# Design and Experiment of Black Soldier Fly Frass Mixture Separation through a Cylinder Sieve with Different Rotation Speeds

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## Featured Application

**In this study, a differential separation roller screen was developed, and the nail teeth and the screen were rotated coaxially with reverse directions. The mixture of black soldier fly sand with a certain moisture content was more effectively separated, and the artificial separation intensity for this mixture was reduced, thus facilitating the classification and utilization of black soldier fly larvae and organic fertilizer of insect sand.**

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Black Soldier Fly Sand and Its Adhesion Nodule Model

#### 2.2. Structure and Working Principle

#### 2.2.1. Overall Structure and Parameters

#### 2.2.2. Key Structure and Parameters of the Differential Trommel Screener

_{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 τ, which is expressed as follows:

#### 2.2.3. The Principle of Separation

#### 2.3. Key Component Parameter Design and Analysis

#### 2.3.1. The Effect of the Rotation Speed on the Material Sieving

#### 2.3.2. Effect of the Spike Teeth Parameters on Material Impacting through the Screener

_{1}is 15 mm, which is less than the average body length of the BSFL, which is beneficial for loosening the BSFL and sand materials. The radius R

_{2}of the rotation axis, which was a solid round tube in our experiments, was 12.5 mm. The number of spike teeth increased, and the frequency with which the spike teeth impacted the BSFL increased with the excessively small spike teeth spacing b, thus reducing the contact time with the screener surface. Since the separation object was the BSF sand, a staggered design of 90° was selected for the spike teeth, i.e., b was 19.625 mm to reduce the repeated impact on the material in the radial direction of the screener and to increase the drop flow frequency.

_{1}. The trommel screener rotated counterclockwise at an angular velocity w. The circle O

_{1}was the simplified BSF sand particles. After the agglutinate BSF sand particles collided with the spikes, they moved obliquely at the speed v. The spikes were fixed on the built-in rotating shaft of the trommel screener. Driven by the motor, the motion state of the spike teeth remained unchanged after the collision. Above, OC is the position of the spike teeth when the spike teeth collide twice with the BSF sand, while (x

_{o}, y

_{o}) denote the coordinates at the collision point A. After the collision, the agglutinate BSF sand particles move obliquely at the speed v. At this time, the motion trajectory equation of the BSF sand particles is expressed as follows:

#### 2.3.3. Effect of the Inclination Angle of the Trommel Screener on the Movement Trajectory of the Material

_{1}, the particle immediately adopted a uniform circular motion, i.e., the trajectory line of the D

_{1}O. The material was lifted to the O point, following the screener surface. The position of the O point was affected by certain parameters (e.g., the static friction coefficient of the BSF sand material, the rotation speed of the trommel, the inclination angle of the trommel, and the inner diameter of the trommel). Next, the BSF sand particles began to leave the screener surface to adopt a parabolic motion, i.e., the trajectory line of the OD

_{2}, and reached the highest point E and then fell back to the point D

_{2}. In such a cycle, the material was discharged from the trommel screener surface under a certain inclination.

_{1}was the plane projection of the trajectory OED

_{2}in the plane perpendicular to the rotation axis of the trommel. Meanwhile, η expressed the angle between the trajectory of the landing point and the vertical direction. It is assumed that the BSF sand particles do not slide axially during the movement of the trommel. The moving distance (D

_{1}D

_{2}) of the two adjacent landing points of the BSF sand particles in the trommel in the axial direction of the trommel screen is expressed as follows:

_{1}and the parabolic motion time t

_{2}are written as follows:

#### 2.4. Test Conditions

#### 2.5. Test Methods and Indicators

#### 2.6. Experimental Design

## 3. Results

#### 3.1. Model Establishment and Significance Test

_{1}, X

_{2}, and X

_{3}are the factor code values), and the regression fitting analyses of the impurity content and the insect impurity rate were conducted using the Design-Expert 8.0.6 software. The regression equations of the impurity content Y

_{1}and the insect rate Y

_{2}were established to conduct the significance test and analysis of the three factors for the test indicators. Lastly, the quadratic polynomial response surface regression model of the significant test factors and evaluation indicators was obtained. The model significance test results are listed in Table 3.

_{1}and P

_{2}of the impurity content and the insect rate are both less than 0.0001, indicating that the regression model is extremely significant. The lack of fit was 0.5025 and 0.5413, respectively, both being greater than 0.05. The lack of fit was not significant. In other words, the quadratic regression equation fitted by the model was highly consistent with the actual test, which reflects the relationship between the impurity content Y

_{1}, the insect rate Y

_{2}, and X

_{1}, X

_{2}, and X

_{3}. The working parameters of the BSF sand can be effectively optimized by the regression model.

_{1}= 5.54 + 0.46X

_{1}+ 0.27X

_{2}− 0.21X

_{3}− 0.58X

_{1}X

_{2}+ 0.05X

_{1}X

_{3}− 0.075X

_{2}X

_{3}+ 1.13X

_{1}

^{2}+ 2.71X

_{2}

^{2}+ 0.18X

_{3}

^{2}

_{2}= 1.70 − 0.29X

_{1}− 0.24X

_{2}+ 0.23X

_{3}− 0.28X

_{1}X

_{3}− 0.17X

_{2}X

_{3}+ 1.20X

_{1}

^{2}− 0.15X

_{2}

^{2}− 0.27X

_{3}

^{2}

#### 3.2. Analysis of the Effects of Various Factors on the Indicators

#### 3.3. Parameter Optimization and Experimental Verification

## 4. Discussion

- (1)
- The differential trommel screener designed to separate the mixture of BSF sand was applied under the test conditions, and the trial production test was performed. If it is essential to complete the large-scale separation of BSF sand mixture, the size parameters of the trommel screener should be optimized in accordance with the feeding amount so as to better meet the actual production requirements.
- (2)
- The moisture content of the BSF sand mixture varied because of the differences in the biotransformation of the BSFL, and the range of the moisture content fluctuated. The differential trommel screen designed in this study had an excellent screening effect under the test conditions. For a BSF sand mixture with a higher moisture content, some operating parameters should be further optimized to increase the screening penetration rate. Furthermore, when the feeding amount of BSF sand mixture fluctuates, the adaptability of the differential trommel screener should be studied in depth.

## 5. Conclusions

- (1)
- In accordance with the requirements for the separation of BSF sand mixture, a type of differential separation trommel screener was developed using a method combining theory and experiments. The trommel screener and the spiked teeth rotated coaxially and reversely, thus increasing the probability of the layering and sieving of the BSF sand mixture. The round-headed spike teeth effectively reduced the rigid impact on the BSFL. The relevant experimental factors for the insect rate and the impurity content were determined through the analysis of the movement of the BSF sand mixture in the differential trommel screener.
- (2)
- According to the Box–Behnken experimental design principle, the three-factor and three-level response surface analysis method was adopted to perform the separation performance test of the differential trommel screener in separating the BSF sand mixture. Through the analysis of the response surface, it was found that the factors affecting the impurity content in the insects and the rate of insect impurities were the same and in the descending order as follows: the trommel rotation speed, spike teeth rotation speed, and inclination angle of the trommel screener.
- (3)
- The quadratic polynomial regression models of the impurity content in the insects, the rate of insect impurities, the rotational speed of the trommel, the rotational speed of the spike teeth, and the inclination of the trommel screener were built, respectively. The optimal operation parameters of the differential separation trommel screener were obtained through optimization and solutions. To be specific, the rotation speed of the trommel was 47.37 r/min, the rotation speed of the spike teeth was 24.16 r/min, and the inclination angle of the trommel was 5°. Under the above parameters, the impurity content in the insects was 6.0%, and the rate of insect impurities reached 1.2%. By revising the optimized parameters, under the combination of the trommel speed of 47 r/min, the spike speed of 24 r/min, and the inclination angle of 5°, the average insect rate and impurity content reached 5.87% and 1.20%, thus satisfying the actual production demands and increasing the BSF sand separation efficiency.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**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.

**Figure 6.**Schematic diagram of the cylinder sieve and nail tooth structure size. 1—tube screen; 2—nail tooth; 3—BSF larvae; 4—BSF sand particle.

**Figure 7.**Stress analysis of BSF sand at the critical location. Note: m denotes the BSF sand mass, g; w is the angular velocity of cylinder sieve, rad·s

^{−1}; I and II represent the low and high points, respectively; w

_{1}represents the angular velocity of the spike teeth, rad·s

^{−1}; $\beta $ is the angle between the lines connecting the BSF sand at the highest point and the circle center and the vertical center line in a force balance state, rad; $\theta $ expresses the angle between the lines connecting the BSF sand passing through the sieve holes and the circle center with the vertical center line, $\theta $ ϵ (α, π−β), rad; D is the internal diameter of the cylinder sieve, m; f

_{2}is the friction at the highest point, N; N

_{2}is the supporting force at the highest point, N; f

_{3}is the friction when the rapeseed passes through the sieve holes, N; and N

_{3}is the supporting force when the rapeseed passes through the sieve holes, N.

**Figure 8.**Arrangement of the nail teeth. Note: a denotes the length of the rotating axis of the trommel screener, m; l

_{1}represents the teeth trace distance, m; R

_{2}is the radius of the rotation axis, m; and b expresses the spike teeth spacing, m.

**Figure 9.**Collision force analysis between the nail teeth and BSF sand. Note: G denotes the self-gravity of the BSFL, N; F

_{f}is the frictional force of the BSFL at the end of the spike teeth, N; F represents the effect of the spike teeth on the BSFL when the spike teeth rotated with a high-speed force, N; N is the support force of the spiked teeth on the BSFL, N; w is the angular velocity of the cylinder sieve, rad·s

^{−1}; and w

_{1}is the angular velocity of the spike teeth, rad·s

^{−1}.

**Figure 10.**Kinematic analytical sketch of the BSF sand in the rotary screen. Note: w denotes the angular velocity of the cylinder sieve, rad·s

^{−1}; w

_{1}is the angular velocity of the spike teeth, rad·s

^{−1}; $\sigma $ is the inclination angle of the trommel screen, °; η expresses the angle between the trajectory of the landing point and the vertical direction, °; R represents the radius of the cylinder sieve, m; $\alpha $ is the angle between the particle and horizontal direction, °.

Code Value | Factors | ||
---|---|---|---|

Drum Rotation Speed | Nail Tooth Speed | Roller Screen Inclination | |

x_{1}/(r·min^{−1}) | x_{2}/(r·min^{−1}) | x_{3}/(°) | |

−1 | 38 | 10 | 5 |

0 | 48 | 25 | 10 |

1 | 58 | 40 | 15 |

Number | X_{1} | X_{2} | X_{3} | Y_{1}/% | Y_{2}/% |
---|---|---|---|---|---|

1 | −1 | −1 | 0 | 8.1 | 3.3 |

2 | 1 | −1 | 0 | 10.2 | 2.8 |

3 | −1 | 1 | 0 | 9.7 | 2.7 |

4 | 1 | 1 | 0 | 9.5 | 2.2 |

5 | −1 | 0 | −1 | 6.5 | 2.4 |

6 | 1 | 0 | −1 | 7.3 | 2.3 |

7 | −1 | 0 | 1 | 6.3 | 3.5 |

8 | 1 | 0 | 1 | 7.3 | 2.3 |

9 | 0 | −1 | −1 | 8.4 | 1.1 |

10 | 0 | 1 | −1 | 9.2 | 1.1 |

11 | 0 | −1 | 1 | 7.8 | 1.8 |

12 | 0 | 1 | 1 | 8.3 | 1.1 |

13 | 0 | 0 | 0 | 5.2 | 1.5 |

14 | 0 | 0 | 0 | 5.9 | 1.9 |

15 | 0 | 0 | 0 | 5.6 | 1.7 |

16 | 0 | 0 | 0 | 5.3 | 1.6 |

17 | 0 | 0 | 0 | 5.7 | 1.8 |

Source | Impurity Content in BSF Larvae | Insect Impurity Rate | ||||||
---|---|---|---|---|---|---|---|---|

df | Mean Square | F_{1} | P_{1} | df | Mean Square | F_{2} | P_{2} | |

Model | 9 | 4.70 | 58.32 | <0.0001 | 9 | 0.92 | 39.42 | <0.0001 |

X_{1} | 1 | 1.71 | 21.22 | 0.0025 | 1 | 0.66 | 28.48 | 0.0011 |

X_{2} | 1 | 0.61 | 7.50 | 0.0290 | 1 | 0.45 | 19.44 | 0.0031 |

X_{3} | 1 | 0.36 | 4.48 | 0.0721 | 1 | 0.41 | 17.45 | 0.0042 |

X_{1}X_{2} | 1 | 1.32 | 16.40 | 0.0049 | 1 | 0.000 | 0.000 | 1.0000 |

X_{1}X_{3} | 1 | 1 × 10^{−2} | 0.12 | 0.7351 | 1 | 0.30 | 13.03 | 0.0086 |

X_{2}X_{3} | 1 | 0.022 | 0.28 | 0.6137 | 1 | 0.12 | 5.28 | 0.0552 |

X_{1}^{2} | 1 | 5.38 | 66.67 | <0.0001 | 1 | 6.06 | 261.18 | <0.0001 |

X_{2}^{2} | 1 | 30.81 | 382.04 | <0.0001 | 1 | 0.095 | 4.08 | 0.0831 |

X_{3}^{2} | 1 | 0.14 | 1.69 | 0.2346 | 1 | 0.32 | 13.72 | 0.0076 |

Residual | 7 | 0.081 | 7 | 0.023 | ||||

Lack of fit | 3 | 0.077 | 0.93 | 0.5025 | 3 | 0.021 | 0.83 | 0.5413 |

Pure error | 4 | 0.083 | 4 | 0.025 |

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**MDPI and ACS Style**

Peng, C.; Zhou, T.; Song, S.; Sun, S.; Yin, Y.; Xu, D.
Design and Experiment of Black Soldier Fly Frass Mixture Separation through a Cylinder Sieve with Different Rotation Speeds. *Appl. Sci.* **2022**, *12*, 10597.
https://doi.org/10.3390/app122010597

**AMA Style**

Peng C, Zhou T, Song S, Sun S, Yin Y, Xu D.
Design and Experiment of Black Soldier Fly Frass Mixture Separation through a Cylinder Sieve with Different Rotation Speeds. *Applied Sciences*. 2022; 12(20):10597.
https://doi.org/10.3390/app122010597

**Chicago/Turabian Style**

Peng, Caiwang, Ting Zhou, Shisheng Song, Songlin Sun, Yulong Yin, and Daojun Xu.
2022. "Design and Experiment of Black Soldier Fly Frass Mixture Separation through a Cylinder Sieve with Different Rotation Speeds" *Applied Sciences* 12, no. 20: 10597.
https://doi.org/10.3390/app122010597