# Study on the Accessibility Impact of Anti-Rolling Tank on the Offshore Wind O&M Gangway

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Calculations

#### 2.1. Ship Motion Model with Controllable Passive Anti-Rolling Tank

_{w}

_{4}represents wave interference moment; $\phi $, $\dot{\phi}$ and $\ddot{\phi}$ represent the roll angle, roll angular velocity, and roll angular acceleration, respectively; $\tau $, $\dot{\tau}$ and $\ddot{\tau}$ represent the tank level angle, angular velocity, and angular acceleration, respectively; I

_{44}and a

_{44}are the inertia moment and added inertia moment, respectively; b

_{44}and c

_{44}are damping and restoring moment coefficients, respectively; a

_{4τ}, c

_{4τ}, a

_{τ}

_{4}and c

_{τ}

_{4}are the coupling coefficients related to the inertia moment and restoring moment between ship rolling and tank, respectively and a

_{ττ}, b

_{ττ}and c

_{ττ}are the coefficients related to roll inertia moment, roll damping moment and roll restoring moment of the tank, respectively.

_{0}in the tank when the valve is closed, then

_{0}, and z

_{1}are the incident hydrostatic pressure of the side tank datum plane, atmospheric pressure, and vertical distance from the datum plane of the side tank to the valve, respectively. n is the index of the variable compression process.

#### 2.2. Inverse Kinematics of Gangway

_{1}and the change of the length of the pitching rod ΔL

_{2}that keep the end effector of the gangway on the ship at the desired position when the ship rolls under the excitation of sea waves.

_{2c}, which can be expressed by the following formula:

_{2c}is shown in Figure 4.

_{20}. a

_{1}is the vertical distance from the pitch axis center to the static hinge point of the pitch rod, and a

_{2}is the distance from the pitch axis coordinate point to the dynamic hinge point of the pitch driver. According to geometric relationship, θ

_{20}can be expressed as:

_{2}is as follows:

#### 2.3. Control of Air Valve

_{0}is the roll amplitude of the ship.

_{β}= arctan(a/ω

_{e}) is the phase difference between the air valve control signal at the switching time and the ship roll motion.

_{0}is the fluid motion amplitude in the tank and θ

_{0}is the phase lag caused by the inertia of the fluid in the tank. It can be seen that when ε

_{β}+ θ

_{0}= π/2, the controllable passive anti-rolling effect is the best.

## 3. Simulation Analysis

#### 3.1. Hydrodynamic Simulation

_{t}is obtained by simulating the free and forced oscillatory motion of the fluid in the tank by Ansys Fluent, the cloud diagram of free oscillation of fluid in the tank is shown in Figure 5.

_{τ}is about 8.975 s and the dimensionless damping coefficient n

_{t}is 0.062.

_{τ}

_{1}= 9.108 s and n

_{τ}

_{1}= 0.108, respectively, with 1 channel. The natural period and dimensionless damping coefficient of the tank are T

_{τ}

_{6}= 8.975 s and n

_{τ}

_{6}= 0.062, respectively, with 6 channels. From the simulation results, it can be seen that the valve opening has an impact on both the period and damping, but the degree of impact varies. Compared to the period and damping of 1 channel, the period and damping of 6 channels have changed by 1.46% and 42.59%, respectively. The simulation results show that the dimensionless damping coefficient of the tank increases with the decrease of the air valve opening, but has little effect on the natural period of the tank. Compared to the tank period, the damping of the tank is more sensitive to the opening of the gas channel.

#### 3.2. Roll Period Prediction Based on Wavelet Neural Network

#### 3.3. Impact of Anti-Rolling Tank on Gangway Accessibility

## 4. Hardware-in-the-Loop Simulation

#### 4.1. Control Architecture

#### 4.2. HIL Simulation Results

_{1}and ΔL

_{2}are 25 mm and 24 mm, respectively. The HIL simulation results of the command length and speed of gangway telescopic rod and pitch rod under the condition of a significant wave height of 2.5 m and ship speed of 0 kn are shown in Figure 17, Figure 18, Figure 19 and Figure 20.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 11.**Roll angle of no tank, passive anti-rolling tank, and controllable passive anti-rolling tank.

**Figure 12.**Roll angular velocity of no tank, passive anti-rolling tank, and controllable passive anti-rolling tank.

**Figure 13.**Tank level angle of passive anti-rolling tank and controllable passive anti-rolling tank.

**Figure 17.**Command length of gangway telescopic rod and pitch rod when the ship is equipped with passive anti-rolling tank.

**Figure 18.**Command speed of gangway telescopic rod and pitch rod when the ship is equipped with passive anti-rolling tank.

**Figure 19.**Command length of gangway telescopic rod and pitch rod when the ship is equipped with controllable passive anti-rolling tank.

**Figure 20.**Command speed of gangway telescopic rod and pitch rod when the ship is equipped with controllable passive anti-rolling tank.

**Figure 21.**Comparison between uncompensated and compensated end effector trajectory when the ship is not equipped with an anti-rolling tank.

**Figure 22.**Comparison between uncompensated and compensated end effector trajectories when the ship is equipped with a passive anti-rolling tank.

**Figure 23.**Comparison between uncompensated and compensated end effector trajectories when the ship is equipped with a controllable passive anti-rolling tank.

Description | Value | Unit |
---|---|---|

Displacement | 3850 | ton |

Water length | 125 | m |

Beam | 13.8 | m |

Depth | 7 | m |

Draft | 4.33 | m |

Height of CG | 5.6 | m |

Metacentric height | 1.5 | m |

Roll period | 9.38 | s |

Description | Value | Unit |
---|---|---|

Height of tank | 4.4 | m |

Width of tank | 11.23 | m |

Depth of tank | 5.85 | m |

Level angle of tank | 0~18 | deg |

Width of liquid channel | 8.8 | m |

Width of side tank | 2.44 | m |

Tank level height | 1.93 | m |

Distance between CG and center line of liquid channel | 3.76 | m |

Tank period | 9.38 | s |

Height of liquid channel | 0.75 | m |

Air channel number | 6 | - |

Description | Symbol | Limitation | Unit |
---|---|---|---|

Length variation of telescopic rod | ΔL_{1} | 0~50 | mm |

Speed of telescopic rod | v_{1} | $\pm $17 | mm/s |

Length variation of pitch rod | ΔL_{2} | 0~50 | mm |

Speed of pitch rod | v_{2} | $\pm $17 | mm/s |

Roll Angle (°) | Roll Rate (rad/s) | Tank Level Angle (°) | |
---|---|---|---|

No tank | −5.15~5.02 | −0.05777~0.05619 | - |

Passive anti-rolling tank | −3.00~3.85 | −0.03945~0.03889 | −7.07~7.91 |

Controllable passive anti-rolling tank | −2.14~2.35 | −0.02798~0.02915 | −6.00~5.44 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, S.; Zhao, P.; Li, C.; Song, Z.; Liang, L.
Study on the Accessibility Impact of Anti-Rolling Tank on the Offshore Wind O&M Gangway. *J. Mar. Sci. Eng.* **2023**, *11*, 848.
https://doi.org/10.3390/jmse11040848

**AMA Style**

Zhang S, Zhao P, Li C, Song Z, Liang L.
Study on the Accessibility Impact of Anti-Rolling Tank on the Offshore Wind O&M Gangway. *Journal of Marine Science and Engineering*. 2023; 11(4):848.
https://doi.org/10.3390/jmse11040848

**Chicago/Turabian Style**

Zhang, Songtao, Peng Zhao, Chenyang Li, Ziqi Song, and Lihua Liang.
2023. "Study on the Accessibility Impact of Anti-Rolling Tank on the Offshore Wind O&M Gangway" *Journal of Marine Science and Engineering* 11, no. 4: 848.
https://doi.org/10.3390/jmse11040848