# Design and Implementation of a Digital Twin System for Log Rotary Cutting Optimization

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Five-Dimensional Model

_{DT}) [14], as shown in (1). The system design is illustrated in Figure 1, consisting of five components: the physical entity (PE) of the log rotary cutting system, the virtual entity (VE) of the log rotary cutting system, the digital twin data (DD) generated by the integration of the physical entity and services, the service system (SS) that supports cutting analysis and simulation, and the connection of data (CN) and information between the components. The digital twin data includes the physical data of the log rotary cutting system during actual operation, data collected by sensors, virtual data generated by the log rotary cutting system model during simulation, and service data generated by the service system.

#### 2.1.1. Materials

#### 2.1.2. Physical Entity of the Log Cutting System

#### 2.1.3. Virtual Entity of the Log Rotary Cutting System

_{1}represents the equipment virtual entity, D

_{2}represents the product virtual entity, and D

_{3}represents the virtual entity of the environment [15].

_{1}represents the equipment virtual entity and S

_{1}represents the equipment behavior model. The digital space should establish a corresponding twin model for the functional components of actual equipment to achieve synchronized mapping in behavior. V

_{1}represents the driving service, and the organic connection and operation of the behavior model require support from various driving services. In Unity3D, C# programming language and control protocols are used to control them. In addition, the implementation of device functions, signal processing, model behavior, and constraints on operating rules can all be achieved through driving services.

_{2}represents the three-dimensional state model of the product and V

_{2}represents the evolution driving service.

_{3}represents the environmental state model, and V

_{3}represents the environmental detection service. The physical layer obtains environmental data through sensors, which is then parsed in the service layer and displayed quantitatively. Combined with data, algorithm models and other technologies are used to study the system, achieving intelligent decision-making and optimization of the digital twin production line operation process.

#### 2.1.4. Digital Twin Data

#### 2.1.5. Service System

Algorithm 1 Finding the largest inscribed cylinder of a log |

Input: ${x}_{i}$: The abscissa of log point cloud data;${y}_{i}$: The ordinate of $\mathrm{l}\mathrm{o}\mathrm{g}$ point cloud data; $n$: The number of log point cloud data; Output: $a$: The abscissa of the center of the log’s largest inscribed cylinder;$b$: The ordinate of the center of the log’s largest inscribed cylinder; $r$: The radius of the center of the log’s largest inscribed cylinder; 1: function GetInsCylinerLog2: for each ${x}_{i},{y}_{i}$ do3: $f\left({x}_{i},{y}_{i};a,b,r\right)={\mathrm{m}\mathrm{i}\mathrm{n}}_{a,b,r}{\sum}_{i=1}^{n}\left({r}^{2}-2a{x}_{i}-2b{y}_{i}-{a}^{2}-{b}^{2}\right)$ 4: $\u25b9$ define the unknown model as a function 5: end for6: for each ${x}_{i},{y}_{i}$ do 7:${e}_{i}=\sqrt{{\left({x}_{i}-a\right)}^{2}+{\left({y}_{i}-b\right)}^{2}}-r$; ▹ build error function 8: end for9: for each ${x}_{i},{y}_{i}$ do10: $\left\{\begin{array}{c}\frac{\partial}{\partial a}\left[{{\displaystyle \sum _{i=1}^{n}}\left(2{x}_{i}^{2}-4a{x}_{i}+2{y}_{i}^{2}-4b{y}_{i}+{a}^{2}+{b}^{2}\right){r}^{2}-2r{\displaystyle \sum _{i=1}^{n}}\left({x}_{i}-a\right)\left({y}_{i}-b\right)+n\left({a}^{2}+{b}^{2}\right)}_{}^{}\right]=0\\ \\ \frac{\partial}{\partial b}\left[{{\displaystyle \sum _{i=1}^{n}}\left(2{x}_{i}^{2}-4a{x}_{i}+2{y}_{i}^{2}-4b{y}_{i}+{a}^{2}+{b}^{2}\right){r}^{2}-2r{\displaystyle \sum _{i=1}^{n}}\left({x}_{i}-a\right)\left({y}_{i}-b\right)+n\left({a}^{2}+{b}^{2}\right)}_{}^{}\right]=0\\ \\ \frac{\partial}{\partial r}\left[{{\displaystyle \sum _{i=1}^{n}}\left(2{x}_{i}^{2}-4a{x}_{i}+2{y}_{i}^{2}-4b{y}_{i}+{a}^{2}+{b}^{2}\right){r}^{2}-2r{\displaystyle \sum _{i=1}^{n}}\left({x}_{i}-a\right)\left({y}_{i}-b\right)+n\left({a}^{2}+{b}^{2}\right)}_{}^{}\right]=0\end{array}\right.$ 11: $\u25b9$ solve for the unknown 12: end for13: return $a,b,r$14: end function |

_{1}, the instantaneous diameter of the log is D

_{2}, the veneer thickness is S, the rotational speed of the drive roller is n, and the rotational speed of the log is N, then the horizontal coordinate of the rotary cutter edge during the log rotary cutting process can be expressed as:

#### 2.1.6. The Connection of Each Part

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**(

**a**) Composition of the experimental platform; (

**b**) The experimental platform. (1: front card shaft; 2: synchronous belt pulley; 3: DC motor; 4: rear card shaft; 5: sensor).

Log Size | 150 mm | 175 mm | 200 mm |
---|---|---|---|

X-axis offset range (mm) | −0.39~0.63 | −0.23~0.95 | −0.21~0.88 |

Y-axis offset range (mm) | −0.05~0.82 | −0.31~0.78 | −0.11~0.50 |

Radius minimum (mm) | 148.73 | 172.55 | 198.36 |

Radius maximum (mm) | 151.52 | 177.34 | 201.68 |

Data Sources | Solidworks Model | System Measurement Results | Manual Measurement Results |
---|---|---|---|

Volume | 0.0842 m^{3} | 0.0865 m^{3} | 0.0950 m^{3} |

Volume error | - | 2.7% | 12.8% |

Maximum inscribed circle radius | 150 mm | 154.23 mm | 166.27 mm |

Yield error | - | 5.7% | 23.5% |

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**MDPI and ACS Style**

Zhao, Y.; Yan, L.; Wu, J.; Song, X.
Design and Implementation of a Digital Twin System for Log Rotary Cutting Optimization. *Future Internet* **2024**, *16*, 7.
https://doi.org/10.3390/fi16010007

**AMA Style**

Zhao Y, Yan L, Wu J, Song X.
Design and Implementation of a Digital Twin System for Log Rotary Cutting Optimization. *Future Internet*. 2024; 16(1):7.
https://doi.org/10.3390/fi16010007

**Chicago/Turabian Style**

Zhao, Yadi, Lei Yan, Jian Wu, and Ximing Song.
2024. "Design and Implementation of a Digital Twin System for Log Rotary Cutting Optimization" *Future Internet* 16, no. 1: 7.
https://doi.org/10.3390/fi16010007