Design, Construction and Finite Element Analysis of a Hexacopter for Precision Agriculture Applications

Abstract

Agriculture drones face important challenges regarding autonomy and construction, as flying time below the 9-minute mark is the norm, and their manufacture requires several tests and research before reaching proper flight dynamics. Therefore, correct design, analysis, and manufacture of the structure are imperative to address the aforementioned problems and ensure a robust build that withstands the tough environments of this application. In this work, the analysis and implementation of a Nylamid motor bracket, aluminum sandwich-type skeleton, and carbon fiber tube arm in a 30 kg agriculture drone is presented. The mechanical response of these components is evaluated using the finite element method in ANSYS Workbench, and the material behavior assumptions are assessed using a universal testing machine before their implementations. The general description of these models and the numerical results are presented. This early prediction of the behavior of the structure allows for mass optimization and cost reductions. The fast dynamics of drone applications set important restrictions in ductile materials such as this, requiring extensive structural analysis before manufacture. Experimental and numerical results showed a maximum variation of 8.7% for the carbon fiber composite and 13% for the Nylamid material. The mechanical properties of polyamide nylon allowed for a 51% mass reduction compared to a 6061 aluminum alloy structure optimized for the same load case in the motor brackets design. The low mechanical complexity of sandwich-type skeletons translated into fast implementation. Finally, the overall performance of the agriculture drone is evaluated through the data gathered during the flight test, showing the adequate design process.

1. Introduction

Unmanned aerial vehicles (UAVs) or drones are a type of aerial robots capable of flying autonomously or remotely, transporting cargo, or performing inspection activities on crops or affected areas that humans cannot reach easily [1].

In agriculture, it has been necessary to develop technological solutions that respond to the growing economic challenge of satisfying society’s high demand for food, an increasingly contaminated environment, and climate change. A fundamental tool to face these challenges is precision agriculture, which allows for an improvement of efficiency in the use of resources, productivity, quality, and sustainability of agricultural production by using strategies on information management, processing, and analysis of temporal crop data. The data obtained reveal zones of interest which can be locally addressed, optimizing crop management practices [2]. UAVs are an alternative that has been used for several decades, presenting indisputable improvements in agricultural processes: speed, precision, and safety. Modern farmers already use high-tech solutions, such as automatically controlled agricultural plants or unmanned aerial vehicles to monitor crops and forecast the state of the field [3,4,5].

Mapping, imaging crop fields, and applying pesticides are the most popular activities with drones in this sector, with immediate positive implications on crop diseases, growth assessment, pest damage, and insect monitoring. However, the costs of precision agriculture UAVs are usually high, making their implementation difficult for small- and medium-sized owners [6,7]. However, there are restrictions to its adoption due to its initial cost, training, and software required, and increasingly restrictive regulations for its use [8]. Based on low operating and energy costs, the trend should make drones increasingly smaller, lighter, more efficient, and cheaper [9]. The data collected by drones is translated into useful and easy-to-understand information for farmers, thanks to specific algorithms [10]. Advances in guidance systems, batteries, construction, and control systems have made these drones efficient and practical, generating an alternative answer for precision agriculture [11]. Integrating drones into the agricultural industry has led to transformative advances in all growth phases and increased crop production with better quality [12].

The autonomy of drones is a topic of great interest, both in academia and industry, where the average flight time in agriculture is below 13 min for multi-rotors. Operators and users are forced to adapt this limitation to their needs, impeding the exploitation of this technology entirely.

Flying time is highly dependent on variables such as the propulsion stage (which includes the Electronic Speed Controller (ESC), motors, propellers, and aerodynamics), the technology and capacity of the battery, and the take-off weight of the vehicle. Here, more research is needed to optimize the mechanical structure, the aerodynamics of the propulsion system, and the correct selection of elements with mathematical and engineering techniques [13]. Comparisons have been made on the performance of aerial and terrestrial methods with different spray volumes, analyzing which results were satisfactory from the use of aerial vehicles [14]. Designs and a detailed analysis of the aerodynamic and structural configuration have been proposed in which aerodynamic forces and moments have been calculated using the Vortex Lattice method (VLM). Two-dimensional models of aerodynamic profiles (NACA0012 and NACA2412) have been analyzed to determine the aerodynamic characteristics. This study provided an optimal blade design strategy for horizontal-axis wind turbines operating with different Reynolds numbers. [15,16]. There are very few related works on data on the performance of speed controllers. However, electronic speed controllers are an important component in the efficiency and performance of electric propulsion systems in unmanned aerial vehicles (UAVs) [17,18].

It is common to find complex structures in drone design, such as irregular figures, holes, and roundings. Structures are complicated to analyze analytically. Specialized numerical simulation software is usually an essential complement for analyzing these types of elements [19]. Its task is to approximate the simulation results to the real response of the system under different physical conditions. Making it possible to optimize the material, reducing take-off weight, and thus improving autonomy even before the assembly process [20]. The optimization and topology design frameworks for structures that include self-weight loading aim to eliminate numerical instabilities due to weight loading and, at the same time, improve the performance and efficiency of aerial vehicles [21]. There are different methods and practical analyses for the development and validation of the design, construction, and flight of unmanned aerial vehicles. The most used are finite element models, which are approximate finite elements required to know the errors in comparison with experimental data [22,23].

In structural simulation, the predominant numerical method to solve this type of problem is the finite element method (FEM). The process used in the FEM is to divide the system into subsystems, that is, ending with small elements called finite elements. The equations resulting from the analysis of each finite element are assembled into a larger system of equations that represent the complete system [24,25,26]. On the other hand, computational fluid dynamics (CFD) is the analysis of fluid systems, heat transfer, and associated phenomena through computational simulation [27]. The tool used to study the aerodynamics and efficiency of the fluid–body interaction of a structure, in terms of aerial vehicles, provides information on the efficiency of the propellers and the aerodynamics of the fuselage, among others. The most widely used numerical method in computational fluid dynamics is finite volume analysis, where the system is divided into small volumes, called finite volumes [28,29,30].

There are few works in the literature that address the design of drones from the structural and/or aerodynamic part. Diaz and Yoon [31] developed high-fidelity fluid simulations to analyze three drones, finding the effect of the fuselage, propulsion stage, and various elements on aerodynamic efficiency. On the other hand, Yao Lei et al. [32] studied the aerodynamic performance of the vehicle by varying the distance between the tips of the propellers in an octocopter using computer fluid analysis. The results show the relationship between the distance between the propellers and the diameter of the propeller ($L/D$) at 1.8 as the optimal point when positioning the propellers. Another work that highlights the use of simulation in engineering as a complement to the optimization and design process is the one by He Zhu et al. [33]. Here, a new and more efficient arm configuration for the octocopter is proposed. They achieved 41.5% thrust compared to a coaxial configuration with the same size propellers. Regarding structural analysis, Muralidharan et al. [34] and Shelare et al. [35] make use of additive manufacturing and engineering simulation to develop the skeleton of the vehicle, optimizing material and resources, highlighting the high-value of 3D printing in fast and low-cost prototyping, while Rituraj et al. [36] make use of the finite element method to evaluate the performance of materials on different drone elements, culminating in an optimized small UAV with both additive manufacturing and traditional materials.

Despite the extensive advancements in the manufacture of small UAVs with modern techniques such as 3D printing, heavy payload agriculture drone structures have been conservative in their design and material implementations. Of particular interest in this research is the evaluation of the implementation of what is yet to become a novel structure in big heavy payload drones, and the use of light, easier-to-manufacture materials in their structural mechanics.

The main contributions of this paper are as follows:

• The analysis and implementation of a polyamide Nylon (Nylamid) motor bracket, aluminum sandwich-type skeleton, and carbon fiber tube arm in a 30 kg agriculture drone, using ANSYS Workbench.
• The validation of the Nylamid and composite by a universal testing machine. The reliability of the models used to compute the structural analysis is demonstrated. The new mechanical implementations are assessed by evaluating the performance of the agriculture UAV on a flying test.

The rest of this paper is organized as follows: Section 2 presents the physical characteristics and the design objectives of the agriculture drone proposed. The methodology of the finite element method, the SOLID187 and SHELL181 theory, is introduced in Section 3. In Section 4, the validation and structural analysis of the motor bracket, carbon fiber tube and skeleton, as well as the modal analysis of the drone’s arm, are presented. The implementation of all the analyzed pieces and the evaluation of the UAV performance is also introduced. Finally, in Section 5, some conclusions and final comments are provided.

2. Aircraft Description

The United Kingdom Civil Aviation Authority classifies light UAVs as those within the interval of 20 kg and 150 kg, where most multi-rotor agriculture drones are to be found. The sandwich-type drone, hereinafter referred to as the test UAV, is a 30 kg light hexacopter for precision agriculture (see Figure 1). The design objectives are focused on the autonomy of the vehicle, an optimized propulsion system, and the simplicity of the skeleton. It was observed in similar commercial agriculture drones, i.e., the line AGRAS from Da Jiang Innovations (DJI), that battery percentage in the overall weight distribution rose to only $17\%$, in contrast with the $33\%$ of the UAV in this work, as shown in Figure 2. A lower battery percentage translates into low autonomy and the need for more batteries.

The propulsion system is the natural next design parameter after selecting the energy source. Figure 3 shows the throttle and current graphs of the motor–propeller combination selected for this agriculture drone for reference values when the drone is hovering. The main components of the propulsion system are given in

Table 1. Propulsion system main elements.

Component	Value
Battery	14 (s)
Propeller	31.2 × 10.9 (in)
ESC	100 (A)
Brushless motor	120 (KV)
Power distribution board	200 (A)

.

Aircraft Mechanical Characteristics

The skeleton is composed of two aluminum plates with 4.7625 mm thickness, bolted to six RJX center plate mount holders that allow for the coupling of the mainframe and carbon fiber (CF) tubes. To assess the mechanical capabilities and due to the low cost of the Nylamid M, a motor support was designed and manufactured for each arm using this material. The CF tube, skeleton, and motor support are further described in Section 4. This motor support is sectioned into two parts to simplify its manufacturing with a 3-axis Computer Numerical Control (CNC) machine. The specifications of the UAV are introduced in

Table 2. Mechanical characteristics of the UAV.

Component	Value
Tip-to-tip distance	2.57 (m)
Skeleton	0.625 × 0.650 (m)
Height	0.35 (m)
CF tube	500 (length) × 1.5 (wall thickness) (mm)
Maximum take-off weight	35 (kg)

.

Once the propulsion system and general mechanical characteristics of the drone are defined, some critical structural components are analyzed numerically using the finite element method. The next section briefly introduces the theory used to compute the numerical results.

3. Finite Element Analysis for the Hexacopter

This section presents the methodology followed to use the finite element method in the mechanical analysis of a hexacopter UAV. In this particular case, three fundamental pieces were analyzed: the carbon fiber tube, the motor bracket, and the skeleton (see Figure 4). In order to validate the mechanical response of the first two components, some experimental tests were performed. After that, the three components were analyzed under the operation conditions.

Based on the geometry, two elements available in ANSYS 2024R2 software were selected for the finite element analysis. On the one hand, to analyze the motor bracket, which is a complex and irregular piece, the element SOLID187 was used. On the other hand, to model the skeleton plate and the carbon fiber tube, which are three-dimensional structures thin in one direction and long in the other two directions, the element SHELL181 was used.

3.1. Element SOLID187

This is a quadratic tetrahedron with four corner nodes and six side nodes (see Figure 5). Each of the four faces is defined by six nodes with three degrees of freedom. These nodes are not restricted to lie in the plane but should not deviate considerably from it, allowing for curved faces [37].

For static elastic problems, this element is governed by the following equations:

• Strain–displacement relations. This expression gives three normal ($\epsilon$) and three shear ($\gamma$) strains as a function of the three unknown displacements ($u,v$ and w).

  $$\epsilon =\left[\begin{array}{c}{\epsilon }_x\\ {\epsilon }_y\\ {\epsilon }_z\\ {\gamma }_{xy}\\ {\gamma }_{yz}\\ {\gamma }_{zx}\end{array}\right]=\left[\begin{array}{c}{\displaystyle \frac{\partial u}{\partial x}}\\ {\displaystyle \frac{\partial v}{\partial y}}\\ {\displaystyle \frac{\partial w}{\partial z}}\\ {\displaystyle \frac{\partial u}{\partial y}}+{\displaystyle \frac{\partial v}{\partial x}}\\ {\displaystyle \frac{\partial v}{\partial z}}+{\displaystyle \frac{\partial w}{\partial y}}\\ {\displaystyle \frac{\partial w}{\partial x}}+{\displaystyle \frac{\partial u}{\partial z}}\end{array}\right]$$

  (1)
• Equations of equilibrium. These relations guarantee that all elasticity stresses (three normal stresses, $\sigma$, and three shear stresses, $\tau$) are in static equilibrium in the presence of the body forces, f.

  $$\begin{array}{cc}\hfill {\displaystyle \frac{\partial {\sigma }_x}{\partial x}}+{\displaystyle \frac{\partial {\tau }_{xy}}{\partial y}}+{\displaystyle \frac{\partial {\tau }_{xz}}{\partial z}}+f_x& =0,\hfill \end{array}$$

  (2)

  $$\begin{array}{cc}\hfill {\displaystyle \frac{\partial {\tau }_{xy}}{\partial x}}+{\displaystyle \frac{\partial {\sigma }_y}{\partial y}}+{\displaystyle \frac{\partial {\tau }_{yz}}{\partial z}}+f_y& =0,\hfill \end{array}$$

  (3)

  $$\begin{array}{cc}\hfill {\displaystyle \frac{\partial {\tau }_{xz}}{\partial x}}+{\displaystyle \frac{\partial {\tau }_{yz}}{\partial y}}+{\displaystyle \frac{\partial {\sigma }_z}{\partial z}}+f_z& =0\hfill \end{array}$$

  (4)
• Stress–strain relations. These are also known as constitutive equations and give the relation between each stress component and the strains. For an isotropic material, with Young’s modulus E and Poisson’s ratio $\nu$, this relation can be written as [38]

  $$\left[\begin{array}{c}{\sigma }_x\\ {\sigma }_y\\ {\sigma }_z\\ {\tau }_{xy}\\ {\tau }_{yz}\\ {\tau }_{zx}\end{array}\right]={\displaystyle \frac{E}{(1+\nu )(1-2\nu )}}\left[\begin{array}{cccccc}1-\nu & \nu & \nu & 0& 0& 0\\ \nu & 1-\nu & \nu & 0& 0& 0\\ \nu & \nu & 1-\nu & 0& 0& 0\\ 0& 0& 0& {\displaystyle \frac{1-2\nu }{2}}& 0& 0\\ 0& 0& 0& 0& {\displaystyle \frac{1-2\nu }{2}}& 0\\ 0& 0& 0& 0& 0& {\displaystyle \frac{1-2\nu }{2}}\end{array}\right]\left[\begin{array}{c}{\epsilon }_x\\ {\epsilon }_y\\ {\epsilon }_z\\ {\gamma }_{xy}\\ {\gamma }_{yz}\\ {\gamma }_{zx}\end{array}\right]$$

  (5)

3.2. Element SHELL181

It is a four-node element with six degrees of freedom at each node: three translational and three rotational (see Figure 6). It can be used for linear, large rotation, and large strain nonlinear applications. The modeling of composite shells is governed by the first-order shear deformation theory, commonly labeled as the Reissner–Mindlin shell theory, with the following displacement field [39]:

$$\left[\begin{array}{c}u\\ v\\ w\end{array}\right]=\sum N_i\left[\begin{array}{c}{u}_i\\ v_i\\ w_i\end{array}\right]+\sum N_i\zeta {\displaystyle \frac{t_i}{2}}\left[{\mu }_i\right]\left[\begin{array}{c}\alpha \\ \beta \end{array}\right]$$

(6)

As for solid elements, the strains can be computed using Equation (1). In this particular case, for orthotropic materials, the constitutive equations are calculated by [38]

$$\left[\begin{array}{c}{\sigma }_1\\ {\sigma }_2\\ {\sigma }_3\\ {\tau }_{12}\\ {\tau }_{23}\\ {\tau }_{31}\end{array}\right]=\left[\begin{array}{cccccc}{C}_{11}& C_{12}& C_{13}& 0& 0& 0\\ C_{12}& C_{22}& C_{23}& 0& 0& 0\\ C_{13}& C_{23}& C_{33}& 0& 0& 0\\ 0& 0& 0& C_{44}& 0& 0\\ 0& 0& 0& 0& C_{55}& 0\\ 0& 0& 0& 0& 0& C_{66}\end{array}\right]\left[\begin{array}{c}{\epsilon }_1\\ {\epsilon }_2\\ {\epsilon }_3\\ {\gamma }_{12}\\ {\gamma }_{23}\\ {\gamma }_{31}\end{array}\right]$$

(7)

where the elasticity constants $C_{ij}$, which are functions of the three elastic moduli ($E_1$, $E_2$, $E_3$), three shear moduli ($G_{12}$, $G_{13}$, $G_{23}$), and three Poisson’s ratios (${\nu }_{12}$, ${\nu }_{13}$, ${\nu }_{23}$), have the following form:

$$C_{ij}=\left[\begin{array}{cccccc}{\displaystyle \frac{1}{E_1}}& -{\displaystyle \frac{{\nu }_{12}}{E_1}}& -{\displaystyle \frac{{\nu }_{13}}{E_1}}& 0& 0& 0\\ -{\displaystyle \frac{{\nu }_{21}}{E_2}}& {\displaystyle \frac{1}{E_2}}& -{\displaystyle \frac{{\nu }_{23}}{E_2}}& 0& 0& 0\\ -{\displaystyle \frac{{\nu }_{31}}{E_3}}& -{\displaystyle \frac{{\nu }_{32}}{E_3}}& {\displaystyle \frac{1}{E_3}}& 0& 0& 0\\ 0& 0& 0& {\displaystyle \frac{1}{G_{23}}}& 0& 0\\ 0& 0& 0& 0& {\displaystyle \frac{1}{G_{13}}}& 0\\ 0& 0& 0& 0& 0& {\displaystyle \frac{1}{G_{12}}}\end{array}\right]$$

(8)

After introducing the models used to numerically represent the structural components of interest, the validation of these models and their structural analysis are described in the next section.

4. Results and Discussion

The finite element results for the pieces analyzed are presented in this section. First, a validation is made for the motor bracket and the carbon fiber tube. After that, these elements and the aluminum skeleton are tested under actual load conditions. Finally, the natural frequencies for some components are reported.

Compression tests were performed on the motor bracket and the carbon fiber tube to validate the assumptions made in the material behavior and element used. The following lines present a description of the elements and materials used, and a comparison between the simulation results and the experimental data.

4.1. Motor Bracket

Motor bracket structures play a relevant role in the mechanics of UAVs, as it is the instance through which the propulsion system imprints force onto the medium. The design objectives for these structures impose restrictions on the directional deformation, the allowable maximum stress, its natural frequencies, and the material to be used. Nylamid is polyamide nylon resistant to friction, wear, and temperature (110 °C). It is a heat and electrical insulator, resistant to abrasion, and presents great machinability. The mechanical properties are obtained from the manufacturer and reported in

Table 3. Material properties for Nylamid.

Property	Nylamid
Density	1.14 (g/cm3)
Young’s Modulus	2354 (MPa)
Poisson’s Ratio	0.277
Tensile Yield Strength	70.6 (MPa)
Compressive Yield Strength	83.35 (MPa)

. These qualities make it a suitable material for the structure. In order to predict the performance of the Nylamid motor bracket (see Figure 7), its lower geometry is imported into ANSYS Workbench, where a series of static analyses are performed.

Once the specific properties of Nylamid were defined in the engineering data in the ANSYS database for materials used in the software, the discretization was conducted. The structure’s complex geometry allowed for tetrahedron elements to form throughout the solid (Figure 8). A total of 56,932 elements were used to ensure the overall good element quality of the mesh.

The mesh independence was tested with a 1% maximum variation convergence criterion.

Table 4. Mesh independence study for motor bracket validation.

Iteration	Normal Stress (MPa)	Change (%)	Nodes	Elements
1	89.25		59,177	38,402
2	97.15	8.1317%	41,010	22,434
3	110.00	11.6818%	179,890	113,776
4	119.31	7.8032%	448,913	301,664
5	119.04	−0.2268%	995,407	693,393

shows the difference between normal stress after each iteration. Also, the number of nodes and elements used is provided.

The boundary conditions to numerically replicate the experimental test on the structure are presented in Figure 9. Four force steps were applied in Region A and remote displacement with free x rotation in Regions B and C.

The normal stresses on the Nylamid motor bracket under a transversal compression load of 1.304 kN are introduced in Figure 10, representing the last step of the simulation. The stress reaches a maximum value of 119.04 MPa close to the flanges.

A qualitative comparison between the deformation under the compression load for the experiment and the numerical simulation is presented in Figure 11, with good agreement. The numerical comparison is presented in Figure 12, where a maximum variation of 13% is obtained in the last step of the simulation. The discrepancy observed between the experimental and numerical simulations accounts for assumptions in the material behavior, modeling abstractions, and stresses exceeding the yield point.

4.2. Carbon Fiber Tube Structural Analysis

The carbon fiber tube geometry is created in the ANSYS Composite PrePost (ACP) environment, shown in Figure 13. ACP is a robust tool dedicated to the modeling and analysis of composites. It is based on the Classical Laminate Theory (CLT) and ply-based modeling technique, which allows for the definition of orthotropic properties, layered elements, and fiber orientations in three levels of modeling: fabrics, stackups, and sublaminates. The composite is made by 15 layers of unidirectional epoxy carbon with a stacking sequence [0/90/0/90/0/90/0/90/0/90/0/90/0/90/0] and properties which are defined in

Table 5. Material properties for epoxy carbon.

Property	Epoxy carbon UD
Density	1.6 (g/cm3)
Young’s Modulus X	135 (GPa)
Young’s Modulus Y	10 (GPa)
Shear Modulus	5 (GPa)
Orthotropic Shear Stress Limit XY	70 (MPa)
Poisson’s Ratio	0.3
Compressive Yield Strength X	1200 (MPa)

. The model has a thickness of 1.5 mm, outer diameter of 30 mm, inner diameter of 27 mm, and length of 500 mm. The element is discretized using the ANSYS workbench mesh tool with 6376 elements. The model is then transferred as shell composite data into Static Structural, where the boundary conditions are imposed: vertical force of 5400 N (Region C) and remote displacements with free x rotation axis (Regions A and B in Figure 14). The objectives for this numerical simulation are normal stress, first-ply failure Tsai–Wu, and maximum stress.

Figure 15 shows the normal stresses in the vertical axis for the tube fabricated with epoxy carbon. According to the analysis, the stresses reach a maximum of $427.11$ MPa and a minimum of $174.11$ MPa. Due to these stress values, composite failure is reached in multiple locations according to the inverse reverse factor obtained (see red zones in Figure 16).

Figure 17 shows a qualitative comparison between the deformation presented in the experiment and the numerical simulation for the carbon fiber tube under compression, where a good agreement is observed.

Table 6. Force required to reach the failure in experimental and numerical simulations for the carbon fiber tube.

Results	Force until Failure
Experimental	5400 (N)
Simulation	4932 (N)
Error	8.7%

presents the numerical results for the validation, where the error between experimental and numerical simulation rose to 8.6%. The discrepancy observed between the force required to reach the failure in experimental and numerical simulations accounts for differences in the mechanical properties and modeling abstractions.

4.3. Static Analysis

The mechanical response of the three main components analyzed in this work is presented in this subsection. The finite element models and boundary conditions applied are listed. Also, stresses and displacements are computed and compared with allowable values.

4.3.1. Motor Bracket under Bending

In order to predict the correct dynamics of the motor bracket in the drone, a bending analysis must be conducted. The maximum take-off weight (MTW) for this agriculture drone is first evaluated at 37 kg. Settling a thrust-to-weight ratio of 1.65 to ensure the proper performance of the UAV in the air, each motor should be capable of providing a $10.175$ kg/force of thrust. The boundary conditions and symmetry region for this numerical simulation are shown in Figure 18.

The mesh independence was tested, and after four iterations, with convergence a criterion of $1\%$ maximum variation, it was reached.

Table 7. Mesh independence study for the motor bracket.

Iteration	Normal Stress (MPa)	Change (%)	Nodes	Elements
1	35.912		14,646	8745
2	38.545	6.83%	16,481	10,009
3	38.730	0.48%	23,118	14,712
4	39.867	2.85%	75,998	53,012
5	40.107	0.60%	147,403	105,369

shows the difference between the normal stress after each iteration. Also, the number of nodes and elements used is provided. The final discretization with a sphere of influence in the highest stress gradient is presented in Figure 19.

The normal stress for this piece, under a bending force, is presented in Figure 20. In order to properly capture high-region gradients with less computational resources, a symmetry region was imposed. The Nylamid structure’s normal stress is below the yield point for the maximum permissible load of 10.17 kg per arm; this load case represents the worst-case scenario of extreme weather conditions and high accelerations. Further analysis showed that a load increase of 10.65% keeps the total deformation below the design objective of 4 mm for the maximum deflection.

Table 8. Nodal displacement for three load cases depending on take-off weight.

MTW	Nodal Displacement
30 (kg)	2.876 (mm)
35 (kg)	3.357 (mm)
37 (kg)	3.548 (mm)

presents the nodal displacement for the Nylamid bracket under three MTWs.

Compared to a 6061 aluminum alloy optimized for this application, it can be seen in

Table 9. Mass comparison between aluminum 6061 and Nylamid motor bracket.

Property	Aluminum	Nylamid
Mass	$116.22$ (g)	60.181 (g)
Thickness	5.8 (mm)	8.0 (mm)

that a polyamide nylon motor bracket reduced mass by 56.039 g for each arm, translating into 336.234 g for the complete setup.

4.3.2. Carbon Fiber Tube under Bending

In practice, the carbon fiber tube is subjected to bending forces by the thrust generated from the propellers. To emulate this condition, Region A is fixed to represent the surface contact with the center plate mount holders, and a force is applied to Region B, which comes from the motor support. These boundary conditions are presented in Figure 21.

The mesh independence test was performed, and after five iterations, the convergence criteria of 1% maximum variation was reached.

Table 10. Mesh independence study for bending analysis of the carbon fiber tube.

Iteration	Normal Stress (MPa)	Change (%)	Nodes	Elements
1	82.275		5338	5200
2	84.843	3.03%	7600	7562
3	85.859	1.18%	11,952	11,904
4	87.171	1.51%	20,646	20,584
5	87.748	0.66%	47,000	46,906
6	88.415	0.75%	73,750	73,632

shows the change in the normal stress and the number of nodes and elements used.

The bending analysis for the carbon fiber tube, presented in Figure 22, shows that for the 37 kg maximum take-off weight of the tested UAV, a thrust-to-weight ratio of 1.65 is perfectly safe. A maximum of 87.75 MPa is obtained with a 100 N or 10.19 kg/force. A maximum vertical allowable deformation of 5 mm on the tube determines a safety factor of 1.85, as a failure on the carbon fiber tube is obtained at forces over 490 N.

4.3.3. Aluminum Skeleton

Sandwich-type skeletons, as presented in Figure 23, are a predominant mainframe in small UAVs (weight ≤ 20 kg) due to their mechanical and manufacturing simplicity. A search in the literature showed no sandwich-type skeletons for light UAVs; as the vehicle enlarges, this type of mainframe becomes inefficient compared to traditional skeletons (see, for example, the one shown in Figure 24).

The 6061 aluminum is a popular alloy used in aerospace, marine fitting and other high-duty applications for its great tension and corrosion resistance, lightness and medium-fatigue strength. In addition to a relatively good machinability, compared to other metals. These characteristics make it a common material for big-sized UAV skeletons, such as the one in this work. The mechanical properties are listed in

Table 11. Material properties for aluminum.

Property	Aluminum
Density	2.713 (g/cm3)
Young’s Modulus	69,040 (MPa)
Poisson’s Ratio	0.330
Tensile Yield Strength	259.2 (MPa)
Tensile Ultimate Strength	313.1 (MPa)

.

The dimensions of the skeleton on UAVs are dictated mainly by the battery and propeller chosen.

Table 12. Mass and volume comparison between sandwich-type and traditional skeleton for this agriculture drone.

Property	Sandwich-Type	Traditional
Mass	$6016.10$ (g)	1095.19 (g)
Volume	2228.18 (cm3)	405.63 (cm3)

shows a comparison between these two mainframes for the proposed drone, having a fixed propeller diameter and battery size. It is clear that for a sandwich-type mainframe to be convenient, it shall be optimized thoroughly later in the design process.

The model in Figure 23 was analyzed in three different scenarios to account for the unknown mechanical properties of the six metal joints purchased in the structure. These scenarios and their boundary conditions are shown in Figure 25 and described in the following lines:

• Scenario 1 (left) represents the influence of the arm in the aluminum plate, applying a load in Region B, while the structure is fixed in the rest of the arms (Region A).
• Scenario 2 (right) depicts the effect of the battery on the plate (Region B) while fixing all the arms (Region A).
• Scenario 3 (bottom) presents the assumption of a 6061 aluminum alloy as the metal joint’s material, the reaction of the arm on the joint is shown on Region B, the effect of the battery on the plate (Region C) and the fixed supports on Region A, representing the legs of the drone.

The reliability of the structure’s discretization is evaluated with the mesh independence for the first two scenarios of the aluminum plate in

Table 13. Mesh independence study for scenario 1.

Iteration	Normal Stress (MPa)	Change (%)	Nodes	Elements
1	30.503		7238	6908
2	30.651	0.48%	7814	7472
3	30.644	−0.02%	8428	8070

and

Table 14. Mesh independence study for scenario 2.

Iteration	Normal Stress (MPa)	Change (%)	Nodes	Elements
1	39.300		7238	6908
2	39.201	−0.25%	7814	7472
3	39.006	−0.50%	8428	8070

. Only a few iterations were needed to settle the convergence criteria at $1\%$ maximum allowable variation. Figure 26 presents the discretization of the aluminum plate with the hex-dominant method using shell elements.

Von Mises stress for scenario 1 in the aluminum skeleton is shown in Figure 27. The maximum stress is 38.992 MPa. This extreme scenario leaves a 6.15 safety factor for an arm of the drone imprinting a force of 130 N or 13.25 kg.

Figure 28 presents the von Mises stress for Scenario 2. The maximum stress for this case is 30.456 MPa. A safety factor equal to 7.88 for a force of 200 N or 20.38 kg of battery is obtained. This safety factor allows for future payload implementation and structure optimization.

In scenario 3, von Mises stress reached a maximum of 20.051 MPa in the longer flanges and battery’s location (Figure 29). Stress gradient distributions were consistent throughout the three cases. Figure 29 reveals the low-stress concentrations (light and dark blue zones), where mass optimization could be executed.

A maximum variation of 48% throughout the three cases is obtained. In order to account for the simplifications and material assumptions, the maximum von Mises stress is taken as the highest stress between the scenarios, translating to a 38.992 MPa maximum stress.

Additionally, the assumption on the metal joint’s material allows for its analysis under the effect of the carbon fiber tube and thrust load. Figure 30 shows the discretization and boundary conditions of the assembly. A total of 44,487 elements and 69,848 nodes were used. As for the boundary conditions, Region B represents the load on the arm, while Region A represents the 12 bolts on the aluminum plate.

Figure 31 shows the load case for the desired maximum thrust-to-weight ratio. This scenario results in a 3.4 mm displacement on the carbon fiber tube fixed to the metal joint. The displacement for three take-off weights are provided in

Table 15. Maximum joint–CF tube displacement for different take-off weights.

Maximum Take-Off Weight	Displacement
30 (kg)	2.762 (mm)
35 (kg)	3.2224 (mm)
37 (kg)	3.4064 (mm)

.

The application of a 100N load on the arm produced a maximum von Mises stress of 85.492 MPa in the metal joint near discontinuities, and an average of 30 MPa in the cylindrical enclosure of the CF tube (see Figure 32). This material assumption reveals a 2.8 security factor, allowing for its implementation under these assumptions.

Now that the structures have separately complied with the design requirements, the complete arm system is computed. A total of 210,093 elements and 321,962 nodes are used to ensure good element quality. The two scenarios of particular interest include the total nodal displacement of the drone arm with a Nylamid motor bracket, in addition to its comparison with an aluminum alloy motor bracket.

Table 16. Nodal displacement comparison between aluminum 6061 and Nylamid motor bracket implemented in the metal joint-and-CF tube combination.

Arm Nodal Displacement
MTW	Aluminum Motor Bracket	Nylamid Motor Bracket
30 (kg)	3.7469 (mm)	5.1064 (mm)
35 (kg)	4.3729 (mm)	5.9595 (mm)
37 (kg)	4.6211 (mm)	6.977 (mm)

shows the maximum values for a 7 kg MTW range on the arm.

A 6.5 mm maximum allowable displacement on the arm sets the ideal MTW for the nylamid motor bracket on 35 kg (57.65 kg mass maneuverability). The linealization in Figure 33 reveals a maximum variation of 22% on the nodal displacement for both materials for a 94.45 N force.

4.4. Modal Analysis

Modal analysis is a common practice in finite element analysis (FEA), as it not only presents the shapes and frequencies at which a structure will amplify loading effects, but it also helps FEA analysts to identify weaknesses in the model [23]. Rotatory actuators, such as drone motors, naturally induce vibrations in the structures they are attached to.

This sandwich-type hexacopter has an operating RPM range of 2500 and 3800, translating into 41.7 and 63.3 Hz, respectively. Once the working revolution-per-minute interval of the selected brushless motor is completed, the modal analysis is conducted. The first four natural frequencies are computed (

Table 17. First four natural frequencies of the Nylamid motor bracket.

Mode	Frequency in Hz
1	192.93
2	486.82
3	701.21
4	945.38

). Figure 34 shows the first natural frequency for the motor bracket. Results predict a safety factor of 3.0 from the motor’s maximum RPM and the model’s first natural frequency.

Additionally, the modal analysis for the complete arm is performed for the first six modes, and the results for the first frequency are shown in Figure 35. In this case, the first natural frequency is presented at 85.458 Hz, which gives a safety factor of 1.35, and the resonance is not expected.

Table 18. Six first natural frequencies of the arm assembly.

Mode	Frequency in Hz
1	85.46
2	86.35
3	373.54
4	480.08
5	586.27
6	766.22

shows the six natural frequencies obtained.

The corresponding modal analysis for the skeleton shows that the first natural frequency rises to 95.447 Hz, compared to the frequency of a single brushless motor, wherein a 1.5 safety factor is obtained (Figure 36). Stiffness can be increased by inserting aluminum spacer studs between the two aluminum plates. Its first four mode frequencies appear in

Table 19. First four natural frequencies for the aluminum skeleton.

Mode	Frequency in Hz
1	95.447
2	105.66
3	139.83
4	157.79

.

Now that the structural elements proposed are assessed through the static structural and modal analyses, the flight test is conducted in the following section.

4.5. Implementation

The next step in the design process, after examining the design, structural analysis, and validation of the mechanical elements, is to manufacture, assemble, and evaluate the performance of the UAV. This subsection presents the final assembly and data gathered during the first flight.

The structures analyzed in Section 4 were manufactured using a 3-axis light-duty milling machine at 4500 RPM.

Table 20. Machining time comparison: Nylamid motor bracket and aluminum motor bracket.

Time [h]	Material
4.03	Nylamid
13	Aluminum

shows the milling time comparison between a Nylamid and aluminum motor bracket. The polyamide piece takes up 31% of the time that it takes the aluminum one.

Figure 37 presents the implementation of the motor bracket, aluminum skeleton, and carbon fiber tubes on the hexarotor. The elasticity of the Nylamid material dotted the structure with long elastic regions before plastic behavior, making it an enduring element throughout the initial tests. However, this same property considerably restricts the take-off weight. Slightly increasing the payload resulted in an excessive thrust decomposition, an undesirable effect for this application. The aluminum skeleton and carbon fiber tube behaved properly, as suggested by the numerical results. The extensive stress safety factors in the aluminum plates allow for future mass optimization. The first flight test was conducted at 1239 m above sea level; conditions are shown in

Table 21. First flight data.

Parameter	Value
Take-off weight	30 (kg)
GPS mode	Loiter
Altitude	3 (m)
Flight time	1 (min)

.

It can be seen in Figure 38 that the throttle rose to around 70% to elevate the UAV 3 m above the ground in loiter mode. Figure 39 presents the PWM supplied to the six motors during the flight. A maximum variation of 3.2% over all the PWM signals was obtained. As for hover, the maximum PWM signal required along the six actuators is in the 55% range.

Vibration is a critical parameter in drone performance. The presence of sensible sensors, such as an accelerometer and barometer, set acceptable vibrations below the 15 ${\displaystyle \frac{m}{s^2}}$ mark. Acceptable vibration values were determined empirically by analyzing multiple UAV setups. Figure 40 shows the measured vibrations; a maximum value of 9.31 ${\displaystyle \frac{m}{s^2}}$ was obtained, indicating a correct design and assembly of the vehicle.

5. Conclusions

Precision agriculture systems have acquired relevance because of the indisputable solutions they bring to the agriculture challenges of this era: extreme weather conditions, inefficiency in the use of resources, and an escalating demand for products. The advancements in data processing, control techniques, and embedded systems must be complemented by optimized and robust mechanical drone structures to ensure effective missions and reliable systems. This research proposed the use of an aluminum sandwich-type skeleton and polyamide nylon (Nylamid) as an alternative material for motor brackets, in addition to an epoxy carbon fiber tube optimized for this application. Their implementation was analyzed in a 30 kg agriculture drone.

The findings demonstrate that the use of alternative materials, such as Nylamid, can accelerate the manufacturing process of drone parts by up to 69%, in light-duty CNC machines. The new Nylamid motor bracket design reduced weight by 51%, compared to an aluminum bracket optimized for the same application. On the other hand, sandwich-type skeletons were found to be particularly effective in the early development stages of big drones; their mechanical simplicity allows for fast implementation and testing. However, extensive mass optimization must be conducted to compete with traditional light UAV skeletons. Despite the high elasticity of plastics, the finite element method proved to be a powerful tool to correctly size the structures to comply with the design requirements of drone agriculture applications. The results of this work can be used to design lighter, faster-to-implement agriculture drones.

In future work, the Nylamid structure will be subjected to more tests and a bigger load. A 6061 aluminum alloy motor support will be designed, optimized, and manufactured to evaluate the performance of both materials under the dynamics of a UAV. To further optimize the mechanics of this vehicle, the sandwich-type skeleton will be optimized to reduce weight and increase autonomy.