# Influence of Die Land Length on the Maximum Extrusion Force and Dry Ice Pellets Density in Ram Extrusion Process

^{*}

## Abstract

**:**

_{2}), which has a significant environmental impact. This study focuses on the conversion of solid CO

_{2}into pellets using ram extrusion, a widely used technique. The length of the die land (DL) in this process plays a critical role in determining the maximum extrusion force and the density of dry ice pellets. However, the influence of DL length on the characteristics of dry ice snow, known as compressed carbon dioxide (CCD), remains understudied. To address this research gap, the authors conducted experimental trials using a customized ram extrusion setup, varying the DL length while keeping the other parameters constant. The results demonstrate a substantial correlation between DL length and both the maximum extrusion force and dry ice pellets density. Increasing the DL length leads to a decreased extrusion force and optimized pellet density. These findings provide valuable insights for optimizing the ram extrusion process of dry ice pellets and improving waste management, energy efficiency, and product quality in industries utilizing this technique.

## 1. Introduction

_{C}) equals the resistance force (F

_{R}), depending on the geometry of the die that the material is pushed through [19]. While moving through the converging portion of the die cavity, the material undergoes plastic deformation. Its transverse dimension is determined by the geometry of the die cavity through which it is pushed. In the next phase, the material is moved through the die land section (DL) in the direction normal to the Z axis. The transversal shape of this portion of the die cavity approximates the shape of the pellets that leave the die. After the completion of the densification process, the compaction piston is withdrawn to its initial position.

_{0}) may substantially exceed the material’s cohesion. Thus, we can adopt a non-zero absolute value of the deformation tensor (ε). With constant transverse dimensions over the whole DL length, in axes other than the Z axis, ε equals zero. If the transversal dimensions of the pressed material are constant, the phenomenon of stress relaxation comes into play. This phenomenon is described, for example, with the Maxwell model for linear viscoelastic response. It combines a purely elastic body with an ideally viscous body, represented by a spring and a damper (as shown in Figure 4). The above system may be described by Equation (1):

_{0}represents initial stress and T

_{R}represents total relaxation time.

_{0}) resulting from the material relaxation phenomenon is time-dependent. In this case, t depends on the DL length (l

_{DL}) and the speed of movement of the material (v

_{DL}

_{,}) (as shown in Figure 2). The maximum value of t is calculated as follows:

_{DL}may be determined assuming the incompressibility of the material over the convergent section. It depends on the initial speed of the material (v

^{in}) and the S

^{in}to S

^{out}ratio (convergent section inlet and outlet cross-sectional areas). Now Equation (2) may be rewritten as follows:

_{DL}in Equation (1) yields:

## 2. Materials and Methods

#### 2.1. Materials

#### 2.1.1. Dry Ice Powder

_{2}into a solid form. The material crystallises in this way. The density of the obtained loose dry ice is 550 kg/m

^{3}[23].

#### 2.1.2. Compression and Extrusion

_{Z}) exerted on the 20 mm dia. ram. A 50 kN accuracy class 0.01 strain gauge sensor was used for this measurement, supplied as standard with the MTS Insight 50 kN test frame.

#### 2.1.3. Dies

_{DL}), which varied from 0 mm to 50 mm. The geometrical parameters of some of the tested dies are illustrated below (Figure 6).

_{DL}range in which the greatest changes of the limit force of F

_{Z}and ρ are observed. To this end, dies with the l

_{DL}increasing at 10 mm intervals (i.e., 0, 10, 20, 30, 40 and 50 mm) were used in the first stage. Next, measurements were carried out on dies with smaller l

_{DL}intervals falling in the range determined based on the previously obtained results. The details are given in Section 3 further below.

#### 2.2. Method of Measurement of the Maximum Extrusion Force

_{C}

^{max}) are described in the groups assigned to the tested single-cavity dies.

#### 2.3. Extrudate Density Measurement

_{0}) is compared with m

_{1}(the weight of the same sample), immersed in the test liquid of known density (ρ

_{TL}). The test setup is shown in Figure 8 below.

_{TL}varies as a function of T

_{TL}, and thus the test setup was equipped with a K-type thermocouple sensor (7) and a Testo 440 multimeter (Pruszków, Poland) (8) to read the sensor output signal.

_{TL}and ρ

_{CCD,}based on the measured values of m

_{0}, m

_{1}, and T

_{TL}. The equations used to calculate ρ

_{TL}and ρ

_{CCD}are given below:

#### 2.4. Statistical Analysis

_{C}

^{max}and ρ

_{CCD}between the data groups. STATISTICA version 13.3, a program of TIBCO Software Inc. was used for the statistical analysis of the experimental data. In all, the comparison one-way test was applied with statistical significance, determined by the value of p below 0.05.

## 3. Results & Discussion

_{C}

^{max}, the value of p varied from 0.11 to 0.80. For ρ

_{CCD}, the range was 0.16–0.62. The values obtained for each of the tested populations exceed 0.05, which confirms the normality of the data.

_{C}

^{max}and 0.84 for ρ

_{CCD}, indicating the homogeneity of variance in both cases.

_{DL}equal to zero and the other dies under analysis. The general population data are given in Table 1 and Table 2 below.

_{DL}s of 5 mm and 2.5 mm. In this way, it was determined that the l

_{DL}variation range should be limited to the range of 0–2.5 mm.

_{DL}s in the range of 0–1.5 mm are different from other populations at a statistically significant level. The key statistical data obtained for these two tests are given in Table 3 and Table 4 below.

_{CCD}, as a function of l

_{DL}, we see a decrease in the variation of ρ

_{CCD}values for l

_{DL}s greater than 1.5 mm. Therefore, we can assume that the stress resulting from the plastic deformation of the sample was reduced to a level at which its effect on the geometrical parameters of the pellets becomes ignorable.

_{DL}for the relaxation to take place in the compacted carbon dioxide should be taken at 1.5 mm. Substituting these parameters in Equation (3), it is now possible to calculate t

_{DL}:

_{DL}has a bearing on the mechanical properties of dry ice pellets and on the extrusion force used in the process. This is in line with the conclusions of the relevant studies on pelletizing of wood chips [26], straw [27], and other particulate materials [28].

_{R}is described as a product of dynamic viscosity (η and E) [29]. Considering the variability of the mechanical parameters of dry ice as a function of ρ [20,30], the results are deemed applicable for extrudates whose density does not exceed the extrudate density determined in the experiments (i.e., 1540 kg/m

^{3}).

## 4. Conclusions

^{3}and a ram speed of 5 mm/s, the minimum relaxation time was 0.78 s. This allowed for a reduction of the stress induced inside the pellets to a level at which it no longer caused any significant deformation of the extrudate and, consequently, no density change.

## Author Contributions

## Funding

_{2}to reduced consumption of electricity and raw material”, number: “LIDER/3/0006/L-11/19/NCBR/2020” financed by National Centre for Research and Development in Poland, https://www.gov.pl/web/ncbr (accessed on: 15 December 2021).

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**The main part of the piston-type pelletizer. 1—compaction chamber, 2—piston, 3—single channel die, 4—dry ice before compression, 5—compressed dry ice, l

_{DL}—length of DL section.

**Figure 5.**Insulated container used to store dry ice powder and condition the experimental setup components, 1—insulated container, 2—dry ice, 3—experimental setup.

**Figure 6.**Geometrical parameters of some of the tested single-cavity dies, (

**a**) zero l

_{DL}, (

**b**) l

_{DL}= 20 mm, (

**c**) l

_{DL}= 50 mm.

**Figure 7.**Dry ice compaction and extrusion test setup, 1—MTS Insight 50 kN test frame, 2—Upper sleeve with the compaction chamber contained inside it, 3—Lower sleeve, 4—Guide assembly, 5—Ram, 6—Single-cavity die, 7—Loose-dry ice, 8—Dry ice pellets.

**Figure 8.**Hydrostatic extrudate density measurement: (

**a**) overview, (

**b**) close-up of the hydrostatic test module; 1—ACN220 balance with the draft shield, 2—hydrostatic test setup, 3—upper plate, 4—lower plate, 5—beaker, 6—test liquid, 7—K-type thermocouple, 8—Testo 440 multimeter used to measure the temperature.

DL | Min | Q25 | Q50 | Q75 | Max | AVR |
---|---|---|---|---|---|---|

0 | 7.9 | 9.1 | 9.5 | 10.1 | 10.5 | 9.5 |

10 | 8.2 | 8.5 | 8.9 | 9.3 | 10.6 | 9.0 |

20 | 7.6 | 7.7 | 8.5 | 8.8 | 9.0 | 8.3 |

30 | 7.9 | 8.1 | 8.6 | 8.9 | 9.3 | 8.6 |

40 | 8.3 | 8.7 | 3.4 | 9.6 | 10.3 | 9.3 |

50 | 8.2 | 8.5 | 8.9 | 9.0 | 9.3 | 8.8 |

DL | Min | Q25 | Q50 | Q75 | Max | AVR |
---|---|---|---|---|---|---|

0 | 1170 | 1220 | 1300 | 1360 | 1480 | 1310 |

10 | 1440 | 1460 | 1480 | 1520 | 1560 | 1490 |

20 | 1310 | 1410 | 1430 | 1460 | 1530 | 1440 |

30 | 1380 | 1450 | 1520 | 1530 | 1550 | 1490 |

40 | 1280 | 1320 | 1360 | 1570 | 1660 | 1430 |

50 | 1310 | 1400 | 1430 | 1470 | 1490 | 1420 |

DL | Min | Q25 | Q50 | Q75 | Max | AVR |
---|---|---|---|---|---|---|

0 | 7.9 | 9.1 | 9.5 | 10.1 | 10.5 | 9.5 |

0.5 | 7.4 | 7.5 | 7.9 | 8.1 | 8.2 | 7.8 |

1 | 7.5 | 7.7 | 7.8 | 8.6 | 9.6 | 8.6 |

1.5 | 7.8 | 8.3 | 8.5 | 9.3 | 9.4 | 8.7 |

2.0 | 7.8 | 8.3 | 8.6 | 9.0 | 9.4 | 8.6 |

2.5 | 7.8 | 8 | 9.0 | 9.7 | 9.9 | 8.9 |

DL | Min | Q25 | Q50 | Q75 | Max | AVR |
---|---|---|---|---|---|---|

0 | 1170 | 1220 | 1300 | 1360 | 1480 | 1310 |

0.5 | 1310 | 1320 | 1380 | 1390 | 1500 | 1380 |

1 | 1310 | 1330 | 1370 | 1420 | 1440 | 1370 |

1.5 | 1430 | 1460 | 1490 | 1500 | 1540 | 1480 |

2.0 | 1450 | 1530 | 1530 | 1540 | 1560 | 1530 |

2.5 | 1410 | 1500 | 1530 | 1590 | 1640 | 1540 |

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**MDPI and ACS Style**

Górecki, J.; Łykowski, W.
Influence of Die Land Length on the Maximum Extrusion Force and Dry Ice Pellets Density in Ram Extrusion Process. *Materials* **2023**, *16*, 4281.
https://doi.org/10.3390/ma16124281

**AMA Style**

Górecki J, Łykowski W.
Influence of Die Land Length on the Maximum Extrusion Force and Dry Ice Pellets Density in Ram Extrusion Process. *Materials*. 2023; 16(12):4281.
https://doi.org/10.3390/ma16124281

**Chicago/Turabian Style**

Górecki, Jan, and Wiktor Łykowski.
2023. "Influence of Die Land Length on the Maximum Extrusion Force and Dry Ice Pellets Density in Ram Extrusion Process" *Materials* 16, no. 12: 4281.
https://doi.org/10.3390/ma16124281