Open AccessArticle

Determining Quasi-Static Load Carrying Capacity of Composite Sandwich Rotor Blades for Copter-Type Drones

Chien Wei Jan

and

Tai Yan Kam

Mechanical Engineering Department, National Yang Ming Chiao Tung University, Hsin Chu 300, China

Author to whom correspondence should be addressed.

Drones 2024, 8(8), 355; https://doi.org/10.3390/drones8080355

Submission received: 16 May 2024 / Revised: 4 July 2024 / Accepted: 26 July 2024 / Published: 30 July 2024

(This article belongs to the Topic Advances in Design, Manufacturing, and Dynamics of Complex Systems)

Download

Browse Figures

Figure 1
Quadcopter drone. "> Figure 2
Rotor blade: (a) Dimensions; (b) NACA 4418 Airfoil showing skin and core. "> Figure 3
Lamination arrangement of composite sandwich blade (a) Type 1 blade, (b) Type 2 blade. "> Figure 3 Cont.
Lamination arrangement of composite sandwich blade (a) Type 1 blade, (b) Type 2 blade. "> Figure 4
Blade element. "> Figure 5
Elemental airfoil aerodynamics. "> Figure 6
Experimental setup for rotor blade thrust measurement. "> Figure 7
Iterative procedure for updating vertical uplifting force. "> Figure 8
Locations of blade elements and resultant thrust. "> Figure 9
Rotational speed vs. rotor blade thrust. "> Figure 10
Finite element mesh for composite sandwich blade. (a) Type 1 blade, (b) Type 2 blade. "> Figure 11
Iterative procedure for updating incipient failure rotational speed. "> Figure 12
Finished rotor blade product. "> Figure 13
Experimental setup. "> Figure 14
Experimental failure pattern of composite blade (a) Type 1 blade, (b) Type 2 blade. "> Figure 15
Failure analysis results for Type 1 blade under resultant thrust. (a) Failure index for Maximum stress criterion (Failure location: x = −0.48, y = 10.99). (b) Failure index for Tsai–Wu criterion (Failure location: x = −0.48, y = 10.59). (c) Buckling mode shape (Failure location: x = −0.323, y = 10.7). "> Figure 15 Cont.
Failure analysis results for Type 1 blade under resultant thrust. (a) Failure index for Maximum stress criterion (Failure location: x = −0.48, y = 10.99). (b) Failure index for Tsai–Wu criterion (Failure location: x = −0.48, y = 10.59). (c) Buckling mode shape (Failure location: x = −0.323, y = 10.7). "> Figure 16
Failure analysis results for Type 2 blade under resultant thrust (a) Failure index for Maximum stress criterion (Failure location: x = 0.12, y = 3.5). (b) Failure index for Tsai–Wu criterion (Failure location: x = 0.12, y = 3.5). (c) Buckling mode shape (Failure location: x = −0.398, y = 4.88). "> Figure 16 Cont.
Failure analysis results for Type 2 blade under resultant thrust (a) Failure index for Maximum stress criterion (Failure location: x = 0.12, y = 3.5). (b) Failure index for Tsai–Wu criterion (Failure location: x = 0.12, y = 3.5). (c) Buckling mode shape (Failure location: x = −0.398, y = 4.88). "> Figure 17
Failure index distribution of composite sandwich blade under elemental thrusts, drag forces, and centrifugal force. (a) Type 1 blade, (b) Type 2 blade. "> Figure 17 Cont.
Failure index distribution of composite sandwich blade under elemental thrusts, drag forces, and centrifugal force. (a) Type 1 blade, (b) Type 2 blade. "> Figure 18
Effects of Region 2 length on blade load carrying capacity and weight. "> Figure 19
Effects of Region 2 on failure rotational speed and specific load carrying capacity. "> Figure 20
Relation between blade rotational speed and displacement. ">

Versions Notes

Abstract

The development of light composite rotor blades with acceptable load carrying capacity is an essential issue to be dealt with in the design of relatively large copter-type drones. In this paper, a method is established to determine the quasi-static blade load carrying capacity which is vital to drone reliability. The proposed method, which provides a systematic procedure to determine blade load carrying capacity, consists of three parts, namely, a procedure to determine the distributed quasi-static blade aerodynamic load via the Blade Element Momentum (BEM) approach, a finite element-based failure analysis method to identify the actual blade failure mode, and an optimization method to determine the actual blade load carrying capacity. The experimental failure characteristics (failure mode, failure thrust, failure location) of two types of composite sandwich rotor blades with different skin lamination arrangements have been used to verify the accuracy of the theoretical results obtained using the proposed load carrying capacity determination method. The skin lamination arrangement for attaining the optimal blade-specific load carrying capacity and the blade incipient rotational speed for safe drone operation has been determined using the proposed method.

Keywords:

drone; rotor blade; aerodynamic load; composite material; failure criterion; finite element analysis; Blade Element Momentum method

1. Introduction

In recent years, copter-type drones consisting of multiple rotor blades have been used to perform different types of tasks [1,2,3,4,5,6,7]. For instance, small drones have been used to detect harmful industrial gases [1] and bridge structural damages [2], and in agriculture to record the ground data of crop fields [3]. With technological advancements, relatively large drones with high payload carrying capabilities have been developed to perform works such as fertilizer/pesticide spraying, transportation service, large parcels delivery, etc. [4]. In a copter-type drone, the geometric and structural properties of each rotor blade (or propeller) driven by an electric motor are directly related to the flight efficiency and payload carrying capability of the drone. It is noted that as the rotational speed increases, the rotor blades can generate higher thrust (vertical uplifting force) to enable the drone to carry more payload. Therefore, the recent widespread use of larger copter-type drones with high payloads prompts the imminent need for developing rotor blades with high load carrying capacity. Like an aircraft wing or wind blade, when the aerodynamic load exceeds the load carrying capacity of a rotor blade, the failure of the rotor blade may lead to the crash of the drone. Therefore, the rotor blade structure must be designed properly and strong enough to ensure flight safety. Recently, many researchers have studied its different aspects, such as aerodynamics [8,9,10,11,12,13], structural analysis/design [14,15,16,17], and fabrication of drone/aircraft propellers [18,19,20,21,22,23,24,25,26,27,28,29]. For instance, Kutty and Rajendran used the Fluent CFD solver to determine the aerodynamic loads for a small and slow flyer propeller blade [11]. Rwigema studied the aerodynamic performance of an aircraft propeller using the Blade Element Momentum theory [13]. Kong and Park used the commercial FEM code MSC NSATRAN to perform the structural design and analysis of the Carbon/Epoxy composite propeller blades under aerodynamic loads for turboprop aircrafts. On the other hand, materials such as wood, plastics, composites, etc. have been chosen to fabricate rotor blades using different manufacturing techniques. Through computer numerical control milling, wooden propellers can be manufactured easily nowadays [18]. Though wood materials have high strength and good fatigue and vibration resistance, they are relatively heavy and susceptible to rain erosion. Plastic rotor blades have been widely used in small commercial drones. The plastic rotor blades are light and can be manufactured efficiently using the 3D printing/injection molding techniques [19,20]. However, the plastic rotor blades are not strong enough to be used in relatively large drones. Therefore, with respect to the goals of achieving efficiency, weight saving, and reliability, it is unsuitable to use wood and plastic materials to fabricate the rotor blades of relatively large drones. Polymeric composite materials, which are made of a conglomerate of fibers and resin matrix, have been used widely for aerospace and military purposes due to their many advantages such as high strength-to-weight ratio, light self-weight, good fatigue and erosion resistance, etc. Therefore, to make drones lighter and more reliable, polymeric composite materials have been used to fabricate drone parts and many researchers have developed methods to analyze drone related structures [25,26,27,28,29]. The finite element method has been widely used to predict the mechanical behavior and integrity of blade-type structures [30,31,32,33,34,35,36,37,38,39]. For instance, Pao et al. [30] studied the failure behavior of helicopter rotor blades using the synergistic damage mechanics and finite element methods to predict the matrix cracking of carbon fiber reinforced composite laminates at different rotational speeds and airfoil angles of attack. Ahmad et al. [31] performed a progressive failure analysis of helicopter rotor blades using the finite element method to identify the structural failure modes and the failure locations in the rotor blades at a high rotational speed. Brischetto and Torre [37] used the commercial finite element code NASTRAN to analyze the mechanical behavior for the arms of a modular drone built using the fused filament fabrication technique. Ahmad et al. [38] used the finite element method to study the vibrational frequencies, stress distribution, and material optimization of a quadcopter’s body frame. In their study, the quadcopter body frame was analyzed for three different materials to find out the best-suited materials, namely, copper, alloy, aluminum, and carbon fiber reinforced polymer for heavy transportation application. It is noted that in performing the finite element analysis of a drone structure, it is essential to establish an appropriate finite element model that can predict the actual mechanical behavior of the structure. Furthermore, regarding the failure analysis of drone rotor blades, it is essential that the adopted finite element model and failure criterion should be able to produce accurate stresses and predict the actual failure load (load carrying capacity) of the blade. However, though important, so far not much work has been devoted to the determination of the actual load carrying capacity of relatively large drone rotor blades. On the other hand, because of their merits such as light weight, high strength and stiffness, etc., composite sandwich materials have been widely used to fabricate weight-sensitive and highly reliable structures in the aerospace industry. Therefore, it is appropriate to use composite sandwich materials to fabricate drone structural parts, especially rotor blades, to enhance drone performance and reduce drone weight. Regarding the failure of a composite rotor blade, different failure modes may be induced by aerodynamic loads depending on the structural configuration of the rotor blade. To attain an accurate prediction of the failure characteristics of a composite rotor blade, an appropriate failure criterion and the finite element model must be used in the failure analysis. In face of the recent blooming of relatively large copter-type drones with multiple rotor blades, as far as reliability and safety are concerned, more work should be devoted to the failure analysis of drone composite sandwich rotor blades. Therefore, the development of efficient and reliable composite sandwich rotor blades, including the determination of the load carrying capacity of the composite sandwich rotor blades, should become an important topic of research.

In this paper, a method is presented to determine the quasi-static load carrying capacity of composite sandwich rotor blades. In the proposed method, with the use of experimental blade thrust data, the aerodynamic loads distributed along the span of the rotor blade at different rotational speeds are approximated via the Blade Element Momentum (BEM) method. A finite element-based failure analysis method is used to study the blade failure characteristics and identify the correct failure mode. The golden section search method is used to determine the quasi-static load carrying capacity of the composite sandwich rotor blades. Experiments were conducted to verify the accuracy of the proposed finite element-based failure analysis method. Finally, the design of light composite sandwich blades is investigated using the proposed method.

2. Composite Sandwich Rotor Blade

The composite sandwich rotor blades for propelling the quadcopter drone shown in Figure 1 are used as an example to illustrate the procedure for load carrying capacity analysis of composite sandwich blades. Herein, each rotor blade consists of two composite sandwich blades with NACA4418 airfoil. The radius of the rotor blade is 40.64 cm. The dimensions and geometric parameters of the composite sandwich blade in Figure 2 are listed in Table 1. The angle of attack has been designed for the rotational speed of 3630 rpm. Two types of blades, namely, Types 1 and 2, were fabricated for studying the blade load carrying capacity and failure characteristics. Each composite sandwich blade consisted of carbon fabric/epoxy skin and a PU foam core. The lamination arrangements of Types 1 and 2 blades are shown in Figure 3. The spans of the blades are divided into two regions, namely, Regions 1 and 2. In Regions 1 and 2, the skin laminates are composed of four and eight carbon fabric/epoxy laminae, respectively. Furthermore, the top four layers in Region 2, same as those in Region 1, extend from the root to the tip of the blade. The length of Region 2 of the Type 1 blade is shorter than that of the Type 2 blade. It is noted that the composite sandwich blade was fabricated using the wrapping technique which allows no openings or free edges to exist in the blade. In the wrapping process, an appropriate wrapping pattern is adopted to wrap the skin laminae around the blade core so that the failure mode of interfacial debonding at the leading and trailing edges of the blade is prevented from occurring.

3. Load Carrying Capacity Determination

In the structural design of a rotor blade, the rotor blade load carrying capacity, which is closely related to the performance and reliability of a drone, must be determined accurately. Furthermore, once the rotor blade load carrying capacity is known, appropriate and affordable electric motors can be chosen to drive the rotor blades in a cost-effective way. Herein, the method for determining the load carrying capacity of a composite sandwich blade consists of three parts, namely, a procedure to determine the distributed quasi-static blade aerodynamic load via the Blade Element Momentum (BEM) approach, a finite element-based failure analysis method to identify the actual blade failure mode, and an optimization method to determine the actual blade load carrying capacity. The three parts of the proposed method are explained in detail as follows.

3.1. Blade Aerodynamic Load Analysis

The distributed aerodynamic load on each blade of a rotor will induce a resultant thrust/vertical uplift force to lift up the drone in the z-direction. The accurate determination of the aerodynamic load distribution on the blade is vital to the reliability design of the blade. The blade quasi-static aerodynamic load distributed along the blade span is approximated via the Blade Element Momentum (BEM) approach [40,41]. According to the BEM method, the span of the blade is divided into several blade elements which may have different geometric characteristics and cross-sectional dimensions as shown in Figure 4. The aerodynamic characteristics of the elemental airfoil at the mid-section of a typical blade element is shown in Figure 5.

When the blade rotates with angular speed ω, the relative wind speed (

V_{T}

) and inflow angle (Ø) expressed in terms of the blade tangential speed (

v_{r}

) and the vertically induced airflow speed (

v_{i}

) at the radial distance of r can be written, respectively, as

V_{T} = \sqrt{{v_{r}}^{2} + {v_{i}}^{2}}

(1)

and

\emptyset = \tan^{- 1} (\frac{v_{i}}{v_{r}}) = \tan^{- 1} (\frac{v_{i}}{ω r})

(2)

It is worth noting that both

v_{r}

and

v_{i}

vary along the blade span. It is also noted that

v_{i}

is not known in advance and will be determined via an iterative process. The inflow angle (Ø) can be related to the angle of attack (α) and twist angle (β) as

\emptyset = β - α

(3)

The angle of attack is a parameter for determining the properties of airfoil lift and drag forces. It is noted that for the NACA4418 airfoil, the aerodynamic moment coefficient is relatively small compared to the lift and drag coefficients. Hence, without loss of generosity, aerodynamic torsion is neglected in the present blade load carrying capacity analysis. The blade elemental lift and drag forces (

d L_{i}

d D_{i}

) at the ith blade element are expressed as

d L_{i} = {\frac{1}{2} C}_{L i} ρ V_{T i}^{2} A_{i}

(4a)

d D_{i} = {\frac{1}{2} C}_{D i} ρ V_{T i}^{2} A_{i}

(4b)

where

C_{L i}

is lift force coefficient,

C_{D i}

drag force coefficient,

V_{T i}

relative wind speed (

m / s

), and

A_{i}

area (

m^{2}

) of the ith element.

The blade elemental lift and drag forces are acting at the elemental aerodynamic center of the blade element middle airfoil section. Herein, without loss of generality, the lift and drag force coefficients (

C_{L i}

C_{D i}

) for the blade element can be obtained from, for instance, “JavaFoil 2.2” software, for angle of attack α = 5° and Reynolds number Re = 500. The resultant thrust T_b of the blade, which is the sum of all the blade elemental thrusts in the z-direction, is expressed as

T_{b} = \sum_{i = 1}^{n} (d L_{i} \cos \emptyset_{i} - d D_{i} \sin \emptyset_{i}) = \sum_{i = 1}^{n} d T_{b i}

(5)

where n is the number of blade elements; dT_bi is the elemental thrust of the ith blade element. It is noted that dT_bi is located at the aerodynamic center of the middle airfoil section of the ith blade element. The radial distance,

r_{g},

of the blade resultant thrust T_b is obtained as

r_{g} = \sum_{i = 1}^{n} (\frac{d T_{b i} r_{i}}{d T_{b i}})

(6)

where

r_{i}

is the radial distance of the ith blade elemental thrust. It is noted that the total thrust is 2T_b for the rotor blade composed of two blades.

The resultant drag force F_b in the x-direction is defined as the in-plane blade drag force, which is obtained as

F_{b} = \sum_{i = 1}^{n} (d L_{i} \sin \emptyset_{i} + d D_{i} \cos \emptyset_{i})

(7)

It is noted that the torque induced by the drag force is an important parameter for choosing an appropriate driving motor. The bending moment at the blade root induced by the blade elemental thrusts is expressed as

M_{e} = \sum_{i = 1}^{n} (d T_{b i} r_{i})

(8)

It is noted that the total blade thrust as well as the distribution of the aerodynamic load along the blade depends on the value of the vertically induced airflow speed (

v_{i}

). Herein, a numerical–experimental technique is established to determine the vertically induced airflow speed as well as the blade elemental aerodynamic loads in compliance with the BEM method. In the proposed numerical–experimental technique, the blade’s resultant thrust is first determined experimentally using the load cell in the test setup shown in Figure 6. It is noted that the rotor blade was in an upside-down position when connected to a driving motor. Therefore, the rotor blade would exert a downward thrust to push the motor when the rotor blade was rotating. On the other hand, the motor, which was supported by an axial thrust-type bearing, could move downwardly to exert a force to the load cell underneath the motor. Once the experimental blade thrust was measured at a specific rotational speed, according to the linear momentum theory, the initial guess of the vertically induced airflow velocity for the blade elements can be attained using the following equation.

v_{i} = \sqrt{\frac{T_{t e s t}}{2 ρ π R^{2}}}

(9)

where

ρ

is air density (kg/

m^{3}

);

T_{t e s t}

is experimental thrust.

In general, the theoretical thrust of the rotor blade determined using the guessed value of the vertically induced airflow velocity as obtained in the above equation is different from the experimental one. An iterative procedure is then used to determine

v_{i}

using the experimental blade thrust data. The flow chart in Figure 7 explains the proposed iterative procedure for determining the “actual” blade thrust using the updated vertically induced airflow velocity and theoretical elemental thrust at each blade element. In the iterative process, the induced velocity at each blade element is updated using the following iterative equation.

v_{i j, (k + 1)} = \frac{T_{t e s t} {- T}_{b (k)}}{{(\frac{Δ T_{b}}{Δ v_{i j}})}_{(k)}} + v_{i j, (k)}

(10)

where T_b_(k) is theoretical thrust at the kth step; Δv_ij = differential increment of v_i at the jth blade element; ΔT_b = T_b (v_i +Δv_i) − T_b(v_i); (ΔT_b/Δv_ij)_(k) = gradient; v_ij_,(k), v_ij_(k+1) = induced velocities at the jth blade element at the kth and (k + 1)th steps, respectively.

Herein, the blade is divided into nine elements as shown in Figure 8 for determining the blade elemental aerodynamic loads as well as the resultant blade thrust following the proposed BEM elemental aerodynamic load determination procedure. The graphical comparison between the theoretical and experimental rotor blade thrusts for different rotational speeds is shown in Figure 9. It is noted that the errors between the predicted and experimental thrusts at different throttles are less than or equal to 0.66%. For instance, when the throttle is equal to 10, the percentage difference between the predicted and experimental thrusts with values of 0.282 and 0.2822 kgf, respectively, is equal to 0.07%. The close agreement between the theoretical and experimental rotor blade thrusts have thus demonstrated the ability of the iterative procedure in producing converged results. Therefore, the present iterative BEM procedure can produce an accurate prediction of the distributed blade elemental aerodynamic loads which can then be used to estimate the actual load carrying capacity and the associated failure characteristics for composite sandwich blades.

Once the load carrying capacity of the rotor blade is known, the incipient failure rotational speed of the rotor blade and payload of the drone can be determined. On the other hand, the BEM elemental thrusts are used to calculate the resultant thrust as well as its location using Equations (6) and (8). It is noted that the location of the resultant thrust will be used in the following static load testing of blades. For instance, referring to the rotational speed vs. rotor blade thrust relation in Figure 8, when the rotational speed is 3630 rpm, the resultant thrust of each blade is about 7.2 kgf and located at r_g = 282.31 mm. Therefore, the load carrying capacity of the quadcopter drone equipped with four rotor blades is 57.6 kgf.

3.2. Finite Element-Based Blade Failure Analysis

The distributed BEM elemental quasi-static aerodynamic loads at a given rotational speed determined in the above section will be used to perform the failure analysis of the blade. In the blade failure analysis, the finite element method is used to determine the stresses in the blade. As an example, the distributed BEM elemental aerodynamic loads at the rotational speed of 3630 rpm are listed in Table 2. It is noted that each elemental aerodynamic load is composed of two components, namely, elemental thrust and drag force. The elemental thrust is acting at the top blade skin in the z-direction along a line passing through the aerodynamic center of the middle section of the BEM element, while the drag force is acting at the blade skin in the x-direction along a line passing through the aerodynamic center of the middle section of the BEM element.

In the blade finite element modeling, the four-node SHELL181 and eight-node SOLID185 elements in the commercial finite element code ANSYS [42] are used to model the blade skin and core, respectively. The BEM elemental thrust and drag forces are treated as nodal forces in the finite element analysis. Besides the thrust and drag force, the centrifugal force will also be generated when the blade rotates. The blade centrifugal force is the sum of all the element centrifugal forces.

P_c = Ʃ P_ci = Ʃ m_iω² y_i

(11)

where P_c is centrifugal force, m_i is element mass, and y_i is the distance of the element center away from the origin at the blade root. It is noted that the element masses of the skin laminate and the PU core are different. Furthermore, besides the moments induced by the blade thrust and drag force, the centrifugal force will also generate moments at the blade root.

M_cx = Ʃ M_cxi = Ʃ P_ci z_i

(12a)

M_cz = Ʃ M_czi = Ʃ P_ci x_i

(12b)

where M_cx, M_cz are moments induced by centrifugal force. The stresses in the blade caused by the blade centrifugal force can be determined using the finite element code of ANSYS. The rule for performing the finite element analysis is first to adopt a coarse mesh for the analysis of the blade to identify the approximate failure location(s) in the blade. Next, the element meshes in the selected possible failure regions are refined to ensure displacement convergence. Finally, the two finite element meshes adopted to model Types 1 and 2 blades, respectively, are shown in Figure 10, and ANSYS Workbench was used to perform the structural analysis. Two failure modes, namely, buckling and first-ply failure, are taken into consideration to determine the failure loads of the blade, respectively. For the buckling failure mode, an eigenvalue problem is solved to determine the linear buckling load and the associated buckling shape for the Type 1 or 2 blade. As for the first-ply failure mode, the blade stresses obtained in the finite element stress analysis are used to predict the first-ply failure load and study the failure characteristics of the blade. It is noted that the role of the foam core is to provide bearing support to the skin. In contrast, the skin laminate is the essential part used to resist the internal bending moment and shear flow in the blade. Hence, in the first-ply failure analysis of the skin laminate, the blade failure load together with the failure location will be determined using one of the following failure criteria [43].

(1): Maximum Stress criterion

Material failure occurs when any stress ratio in the following bracket is equal to or larger than 1.

(|\frac{σ_{x}}{X_{T}}|, |\frac{σ_{y}}{Y_{T}}|, |\frac{τ_{x y}}{S_{x y}}|, |\frac{τ_{y z}}{S_{y z}}|, |\frac{τ_{x z}}{S_{x z}}|) \geq 1

(13)

where

σ_{x}, σ_{y}

are normal stresses in the material x and y directions, respectively;

τ_{x y}, τ_{y z}, τ_{x z}

are shear stresses;

{X = X}_{T} o r X c

{Y = Y}_{T} or Y c

are tensile or compressive strengths in the material x and y directions, respectively;

S_{x y}

S_{y z}

S_{x z}

are material shear strengths.

(2): Tsai–Wu failure criterion

Among the quadratic interaction criteria, the Tsai–Wu criterion is commonly used for the failure analysis of composite materials. According to the Tsai–Wu criterion, material failure occurs when the following equation is satisfied.

F_{i} σ_{i} + F_{i j} σ_{i} σ_{j} \geq 1

(14)

where F_i and F_ij are strength parameters; σ_i are stress components. For the case of plane stress, the stress components in the z-direction are assumed to be negligible. The above equation can be simplified as

F_{1} σ_{1} + F_{2} σ_{2} + F_{11} σ_{1}^{2} + F_{22} σ_{2}^{2} + F_{66} τ_{12}^{2} + {2 F}_{12} σ_{1} σ_{2} \geq 1

(15)

where

F_{1} = \frac{1}{X_{T}} - \frac{1}{X_{C}}

F_{2} = \frac{1}{Y_{T}} - \frac{1}{Y_{C}}

F_{11} = \frac{1}{X_{T} X_{C}}, F_{22} = \frac{1}{Y_{T} Y_{C}}, F_{66} = \frac{1}{S^{2}}, F_{12} = \frac{- 0.5}{\sqrt{X_{T} X_{C} Y_{T} Y_{C}}}

It is noted that due to the small thickness of the skin laminate, the stresses in the skin thickness direction become negligible. Therefore, the Tsai–Wu criterion of Equation (15) together with the SHELL181 elements will be used to study the failure behavior of the blade skin. On the other hand, due to the fact that the adopted wrapping technique allows no openings or free edges to exist in the blade, the failure mode of interfacial debonding will not be considered in the failure analysis of the composite sandwich blade. The blade core failure is also considered in the failure analysis of the composite sandwich blade. The Tsai–Wu criterion of Equation (14) together with the SOLID185 elements will be used to identify the initiation of core material failure. Once the failure index at any point in a core element exceeds 1, the initial Young’s modulus E_c of the core element will be replaced by αE_c where α is a small number much less than 1. In the failure analysis, both the core failure zone size and the blade failure load are determined simultaneously in an iterative process. In searching for the actual core failure zone size iteratively, a number of blade failure load analyses will be performed in such a way that the size of the core failure zone is updated after the completion of any failure load analysis. Furthermore, the updated core failure zone size will be used in another failure load analysis to update the failure load until the size of the core failure zone converges. In general, α = 10⁻³ and around four iterations are required to make the core failure zone size and the blade failure load converge. To verify the accuracy of the present finite element-based failure analysis, the blade resultant thrust will be used to study the failure characteristics of the blade via both theoretical and experimental approaches.

3.3. Optimization Method for Load Carrying Capacity Determination

It is noted that for a blade with a given skin lamination arrangement, the incipient failure rotational speed that can cause the blade to fail is not known in advance. Therefore, the incipient failure rotational speed as well as the load carrying capacity of the blade must be determined via an iterative process. In the iterative process, the initial guess of the incipient failure rotational speed is used to determine the quasi-static BEM elemental aerodynamic loads which are then used to perform the finite element-based failure analysis of the blade. The failure index determined in the failure analysis can be used to construct the following objective function.

f (ω) = {(D - 1)}^{2} = 0

(16)

Here, f(ω) is implicitly a function of rotational speed ω. The incipient failure rotational speed can be determined by solving the following optimization problem.

Minimize f (ω)

(17)

The above optimization problem can be solved efficiently and effectively using the golden section search method [44]. The flow chart explaining the use of the golden section search method to search for the incipient failure rotational speed and load carrying capacity of the blade is shown Figure 11.

4. Experimental Investigation of Blade Failure Characteristics

The suitability of the finite element-based blade failure analysis method must be verified before proceeding to the determination of the blade load carrying capacity. Herein, several composite sandwich rotor blades of Types 1 and 2 as shown in Figure 12 were tested to failure to verify the accuracy of the theoretical predictions. The average weights of Types 1 and 2 blades were 104 and 150 g, respectively. The experimental setup for the static load testing of the rotor blade is shown schematically in Figure 13. The center of the rotor blade was screwed to a rigid fixture to simulate the fixed end of the composite sandwich blade. The theoretical failure analysis of the two types of composite sandwich blades was first performed to identify the locations of the failure resultant thrusts and the failure rotational speeds of the blades. A bucket filled with steel balls was then hung to the blade at the location of the failure resultant blade thrust which was determined using the proposed finite element-based failure analysis. The locations of the applied loads chosen in the static load testing were 288.3 and 279.7 mm for Types 1 and 2 blades, respectively. Steel balls were placed in the bucket intermittently so that the total weight of the bucket with the steel balls inside was increased incrementally until the collapse of the blade. The failure patterns of Types 1 and 2 blades are shown in Figure 14. It is noted that no skin wrinkles or dimples have been observed on the skins of the composite sandwich blades. Therefore, the failure mode of blade skin buckling can be excluded for the blades. In fact, the failure mode for the two types of composite sandwich blades was skin fracture. It was noted that a crack in the chord-wise direction extending from the trailing to the leading edges of each blade was clearly visualized. For each blade, a detailed inspection of the crack indicated that the failure of the blade was fiber fracture, which could be attributed to the first-ply failure of the skin laminate. It was also noted that the crack of the Type 1 blade, located at the boundary between Regions 1 and 2, was far away from the blade root, while the crack of Type 2 blade was located at the blade root. The average static failure thrusts of Types 1 and 2 blades were 11 kgf and 15.7 kgf, respectively. On the other hand, the material properties of the carbon fabric/epoxy lamina and PU foam as listed in Table 3 were determined experimentally for the theoretical study of the failure behavior of the composite sandwich blades. It is noted for the composite lamina that the compressive strength X_C (Y_C) is less than the tensile strength X_T (Y_T).

5. Results and Discussion

The above experimental failure thrust data will be used to verify the accuracy of the proposed finite element-based failure analysis method. It is noted that only the quasi-static resultant thrust of the elemental aerodynamic loads are used in the theoretical failure analysis of the composite sandwich blade. In the failure analysis of Type 1 composite sandwich blade, the resultant thrust acts at the experimental location of r_g = 288.3 mm. The failure index (D) distribution for the first-ply failure mode and the buckling shape for the buckling failure mode shown in Figure 15 are used to identify the failure location in the blade. It is noted that the Maximum stress criterion predicts the failure location at y = 10.99 cm while the Tsai–Wu criterion predicts at y = 10.59 cm. As for the buckling failure mode, the failure location is at y = 10.7 cm, which is the center of the bucking dimple. It is noted that all the failure criteria have predicted similar failure locations which are close to the boundary between Regions 1 and 2. On the other hand, for the Type 2 composite sandwich blade with r_g = 279.7 mm, the failure locations predicted using the Maximum stress criterion, Tsai–Wu criterion, and buckling mode shape as shown in Figure 16 are at y = 3.5, 3.5 and 4.88 cm, respectively. It is noted that all the failure criteria have predicted similar failure locations which are near the blade root. In summary, the theoretical failure thrusts and locations for different failure modes and criteria for both Types 1 and 2 blades are listed in Table 4 in comparison with the experimental results. It is noted that amongst the adopted failure criteria, the Tsai–Wu criterion is able to predict relatively accurate static failure loads and locations for both Types 1 and 2 blades, with percentage errors less than or equal to 1.2% for failure thrust and 3.42% for failure location, respectively. In view of the percentage errors predicted using the failure criteria, it seems appropriate to use the Tsai–Wu criterion in the failure analysis to determine the failure rotational speed and load carrying capacity of the composite sandwich blades.

The proposed load carrying capacity determination method together with the Tsai–Wu failure criterion will be used to determine the blade load carrying capacities and incipient failure rotational speeds of the two types of composite sandwich blades. It is noted that different loading conditions will be considered in the load carrying capacity analysis. First, consider the cases where thrust, drag force, and centrifugal force are included in the load carrying capacity analysis. The failure index distributions for the first-ply failure of Types 1 and 2 blades are shown in Figure 17 with the indication of the blade failure locations. The failure locations for Types 1 and 2 are at y = 10.59 and 3.50 cm, respectively. Here, the incipient failure resultant thrust is defined as the load carrying capacity of the blade. For comparison, the load carrying capacity characteristics of the two types of blades for different loading conditions are listed in Table 5. Three types of loading conditions will be considered in the blade load carrying capacity analysis. In particular, Load condition 1 includes thrust, drag force, and centrifugal force; Load condition 2 includes thrust and drag force; Load condition 3 only includes thrust. It is noted that the adopted three types of loading conditions have predicted the same failure locations for each type of blade. However, the comparison among the load carrying capacities obtained for the three loading conditions shows that Loading condition 1 can produce the highest load carrying capacities for the blades. This implies that the inclusion of the centrifugal force in the load carrying capacity analysis can increase the blade load carrying capacity. It is noted that when the blade is subjected to thrust and drag force, due to the fact that X_c is much smaller than X_T, the failure of the two types of blades will be dominated by the compressive stress induced in the top skin laminate. Nevertheless, as the tensile stress induced by the centrifugal force is applied to the top skin laminate, the compressive stress at the top skin will be reduced and thus a higher thrust load is required to make the blade fail. Regarding the lamination arrangements of the two types of blades, it is noted that when the length of Region 2 in the Type 1 blade increases 50% from 10 to 20 cm, the load carrying capacity can increase 63.5% from 11.52 to 18.83 kgf.

Next, the proposed blade load carrying capacity determination method is used to study the weight reduction in composite sandwich blades. First consider the effects of the length of Region 2 on the load carrying capacity and weight of the composite sandwich blade. The load carrying capacities and weights for different lengths of Region 2 are plotted in Figure 18. It is noted that when the length of Region 2 is zero, i.e., only two laminae are in the top and bottom blade skins, respectively, the failure mode of the blade is skin buckling and the failure location is at the top skin near the blade root. On the other hand, the failure mode for the length of Region 2 not equal to zero is first-ply failure. The load carrying capacity starts to decrease even though the blade weight keeps increasing for a Region 2 length longer than 20 cm. It is noted that when the length of Region 2 is 25 cm, the tension stress induced by the centrifugal force becomes so high that the first-ply failure occurs at the bottom skin laminate near the blade root. Therefore, the length of Region 2 equal to 20 cm can produce the minimum blade weight and the highest load carrying capacity. The specific load carrying capacities, which is defined as the load carrying capacity per unit weight, and the failure rotational speeds for different Region 2 lengths are also determined and their relations plotted in Figure 19. It is noted that the incipient failure rotational speed as well as the specific load carrying capacity starts to decrease as the length of Region 2 becomes longer than 20 cm. The information about the incipient failure rotational speeds together with the torque induced by the drag force is useful in the selection of a motor with a rated speed higher than the blade incipient failure rotational speed and with sufficient power to drive the rotor blade. The relations of blade tip displacement vs. incipient failure rotational speed for different Region 2 lengths are shown in Figure 20. For each Region 2 length, the relation between the blade tip displacement and the blade incipient failure rotational speed can be used to choose the operating rotor blade rotational speed to satisfy the required factor of safety. Furthermore, the information about the blade displacement may be useful in the assessment of the effects on the aerodynamic performance of the blade. It is noted that the accurate predictions of the failure characteristics and load carrying capacities of composite sandwich blades can help not only design more reliable drones but also select proper payload and appropriate rotor rotational speed for safe drone operation. Furthermore, the capability of the present method in producing accurate blade failure loads reveals that the present method has the potential to be used in the reliability analysis and fatigue life assessment of the blades.

6. Conclusions

The failure characteristics and load carrying capabilities of composite sandwich rotor blades for copter-type drones have been studied via both theoretical and experimental approaches. In the experimental study, two types of composite sandwich blades with different lengths of Region 2 were fabricated for blade thrust measurement and failure load testing. The experimental rotational speed vs. blade thrust relation and blade failure characteristics were determined for theoretical model verification. In the theoretical study, a method, which provides a systematic way to determine blade load carrying capacity, consisting of three parts; namely, an iterative procedure for determining the distributed quasi-static blade aerodynamic load via the Blade Element Momentum (BEM) approach, a finite element-based failure analysis method for identifying the actual blade failure mode, and an optimization method for estimating the actual blade load carrying capacity have been presented. Based on the experimental results, it has been shown that the failure mode of the composite sandwich blades is the first-ply failure, and among the adopted three failure criteria, the Tsai–Wu criterion is capable of predicting more accurate failure locations and loads for the composite sandwich blades. The proposed method has been used to construct the useful relations from which the load carrying capacities and incipient failure rotational speeds for blades with different lengths of Region 2 can be determined. For the composite sandwich blades under consideration, the length of Region 2 that can give the highest specific blade load carrying capacity has been determined as 20 cm. The information about the blade load carrying capacity at the incipient rotational speed determined from the relation of rotational speed vs. load carrying capacity should be useful for the selection of appropriate drone payload and driving motor specification.

Author Contributions

Conceptualization, T.Y.K.; methodology, T.Y.K.; software, C.W.J.; validation, C.W.J. and T.Y.K.; formal analysis, C.W.J.; investigation, C.W.J. and T.Y.K.; resources, T.Y.K.; data curation, C.W.J.; writing—original draft preparation, T.Y.K.; writing—review and editing, T.Y.K.; supervision, T.Y.K.; project administration, T.Y.K.; funding acquisition, T.Y.K. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by National Science and Technology Council of the Republic of China under the grant NSTC 112-2221-E-A49-024.

Institutional Review Board Statement

The study was conducted in accordance with the Declara-tion of Helsinki, and approved by the Institutional Review Board of National Yang Ming Chiao Tung University (protocol code: Hsin Chu 300 and date of approval: 16 April 2023).

Informed Consent Statement

No new data were created.

Data Availability Statement

No new data were created.

Conflicts of Interest

The authors declare no conflicts of interest.

References

Hussein, M.; Aidaros, O.A.; Raahim, B.; Dhahri, M.A.; Neyadi, S.A.; Asad, M. Development of autonomous drone for gas sensing application. In Proceedings of the 2017 International Conference on Electrical and Computing Technologies and Applications (ICECTA), Ras Al Khaimah, United Arab Emirates, 21–23 November 2017. [Google Scholar]
Hallermann, N.; Morgenthal, G. Visual inspection strategies for large bridges using Unmanned Aerial Vehicles (UAV). In Proceedings of the International Conference on Bridge Maintenance, Safety and Management (IABMAS) 2014, Shanghai, China, 7–11 July 2014. [Google Scholar]
Daponte, P.; Vito, L.D.; Glielmo, L.; Iannelli, L.; Liuzza, D.; Picariello, F.; Silano, G. A review on the use of drones for precision agriculture. IOP Conf. Ser. Earth Environ. Sci. 2018, 275, 1–10. [Google Scholar] [CrossRef]
Eichleay, M.; Evens, E.; Stankevitz, K.; Parker, C. Using the unmanned aerial vehicle delivery decision tool to consider transporting medical supplies via drone. Glob. Health Sci. Pract. 2019, 7, 500–506. [Google Scholar] [CrossRef]
Nawaz, H.; Ali, H.M.; Massan, S.U.R. Applications of unmanned aerial vehicles: A review. 3C Tecnol. Glosas Innovación Apl. La Pyme 2019, 85–105. [Google Scholar] [CrossRef]
Molina, A.A.; Huang, Y.; Jiang, Y. A review of unmanned aerial vehicle applications in construction management: 2016–2021. Standards 2023, 3, 95–109. [Google Scholar] [CrossRef]
Outay, F.; Mengash, H.A.; Adnan, M. Applications of unmanned aerial vehicle (UAV) in road safety, traffic and highway infrastructure management: Recent advances and challenges. Transp. Res. Part A Policy Pract. 2020, 141, 116–129. [Google Scholar] [CrossRef]
Dumitrache, A.; Pricop, M.V.; Niculescu, M.L.; Cojocaru, M.G.; Ionescu, T. Design and analysis methods for UAV rotor blades. Sci. Res. Educ. Air Force 2017, 19, 115–126. [Google Scholar] [CrossRef]
Adkins, C.N.; Liebeck, R.H. Design of optimum propellers. J. Propuls. Power 1994, 10, 676–682. [Google Scholar] [CrossRef]
You, K.; Zhao, X.; Zhao, S.Z.; Faisal, M. Design and optimization of a high-altitude long endurance UAV propeller. IOP Conf. Ser. Mater. Sci. Eng. 2020, 926, 1–6. [Google Scholar] [CrossRef]
Kutty, H.A.; Rajendran, P. 3D CFD simulation and experimental validation of small APC slow flyer propeller blade. Aerospace 2017, 4, 10. [Google Scholar] [CrossRef]
Chung, P.H.; Ma, D.M.; Shiau, J.K. Design, manufacturing, and flight testing of an experimental flying wing UAV. Appl. Sci. 2019, 9, 3043. [Google Scholar] [CrossRef]
Rwigema, M.K. Propeller blade element momentum theory with vortex wake deflection, manufacturing and testing. In Proceedings of the 27th International Congress of the Aeronautical Sciences (ICAS), Nice, France, 19–24 September 2010; pp. 1–9. [Google Scholar]
Kong, C.; Park, H.; Lee, K.; Choi, W. A study on structural design and analysis of composite propeller blade of turboprop for high efficiency and light weight. In Proceedings of the European Conference on Composite Materials (ECCM), Venice, Italy, 24–28 June 2012; pp. 1–12. [Google Scholar]
Cruzatty, C.; Sarmiento, E.; Valencia, E.; Cando, E. Design methodology of a UAV propeller implemented in monitoring activities. Mater. Today Proc. 2021, 49, 115–121. [Google Scholar] [CrossRef]
Prathapanayaka, R.; Kumar, N.V.; Krishnamurthy, S.J. Design, analysis, fabrication and testing of mini propeller for MAVS. In Proceedings of the Symposium on Applied Aerodynamics and Design of Aerospace Vehicle (SAROD 2011), Bangalore, India, 16–18 November 2011. [Google Scholar]
Ramesh, M.; Vijayanandh, R.; Kumar, G.R.; Mathaiyan, V.; Jagadeeshwaran, P.; Kumar, M.S. Comparative structural analysis of various composite materials based unmanned aerial vehicle’s propeller by using advanced methodologies. IOP Conf. Ser. Mater. Sci. Eng. 2021, 1017, 012032. [Google Scholar] [CrossRef]
Sarmiento, E.; Campoverde, C.D.; Rivera, J.; Cruzatty, C.; Cando, E.; Valencia, E. Aero-structural numerical analysis of a blended wing body unmanned aerial vehicle using a jute-based composite material. Mater. Today Proc. 2021, 49, 50–57. [Google Scholar] [CrossRef]
Shaheen, M.; Latif, M.A.E. Reverse engineering using laser scanned and manufacturing of a powered paraglider propeller. J. Multidiscip. Eng. Sci. Technol. (JMEST) 2020, 7, 12810–12815. [Google Scholar]
Rutkay, B.D. A Process for the Design and Manufacture of Propellers for Small Unmanned Aerial Vehicles. Master’s Thesis, Aerospace Engineering, Carleton University, Ottawa, ON, Canada, 2014. [Google Scholar]
Toleos, L.R., Jr.; Luna, N.J.A.B.D.; Manuel, M.C.E.; Chua, J.M.R.; Sangalang, E.M.A.; So, P.C. Feasibility study for Fused Deposition Modeling (FDM) 3D-printed propellers for unmanned aerial vehicles. Int. J. Mech. Eng. Robot. Res. 2020, 9, 548–558. [Google Scholar] [CrossRef]
Wojtas, M.; Wyszkowski, P.; Kmita, P.; Osiewicz, M. Prototype carbon fibre propeller dedicated for hybrid power unmanned aerial vehicles with mtow up to 300 KG. In Proceedings of the 48th European Rotorcraft Forum, Winterthur, Switzerland, 6–8 September 2022. [Google Scholar]
Rutkay, B.; Laliberte, J. Design and manufacture of propellers for small unmanned aerial vehicles. J. Unmanned Veh. Syst. 2016, 228–245. [Google Scholar] [CrossRef]
Gatti, M. Design and Prototyping High Endurance Multi-Rotor. PhD Thesis, Università di Bologna, Meccanica e Scienze Avanzate Dell’ingegneria, Bologna, Italy, 2015. [Google Scholar]
Grodzki, W.; Łukaszewicz, A. Design and manufacture of Umanned Aerial Vehicles (UAV) wing structure using composite materials. Mater. Und Werkst. 2015, 46, 269–278. [Google Scholar] [CrossRef]
Verma, A.K.; Pradhan, N.K.; Nehra, R.; Prateek. Challenge and advantage of materials in design and fabrication of composite UAV. IOP Conf. Ser. Mater. Sci. Eng. 2018, 455, 012005. [Google Scholar] [CrossRef]
Arif, M.; Asif, M.; Ahmed, I. Advanced composite material for aerospace application—A review. Int. J. Eng. Manuf. Sci. 2017, 7, 393–409. [Google Scholar]
Borchardt, J.K. Unmanned aerial vehicles spur composites use. Reinf. Plast. 2004, 48, 28–31. [Google Scholar] [CrossRef]
Hadar, A.; Voicu, A.D.; Baciu, F.; Vlasceanu, D.; Tudose, D.I.; Pastrama, S.D. A Novel Composite helicopter tail rotor blade with enhanced mechanical properties. Aerospace 2023, 10, 647. [Google Scholar] [CrossRef]
Pao, W.Y.; Haldar, S.; Singh, C.V. Performance analysis of composite helicopter blade using synergistic damage mechanics approach. AIAA J. 2019, 58, 968–976. [Google Scholar] [CrossRef]
Ahmad, K.; Baig, Y.; Bahman, H.; Hasham, H.J. Progressive failure analysis of helicopter rotor blade under aeroelastic loading. Aviation 2020, 24, 33–41. [Google Scholar] [CrossRef]
Kliza, R.; Scislowski, K.; Siadkowska, K.; Padyjasek, J.; Wendeker, M. Strength analysis of a prototype composite helicopter rotor blade spar. Appl. Comput. Sci. (ACS) 2022, 18, 5–19. [Google Scholar] [CrossRef]
Gladys, N.; Laura, V. Analysis of rotor-blade failure due to high-temperature corrosion/erosion. Surf. Coat. Technol. 1999, 120–121, 145–150. [Google Scholar] [CrossRef]
Chen, C.P.; Kam, T.Y. Failure analysis of small composite sandwich turbine blade subjected to extreme wind load. Procedia Eng. 2011, 14, 1973–1981. [Google Scholar] [CrossRef]
Mazhar, F.; Khan, A.M. Structural design of a UAV wing using finite element method. In Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Orlando, FL, USA, 12–15 April 2010. [Google Scholar]
Shelare, S.D.; Aglawe, K.R.; Khope, P.B. Computer aided modeling and finite element analysis of 3-D printed drone. Mater. Today Proc. 2011, 47, 3375–3379. [Google Scholar] [CrossRef]
Brischetto, S.; Torre, R. Preliminary finite element analysis and flight simulations of a modular drone built through fused filament fabrication. J. Compos. Sci. 2021, 5, 293. [Google Scholar] [CrossRef]
Ahmad, F.; Kumar, P.; Patil, P.P.; Kumar, V. FEA based frequency analysis of unmanned aerial vehicle (UAV). Mater. Today Proc. 2021, 46, 10396–10403. [Google Scholar] [CrossRef]
Ahmad, F.; Kumar, P.; Patil, P.P. Structural analysis of a quadcopter propeller using finite element method. In Proceedings of the 2020 International Conference on Advances in Computing, Communication & Materials (ICACCM), Dehradun, India, 21–22 August 2020; pp. 59–64. [Google Scholar]
James, F.M.; Jon, G.M.; Anthony, L.R. Wind Energy Explained; John Wiley & Sons Ltd.: Hoboken, NJ, USA, 2009; pp. 91–155. [Google Scholar]
Zhu, H.; Jiang, Z.; Zhao, H.; Pei, S.; Li, H.; Lan, Y. Aerodynamic performance of propellers for multirotor unmanned aerial vehicles: Measurement, analysis, and experiment. Shock. Vib. 2021, 2021, 9538647. [Google Scholar] [CrossRef]
ANSYS 12.1; ANSYS Inc.: Canonsburg, PA, USA, 2010.
Tsai, S.W.; Hahn, H.T. Introduction to Composite Materials. Technomic Publishing Co.: Westport, CO, USA, 1980. [Google Scholar]
Available online: https://en.wikipedia.org/wiki/Golden-section_search (accessed on 19 June 2024).

Figure 1. Quadcopter drone.

Figure 2. Rotor blade: (a) Dimensions; (b) NACA 4418 Airfoil showing skin and core.

Figure 3. Lamination arrangement of composite sandwich blade (a) Type 1 blade, (b) Type 2 blade.

Figure 4. Blade element.

Figure 5. Elemental airfoil aerodynamics.

Figure 6. Experimental setup for rotor blade thrust measurement.

Figure 7. Iterative procedure for updating vertical uplifting force.

Figure 8. Locations of blade elements and resultant thrust.

Figure 9. Rotational speed vs. rotor blade thrust.

Figure 10. Finite element mesh for composite sandwich blade. (a) Type 1 blade, (b) Type 2 blade.

Figure 11. Iterative procedure for updating incipient failure rotational speed.

Figure 12. Finished rotor blade product.

Figure 13. Experimental setup.

Figure 14. Experimental failure pattern of composite blade (a) Type 1 blade, (b) Type 2 blade.

Figure 15. Failure analysis results for Type 1 blade under resultant thrust. (a) Failure index for Maximum stress criterion (Failure location: x = −0.48, y = 10.99). (b) Failure index for Tsai–Wu criterion (Failure location: x = −0.48, y = 10.59). (c) Buckling mode shape (Failure location: x = −0.323, y = 10.7).

Figure 16. Failure analysis results for Type 2 blade under resultant thrust (a) Failure index for Maximum stress criterion (Failure location: x = 0.12, y = 3.5). (b) Failure index for Tsai–Wu criterion (Failure location: x = 0.12, y = 3.5). (c) Buckling mode shape (Failure location: x = −0.398, y = 4.88).

Figure 17. Failure index distribution of composite sandwich blade under elemental thrusts, drag forces, and centrifugal force. (a) Type 1 blade, (b) Type 2 blade.

Figure 18. Effects of Region 2 length on blade load carrying capacity and weight.

Figure 19. Effects of Region 2 on failure rotational speed and specific load carrying capacity.

Figure 20. Relation between blade rotational speed and displacement.

Table 1. Geometric parameters of composite sandwich blade.

Airfoil Type	Blade Span R (m)	r/R	Chord Length (m)	Inflow Angle $\emptyset$	Angle of Attack α (Rotational Speed of 3630 rpm)	Twist Angle β
NACA 4418	0.82	0.95	0.0287	3.3°	5.0°	8.3°
		0.85	0.0518	3.7°		8.7°
		0.75	0.0650	4.1°		9.1°
		0.65	0.0723	4.8°		9.8°
		0.55	0.0746	5.6°		10.6°
		0.45	0.0713	6.9°		11.9°
		0.35	0.0637	8.8°		13.8°
		0.25	0.0515	12.3°		17.3°
		0.15	0.0360	19.9°		24.9°

Table 2. Force distribution along rotor blade span.

Rotational Speed (rpm)	Section	1	2	3	4	5	6	7	8	9	Total
3630	$r_{i}$ (m)	0.061	0.102	0.142	0.183	0.224	0.264	0.305	0.345	0.386
	$Elemental Thrust d T_{b}$ (N)	0.582	0.217	1.731	4.893	8.789	12.763	15.545	16.164	10.596	70.7 N (=7.21 kgf)
	$Elemental drag force d F_{b}$ (N)	0.23	0.13	0.57	1.19	1.76	2.28	2.54	2.48	1.64	12.82 N (=1.3 kgf)

Table 3. Material properties of carbon fabric/epoxy lamina and PU foam.

Material Type	Woven Carbon Fabric (Orthotropic)	PU Foam (Isotropic)
$E_{X}$	5.417 × 10¹⁰	1.81 × 10⁷
$E_{Y}$	5.417 × 10¹⁰	--
$v_{X Y}$	0.042	0.3
$G_{X Y}$	9.37 × 10⁸	--
$G_{Y Z}$	9.37 × 10⁸	--
$G_{Z X}$	9.37 × 10⁸	--
Strength
$X_{T}$	7.42 × 10⁸	5.67 × 10⁵
$Y_{T}$	7.42 × 10⁸	5.67 × 10⁵
$X_{C}$	4.55 × 10⁸	5.6 × 10⁵
$Y_{C}$	4.55 × 10⁸	5.6 × 10⁵
$S_{X Y} = S_{X Z} = S_{Y Z}$	4.67 × 10⁸	4.13 × 10⁵

Table 4. Failure characteristics of composite sandwich blade under resultant thrust.

Blade Type	Failure Mode		Failure Loading (kgf)	Failure Location (cm)
Type 1	Experimental	First-ply material failure	11	(−0.45, 10.24)
	First-ply failure (Max. stress)		14.78 (+34.36%) *	(−0.48, 10.99) (+7.32%)
	First-ply failure (Tsai–Wu)		11.1 (+0.91%)	(−0.48, 10.59) (+3.42%)
	Buckling		17.9 (+62.72%)	(−0.323, 10.7) (+4.49%)
Type 2	Experimental	First-ply material failure	15.71	(−0.2, 3.48)
	First-ply failure (Max. stress)		16.46 (+14.77%)	(0.12, 3.50) (+0.57%)
	First-ply failure (Tsai–Wu)		15.9 (+1.2%)	(0.12, 3.50) (+0.57%)
	Buckling		20.62 (+31.25%)	(−0.398, 4.88) (+40.22%)

* Percentage difference: ((Experimental − Theoretical)/Experimental) × 100%.

Table 5. Failure characteristics of composite sandwich blade under distributed elemental aerodynamic load.

Blade Type	Loading Condition	Failure Resultant Thrust (kgf)	Failure Location (x, y) cm
Type 1	Thrust, drag, and centrifugal force	11.52	(−0.48, 10.59)
	Thrust and drag	10.75	(−0.48, 10.59)
	Thrust alone	11.1	(−0.48, 10.59)
Type 2	Thrust, drag, and centrifugal force	18.83	(0.12, 3.50)
	Thrust and drag	14.99	(0.12, 3.50)
	Thrust alone	15.9	(0.12, 3.50)

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Share and Cite

MDPI and ACS Style

Jan, C.W.; Kam, T.Y. Determining Quasi-Static Load Carrying Capacity of Composite Sandwich Rotor Blades for Copter-Type Drones. Drones 2024, 8, 355. https://doi.org/10.3390/drones8080355

AMA Style

Jan CW, Kam TY. Determining Quasi-Static Load Carrying Capacity of Composite Sandwich Rotor Blades for Copter-Type Drones. Drones. 2024; 8(8):355. https://doi.org/10.3390/drones8080355

Chicago/Turabian Style

Jan, Chien Wei, and Tai Yan Kam. 2024. "Determining Quasi-Static Load Carrying Capacity of Composite Sandwich Rotor Blades for Copter-Type Drones" Drones 8, no. 8: 355. https://doi.org/10.3390/drones8080355

APA Style

Jan, C. W., & Kam, T. Y. (2024). Determining Quasi-Static Load Carrying Capacity of Composite Sandwich Rotor Blades for Copter-Type Drones. Drones, 8(8), 355. https://doi.org/10.3390/drones8080355

Article Menu

Determining Quasi-Static Load Carrying Capacity of Composite Sandwich Rotor Blades for Copter-Type Drones

Abstract

1. Introduction

2. Composite Sandwich Rotor Blade

3. Load Carrying Capacity Determination

3.1. Blade Aerodynamic Load Analysis

3.2. Finite Element-Based Blade Failure Analysis

3.3. Optimization Method for Load Carrying Capacity Determination

4. Experimental Investigation of Blade Failure Characteristics

5. Results and Discussion

6. Conclusions

Author Contributions

Funding

Institutional Review Board Statement

Informed Consent Statement

Data Availability Statement

Conflicts of Interest

References

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI