## 2 Materials and Methods
### Structure and Working Principle
#### 2.2.2 Key Structure and Parameters of the Differential Trommel Screener  
Figure 5 presents the overall structure of the differential trommel screener, which was the key structure for the separation, classification, and utilization of the BSF sand mixture. It primarily comprised of the base, the speed regulating motor, the screen, the spike teeth, the collecting box, and other components. The screening process of the differential trommel screener was captured by a high-speed camera, and the screening dynamic image was recorded in real time by its connection to a computer. The BSF sand easily agglomerates into clusters if the inner diameter of the trommel screener is too small. Moreover, a smaller inner diameter of the trommel screener will narrow the screening area of the trommel screener, whereas an inner diameter of the trommel screener that is too large will increase the power consumption of the screening operation. Given the installation space, the radius \(R\) of the trommel screener was set  
Figure 4: Structure and working principle of the ground trough BSF sand conveying and sorting machine. 1—BSF mixture; 2—parallel double-impeller collecting device; 3—BSF larvae; 4—BSF frass; 5—chassis; 6—sieve device with different rotational speeds. Figure 5: Cylinder sieve with promoting device with different rotational speeds. 1—computer; 2—high-speed camera; 3—tubular screen surface; 4—base; 5—spike teeth; 6—collection box. as 250 mm. In the internal screening process of the trommel screener, the design of the coaxial counter-rotating spikes can be beneficial for loosening, breaking, and stratifying BSF sand with a moisture content ranging from 40% to 50%, reduce the phenomenon of agglomeration and agglomeration, and increase the screening efficiency. The edges and corners of the general trapezoidal spike teeth may collide with the BSFL in the BSF sand mixture, thus causing damage to the surface of the insects. Accordingly, the spherical contact between the round-headed spike teeth and the BSF sand was established in order to reduce the rigid impact force on the BSF sand, increase the friction between the ends of the spike teeth and the BSF sand particles, and decrease the damage to the bodies of the BSF caused by the spike teeth. The round-headed nail teeth were established as ball heads. Figure 6 presents the collision between the round-headed nail teeth and the BSFL. Given the BSFL body and the particle size parameters of BSF sand, the gap between the spike teeth and the tubular screen surface was set to be slightly larger than the width of the BSL body to ensure that the BSF sand was fully in contact with the trommel screener, and to ensure that the BSFL would not be squeezed out through the gap of the tubular screen. In other word, \(h\) was formulated to be 6 mm, the radius \(R_{1}\) of the spike teeth around the rotation center was 244 mm, and the radius \(R_{2}\) of the spike teeth ball head was 3 mm, which is smaller than the particle size of the agglomerated BSF sand particles, increasing the probability of the breaking of the sticky sand particles. The outer diameter of the tubular screener was smaller than the diameter of the agglomerated particles, and a solid stainless steel round tube with a diameter of 3 mm was established to reduce the possibility of larger BSF sand particles adhering to the surface of the tubular screener. To prevent the BSFL from leaking out of the gap on the surface of the tubular screener, the gap was large enough to allow the BSF sand particles to pass through the screener. The gap \(L\) between the two adjacent circular tubes was set to 4 mm, and the angle between the two adjacent circular tubes was \(\tau\), which is expressed as follows:  
\[L=\frac{\pi R\tau}{180^{\circ}}-d \tag{6}\]  
where \(\tau\) was calculated as 1.605\({}^{\circ}\), and the angle \(\tau\) between the two adjacent tubes was set as 1.5\({}^{\circ}\) for the sake of convenient machining and installation.