# Design and Implementation of a Digital Twin System for Log Rotary Cutting Optimization
## 2 Materials and Methods
### Five-Dimensional Model
#### 2.1.3 Virtual Entity of the Log Rotary Cutting System  
The virtual entity is based on the production factors and characteristics of the actual log rotary-cutting line and is capable of accurately reflecting the high-fidelity model of the physical log rotary-cutting system. It encompasses a three-dimensional visualization model that reflects the geometric parameters of the entire production line, a physical model that describes the physical properties of the production line, a behavioral model that characterizes the response and process features of the log rotary cutting system, and a rule model that embodies the operational rules and constraints of the system. By integrating the three-dimensional visualization model, physical model, behavioral model, and rule model, the virtual model of the log rotary cutting system comprehensively represents its actual operating state, providing a true mapping of its physical entity. Based on the contents of the rotary cutting production of logs, the virtual entity of the rotary cutting system can be specifically refined into the following aspects:  
\[\mathrm{D}=\mathrm{D}_{1}\cup\mathrm{D}_{2}\cup\mathrm{D}_{3} \tag{2}\]  
In (2), \(\mathrm{D}\) represents the virtual entity of the rotary cutting system, \(\mathrm{D}_{1}\) represents the equipment virtual entity, \(\mathrm{D}_{2}\) represents the product virtual entity, and \(\mathrm{D}_{3}\) represents the virtual entity of the environment [15]. 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). Regarding the core equipment resources involved in the rotary cutting production line of logs, including the log centering machine, log debarker, and veneer peeling machine, modeling tools such as 3 Dmax and Solidworks are used to create geometric models based on the actual equipment (Figure 4). The geometric model is imported into Unity3D and physical properties are added, achieving good spatiotemporal consistency with physical entities. At the same time, the virtual entity needs to complete its production behavior through control commands and program driving, which requires the definition of relevant virtual services [16]. Therefore, the behavior criteria of the equipment virtual entity are defined as follows:  
\[\text{D}_{1}=\{\text{S}_{1},\text{V}_{1}\} \tag{3}\]  
In (3), \(\text{D}_{1}\) represents the equipment virtual entity and \(\text{S}_{1}\) 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. \(\text{V}_{1}\) 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. For logs, different geometric forms correspond to different processing stages. Different stages drive the evolution of product geometric states based on their process data. Therefore, the product digital twin model is positioned as follows:  
\[\text{D}_{2}=\{\text{S}_{2},\text{V}_{2}\} \tag{4}\]  
In (4), \(\text{S}_{2}\) represents the three-dimensional state model of the product and \(\text{V}_{2}\) represents the evolution driving service. The digital twin model of the rotary cutting system production environment is:  
\[\text{D}_{3}=\{\text{C},\text{S}_{3},\text{V}_{3}\} \tag{5}\]  
In (5), C represents the environmental rule constraint model, \(\text{S}_{3}\) represents the environmental state model, and \(\text{V}_{3}\) represents the environmental detection service. The physical layer obtains environmental data through sensors, which is then parsed in the service layer and displayed quantitatively.