## 2 Basic Principles  
### Processing Principle of DDSGL  
The processing areas and external circulation systems of DDSGL are shown in Figure 2. The circulation system mainly includes demagnetization mechanisms, cleaning and drying mechanisms, material sorting mechanism, and feeding mechanisms, etc. The double-disk structure includes an upper disk supported by a spring-elastic support, with its processing surface featuring a spiral groove; and a lower disk with rigid support, with its processing surface featuring evenly distributed radial straight-line grooves. The cylindrical roller is located at the intersection of the upper disk's spiral groove and the lower disk's straight groove. The motion of the upper and lower disks is as follows: the lower disk rotates around the main shaft, and the upper disk can move up and down. As the upper disk uses elastic support, it provides floating loading to the roller.  
The state of the cylindrical roller at the intersection of the spiral groove and the straight groove is shown in Figure 2a. The processing surface I of the upper disk's spiral groove contacts the cylindrical surface of the roller, and processing surface II contacts the end surface of the roller. The processing surface III of the lower disk's straight groove contacts the cylindrical surface of the roller. The forming movement of the roller mainly includes the following aspects:  
1. When the lower disk rotates, the double disks generate a driving torque on the roller through the joint action of processing surfaces I and III, causing the roller to rotate around itself. To ensure stable self-rotation of the roller in the processing area, the upper disk is designed as an electromagnetic disk. Electromagnetic force is added between the roller and processing surface I, thereby increasing the frictional driving torque of processing surface I on the roller.
2. The roller's radial movement is realized by pushing the end surface of the roller through processing surface II of the upper disk's spiral groove. This causes the roller to move radially from the center of the lower disk to outside the processing area, cooperating with the external circulation system to achieve a closed loop for the entire circulation process.  
The operation mode of the roller in the DDSGL system is shown in Figure 3. The mapping system includes a lapping processing area and an external circulation system. During the processing, the position of the roller is in the space formed at the intersection of the spiral groove and the straight groove (as shown in Figure 2), and these spaces in the processing area are defined as processing space A. Although the external circulation system includes multiple functional mechanisms and the operating characteristics of the roller inside the circulation system are single-line and serially arranged, the circulation system can be characterized as a series of external spaces B. Taking the example of a single-batch processing 500 rollers, the circulation movement path of the single roller in the system is: A\({}_{1}\)--A\({}_{8}\)--B\({}_{1}\)--B\({}_{492}\)--A\({}_{1}\).  
Figure 2: DDSGL method, (**a**) Processing principle, (**b**) Equipment picture.