ORIGINAL ARTICLE

Design of an Industrial Rotary Cylinder Grain Dryer

Dr.C. Yanoy Morejón Mesa^{1  *}  , Ing. Daniel Silva Junco¹  , Ing. Yarian Reyes Suárez¹ 

¹Universidad Agraria de La Habana, Facultad de Ciencias Técnicas, San José de Las Lajas, Mayabeque, Cuba.

ABSTRACT

The present investigation was oriented to establish the foundations for the design of an industrial grain dryer. For the fulfillment of the proposed objective, the theoretical-methodological bases referring to the subject were established and the pertinent computer tools were used for this purpose. Among the main results obtained, it was evident that the theoretical-methodological foundations proposed made it possible to establish the design parameters for an industrial grain dryer. On the other hand, with the use of SolidWorks, MATHCAD 2000 Professional and Termotransf computer tools, the thermal and kinetic modeling of the conceived design were carried out, as well as the determination of the main design parameters and the selection of component parts. It was also obtained that the total heat to be generated inside the proposed drying installation amounts to 28.75 kW with an efficiency of 89.2%, which demonstrates its functionality. From the economic point of view, the proposed design reaches an amount of 10 450.25 total currencies (5 861.40 CUC and 4 588.86 CUP), which represents only 34.8% of the minimum price of similar facilities in the international market.

Key words: mechanical design; grain drying; heat transfer

INTRODUCTION

Currently, the drying of agricultural products not only constitutes a way for self-sufficiency, but also offers a productive and commercial alternative for the national and international market. The current trend, given by the new lifestyles and eating habits, influences the increase in the consumption rates of healthy and natural products that meet the terms of the established quality standards (^{Soliva-Fortuny, 2002}).

The drying process is carried out with the aim of inhibiting the germination of the seeds and reducing their moisture content in order to prevent the growth of fungi and their deterioration. Several authors define this process as "the universal method of conditioning the grains through the elimination of water to a level that allows its balance with the ambient air, in such a way that it preserves its appearance and its nutritional characteristics, based fundamentally on its nutritional quality and viability of the seed" (^{Boffa et al., 2012}).

There are two methods used to perform the drying of grains, which are natural and artificial, the most widely used today is artificial since grain production in the world has increased steadily.

The quality of artificial drying and its performance are evaluated based on the proportion of the grain that remains whole or three-fourths of its size after being processed. When the drying process is carried out, the most feasible is to use methods that give a good IP pile index (high mass of whole grains). These indices are determined by environmental and management factors, such as harvesting, threshing, storage, and especially drying (^{Cubillos y Barrero, 2010}).

An industrial artificial drying system requires relatively high investment costs. According to the online agriculture show ^{AGRIESPO (2019)}, the price of this type of installation ranges between 2,000 and 200,000 USD depending on the model, capacity, types and quantity of burners installed and the manufacturer. The acquisition of such a system also requires the operator's technical training, so that the benefits of this technology can be fully exploited (^{Antoninho et al., 1991}).

For underdeveloped countries where the majority of the population depends on agriculture for their livelihood, it is difficult to acquire conventional drying systems, since considerable investments are required, due to their high costs of installation, operation and maintenance. For these reasons, it is of utmost importance to encourage the use of drying machines and installations that are easy to build and that make it possible to achieve the lowest investment and operating costs.

In studies carried out in Cuba, it has been found that the grain that arrives in the dryers does not always have the optimal cultivation and humidity parameters required. In addition, there are operational deficiencies in the drying, which cause a high percentage of broken grains, and consequently the diminishing of their industrial quality.

Among the main causes that provoke these losses is the impossibility of achieving the adequate percentage of humidity for storage, since the producers dry their productions in the field or on roads with little traffic, being the product exposed to the elements, susceptible to attack by insects, birds and rodents, and to the contamination by microorganisms.

Due to the importance of the drying operation in the technological efficiency and quality of the grains, the objective of this research was to design an industrial rotary cylinder type grain dryer.

MATERIALS AND METHODS

Bases for the Design of a Grain Drying Installation

For the design of a grain drying installation according to ^{Lisboa et al. (2007)} and ^{Castaño et al. (2009)}, it is necessary to know the parameters involved in the drying process and the factors related to it, which allow carrying the process out. The importance of each of them depends on the product to be dried.

• Parameters involved in the drying process:

  • Heat transfer

  • Psicrometric process

  • Drying atmosphere

  • External conditions

  • Type of grain

  • Air temperature

  • Air speed

  • Moisture content of the grain

  • Amount of grain to dry

In reference to the type of grain to be dried, it is very important to know:

• Moisture content present in the grain to be dried.

• Maximum drying temperature that the product can withstand without losing its properties.

• Specific volume, density and porosity of the grain.

• Percent of extraction of grain moisture per hour without losing its physical, chemical, nutritional and quality properties.

Air Velocity

The main functions of the air speed inside the dryer are to transmit the energy required to heat the water contained in the grain, facilitating its evaporation and transporting the moisture evaporated by the material. The air speed for the correct drying of the grains in the rotary dryers must be between 0,25 to 2,5 m/s.

Moisture Content of the Grain

During the drying process it is necessary to know and define some terms that allow expressing the amount of water contained in the grain to be dried, as well as the amount of water that must be removed. The following expression is used to calculate them:

$X_h= \frac{m_a}{{m_{a+ }m}_s} ;\frac{kg of water}{kg solid}$ (1)

where:

Xh	- moisture content on wet basis
ma	- mass of water contained in the solid, kg
ms	- totally dry solid mass, kg

$Xs= \frac{m_a}{m_s};\frac{kg de agua}{kg sólido seco}$ (2)

where:

Xs	- moisture content on a dry basis.

Theoretical-Methodological Bases for the Dimensioning of Rotary Cylinder Type Drying Facilities

The sizing of a drying installation is based on the production parameter and the product to be dried (^{Lisboa et al., 2007}; ^{Castaño et al., 2009}).

Diameter of the Rotating Cylinder

In rotary cylinder type grain dryers, the diameter must be between 0,3 and 3m, depending on the volume of product to be processed.

Rotary Cylinder Length

For the calculation of the total length of the rotary dryer, it should only be taken into account that the diameter is 10 to 25% of its length.

Retention Time

The retention time of the grain in the dryer must be equal to the required drying time if the grain is to come out with the desired moisture content, depending on the drying temperature and the percentage of moisture extraction.

Grain Discharge Time

The discharge time will be equal to the grain retention time in continuous flow rotary dryers. The retention time (t_ret) is calculated with the following equation, based on the volume occupied by the grain at all times, which depends on the filling fraction f used in%.

${\mathrm{t}}_{ret}=\frac{60* \pi \mathrm{*}\mathrm{ }{D}^{2 }*L*f* {\rho }_p}{4*mp},\mathrm{ }\mathrm{m}\mathrm{i}\mathrm{n}$ (3)

where:

mp	- grain mass flow, kg/h
D	- cylinder diameter, m
L	- cylinder length, m
ρp	- grain density, kg/m^3

Slope of Cylinder Inclination

The slope of inclination (s) is obtained from the clearance of the Saeman and Mitchell Equation, to determine the discharge time.

${\mathrm{t}}_{ret}=\frac{L}{a*\omega *D (s+b*Va)},\mathrm{ }\mathrm{h}$ (4)

where:

s	- cylinder slope
a and b	- 2,5 and 1,52 .10^3 are constant, respectively
ω	- cylinder rotation frequency, rad/s or s^-1
Va	- air speed, m/s

According to Saeman and Mitchell, the value of a can vary between 2,0 and 3,14 (π). With elevators designed to get the best waterfalls, the value of a approaches 3,0, but 2,5 is likely to be a more realistic value. The value of b applicable to thick materials is 9,1 . 10^-4. For fine materials Saeman and Mitchell give a value of 1,52 .10^-3.

Hopper Dimensions

The hopper is the element that stores and distributes the grain to the drying chamber. Its volume depends on the amount of grain to be processed which is determined by the following equation.

$V= \left[\frac{h}{3} \left(a^2+ b^2+ \sqrt{a*b}\right) \right]+ a^2*c,m^3$ (5)

where:

V	- hopper volume, m^3
h	- height of the truncated pyramid, m
a	- side of the upper prism, m
b	- lower side of the lower prism hopper, m
c	- height of the upper prism, m

Methodologically, the SolidWorks 2017 program is used for the design of the drying installation, which allows 3D modeling to be carried out, as well as the part drawings of each component part of the installation.

Theoretical Bases for Calculating the Power Required to Move the Rotary Cylinder of the Drying Installation

The element of the reduction system that generates the power necessary to move the rotary cylinder is the electric motor. The other elements of the speed reduction system such as the gear box, belt, sprockets and chain are responsible for transmitting this power to the drive shaft that drives the rotary cylinder. To calculate this power, the power law shown below is used:

$P_M= P_O{\left(\frac{M_R}{M_O}\right)}^{1/3},\mathrm{ }\mathrm{h}\mathrm{p}$ (6)

where:

PM	- nominal power of the electric motor of the speed reduction system, hp
MR	- Total mass to rotate, kg
Starting functions	- PO = 0.5 hp, MO = 10 kg

Theoretical-Methodological Bases for Calculating the Resistance of the Drying Installation

Resistance calculations were based on the determination of displacement, unitary stresses and the resulting stresses by applying the third resistance hypothesis (Von Mises) ) ^{Miroliúbov (1979)}; ^{Feodosiev (1980)}; ^{Stiopin (1985)}. SolidWorks 2017 software was used for determining, the resistance of the cylinder, vanes, bearing shafts, the hopper to a weight force and that of the complete structure of the installation.

Theoretical-Methodological Bases for Calculating Transmission in the Drying Installation

The TE-Cilíndrico computer program was used to calculate the transmission, which allows calculations to be developed for the design of cylindrical gear transmissions in the MATHCAD 2000 Professional environment (^{Valdés y Laffita, 2012}).

This computer program aims to determine the minimum dimensions, for which the danger of deterioration of the sprockets does not appear. The most rational solution to this problem is possible only by mutually relating the calculation of mechanical resistance and the geometry of the gear. In addition, the different kinematic parameters and the forces acting on the shafts or shafts of a cylindrical gear transmission with straight teeth are calculated. Likewise, the criterion used is the calculation of closed transmissions with a hardness of HB < 350. The fundamental calculation was the fatigue resistance of the working surfaces of the teeth and, as a check, the resistance to flexion fracture of the teeth for normal (uncorrected) wheels with an evolving profile and made of carbon steel (0,55%), with mechanical resistance of 70-75 kg/mm² hardness of 200-220 HB.

Theoretical Bases for the Calculation of Transmission by Cylindrical Gear with Straight Teeth

Based in the proposed by ^{Dobrovolski (1980)} y ^{Reshetov (1980)} for closed transmissions with HB <350 hardness, taking as initial data the power at the input of the cylindrical gear from the energy source, the gear frequency of rotation and the gear ratio, as well as the type of material, the hardness of the wheel and pinion, the degree of precision, the load regime and the efficiency, it is possible to determine:

• Minimum axial distance between centers (b)

• Checking the assumed speed of the wheels (V2)

• Readjustment of the axial distance value (à).

• Gear module (m).

• Check of the flexural break of the pinion spur [σ]_flex

• Definitive axial distance (a).

• Wheel width (B2).

• Primitive diameters of the pinion (d1) and the wheel (d2).

• Load on the shafts.

Theoretical Foundations for the Determination of Heat Transfer Mechanisms

One of the most important aspects to consider in the manufacture of thermal installations and devices is the selection of materials and of the drying method, considering the economic and energy aspects, for which the study of heat transfer mechanisms is required. ^{Faires y Simmang (1978)}; ^{Zuritz et al. (1990)}; ^{Geankoplis (1998)}; ^{Welti et al. (2005)}. To speed up these calculations, the Termotransf computer program is used.

RESULTS Y DISCUSSION

Results of the Design of the Industrial Grain Drying Facility

The conceived dryer constitutes a batch drying installation, to which the grain is supplied through a storage hopper with a capacity of one ton (1000 kg). Once the drying process has started the grain moves by gravity through the interior of the horizontally positioned rotary cylinder type drying chamber, through which a flow of hot air circulates, which is supplied by a diesel burner. The rotary cylinder is supported by four bearings that are those that allow its rotational movement, which is achieved by means of a motor-reducer, all this coupled on a frame.

Inside the cylinder there are a series of paddles or welded fins that promote the lifting and turning of the grain, allowing better contact between the grain and the hot air stream.

Considering the main grains that are produced in Cuba, Table 1 shows their physical properties, as well as the conditions they must have during the drying process for the grains to retain their quality.

TABLE 1 Properties of grains of paddy rice, corn and black beans 

Grain type	Paddy Rice	Black bean	Corn
Bulk density; kg/m^3	500 - 630	750 - 850	700 - 820
Specific volume; m^3/t	1,6	1,3	1,8
Moisture extraction; %/h	<1	<3	< 5
Maximum drying temperature; °C	40	40	40
Initial Moisture Content, %	20-25	20-25	20-25
Final Moisture Content, %	12-14	12-14	12-14
Retention time, h	8	3,6	2

Source: ^{Casini et al. (2006)}; ^{FAO (2019)}

Design and Dimensioning of the Grain Inlet Hopper

AISI 304 steel with a thickness of 2.5 mm was selected for the design and dimensioning of the grain inlet hopper. From the maximum specific volume of possible grains to be processed in the conceived installation, a hopper volume of 2 m³ was considered, for a hopper capacity of 1 000 kg (1t).

Design and Dimensioning of the Rotating Cylinder

Considering that the grain represents at most only 50% of the volume of the rotary cylinder or drying chamber, so that it can move, through the action of the rotary movement of the cylinder and the blades, the remaining volume allows the volumetric flow of air efficiently traverses the grain mass placed inside the drying chamber. Table 2 shows the results of the dimensioning of the rotary cylinder.

TABLE 2 Rotary cylinder dimensioning 

Diameter, m	Length, m	Thickness, m	Mass, kg	Weight, N	Volume, m^3
1,0	4,5	0,002	595	5831	3,6

As a result of the design, the rotary cylinder resistance calculations were performed, considering the mass of grains that can potentially be processed, and the properties of the material used, which was AISI 304 stainless steel.

FIGURE 1 Values of structural resistance of the rotating cylinder: a) Von Mises stresses, b) displacement and c) unit deformations. 

To determine these values, the mass of grains to be dried (1000 kg) was taken as a reference, considering both the capacity of the hopper and the rotating cylinder.

As observed in Figure 1 (a), the maximum Von Mises stresses are obtained in the bearing guide, reaching a value of 2,5. 106 N / m², which is less than the maximum admissible tension of the material in 1,6. 108 N / m². When observing the displacement (Figure 1 b), it is evident that the maximum value is obtained at the ends of the rotating cylinder reaching a value of 0,016 mm and in the specific case of unit deformation (Figure 1 c), it reached a maximum value of 8,7. 10^-6. As it is evident, the structure of the rotating cylinder resists the loads to which it is subjected.

Design and Dimensioning of the Inner Blades of the Rotating Cylinder

In order to size the blades, it was taken into account that they do not reach the total length of the cylinder to avoid mechanical damage to the grain by contact with the blades and covers of the rotating cylinder. Table 3 shows their dimensioning.

TABLE 3 Blade dimensions 

Length, mm	Width, mm	Thicknes, mm	Angle of repose
4100	150	2	150^0

As part of the design result, the resistance calculations of the blades were performed, considering the total mass of the grain that can potentially be processed, and the properties of the material used, which was AISI 304 stainless steel.

FIGURA 2 Values of structural resistance of the blades: a) Von Mises stresses, b) displacement and c) unit deformations. 

To determine these values, it was taken as a reference that a third of the mass of grains to dry (333,3 kg), is the one that exerts a load on the structure of the blades.

As observed in Figure 2 (a), the maximum Von Mises stresses are obtained at the base of the blades, reaching a value of 7,596.10⁷ N / m², being less than the maximum allowable stress of the material at 1,308.10⁸ N/m². When observing the displacement (Figure 2 b), it is evident that the maximum value is obtained along the tip of the blades, reaching a value of 2,6 mm and in the specific case of unit deformation (Figure 2 c), it reached a maximum value of 2,38. 10^-4. As it is evident, the structure of the blades resists the loads to which they are subjected.

Selection and Dimensioning of Bearings

The selection of the bearings was made on the basis of the useful life of the proposed drying installation, considering a period of 10 years for this. Using the bearing calculation methodology of the SolidWorks 2017 program and the SKF catalog, the required bearing calculations were carried out, for a duration of 10 years. Considering the maximum load acting on the bearing (4 542,09 N), which constitutes a quarter of the weight exerted by the cylinder mass plus the mass of the grains to be processed. The results obtained are shown in Table 4.

TABLE 4 Bearings characteristics and sizing 

Type of bearing	Ball stiff 6403
Reliability, %	99
Caliber, mm	35
Diameter, mm	100
Number of balls	8
Diameter of balls, mm	19,5
Capacity, N	61 784, 861

As it was evidenced, when comparing the actual load acting on the bearing and its capacity, this is 13,60 times higher than the actual load, an aspect that reveals that the dimensioning and type of bearing selected meets the technical requirements for which it is proposed.

Bearing Shaft Resistance Calculation

The bearing shafts are one of the parts most susceptible to mechanical damage, given that the entire weight of the installation and the grains to be processed affect them. The determination of the diameter of the shafts was carried out according to the measurements of the selected bearing, so its diameter will be 35 mm. The steel selected for the design was 45 steel, since it will be subjected to radial loads and is the most suitable material for shafts due to its properties and high machinability.

Axis resistance calculations were performed as part of the design result, for which the corresponding expressions were used, which consider the Von Mises criterion.

FIGURE 3 Values of structural resistance of the axes: a) Von Mises stresses, b) displacement and c) unit deformations. 

To determine these values, the weight that each axle will support was taken as a reference; where the mass of grains to dry (1000 kg) would be involved, plus that of the rotary cylinder with its components (595 kg). Therefore, the weight that each axis must bear is 4 542,09 N. As observed in Figure 3 (a), the maximum stress of Von Mises reach a value of 6,74.10⁵ N / m², which is less than the maximum tension admissible of the material at 5,79.10⁸ N/m². When observing the displacement (Figure 3 b), it is evident that the maximum value reaches a value of 5,4.10^-5 mm and in the specific case of the unit deformation (Figure 3 c), it reached a maximum value of 2,78.10^-6. As it is evident, the structure of the shafts resists the loads to which they will be subjected.

Determination of the Necessary Power of the Gear Motor to Move the Rotary Cylinder and the Grain Mass

To calculate the power required to move the rotary cylinder, the mass of the rotary cylinder and the mass of the grain (which are 595 kg and 1000 kg, respectively), were considered. Obtaining as a result a minimum necessary power of 2,71 hp.

Using the Catalog ^{UNE-EN-ISO 9001: 2000 (2003)}, the motor-reducer selection was made. As the power in the catalog is 0,25 hp to 25 hp, a gear motor with a power of 3 hp (2,23 kW) was selected.

It was selected a gear reduction motor (MRC230), with an output rotation frequency of 90 rpm, a gear ratio of i=16, an output torque of 225 Nm, and a mass of 44 kg. Therefore, when using the methodology described in Resolution No. 28-2011, regarding the Electric Rate System for the Non-Residential Sector, considering only the time of day, as well as the operating time of the motor-reducer for each grain to be processed, there would be an expense for electricity for rice, corn and beans of 0,18 peso/ h; 0,047 peso / h and 0,085 peso/ h, respectively.

Calculation and Design of Spur Gear Transmission

The calculation of the main parameters was made taking into account the characteristics of the selected motor and taking into account that the driven wheel must rotate at low revolutions between 5 and 10 rpm, choosing the average value of 7,5 rpm, a value that allows establishing a relationship transmission i=12, from which the values of the fundamental geometric parameters for the design were obtained (Table 5).

The material used in the transmission was 45 steel, which has a flexural strength of 532 MPa, proving to be the most suitable for the selected transmission. The difference between the admissible and real stresses was 269,069 MPa, so the design of the transmission will resist the forces to which it is subjected.

TABLE 5 Results of the fundamental geometric and dynamic parameters 

Calculated parameters	Value
Cylindrical gear angular speed (ωp), rad/s	9,5
Wheel angular speed (ωr),rad/s	0,78
Axial distance (a), mm	550,65
Wheel width (B2), mm	130
Width of cylindrical gear (B1), mm	135
Wheel primitive diameters (d2), mm	1 200
Cylindrical gear primitive diameters (d1), mm	100
Torque moment to transmit by the cylindrical gear (Mt1), Nm	233,4
Peripheral force acting on shafts, N	4 669
Radial force acting on the shafts,N	10 440
Allowable normal stress at break by bending, MPa	272,821
Real normal stress at break by flexion, MPa	3,752

Determination of the Necessary Heat and Efficiency to Dry the Grain inside the Drying Chamber

The heat flow required to dry the grain and the drying efficiency. For this, it was necessary to determine different parameters, such as the temperature of the wet bulb, for which the ambient temperature was considered, the air temperature at the outlet, for a number of transfer units of 1.5 and an inlet temperature of 40 ^oC.

The air mass flow reached a value of 1,92 kg/s, for a speed of 1,5 m/s, an air density of 1 kg/m³ and a cross-sectional area of 0,78 m², another important data consider is the caloric capacity of air, which has a value of 1,005 kJ / kg^oK. (Table 6).

TABLE 6 Results of the necessary heat and the efficiency of the drying installation 

Calculated parameters	Value
Outlet air temperature, ^oC	25,1
Wet bulb temperature, ^oC	23,3
Temperature transferred by the cylinder without considering thermal insulation, ^oC	36,85
Mass air flow, kg/s	1,92
Required heat, kW	28,75
Efficiency, %	89,2

Taking into account the heat flow necessary to dry the grain, using the catalog Rigor Tecnológico y Respeto Ecológico, a diesel burner G Series SO 2001/2003 * - GOH 2001 is selected, which has a fuel cost of 2,91 L / h.

Knowing the hourly fuel cost and the time required (Table 1) for drying the grains: rice, beans and corn in the conceived installation, it is obtained that the specific fuel consumption for each grain amounts to 23,2 L/t, 10,44 L/t and 6,38 L/t.

Economic Evaluation of the Design Obtained in the Research

The proposed design, shown in Figure 4, reaches an amount of 10 450,25 Total Currency (5 861,40 CUC and 4 588,86 CUP), representing approximately 34,8% of the minimum price of similar facilities on the international market. This aspect demonstrates the economic feasibility of the proposal.

Figure 4 Isometric of the conceived drying installation. 

CONCLUSIONS

• The proposed theoretical-methodological foundations made it possible to establish the design parameters for a rotary cylinder-type industrial grain dryer.

• Using SolidWorks, MATHCAD 2000 Professional and Termotransf, the thermal and kinetic modeling of the conceived design were carried out, as well as the determination of the main design parameters and selection of component parts.

• The total heat to be generated inside the proposed drying installation amounts to 28,75 kW with an efficiency of 89,2%, which demonstrates its functionality.

• The proposed design reaches an amount of 10 450,25 Total Currency (5 861,40 CUC and 4 588,86 CUP), representing 34,8% of the minimum price for similar facilities in the international market.

REFERENCES

AGRIESPO: Catálogos AGRIESPO, [en línea], AGRIESPO, 2019, Disponible en:http://www.agriexpo.online/esconsultado.

ANTONINHO, V.M.D.; MARQUES, J.A.; SINICIO, R.: Secado de Granos: Natural, Solar y a Bajas Temperaturas, Oficina Regional de la FAO para América Latina y el Caribe, Santiago de Chile, Chile, 1991.

BOFFA, G.; DEUTSCHMAN, A.M.; CASIELLO, F.A.; GALARETTO, O.: “Secado industrial de granos de origen agrícola: estado del arte, herramientas de cálculo en la determinación de parámetros psicrométricos del aire de secado y aplicación de redes neuronales al control de procesos de secado”, Energía, 10(10), 2012, Disponible en:http://bibliotecadigital.uca.edu.ar/repositorio/rev.pdf.

CASINI, C.; RODRÍGUEZ, J.C.; BARTISIK, R.: Secado de granos, Proyecto eficiencia de cosecha y poscosecha, Actualización técnica PRECOP mas granos con más calidad N0 16, Instituto Nacional de Tecnología Agropecuaria (INTA), Córdova, España, 2006.

CASTAÑO, F.; RUBIO, F.R.; ORTEGA, M.G.: “Modelado de Secaderos Rotatorios en Isocorriente”, Revista Iberoamericana de Automática e Informática Industrial (RIAI), 6(4): 32-33, 2009, ISSN: 1696-7912.

CUBILLOS, A.; BARRERO, O.: “Diseño e implementación de una estrategia de control predictivo para el secado de arroz paddy”, Revista Facultad de Ingeniería Universidad de Antioquia, 56: 78-86, 2010, ISSN: 0120-6230.

DOBROVOLSKI, V.: Engranajes generales y cilíndricos dientes rectos, Editorial MIR, Moscú, Rusia, URSS, 246-301 p., 1980.

FAIRES, V.M.; SIMMANG, C.M.: Thermodynamics, Ed. Editorial MacMillan, USA, 578-600 p., 1978, ISBN: 0-02-335530-1.

FAO: Equivalencia de diversas unidades mundiales, [en línea], FAO, 2019, Disponible en:http://www.fao.org.

FEODOSIEV, V.I.: Resistencia de Materiales, Editorial Mir, Moscú, Rusia, URSS, 1980.

GEANKOPLIS, C.J.: Procesos de transporte y operaciones unitarias., Compañía Editorial Continental, Universidad de Minnesota, Tercera Edición, México D. F., 1998, ISBN: 968-26-1316-7.

LISBOA, M.H.; VITORINO, D.S.; DELAIDA, W.B.; FINZER, J.; BARROZO, M.: “A Study of Particle Motion in Rotary Dryer”, Brazilian Journal of Chemical Engineering, 24(3), 2007, ISSN: 0104-6632.

MIROLIÚBOV, I.: Problemas de Resistencia de Materiales, Editorial Pueblo y Educación, La Habana, Cuba, 1979.

RESHETOV, D.: Diseño y Elementos de máquinas, Editorial MIR, Moscú, Rusia, URSS, 1980.

SOLIVA-FORTUNY: Effect of minimum processing on the texture properties of fresh-cut pears, no. 82, SCI Food Agric. 82, 1688-1862 p., 2002.

STIOPIN, P.A.: Resistencia de Materiales, Editorial Mir, Moscú, Rusia, URSS, 1985.

UNE-EN-ISO 9001: 2000: Catálogo General, Comercialización y reparación de equipos de transmisión de potencia, Actor Gerima S.A, Barcelona, España, 2003.

VALDÉS, H.P.A.; LAFFITA, A.: TE-Cilíndrico software para el diseño de las transmisiones por engranaje cilíndrico en ambiente MATHCAD 2000 Profesional, Universidad Agraria de La Habana, Facultad de Ciencias Técnicas, Departamento de Ingeniería, San José de Las Lajas, Mayabeque, Cuba, 2012.

WELTI, C.J.; VELGARA, B.F.; BERMÚDEZ, A.D.: “Transport Phenomena in Food Engineering: Basic Concepts and Advances.”, Journal of Food Engineering, 67: 113-128, 2005, ISSN: 0260-8774.

ZURITZ, C.A.; MCCOY, S.; S K: “Convection heat transfer coefficients for irregular particles immersed in non-Newtonian fluids during tube flow”, Journal of Food Engineering, 11: 159-174, 1990, ISSN: 0260-8774.

5The mention of trademarks of specific equipment, instruments or materials is for identification purposes, there being no promotional commitment in relation to them, neither by the authors nor by the publisher.

Received: December 16, 2019; Accepted: June 14, 2020

^*Author for correspondence: Yanoy Morejón Mesa, e-mail: [e-mail]

Yanoy Morejón Mesa, Profesor Titular, Universidad Agraria de la Habana, Facultad de Ciencias Técnicas, San José de las Lajas, Mayabeque, Cuba, e-mail: [e-mail]

Daniel Silva Junco, Ingeniero egresado de la Universidad Agraria de la Habana, Facultad de Ciencias Técnicas, San José de las Lajas, Mayabeque, Cuba, e-mail: [e-mail]

Yarian Reyes Suárez, Ingeniero y especialista, Universidad Agraria de la Habana, Facultad de Ciencias Técnicas, Centro de Mecanización Agropecuaria, Cuba, San José de las Lajas, Mayabeque, Cuba, e-mail: [e-mail]

The authors of this work declare no conflict of interests.