# Parameters Optimization of a Hydraulic Buffer System for Belt Arrestor in Downward Belt Conveyors

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Belt Arrestors

#### 2.2. Hydraulic Buffer Device

#### 2.3. Discussion

## 3. The Working Principle of the Hydraulic Buffer System

## 4. Parameters Optimization Method of the Hydraulic Buffer System

#### 4.1. Model of the Hydraulic Buffer System

_{f}is the resistance of the buffer process, θ is the lean angle of the conveyor, {x

_{c}} are the displacement of the belt, {x

_{p}} are the displacement of the piston rod, k

_{c}is the equivalent stiffness of the conveyer belt, and c is the equivalent damping coefficient of the conveyer belt.

_{p}} is the mass of the belt arrestor and the piston rod, B

_{p}is the damping coefficient of the damping cylinder, P is the hydraulic buffer pressure, and A

_{p}is the section area of the piston rod.

_{p}is the real-time volume of the buffer cavity, ${V}_{p}={A}_{p}\left({L}_{0}-{x}_{p}\right)$, L

_{0}is the stroke of the buffer cylinder, β is the elastic modulus of the hydraulic oil, and Q is the flow out of the buffer cavity.

_{0}is the spring pre-compression.

_{0}is the spool throttle area of the relief valve and A

_{0}is simplified as ${A}_{0}=\pi x\mathrm{sin}\text{}\left(\alpha \right)$.

#### 4.2. Reference Model of the Hydraulic Buffer System

_{n}is the natural frequency and ζ is the damping ratio.

_{n}is chosen as the rise time of the pressure response for the relief valve.

_{r}gives Equation (10).

#### 4.3. Optimization Algorithm

## 5. Simulation Example

#### 5.1. Preparing Work

_{0}, K are as follows, D: 0–50 mm; x

_{0}: 0–100 mm; and K: 0–1000 N/mm.

#### 5.2. Simulation Results and Analysis

_{1}is set as 100 mm and the piston rod diameter of the buffer cylinder d

_{2}is set as 50 mm.

## 6. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The working principle of the hydraulic buffer system. 1, Broken-belt of downward belt conveyor; 2, Belt arrestor; 2.1, Torsional spring; 2.2, Arrestor brake; 2.2.1, Groove; 2.3, Trigger latch; 2.4, Limiting mechanism; 2.5, Arrestor cylinder; 3, Buffer motion link; 4, Conveyor rail; 5, Buffer cylinder; 6, Buffer cylinder fixed device; 7, Solenoid valve; 8, Check valve; 9. Pump; 10, Oil tank; 11, Relief valve.

**Figure 2.**The buffer process for the belt arrestor. F corresponds to the arrest force of arrestor, P is the pressure of buffer chamber and Q is the flow out of the buffer cavity.

**Figure 4.**The model of the hydraulic buffer system. C corresponds to the equivalent damping coefficient of the conveyer belt, k

_{c}is the equivalent stiffness of the conveyer belt and M indicates the mass of the conveyor belt.

**Figure 5.**The simulation model of the hydraulic buffer system. P corresponds to the pressure of buffer chamber, Q is the flow out of the buffer cavity, x is the spool displacement, x

_{p}indicates the displacement of the piston rod, x

_{c}is the displacement of belt, v

_{c}corresponds to the speed of the belt and v

_{p}is the speed of the piston rod.

**Figure 8.**The optimized performance curves: (

**a**) The pressure reference model of d

_{1}= 100 mm, d

_{2}= 50 mm; (

**b**) The buffer pressure; (

**c**) The displacement of piston rod and (

**d**) The speed of piston rod.

**Figure 9.**The optimized performance curves in different buffer cylinder: (

**a**) The pressure reference model of d

_{1}= 87 mm, d

_{2}= 70 mm; (

**b**) The buffer pressure; (

**c**) The displacement of piston rod and (

**d**) The speed of piston rod.

Parameters | Units |
---|---|

Spacing of bearing roller | 1.5 m |

Belt speed (v_{0}) | 4 m/s |

Delivery capacity | 2500 t/h |

Unit mass of belt | 35 kg |

Unit mass of load | 173.61 kg |

Equivalent stiffness | 10^{7} N/m/s |

Equivalent damping coefficient | 10^{6} N/m/s |

Lean angle of the belt conveyor | 20° |

Components | Parameters | Symbols | Units |
---|---|---|---|

Buffer cylinder | Initial pressure | P_{0} | 2 MPa |

Damping coefficient | B_{p} | 50 N/m/s | |

Relief valve | Diameter of spool | D | 0.03 m |

Damping coefficient | B | 10 N/m/s | |

Spring stiffness | K | 600 N/mm | |

Spring pre compression | x_{0} | 0.035 m | |

Hydraulic oil | Density | ρ | 870 kg/m^{3} |

Elastic modulus | E | 1.4 × 10^{9} MPa |

Optimization Results | Symbols | Frist Optimization | Second Optimization | ||
---|---|---|---|---|---|

Units | Integers | Units | Integers | ||

Spool diameter of relief valve | D | 43.68 | 44 | 40.27 | 40 |

Spring stiffness | K | 204.29 | 204 | 410.15 | 410 |

Spring pre-compression | x_{0} | 63.46 | 63 | 24.31 | 24 |

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**MDPI and ACS Style**

Yin, W.; Yang, Y.; Wang, Z.; Xu, J.
Parameters Optimization of a Hydraulic Buffer System for Belt Arrestor in Downward Belt Conveyors. *Math. Comput. Appl.* **2016**, *21*, 42.
https://doi.org/10.3390/mca21040042

**AMA Style**

Yin W, Yang Y, Wang Z, Xu J.
Parameters Optimization of a Hydraulic Buffer System for Belt Arrestor in Downward Belt Conveyors. *Mathematical and Computational Applications*. 2016; 21(4):42.
https://doi.org/10.3390/mca21040042

**Chicago/Turabian Style**

Yin, Wenjun, Yinwei Yang, Zhanyu Wang, and Jing Xu.
2016. "Parameters Optimization of a Hydraulic Buffer System for Belt Arrestor in Downward Belt Conveyors" *Mathematical and Computational Applications* 21, no. 4: 42.
https://doi.org/10.3390/mca21040042