# Comparison of Different-Energy-Level Abrasion in Los Angeles and Micro-Deval Apparatuses Using Mass Loss and Rounding of Sediment Particles

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{3}.

^{2}) between correlations could be compared. Additionally, Spearman’s rank correlation was performed between the previously mentioned data, to compare Spearman’s rank correlation coefficients (rho) between the parameters. The resulting values of shape parameters and mass losses were taken as a mean value of all tested particles (in case of single-clast abrasion tests), or as a mean value of all tested sample mixtures (in case of grain mixture abrasion tests).

#### 2.1. Abrasion in Micro-Deval Apparatus

#### 2.2. Abrasion in Los Angeles Machine

#### 2.3. Dynamic Image Analysis

_{a}—calculated according to area A) and the equivalent perimeter diameter (D

_{p}—calculated according to perimeter PERIM) (Equation (1)). The parameter “angularity” (ANG) was selected to describe the roundness/angularity aspect of the particles’ shapes. The parameter “angularity” was calculated according to Equation (2). Particles’ outlines were described by a polygon with n sides. The angle at each vortex was measured and the changes in angles were grouped into intervals of 10 degrees, with the value e being the starting value of each interval. P(e) is the probability that the change in angle has a value between e and e + 10. More angular particles had higher values (up to 180) and those that were more rounded had lower values (up to 0) of the “angularity” parameter. The calculation of ANG value is described in detail in Rao et al. [39] and Wang et al. [3]. The parameter “convexity” (CONV) was selected to describe the surface roughness or surface texture of particles. It was calculated as a ratio between the convex hull perimeter (PERIM

_{CHULL}) and the perimeter of the particle (PERIM) (Equation (3)). Convexity values are between 0 and 1, where 1 represents a perfectly smooth particle (a particle with an aligned perimeter and convex hull perimeter).

#### 2.4. Abrasion Energy Input (Mechanical Work) and Power Estimation

_{NET}), used for the comminution process, and the idling/no load power draw (P

_{NL}) (Equation (4)).

_{k}) of the charge (including steel charge and a rock particle) inside the drum. For the calculation, all of the charge (water, steel balls, and rock particle) was considered as a whole, with an equally distributed mass. Buoyancy was neglected. It was assumed that there is no friction between the steel balls, and between the steel balls and the drum lining. Also, due to the absence of friction, the material was assumed to be rolling around the lowest point of the drum’s cross section.

_{rot}—mechanical work introduced by rotation (J); E

_{k}—kinetic energy (J); Δϕ—angular displacement (-);

^{2}); ω—angular velocity (rad/s);

_{m}—distance from the centre of the drum cross section to the centre of mass of charge (m);

_{imp}—mechanical work introduced by impact (J);

_{k}

_{2}—kinetic energy of charge at the toe of the drum (J); E

_{k}

_{1}—kinetic energy of charge at the shoulder of the drum (J); E

_{p}

_{2}—potential energy of the charge at the toe of the drum (J); E

_{p}

_{1}—potential energy at the shoulder of the charge (J); m—mass of the charge (kg); g—gravitational acceleration (m/s

^{2}); h—height of the fall (m).

_{rot}) was calculated the same way as for the micro-Deval.

_{rev}—work of one revolution (J); t

_{rev}—time needed for one revolution of a drum (s).

## 3. Results and Discussion

#### 3.1. Mass

^{2}= 0.99) with the amount of energy introduced (mechanical work) to the material. However, the same amount of introduced energy in two different machines did not result in a similar amount of wear (Figure 6). This was expected, given the power (energy introduction rate) differences of the two systems (in Watts (J/s)). If comparing the two machines, we can say that, in given conditions, the micro-Deval is a low-energy machine with an energy introduction rate (power) of 5.7 J/s. On the other hand, the Los Angeles machine is a high-energy machine with an energy introduction rate (power) of around 9.5 J/s in the first cycle and 7.7 J/s in the fifth cycle. Power decreased with cycles due to the considerable mass loss, which was absent in experiments in the micro-Deval. The Los Angeles machine in the setup used had between 35% and 67% more power than the micro-Deval, resulting in an almost 10 times higher mass loss (for the same introduced energy). Surely, the selected sieve size determining the mass loss fraction influenced the results of the Los Angeles tests. However, if the selected size of 0.63 mm (as described in the section “Abrasion in Los Angeles Machine”) was replaced by a larger one, e.g., 1.0 mm, the mass loss values increased by only between 0.7% and 1.3% per cycle (known from the sieve analysis). This accounts for about 50% of the standard deviation (between three tested samples) of the mass loss results on the 0.63 sieve.

_{0})

^{−1}(Equation (15)). Both the filling and dimensions of a mill (any tumbling drum) have an impact on its power, which can also be seen in the theoretical equations for the power and introduced energy (mechanical work) estimation (section “Abrasion Energy Input (Mechanical Work) and Power Estimation”). Specific mass loss (mass loss per unit of mass per power) data, obtained from both tests, and energy inputs were highly correlated, with R

^{2}= 0.99 (p-value < 0.01) (according to a linear correlation of linearized, log-transformed data) and RHO = 0.99 (p-value < 0.01) (according to Spearman rank correlation). Obvious discordance appeared in the last Los Angeles cycle data. This might have been caused by the handling of the material—exaggerated mass loss due to the additional loss of the material, as described in the sections “Abrasion in Micro-Deval Apparatus” and “Abrasion in Los Angeles Machine”. However, if the power decrease was disregarded, that is, if mass loss was considered constant throughout the whole abrasion process (all cycles) in both machines, the datasets overlap slightly better (Figure 7a), although the general function fitted to both datasets did not considerably change. If we observed only the energy input scope with data from both machines (up to about 30 kJ), the same could be noted. The curve fitted to such data (Figure 7b) (with available energy input data for both tests) follows Equation (16). Similar approaches, with expressing comminution using various machine or process properties (e.g., specific power), are often used in mineral processing, for mill scaling. An example of such an approach can be found in Yahyaei et al. [48], where mass loss was normalised by “surface specific comminution energy” to be able to compare the grinding rates obtained by mills with different dimensions, filling, and power.

_{S}—specific mass loss (%/(kg*J)); ML—mass loss (%); E—input energy (mechanical work); C

_{ML}—mass loss coefficient; P—power (W (J/s)); m

_{0}—initial mass of the sample material (kg).

_{res}—residual mass (kg).

_{res}/m

_{0}) and the energy input for each process was obtained (Figure 9), with the general expression following Equation (21) and also Equation (22). Exponent c is an abrasion coefficient, which is lithology specific, but also seems to be process (power conditions) dependent. The coefficient c obtained was 0.012/kJ and 0.0006/kJ for high-energy abrasion (in Los Angeles) and low-energy abrasion (in micro-Deval), respectively.

^{2}= 0.88 for micro-Deval, and R

^{2}= 0.90 for Los Angeles) (Figure 10b). This can be explained by the angular particles experiencing chipping of angular parts faster, contributing to greater mass loss. When roundness increases, there is a smaller presence of angular parts to be chipped off, and a particle is abraded at a slower rate—observed already by Schoklitsch [49] in his laboratory experiments in a tumbling mill using angular and rounded clasts. This is also in accordance with the observations of Yao et al. [46], who found that angular particles lose significantly more mass in contrast to rounded ones in a series of two-cycle abrasion tests in a micro-Deval. They studied the influence of fluid in a tumbling test and found greater mass losses of material abraded in water compared to the material abraded in dry conditions. This is definitely a difference between the here-presented dry experiments in the Los Angeles apparatus and the wet experiments in the micro-Deval apparatus, respectively. In this study, the influence of water was acknowledged and taken into account by its mass that contributes to the overall energy (and power) of the abrasion in each setup. Paixão and Fortunato [50], in two-cycle abrasion tests, found higher wear rates in the first cycle when compared to the second abrasion cycle. Similar observations were made by Manga et al. [51]. Deiros Quintanilla et al. [52] explained the reduction of wear rates by the asperities becoming rounder, resulting in higher resistance to wear. In contrast, during the low-energy abrasion, wear rates decreased rapidly in the beginning of the abrasion (in the first several cycles). Later on, the wear rate began to change (lower) at a slower rate. It should be noted that in the 10th and 11th cycles, one of the particles abraded in single-clast abrasion experiments (micro-Deval) experienced a major breakage, resulting in a considerable fragment being broken off. Consequently, this event contributed to the jump in wear rate values in the 10th and 11th cycles.

_{50}), coefficients of uniformity (C

_{U}), and coefficients of curvature (C

_{C}) were determined from particle size distribution curves of the tested material (shown in Figure 11). The initial (at t

_{0}) mean median grain size d

_{50}was 51 mm, the mean coefficient of uniformity C

_{U}= 1.26, and the mean coefficient of curvature C

_{C}= 0.99. This describes the material as evenly graded [53]. During the first ~5 min of rotation (160 rotations), the initial particle size distribution experienced a fast change. During the further abrasion, the change in size slowed down. After the first abrasion cycle in the Los Angeles machine, the mean median grain size dropped to 37.03 mm, the C

_{U}changed to 5.88, and the C

_{C}to 2.50. By the end of the fifth cycle (1500 rotations, ~47 min), the mean d

_{50}diminished to 23.37 mm and the C

_{C}to 14.64, whereas the C

_{U}grew until the end of the 4th cycle (to 47.97) and then started getting smaller again, reaching 45.86. The particle size distribution curve migrated from poorly graded to well graded, until the fifth cycle. According to Erichsen et al. [25], well-graded distribution curves of material after the Los Angeles test indicate domination of breakage, whereas the domination of abrasion results in poorly graded or gap-graded distribution curves. After the fifth cycle, most of the biggest particles were broken, and the material started shifting towards even gradation again. This can also be seen from the particle size distribution curves (Figure 11). From the initial (t

_{0}) narrow and vertical distribution curve, the curve became wider and more horizontal. After the fifth cycle, the curve started narrowing and becoming more vertical again, which shows that the material particles were all becoming smaller and narrower in range. Particle size distributions of one of the samples tested in the Los Angeles machine (LA1) for all of the abrasion cycles and the initial state are presented in Figure 11.

#### 3.2. Morphology

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Experimental methodology schemes: (

**a**) abrasion in micro-Deval apparatus, (

**b**) abrasion in Los Angeles machine.

**Figure 5.**Power draw measurements results for (

**a**) micro-Deval abrasion tests; (

**b**) Los Angeles abrasion tests.

**Figure 6.**Input energy of abrasion tests—cumulative mass loss of material plot (from micro-Deval test marked blue, from Los Angeles test marked orange).

**Figure 7.**Transformed mass loss data plot of input energy—“specific mass loss” for both machines combined (data from micro-Deval tests marked blue, data from Los Angeles tests marked orange): (

**a**) all data, (

**b**) for the energy input scope with data from both machines.

**Figure 8.**(

**a**) Graphical representation of Equation (19) (data from micro-Deval tests are marked blue, and from the Los Angeles tests marked orange), (

**b**) measured vs. calculated residual mass using Equation (20). One should note that in Figure (

**b**), there are multiple points marked blue (representing data from micro-Deval tests), but they are close to each other.

**Figure 9.**Relation between relative residual mass and input energy for both abrasion tests (results from micro-Deval tests marked blue, results from Los Angeles tests marked orange).

**Figure 10.**Wear rates from micro-Deval tests (marked blue) and Los Angeles tests (marked orange) in relation to (

**a**) input energy; (

**b**) angularity.

**Figure 11.**Evolution of particle size distribution of material (one of the samples) abraded in Los Angeles machine in each abrasion cycle.

**Figure 12.**Particle form classification according to Zingg [5]. (

**a**) Particles’ form before testing in micro-Deval apparatus (marked with squares) and after 15 cycles of abrasion in micro-Deval apparatus (marked with circles) A square and a circle of the same colour represent the same particle. (

**b**) Particles’ form before testing in Los Angeles machine (marked with squares), after first cycle of abrasion (marked with Xs), and after fifth cycle of abrasion in Los Angeles machine (marked with circles).

**Figure 13.**Particles from the abrasion tests. Particles from tests in Los Angeles machine (at initial state, after first cycle, and after fifth cycle) in the first row. Particle from tests in micro-Deval apparatus (at initial state, after fifth cycle, and after fifteenth cycle) in the second row.

**Figure 14.**Sphericity changes of abraded material. Data for micro-Deval abrasion tests are marked blue and data for Los Angeles tests are marked orange—(

**a**) relation between input energy and sphericity change; (

**b**) relation between cumulative mass loss and sphericity change; (

**c**) relation between input energy and sphericity value; (

**d**) relation between cumulative mass loss and sphericity value.

**Figure 15.**Angularity changes of abraded material. Data for micro-Deval abrasion tests are marked blue and data for Los Angeles tests are marked orange—(

**a**) relation between input energy and angularity change; (

**b**) relation between cumulative mass loss and angularity change; (

**c**) relation between input energy and angularity value; (

**d**) relation between cumulative mass loss and angularity value.

**Figure 16.**Convexity changes of abraded material. Data for micro-Deval abrasion tests are marked blue and data for Los Angeles tests are marked orange—(

**a**) relation between input energy and convexity change; (

**b**) relation between cumulative mass loss and convexity change; (

**c**) relation between input energy and convexity value; (

**d**) relation between cumulative mass loss and convexity value.

**Figure 17.**Distribution of angularity values according to size class before tests and after each abrasion cycle in Los Angeles machine, for particles coarser than 20 mm.

**Table 1.**Main characteristics of the machines and power estimates. (D—inner diameter of the drum, L—inner length of the drum, ω—rotational speed of the drum, Mean m

_{0}—mean initial mass of the sample, Filling—filled portion of the drum, P

_{0}—power of the machine in the first cycle, ∑E—cumulative introduced energy, ∑t—cumulative time of abrasion (sum of all cycles’ duration), ∑Rev—cumulative number of revolutions).

Micro-Deval | Los Angeles | |
---|---|---|

D (drum) (mm) | 200 | 711 |

L (drum) (mm) | 154 | 508 |

ω (rpm) | 100 | 32 |

Mean m_{0} (kg) | 0.22 | 1.96 |

No. of samples | 9 | 3 |

Filling (%) | 56.3 | 0.35 |

P_{0} (W) | 5.67 | 9.52 |

∑E (kJ) | 315.93 | 23.71 |

∑t (min) | 930 | ~47 |

∑Rev (n) | 93000 | 1500 |

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**MDPI and ACS Style**

Kuzmanić, T.; Lebar, K.; Mikoš, M.
Comparison of Different-Energy-Level Abrasion in Los Angeles and Micro-Deval Apparatuses Using Mass Loss and Rounding of Sediment Particles. *Appl. Sci.* **2023**, *13*, 6102.
https://doi.org/10.3390/app13106102

**AMA Style**

Kuzmanić T, Lebar K, Mikoš M.
Comparison of Different-Energy-Level Abrasion in Los Angeles and Micro-Deval Apparatuses Using Mass Loss and Rounding of Sediment Particles. *Applied Sciences*. 2023; 13(10):6102.
https://doi.org/10.3390/app13106102

**Chicago/Turabian Style**

Kuzmanić, Tamara, Klaudija Lebar, and Matjaž Mikoš.
2023. "Comparison of Different-Energy-Level Abrasion in Los Angeles and Micro-Deval Apparatuses Using Mass Loss and Rounding of Sediment Particles" *Applied Sciences* 13, no. 10: 6102.
https://doi.org/10.3390/app13106102