Caracterización de las propiedades físicas y modales de los raquis de
racimos de mbocayá para recolección mecanizada
Characterization of physical and modal
properties of the rachis of macaw palm bunches aiming mechanized harvesting
Zenil Ricardo Cunha Rodrigues de Oliveira1,*, Fábio Lúcio
Santos2, Domingos Sarvio Magalhães Valente1, Francisco de
Assis de Carvalho Pinto1, Mateus Resende Rodrigues2
1- Universidade Federal de Viçosa. Brasil.
2- Universidade Federal de Lavras. Brasil.
* E-mail: zenilricardo@gmail.com
Recibido:
26/05/2020; Aprobado: 20/10/2020
Resumen
La mbocayá (Acrocomia aculeata) es una alternativa
para la producción de biodiésel debido a las características de la planta como
la gran adaptabilidad a los diferentes climas y la alta producción de aceite.
Sin embargo, su explotación sigue siendo un obstáculo. Dado que el desarrollo
de máquinas eficientes para la cosecha y poscosecha de la mbocayá requiere el
estudio del comportamiento dinámico de la planta. El método de elementos
finitos se puede utilizar en el diseño de máquinas para estudiar el
comportamiento dinámico de la planta. Como parámetros de entrada para usar el
método de elementos finitos, se les debe informar el sistema geométrico, físico
y mecánico en estudio. El objetivo de este estudio fue determinar y evaluar las
propiedades geométricas y físicas de los raquis de la mbocayá, además de
investigar la transmisibilidad y el barrido de frecuencia mediante vibraciones
mecánicas, en diferentes etapas de maduración. Se concluyó que las propiedades
físicas y geométricas eran fundamentales para la construcción del modelo y la
comprensión del comportamiento dinámico del raquis de la mbocayá. En la
evolución de la etapa de maduración de inmaduro a maduro, la primera frecuencia
natural cambia en magnitud de 22.66 a 15.90Hz.
Palabras claves: Acrocomia aculeate; Transmisibilidad;
Frecuencias naturales; Vibración mecánica; Barrido de frecuencia.
Abstact
The
Mbocaya palm (Acrocomia aculeata) is
an alternative for the production of biodiesel due to the characteristics of
the plant such as the great adaptability to different climates and high
production of oil. However, its exploitation remains an obstacle. Since the
development of efficient machines for harvesting and post-harvesting of the
macaw palm requires the study of the dynamic behavior of the plant, the finite
element method can be used in machine design to study the dynamic behavior of
the plant. As input parameters for using the finite element method, they should
be informed about the geometrical, physical and mechanical system under study.
The aim of this study was to determine and evaluate the geometric and physical
properties of the rachis of Mbocaya palm, in addition to investigating the
transmissibility and frequency sweep by means of mechanical vibrations, at
different stages of maturation. It was concluded that the physical and
geometric properties were fundamental for the construction of the model and
understanding of the dynamic behavior of Mbocaya palm rachis. In the evolution
of the maturation stage from immature to mature, the first natural frequency
changes in magnitude from 22.66 to 15.90Hz.
Keywords: Acrocomia aculeate; Transmissibility; Natural frequencies; Mechanical vibration; Frequency sweeping.
Introduction
The macaw palm (Acrocomia
aculeata) is a native palm of tropical America, naturally occurring from
Central America to extreme south of the American continent (Motoike et al., 2013). In Brazil, it is
considered one of the most dispersed palm trees, tolerant to drought and low
temperatures; this palm is found along in practically all regions of the
country, growing in large populations in degraded or intact areas and is
well-adapted to different ecosystems [2], [3].
Worldwide demand for renewable energy sources has been lead the
agro-industrial sectors focus on oil crops. Macaw palm can be considered a
solution to be introduced as alternative option among the classical oleaginous
plants (i.e., soy, peanuts, maize, sunflower, etc.) due to high productivity
and quality of its oil, including for the production of biofuels and
pharmaceutical products [4], [5].
Commercial plantation, following suitable agronomic care, can
yield 16,000–25,000 kg of fruit per hectare and produce up to 6200 kg ha-1
of oil [6]. However, in
spite of the potential of macaw palm, its exploitation is based on extractivism,
resulting in low productivity and poor quality of the generated products [3], [7]. Nowadays, the harvest is not mechanized, besides being made in a
precarious way with scythes adapted to bamboo rods for the cutting the bunch of
macaw palm. Due to the large number of spines in the stem and the great height
of the plant, the harvest becomes a very expensive operation, causing a great
amount of work accidents [1].
Considering that some crops such as coffee [8], olives [9] and tomato [10] employ mechanical harvesting based on mechanical vibrations with
expressive results for fruit detachment, this principle can be used for
mechanized harvesting of macaw palm fruits [11], [12]. Recently, Grupioni et al. (2018) used the principles of
mechanical vibration in a prototype developed for the semi-mechanized harvest
of macaw palm.
Since each body has infinite natural frequencies, and these vary
with the stage of maturation, one can select the fruits through this principle.
Using a source of vibrational energy with the same natural frequency of the
fruit, the phenomenon of resonance will occur, in which the fruits tended to a great
amplitude of oscillation, causing fruit to detach. Therefore, it will be
possible to select the fruits by the maturation stage [14]. However, the path that this vibrational energy passes is the
source of excitation (machine), rachis, rachilla and fruit. That is, it is
necessary to know the transmissibility of this energy throughout the rachis,
for that, one has to first know the properties of the rachis. Thus, for
understanding the dynamic phenomena involved during the harvesting by
mechanical vibrations, it is necessary the geometric and physical knowledge of
the plant structure and fruit.
The determination of physical and geometric properties of the
macaw palm rachis is essential for the improvement of the harvesting and the
emergence of new processing techniques, providing a knowledge basis for
machine-plant interaction project. Mechanical properties of the macaw palm
fruit-rachilla system were analyzed by Velloso et al. (2017) and Villar et al. (2017). In addition to mechanical properties, Rangel et al. (2019) also studied the geometric and physical properties of the macaw
palm fruit-rachilla system.
In this context, considering
the potential of the crop, the aim of this work was to determine and evaluate
the geometric and physical properties of the rachis of macaw palm. This work proposes an investigation of the vibration
transmissibility and frequency sweeping by means of mechanical vibrations on
macaw palm rachis. In addition, in order to study the
dynamic behaviour of the rachis of macaw palm, a numerical modal analysis was
performed and validated from the frequency spectrum data obtained from
frequency sweep tests. The results obtained from this study will constitute a
basis of knowledge for aiding designers on development of harvesting and post-processing machines.
Material and methods
The research was carried out using macaw
palm bunches collected at the Active Germplasm Bank (AGB) of the Federal
University of Viçosa, this experimental area was also used in another works
such as Villar et
al. (2017), Velloso et
al. (2017) and Grupioni et
al. (2018). The Active Germplasm Bank is located at
Experimental Farm in Araponga – MG, at 20° 40' South latitude and 42° 31' West
longitude, Brazil. Samples of macaw palm rachis
came from four sites: BGP 12 - Ibiá - Araxá; BGP 13 - Sítio Paraíso - Belo
Horizonte; BGP 31 - Três Marias; BGP 53 - Lavras - São João Del Rey.
The samples were always collected in the
morning and the tests performed during the same day of collection and also the
day after. The ambient temperature of 20°C was maintained in the analytical
laboratory.
The geometric dimensions, mass, volume,
specific mass, tests of vibration transmissibility, frequency sweep and modulus
of elasticity were determined for the samples at each stage of maturation
(rachis with immature and mature fruits). It was considered the maturation
stage of immature fruits aged 180 days and mature when the natural detachment
of the fruits occurs. This work does not evaluate issues related from macaw
palm fruits, it only evaluates properties related to the rachis from macaw palm
bunches. The different maturation stages of the macaw palm fruits are mentioned
throughout this work to distinguish the time of permanence of the rachis in the
plant.
Geometric dimensions
For each stage of maturation, the macaw
palm rachis was divided into three parts (Figure 1): lower, middle and upper
third. The average length of each third was obtained by performing a length
measurement of the longitudinal axis from end to end, using a measurement tape
with 1 mm of precision.
Figure 1. Image
of a sample of the macaw palm rachis partitioned in thirds.
The average diameter of each third was
obtained by performing measurements of the diameter in five cross sections
along the macaw palm rachis sample (third part of sample), equally distributed
from the ends. The diameter was measured in the cross sections on the X and Y
axis (Figure 2). The instrument used for measurement was an analog caliper with
a precision of 0.01 mm.
Figure 2.
Equidistant measurements of the third of the macaw palm rachis (A) and cross
section of each third in the X and Y (B) axis.
Mass and volume
The average masses of each third part of
the macaw palm rachis were determined using five trial bodies with 1.5 cm of
height for each stage of maturation, using a digital scale, with a resolution
of 0.01 g.
For the determination of the average
volumes, macaw palm trial bodies, for each stage of maturation, was employed a
100 mL beaker, with a resolution of 1 mL. Volume measurements were performed by
the immersion of a sample into water.
Specific mass
The
specific mass was determined for the rachis samples by using the average mass
and volume obtained experimentally.
Transmissibility test
Transmissibility tests were
performed using a vibration system manufactured by Ling Dynamic Systems (LDS),
which consisted of a signal generator, an amplifier model PA 1000 L coupled to
a field power source model FPS-10 L , an electromagnetic shaker model V 555
M6-CE and a Dactron controller model Comet USB. In addition, an
apparatus was developed for the purpose of coupling the sample of the rachis to
the electromagnetic vibrator.
At first, the macaw palm
rachis was set to the apparatus developed for attachment to the mobile base of
the electromagnetic shaker, then the high-sensitivity acceleration
piezoelectric transducers (100.7 mv/g (Eu)), were fixed vertically, along the
rachis one at each midpoint of each monitored third (fractions of the rachis).
Considering that the accelerometers were placed directly on the rachis and
fixed with the aid of wax fixation and adhesive tape (Figure 3).
Figure 3. Electromagnetic
shaker prepared for carrying out the vibration tests (A) and macaw palm rachis
fixed for the test (B).
The transmissibility of the
rachis was determined from a sinusoidal signal with frequency of 10 Hz and
amplitudes 0.25 mm, both constants, when the frequency of
the vibration that was used is the same as the natural frequency of the fruit,
resonance occurs, even for small amplitudes. The way to evaluate the input of
movement and the response of the system was performed from the value RMS (Root
Mean Square) of the system. Thus, the transmissibility was determined for the
rachis of bunches with predominance of fruits in the maturation stages of
immature and mature from different sites.
For the measurement of the
acceleration signals from the three fractions of the rachis, a National
Instruments data acquisition system was used, consisting of a base chassis NI cDAQ-9174 and a four-channel NI
9234
module used for acceleration signal acquisition. The acquisition
system was connected to a computer and managed by LabView version 5.0
software. Acceleration data, as a time function, were submitted to Fast
Fourier Transform (FFT) for the determination of the frequency spectra. The
rachis transmissibility was calculated by Equation 1.
(1)
where,
T =
transmissibility, %;
Yp = acceleration
of the monitored point, m s-²;
Ye = acceleration
of excitation, m s-².
Frequency
sweep test
The frequency sweep test was
carried out in a manner analogous to the transmissibility test, with the macaw
palm rachis attached to the apparatus coupled to the electromagnetic shaker shown in Figure 3 (A). However, the analysis was performed from the
acceleration of the system from a sinusoidal signal in the frequency range from
10 to 80 Hz and amplitude of 0.25 mm. Three high-sensitivity piezoelectric
transducers (100.7 mv/g (Eu)) were installed at the measurement points shown in
Figure 3 (B). The accelerometers were placed directly on the rachis and fixed
with the aid of fixing wax and adhesive tape. The same plane and the same
maturation stages were monitored.
For the measurement of the
acceleration signals from the three monitoring points, a National Instruments
data acquisition system was used, consisting of a base chassis NI cDAQ-9174 and a four-channel NI
9234
module. The acquisition system connected to the computer was managed by LabView
software version 5.0. The natural frequencies were determined from the
frequency spectra, after performing the Fast Fourier Transform (FFT). From the
frequency sweep tests, the natural frequencies were identified considering the
response amplification peaks on the frequency spectra.
Compression test
Simultaneously with the
sweep test, the macaw palm rachis compression test was performed to obtain the
modulus of elasticity for the immature and mature maturation stages. The
objective of this study was to evaluate the parameters associated with the
system stiffness and its correlation with the variation of the natural
frequencies. For the compression tests, INSTRON 3360 Series Dual Column Table
Frames universal testing machine was used, using 20 cylindrical test bodies for
each maturation stage. These test bodies were made from the upper third of the
rachis with a circular cross section of 20 mm in diameter and 15 mm in length.
The tests were performed by
means of compression, and the test bodies were placed between two parallel flat
circular plates, submitted to constant deformations of small magnitude on the
two opposite faces of the test body. The loading rate provided was 15.0 mm min-1,
was monitored by Bluehill 3 software and managed by the computer coupled
to the universal testing machine. The elasticity modulus of the rachis was
calculated directly by the software.
Modeling of the rachis from
macaw palm
The physical and geometric
data were used to develop a model of the macaw palm
rachis using 3D-CAD Fusion 360 software. The modeling was carried out for the immature and mature maturation
stages scenarios. Two three-dimensional models, with different levels of detail, of the macaw palm rachis
were developed. The first model was developed considering a less sophisticated geometry, a mesh refinement of 5942 nodes
and 3238 elements. A second model was elaborated considering a more sophisticated
geometry, this model presented a
mesh with 12426 nodes and 7046 elements. The discretization of both models
was made from 10-node tetrahedral elements and the interpolation function used
was a hyperbolic function. The final meshes used was obtained after
a convergence test of models.
From
the three-dimensional
models of rachis, using the finite element method, a numerical modal analysis was performed. This analysis allowed the determination of eigenvalues
(natural frequencies) and eigenvectors (mode shapes) of the system. Then, the flexural mode shapes, associated
with the corresponding natural frequencies, were determined.
The model was validated
comparing the average natural frequencies, that was
determined from experimental frequency sweep tests, with the simulated natural
frequencies, obtained from numerical modal analysis. Regardless the sites, the
validation process was performed for the immature and mature stages of
maturation, considering the frequency range from 10 to 80 Hz. The model
validation will enable to improve the
comprehension of the dynamic
behavior of the rachis, during the excitation by mechanical vibrations on
mechanized harvesting process.
Statistical analysis
The
data of geometric dimensions, mass, volume, specific mass, vibration
transmissibility and frequency sweep tests of
the samples were submitted to analysis of variance, according to a completely
randomized design, with two treatments (immature and mature stages of
maturation stages of the fruits) and using
three replicates. The effect of the stage of maturation on behavior of
geometric and physical properties, the transmissibility and the natural
frequencies of the system was studied by
Tukey test, at a significance level of 5%. Statistical analyses were performed
using Assistat Statistic software, version 7.7 beta [17].
Results
and discussion
Geometric
dimensions
Length
Significant differences were observed only
between stages of maturation (Table 1). The stage of maturation of the fruits
influences the rachis length, thus, it is possible to infer that the rachis
length tends decrease when the stage of maturation pass from immature to
mature. However, there was no significant difference in the length of the
rachis for the sites.
Table
1. Macaw palm rachis length and average diameters for
immature and mature stages of maturation.
|
Stages of Maturation |
Length (cm) |
Diameter X (cm) |
Diameter Y (cm) |
|
|
Immature Mature |
|
88.50 a 73.60 b |
2.75 a 2.31 b |
2.16 a 1.90 b |
Means followed by the same letter in the column are not
significantly different by the Tukey test at 5% probability.
Similar behavior was observed by Ghavami and Marinho (2005) in bamboos of the Guadua angustifolia species. The author
detected a gradual decrease of the length from the base to the top due to
advance of the stage of maturation. Between the sites, significant differences
were not detected. The largest length belongs to the BGP 12 access, with the
size of 91.85 cm and the shortest length belongs to the BGP 31 access with
70.85 cm.
Diameter
Considering the diameters were measured on X
and Y axis, it was observed that there is statistical significant difference
between the axes, where X axis tends to be larger than the Y axis. The average diameter found for the X axis was
2.52 cm and for the Y axis it was 2.03 cm. However,
there was no significant difference for the diameter of the rachis for the
means of sites.
The average diameters were analyzed regarding the stages
of maturation and the results are presented in Table 1. The average diameters for
the both axes tend to decrease when the stage of maturation pass from immature
to mature stage. According to Carlin et al. (2008), in a study about sugarcane, verified that the change in diameter
occurred due to cell stretching. Similar behavior was observed for macaw palm
rachis, which can be explained due the cells elongation caused by the bunch
weight.
The average diameters were analyzed regarding the
comparison between the sites (Table 2).
Table 2.
Average diameters on X and Y axes, mass, volume and specific mass from the
macaw palm rachis to the sites.
|
Sites |
Diameter X (cm) |
Diameter Y (cm) |
Mass (g) |
Volume (cm3) |
Specific mass (g cm-3) |
|
BGP 12 BGP 13 BGP 31 BGP 53 |
3.06 a 2.20 b 2.32 b 2.53 ab |
2.60 a 1.80 b 1.82 b 1.95 b |
13.14 a 6.35 b 7.00 ab 10.22 ab |
14.60 a 7.98 b 8.13 b 9.93 ab |
0.88 ab 0.75 b 0.83 ab 1.01 a |
Means followed by the same letter in the
column are not significantly different by the Tukey test at 5% probability.
For the diameter on X axis, the BGP 12 site
was larger than the BGP 13 and BGP 31 sites. As for the diameter on the Y axis,
the BGP 12 site was larger than the diameters of the other sites.
The average diameters was evaluated
considering the different parts of the macaw rachis (Table 3), which was divide
in three thirds as illustrated in Figure 1.
Table
3. Average diameters on the X axis and Y axis, mass,
volume and specific mass of the macaw palm rachis for the lower, middle and
upper third
|
Third |
Diameter X (cm) |
Diameter Y (cm) |
Mass (g) |
Volume (cm3) |
Specific mass (g cm-3) |
|
Lower Middle Upper |
3.40 a 2.64 b 1.56 c |
2.40 a 2.27 a 1.44 b |
12.41 a 9.50 ab 5.63 b |
12.82 a 10.70 ab 7.00 b |
0.98 a 0.89 ab 0.74 b |
Means followed by the same letter in the column are not
significantly different by the Tukey test at 5% probability.
Analyzing the thirds of the macaw palm
rachis, for the diameter on the X axis, it was observed significant differences
between all parts of the rachis. The largest rachis diameter was determined for
the lower third, followed by the middle and upper third. On the Y axis, there
was not observed significant difference between the lower and middle thirds.
The upper third presented significant difference in relation to the others. It
can be noted that for the both axes the diameters tend to reduce from lower to upper
third.
Mass and volume
The results obtained for masses and volumes, considering
immature and mature stages of maturation, there were not observed significant
differences for these parameters.
The results for the masses and volumes of the macaw palm
rachis were analyzed for the sites (Table 2). Regarding the sites, for
the mass, BGP 12 differed significantly from BGP 13, presenting an average mass
higher. However, comparing BGP 12 site with BGP 31 and BGP 53, there was not
observed significant difference between the mass values.
For the volumes, BGP 12 site presented an average volume
higher than the others, differing significantly from the BGP 13 and BGP 31
sites, which did not differ from each other. However, BGP 12 site did not
differ statistically of the BGP 53.
The results for the average masses and volumes were
analyzed for the thirds of the macaw palm rachis (Table 3). From the results
presented in Table 3 for mass and volume, it can be stated that the average
mass of the lower third is almost three times greater than the average mass of
the upper third. For the volume, it can be inferred that the volume of the
thirds of the macaw palm rachis tends to be larger at the lower third of the
bunch, precisely where the cut during the harvesting process occurs.
Specific mass
The results for the specific mass of the macaw palm
rachis were analyzed considering immature and mature stages of maturation and
the sites (Table 2). However, there were not observed significant differences
were observed for the maturation stage.
For the sites, BGP 53 differed from the BGP 13, the average specific mass
determined was 1.01 g cm-3, while for the BGP 13 was 0.75 g cm-3.
This means that for the same amount of volume, the BGP 53 site will have a
largest amount of mass. The sites BGP 12 and BGP 31, did not differ from the
other sites. The results for specific mass were analyzed for the thirds of the
macaw palm rachis (Table 3).
From the results presented in Table 3 for specific mass,
lower and upper thirds presented significant difference between them. Similarly
the results for the volume of the rachis (Table 3), the specific mass tends to
be larger at the lower third of the bunch. The lower third has the highest
specific mass, 0.98 g cm-3, followed by the middle third, 0.89 g cm-3
and, finally, the upper third, 0.74 g cm-3.
Evaristo et al. (2017), verified that the physical and chemical characteristics of the fruits
from macaw palm vary according to the region, this fact did not occur with the
rachis from macaw palm bunches. As evidenced, the rachis from macaw palm
belongs to distant regions themselves. However, the results found in the
present study show that there is a similarity between the rachis from macaw
palm for these different sites, evidencing a data pattern.
Physical
properties of agriculture products can influence many steps of the
mechanization process and post-harvesting of products [21], [22]. Thus, determination of
physical and geometric properties of the macaw palm rachis is essential for the
improvement of the harvesting and the emergence of new processing techniques [13], [23]. Considering the
harvesting of the macaw fruits, performed by machines, it is fundamental the
determination of physical properties of all structures that constitute the
bunches, in order to study and comprehend its mechanical behavior during the
interaction with the machines.
Transmissibility
test
During the monitoring of the
immature and mature maturation stages, it can be inferred that there was no
significantly difference for the results found. The transmissibility result
indicates that for the same vibrational energy applied under the conditions
proposed by the test, more energy will be transmitted to the macaw palm rachis
during the mature ripening stage, about 46% of the initial value, while 32% of
the initial energy will transmitted to the rachis.
Regarding the sites, the
results of the transmissibility indicate that for the same vibrational energy
applied under the conditions proposed by the test, more energy will be
transmitted to the macaw palm rachis belonging to the BGP 12 site, with 50% of
the initial energy value; while, the BGP 13 site, has the lowest average value
of transmissibility, about 25%. The sites BGP 31 and BGP 53, hold intermediate
values, being 46 and 42%, respectively.
According to Rao (2008), the transmissibility depends on factors such as frequency ratio
and damping ratio. Considering that these parameters are similar for the
different sites, since the biological material, that is, the macaw palm
rachises are similar to each other. These have the same geometric
conformations, subject to the same weather conditions, besides having the same
type of management. Thus, it is expected that the magnitude of the
transmissibility be close to the different sites. This fact is evidenced by
Tukey test at a significance level of 5%, which did not detect significant
statistical difference for the transmissibility. Due to the stiffness of the
material, transmissibility tends to occur differently in different materials [25]. The stiffness that macaw palm rachis present was similar to that
found by Villibor et al. (2019). The biological material
has, in its composition, constituents that can function as shock absorbers of
vibrational energy, such as cell membranes, cell walls and fibers [27].
It was observed that for the
macaw palm rachis input frequency and amplitude, there was no amplification of
the output response, different from that reported by Castro-Garcia et al. (2017) in oranges, evidencing
better transmission of energy at low frequency, for both stages of maturation.
Frequency sweep tests
From the macaw palm rachis
frequency sweep tests, performed for the 10 to 80 Hz range and amplitude of
0.25 mm, the natural frequencies were determined using the Fast Fourier
Transform and frequency spectrum analysis. Figure 4 illustrates the frequency
spectrum obtained for site BGP 31, from which the natural frequencies were
extracted. The natural frequencies were identified considering the response
amplification peaks on the frequency spectra. Similar methodology was applied for all sites considering immature and mature stages of maturation.
Figure 4. The frequency
spectrum of the BGP 31 site showing three natural frequency peaks within the
excitation range.
In Table 4 are present the experimental
results obtained by the frequency sweep, which show the natural frequencies for
the macaw palm rachis at different stages of maturation.
Table 4. Natural
frequencies of the macaw palm rachis for the immature and mature maturation
stages at the monitored points.
|
Sites |
Natural frequencies (Hz) |
|
|
Immature |
Mature |
|
|
BGP 12 BGP 13 BGP 31 BGP 53 |
22.66,
45.26 and 67.85 22.65,
45.25 and 67.85 22.67, 45.26 and 67.86 22.65,
45.26 and 67.85 |
15.95, 22.68 and 45.27 15.90, 22.66 and 45.27 15.90, 22.66 and 45.27 15.72, 22.66 and 45.27 |
According to the results
presented in Table 4, for each site, three natural frequencies were found
within the frequency range scanned during the test. It is observed that all
sites showed a similar behavior for natural frequencies, since, with the
evolution of the maturation stage from immature to mature, the mode of
vibration changed its magnitude from 22.66 to 15.90 Hz.
According to Rao (2008), the natural frequency is dependent of the stiffness and mass of
the material, with the evolution of the maturation stage, there was a tendency
of a decrease in the stiffness of the macaw palm rachis for the different
maturation stages, once that a decrease of the modulus of elasticity occurred
with the evolution of the maturation stage, going from 51.97 MPa when immature
to 37.93 MPa when mature, implying in a lower stiffness of the material,
resulting, therefore, in lower natural frequencies. However, BGP 53 site
maintained similar natural frequency magnitudes for both maturation stages,
which can be attributed by heterogeneity of the plant.
In addition, the results
reported in Table 4 indicate that the natural frequency tends to decrease with
the evolution of the maturation stage, which is interesting because in this way
it is possible to separate the different maturation stages. Similar results
were observed by Santos et al. (2010) and Villibor et al. (2016), both for coffee fruits,
the authors were able to separate the different maturation stages of coffee
from different natural frequencies. By means of mechanical vibrations, as well
as (Pezzi and Caprara (2009) obtained for the grape crop
and He et al. (2013), for the sweet cherry trees, it was observed amplitude
amplification in the natural frequencies for the macaw palm rachis.
Modeling of the rachis from
macaw palm
In Table 5 are presented the results obtained for the frequencies
in the mode of vibration of the rachis from macaw palm. Both models presented the response close
to the experimental test. From the validation process, it can be observed that the immature stage of maturation presented an average error less than 5% for all natural frequencies evaluated.
Comparing
the results presented in Table 5 with the results in Table 4, it can be
observed that both models represent properly the dynamic behaviour of the macaw palm rachis. However, the error observed for mature stage of maturation (Table
6), for second natural frequency evaluated for models 1 and 2, may be associated with the lack of
uniformity of the geometric and physical characteristics along the structure of the rachis.
Table 5.
Frequencies of the macaw palm rachis for the Model 1 and Model 2.
|
Stages of maturation |
Frequencies (Hz) |
|
|
Model 1 |
Model 2 |
|
|
Immature Mature |
23.40, 43.11 and 68.87 16.64, 30.62 and 48.81 |
23.41, 43.01 and 69.01 16.90, 31.02 and 49.47 |
Table 6. Validation error between simulated and
experimental results for frequencies of the macaw palm rachis for the Model 1 and Model 2.
|
Stages of maturation |
Error (%) |
|
|
Model 1 |
Model 2 |
|
|
Immature Mature |
3.1, 4.7 and 1.4 4.4, 25.9 and 7.2 |
3.2, 4.9 and 1.6 5.9, 26.9 and 8.4 |
The
vibration modes (Figure 5), obtained for the macaw palm rachis models,
corroborate the results obtained by the experimental test. Each mode of
vibration is associated with a different natural frequency. The higher the
printed frequency, the greater deflections will occur, resulting in possible
stress concentration points. Note that the vibration modes are different for
the same model; however, when the two models are compared, the vibration modes
show similarities.
Figure 5. Vibration mode for macaw palm rachis in the immature maturation
stage, model 1 (A, B, C) and model 2 (D, E, F).
The
efficiency in detaching the fruit of the macaw palm occurs as the frequency of
vibration that excites the plant is equal to or close to the vibration modes.
In general, a more sophisticated mode of vibration of macaw palm can generate
greater tensions favoring the detachment of the fruit [32]. In this way, the vibrational energy must be transmitted through the
bunch to the fruit-rachilla system, similar to the coffee harvest by
vibrations, in which the energy is transmitted to the fruit-stem system,
resulting in the detachment [11], [12].
When the frequency of the vibration
employed is the same as the natural frequency of the fruit. The amplitude
amplification due to the phenomenon of resonance observed in the rachis
reinforces the potential of using the principle of mechanical vibrations for
the detachment of the fruit of the macaw palm bunches. In addition, it is
important to note that this process has been used for the mechanized harvesting
of several agricultural products, such as coffee [8], olive [9], pistachio [33], orange [28] and sweet cherry [31].
Conclusion
Under the
conditions in which this work was conducted it can be concluded the length of
the macaw palm rachis tended to decrease from immature to mature stage of
maturation. The mass and volume of the macaw palm rachis tends to decrease
along the length of the rachis. The specific mass of the macaw palm rachis
tends to decrease from the lower third to the upper third. With the evolution of
the stage of maturation from immature to mature, the first natural frequency, associated to the
first flexural mode shape studied, changes in magnitude from 22.66 to 15.90Hz, which can be
important during the mechanized harvesting by mechanical vibrations. Both models developed can represented properly the dynamic
behavior of the macaw palm rachis and can be used for the study of
the rachis in different scenarios.
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