72067d57-b90c-4ca5-8bd0-f876e25e6a6e/en-12195-1-2010 (accessed on 20 June 2023).
- Vlkovský, M.; Veselík, P. Cargo securing—Comparison of different quality roads. Acta Univ. Agric. Silvic. Mendel. Brun.
**2019**, 67, 1015–1023. [Google Scholar] [CrossRef] [Green Version] - Vlkovský, M.; Vlachova, H. Securing cargo during transport on roads of different quality. In Proceedings of the International Conference on Vehicle Technology and Intelligent Transport Systems, Heraklion, Greece, 3–5 May 2019; pp. 25–32. [Google Scholar]
- Vlkovský, M. Impact of vehicle type and road quality on cargo securing. Komunikacie
**2020**, 22, 9–14. [Google Scholar] [CrossRef] - Vlkovský, M.; Neubauer, J.; Malíšek, J.; Michálek, J. Improvement of road safety through appropriate cargo securing using outliers. Sustainability
**2021**, 13, 2688. [Google Scholar] [CrossRef] - Elnashar, G.; Bhat, R.B.; Sedaghati, R. Modeling and dynamic analysis of a vehicle-flexible pavement coupled system subjected to road surface excitation. J. Mech. Sci. Technol.
**2019**, 33, 3115–3125. [Google Scholar] [CrossRef] - Chen, Y.; Ahmadian, M. Countering the destabilizing effects of shifted loads through pneumatic suspension design. SAE Int. J. Veh. Dyn. Stab. NVH
**2019**, 4, 5–17. [Google Scholar] [CrossRef] - Misaghi, S.; Tirado, C.; Nazarian, S.; Carrasco, C. Impact of pavement roughness and suspension systems on vehicle dynamic loads on flexible pavements. Transp. Eng.
**2021**, 3, 100045. [Google Scholar] [CrossRef] - Sindha, J.; Chakraborty, B.; Chakravarty, D. Rigid body modeling of three wheel vehicle to determine the dynamic stability—A practical approach. In Proceedings of the 2015 IEEE International Transportation Electrification Conference (ITEC) IEEE, Chennai, India, 27–29 August 2015. [Google Scholar]

**Figure 1.**Holistic diagram of stability analysis of a vehicle–cargo securing system for autonomous trucks based on 6-SPS-type parallel mechanisms.

**Figure 5.**The three-dimensional vehicle–cargo system modeled in Creo with the diagram of the cargo securing system.

**Figure 11.**Virtual model of the whole vehicle–cargo securing system, with cargo securing system, in ADAMS.

**Figure 14.**Displacement response curves of the cargo and the transportation platform under class E road pavement roughness excitation based on the white noise power spectrum method.

**Figure 15.**Tension curve of securing rope l

_{2}/l

_{5}under class E road pavement roughness excitation based on the white noise power spectrum method.

**Figure 16.**Kinetic energy curve of the cargo under class E road pavement roughness excitation based on the white noise power spectrum method.

Rope No. | Securing Length (mm) |
---|---|

1 | 916.254 |

2 | 826.480 |

3 | 916.254 |

4 | 916.254 |

5 | 826.480 |

6 | 916.254 |

Item | Value |
---|---|

Fiber | Long |

Dry fracture strength | 3.8~5.3 cN/dtex |

Relative collusion strength | 85~100% |

Elastic recovery rate at 3% elongation | 95~100% |

Initial modulus | 79.2~140 cN/dtex |

Density | 1.38 g/cm^{3} |

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

m_{3} | 3 t |

k_{3} | 8 × 10^{4} N/m |

c_{3} | 1.2 × 10^{3} N·s/m |

F_{i} (i = 1, 2, …, 6) | 22.34 kN |

m_{2} | 4 t |

k_{2} | 265 kN/m |

c_{2} | 4.2 kN·s/m |

m_{1} | 30 kg |

k_{1} | 400 kN/m |

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**MDPI and ACS Style**

Zhang, G.; Wang, T.; Wang, H.; Wu, S.; Shao, Z.
Stability Analysis of a Vehicle–Cargo Securing System for Autonomous Trucks Based on 6-SPS-Type Parallel Mechanisms. *Machines* **2023**, *11*, 745.
https://doi.org/10.3390/machines11070745

**AMA Style**

Zhang G, Wang T, Wang H, Wu S, Shao Z.
Stability Analysis of a Vehicle–Cargo Securing System for Autonomous Trucks Based on 6-SPS-Type Parallel Mechanisms. *Machines*. 2023; 11(7):745.
https://doi.org/10.3390/machines11070745

**Chicago/Turabian Style**

Zhang, Guosheng, Tao Wang, Han Wang, Shilei Wu, and Zhongxi Shao.
2023. "Stability Analysis of a Vehicle–Cargo Securing System for Autonomous Trucks Based on 6-SPS-Type Parallel Mechanisms" *Machines* 11, no. 7: 745.
https://doi.org/10.3390/machines11070745