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Introduction
The plant commonly called nopal is a cactus that lacks leaves; instead, it is formed by racket-shaped, fleshy leaves, which in botanic terms are called cladodes or quills; an important characteristic of this plant is the presence of thorns in the fleshy leaf. The nopal (Opuntia spp) develops favorably in low-precipitation conditions, in soils typical of arid zones, where other crops can only thrive at certain times of the year. It extends over a great part of Mexico in natural and abundant form. It occupies 16 575 408 ha and is cultivated in 55 000 ha for forage purposes (Instituto Nacional de Estadística y Geografía[INEGI], 2014). Also, in central Mexico, the nopal is cultivated for the production of prickly-pear fruit (also known as tunas) occupying an area of 80 000 ha, and 12 000 ha for the production of nopal for human consumption (Secretaría de Agricultura, Ganadería, Desarrollo Rural, Pesca y Alimentación[Sagarpa], 2016). The nopal is a plant with oblong and flattened cladodes with a tendency to be thicker near the internode as age increases. Most species, according to different authors (Meraz et al., 2012; Muñoz, 2016; Tavera, Escamilla, Alvarado, Salinas & Galicia, 2014), have a maximum thickness of 60 mm, 600 mm long, and 350 mm wide for cladodes of three years. Cladodes younger than two years are typically 20 mm thick, 400 mm long, and 190 mm wide, this being the maximum age recommended for dehydration. As pointed out, an increased consumption of nopal has been observed in Mexico during the last ten years, becoming one of the most consumed foods by both humans and animals, especially ruminants. According to producers of milk and meat of bovine origin, the cladodes suitable as food material are the ones located up to the third position, from the upper end of the plant down. Further down, the cladode becomes very hard, and its fibers become quite lignified due to aging; such characteristic considerably reduce the capacity of the cattle to digest such material. Based on this consideration, the biological material of interest comprises from the first to the third cladode. In general, biological products are difficult to handle because the harvesting, transporting, or storing involves an interval of time in which, if not consumed or kept in a suitable place, they decompose.
In the design of machines for nopal chopping, the knowledge of the physical-mechanical properties is an important aspect, as these are determinant to improve and increase energy efficiency and establish guidelines that serve as parameters for cutting, avoiding damage to the raw material. As it is known, there is no commercially available equipment capable to cut the nopal in an efficient way, since it possesses thorn and shape characteristics that do not facilitate its processing. Some machines require the thorns of the nopal to be removed and the nopal itself to be restricted to a specific size. If cutting of a different size is required, a change of some mechanical components is also required. In addition, one nopal at a time must be supplied. The objective of the present work is to determine the physical properties of the nopal that influence the design of machinery that facilitates its processing, specifically, size and shape, coefficient of friction (static and dynamic), specific cutting power and apparent density.
Materials and Methods
One of the most important tasks in the design and construction of agricultural machinery is the determination of the physical-mechanical properties of the product to be processed, in order to know and evaluate, first, the construction material and, then, to choose the work elements or mechanisms that will intervene in the machine. The main reasons for the study of these properties are: a) influence in the design and construction of machines and facilities; b) quality-control improvement of agricultural products; and c) in industrial processes, physical and mechanical properties are important in a wide range of equipment.
The material used in the experiment was collected in the arid zone of the state San Luis Potosí, where the climate according to the climatic classification of Köppen, modified by García (1973), corresponds to a BS or KW (w) (i), which is equivalent to a cold dry steppe climate, with an annual average temperature of 18 oC, being 7.5 oC the minimum and 35 oC the maximum, with an average annual rainfall of 374 mm. The vegetation is microphytic desert scrub (Rzedowski, 1996), with dominant abundance of shrubs, mesquite, huizache, and nopal. The physical-mechanical properties of the nopal that were determined are: size and shape, coefficient of static and dynamic friction, apparent density and specific cutting energy.
Statistical analysis
In order to determine the physical-mechanical properties of the cactus, the mean values and the standard deviation for ten cladodes (Fe = 10) of each of the species studied were considered. The data analysis was performed by means of descriptive statistics, using the UNIVARIATE procedure of the Statistical Analysis System (SAS) program (1999).
Determination of the friction coefficient
The friction force acts in a plane containing the points of contact, opposing the relative motion between surfaces. It plays an important and, in many cases, decisive role in all fields of mechanics. The friction is always present during the motion of bodies and is produced by a force exerted over a surface (Valdés, González & Martínez, 2008). The coefficient of static friction (Fe) occurs when a surface is about to slide relative to another one, by the action of a force (F). If the magnitude of the F exceeds the value of the Fe, the static state is broken; in this condition, the frictional force (Ff) between the contact surfaces decreases relative to the Fe to a slightly smaller value referred to as the dynamic friction force (Fd), then the coefficient of fd will be considered. In order to determine the coefficient of friction, the following materials were used: a piece of unpainted steel sheet of approximately 1 m2 and a protractor. One end of the sheet is matched with the center of the protractor, placing a stop to prevent it from sliding when it is lifted at the opposite end. With this test the angle of repose (or slope) (φ) is obtained, which is used to calculate the coefficient of friction. The magnitude of φ depends on the adhesion force between the nopal particles and the Ff that arise in the displacement of this with a contact surface of interest. Then, two types of tests were carried out. The first one was performed with the whole cactus, i.e. with epidermis; the second test was performed with nopal without the epidermis (the thorns were removed).
Determination of apparent density
In order to determine the apparent density, the cactus prick is first weighed and then immersed in a vessel with water (Laffita, Martínez, Toledo, Sabin & Valdés, 2014). Once the displaced volume of water is known, the density is determined by the expression: ρ = m/V;
Determination of specific cutting energy
In accordance with Singler, Valdés, Laffita, Ayala & Maldonado (2015), the specific cutting energy is calculated as follows: ec = Ec/Fg (equation 1);
where:
ec = |
Specific cutting energy, J/mm2; |
Ec = |
Cutting energy consumed by the sample, J; |
Fg = |
Geometric surface of the sample, mm2. |
In order to determine the cutting energy (Ec) a pendulum-like device was devised, where the oscillating mass is that of the blade, with a cutting edge of 25° and a thickness of 4.76 mm, as shown in Figure 1 (Pendulum for determination of cutting energy). The test was performed as follows: along the trajectory of the center of gravity of the blade (point b of Figure 2) and under the pivot point, a sample with known cross-section was placed. The blade is released from a vertical position on its rotating path (point a); the circular motion is recorded by using a pen on a sheet of paper, placed near the center of rotation, and then the same operation is performed by releasing the blade from the same position but without obstructing its rotation. So, the trajectory described in this case was greater than the previous one as no energy is consumed to cut material. In this way, two displacement angles (θ1 and θ2) are obtained, formed by the vertical that passes through the pivot point and the string holding blade at the highest point on its path (points c and d, respectively) where the kinetic energy is equal to zero. The potential energy is determined by using the equation V = W (L) (L-cos θ), (equation 2);
where:
V = |
potential energy of the blade, J; |
W = |
blade weight, N; |
L = |
pivot length to center of gravity of blade, m; |
θ = |
angle described by the blade rope with respect to the vertical, °. |
Assuming that the difference in the potential energy of the two positions corresponds to the energy consumed in cutting a sample of material, the following relation is obtained: Ec = V2 = V1 (equation 3);
By substituting equations (1, 2, and 3): Ec = (W) (L) (cos θ1-cos θ2)/Fg (equation 4)
Results and Discussion
Each of these species of nopal has characteristics that make them very different from each other, in terms of the properties described in this paper. Regarding the general characteristics, it can be observed that, in the case of the Nopalea cochenillifera species, the thorns are small and scarce, on average 14 areolas per side of the cladode, each areola has two very fine thorns. In the case of the Opuntia ficus indica, it is observed that it has 35 areolas in average on each side of the cladode, from which two or three thorns sprout reaching a maximum size of 10 mm. Finally, the Opuntia robusta species has an average of 25 areolas per side of the cladode, from which two or three thorns sprout, each of 10 mm but very thick. Table 1 shows the results obtained from the nopal suitable for human consumption that was studied (Nopalea cochenilli Ff ra, Opuntia ficus indica and Opuntia robusta).
Table 1 Physical mechanical properties of nopal for human consumption.
| Parameter Thickness, mm |
Nopalea Cochenillifera 41.24 ± 6.12 |
Opuntia
ficus indica 59.32 ± 7.22 |
Opuntia robusta 60.7 ± 6.55 |
| Length, mm | 201.42 ± 13.27 | 589.14 ± 23.34 | 403.21 ± 17.33 |
| Width, mm | 150.6 ± 7.45 | 348.78 ± 9.23 | 301.54 ± 8.75 |
| Density, ρ, t/m3 | 0.88 ± 0.003 | 0.97 ± 0.007 | 0.95 ± 0.004 |
| Resting angle with cuticle, φ1, (o) | 17.31 ± 2.34 | 22.10 ± 2.67 | 19.11 ± 3.06 |
| Resting angle without cuticle, φ2, (o) | 25.43 ± 2.87 | 28.13 ± 3.22 | 27.12 ± 3.16 |
| Static coefficient of friction with epidermis, f1 | 0.31 ± 0.006 | 0.40 ± 0.003 | 0.34 ± 0.009 |
| Static coefficient of
friction without epidermis, f2 |
0.47 ± 0.005 | 0.53 ± 0.004 | 0.51 ± 0.002 |
| Dynamic coefficient of
friction with epidermis, fd1 |
0.24 ± 0.009 | 0.32 ± 0.005 | 0.27 ± 0.006 |
| Dynamic coefficient of
friction without epidermis, fd2 |
0.38 ± 0.001 | 0.42 ± 0.008 | 0.40 ± 0.009 |
| Specific cutting energy, ec | 7156.13 ± 50.9 | 7941.75 ± 56.7 | 8653.65 ± 63.7 |
Source: Author’s own elaboration.
Density
The density varies greatly from species to species. The Opuntia ficus indica is the species with the highest density, followed by Opuntia robusta and Nopalea cochellinifera. It can be observed that there is a direct relationship between the number of areolas per cladode and density; also, the direct relationship between the angle of repose and the coefficient of friction is visible, but such a relationship is not observed in terms of the specific energy of cut, since Opuntia robusta is the one demanding the most energy.
Coefficient of friction
Two types of tests were carried out. The first one was done with the whole cactus, i.e. the part in contact with the metallic surface was the fleshy leaves with spines, obtaining a value of φ1 equal to 22.10° ± 2.67°. In the case of Opuntia ficus indica, the second test consisted of placing nopal without thorns in contact with the metal surface, obtaining a value of φ2 equal to 28.13° ± 3.22°. The coefficient of friction is related to the angle by the following expression: μ = tanφ (Durán, González & Márquez, 2012). Substituting φ1 and φ2 gives the corresponding coefficients of friction: f1 = 0.40 ± 0.003 and f2 = 0.53±0.004. The coefficient of fd is directly related by the expression: fd = (0.7 ... .0.9) (f); considering fd = 0.8 (f) and substituting data for the two types of tests done, f fd1 = 0.32 ± 0.005 and fd2 = 0.42 ± 0.008.
Specific cutting energy
In the determination of this property, several repetitions were performed in order to reduce possible errors and to make the results more representative; the mean value obtained was ec = 7941.75 J/m2 ± 56.7 J/m2 for Opuntia ficus indica, 7156.13 J/m2 ± 50.9 J/ m2 for Nopalea Cochenillifera and 8653.65 J/ m2 ± 63.7 J/m2 for Opuntia robusta. The test of specific resistance to the cut was performed both in the ends of the fleshy leaf as well as in the central part. Considering the different values of the specific cutting energy between species, it is assumed that there is a direct relationship between the hardness of the thorn (specifically in Opuntia robusta) and the fiber content, as consulted literature mentions that the resistance to the penetration is associated to insoluble fiber content (Singler et al., 2015); therefore, the presence of lignin is undesirable. It is considered that a penetration force greater than 6.4 kgf (62.72 N) is unacceptable. Penetration has been evaluated in vegetables such as asparagus, with a permissible value less than 62 N (Sanchez, Cano & Hermida, 1994). Singler et al. (2015) mention that the specific cutting energy depends on the type of material to be processed, its growth stage, moisture content, and the cutting site in the plant. In addition to the above, the conditions of production are also important (Rössel, Durán & Ortíz, 2015). The authors mentioned that the differences found in the various studies are probably related to the content and availability of water in parent plants, lignin content and cuticle thickness. Calvo, Hernández, Peña, Corrales & Aguirre (2010) also mention that aridity conditions can also influence the physical-mechanical properties, since they observed that the greater the aridity, the greater the content of calcium oxalate crystals aligned between the epidermis and collenchyma.
The results presented herein can be used as a basis for the design of machine components associated with the mechanical processing of the nopal leaves. The design of this type of machines is relevant considering the elevated rate of consumption of this plant and, among the machine components whose design may depend on the properties presented, material feed accesses, cutting elements, conveyor for processed material, etc., can be considered. As presented, the design of such machine components must be accommodated specifically for the species of nopal that is to be processed.
Conclusions
In this paper, important mechanical and physical properties of three highly consumed species of nopal were presented. It was found that the presence of areolas and thorns directly affects the angle of repose, the coefficient of friction, and the density. As it is observed, as the number of areolas increases, the angle of repose, the coefficient of friction, and the density also increase.
The specific cutting energy does not have the same behavior as the density, the angle of repose, and the coefficient of friction; therefore, it can be assumed that the cutting energy is more related to the hardness of the spine, the geometry of the cladode, and the uniformity of the thickness.
