# Innovative Approaches to Wear Reduction in Horizontal Powder Screw Conveyors: A Design of Experiments-Guided Numerical Study

^{*}

## Abstract

**:**

## 1. Introduction

- Can the abrasive powder material model be effectively calibrated through a combination of literature review, angle of repose, and shear tests to ensure an accurate representation of material behaviour within DEM simulations?
- Can Design of Experiments (DOE) be applied to systematically analyze the impact of various factors, such as screw pitch, clearance, wear, and rotational velocity, on critical screw conveyor performance metrics including mass flow, power consumption, wear, stresses, deformations, and their dependencies?
- Can response surface optimization be applied to identify optimum parameters for maximizing mass flow while minimizing wear?
- Can insights from parametric numerical analysis and utilization of DOE and response surface optimization be translated into practical guidelines for engineers designing efficient conveyor systems?

## 2. Materials and Methods

#### 2.1. Discrete Element Method

#### Contact Model

#### 2.2. Used Particle Properties

_{2}O

_{3}), has exceptional qualities such as hardness, wear resistance, and chemical inertness, making it a premier choice for various industrial applications involving abrasion. In the field of grinding tools, alumina is a standout choice, serving as either an abrasive grain or a crucial component in abrasive formulations. Alongside alumina, a diverse range of abrasive materials, including silicon carbide, diamond, cubic boron nitride, and corundum, plays a significant role in this sector. The applications of aluminium oxide are extensive, spanning from wear protection coatings in machines and plants to corrosion protection in the chemical industry. Additionally, it finds use as insulation material in electronics and high-temperature applications. The suitability of aluminium oxide, corundum, and other materials depends on factors such as their content, grain size, and porosity, all of which are decisive for their specific areas of application in diverse industrial scenarios involving abrasion, wear protection, and corrosion resistance [35,36].

#### Particle Shape and Size Distribution

#### 2.3. Numerical Calibration

^{8}Pa, resulting in overlaps of 0.3% or less did not significantly change resistance. Conversely, lower stiffness values, leading to overlaps exceeding 0.3%, resulted in smoother interaction and resistance. Due to computational limitations, the modulus was reduced, a decision supported by findings in articles [41,42], where a similar analysis was conducted with erosive sand of comparable sizes. Calibration based on these considerations provided a satisfactory approximation for entry data. Moreover, throughout all simulations, contact overlap was consistently monitored during simulations. We investigated sliding friction between powder and steel by employing an inclined plate (Figure 4), where particles were adhered to the contact surface of a suitably large object. In our examination of rolling and sliding friction between powder particles and steel, we adopted a method involving a steel ball. By compacting the powder and observing the ball’s rolling behaviour, we addressed the complexities associated with fine powders. While this method didn’t yield superior results, it provided results fine-tuned enough for our numerical simulations. The material properties utilized in the simulation are presented in Table 1. Calibration also involved conducting a direct shear test using a 60 × 60 mm shear box. Previous findings indicated that differences in shear results are unclear when the shear velocity is below 0.1 m/s. This velocity significantly differs from the experimental test, where particle contacts might dissipate kinetic energy due to damping.

Property | Unit | Value | Note/Reference |
---|---|---|---|

Geometry: | |||

Geometry density ${\rho}_{g}$ | [$kg$/${m}^{3}$] | $7800$ | Structural steel [46] |

Young’s modulus ${E}_{g}$ | [Pa] | $1\xb7{10}^{10}$ | Reduced modulus [46] |

Poisson ratio ${{\nu}_{}}_{g}$ | [–] | 0.3 | Structural steel [46] |

Particle: | |||

Young’s modulus ${E}_{p}$ | [Pa] | $2.8\xb7{10}^{8}$ | Reduced modulus [40,41] |

Poisson ratio ${{\nu}_{}}_{p}$ | [–] | 0.4 | Abrasive sand [41] |

Mean Particle Diameter${d}_{p}$ | [$\mu $m] | 150 | Measured |

Coarse graining ${c}_{gr}$ | [–] | 18 | Coarse ratio |

Bulk density ${\rho}_{bulk}$ | [$kg$/${m}^{3}$] | 1780 | Measured |

Particle density ${\rho}_{p}$ | [$kg$/${m}^{3}$] | 3490 | Calibrated Figure 3 |

Contact: | |||

Hertz Mindlin | No Slip | ||

Sliding friction p-p ${{\mu}_{}}_{p}$ | [–] | 0.55 | Calibrated Figure 3 |

Sliding friction p-g ${{\mu}_{}}_{g}$ | [–] | 0.6 | Determined—Inclined plate |

Rolling friction p-p ${{{\mu}_{}}_{p}^{r}}_{}$ | [–] | 0.1 | Calibrated Figure 3 |

Rolling friction p-g ${{{\mu}_{}}_{g}^{r}}_{}$ | [–] | 0.1 | Determined—Inclined plate |

Coeficient of Restitution p-p ${c}_{rp}$ | [–] | 0.44 | Assumption based on [41] |

Coeficient of Restitution p-g ${c}_{rg}$ | [–] | 0.50 | Assumption based on [41] |

Simulation: | |||

DEM Particle count | [–] | 308,609 | - |

FEM elements count | [–] | 2,138,521 | 4-noded quadratic tetrahedral elements |

FEM element size | [mm] | 1.5 |

#### Design of Experiments

## 3. Results and Discussion

^{2}) which serves as an indicator of the accuracy of the desired function and its consistency with the observed behaviour of the analyzed parameter. The proximity of this parameter to the value of 100% directly correlates with the accuracy of the function.

#### 3.1. Parameters Optimization

#### 3.2. Response Surface

## 4. Conclusions

- Our research study focused on calibrating the abrasive powder material model to ensure an accurate representation of material behaviour. We successfully approximated and calibrated the abrasive powder material within DEM simulations. This calibration process was crucial for achieving verified material flow, laying a solid foundation for reliable and realistic simulations.
- During the research, we build an advanced numerical model that integrates parametric modelled geometry, DEM, FEM, DOE and response surface optimization to simulate the complex environment of the screw conveyor. The automated parametric numerical model facilitates the exploration of various operating conditions and design parameters, offering valuable insights into the performance of the screw conveyor, wear depth, and structural adequacy of the screw blade.
- Clearance has emerged as an important parameter in the optimization process. The mass flow rate demonstrates an increase as the clearance widens, this contributes to the expanded area between the screw blade and the housing. This feature results in a higher mass flow rate. Additionally, as expected, clearance was found to have the most significant influence on power consumption, wear depth, stress, and deformations. Moreover, because of the complexity of the employed material coarse-graining methodology, particle shape and size underwent approximation and adjustment during the calibration process. Consequently, “particle entrapment” between the screw blade and the housing may also occur. Further studies incorporating real particle shape and size are of major importance in order to fully address the clearance effect. It’s crucial to acknowledge that neglecting this aspect may lead to potentially misleading results.
- During the simulations, the stresses on the screw blade were identified to be minor, therefore we have excluded them from further consideration in the optimization phase, which exclusively prioritized wear depth and mass flow.
- Through the utilization of the Design of Experiments, we systematically investigated critical parameters such as screw pitch, clearance, wear depth, rotational velocity, and additional structural factors. We demonstrated how this systematic investigation allows us to not only analyze the individual effects of each parameter but also to consider their interdependencies. The optimization process was a success in focusing on mass flow and reducing wear depth. After carefully studying and applying small adjustments, we achieved our goals. We found an optimal set of factors that would give us a good balance between the mass flow and wear depth. In future studies focusing on screw conveyors where stresses and deformations are higher, it would be beneficial, to include structural parameters in the optimization process (shaft thickness etc.).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Contact model based on Hertzian mechanics and Mindlin’s theory, used to simulate particle interactions within the Discrete Element Method (DEM); (

**b**) Soft sphere contact forces decomposition process illustrating the breakdown of contact forces into their constituent components.

**Figure 2.**A representative sample of abrasive alumina particles, with an average size of 150 μm, as viewed under the microscope.

**Figure 3.**Particle Size Distribution (blue line) of Abrasive Powder Analyzed Using Anton Paar Litesizer 500. Dashed lines delineate the proportional distribution and magnitudes of selected particle sizes. Supplementary visual aids include a smaller graph and a table illustrating the particle distribution function utilized in simulation before coarse-graining.

**Figure 4.**Visual representation of the main calibration scheme for obtaining numerical simulation data using modified partial solutions from the Rocky Calibration Suite.

**Figure 5.**Key Parameters and Control Regions for the Screw Conveyor System. The figure illustrates essential study parameters including rotational velocity (A, in rpm), clearance (B, in mm), screw diameter (C, in mm), shaft diameter (D, in mm), and Pitch (E, in mm), alongside delineated control regions.

**Figure 7.**Pareto Chart illustrating the Standardized Effects of Mass Flow (α = 0.05) on the left, accompanied by a Normal Probability Plot depicting the distribution of Mass Flow on the right.

**Figure 8.**Pareto Chart illustrating the Standardized Effects of Power (α = 0.05) on the left, accompanied by a Normal Probability Plot depicting the distribution of Power on the right.

**Figure 9.**Pareto Chart illustrating the Standardized Effects of Shear Intensity (α = 0.05) on the left, accompanied by a Normal Probability Plot depicting the distribution of Shear Intensity on the right.

**Figure 10.**Pareto Chart illustrating the Standardized Effects of Deformation (α = 0.05) on the left, accompanied by a Normal Probability Plot depicting the distribution of Deformation on the right.

**Figure 11.**Pareto Chart illustrating the Standardized Effects of Stress (α = 0.05) on the left, accompanied by a Normal Probability Plot depicting the distribution of Stress on the right.

**Figure 12.**Parametric Mapping of Mass Flow Dynamics in [t/h]: Contour Analysis Across Pitch, Angular Velocity, Shaft Diameter, Screw Diameter, and Clearance with Hold Values from Response Optimization.

**Figure 13.**Parametric Mapping of Power Dynamics in [W]: Contour Analysis Across Angular Velocity, Shaft Diameter and Clearance with Hold Values from Response Optimization.

**Figure 14.**Qualitative screw blade wear (

**left**), Parametric Mapping of Shear Intensity Dynamics in [W/m

^{2}]: Contour Analysis Across Pitch, Angular Velocity, Shaft Diameter, Screw Diameter, and Clearance with Hold Values from Response Optimization (

**right**).

**Figure 15.**Stress Field Analysis with Parametric Surface Plot of Stress in Relation to Clearance and Angular Velocity: with Fixed Values from Response Optimization.

**Figure 16.**Deformation Field Analysis with Parametric Surface Plot of Deformation in Relation to Clearance and Angular Velocity: with Fixed Values from Response Optimization.

**Table 2.**The provided table encapsulates the design points generated through a central composite design approach, serving as simulation input parameters.

Run Order | Coded Value A B C D E | N [rpm] {150–250} | Clearance [mm] {2–10} | D_{screw} [mm]{70–85} | D_{shaft} [mm]{20–35} | Pitch [mm] {75–90} | ||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 0 | 0 | 0 | −2 | 200.0 | 6.0 | 77.5 | 27.5 | 75.0 |

2 | 1 | −1 | −1 | −1 | −1 | 214.2 | 4.9 | 75.4 | 25.4 | 80.4 |

3 | −1 | 1 | −1 | −1 | −1 | 185.8 | 7.1 | 75.4 | 25.4 | 80.4 |

4 | −1 | −1 | 1 | −1 | −1 | 185.8 | 4.9 | 79.6 | 25.4 | 80.4 |

5 | 1 | 1 | 1 | −1 | −1 | 214.2 | 7.1 | 79.6 | 25.4 | 80.4 |

6 | −1 | −1 | −1 | 1 | −1 | 185.8 | 4.9 | 75.4 | 29.6 | 80.4 |

7 | 1 | 1 | −1 | 1 | −1 | 214.2 | 7.1 | 75.4 | 29.6 | 80.4 |

8 | 1 | −1 | 1 | 1 | −1 | 214.2 | 4.9 | 79.6 | 29.6 | 80.4 |

9 | −1 | 1 | 1 | 1 | −1 | 185.8 | 7.1 | 79.6 | 29.6 | 80.4 |

10 | 0 | 0 | 0 | −2 | 0 | 200.0 | 6.0 | 77.5 | 20.0 | 82.5 |

11 | 0 | 0 | −2 | 0 | 0 | 200.0 | 6.0 | 70.0 | 27.5 | 82.5 |

12 | 0 | −2 | 0 | 0 | 0 | 200.0 | 2.0 | 77.5 | 27.5 | 82.5 |

13 | −2 | 0 | 0 | 0 | 0 | 150.0 | 6.0 | 77.5 | 27.5 | 82.5 |

14 | 0 | 0 | 0 | 0 | 0 | 200.0 | 6.0 | 77.5 | 27.5 | 82.5 |

15 | 2 | 0 | 0 | 0 | 0 | 250.0 | 6.0 | 77.5 | 27.5 | 82.5 |

16 | 0 | 2 | 0 | 0 | 0 | 200.0 | 10.0 | 77.5 | 27.5 | 82.5 |

17 | 0 | 0 | 2 | 0 | 0 | 200.0 | 6.0 | 85.0 | 27.5 | 82.5 |

18 | 0 | 0 | 0 | 2 | 0 | 200.0 | 6.0 | 77.5 | 35.0 | 82.5 |

19 | −1 | −1 | −1 | −1 | 1 | 185.8 | 4.9 | 75.4 | 25.4 | 84.6 |

20 | 1 | 1 | −1 | −1 | 1 | 214.2 | 7.1 | 75.4 | 25.4 | 84.6 |

21 | 1 | −1 | 1 | −1 | 1 | 214.2 | 4.9 | 79.6 | 25.4 | 84.6 |

22 | −1 | 1 | 1 | −1 | 1 | 185.8 | 7.1 | 79.6 | 25.4 | 84.6 |

23 | 1 | −1 | −1 | 1 | 1 | 214.2 | 4.9 | 75.4 | 29.6 | 84.6 |

24 | −1 | 1 | −1 | 1 | 1 | 185.8 | 7.1 | 75.4 | 29.6 | 84.6 |

25 | −1 | −1 | 1 | 1 | 1 | 185.8 | 4.9 | 79.6 | 29.6 | 84.6 |

26 | 1 | 1 | 1 | 1 | 1 | 214.2 | 7.1 | 79.6 | 29.6 | 84.6 |

27 | 0 | 0 | 0 | 0 | 2 | 200.0 | 6.0 | 77.5 | 27.5 | 90.0 |

Source | DF | Adj SS | Adj MS | F-Value | p-Value |
---|---|---|---|---|---|

Model | 20 | 2.49783 | 0.12489 | 19.94 | 0.001 |

Linear | 5 | 2.42307 | 0.48461 | 77.39 | 0 |

$N$ | 1 | 0.04015 | 0.04015 | 6.41 | 0.045 |

$Clearance$ | 1 | 1.02763 | 1.02763 | 164.1 | 0 |

${D}_{screw}$ | 1 | 1.12376 | 1.12376 | 179.45 | 0 |

${D}_{shaft}$ | 1 | 0.16574 | 0.16574 | 26.47 | 0.002 |

$Pitch$ | 1 | 0.06578 | 0.06578 | 10.5 | 0.018 |

Square | 5 | 0.0197 | 0.00394 | 0.63 | 0.686 |

${N}^{2}$ | 1 | 0.00012 | 0.00012 | 0.02 | 0.893 |

${Clearance}^{2}$ | 1 | 0.00003 | 0.00003 | 0 | 0.947 |

${{D}_{screw}}^{2}$ | 1 | 0.00012 | 0.00012 | 0.02 | 0.893 |

${{D}_{shaft}}^{2}$ | 1 | 0.00052 | 0.00052 | 0.08 | 0.784 |

${Pitch}^{2}$ | 1 | 0.01398 | 0.01398 | 2.23 | 0.186 |

2-Way Interaction | 10 | 0.05507 | 0.00551 | 0.88 | 0.592 |

$N\xb7Clearance$ | 1 | 0.00766 | 0.00766 | 1.22 | 0.311 |

$N\xb7{D}_{screw}$ | 1 | 0.00601 | 0.00601 | 0.96 | 0.365 |

$N\xb7{D}_{shaft}$ | 1 | 0.00526 | 0.00526 | 0.84 | 0.395 |

$N\xb7Pitch$ | 1 | 0.00331 | 0.00331 | 0.53 | 0.495 |

$Clearance\xb7{D}_{screw}$ | 1 | 0.00526 | 0.00526 | 0.84 | 0.395 |

$Clearance\xb7{D}_{shaft}$ | 1 | 0.01156 | 0.01156 | 1.85 | 0.223 |

$Clearance\xb7Pitch$ | 1 | 0.00275 | 0.00275 | 0.44 | 0.532 |

${D}_{screw}\xb7{D}_{shaft}$ | 1 | 0.00766 | 0.00766 | 1.22 | 0.311 |

${D}_{screw}\xb7Pitch$ | 1 | 0.00106 | 0.00106 | 0.17 | 0.696 |

${D}_{shaft}\xb7Pitch$ | 1 | 0.00456 | 0.00456 | 0.73 | 0.426 |

Error | 6 | 0.03757 | 0.00626 | ||

Total | 26 | 2.5354 |

Opti. Function | Prediction | Simulation | Error | |
---|---|---|---|---|

Mass flow [t/h] | Target value (5.35) | 5.35 | 5.31 | 0.75% |

Shear Intensity [W/m^{2}] | Minimum | 14 | 14.56 | 4% |

Optimum parameters: | ||||

N [rpm] | Clearance [mm] | D_{screw} [mm] | D_{shaft} [mm] | Pitch [mm] |

167 | 8.60 | 80 | 27 | 87 |

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**MDPI and ACS Style**

Motaln, M.; Lerher, T.
Innovative Approaches to Wear Reduction in Horizontal Powder Screw Conveyors: A Design of Experiments-Guided Numerical Study. *Appl. Sci.* **2024**, *14*, 3064.
https://doi.org/10.3390/app14073064

**AMA Style**

Motaln M, Lerher T.
Innovative Approaches to Wear Reduction in Horizontal Powder Screw Conveyors: A Design of Experiments-Guided Numerical Study. *Applied Sciences*. 2024; 14(7):3064.
https://doi.org/10.3390/app14073064

**Chicago/Turabian Style**

Motaln, Marko, and Tone Lerher.
2024. "Innovative Approaches to Wear Reduction in Horizontal Powder Screw Conveyors: A Design of Experiments-Guided Numerical Study" *Applied Sciences* 14, no. 7: 3064.
https://doi.org/10.3390/app14073064